From efd303d35dd5ecb8a9bc57c44d4aa3f6c57044d2 Mon Sep 17 00:00:00 2001 From: Tim Daly Date: Fri, 8 May 2015 19:21:55 -0400 Subject: [PATCH] books/bookvol*pamphlet add more test cases --- books/bookvol10.2.pamphlet | 3754 ++++---- books/bookvol10.3.pamphlet |15693 ++++++++++++++++++++++--------- books/bookvol10.4.pamphlet | 7847 ++++++++++++++-- books/bookvol10.pamphlet | 5 +- books/bookvol5.pamphlet | 1 + changelog | 16 + patch | 8 +- src/axiom-website/patches.html | 2 + src/input/Makefile.pamphlet | 5 + src/input/cmds.input.pamphlet | 13 +- src/interp/clam.lisp.pamphlet | 2 +- src/interp/msgdb.lisp.pamphlet | 81 +- src/interp/vmlisp.lisp.pamphlet | 25 +- src/share/algebra/browse.daase | 34 +- src/share/algebra/category.daase | 2 +- src/share/algebra/interp.daase | 44 +- src/share/algebra/operation.daase | 6341 +++++++------- src/share/algebra/users.daase/index.kaf | 12 +- 18 files changed, 23642 insertions(+), 10243 deletions(-) diff --git a/books/bookvol10.2.pamphlet b/books/bookvol10.2.pamphlet index 7cac65d..03c8a4b 100644 --- a/books/bookvol10.2.pamphlet +++ b/books/bookvol10.2.pamphlet @@ -127,7 +127,23 @@ digraph pic { )clear all --S 1 of 1 -1 +)show AdditiveValuationAttribute +--R +--R AdditiveValuationAttribute is a category constructor +--R Abbreviation for AdditiveValuationAttribute is ATADDVA +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for ATADDVA +--R +--R------------------------------- Operations -------------------------------- +--R AdditiveValuationAttribute is a category constructor. +--R Abbreviation for AdditiveValuationAttribute is ATADDVA +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for ATADDVA +--R +--R------------------------------- Operations -------------------------------- +--R +--R +--R --E 1 )spool )lisp (bye) @@ -191,7 +207,23 @@ digraph pic { )clear all --S 1 of 1 -1 +)show ApproximateAttribute +--R +--R ApproximateAttribute is a category constructor +--R Abbreviation for ApproximateAttribute is ATAPPRO +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for ATAPPRO +--R +--R------------------------------- Operations -------------------------------- +--R ApproximateAttribute is a category constructor. +--R Abbreviation for ApproximateAttribute is ATAPPRO +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for ATAPPRO +--R +--R------------------------------- Operations -------------------------------- +--R +--R +--R --E 1 )spool )lisp (bye) @@ -254,7 +286,23 @@ digraph pic { )clear all --S 1 of 1 -1 +)show ArbitraryExponentAttribute +--R +--R ArbitraryExponentAttribute is a category constructor +--R Abbreviation for ArbitraryExponentAttribute is ATARBEX +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for ATARBEX +--R +--R------------------------------- Operations -------------------------------- +--R ArbitraryExponentAttribute is a category constructor. +--R Abbreviation for ArbitraryExponentAttribute is ATARBEX +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for ATARBEX +--R +--R------------------------------- Operations -------------------------------- +--R +--R +--R --E 1 )spool )lisp (bye) @@ -317,7 +365,23 @@ digraph pic { )clear all --S 1 of 1 -1 +)show ArbitraryPrecisionAttribute +--R +--R ArbitraryPrecisionAttribute is a category constructor +--R Abbreviation for ArbitraryPrecisionAttribute is ATARBPR +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for ATARBPR +--R +--R------------------------------- Operations -------------------------------- +--R ArbitraryPrecisionAttribute is a category constructor. +--R Abbreviation for ArbitraryPrecisionAttribute is ATARBPR +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for ATARBPR +--R +--R------------------------------- Operations -------------------------------- +--R +--R +--R --E 1 )spool )lisp (bye) @@ -383,6 +447,7 @@ digraph pic { --S 1 of 1 )show ArcHyperbolicFunctionCategory +--R --R ArcHyperbolicFunctionCategory is a category constructor --R Abbreviation for ArcHyperbolicFunctionCategory is AHYP --R This constructor is exposed in this frame. @@ -493,6 +558,7 @@ intermediate test to check that the argument has a reciprocal values. --S 1 of 1 )show ArcTrigonometricFunctionCategory +--R --R ArcTrigonometricFunctionCategory is a category constructor --R Abbreviation for ArcTrigonometricFunctionCategory is ATRIG --R This constructor is exposed in this frame. @@ -610,6 +676,23 @@ digraph pic { --S 1 of 1 )show AttributeRegistry +--R +--R AttributeRegistry is a category constructor +--R Abbreviation for AttributeRegistry is ATTREG +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for ATTREG +--R +--R------------------------------- Operations -------------------------------- +--R AttributeRegistry is a category constructor. +--R Abbreviation for AttributeRegistry is ATTREG +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for ATTREG +--R +--R------------------------------- Operations -------------------------------- +--R +--R +--R +--R --E 1 )spool @@ -807,6 +890,7 @@ digraph pic { --S 1 of 1 )show BasicType +--R --R BasicType is a category constructor --R Abbreviation for BasicType is BASTYPE --R This constructor is exposed in this frame. @@ -906,7 +990,23 @@ digraph pic { )clear all --S 1 of 1 -1 +)show CanonicalAttribute +--R +--R CanonicalAttribute is a category constructor +--R Abbreviation for CanonicalAttribute is ATCANON +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for ATCANON +--R +--R------------------------------- Operations -------------------------------- +--R CanonicalAttribute is a category constructor. +--R Abbreviation for CanonicalAttribute is ATCANON +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for ATCANON +--R +--R------------------------------- Operations -------------------------------- +--R +--R +--R --E 1 )spool )lisp (bye) @@ -971,7 +1071,23 @@ digraph pic { )clear all --S 1 of 1 -1 +)show CanonicalClosedAttribute +--R +--R CanonicalClosedAttribute is a category constructor +--R Abbreviation for CanonicalClosedAttribute is ATCANCL +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for ATCANCL +--R +--R------------------------------- Operations -------------------------------- +--R CanonicalClosedAttribute is a category constructor. +--R Abbreviation for CanonicalClosedAttribute is ATCANCL +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for ATCANCL +--R +--R------------------------------- Operations -------------------------------- +--R +--R +--R --E 1 )spool )lisp (bye) @@ -1035,7 +1151,23 @@ digraph pic { )clear all --S 1 of 1 -1 +)show CanonicalUnitNormalAttribute +--R +--R CanonicalUnitNormalAttribute is a category constructor +--R Abbreviation for CanonicalUnitNormalAttribute is ATCUNOR +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for ATCUNOR +--R +--R------------------------------- Operations -------------------------------- +--R CanonicalUnitNormalAttribute is a category constructor. +--R Abbreviation for CanonicalUnitNormalAttribute is ATCUNOR +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for ATCUNOR +--R +--R------------------------------- Operations -------------------------------- +--R +--R +--R --E 1 )spool )lisp (bye) @@ -1104,7 +1236,23 @@ digraph pic { )clear all --S 1 of 1 -1 +)show CentralAttribute +--R +--R CentralAttribute is a category constructor +--R Abbreviation for CentralAttribute is ATCENRL +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for ATCENRL +--R +--R------------------------------- Operations -------------------------------- +--R CentralAttribute is a category constructor. +--R Abbreviation for CentralAttribute is ATCENRL +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for ATCENRL +--R +--R------------------------------- Operations -------------------------------- +--R +--R +--R --E 1 )spool )lisp (bye) @@ -1283,6 +1431,7 @@ digraph pic { --S 1 of 1 )show CombinatorialFunctionCategory +--R --R CombinatorialFunctionCategory is a category constructor --R Abbreviation for CombinatorialFunctionCategory is CFCAT --R This constructor is exposed in this frame. @@ -1390,7 +1539,23 @@ digraph pic { )clear all --S 1 of 1 -1 +)show CommutativeStarAttribute +--R +--R CommutativeStarAttribute is a category constructor +--R Abbreviation for CommutativeStarAttribute is ATCS +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for ATCS +--R +--R------------------------------- Operations -------------------------------- +--R CommutativeStarAttribute is a category constructor. +--R Abbreviation for CommutativeStarAttribute is ATCS +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for ATCS +--R +--R------------------------------- Operations -------------------------------- +--R +--R +--R --E 1 )spool )lisp (bye) @@ -1619,6 +1784,7 @@ digraph pic { --S 1 of 1 )show ElementaryFunctionCategory +--R --R ElementaryFunctionCategory is a category constructor --R Abbreviation for ElementaryFunctionCategory is ELEMFUN --R This constructor is exposed in this frame. @@ -1724,6 +1890,7 @@ digraph pic { --S 1 of 1 )show Eltable +--R --R Eltable(S: SetCategory,Index: Type) is a category constructor --R Abbreviation for Eltable is ELTAB --R This constructor is exposed in this frame. @@ -1837,7 +2004,23 @@ digraph pic { )clear all --S 1 of 1 -1 +)show FiniteAggregateAttribute +--R +--R FiniteAggregateAttribute is a category constructor +--R Abbreviation for FiniteAggregateAttribute is ATFINAG +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for ATFINAG +--R +--R------------------------------- Operations -------------------------------- +--R FiniteAggregateAttribute is a category constructor. +--R Abbreviation for FiniteAggregateAttribute is ATFINAG +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for ATFINAG +--R +--R------------------------------- Operations -------------------------------- +--R +--R +--R --E 1 )spool )lisp (bye) @@ -1905,6 +2088,7 @@ intermediate test to check that the argument has a reciprocal values. --S 1 of 1 )show HyperbolicFunctionCategory +--R --R HyperbolicFunctionCategory is a category constructor --R Abbreviation for HyperbolicFunctionCategory is HYPCAT --R This constructor is exposed in this frame. @@ -2164,7 +2348,23 @@ digraph pic { )clear all --S 1 of 1 -1 +)show JacobiIdentityAttribute +--R +--R JacobiIdentityAttribute is a category constructor +--R Abbreviation for JacobiIdentityAttribute is ATJACID +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for ATJACID +--R +--R------------------------------- Operations -------------------------------- +--R JacobiIdentityAttribute is a category constructor. +--R Abbreviation for JacobiIdentityAttribute is ATJACID +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for ATJACID +--R +--R------------------------------- Operations -------------------------------- +--R +--R +--R --E 1 )spool )lisp (bye) @@ -2229,7 +2429,23 @@ digraph pic { )clear all --S 1 of 1 -1 +)show LazyRepresentationAttribute +--R +--R LazyRepresentationAttribute is a category constructor +--R Abbreviation for LazyRepresentationAttribute is ATLR +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for ATLR +--R +--R------------------------------- Operations -------------------------------- +--R LazyRepresentationAttribute is a category constructor. +--R Abbreviation for LazyRepresentationAttribute is ATLR +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for ATLR +--R +--R------------------------------- Operations -------------------------------- +--R +--R +--R --E 1 )spool )lisp (bye) @@ -2292,7 +2508,23 @@ digraph pic { )clear all --S 1 of 1 -1 +)show LeftUnitaryAttribute +--R +--R LeftUnitaryAttribute is a category constructor +--R Abbreviation for LeftUnitaryAttribute is ATLUNIT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for ATLUNIT +--R +--R------------------------------- Operations -------------------------------- +--R LeftUnitaryAttribute is a category constructor. +--R Abbreviation for LeftUnitaryAttribute is ATLUNIT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for ATLUNIT +--R +--R------------------------------- Operations -------------------------------- +--R +--R +--R --E 1 )spool )lisp (bye) @@ -2357,6 +2589,7 @@ digraph pic { --S 1 of 1 )show ModularAlgebraicGcdOperations +--R --R ModularAlgebraicGcdOperations(MPT: Type,MD: Type) is a category constructor --R Abbreviation for ModularAlgebraicGcdOperations is MAGCDOC --R This constructor is exposed in this frame. @@ -2503,7 +2736,23 @@ digraph pic { )clear all --S 1 of 1 -1 +)show MultiplicativeValuationAttribute +--R +--R MultiplicativeValuationAttribute is a category constructor +--R Abbreviation for MultiplicativeValuationAttribute is ATMULVA +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for ATMULVA +--R +--R------------------------------- Operations -------------------------------- +--R MultiplicativeValuationAttribute is a category constructor. +--R Abbreviation for MultiplicativeValuationAttribute is ATMULVA +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for ATMULVA +--R +--R------------------------------- Operations -------------------------------- +--R +--R +--R --E 1 )spool )lisp (bye) @@ -2568,7 +2817,23 @@ digraph pic { )clear all --S 1 of 1 -1 +)show NotherianAttribute +--R +--R NotherianAttribute is a category constructor +--R Abbreviation for NotherianAttribute is ATNOTHR +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for ATNOTHR +--R +--R------------------------------- Operations -------------------------------- +--R NotherianAttribute is a category constructor. +--R Abbreviation for NotherianAttribute is ATNOTHR +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for ATNOTHR +--R +--R------------------------------- Operations -------------------------------- +--R +--R +--R --E 1 )spool )lisp (bye) @@ -2631,7 +2896,23 @@ digraph pic { )clear all --S 1 of 1 -1 +)show NoZeroDivisorsAttribute +--R +--R NoZeroDivisorsAttribute is a category constructor +--R Abbreviation for NoZeroDivisorsAttribute is ATNZDIV +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for ATNZDIV +--R +--R------------------------------- Operations -------------------------------- +--R NoZeroDivisorsAttribute is a category constructor. +--R Abbreviation for NoZeroDivisorsAttribute is ATNZDIV +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for ATNZDIV +--R +--R------------------------------- Operations -------------------------------- +--R +--R +--R --E 1 )spool )lisp (bye) @@ -2696,7 +2977,23 @@ digraph pic { )clear all --S 1 of 1 -1 +)show NullSquareAttribute +--R +--R NullSquareAttribute is a category constructor +--R Abbreviation for NullSquareAttribute is ATNULSQ +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for ATNULSQ +--R +--R------------------------------- Operations -------------------------------- +--R NullSquareAttribute is a category constructor. +--R Abbreviation for NullSquareAttribute is ATNULSQ +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for ATNULSQ +--R +--R------------------------------- Operations -------------------------------- +--R +--R +--R --E 1 )spool )lisp (bye) @@ -2761,6 +3058,7 @@ digraph pic { --S 1 of 1 )show OpenMath +--R --R OpenMath is a category constructor --R Abbreviation for OpenMath is OM --R This constructor is exposed in this frame. @@ -2868,7 +3166,23 @@ digraph pic { )clear all --S 1 of 1 -1 +)show PartiallyOrderedSetAttribute +--R +--R PartiallyOrderedSetAttribute is a category constructor +--R Abbreviation for PartiallyOrderedSetAttribute is ATPOSET +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for ATPOSET +--R +--R------------------------------- Operations -------------------------------- +--R PartiallyOrderedSetAttribute is a category constructor. +--R Abbreviation for PartiallyOrderedSetAttribute is ATPOSET +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for ATPOSET +--R +--R------------------------------- Operations -------------------------------- +--R +--R +--R --E 1 )spool )lisp (bye) @@ -2942,9 +3256,12 @@ digraph pic { --R Issue )edit bookvol10.2.pamphlet to see algebra source code for PTRANFN --R --R------------------------------- Operations -------------------------------- ---R acosIfCan : K -> Union(K,"failed") acotIfCan : K -> Union(K,"failed") ---R acscIfCan : K -> Union(K,"failed") asecIfCan : K -> Union(K,"failed") ---R asinIfCan : K -> Union(K,"failed") atanIfCan : K -> Union(K,"failed") +--R acosIfCan : K -> Union(K,"failed") acoshIfCan : K -> Union(K,"failed") +--R acotIfCan : K -> Union(K,"failed") acothIfCan : K -> Union(K,"failed") +--R acscIfCan : K -> Union(K,"failed") acschIfCan : K -> Union(K,"failed") +--R asecIfCan : K -> Union(K,"failed") asechIfCan : K -> Union(K,"failed") +--R asinIfCan : K -> Union(K,"failed") asinhIfCan : K -> Union(K,"failed") +--R atanIfCan : K -> Union(K,"failed") atanhIfCan : K -> Union(K,"failed") --R cosIfCan : K -> Union(K,"failed") coshIfCan : K -> Union(K,"failed") --R cotIfCan : K -> Union(K,"failed") cothIfCan : K -> Union(K,"failed") --R cscIfCan : K -> Union(K,"failed") cschIfCan : K -> Union(K,"failed") @@ -2952,12 +3269,6 @@ digraph pic { --R secIfCan : K -> Union(K,"failed") sechIfCan : K -> Union(K,"failed") --R sinIfCan : K -> Union(K,"failed") sinhIfCan : K -> Union(K,"failed") --R tanIfCan : K -> Union(K,"failed") tanhIfCan : K -> Union(K,"failed") ---R acoshIfCan : K -> Union(K,"failed") ---R acothIfCan : K -> Union(K,"failed") ---R acschIfCan : K -> Union(K,"failed") ---R asechIfCan : K -> Union(K,"failed") ---R asinhIfCan : K -> Union(K,"failed") ---R atanhIfCan : K -> Union(K,"failed") --R nthRootIfCan : (K,NonNegativeInteger) -> Union(K,"failed") --R --E 1 @@ -3400,8 +3711,8 @@ digraph pic { --R Issue )edit bookvol10.2.pamphlet to see algebra source code for RADCAT --R --R------------------------------- Operations -------------------------------- ---R nthRoot : (%,Integer) -> % sqrt : % -> % ---R ?**? : (%,Fraction(Integer)) -> % +--R ?**? : (%,Fraction(Integer)) -> % nthRoot : (%,Integer) -> % +--R sqrt : % -> % --R --E 1 @@ -3687,7 +3998,22 @@ digraph pic { )clear all --S 1 of 1 -1 +--R +--R RightUnitaryAttribute is a category constructor +--R Abbreviation for RightUnitaryAttribute is ATRUNIT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for ATRUNIT +--R +--R------------------------------- Operations -------------------------------- +--R RightUnitaryAttribute is a category constructor. +--R Abbreviation for RightUnitaryAttribute is ATRUNIT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for ATRUNIT +--R +--R------------------------------- Operations -------------------------------- +--R +--R +--R --E 1 )spool )lisp (bye) @@ -3750,7 +4076,23 @@ digraph pic { )clear all --S 1 of 1 -1 +)show ShallowlyMutableAttribute +--R +--R ShallowlyMutableAttribute is a category constructor +--R Abbreviation for ShallowlyMutableAttribute is ATSHMUT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for ATSHMUT +--R +--R------------------------------- Operations -------------------------------- +--R ShallowlyMutableAttribute is a category constructor. +--R Abbreviation for ShallowlyMutableAttribute is ATSHMUT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for ATSHMUT +--R +--R------------------------------- Operations -------------------------------- +--R +--R +--R --E 1 )spool )lisp (bye) @@ -3819,6 +4161,7 @@ digraph pic { --S 1 of 1 )show SpecialFunctionCategory +--R --R SpecialFunctionCategory is a category constructor --R Abbreviation for SpecialFunctionCategory is SPFCAT --R This constructor is exposed in this frame. @@ -3962,6 +4305,7 @@ intermediate test to check that the argument has a reciprocal values. --S 1 of 1 )show TrigonometricFunctionCategory +--R --R TrigonometricFunctionCategory is a category constructor --R Abbreviation for TrigonometricFunctionCategory is TRIGCAT --R This constructor is exposed in this frame. @@ -4082,6 +4426,22 @@ digraph pic { --S 1 of 1 )show Type +--R +--R Type is a category constructor +--R Abbreviation for Type is TYPE +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for TYPE +--R +--R------------------------------- Operations -------------------------------- +--R Type is a category constructor. +--R Abbreviation for Type is TYPE +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for TYPE +--R +--R------------------------------- Operations -------------------------------- +--R +--R +--R --E 1 )spool @@ -4159,7 +4519,23 @@ digraph pic { )clear all --S 1 of 1 -1 +)show UnitsKnownAttribute +--R +--R UnitsKnownAttribute is a category constructor +--R Abbreviation for UnitsKnownAttribute is ATUNIKN +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for ATUNIKN +--R +--R------------------------------- Operations -------------------------------- +--R UnitsKnownAttribute is a category constructor. +--R Abbreviation for UnitsKnownAttribute is ATUNIKN +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for ATUNIKN +--R +--R------------------------------- Operations -------------------------------- +--R +--R +--R --E 1 )spool )lisp (bye) @@ -4229,6 +4605,7 @@ digraph pic { --S 1 of 1 )show Aggregate +--R --R Aggregate is a category constructor --R Abbreviation for Aggregate is AGG --R This constructor is exposed in this frame. @@ -4642,6 +5019,7 @@ digraph pic { --S 1 of 1 )show EltableAggregate +--R --R EltableAggregate(Dom: SetCategory,Im: Type) is a category constructor --R Abbreviation for EltableAggregate is ELTAGG --R This constructor is exposed in this frame. @@ -4807,9 +5185,8 @@ digraph pic { --R Issue )edit bookvol10.2.pamphlet to see algebra source code for EVALAB --R --R------------------------------- Operations -------------------------------- ---R eval : (%,Equation(R)) -> % eval : (%,R,R) -> % ---R eval : (%,List(R),List(R)) -> % ---R eval : (%,List(Equation(R))) -> % +--R eval : (%,List(Equation(R))) -> % eval : (%,Equation(R)) -> % +--R eval : (%,R,R) -> % eval : (%,List(R),List(R)) -> % --R --E 1 @@ -4935,6 +5312,7 @@ digraph pic { --S 1 of 1 )show FortranProgramCategory +--R --R FortranProgramCategory is a category constructor --R Abbreviation for FortranProgramCategory is FORTCAT --R This constructor is exposed in this frame. @@ -5391,6 +5769,7 @@ digraph pic { --S 1 of 1 )show Logic +--R --R Logic is a category constructor --R Abbreviation for Logic is LOGIC --R This constructor is exposed in this frame. @@ -5515,10 +5894,9 @@ digraph pic { --R Issue )edit bookvol10.2.pamphlet to see algebra source code for PPCURVE --R --R------------------------------- Operations -------------------------------- ---R coerce : % -> OutputForm +--R coerce : % -> OutputForm xRange : % -> Segment(DoubleFloat) +--R yRange : % -> Segment(DoubleFloat) --R listBranches : % -> List(List(Point(DoubleFloat))) ---R xRange : % -> Segment(DoubleFloat) ---R yRange : % -> Segment(DoubleFloat) --R --E 1 @@ -5643,11 +6021,9 @@ digraph pic { --R Issue )edit bookvol10.2.pamphlet to see algebra source code for PSCURVE --R --R------------------------------- Operations -------------------------------- ---R coerce : % -> OutputForm +--R coerce : % -> OutputForm xRange : % -> Segment(DoubleFloat) +--R yRange : % -> Segment(DoubleFloat) zRange : % -> Segment(DoubleFloat) --R listBranches : % -> List(List(Point(DoubleFloat))) ---R xRange : % -> Segment(DoubleFloat) ---R yRange : % -> Segment(DoubleFloat) ---R zRange : % -> Segment(DoubleFloat) --R --E 1 @@ -5775,6 +6151,7 @@ digraph pic { --S 1 of 1 )show RealConstant +--R --R RealConstant is a category constructor --R Abbreviation for RealConstant is REAL --R This constructor is exposed in this frame. @@ -6031,6 +6408,7 @@ digraph pic { --S 1 of 1 )show SetCategory +--R --R SetCategory is a category constructor --R Abbreviation for SetCategory is SETCAT --R This constructor is exposed in this frame. @@ -6188,6 +6566,7 @@ digraph pic { --S 1 of 1 )show TranscendentalFunctionCategory +--R --R TranscendentalFunctionCategory is a category constructor --R Abbreviation for TranscendentalFunctionCategory is TRANFUN --R This constructor is exposed in this frame. @@ -6437,6 +6816,7 @@ digraph pic { --S 1 of 1 )show AbelianSemiGroup +--R --R AbelianSemiGroup is a category constructor --R Abbreviation for AbelianSemiGroup is ABELSG --R This constructor is exposed in this frame. @@ -6754,11 +7134,11 @@ digraph pic { --R cyclic? : % -> Boolean distance : (%,%) -> Integer --R ?.value : (%,value) -> S empty : () -> % --R empty? : % -> Boolean eq? : (%,%) -> Boolean ---R leaf? : % -> Boolean leaves : % -> List(S) ---R map : ((S -> S),%) -> % nodes : % -> List(%) ---R sample : () -> % tree : List(S) -> % ---R tree : S -> % tree : (S,List(%)) -> % ---R value : % -> S +--R latex : % -> String if S has SETCAT leaf? : % -> Boolean +--R leaves : % -> List(S) map : ((S -> S),%) -> % +--R nodes : % -> List(%) sample : () -> % +--R tree : List(S) -> % tree : S -> % +--R tree : (S,List(%)) -> % value : % -> S --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R ?=? : (%,%) -> Boolean if S has SETCAT --R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate @@ -6772,7 +7152,6 @@ digraph pic { --R eval : (%,List(Equation(S))) -> % if S has EVALAB(S) and S has SETCAT --R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate --R hash : % -> SingleInteger if S has SETCAT ---R latex : % -> String if S has SETCAT --R less? : (%,NonNegativeInteger) -> Boolean --R map! : ((S -> S),%) -> % if $ has shallowlyMutable --R member? : (S,%) -> Boolean if S has SETCAT and $ has finiteAggregate @@ -6993,12 +7372,11 @@ digraph pic { --R------------------------------- Operations -------------------------------- --R coerce : FortranCode -> % coerce : List(FortranCode) -> % --R coerce : % -> OutputForm outputAsFortran : % -> Void ---R retract : Polynomial(Float) -> % retract : Expression(Float) -> % +--R retract : Polynomial(Integer) -> % retract : Polynomial(Float) -> % +--R retract : Expression(Integer) -> % retract : Expression(Float) -> % --R coerce : Record(localSymbols: SymbolTable,code: List(FortranCode)) -> % --R retract : Fraction(Polynomial(Integer)) -> % --R retract : Fraction(Polynomial(Float)) -> % ---R retract : Polynomial(Integer) -> % ---R retract : Expression(Integer) -> % --R retractIfCan : Fraction(Polynomial(Integer)) -> Union(%,"failed") --R retractIfCan : Fraction(Polynomial(Float)) -> Union(%,"failed") --R retractIfCan : Polynomial(Integer) -> Union(%,"failed") @@ -7187,9 +7565,9 @@ digraph pic { --R --R------------------------------- Operations -------------------------------- --R coerce : FortranCode -> % coerce : List(FortranCode) -> % ---R coerce : % -> OutputForm outputAsFortran : % -> Void +--R coerce : Matrix(MachineFloat) -> % coerce : % -> OutputForm +--R outputAsFortran : % -> Void --R coerce : Record(localSymbols: SymbolTable,code: List(FortranCode)) -> % ---R coerce : Matrix(MachineFloat) -> % --R --E 1 @@ -7520,9 +7898,9 @@ digraph pic { --R --R------------------------------- Operations -------------------------------- --R coerce : FortranCode -> % coerce : List(FortranCode) -> % ---R coerce : % -> OutputForm outputAsFortran : % -> Void +--R coerce : Vector(MachineFloat) -> % coerce : % -> OutputForm +--R outputAsFortran : % -> Void --R coerce : Record(localSymbols: SymbolTable,code: List(FortranCode)) -> % ---R coerce : Vector(MachineFloat) -> % --R --E 1 @@ -8016,6 +8394,7 @@ digraph pic { --S 1 of 1 )show FileCategory +--R --R FileCategory(Name: SetCategory,S: SetCategory) is a category constructor --R Abbreviation for FileCategory is FILECAT --R This constructor is exposed in this frame. @@ -8196,6 +8575,7 @@ digraph pic { --S 1 of 1 )show Finite +--R --R Finite is a category constructor --R Abbreviation for Finite is FINITE --R This constructor is exposed in this frame. @@ -8364,6 +8744,7 @@ digraph pic { --S 1 of 1 )show FileNameCategory +--R --R FileNameCategory is a category constructor --R Abbreviation for FileNameCategory is FNCAT --R This constructor is exposed in this frame. @@ -8537,6 +8918,7 @@ digraph pic { --S 1 of 1 )show GradedModule +--R --R GradedModule(R: CommutativeRing,E: AbelianMonoid) is a category constructor --R Abbreviation for GradedModule is GRMOD --R This constructor is exposed in this frame. @@ -8711,6 +9093,45 @@ digraph pic { %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \pagehead{LeftOreRing}{LORER} \pagepic{ps/v102leftorering.eps}{LORER}{1.00} +\begin{chunk}{LeftOreRing.input} +)set break resume +)sys rm -f LeftOreRing.output +)spool LeftOreRing.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show LeftOreRing +--R +--R LeftOreRing is a category constructor +--R Abbreviation for LeftOreRing is LORER +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for LORER +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R one? : % -> Boolean recip : % -> Union(%,"failed") +--R sample : () -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R characteristic : () -> NonNegativeInteger +--R lcmCoef : (%,%) -> Record(llcmres: %,coeff1: %,coeff2: %) +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +\end{chunk} + \begin{chunk}{LeftOreRing.help} ==================================================================== LeftOreRing @@ -8788,7 +9209,8 @@ digraph pic { --R------------------------------- Operations -------------------------------- --R copy : % -> % empty : () -> % --R empty? : % -> Boolean eq? : (%,%) -> Boolean ---R map : ((S -> S),%) -> % sample : () -> % +--R latex : % -> String if S has SETCAT map : ((S -> S),%) -> % +--R sample : () -> % --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R ?=? : (%,%) -> Boolean if S has SETCAT --R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate @@ -8801,7 +9223,6 @@ digraph pic { --R eval : (%,List(Equation(S))) -> % if S has EVALAB(S) and S has SETCAT --R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate --R hash : % -> SingleInteger if S has SETCAT ---R latex : % -> String if S has SETCAT --R less? : (%,NonNegativeInteger) -> Boolean --R map! : ((S -> S),%) -> % if $ has shallowlyMutable --R member? : (S,%) -> Boolean if S has SETCAT and $ has finiteAggregate @@ -9082,6 +9503,7 @@ digraph pic { --S 1 of 1 )show IndexedDirectProductCategory +--R --R IndexedDirectProductCategory(A: SetCategory,S: OrderedSet) is a category constructor --R Abbreviation for IndexedDirectProductCategory is IDPC --R This constructor is exposed in this frame. @@ -9490,6 +9912,7 @@ digraph pic { --S 1 of 1 )show Monad +--R --R Monad is a category constructor --R Abbreviation for Monad is MONAD --R This constructor is exposed in this frame. @@ -10239,6 +10662,7 @@ digraph pic { --S 1 of 1 )show OrderedSet +--R --R OrderedSet is a category constructor --R Abbreviation for OrderedSet is ORDSET --R This constructor is exposed in this frame. @@ -10778,11 +11202,10 @@ digraph pic { --R ?=? : (%,%) -> Boolean allRootsOf : ThePols -> List(%) --R coerce : % -> OutputForm definingPolynomial : % -> ThePols --R hash : % -> SingleInteger latex : % -> String +--R negative? : (ThePols,%) -> Boolean positive? : (ThePols,%) -> Boolean --R sign : (ThePols,%) -> Integer zero? : (ThePols,%) -> Boolean --R ?~=? : (%,%) -> Boolean --R approximate : (ThePols,%,TheField) -> TheField ---R negative? : (ThePols,%) -> Boolean ---R positive? : (ThePols,%) -> Boolean --R recip : (ThePols,%) -> Union(ThePols,"failed") --R relativeApprox : (ThePols,%,TheField) -> TheField --R rootOf : (ThePols,PositiveInteger) -> Union(%,"failed") @@ -11154,6 +11577,7 @@ operator ``*''. A Semigroup $G(S,*)$ is: --S 1 of 1 )show SemiGroup +--R --R SemiGroup is a category constructor --R Abbreviation for SemiGroup is SGROUP --R This constructor is exposed in this frame. @@ -11322,6 +11746,7 @@ digraph pic { --S 1 of 1 )show SetCategoryWithDegree +--R --R SetCategoryWithDegree is a category constructor --R Abbreviation for SetCategoryWithDegree is SETCATD --R This constructor is exposed in this frame. @@ -11694,6 +12119,7 @@ digraph pic { --S 1 of 1 )show StepThrough +--R --R StepThrough is a category constructor --R Abbreviation for StepThrough is STEP --R This constructor is exposed in this frame. @@ -11702,8 +12128,8 @@ digraph pic { --R------------------------------- Operations -------------------------------- --R ?=? : (%,%) -> Boolean coerce : % -> OutputForm --R hash : % -> SingleInteger init : () -> % ---R latex : % -> String ?~=? : (%,%) -> Boolean ---R nextItem : % -> Union(%,"failed") +--R latex : % -> String nextItem : % -> Union(%,"failed") +--R ?~=? : (%,%) -> Boolean --R --E 1 @@ -11864,8 +12290,9 @@ digraph pic { --R point : Point(R) -> % point : (%,List(R)) -> % --R point : (%,Point(R)) -> % point? : % -> Boolean --R polygon : % -> List(Point(R)) polygon : List(Point(R)) -> % ---R polygon : (%,List(List(R))) -> % polygon? : % -> Boolean ---R subspace : % -> SubSpace(3,R) ?~=? : (%,%) -> Boolean +--R polygon : (%,List(List(R))) -> % polygon : (%,List(Point(R))) -> % +--R polygon? : % -> Boolean subspace : % -> SubSpace(3,R) +--R ?~=? : (%,%) -> Boolean --R closedCurve : (%,List(List(R))) -> % --R closedCurve : (%,List(Point(R))) -> % --R enterPointData : (%,List(Point(R))) -> NonNegativeInteger @@ -11883,7 +12310,6 @@ digraph pic { --R numberOfComposites : % -> NonNegativeInteger --R objects : % -> Record(points: NonNegativeInteger,curves: NonNegativeInteger,polygons: NonNegativeInteger,constructs: NonNegativeInteger) --R point : (%,NonNegativeInteger) -> % ---R polygon : (%,List(Point(R))) -> % --R --E 1 @@ -12405,18 +12831,19 @@ digraph pic { --S 1 of 1 )show AbelianMonoid +--R --R AbelianMonoid is a category constructor --R Abbreviation for AbelianMonoid is ABELMON --R This constructor is exposed in this frame. --R Issue )edit bookvol10.2.pamphlet to see algebra source code for ABELMON --R --R------------------------------- Operations -------------------------------- ---R ?*? : (PositiveInteger,%) -> % ?+? : (%,%) -> % ---R ?=? : (%,%) -> Boolean 0 : () -> % ---R coerce : % -> OutputForm hash : % -> SingleInteger ---R latex : % -> String sample : () -> % ---R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?+? : (%,%) -> % ?=? : (%,%) -> Boolean +--R 0 : () -> % coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R sample : () -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean --R --E 1 @@ -12825,7 +13252,8 @@ digraph pic { --R empty : () -> % empty? : % -> Boolean --R eq? : (%,%) -> Boolean extract! : % -> S --R insert! : (S,%) -> % inspect : % -> S ---R map : ((S -> S),%) -> % sample : () -> % +--R latex : % -> String if S has SETCAT map : ((S -> S),%) -> % +--R sample : () -> % --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R ?=? : (%,%) -> Boolean if S has SETCAT --R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate @@ -12838,7 +13266,6 @@ digraph pic { --R eval : (%,List(Equation(S))) -> % if S has EVALAB(S) and S has SETCAT --R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate --R hash : % -> SingleInteger if S has SETCAT ---R latex : % -> String if S has SETCAT --R less? : (%,NonNegativeInteger) -> Boolean --R map! : ((S -> S),%) -> % if $ has shallowlyMutable --R member? : (S,%) -> Boolean if S has SETCAT and $ has finiteAggregate @@ -13047,6 +13474,7 @@ digraph pic { --S 1 of 1 )show CachableSet +--R --R CachableSet is a category constructor --R Abbreviation for CachableSet is CACHSET --R This constructor is exposed in this frame. @@ -13058,8 +13486,7 @@ digraph pic { --R ?>=? : (%,%) -> Boolean coerce : % -> OutputForm --R hash : % -> SingleInteger latex : % -> String --R max : (%,%) -> % min : (%,%) -> % ---R ?~=? : (%,%) -> Boolean ---R position : % -> NonNegativeInteger +--R position : % -> NonNegativeInteger ?~=? : (%,%) -> Boolean --R setPosition : (%,NonNegativeInteger) -> Void --R --E 1 @@ -13202,8 +13629,8 @@ digraph pic { --R------------------------------- Operations -------------------------------- --R construct : List(S) -> % copy : % -> % --R empty : () -> % empty? : % -> Boolean ---R eq? : (%,%) -> Boolean map : ((S -> S),%) -> % ---R sample : () -> % +--R eq? : (%,%) -> Boolean latex : % -> String if S has SETCAT +--R map : ((S -> S),%) -> % sample : () -> % --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R ?=? : (%,%) -> Boolean if S has SETCAT --R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate @@ -13218,7 +13645,6 @@ digraph pic { --R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate --R find : ((S -> Boolean),%) -> Union(S,"failed") --R hash : % -> SingleInteger if S has SETCAT ---R latex : % -> String if S has SETCAT --R less? : (%,NonNegativeInteger) -> Boolean --R map! : ((S -> S),%) -> % if $ has shallowlyMutable --R member? : (S,%) -> Boolean if S has SETCAT and $ has finiteAggregate @@ -13845,37 +14271,33 @@ digraph pic { --R box : List(%) -> % box : % -> % --R coerce : Kernel(%) -> % coerce : % -> OutputForm --R distribute : (%,%) -> % distribute : % -> % +--R elt : (BasicOperator,List(%)) -> % elt : (BasicOperator,%,%,%) -> % --R elt : (BasicOperator,%,%) -> % elt : (BasicOperator,%) -> % +--R eval : (%,Symbol,(% -> %)) -> % eval : (%,List(%),List(%)) -> % --R eval : (%,%,%) -> % eval : (%,Equation(%)) -> % ---R eval : (%,Kernel(%),%) -> % freeOf? : (%,Symbol) -> Boolean ---R freeOf? : (%,%) -> Boolean hash : % -> SingleInteger ---R height : % -> NonNegativeInteger is? : (%,Symbol) -> Boolean +--R eval : (%,List(Equation(%))) -> % eval : (%,Kernel(%),%) -> % +--R freeOf? : (%,Symbol) -> Boolean freeOf? : (%,%) -> Boolean +--R hash : % -> SingleInteger height : % -> NonNegativeInteger +--R is? : (%,Symbol) -> Boolean is? : (%,BasicOperator) -> Boolean --R kernel : (BasicOperator,%) -> % kernels : % -> List(Kernel(%)) ---R latex : % -> String max : (%,%) -> % ---R min : (%,%) -> % paren : List(%) -> % ---R paren : % -> % retract : % -> Kernel(%) ---R subst : (%,Equation(%)) -> % tower : % -> List(Kernel(%)) ---R ?~=? : (%,%) -> Boolean +--R latex : % -> String map : ((% -> %),Kernel(%)) -> % +--R max : (%,%) -> % min : (%,%) -> % +--R paren : List(%) -> % paren : % -> % +--R retract : % -> Kernel(%) subst : (%,Equation(%)) -> % +--R tower : % -> List(Kernel(%)) ?~=? : (%,%) -> Boolean --R definingPolynomial : % -> % if $ has RING ---R elt : (BasicOperator,List(%)) -> % --R elt : (BasicOperator,%,%,%,%) -> % ---R elt : (BasicOperator,%,%,%) -> % --R eval : (%,BasicOperator,(% -> %)) -> % --R eval : (%,BasicOperator,(List(%) -> %)) -> % --R eval : (%,List(BasicOperator),List((List(%) -> %))) -> % --R eval : (%,List(BasicOperator),List((% -> %))) -> % ---R eval : (%,Symbol,(% -> %)) -> % --R eval : (%,Symbol,(List(%) -> %)) -> % --R eval : (%,List(Symbol),List((List(%) -> %))) -> % --R eval : (%,List(Symbol),List((% -> %))) -> % ---R eval : (%,List(%),List(%)) -> % ---R eval : (%,List(Equation(%))) -> % --R eval : (%,List(Kernel(%)),List(%)) -> % --R even? : % -> Boolean if $ has RETRACT(INT) ---R is? : (%,BasicOperator) -> Boolean --R kernel : (BasicOperator,List(%)) -> % --R mainKernel : % -> Union(Kernel(%),"failed") ---R map : ((% -> %),Kernel(%)) -> % --R minPoly : Kernel(%) -> SparseUnivariatePolynomial(%) if $ has RING --R odd? : % -> Boolean if $ has RETRACT(INT) --R operator : BasicOperator -> BasicOperator @@ -14438,6 +14860,7 @@ digraph pic { --S 1 of 1 )show GradedAlgebra +--R --R GradedAlgebra(R: CommutativeRing,E: AbelianMonoid) is a category constructor --R Abbreviation for GradedAlgebra is GRALG --R This constructor is exposed in this frame. @@ -14990,21 +15413,21 @@ digraph pic { --S 1 of 1 )show MonadWithUnit +--R --R MonadWithUnit is a category constructor --R Abbreviation for MonadWithUnit is MONADWU --R This constructor is exposed in this frame. --R Issue )edit bookvol10.2.pamphlet to see algebra source code for MONADWU --R --R------------------------------- Operations -------------------------------- ---R ?*? : (%,%) -> % ?**? : (%,PositiveInteger) -> % ---R ?=? : (%,%) -> Boolean 1 : () -> % ---R coerce : % -> OutputForm hash : % -> SingleInteger ---R latex : % -> String one? : % -> Boolean +--R ?*? : (%,%) -> % ?**? : (%,NonNegativeInteger) -> % +--R ?**? : (%,PositiveInteger) -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R leftRecip : % -> Union(%,"failed") one? : % -> Boolean --R recip : % -> Union(%,"failed") ?~=? : (%,%) -> Boolean ---R ?**? : (%,NonNegativeInteger) -> % --R leftPower : (%,NonNegativeInteger) -> % --R leftPower : (%,PositiveInteger) -> % ---R leftRecip : % -> Union(%,"failed") --R rightPower : (%,NonNegativeInteger) -> % --R rightPower : (%,PositiveInteger) -> % --R rightRecip : % -> Union(%,"failed") @@ -15231,20 +15654,20 @@ digraph pic { --S 1 of 1 )show Monoid +--R --R Monoid is a category constructor --R Abbreviation for Monoid is MONOID --R This constructor is exposed in this frame. --R Issue )edit bookvol10.2.pamphlet to see algebra source code for MONOID --R --R------------------------------- Operations -------------------------------- ---R ?*? : (%,%) -> % ?**? : (%,PositiveInteger) -> % ---R ?=? : (%,%) -> Boolean 1 : () -> % +--R ?*? : (%,%) -> % ?**? : (%,NonNegativeInteger) -> % +--R ?**? : (%,PositiveInteger) -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % ?^? : (%,NonNegativeInteger) -> % --R ?^? : (%,PositiveInteger) -> % coerce : % -> OutputForm --R hash : % -> SingleInteger latex : % -> String --R one? : % -> Boolean recip : % -> Union(%,"failed") --R sample : () -> % ?~=? : (%,%) -> Boolean ---R ?**? : (%,NonNegativeInteger) -> % ---R ?^? : (%,NonNegativeInteger) -> % --R --E 1 @@ -15429,6 +15852,7 @@ digraph pic { --S 1 of 1 )show OrderedFinite +--R --R OrderedFinite is a category constructor --R Abbreviation for OrderedFinite is ORDFIN --R This constructor is exposed in this frame. @@ -16061,9 +16485,10 @@ digraph pic { --R cyclic? : % -> Boolean distance : (%,%) -> Integer --R ?.value : (%,value) -> S empty : () -> % --R empty? : % -> Boolean eq? : (%,%) -> Boolean ---R leaf? : % -> Boolean leaves : % -> List(S) ---R map : ((S -> S),%) -> % nodes : % -> List(%) ---R sample : () -> % value : % -> S +--R latex : % -> String if S has SETCAT leaf? : % -> Boolean +--R leaves : % -> List(S) map : ((S -> S),%) -> % +--R nodes : % -> List(%) sample : () -> % +--R value : % -> S --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R ?=? : (%,%) -> Boolean if S has SETCAT --R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate @@ -16077,7 +16502,6 @@ digraph pic { --R eval : (%,List(Equation(S))) -> % if S has EVALAB(S) and S has SETCAT --R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate --R hash : % -> SingleInteger if S has SETCAT ---R latex : % -> String if S has SETCAT --R less? : (%,NonNegativeInteger) -> Boolean --R map! : ((S -> S),%) -> % if $ has shallowlyMutable --R member? : (S,%) -> Boolean if S has SETCAT and $ has finiteAggregate @@ -16360,14 +16784,15 @@ first column in an array and vice versa. --R elt : (%,Integer,Integer,R) -> R elt : (%,Integer,Integer) -> R --R empty : () -> % empty? : % -> Boolean --R eq? : (%,%) -> Boolean fill! : (%,R) -> % ---R map : (((R,R) -> R),%,%,R) -> % map : (((R,R) -> R),%,%) -> % ---R map : ((R -> R),%) -> % map! : ((R -> R),%) -> % ---R maxColIndex : % -> Integer maxRowIndex : % -> Integer ---R minColIndex : % -> Integer minRowIndex : % -> Integer ---R ncols : % -> NonNegativeInteger nrows : % -> NonNegativeInteger ---R parts : % -> List(R) qelt : (%,Integer,Integer) -> R ---R row : (%,Integer) -> Row sample : () -> % ---R setRow! : (%,Integer,Row) -> % +--R latex : % -> String if R has SETCAT map : (((R,R) -> R),%,%,R) -> % +--R map : (((R,R) -> R),%,%) -> % map : ((R -> R),%) -> % +--R map! : ((R -> R),%) -> % maxColIndex : % -> Integer +--R maxRowIndex : % -> Integer minColIndex : % -> Integer +--R minRowIndex : % -> Integer ncols : % -> NonNegativeInteger +--R nrows : % -> NonNegativeInteger parts : % -> List(R) +--R qelt : (%,Integer,Integer) -> R row : (%,Integer) -> Row +--R sample : () -> % setColumn! : (%,Integer,Col) -> % +--R setRow! : (%,Integer,Row) -> % setelt : (%,Integer,Integer,R) -> R --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R ?=? : (%,%) -> Boolean if R has SETCAT --R any? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate @@ -16380,15 +16805,12 @@ first column in an array and vice versa. --R eval : (%,List(Equation(R))) -> % if R has EVALAB(R) and R has SETCAT --R every? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate --R hash : % -> SingleInteger if R has SETCAT ---R latex : % -> String if R has SETCAT --R less? : (%,NonNegativeInteger) -> Boolean --R member? : (R,%) -> Boolean if R has SETCAT and $ has finiteAggregate --R members : % -> List(R) if $ has finiteAggregate --R more? : (%,NonNegativeInteger) -> Boolean --R new : (NonNegativeInteger,NonNegativeInteger,R) -> % --R qsetelt! : (%,Integer,Integer,R) -> R ---R setColumn! : (%,Integer,Col) -> % ---R setelt : (%,Integer,Integer,R) -> R --R size? : (%,NonNegativeInteger) -> Boolean --R ?~=? : (%,%) -> Boolean if R has SETCAT --R @@ -16971,10 +17393,11 @@ digraph pic { --R ?.right : (%,right) -> % ?.left : (%,left) -> % --R ?.value : (%,value) -> S empty : () -> % --R empty? : % -> Boolean eq? : (%,%) -> Boolean ---R leaf? : % -> Boolean leaves : % -> List(S) ---R left : % -> % map : ((S -> S),%) -> % ---R nodes : % -> List(%) right : % -> % ---R sample : () -> % value : % -> S +--R latex : % -> String if S has SETCAT leaf? : % -> Boolean +--R leaves : % -> List(S) left : % -> % +--R map : ((S -> S),%) -> % nodes : % -> List(%) +--R right : % -> % sample : () -> % +--R value : % -> S --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R ?=? : (%,%) -> Boolean if S has SETCAT --R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate @@ -16988,7 +17411,6 @@ digraph pic { --R eval : (%,List(Equation(S))) -> % if S has EVALAB(S) and S has SETCAT --R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate --R hash : % -> SingleInteger if S has SETCAT ---R latex : % -> String if S has SETCAT --R less? : (%,NonNegativeInteger) -> Boolean --R map! : ((S -> S),%) -> % if $ has shallowlyMutable --R member? : (S,%) -> Boolean if S has SETCAT and $ has finiteAggregate @@ -17322,18 +17744,19 @@ digraph pic { --S 1 of 1 )show CancellationAbelianMonoid +--R --R CancellationAbelianMonoid is a category constructor --R Abbreviation for CancellationAbelianMonoid is CABMON --R This constructor is exposed in this frame. --R Issue )edit bookvol10.2.pamphlet to see algebra source code for CABMON --R --R------------------------------- Operations -------------------------------- ---R ?*? : (PositiveInteger,%) -> % ?+? : (%,%) -> % ---R ?=? : (%,%) -> Boolean 0 : () -> % ---R coerce : % -> OutputForm hash : % -> SingleInteger ---R latex : % -> String sample : () -> % ---R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?+? : (%,%) -> % ?=? : (%,%) -> Boolean +--R 0 : () -> % coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R sample : () -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean --R subtractIfCan : (%,%) -> Union(%,"failed") --R --E 1 @@ -17494,8 +17917,8 @@ digraph pic { --R dictionary : () -> % empty : () -> % --R empty? : % -> Boolean eq? : (%,%) -> Boolean --R extract! : % -> S insert! : (S,%) -> % ---R inspect : % -> S map : ((S -> S),%) -> % ---R sample : () -> % +--R inspect : % -> S latex : % -> String if S has SETCAT +--R map : ((S -> S),%) -> % sample : () -> % --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R ?=? : (%,%) -> Boolean if S has SETCAT --R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate @@ -17510,7 +17933,6 @@ digraph pic { --R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate --R find : ((S -> Boolean),%) -> Union(S,"failed") --R hash : % -> SingleInteger if S has SETCAT ---R latex : % -> String if S has SETCAT --R less? : (%,NonNegativeInteger) -> Boolean --R map! : ((S -> S),%) -> % if $ has shallowlyMutable --R member? : (S,%) -> Boolean if S has SETCAT and $ has finiteAggregate @@ -17801,11 +18223,11 @@ digraph pic { --R ?.value : (%,value) -> S empty : () -> % --R empty? : % -> Boolean eq? : (%,%) -> Boolean --R head : % -> % last : % -> S ---R leaf? : % -> Boolean leaves : % -> List(S) ---R map : ((S -> S),%) -> % next : % -> % ---R nodes : % -> List(%) previous : % -> % ---R sample : () -> % tail : % -> % ---R value : % -> S +--R latex : % -> String if S has SETCAT leaf? : % -> Boolean +--R leaves : % -> List(S) map : ((S -> S),%) -> % +--R next : % -> % nodes : % -> List(%) +--R previous : % -> % sample : () -> % +--R tail : % -> % value : % -> S --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R ?=? : (%,%) -> Boolean if S has SETCAT --R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate @@ -17820,7 +18242,6 @@ digraph pic { --R eval : (%,List(Equation(S))) -> % if S has EVALAB(S) and S has SETCAT --R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate --R hash : % -> SingleInteger if S has SETCAT ---R latex : % -> String if S has SETCAT --R less? : (%,NonNegativeInteger) -> Boolean --R map! : ((S -> S),%) -> % if $ has shallowlyMutable --R member? : (S,%) -> Boolean if S has SETCAT and $ has finiteAggregate @@ -18077,6 +18498,7 @@ digraph pic { --S 1 of 1 )show Group +--R --R Group is a category constructor --R Abbreviation for Group is GROUP --R This constructor is exposed in this frame. @@ -18084,16 +18506,15 @@ digraph pic { --R --R------------------------------- Operations -------------------------------- --R ?*? : (%,%) -> % ?**? : (%,Integer) -> % ---R ?**? : (%,PositiveInteger) -> % ?/? : (%,%) -> % ---R ?=? : (%,%) -> Boolean 1 : () -> % ---R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % +--R ?/? : (%,%) -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % ?^? : (%,Integer) -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % --R coerce : % -> OutputForm commutator : (%,%) -> % --R conjugate : (%,%) -> % hash : % -> SingleInteger --R inv : % -> % latex : % -> String --R one? : % -> Boolean recip : % -> Union(%,"failed") --R sample : () -> % ?~=? : (%,%) -> Boolean ---R ?**? : (%,NonNegativeInteger) -> % ---R ?^? : (%,NonNegativeInteger) -> % --R --E 1 @@ -18309,9 +18730,10 @@ digraph pic { --R empty? : % -> Boolean entries : % -> List(S) --R eq? : (%,%) -> Boolean index? : (Integer,%) -> Boolean --R indices : % -> List(Integer) insert : (%,%,Integer) -> % ---R insert : (S,%,Integer) -> % map : (((S,S) -> S),%,%) -> % ---R map : ((S -> S),%) -> % new : (NonNegativeInteger,S) -> % ---R qelt : (%,Integer) -> S sample : () -> % +--R insert : (S,%,Integer) -> % latex : % -> String if S has SETCAT +--R map : (((S,S) -> S),%,%) -> % map : ((S -> S),%) -> % +--R new : (NonNegativeInteger,S) -> % qelt : (%,Integer) -> S +--R sample : () -> % --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R ?=? : (%,%) -> Boolean if S has SETCAT --R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate @@ -18331,7 +18753,6 @@ digraph pic { --R find : ((S -> Boolean),%) -> Union(S,"failed") --R first : % -> S if Integer has ORDSET --R hash : % -> SingleInteger if S has SETCAT ---R latex : % -> String if S has SETCAT --R less? : (%,NonNegativeInteger) -> Boolean --R map! : ((S -> S),%) -> % if $ has shallowlyMutable --R maxIndex : % -> Integer if Integer has ORDSET @@ -19503,30 +19924,31 @@ inverse matrix [[j**i for i in 0..4] for j in 1..5] --R ?*? : (Row,%) -> Row ?*? : (%,Col) -> Col --R ?*? : (Integer,%) -> % ?*? : (%,R) -> % --R ?*? : (R,%) -> % ?*? : (%,%) -> % ---R ?+? : (%,%) -> % -? : % -> % ---R ?-? : (%,%) -> % antisymmetric? : % -> Boolean +--R ?**? : (%,NonNegativeInteger) -> % ?+? : (%,%) -> % +--R -? : % -> % ?-? : (%,%) -> % +--R ?/? : (%,R) -> % if R has FIELD antisymmetric? : % -> Boolean --R coerce : Col -> % column : (%,Integer) -> Col --R copy : % -> % diagonal? : % -> Boolean --R diagonalMatrix : List(%) -> % diagonalMatrix : List(R) -> % --R elt : (%,Integer,Integer,R) -> R elt : (%,Integer,Integer) -> R --R empty : () -> % empty? : % -> Boolean --R eq? : (%,%) -> Boolean fill! : (%,R) -> % ---R horizConcat : (%,%) -> % listOfLists : % -> List(List(R)) ---R map : (((R,R) -> R),%,%,R) -> % map : (((R,R) -> R),%,%) -> % ---R map : ((R -> R),%) -> % map! : ((R -> R),%) -> % ---R matrix : List(List(R)) -> % maxColIndex : % -> Integer ---R maxRowIndex : % -> Integer minColIndex : % -> Integer ---R minRowIndex : % -> Integer ncols : % -> NonNegativeInteger ---R nrows : % -> NonNegativeInteger parts : % -> List(R) +--R horizConcat : (%,%) -> % latex : % -> String if R has SETCAT +--R listOfLists : % -> List(List(R)) map : (((R,R) -> R),%,%,R) -> % +--R map : (((R,R) -> R),%,%) -> % map : ((R -> R),%) -> % +--R map! : ((R -> R),%) -> % matrix : List(List(R)) -> % +--R maxColIndex : % -> Integer maxRowIndex : % -> Integer +--R minColIndex : % -> Integer minRowIndex : % -> Integer +--R ncols : % -> NonNegativeInteger nrows : % -> NonNegativeInteger +--R parts : % -> List(R) pfaffian : % -> R if R has COMRING --R qelt : (%,Integer,Integer) -> R row : (%,Integer) -> Row ---R sample : () -> % setRow! : (%,Integer,Row) -> % +--R sample : () -> % setColumn! : (%,Integer,Col) -> % +--R setRow! : (%,Integer,Row) -> % setelt : (%,Integer,Integer,R) -> R --R square? : % -> Boolean squareTop : % -> % --R symmetric? : % -> Boolean transpose : % -> % --R transpose : Row -> % vertConcat : (%,%) -> % --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R ?**? : (%,Integer) -> % if R has FIELD ---R ?**? : (%,NonNegativeInteger) -> % ---R ?/? : (%,R) -> % if R has FIELD --R ?=? : (%,%) -> Boolean if R has SETCAT --R any? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate --R coerce : % -> OutputForm if R has SETCAT @@ -19543,7 +19965,6 @@ inverse matrix [[j**i for i in 0..4] for j in 1..5] --R exquo : (%,R) -> Union(%,"failed") if R has INTDOM --R hash : % -> SingleInteger if R has SETCAT --R inverse : % -> Union(%,"failed") if R has FIELD ---R latex : % -> String if R has SETCAT --R less? : (%,NonNegativeInteger) -> Boolean --R matrix : (NonNegativeInteger,NonNegativeInteger,((Integer,Integer) -> R)) -> % --R member? : (R,%) -> Boolean if R has SETCAT and $ has finiteAggregate @@ -19553,14 +19974,11 @@ inverse matrix [[j**i for i in 0..4] for j in 1..5] --R new : (NonNegativeInteger,NonNegativeInteger,R) -> % --R nullSpace : % -> List(Col) if R has INTDOM --R nullity : % -> NonNegativeInteger if R has INTDOM ---R pfaffian : % -> R if R has COMRING --R qsetelt! : (%,Integer,Integer,R) -> R --R rank : % -> NonNegativeInteger if R has INTDOM --R rowEchelon : % -> % if R has EUCDOM --R scalarMatrix : (NonNegativeInteger,R) -> % ---R setColumn! : (%,Integer,Col) -> % --R setelt : (%,List(Integer),List(Integer),%) -> % ---R setelt : (%,Integer,Integer,R) -> R --R setsubMatrix! : (%,Integer,Integer,%) -> % --R size? : (%,NonNegativeInteger) -> Boolean --R subMatrix : (%,Integer,Integer,Integer,Integer) -> % @@ -21093,6 +21511,7 @@ digraph pic { --S 1 of 1 )show OrderedMonoid +--R --R OrderedMonoid is a category constructor --R Abbreviation for OrderedMonoid is ORDMON --R This constructor is exposed in this frame. @@ -21100,16 +21519,15 @@ digraph pic { --R --R------------------------------- Operations -------------------------------- --R ?*? : (%,%) -> % ?**? : (%,PositiveInteger) -> % ---R ? Boolean ?<=? : (%,%) -> Boolean ---R ?=? : (%,%) -> Boolean ?>? : (%,%) -> Boolean ---R ?>=? : (%,%) -> Boolean 1 : () -> % ---R ?^? : (%,PositiveInteger) -> % coerce : % -> OutputForm +--R ?**? : (%,NonNegativeInteger) -> % ? Boolean +--R ?<=? : (%,%) -> Boolean ?=? : (%,%) -> Boolean +--R ?>? : (%,%) -> Boolean ?>=? : (%,%) -> Boolean +--R 1 : () -> % ?^? : (%,PositiveInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % coerce : % -> OutputForm --R hash : % -> SingleInteger latex : % -> String --R max : (%,%) -> % min : (%,%) -> % --R one? : % -> Boolean recip : % -> Union(%,"failed") --R sample : () -> % ?~=? : (%,%) -> Boolean ---R ?**? : (%,NonNegativeInteger) -> % ---R ?^? : (%,NonNegativeInteger) -> % --R --E 1 @@ -21976,9 +22394,9 @@ digraph pic { --R empty : () -> % empty? : % -> Boolean --R eq? : (%,%) -> Boolean extract! : % -> S --R insert! : (S,%) -> % inspect : % -> S ---R map : ((S -> S),%) -> % max : % -> S ---R merge : (%,%) -> % merge! : (%,%) -> % ---R sample : () -> % +--R latex : % -> String if S has SETCAT map : ((S -> S),%) -> % +--R max : % -> S merge : (%,%) -> % +--R merge! : (%,%) -> % sample : () -> % --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R ?=? : (%,%) -> Boolean if S has SETCAT --R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate @@ -21991,7 +22409,6 @@ digraph pic { --R eval : (%,List(Equation(S))) -> % if S has EVALAB(S) and S has SETCAT --R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate --R hash : % -> SingleInteger if S has SETCAT ---R latex : % -> String if S has SETCAT --R less? : (%,NonNegativeInteger) -> Boolean --R map! : ((S -> S),%) -> % if $ has shallowlyMutable --R member? : (S,%) -> Boolean if S has SETCAT and $ has finiteAggregate @@ -22212,8 +22629,9 @@ digraph pic { --R enqueue! : (S,%) -> S eq? : (%,%) -> Boolean --R extract! : % -> S front : % -> S --R insert! : (S,%) -> % inspect : % -> S ---R length : % -> NonNegativeInteger map : ((S -> S),%) -> % ---R rotate! : % -> % sample : () -> % +--R latex : % -> String if S has SETCAT length : % -> NonNegativeInteger +--R map : ((S -> S),%) -> % rotate! : % -> % +--R sample : () -> % --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R ?=? : (%,%) -> Boolean if S has SETCAT --R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate @@ -22226,7 +22644,6 @@ digraph pic { --R eval : (%,List(Equation(S))) -> % if S has EVALAB(S) and S has SETCAT --R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate --R hash : % -> SingleInteger if S has SETCAT ---R latex : % -> String if S has SETCAT --R less? : (%,NonNegativeInteger) -> Boolean --R map! : ((S -> S),%) -> % if $ has shallowlyMutable --R member? : (S,%) -> Boolean if S has SETCAT and $ has finiteAggregate @@ -22463,8 +22880,9 @@ digraph pic { --R latex : % -> String map : ((S -> S),%) -> % --R sample : () -> % set : List(S) -> % --R set : () -> % subset? : (%,%) -> Boolean ---R union : (S,%) -> % union : (%,S) -> % ---R union : (%,%) -> % ?~=? : (%,%) -> Boolean +--R symmetricDifference : (%,%) -> % union : (S,%) -> % +--R union : (%,S) -> % union : (%,%) -> % +--R ?~=? : (%,%) -> Boolean --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate --R convert : % -> InputForm if S has KONVERT(INFORM) @@ -22490,7 +22908,6 @@ digraph pic { --R removeDuplicates : % -> % if S has SETCAT and $ has finiteAggregate --R select : ((S -> Boolean),%) -> % if $ has finiteAggregate --R size? : (%,NonNegativeInteger) -> Boolean ---R symmetricDifference : (%,%) -> % --R --E 1 @@ -22817,9 +23234,10 @@ digraph pic { --R depth : % -> NonNegativeInteger empty : () -> % --R empty? : % -> Boolean eq? : (%,%) -> Boolean --R extract! : % -> S insert! : (S,%) -> % ---R inspect : % -> S map : ((S -> S),%) -> % ---R pop! : % -> S push! : (S,%) -> S ---R sample : () -> % top : % -> S +--R inspect : % -> S latex : % -> String if S has SETCAT +--R map : ((S -> S),%) -> % pop! : % -> S +--R push! : (S,%) -> S sample : () -> % +--R top : % -> S --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R ?=? : (%,%) -> Boolean if S has SETCAT --R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate @@ -22832,7 +23250,6 @@ digraph pic { --R eval : (%,List(Equation(S))) -> % if S has EVALAB(S) and S has SETCAT --R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate --R hash : % -> SingleInteger if S has SETCAT ---R latex : % -> String if S has SETCAT --R less? : (%,NonNegativeInteger) -> Boolean --R map! : ((S -> S),%) -> % if $ has shallowlyMutable --R member? : (S,%) -> Boolean if S has SETCAT and $ has finiteAggregate @@ -23073,12 +23490,13 @@ digraph pic { --R ?.first : (%,first) -> S ?.value : (%,value) -> S --R empty : () -> % empty? : % -> Boolean --R eq? : (%,%) -> Boolean first : % -> S ---R last : % -> S leaf? : % -> Boolean +--R last : (%,NonNegativeInteger) -> % last : % -> S +--R latex : % -> String if S has SETCAT leaf? : % -> Boolean --R leaves : % -> List(S) map : ((S -> S),%) -> % ---R nodes : % -> List(%) rest : % -> % ---R sample : () -> % second : % -> S ---R tail : % -> % third : % -> S ---R value : % -> S +--R nodes : % -> List(%) rest : (%,NonNegativeInteger) -> % +--R rest : % -> % sample : () -> % +--R second : % -> S tail : % -> % +--R third : % -> S value : % -> S --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R ?=? : (%,%) -> Boolean if S has SETCAT --R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate @@ -23097,8 +23515,6 @@ digraph pic { --R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate --R first : (%,NonNegativeInteger) -> % --R hash : % -> SingleInteger if S has SETCAT ---R last : (%,NonNegativeInteger) -> % ---R latex : % -> String if S has SETCAT --R less? : (%,NonNegativeInteger) -> Boolean --R map! : ((S -> S),%) -> % if $ has shallowlyMutable --R member? : (S,%) -> Boolean if S has SETCAT and $ has finiteAggregate @@ -23106,7 +23522,6 @@ digraph pic { --R more? : (%,NonNegativeInteger) -> Boolean --R node? : (%,%) -> Boolean if S has SETCAT --R parts : % -> List(S) if $ has finiteAggregate ---R rest : (%,NonNegativeInteger) -> % --R setchildren! : (%,List(%)) -> % if $ has shallowlyMutable --R setelt : (%,last,S) -> S if $ has shallowlyMutable --R setelt : (%,rest,%) -> % if $ has shallowlyMutable @@ -23621,20 +24036,20 @@ digraph pic { --S 1 of 1 )show AbelianGroup +--R --R AbelianGroup is a category constructor --R Abbreviation for AbelianGroup is ABELGRP --R This constructor is exposed in this frame. --R Issue )edit bookvol10.2.pamphlet to see algebra source code for ABELGRP --R --R------------------------------- Operations -------------------------------- ---R ?*? : (Integer,%) -> % ?*? : (PositiveInteger,%) -> % ---R ?+? : (%,%) -> % ?-? : (%,%) -> % ---R -? : % -> % ?=? : (%,%) -> Boolean ---R 0 : () -> % coerce : % -> OutputForm ---R hash : % -> SingleInteger latex : % -> String ---R sample : () -> % zero? : % -> Boolean ---R ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % +--R ?*? : (Integer,%) -> % ?*? : (NonNegativeInteger,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?+? : (%,%) -> % +--R ?-? : (%,%) -> % -? : % -> % +--R ?=? : (%,%) -> Boolean 0 : () -> % +--R coerce : % -> OutputForm hash : % -> SingleInteger +--R latex : % -> String sample : () -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean --R subtractIfCan : (%,%) -> Union(%,"failed") --R --E 1 @@ -23820,11 +24235,11 @@ digraph pic { --R ?.right : (%,right) -> % ?.left : (%,left) -> % --R ?.value : (%,value) -> S empty : () -> % --R empty? : % -> Boolean eq? : (%,%) -> Boolean ---R leaf? : % -> Boolean leaves : % -> List(S) ---R left : % -> % map : ((S -> S),%) -> % ---R node : (%,S,%) -> % nodes : % -> List(%) ---R right : % -> % sample : () -> % ---R value : % -> S +--R latex : % -> String if S has SETCAT leaf? : % -> Boolean +--R leaves : % -> List(S) left : % -> % +--R map : ((S -> S),%) -> % node : (%,S,%) -> % +--R nodes : % -> List(%) right : % -> % +--R sample : () -> % value : % -> S --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R ?=? : (%,%) -> Boolean if S has SETCAT --R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate @@ -23838,7 +24253,6 @@ digraph pic { --R eval : (%,List(Equation(S))) -> % if S has EVALAB(S) and S has SETCAT --R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate --R hash : % -> SingleInteger if S has SETCAT ---R latex : % -> String if S has SETCAT --R less? : (%,NonNegativeInteger) -> Boolean --R map! : ((S -> S),%) -> % if $ has shallowlyMutable --R member? : (S,%) -> Boolean if S has SETCAT and $ has finiteAggregate @@ -24116,8 +24530,8 @@ digraph pic { --R dictionary : () -> % empty : () -> % --R empty? : % -> Boolean eq? : (%,%) -> Boolean --R extract! : % -> S insert! : (S,%) -> % ---R inspect : % -> S map : ((S -> S),%) -> % ---R sample : () -> % +--R inspect : % -> S latex : % -> String if S has SETCAT +--R map : ((S -> S),%) -> % sample : () -> % --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R ?=? : (%,%) -> Boolean if S has SETCAT --R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate @@ -24132,7 +24546,6 @@ digraph pic { --R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate --R find : ((S -> Boolean),%) -> Union(S,"failed") --R hash : % -> SingleInteger if S has SETCAT ---R latex : % -> String if S has SETCAT --R less? : (%,NonNegativeInteger) -> Boolean --R map! : ((S -> S),%) -> % if $ has shallowlyMutable --R member? : (S,%) -> Boolean if S has SETCAT and $ has finiteAggregate @@ -24424,11 +24837,12 @@ digraph pic { --R extractTop! : % -> S front : % -> S --R height : % -> NonNegativeInteger insert! : (S,%) -> % --R insertBottom! : (S,%) -> S insertTop! : (S,%) -> S ---R inspect : % -> S length : % -> NonNegativeInteger ---R map : ((S -> S),%) -> % pop! : % -> S ---R push! : (S,%) -> S reverse! : % -> % ---R rotate! : % -> % sample : () -> % ---R top : % -> S top! : % -> S +--R inspect : % -> S latex : % -> String if S has SETCAT +--R length : % -> NonNegativeInteger map : ((S -> S),%) -> % +--R pop! : % -> S push! : (S,%) -> S +--R reverse! : % -> % rotate! : % -> % +--R sample : () -> % top : % -> S +--R top! : % -> S --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R ?=? : (%,%) -> Boolean if S has SETCAT --R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate @@ -24441,7 +24855,6 @@ digraph pic { --R eval : (%,List(Equation(S))) -> % if S has EVALAB(S) and S has SETCAT --R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate --R hash : % -> SingleInteger if S has SETCAT ---R latex : % -> String if S has SETCAT --R less? : (%,NonNegativeInteger) -> Boolean --R map! : ((S -> S),%) -> % if $ has shallowlyMutable --R member? : (S,%) -> Boolean if S has SETCAT and $ has finiteAggregate @@ -24727,9 +25140,10 @@ digraph pic { --R index? : (Integer,%) -> Boolean indices : % -> List(Integer) --R insert : (%,%,Integer) -> % insert : (S,%,Integer) -> % --R insert! : (%,%,Integer) -> % insert! : (S,%,Integer) -> % ---R map : (((S,S) -> S),%,%) -> % map : ((S -> S),%) -> % ---R new : (NonNegativeInteger,S) -> % qelt : (%,Integer) -> S ---R sample : () -> % +--R latex : % -> String if S has SETCAT map : (((S,S) -> S),%,%) -> % +--R map : ((S -> S),%) -> % new : (NonNegativeInteger,S) -> % +--R qelt : (%,Integer) -> S remove! : ((S -> Boolean),%) -> % +--R sample : () -> % select! : ((S -> Boolean),%) -> % --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R ?=? : (%,%) -> Boolean if S has SETCAT --R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate @@ -24750,7 +25164,6 @@ digraph pic { --R find : ((S -> Boolean),%) -> Union(S,"failed") --R first : % -> S if Integer has ORDSET --R hash : % -> SingleInteger if S has SETCAT ---R latex : % -> String if S has SETCAT --R less? : (%,NonNegativeInteger) -> Boolean --R map! : ((S -> S),%) -> % if $ has shallowlyMutable --R maxIndex : % -> Integer if Integer has ORDSET @@ -24768,11 +25181,9 @@ digraph pic { --R remove : ((S -> Boolean),%) -> % if $ has finiteAggregate --R remove : (S,%) -> % if S has SETCAT and $ has finiteAggregate --R remove! : (S,%) -> % if S has SETCAT ---R remove! : ((S -> Boolean),%) -> % --R removeDuplicates : % -> % if S has SETCAT and $ has finiteAggregate --R removeDuplicates! : % -> % if S has SETCAT --R select : ((S -> Boolean),%) -> % if $ has finiteAggregate ---R select! : ((S -> Boolean),%) -> % --R setelt : (%,UniversalSegment(Integer),S) -> S if $ has shallowlyMutable --R setelt : (%,Integer,S) -> S if $ has shallowlyMutable --R size? : (%,NonNegativeInteger) -> Boolean @@ -25118,10 +25529,12 @@ digraph pic { --R empty? : % -> Boolean entries : % -> List(S) --R eq? : (%,%) -> Boolean index? : (Integer,%) -> Boolean --R indices : % -> List(Integer) insert : (%,%,Integer) -> % ---R insert : (S,%,Integer) -> % map : (((S,S) -> S),%,%) -> % ---R map : ((S -> S),%) -> % new : (NonNegativeInteger,S) -> % ---R qelt : (%,Integer) -> S reverse : % -> % ---R sample : () -> % +--R insert : (S,%,Integer) -> % latex : % -> String if S has SETCAT +--R map : (((S,S) -> S),%,%) -> % map : ((S -> S),%) -> % +--R max : (%,%) -> % if S has ORDSET min : (%,%) -> % if S has ORDSET +--R new : (NonNegativeInteger,S) -> % qelt : (%,Integer) -> S +--R reverse : % -> % sample : () -> % +--R sort : % -> % if S has ORDSET sort : (((S,S) -> Boolean),%) -> % --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R ? Boolean if S has ORDSET --R ?<=? : (%,%) -> Boolean if S has ORDSET @@ -25146,16 +25559,13 @@ digraph pic { --R find : ((S -> Boolean),%) -> Union(S,"failed") --R first : % -> S if Integer has ORDSET --R hash : % -> SingleInteger if S has SETCAT ---R latex : % -> String if S has SETCAT --R less? : (%,NonNegativeInteger) -> Boolean --R map! : ((S -> S),%) -> % if $ has shallowlyMutable ---R max : (%,%) -> % if S has ORDSET --R maxIndex : % -> Integer if Integer has ORDSET --R member? : (S,%) -> Boolean if S has SETCAT and $ has finiteAggregate --R members : % -> List(S) if $ has finiteAggregate --R merge : (%,%) -> % if S has ORDSET --R merge : (((S,S) -> Boolean),%,%) -> % ---R min : (%,%) -> % if S has ORDSET --R minIndex : % -> Integer if Integer has ORDSET --R more? : (%,NonNegativeInteger) -> Boolean --R parts : % -> List(S) if $ has finiteAggregate @@ -25174,8 +25584,6 @@ digraph pic { --R setelt : (%,UniversalSegment(Integer),S) -> S if $ has shallowlyMutable --R setelt : (%,Integer,S) -> S if $ has shallowlyMutable --R size? : (%,NonNegativeInteger) -> Boolean ---R sort : % -> % if S has ORDSET ---R sort : (((S,S) -> Boolean),%) -> % --R sort! : % -> % if S has ORDSET and $ has shallowlyMutable --R sort! : (((S,S) -> Boolean),%) -> % if $ has shallowlyMutable --R sorted? : % -> Boolean if S has ORDSET @@ -25561,17 +25969,17 @@ digraph pic { --R Issue )edit bookvol10.2.pamphlet to see algebra source code for FAMONC --R --R------------------------------- Operations -------------------------------- ---R ?*? : (E,S) -> % ?*? : (PositiveInteger,%) -> % ---R ?+? : (S,%) -> % ?+? : (%,%) -> % ---R ?=? : (%,%) -> Boolean 0 : () -> % ---R coefficient : (S,%) -> E coerce : S -> % ---R coerce : % -> OutputForm hash : % -> SingleInteger ---R latex : % -> String mapCoef : ((E -> E),%) -> % ---R mapGen : ((S -> S),%) -> % nthCoef : (%,Integer) -> E ---R nthFactor : (%,Integer) -> S retract : % -> S ---R sample : () -> % size : % -> NonNegativeInteger ---R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % +--R ?*? : (E,S) -> % ?*? : (NonNegativeInteger,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?+? : (S,%) -> % +--R ?+? : (%,%) -> % ?=? : (%,%) -> Boolean +--R 0 : () -> % coefficient : (S,%) -> E +--R coerce : S -> % coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R mapCoef : ((E -> E),%) -> % mapGen : ((S -> S),%) -> % +--R nthCoef : (%,Integer) -> E nthFactor : (%,Integer) -> S +--R retract : % -> S sample : () -> % +--R size : % -> NonNegativeInteger zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean --R highCommonTerms : (%,%) -> % if E has OAMON --R retractIfCan : % -> Union(S,"failed") --R subtractIfCan : (%,%) -> Union(%,"failed") @@ -25804,8 +26212,9 @@ digraph pic { --R dictionary : () -> % empty : () -> % --R empty? : % -> Boolean eq? : (%,%) -> Boolean --R extract! : % -> S insert! : (S,%) -> % ---R inspect : % -> S map : ((S -> S),%) -> % ---R removeDuplicates! : % -> % sample : () -> % +--R inspect : % -> S latex : % -> String if S has SETCAT +--R map : ((S -> S),%) -> % removeDuplicates! : % -> % +--R sample : () -> % --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R ?=? : (%,%) -> Boolean if S has SETCAT --R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate @@ -25822,7 +26231,6 @@ digraph pic { --R find : ((S -> Boolean),%) -> Union(S,"failed") --R hash : % -> SingleInteger if S has SETCAT --R insert! : (S,%,NonNegativeInteger) -> % ---R latex : % -> String if S has SETCAT --R less? : (%,NonNegativeInteger) -> Boolean --R map! : ((S -> S),%) -> % if $ has shallowlyMutable --R member? : (S,%) -> Boolean if S has SETCAT and $ has finiteAggregate @@ -26071,21 +26479,22 @@ digraph pic { --S 1 of 1 )show OrderedAbelianMonoid +--R --R OrderedAbelianMonoid is a category constructor --R Abbreviation for OrderedAbelianMonoid is OAMON --R This constructor is exposed in this frame. --R Issue )edit bookvol10.2.pamphlet to see algebra source code for OAMON --R --R------------------------------- Operations -------------------------------- ---R ?*? : (PositiveInteger,%) -> % ?+? : (%,%) -> % ---R ? Boolean ?<=? : (%,%) -> Boolean ---R ?=? : (%,%) -> Boolean ?>? : (%,%) -> Boolean ---R ?>=? : (%,%) -> Boolean 0 : () -> % ---R coerce : % -> OutputForm hash : % -> SingleInteger ---R latex : % -> String max : (%,%) -> % ---R min : (%,%) -> % sample : () -> % ---R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?+? : (%,%) -> % ? Boolean +--R ?<=? : (%,%) -> Boolean ?=? : (%,%) -> Boolean +--R ?>? : (%,%) -> Boolean ?>=? : (%,%) -> Boolean +--R 0 : () -> % coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R max : (%,%) -> % min : (%,%) -> % +--R sample : () -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean --R --E 1 @@ -26226,9 +26635,10 @@ digraph pic { --R --R------------------------------- Operations -------------------------------- --R ?*? : (%,%) -> % ?**? : (%,Integer) -> % ---R ?**? : (%,PositiveInteger) -> % ?/? : (%,%) -> % ---R ? Boolean ?=? : (%,%) -> Boolean ---R 1 : () -> % ?^? : (%,Integer) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % +--R ?/? : (%,%) -> % ? Boolean +--R ?=? : (%,%) -> Boolean 1 : () -> % +--R ?^? : (%,Integer) -> % ?^? : (%,NonNegativeInteger) -> % --R ?^? : (%,PositiveInteger) -> % coerce : % -> OutputForm --R commutator : (%,%) -> % conjugate : (%,%) -> % --R cycle : List(S) -> % cycles : List(List(S)) -> % @@ -26237,11 +26647,9 @@ digraph pic { --R latex : % -> String one? : % -> Boolean --R orbit : (%,S) -> Set(S) recip : % -> Union(%,"failed") --R sample : () -> % ?~=? : (%,%) -> Boolean ---R ?**? : (%,NonNegativeInteger) -> % --R ?<=? : (%,%) -> Boolean if S has ORDSET or S has FINITE --R ?>? : (%,%) -> Boolean if S has ORDSET or S has FINITE --R ?>=? : (%,%) -> Boolean if S has ORDSET or S has FINITE ---R ?^? : (%,NonNegativeInteger) -> % --R max : (%,%) -> % if S has ORDSET or S has FINITE --R min : (%,%) -> % if S has ORDSET or S has FINITE --R @@ -26493,14 +26901,15 @@ digraph pic { --R explicitlyFinite? : % -> Boolean first : % -> S --R index? : (Integer,%) -> Boolean indices : % -> List(Integer) --R insert : (S,%,Integer) -> % insert : (%,%,Integer) -> % ---R last : % -> S leaf? : % -> Boolean +--R last : (%,NonNegativeInteger) -> % last : % -> S +--R latex : % -> String if S has SETCAT leaf? : % -> Boolean --R leaves : % -> List(S) map : (((S,S) -> S),%,%) -> % --R map : ((S -> S),%) -> % new : (NonNegativeInteger,S) -> % --R nodes : % -> List(%) possiblyInfinite? : % -> Boolean ---R qelt : (%,Integer) -> S rest : % -> % ---R sample : () -> % second : % -> S ---R tail : % -> % third : % -> S ---R value : % -> S +--R qelt : (%,Integer) -> S rest : (%,NonNegativeInteger) -> % +--R rest : % -> % sample : () -> % +--R second : % -> S tail : % -> % +--R third : % -> S value : % -> S --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R ?=? : (%,%) -> Boolean if S has SETCAT --R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate @@ -26525,8 +26934,6 @@ digraph pic { --R find : ((S -> Boolean),%) -> Union(S,"failed") --R first : (%,NonNegativeInteger) -> % --R hash : % -> SingleInteger if S has SETCAT ---R last : (%,NonNegativeInteger) -> % ---R latex : % -> String if S has SETCAT --R less? : (%,NonNegativeInteger) -> Boolean --R map! : ((S -> S),%) -> % if $ has shallowlyMutable --R maxIndex : % -> Integer if Integer has ORDSET @@ -26543,7 +26950,6 @@ digraph pic { --R remove : (S,%) -> % if S has SETCAT and $ has finiteAggregate --R remove : ((S -> Boolean),%) -> % if $ has finiteAggregate --R removeDuplicates : % -> % if S has SETCAT and $ has finiteAggregate ---R rest : (%,NonNegativeInteger) -> % --R select : ((S -> Boolean),%) -> % if $ has finiteAggregate --R setchildren! : (%,List(%)) -> % if $ has shallowlyMutable --R setelt : (%,Integer,S) -> S if $ has shallowlyMutable @@ -27010,7 +27416,8 @@ digraph pic { --R normalized? : (P,%) -> Boolean reduceByQuasiMonic : (P,%) -> P --R removeZero : (P,%) -> P rest : % -> Union(%,"failed") --R retract : List(P) -> % sample : () -> % ---R stronglyReduce : (P,%) -> P stronglyReduced? : % -> Boolean +--R select : (%,V) -> Union(P,"failed") stronglyReduce : (P,%) -> P +--R stronglyReduced? : % -> Boolean stronglyReduced? : (P,%) -> Boolean --R trivialIdeal? : % -> Boolean variables : % -> List(V) --R zeroSetSplit : List(P) -> List(%) ?~=? : (%,%) -> Boolean --R #? : % -> NonNegativeInteger if $ has finiteAggregate @@ -27055,11 +27462,9 @@ digraph pic { --R roughEqualIdeals? : (%,%) -> Boolean if R has INTDOM --R roughSubIdeal? : (%,%) -> Boolean if R has INTDOM --R roughUnitIdeal? : % -> Boolean if R has INTDOM ---R select : (%,V) -> Union(P,"failed") --R select : ((P -> Boolean),%) -> % if $ has finiteAggregate --R size? : (%,NonNegativeInteger) -> Boolean --R sort : (%,V) -> Record(under: %,floor: %,upper: %) ---R stronglyReduced? : (P,%) -> Boolean --R triangular? : % -> Boolean if R has INTDOM --R zeroSetSplitIntoTriangularSystems : List(P) -> List(Record(close: %,open: List(P))) --R @@ -27925,20 +28330,19 @@ digraph pic { --R Issue )edit bookvol10.2.pamphlet to see algebra source code for FDIVCAT --R --R------------------------------- Operations -------------------------------- ---R ?*? : (Integer,%) -> % ?*? : (PositiveInteger,%) -> % ---R ?+? : (%,%) -> % ?-? : (%,%) -> % ---R -? : % -> % ?=? : (%,%) -> Boolean ---R 0 : () -> % coerce : % -> OutputForm ---R divisor : (R,UP,UP,UP,F) -> % divisor : (F,F,Integer) -> % ---R divisor : (F,F) -> % divisor : R -> % +--R ?*? : (Integer,%) -> % ?*? : (NonNegativeInteger,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?+? : (%,%) -> % +--R ?-? : (%,%) -> % -? : % -> % +--R ?=? : (%,%) -> Boolean 0 : () -> % +--R coerce : % -> OutputForm divisor : (R,UP,UP,UP,F) -> % +--R divisor : (F,F,Integer) -> % divisor : (F,F) -> % +--R divisor : R -> % generator : % -> Union(R,"failed") --R hash : % -> SingleInteger latex : % -> String --R principal? : % -> Boolean reduce : % -> % --R sample : () -> % zero? : % -> Boolean --R ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % --R decompose : % -> Record(id: FractionalIdeal(UP,Fraction(UP),UPUP,R),principalPart: R) --R divisor : FractionalIdeal(UP,Fraction(UP),UPUP,R) -> % ---R generator : % -> Union(R,"failed") --R ideal : % -> FractionalIdeal(UP,Fraction(UP),UPUP,R) --R subtractIfCan : (%,%) -> Union(%,"failed") --R @@ -28144,6 +28548,7 @@ digraph pic { --S 1 of 1 )show FiniteSetAggregate +--R --R FiniteSetAggregate(S: SetCategory) is a category constructor --R Abbreviation for FiniteSetAggregate is FSAGG --R This constructor is exposed in this frame. @@ -28162,10 +28567,12 @@ digraph pic { --R inspect : % -> S intersect : (%,%) -> % --R latex : % -> String map : ((S -> S),%) -> % --R max : % -> S if S has ORDSET min : % -> S if S has ORDSET ---R sample : () -> % set : () -> % ---R set : List(S) -> % subset? : (%,%) -> Boolean +--R random : () -> % if S has FINITE sample : () -> % +--R set : () -> % set : List(S) -> % +--R subset? : (%,%) -> Boolean symmetricDifference : (%,%) -> % --R union : (%,%) -> % union : (%,S) -> % ---R union : (S,%) -> % ?~=? : (%,%) -> Boolean +--R union : (S,%) -> % universe : () -> % if S has FINITE +--R ?~=? : (%,%) -> Boolean --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate --R cardinality : % -> NonNegativeInteger @@ -28188,7 +28595,6 @@ digraph pic { --R members : % -> List(S) if $ has finiteAggregate --R more? : (%,NonNegativeInteger) -> Boolean --R parts : % -> List(S) if $ has finiteAggregate ---R random : () -> % if S has FINITE --R reduce : (((S,S) -> S),%) -> S if $ has finiteAggregate --R reduce : (((S,S) -> S),%,S) -> S if $ has finiteAggregate --R reduce : (((S,S) -> S),%,S,S) -> S if S has SETCAT and $ has finiteAggregate @@ -28201,8 +28607,6 @@ digraph pic { --R select! : ((S -> Boolean),%) -> % if $ has finiteAggregate --R size : () -> NonNegativeInteger if S has FINITE --R size? : (%,NonNegativeInteger) -> Boolean ---R symmetricDifference : (%,%) -> % ---R universe : () -> % if S has FINITE --R --E 1 @@ -28898,17 +29302,18 @@ digraph pic { --R extend : (%,Integer) -> % first : % -> S --R frst : % -> S index? : (Integer,%) -> Boolean --R indices : % -> List(Integer) insert : (S,%,Integer) -> % ---R insert : (%,%,Integer) -> % last : % -> S +--R insert : (%,%,Integer) -> % last : (%,NonNegativeInteger) -> % +--R last : % -> S latex : % -> String if S has SETCAT --R lazy? : % -> Boolean lazyEvaluate : % -> % --R leaf? : % -> Boolean leaves : % -> List(S) --R map : (((S,S) -> S),%,%) -> % map : ((S -> S),%) -> % --R new : (NonNegativeInteger,S) -> % nodes : % -> List(%) --R possiblyInfinite? : % -> Boolean qelt : (%,Integer) -> S ---R remove : ((S -> Boolean),%) -> % rest : % -> % ---R rst : % -> % sample : () -> % ---R second : % -> S select : ((S -> Boolean),%) -> % ---R tail : % -> % third : % -> S ---R value : % -> S +--R remove : ((S -> Boolean),%) -> % rest : (%,NonNegativeInteger) -> % +--R rest : % -> % rst : % -> % +--R sample : () -> % second : % -> S +--R select : ((S -> Boolean),%) -> % tail : % -> % +--R third : % -> S value : % -> S --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R ?=? : (%,%) -> Boolean if S has SETCAT --R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate @@ -28933,8 +29338,6 @@ digraph pic { --R find : ((S -> Boolean),%) -> Union(S,"failed") --R first : (%,NonNegativeInteger) -> % --R hash : % -> SingleInteger if S has SETCAT ---R last : (%,NonNegativeInteger) -> % ---R latex : % -> String if S has SETCAT --R less? : (%,NonNegativeInteger) -> Boolean --R map! : ((S -> S),%) -> % if $ has shallowlyMutable --R maxIndex : % -> Integer if Integer has ORDSET @@ -28951,7 +29354,6 @@ digraph pic { --R reduce : (((S,S) -> S),%) -> S if $ has finiteAggregate --R remove : (S,%) -> % if S has SETCAT and $ has finiteAggregate --R removeDuplicates : % -> % if S has SETCAT and $ has finiteAggregate ---R rest : (%,NonNegativeInteger) -> % --R setchildren! : (%,List(%)) -> % if $ has shallowlyMutable --R setelt : (%,Integer,S) -> S if $ has shallowlyMutable --R setelt : (%,UniversalSegment(Integer),S) -> S if $ has shallowlyMutable @@ -29828,13 +30230,13 @@ digraph pic { --R --R------------------------------- Operations -------------------------------- --R ?*? : (R,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?+? : (%,%) -> % ---R ?-? : (%,%) -> % -? : % -> % ---R ?=? : (%,%) -> Boolean 0 : () -> % ---R coerce : % -> OutputForm hash : % -> SingleInteger ---R latex : % -> String sample : () -> % ---R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 0 : () -> % coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R sample : () -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean --R subtractIfCan : (%,%) -> Union(%,"failed") --R --E 1 @@ -30003,15 +30405,20 @@ digraph pic { --R first : % -> S index? : (Integer,%) -> Boolean --R indices : % -> List(Integer) insert : (S,%,Integer) -> % --R insert : (%,%,Integer) -> % insert! : (S,%,Integer) -> % ---R insert! : (%,%,Integer) -> % last : % -> S +--R insert! : (%,%,Integer) -> % last : (%,NonNegativeInteger) -> % +--R last : % -> S latex : % -> String if S has SETCAT --R leaf? : % -> Boolean leaves : % -> List(S) --R list : S -> % map : (((S,S) -> S),%,%) -> % ---R map : ((S -> S),%) -> % new : (NonNegativeInteger,S) -> % +--R map : ((S -> S),%) -> % max : (%,%) -> % if S has ORDSET +--R min : (%,%) -> % if S has ORDSET new : (NonNegativeInteger,S) -> % --R nodes : % -> List(%) possiblyInfinite? : % -> Boolean ---R qelt : (%,Integer) -> S rest : % -> % +--R qelt : (%,Integer) -> S remove! : ((S -> Boolean),%) -> % +--R rest : (%,NonNegativeInteger) -> % rest : % -> % --R reverse : % -> % sample : () -> % ---R second : % -> S tail : % -> % ---R third : % -> S value : % -> S +--R second : % -> S select! : ((S -> Boolean),%) -> % +--R sort : (((S,S) -> Boolean),%) -> % sort : % -> % if S has ORDSET +--R tail : % -> % third : % -> S +--R value : % -> S --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R ? Boolean if S has ORDSET --R ?<=? : (%,%) -> Boolean if S has ORDSET @@ -30040,11 +30447,8 @@ digraph pic { --R find : ((S -> Boolean),%) -> Union(S,"failed") --R first : (%,NonNegativeInteger) -> % --R hash : % -> SingleInteger if S has SETCAT ---R last : (%,NonNegativeInteger) -> % ---R latex : % -> String if S has SETCAT --R less? : (%,NonNegativeInteger) -> Boolean --R map! : ((S -> S),%) -> % if $ has shallowlyMutable ---R max : (%,%) -> % if S has ORDSET --R maxIndex : % -> Integer if Integer has ORDSET --R member? : (S,%) -> Boolean if S has SETCAT and $ has finiteAggregate --R members : % -> List(S) if $ has finiteAggregate @@ -30052,7 +30456,6 @@ digraph pic { --R merge : (%,%) -> % if S has ORDSET --R merge! : (((S,S) -> Boolean),%,%) -> % --R merge! : (%,%) -> % if S has ORDSET ---R min : (%,%) -> % if S has ORDSET --R minIndex : % -> Integer if Integer has ORDSET --R more? : (%,NonNegativeInteger) -> Boolean --R node? : (%,%) -> Boolean if S has SETCAT @@ -30066,14 +30469,11 @@ digraph pic { --R reduce : (((S,S) -> S),%) -> S if $ has finiteAggregate --R remove : (S,%) -> % if S has SETCAT and $ has finiteAggregate --R remove : ((S -> Boolean),%) -> % if $ has finiteAggregate ---R remove! : ((S -> Boolean),%) -> % --R remove! : (S,%) -> % if S has SETCAT --R removeDuplicates : % -> % if S has SETCAT and $ has finiteAggregate --R removeDuplicates! : % -> % if S has SETCAT ---R rest : (%,NonNegativeInteger) -> % --R reverse! : % -> % if $ has shallowlyMutable --R select : ((S -> Boolean),%) -> % if $ has finiteAggregate ---R select! : ((S -> Boolean),%) -> % --R setchildren! : (%,List(%)) -> % if $ has shallowlyMutable --R setelt : (%,Integer,S) -> S if $ has shallowlyMutable --R setelt : (%,UniversalSegment(Integer),S) -> S if $ has shallowlyMutable @@ -30086,8 +30486,6 @@ digraph pic { --R setrest! : (%,%) -> % if $ has shallowlyMutable --R setvalue! : (%,S) -> S if $ has shallowlyMutable --R size? : (%,NonNegativeInteger) -> Boolean ---R sort : (((S,S) -> Boolean),%) -> % ---R sort : % -> % if S has ORDSET --R sort! : (((S,S) -> Boolean),%) -> % if $ has shallowlyMutable --R sort! : % -> % if S has ORDSET and $ has shallowlyMutable --R sorted? : (((S,S) -> Boolean),%) -> Boolean @@ -30715,9 +31113,9 @@ digraph pic { --R latex : % -> String map : ((S -> S),%) -> % --R removeDuplicates! : % -> % sample : () -> % --R set : () -> % set : List(S) -> % ---R subset? : (%,%) -> Boolean union : (%,%) -> % ---R union : (%,S) -> % union : (S,%) -> % ---R ?~=? : (%,%) -> Boolean +--R subset? : (%,%) -> Boolean symmetricDifference : (%,%) -> % +--R union : (%,%) -> % union : (%,S) -> % +--R union : (S,%) -> % ?~=? : (%,%) -> Boolean --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate --R convert : % -> InputForm if S has KONVERT(INFORM) @@ -30748,7 +31146,6 @@ digraph pic { --R select : ((S -> Boolean),%) -> % if $ has finiteAggregate --R select! : ((S -> Boolean),%) -> % if $ has finiteAggregate --R size? : (%,NonNegativeInteger) -> Boolean ---R symmetricDifference : (%,%) -> % --R --E 1 @@ -30987,6 +31384,7 @@ digraph pic { --S 1 of 1 )show NonAssociativeRng +--R --R NonAssociativeRng is a category constructor --R Abbreviation for NonAssociativeRng is NARNG --R This constructor is exposed in this frame. @@ -30994,15 +31392,15 @@ digraph pic { --R --R------------------------------- Operations -------------------------------- --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % ---R ?+? : (%,%) -> % ?-? : (%,%) -> % ---R -? : % -> % ?=? : (%,%) -> Boolean ---R 0 : () -> % antiCommutator : (%,%) -> % ---R associator : (%,%,%) -> % coerce : % -> OutputForm ---R commutator : (%,%) -> % hash : % -> SingleInteger ---R latex : % -> String sample : () -> % ---R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % +--R ?-? : (%,%) -> % -? : % -> % +--R ?=? : (%,%) -> Boolean 0 : () -> % +--R antiCommutator : (%,%) -> % associator : (%,%,%) -> % +--R coerce : % -> OutputForm commutator : (%,%) -> % +--R hash : % -> SingleInteger latex : % -> String +--R sample : () -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean --R leftPower : (%,PositiveInteger) -> % --R rightPower : (%,PositiveInteger) -> % --R subtractIfCan : (%,%) -> Union(%,"failed") @@ -31204,10 +31602,12 @@ digraph pic { --R empty? : % -> Boolean entries : % -> List(S) --R eq? : (%,%) -> Boolean index? : (Integer,%) -> Boolean --R indices : % -> List(Integer) insert : (%,%,Integer) -> % ---R insert : (S,%,Integer) -> % map : (((S,S) -> S),%,%) -> % ---R map : ((S -> S),%) -> % new : (NonNegativeInteger,S) -> % ---R qelt : (%,Integer) -> S reverse : % -> % ---R sample : () -> % +--R insert : (S,%,Integer) -> % latex : % -> String if S has SETCAT +--R map : (((S,S) -> S),%,%) -> % map : ((S -> S),%) -> % +--R max : (%,%) -> % if S has ORDSET min : (%,%) -> % if S has ORDSET +--R new : (NonNegativeInteger,S) -> % qelt : (%,Integer) -> S +--R reverse : % -> % sample : () -> % +--R sort : % -> % if S has ORDSET sort : (((S,S) -> Boolean),%) -> % --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R ? Boolean if S has ORDSET --R ?<=? : (%,%) -> Boolean if S has ORDSET @@ -31232,16 +31632,13 @@ digraph pic { --R find : ((S -> Boolean),%) -> Union(S,"failed") --R first : % -> S if Integer has ORDSET --R hash : % -> SingleInteger if S has SETCAT ---R latex : % -> String if S has SETCAT --R less? : (%,NonNegativeInteger) -> Boolean --R map! : ((S -> S),%) -> % if $ has shallowlyMutable ---R max : (%,%) -> % if S has ORDSET --R maxIndex : % -> Integer if Integer has ORDSET --R member? : (S,%) -> Boolean if S has SETCAT and $ has finiteAggregate --R members : % -> List(S) if $ has finiteAggregate --R merge : (%,%) -> % if S has ORDSET --R merge : (((S,S) -> Boolean),%,%) -> % ---R min : (%,%) -> % if S has ORDSET --R minIndex : % -> Integer if Integer has ORDSET --R more? : (%,NonNegativeInteger) -> Boolean --R parts : % -> List(S) if $ has finiteAggregate @@ -31260,8 +31657,6 @@ digraph pic { --R setelt : (%,UniversalSegment(Integer),S) -> S if $ has shallowlyMutable --R setelt : (%,Integer,S) -> S if $ has shallowlyMutable --R size? : (%,NonNegativeInteger) -> Boolean ---R sort : % -> % if S has ORDSET ---R sort : (((S,S) -> Boolean),%) -> % --R sort! : % -> % if S has ORDSET and $ has shallowlyMutable --R sort! : (((S,S) -> Boolean),%) -> % if $ has shallowlyMutable --R sorted? : % -> Boolean if S has ORDSET @@ -31807,21 +32202,22 @@ digraph pic { --S 1 of 1 )show OrderedCancellationAbelianMonoid +--R --R OrderedCancellationAbelianMonoid is a category constructor --R Abbreviation for OrderedCancellationAbelianMonoid is OCAMON --R This constructor is exposed in this frame. --R Issue )edit bookvol10.2.pamphlet to see algebra source code for OCAMON --R --R------------------------------- Operations -------------------------------- ---R ?*? : (PositiveInteger,%) -> % ?+? : (%,%) -> % ---R ? Boolean ?<=? : (%,%) -> Boolean ---R ?=? : (%,%) -> Boolean ?>? : (%,%) -> Boolean ---R ?>=? : (%,%) -> Boolean 0 : () -> % ---R coerce : % -> OutputForm hash : % -> SingleInteger ---R latex : % -> String max : (%,%) -> % ---R min : (%,%) -> % sample : () -> % ---R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?+? : (%,%) -> % ? Boolean +--R ?<=? : (%,%) -> Boolean ?=? : (%,%) -> Boolean +--R ?>? : (%,%) -> Boolean ?>=? : (%,%) -> Boolean +--R 0 : () -> % coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R max : (%,%) -> % min : (%,%) -> % +--R sample : () -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean --R subtractIfCan : (%,%) -> Union(%,"failed") --R --E 1 @@ -31988,17 +32384,20 @@ digraph pic { --R headReduce : (P,%) -> P headReduced? : % -> Boolean --R headReduced? : (P,%) -> Boolean infRittWu? : (%,%) -> Boolean --R initiallyReduce : (P,%) -> P initiallyReduced? : % -> Boolean ---R initials : % -> List(P) internalAugment : (P,%) -> % ---R intersect : (P,%) -> List(%) invertible? : (P,%) -> Boolean ---R invertibleSet : (P,%) -> List(%) last : % -> Union(P,"failed") ---R latex : % -> String mainVariable? : (V,%) -> Boolean ---R mainVariables : % -> List(V) map : ((P -> P),%) -> % ---R mvar : % -> V normalized? : % -> Boolean ---R normalized? : (P,%) -> Boolean purelyAlgebraic? : % -> Boolean +--R initials : % -> List(P) internalAugment : (List(P),%) -> % +--R internalAugment : (P,%) -> % intersect : (P,List(%)) -> List(%) +--R intersect : (List(P),%) -> List(%) intersect : (P,%) -> List(%) +--R invertible? : (P,%) -> Boolean invertibleSet : (P,%) -> List(%) +--R last : % -> Union(P,"failed") latex : % -> String +--R mainVariable? : (V,%) -> Boolean mainVariables : % -> List(V) +--R map : ((P -> P),%) -> % mvar : % -> V +--R normalized? : % -> Boolean normalized? : (P,%) -> Boolean +--R purelyAlgebraic? : % -> Boolean purelyAlgebraic? : (P,%) -> Boolean --R reduceByQuasiMonic : (P,%) -> P removeZero : (P,%) -> P --R rest : % -> Union(%,"failed") retract : List(P) -> % ---R sample : () -> % stronglyReduce : (P,%) -> P ---R stronglyReduced? : % -> Boolean trivialIdeal? : % -> Boolean +--R sample : () -> % select : (%,V) -> Union(P,"failed") +--R stronglyReduce : (P,%) -> P stronglyReduced? : % -> Boolean +--R stronglyReduced? : (P,%) -> Boolean trivialIdeal? : % -> Boolean --R variables : % -> List(V) zeroSetSplit : List(P) -> List(%) --R ?~=? : (%,%) -> Boolean --R #? : % -> NonNegativeInteger if $ has finiteAggregate @@ -32022,10 +32421,7 @@ digraph pic { --R find : ((P -> Boolean),%) -> Union(P,"failed") --R headRemainder : (P,%) -> Record(num: P,den: R) if R has INTDOM --R initiallyReduced? : (P,%) -> Boolean ---R internalAugment : (List(P),%) -> % ---R intersect : (P,List(%)) -> List(%) --R intersect : (List(P),List(%)) -> List(%) ---R intersect : (List(P),%) -> List(%) --R invertible? : (P,%) -> List(Record(val: Boolean,tower: %)) --R invertibleElseSplit? : (P,%) -> Union(Boolean,List(%)) --R lastSubResultant : (P,P,%) -> List(Record(val: P,tower: %)) @@ -32036,7 +32432,6 @@ digraph pic { --R members : % -> List(P) if $ has finiteAggregate --R more? : (%,NonNegativeInteger) -> Boolean --R parts : % -> List(P) if $ has finiteAggregate ---R purelyAlgebraic? : (P,%) -> Boolean --R purelyAlgebraicLeadingMonomial? : (P,%) -> Boolean --R purelyTranscendental? : (P,%) -> Boolean --R quasiComponent : % -> Record(close: List(P),open: List(P)) @@ -32057,12 +32452,10 @@ digraph pic { --R roughEqualIdeals? : (%,%) -> Boolean if R has INTDOM --R roughSubIdeal? : (%,%) -> Boolean if R has INTDOM --R roughUnitIdeal? : % -> Boolean if R has INTDOM ---R select : (%,V) -> Union(P,"failed") --R select : ((P -> Boolean),%) -> % if $ has finiteAggregate --R size? : (%,NonNegativeInteger) -> Boolean --R sort : (%,V) -> Record(under: %,floor: %,upper: %) --R squareFreePart : (P,%) -> List(Record(val: P,tower: %)) ---R stronglyReduced? : (P,%) -> Boolean --R triangular? : % -> Boolean if R has INTDOM --R zeroSetSplit : (List(P),Boolean) -> List(%) --R zeroSetSplitIntoTriangularSystems : List(P) -> List(Record(close: %,open: List(P))) @@ -32795,13 +33188,13 @@ digraph pic { --R --R------------------------------- Operations -------------------------------- --R ?*? : (%,R) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?+? : (%,%) -> % ---R ?-? : (%,%) -> % -? : % -> % ---R ?=? : (%,%) -> Boolean 0 : () -> % ---R coerce : % -> OutputForm hash : % -> SingleInteger ---R latex : % -> String sample : () -> % ---R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 0 : () -> % coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R sample : () -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean --R subtractIfCan : (%,%) -> Union(%,"failed") --R --E 1 @@ -32945,6 +33338,7 @@ Rng is a Ring that does not necessarily have a unit. --S 1 of 1 )show Rng +--R --R Rng is a category constructor --R Abbreviation for Rng is RNG --R This constructor is exposed in this frame. @@ -32952,14 +33346,14 @@ Rng is a Ring that does not necessarily have a unit. --R --R------------------------------- Operations -------------------------------- --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % ---R ?+? : (%,%) -> % ?-? : (%,%) -> % ---R -? : % -> % ?=? : (%,%) -> Boolean ---R 0 : () -> % ?^? : (%,PositiveInteger) -> % ---R coerce : % -> OutputForm hash : % -> SingleInteger ---R latex : % -> String sample : () -> % ---R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % +--R ?-? : (%,%) -> % -? : % -> % +--R ?=? : (%,%) -> Boolean 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R sample : () -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean --R subtractIfCan : (%,%) -> Union(%,"failed") --R --E 1 @@ -33118,6 +33512,7 @@ digraph pic { --S 1 of 1 )show BiModule +--R --R BiModule(R: Ring,S: Ring) is a category constructor --R Abbreviation for BiModule is BMODULE --R This constructor is exposed in this frame. @@ -33125,14 +33520,13 @@ digraph pic { --R --R------------------------------- Operations -------------------------------- --R ?*? : (%,S) -> % ?*? : (R,%) -> % ---R ?*? : (Integer,%) -> % ?*? : (PositiveInteger,%) -> % ---R ?+? : (%,%) -> % ?-? : (%,%) -> % ---R -? : % -> % ?=? : (%,%) -> Boolean ---R 0 : () -> % coerce : % -> OutputForm ---R hash : % -> SingleInteger latex : % -> String ---R sample : () -> % zero? : % -> Boolean ---R ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % +--R ?*? : (Integer,%) -> % ?*? : (NonNegativeInteger,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?+? : (%,%) -> % +--R ?-? : (%,%) -> % -? : % -> % +--R ?=? : (%,%) -> Boolean 0 : () -> % +--R coerce : % -> OutputForm hash : % -> SingleInteger +--R latex : % -> String sample : () -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean --R subtractIfCan : (%,%) -> Union(%,"failed") --R --E 1 @@ -33328,14 +33722,14 @@ digraph pic { --R empty : () -> % empty? : % -> Boolean --R entries : % -> List(Boolean) eq? : (%,%) -> Boolean --R hash : % -> SingleInteger index? : (Integer,%) -> Boolean ---R indices : % -> List(Integer) insert : (%,%,Integer) -> % ---R latex : % -> String max : (%,%) -> % ---R min : (%,%) -> % nand : (%,%) -> % ---R nor : (%,%) -> % not? : % -> % ---R ?or? : (%,%) -> % qelt : (%,Integer) -> Boolean ---R reverse : % -> % sample : () -> % ---R xor : (%,%) -> % ~? : % -> % ---R ?~=? : (%,%) -> Boolean +--R indices : % -> List(Integer) insert : (Boolean,%,Integer) -> % +--R insert : (%,%,Integer) -> % latex : % -> String +--R max : (%,%) -> % min : (%,%) -> % +--R nand : (%,%) -> % nor : (%,%) -> % +--R not? : % -> % ?or? : (%,%) -> % +--R qelt : (%,Integer) -> Boolean reverse : % -> % +--R sample : () -> % xor : (%,%) -> % +--R ~? : % -> % ?~=? : (%,%) -> Boolean --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R any? : ((Boolean -> Boolean),%) -> Boolean if $ has finiteAggregate --R convert : % -> InputForm if Boolean has KONVERT(INFORM) @@ -33354,7 +33748,6 @@ digraph pic { --R fill! : (%,Boolean) -> % if $ has shallowlyMutable --R find : ((Boolean -> Boolean),%) -> Union(Boolean,"failed") --R first : % -> Boolean if Integer has ORDSET ---R insert : (Boolean,%,Integer) -> % --R less? : (%,NonNegativeInteger) -> Boolean --R map : ((Boolean -> Boolean),%) -> % --R map : (((Boolean,Boolean) -> Boolean),%,%) -> % @@ -33768,6 +34161,7 @@ digraph pic { --S 1 of 1 )show NonAssociativeRing +--R --R NonAssociativeRing is a category constructor --R Abbreviation for NonAssociativeRing is NASRING --R This constructor is exposed in this frame. @@ -33775,22 +34169,21 @@ digraph pic { --R --R------------------------------- Operations -------------------------------- --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ?=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % --R antiCommutator : (%,%) -> % associator : (%,%,%) -> % --R coerce : Integer -> % coerce : % -> OutputForm --R commutator : (%,%) -> % hash : % -> SingleInteger ---R latex : % -> String one? : % -> Boolean ---R recip : % -> Union(%,"failed") sample : () -> % ---R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % +--R latex : % -> String leftRecip : % -> Union(%,"failed") +--R one? : % -> Boolean recip : % -> Union(%,"failed") +--R sample : () -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean --R characteristic : () -> NonNegativeInteger --R leftPower : (%,NonNegativeInteger) -> % --R leftPower : (%,PositiveInteger) -> % ---R leftRecip : % -> Union(%,"failed") --R rightPower : (%,NonNegativeInteger) -> % --R rightPower : (%,PositiveInteger) -> % --R rightRecip : % -> Union(%,"failed") @@ -34011,17 +34404,20 @@ digraph pic { --R headReduce : (P,%) -> P headReduced? : % -> Boolean --R headReduced? : (P,%) -> Boolean infRittWu? : (%,%) -> Boolean --R initiallyReduce : (P,%) -> P initiallyReduced? : % -> Boolean ---R initials : % -> List(P) internalAugment : (P,%) -> % ---R intersect : (P,%) -> List(%) invertible? : (P,%) -> Boolean ---R invertibleSet : (P,%) -> List(%) last : % -> Union(P,"failed") ---R latex : % -> String mainVariable? : (V,%) -> Boolean ---R mainVariables : % -> List(V) map : ((P -> P),%) -> % ---R mvar : % -> V normalized? : % -> Boolean ---R normalized? : (P,%) -> Boolean purelyAlgebraic? : % -> Boolean +--R initials : % -> List(P) internalAugment : (List(P),%) -> % +--R internalAugment : (P,%) -> % intersect : (P,List(%)) -> List(%) +--R intersect : (List(P),%) -> List(%) intersect : (P,%) -> List(%) +--R invertible? : (P,%) -> Boolean invertibleSet : (P,%) -> List(%) +--R last : % -> Union(P,"failed") latex : % -> String +--R mainVariable? : (V,%) -> Boolean mainVariables : % -> List(V) +--R map : ((P -> P),%) -> % mvar : % -> V +--R normalized? : % -> Boolean normalized? : (P,%) -> Boolean +--R purelyAlgebraic? : % -> Boolean purelyAlgebraic? : (P,%) -> Boolean --R reduceByQuasiMonic : (P,%) -> P removeZero : (P,%) -> P --R rest : % -> Union(%,"failed") retract : List(P) -> % ---R sample : () -> % stronglyReduce : (P,%) -> P ---R stronglyReduced? : % -> Boolean trivialIdeal? : % -> Boolean +--R sample : () -> % select : (%,V) -> Union(P,"failed") +--R stronglyReduce : (P,%) -> P stronglyReduced? : % -> Boolean +--R stronglyReduced? : (P,%) -> Boolean trivialIdeal? : % -> Boolean --R variables : % -> List(V) zeroSetSplit : List(P) -> List(%) --R ?~=? : (%,%) -> Boolean --R #? : % -> NonNegativeInteger if $ has finiteAggregate @@ -34045,10 +34441,7 @@ digraph pic { --R find : ((P -> Boolean),%) -> Union(P,"failed") --R headRemainder : (P,%) -> Record(num: P,den: R) if R has INTDOM --R initiallyReduced? : (P,%) -> Boolean ---R internalAugment : (List(P),%) -> % ---R intersect : (P,List(%)) -> List(%) --R intersect : (List(P),List(%)) -> List(%) ---R intersect : (List(P),%) -> List(%) --R invertible? : (P,%) -> List(Record(val: Boolean,tower: %)) --R invertibleElseSplit? : (P,%) -> Union(Boolean,List(%)) --R lastSubResultant : (P,P,%) -> List(Record(val: P,tower: %)) @@ -34059,7 +34452,6 @@ digraph pic { --R members : % -> List(P) if $ has finiteAggregate --R more? : (%,NonNegativeInteger) -> Boolean --R parts : % -> List(P) if $ has finiteAggregate ---R purelyAlgebraic? : (P,%) -> Boolean --R purelyAlgebraicLeadingMonomial? : (P,%) -> Boolean --R purelyTranscendental? : (P,%) -> Boolean --R quasiComponent : % -> Record(close: List(P),open: List(P)) @@ -34080,12 +34472,10 @@ digraph pic { --R roughEqualIdeals? : (%,%) -> Boolean if R has INTDOM --R roughSubIdeal? : (%,%) -> Boolean if R has INTDOM --R roughUnitIdeal? : % -> Boolean if R has INTDOM ---R select : (%,V) -> Union(P,"failed") --R select : ((P -> Boolean),%) -> % if $ has finiteAggregate --R size? : (%,NonNegativeInteger) -> Boolean --R sort : (%,V) -> Record(under: %,floor: %,upper: %) --R squareFreePart : (P,%) -> List(Record(val: P,tower: %)) ---R stronglyReduced? : (P,%) -> Boolean --R triangular? : % -> Boolean if R has INTDOM --R zeroSetSplit : (List(P),Boolean) -> List(%) --R zeroSetSplitIntoTriangularSystems : List(P) -> List(Record(close: %,open: List(P))) @@ -34470,23 +34860,23 @@ digraph pic { --S 1 of 1 )show OrderedAbelianGroup +--R --R OrderedAbelianGroup is a category constructor --R Abbreviation for OrderedAbelianGroup is OAGROUP --R This constructor is exposed in this frame. --R Issue )edit bookvol10.2.pamphlet to see algebra source code for OAGROUP --R --R------------------------------- Operations -------------------------------- ---R ?*? : (Integer,%) -> % ?*? : (PositiveInteger,%) -> % ---R ?+? : (%,%) -> % -? : % -> % ---R ?-? : (%,%) -> % ? Boolean ---R ?<=? : (%,%) -> Boolean ?=? : (%,%) -> Boolean ---R ?>? : (%,%) -> Boolean ?>=? : (%,%) -> Boolean ---R 0 : () -> % coerce : % -> OutputForm ---R hash : % -> SingleInteger latex : % -> String ---R max : (%,%) -> % min : (%,%) -> % ---R sample : () -> % zero? : % -> Boolean ---R ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % +--R ?*? : (Integer,%) -> % ?*? : (NonNegativeInteger,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?+? : (%,%) -> % +--R -? : % -> % ?-? : (%,%) -> % +--R ? Boolean ?<=? : (%,%) -> Boolean +--R ?=? : (%,%) -> Boolean ?>? : (%,%) -> Boolean +--R ?>=? : (%,%) -> Boolean 0 : () -> % +--R coerce : % -> OutputForm hash : % -> SingleInteger +--R latex : % -> String max : (%,%) -> % +--R min : (%,%) -> % sample : () -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean --R subtractIfCan : (%,%) -> Union(%,"failed") --R --E 1 @@ -34627,22 +35017,22 @@ digraph pic { --S 1 of 1 )show OrderedAbelianMonoidSup +--R --R OrderedAbelianMonoidSup is a category constructor --R Abbreviation for OrderedAbelianMonoidSup is OAMONS --R This constructor is exposed in this frame. --R Issue )edit bookvol10.2.pamphlet to see algebra source code for OAMONS --R --R------------------------------- Operations -------------------------------- ---R ?*? : (PositiveInteger,%) -> % ?+? : (%,%) -> % ---R ? Boolean ?<=? : (%,%) -> Boolean ---R ?=? : (%,%) -> Boolean ?>? : (%,%) -> Boolean ---R ?>=? : (%,%) -> Boolean 0 : () -> % ---R coerce : % -> OutputForm hash : % -> SingleInteger ---R latex : % -> String max : (%,%) -> % ---R min : (%,%) -> % sample : () -> % ---R sup : (%,%) -> % zero? : % -> Boolean ---R ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?+? : (%,%) -> % ? Boolean +--R ?<=? : (%,%) -> Boolean ?=? : (%,%) -> Boolean +--R ?>? : (%,%) -> Boolean ?>=? : (%,%) -> Boolean +--R 0 : () -> % coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R max : (%,%) -> % min : (%,%) -> % +--R sample : () -> % sup : (%,%) -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean --R subtractIfCan : (%,%) -> Union(%,"failed") --R --E 1 @@ -34828,9 +35218,9 @@ digraph pic { --R merge! : (%,%) -> % min : % -> S --R removeDuplicates! : % -> % sample : () -> % --R set : () -> % set : List(S) -> % ---R subset? : (%,%) -> Boolean union : (%,%) -> % ---R union : (%,S) -> % union : (S,%) -> % ---R ?~=? : (%,%) -> Boolean +--R subset? : (%,%) -> Boolean symmetricDifference : (%,%) -> % +--R union : (%,%) -> % union : (%,S) -> % +--R union : (S,%) -> % ?~=? : (%,%) -> Boolean --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate --R convert : % -> InputForm if S has KONVERT(INFORM) @@ -34861,7 +35251,6 @@ digraph pic { --R select : ((S -> Boolean),%) -> % if $ has finiteAggregate --R select! : ((S -> Boolean),%) -> % if $ has finiteAggregate --R size? : (%,NonNegativeInteger) -> Boolean ---R symmetricDifference : (%,%) -> % --R --E 1 @@ -35140,6 +35529,7 @@ digraph pic { --S 1 of 1 )show Ring +--R --R Ring is a category constructor --R Abbreviation for Ring is RING --R This constructor is exposed in this frame. @@ -35147,18 +35537,17 @@ digraph pic { --R --R------------------------------- Operations -------------------------------- --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ?=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % coerce : Integer -> % ---R coerce : % -> OutputForm hash : % -> SingleInteger ---R latex : % -> String one? : % -> Boolean ---R recip : % -> Union(%,"failed") sample : () -> % ---R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R one? : % -> Boolean recip : % -> Union(%,"failed") +--R sample : () -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean --R characteristic : () -> NonNegativeInteger --R subtractIfCan : (%,%) -> Union(%,"failed") --R @@ -35427,17 +35816,20 @@ digraph pic { --R headReduce : (P,%) -> P headReduced? : % -> Boolean --R headReduced? : (P,%) -> Boolean infRittWu? : (%,%) -> Boolean --R initiallyReduce : (P,%) -> P initiallyReduced? : % -> Boolean ---R initials : % -> List(P) internalAugment : (P,%) -> % ---R intersect : (P,%) -> List(%) invertible? : (P,%) -> Boolean ---R invertibleSet : (P,%) -> List(%) last : % -> Union(P,"failed") ---R latex : % -> String mainVariable? : (V,%) -> Boolean ---R mainVariables : % -> List(V) map : ((P -> P),%) -> % ---R mvar : % -> V normalized? : % -> Boolean ---R normalized? : (P,%) -> Boolean purelyAlgebraic? : % -> Boolean +--R initials : % -> List(P) internalAugment : (List(P),%) -> % +--R internalAugment : (P,%) -> % intersect : (P,List(%)) -> List(%) +--R intersect : (List(P),%) -> List(%) intersect : (P,%) -> List(%) +--R invertible? : (P,%) -> Boolean invertibleSet : (P,%) -> List(%) +--R last : % -> Union(P,"failed") latex : % -> String +--R mainVariable? : (V,%) -> Boolean mainVariables : % -> List(V) +--R map : ((P -> P),%) -> % mvar : % -> V +--R normalized? : % -> Boolean normalized? : (P,%) -> Boolean +--R purelyAlgebraic? : % -> Boolean purelyAlgebraic? : (P,%) -> Boolean --R reduceByQuasiMonic : (P,%) -> P removeZero : (P,%) -> P --R rest : % -> Union(%,"failed") retract : List(P) -> % ---R sample : () -> % stronglyReduce : (P,%) -> P ---R stronglyReduced? : % -> Boolean trivialIdeal? : % -> Boolean +--R sample : () -> % select : (%,V) -> Union(P,"failed") +--R stronglyReduce : (P,%) -> P stronglyReduced? : % -> Boolean +--R stronglyReduced? : (P,%) -> Boolean trivialIdeal? : % -> Boolean --R variables : % -> List(V) zeroSetSplit : List(P) -> List(%) --R ?~=? : (%,%) -> Boolean --R #? : % -> NonNegativeInteger if $ has finiteAggregate @@ -35461,10 +35853,7 @@ digraph pic { --R find : ((P -> Boolean),%) -> Union(P,"failed") --R headRemainder : (P,%) -> Record(num: P,den: R) if R has INTDOM --R initiallyReduced? : (P,%) -> Boolean ---R internalAugment : (List(P),%) -> % ---R intersect : (P,List(%)) -> List(%) --R intersect : (List(P),List(%)) -> List(%) ---R intersect : (List(P),%) -> List(%) --R invertible? : (P,%) -> List(Record(val: Boolean,tower: %)) --R invertibleElseSplit? : (P,%) -> Union(Boolean,List(%)) --R lastSubResultant : (P,P,%) -> List(Record(val: P,tower: %)) @@ -35475,7 +35864,6 @@ digraph pic { --R members : % -> List(P) if $ has finiteAggregate --R more? : (%,NonNegativeInteger) -> Boolean --R parts : % -> List(P) if $ has finiteAggregate ---R purelyAlgebraic? : (P,%) -> Boolean --R purelyAlgebraicLeadingMonomial? : (P,%) -> Boolean --R purelyTranscendental? : (P,%) -> Boolean --R quasiComponent : % -> Record(close: List(P),open: List(P)) @@ -35496,12 +35884,10 @@ digraph pic { --R roughEqualIdeals? : (%,%) -> Boolean if R has INTDOM --R roughSubIdeal? : (%,%) -> Boolean if R has INTDOM --R roughUnitIdeal? : % -> Boolean if R has INTDOM ---R select : (%,V) -> Union(P,"failed") --R select : ((P -> Boolean),%) -> % if $ has finiteAggregate --R size? : (%,NonNegativeInteger) -> Boolean --R sort : (%,V) -> Record(under: %,floor: %,upper: %) --R squareFreePart : (P,%) -> List(Record(val: P,tower: %)) ---R stronglyReduced? : (P,%) -> Boolean --R triangular? : % -> Boolean if R has INTDOM --R zeroSetSplit : (List(P),Boolean) -> List(%) --R zeroSetSplitIntoTriangularSystems : List(P) -> List(Record(close: %,open: List(P))) @@ -35893,14 +36279,14 @@ digraph pic { --R empty : () -> % empty? : % -> Boolean --R entries : % -> List(Character) eq? : (%,%) -> Boolean --R index? : (Integer,%) -> Boolean indices : % -> List(Integer) ---R insert : (%,%,Integer) -> % leftTrim : (%,Character) -> % ---R lowerCase : % -> % lowerCase! : % -> % ---R prefix? : (%,%) -> Boolean qelt : (%,Integer) -> Character ---R reverse : % -> % rightTrim : (%,Character) -> % ---R sample : () -> % split : (%,Character) -> List(%) ---R suffix? : (%,%) -> Boolean trim : (%,CharacterClass) -> % ---R trim : (%,Character) -> % upperCase : % -> % ---R upperCase! : % -> % +--R insert : (%,%,Integer) -> % leftTrim : (%,CharacterClass) -> % +--R leftTrim : (%,Character) -> % lowerCase : % -> % +--R lowerCase! : % -> % prefix? : (%,%) -> Boolean +--R qelt : (%,Integer) -> Character reverse : % -> % +--R rightTrim : (%,Character) -> % sample : () -> % +--R split : (%,Character) -> List(%) suffix? : (%,%) -> Boolean +--R trim : (%,CharacterClass) -> % trim : (%,Character) -> % +--R upperCase : % -> % upperCase! : % -> % --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R ? Boolean if Character has ORDSET --R ?<=? : (%,%) -> Boolean if Character has ORDSET @@ -35928,7 +36314,6 @@ digraph pic { --R hash : % -> SingleInteger if Character has SETCAT --R insert : (Character,%,Integer) -> % --R latex : % -> String if Character has SETCAT ---R leftTrim : (%,CharacterClass) -> % --R less? : (%,NonNegativeInteger) -> Boolean --R map : (((Character,Character) -> Character),%,%) -> % --R map : ((Character -> Character),%) -> % @@ -36973,24 +37358,26 @@ digraph pic { --R Issue )edit bookvol10.2.pamphlet to see algebra source code for VECTCAT --R --R------------------------------- Operations -------------------------------- +--R ?*? : (%,R) -> % if R has MONOID ?*? : (R,%) -> % if R has MONOID +--R ?+? : (%,%) -> % if R has ABELSG ?-? : (%,%) -> % if R has ABELGRP --R -? : % -> % if R has ABELGRP concat : List(%) -> % --R concat : (%,%) -> % concat : (R,%) -> % --R concat : (%,R) -> % construct : List(R) -> % ---R copy : % -> % delete : (%,Integer) -> % +--R copy : % -> % cross : (%,%) -> % if R has RING +--R delete : (%,Integer) -> % dot : (%,%) -> R if R has RING --R ?.? : (%,Integer) -> R elt : (%,Integer,R) -> R --R empty : () -> % empty? : % -> Boolean --R entries : % -> List(R) eq? : (%,%) -> Boolean --R index? : (Integer,%) -> Boolean indices : % -> List(Integer) --R insert : (%,%,Integer) -> % insert : (R,%,Integer) -> % ---R map : (((R,R) -> R),%,%) -> % map : ((R -> R),%) -> % ---R new : (NonNegativeInteger,R) -> % qelt : (%,Integer) -> R ---R reverse : % -> % sample : () -> % +--R latex : % -> String if R has SETCAT map : (((R,R) -> R),%,%) -> % +--R map : ((R -> R),%) -> % max : (%,%) -> % if R has ORDSET +--R min : (%,%) -> % if R has ORDSET new : (NonNegativeInteger,R) -> % +--R qelt : (%,Integer) -> R reverse : % -> % +--R sample : () -> % sort : % -> % if R has ORDSET +--R sort : (((R,R) -> Boolean),%) -> % --R #? : % -> NonNegativeInteger if $ has finiteAggregate ---R ?*? : (%,R) -> % if R has MONOID ---R ?*? : (R,%) -> % if R has MONOID --R ?*? : (Integer,%) -> % if R has ABELGRP ---R ?+? : (%,%) -> % if R has ABELSG ---R ?-? : (%,%) -> % if R has ABELGRP --R ? Boolean if R has ORDSET --R ?<=? : (%,%) -> Boolean if R has ORDSET --R ?=? : (%,%) -> Boolean if R has SETCAT @@ -37002,9 +37389,7 @@ digraph pic { --R copyInto! : (%,%,Integer) -> % if $ has shallowlyMutable --R count : (R,%) -> NonNegativeInteger if R has SETCAT and $ has finiteAggregate --R count : ((R -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate ---R cross : (%,%) -> % if R has RING --R delete : (%,UniversalSegment(Integer)) -> % ---R dot : (%,%) -> R if R has RING --R ?.? : (%,UniversalSegment(Integer)) -> % --R entry? : (R,%) -> Boolean if $ has finiteAggregate and R has SETCAT --R eval : (%,List(R),List(R)) -> % if R has EVALAB(R) and R has SETCAT @@ -37016,18 +37401,15 @@ digraph pic { --R find : ((R -> Boolean),%) -> Union(R,"failed") --R first : % -> R if Integer has ORDSET --R hash : % -> SingleInteger if R has SETCAT ---R latex : % -> String if R has SETCAT --R length : % -> R if R has RING and R has RADCAT --R less? : (%,NonNegativeInteger) -> Boolean --R magnitude : % -> R if R has RING and R has RADCAT --R map! : ((R -> R),%) -> % if $ has shallowlyMutable ---R max : (%,%) -> % if R has ORDSET --R maxIndex : % -> Integer if Integer has ORDSET --R member? : (R,%) -> Boolean if R has SETCAT and $ has finiteAggregate --R members : % -> List(R) if $ has finiteAggregate --R merge : (%,%) -> % if R has ORDSET --R merge : (((R,R) -> Boolean),%,%) -> % ---R min : (%,%) -> % if R has ORDSET --R minIndex : % -> Integer if Integer has ORDSET --R more? : (%,NonNegativeInteger) -> Boolean --R outerProduct : (%,%) -> Matrix(R) if R has RING @@ -37047,8 +37429,6 @@ digraph pic { --R setelt : (%,UniversalSegment(Integer),R) -> R if $ has shallowlyMutable --R setelt : (%,Integer,R) -> R if $ has shallowlyMutable --R size? : (%,NonNegativeInteger) -> Boolean ---R sort : % -> % if R has ORDSET ---R sort : (((R,R) -> Boolean),%) -> % --R sort! : % -> % if R has ORDSET and $ has shallowlyMutable --R sort! : (((R,R) -> Boolean),%) -> % if $ has shallowlyMutable --R sorted? : % -> Boolean if R has ORDSET @@ -37468,9 +37848,10 @@ digraph pic { --R indices : % -> List(Integer) indices : % -> List(Key) --R insert : (%,%,Integer) -> % insert! : (%,%,Integer) -> % --R key? : (Key,%) -> Boolean keys : % -> List(Key) ---R leaf? : % -> Boolean map : ((Entry -> Entry),%) -> % ---R nodes : % -> List(%) possiblyInfinite? : % -> Boolean ---R qelt : (%,Key) -> Entry rest : % -> % +--R last : (%,NonNegativeInteger) -> % leaf? : % -> Boolean +--R map : ((Entry -> Entry),%) -> % nodes : % -> List(%) +--R possiblyInfinite? : % -> Boolean qelt : (%,Key) -> Entry +--R rest : % -> % rest : (%,NonNegativeInteger) -> % --R reverse : % -> % sample : () -> % --R setelt : (%,Key,Entry) -> Entry table : () -> % --R tail : % -> % @@ -37543,7 +37924,6 @@ digraph pic { --R insert! : (Record(key: Key,entry: Entry),%) -> % --R inspect : % -> Record(key: Key,entry: Entry) --R last : % -> Record(key: Key,entry: Entry) ---R last : (%,NonNegativeInteger) -> % --R latex : % -> String if Record(key: Key,entry: Entry) has SETCAT or Entry has SETCAT or Record(key: Key,entry: Entry) has SETCAT --R leaves : % -> List(Record(key: Key,entry: Entry)) --R less? : (%,NonNegativeInteger) -> Boolean @@ -37600,7 +37980,6 @@ digraph pic { --R remove! : (Record(key: Key,entry: Entry),%) -> % if $ has finiteAggregate --R removeDuplicates : % -> % if Record(key: Key,entry: Entry) has SETCAT and $ has finiteAggregate or Record(key: Key,entry: Entry) has SETCAT and $ has finiteAggregate --R removeDuplicates! : % -> % if Record(key: Key,entry: Entry) has SETCAT ---R rest : (%,NonNegativeInteger) -> % --R reverse! : % -> % if $ has shallowlyMutable --R search : (Key,%) -> Union(Entry,"failed") --R second : % -> Record(key: Key,entry: Entry) @@ -38172,6 +38551,7 @@ digraph pic { --S 1 of 1 )show CharacteristicNonZero +--R --R CharacteristicNonZero is a category constructor --R Abbreviation for CharacteristicNonZero is CHARNZ --R This constructor is exposed in this frame. @@ -38179,18 +38559,17 @@ digraph pic { --R --R------------------------------- Operations -------------------------------- --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ?=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % coerce : Integer -> % ---R coerce : % -> OutputForm hash : % -> SingleInteger ---R latex : % -> String one? : % -> Boolean ---R recip : % -> Union(%,"failed") sample : () -> % ---R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R one? : % -> Boolean recip : % -> Union(%,"failed") +--R sample : () -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean --R characteristic : () -> NonNegativeInteger --R charthRoot : % -> Union(%,"failed") --R subtractIfCan : (%,%) -> Union(%,"failed") @@ -38365,6 +38744,7 @@ digraph pic { --S 1 of 1 )show CharacteristicZero +--R --R CharacteristicZero is a category constructor --R Abbreviation for CharacteristicZero is CHARZ --R This constructor is exposed in this frame. @@ -38372,18 +38752,17 @@ digraph pic { --R --R------------------------------- Operations -------------------------------- --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ?=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % coerce : Integer -> % ---R coerce : % -> OutputForm hash : % -> SingleInteger ---R latex : % -> String one? : % -> Boolean ---R recip : % -> Union(%,"failed") sample : () -> % ---R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R one? : % -> Boolean recip : % -> Union(%,"failed") +--R sample : () -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean --R characteristic : () -> NonNegativeInteger --R subtractIfCan : (%,%) -> Union(%,"failed") --R @@ -38551,6 +38930,7 @@ digraph pic { --S 1 of 1 )show CommutativeRing +--R --R CommutativeRing is a category constructor --R Abbreviation for CommutativeRing is COMRING --R This constructor is exposed in this frame. @@ -38558,18 +38938,17 @@ digraph pic { --R --R------------------------------- Operations -------------------------------- --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ?=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % coerce : Integer -> % ---R coerce : % -> OutputForm hash : % -> SingleInteger ---R latex : % -> String one? : % -> Boolean ---R recip : % -> Union(%,"failed") sample : () -> % ---R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R one? : % -> Boolean recip : % -> Union(%,"failed") +--R sample : () -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean --R characteristic : () -> NonNegativeInteger --R subtractIfCan : (%,%) -> Union(%,"failed") --R @@ -38765,6 +39144,7 @@ digraph pic { --S 1 of 1 )show DifferentialRing +--R --R DifferentialRing is a category constructor --R Abbreviation for DifferentialRing is DIFRING --R This constructor is exposed in this frame. @@ -38772,20 +39152,18 @@ digraph pic { --R --R------------------------------- Operations -------------------------------- --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ?=? : (%,%) -> Boolean --R D : (%,NonNegativeInteger) -> % D : % -> % --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % coerce : Integer -> % ---R coerce : % -> OutputForm differentiate : % -> % ---R hash : % -> SingleInteger latex : % -> String ---R one? : % -> Boolean recip : % -> Union(%,"failed") ---R sample : () -> % zero? : % -> Boolean ---R ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R differentiate : % -> % hash : % -> SingleInteger +--R latex : % -> String one? : % -> Boolean +--R recip : % -> Union(%,"failed") sample : () -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean --R characteristic : () -> NonNegativeInteger --R differentiate : (%,NonNegativeInteger) -> % --R subtractIfCan : (%,%) -> Union(%,"failed") @@ -38992,6 +39370,7 @@ digraph pic { --S 1 of 1 )show EntireRing +--R --R EntireRing is a category constructor --R Abbreviation for EntireRing is ENTIRER --R This constructor is exposed in this frame. @@ -38999,18 +39378,17 @@ digraph pic { --R --R------------------------------- Operations -------------------------------- --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ?=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % coerce : Integer -> % ---R coerce : % -> OutputForm hash : % -> SingleInteger ---R latex : % -> String one? : % -> Boolean ---R recip : % -> Union(%,"failed") sample : () -> % ---R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R one? : % -> Boolean recip : % -> Union(%,"failed") +--R sample : () -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean --R characteristic : () -> NonNegativeInteger --R subtractIfCan : (%,%) -> Union(%,"failed") --R @@ -39210,19 +39588,18 @@ digraph pic { --R------------------------------- Operations -------------------------------- --R ?*? : (R,Basis) -> % ?*? : (%,R) -> % --R ?*? : (R,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?+? : (%,%) -> % ---R ?-? : (%,%) -> % -? : % -> % ---R ?=? : (%,%) -> Boolean 0 : () -> % ---R coefficient : (%,Basis) -> R coefficients : % -> List(R) ---R coerce : Basis -> % coerce : % -> OutputForm ---R hash : % -> SingleInteger latex : % -> String ---R leadingCoefficient : % -> R leadingMonomial : % -> Basis ---R map : ((R -> R),%) -> % monom : (Basis,R) -> % ---R monomial? : % -> Boolean monomials : % -> List(%) ---R reductum : % -> % retract : % -> Basis ---R sample : () -> % zero? : % -> Boolean ---R ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 0 : () -> % coefficient : (%,Basis) -> R +--R coefficients : % -> List(R) coerce : Basis -> % +--R coerce : % -> OutputForm hash : % -> SingleInteger +--R latex : % -> String leadingCoefficient : % -> R +--R leadingMonomial : % -> Basis map : ((R -> R),%) -> % +--R monom : (Basis,R) -> % monomial? : % -> Boolean +--R monomials : % -> List(%) reductum : % -> % +--R retract : % -> Basis sample : () -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean --R leadingTerm : % -> Record(k: Basis,c: R) --R listOfTerms : % -> List(Record(k: Basis,c: R)) --R numberOfMonomials : % -> NonNegativeInteger @@ -39481,19 +39858,18 @@ digraph pic { --R --R------------------------------- Operations -------------------------------- --R ?*? : (R,%) -> % ?*? : (%,%) -> % ---R ?*? : (Integer,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?*? : (Integer,%) -> % ?*? : (NonNegativeInteger,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,NonNegativeInteger) -> % --R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % --R ?-? : (%,%) -> % -? : % -> % --R ?=? : (%,%) -> Boolean 1 : () -> % ---R 0 : () -> % ?^? : (%,PositiveInteger) -> % ---R coerce : R -> % coerce : Integer -> % ---R coerce : % -> OutputForm hash : % -> SingleInteger ---R latex : % -> String one? : % -> Boolean ---R recip : % -> Union(%,"failed") sample : () -> % ---R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R ?^? : (%,NonNegativeInteger) -> % +--R 0 : () -> % ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,PositiveInteger) -> % coerce : R -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R one? : % -> Boolean recip : % -> Union(%,"failed") +--R sample : () -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean --R characteristic : () -> NonNegativeInteger --R subtractIfCan : (%,%) -> Union(%,"failed") --R @@ -39673,18 +40049,17 @@ digraph pic { --R --R------------------------------- Operations -------------------------------- --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ?=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % coerce : Integer -> % ---R coerce : % -> OutputForm hash : % -> SingleInteger ---R latex : % -> String one? : % -> Boolean ---R recip : % -> Union(%,"failed") sample : () -> % ---R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R one? : % -> Boolean recip : % -> Union(%,"failed") +--R sample : () -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean --R characteristic : () -> NonNegativeInteger --R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(R),vec: Vector(R)) --R reducedSystem : Matrix(%) -> Matrix(R) @@ -39880,14 +40255,13 @@ digraph pic { --R --R------------------------------- Operations -------------------------------- --R ?*? : (%,R) -> % ?*? : (R,%) -> % ---R ?*? : (Integer,%) -> % ?*? : (PositiveInteger,%) -> % ---R ?+? : (%,%) -> % ?-? : (%,%) -> % ---R -? : % -> % ?=? : (%,%) -> Boolean ---R 0 : () -> % coerce : % -> OutputForm ---R hash : % -> SingleInteger latex : % -> String ---R sample : () -> % zero? : % -> Boolean ---R ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % +--R ?*? : (Integer,%) -> % ?*? : (NonNegativeInteger,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?+? : (%,%) -> % +--R ?-? : (%,%) -> % -? : % -> % +--R ?=? : (%,%) -> Boolean 0 : () -> % +--R coerce : % -> OutputForm hash : % -> SingleInteger +--R latex : % -> String sample : () -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean --R subtractIfCan : (%,%) -> Union(%,"failed") --R --E 1 @@ -40052,6 +40426,7 @@ digraph pic { --S 1 of 1 )show OrderedRing +--R --R OrderedRing is a category constructor --R Abbreviation for OrderedRing is ORDRING --R This constructor is exposed in this frame. @@ -40059,23 +40434,22 @@ digraph pic { --R --R------------------------------- Operations -------------------------------- --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,PositiveInteger) -> % ?**? : (%,NonNegativeInteger) -> % --R ?+? : (%,%) -> % -? : % -> % --R ?-? : (%,%) -> % ? Boolean --R ?<=? : (%,%) -> Boolean ?=? : (%,%) -> Boolean --R ?>? : (%,%) -> Boolean ?>=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % abs : % -> % ---R coerce : Integer -> % coerce : % -> OutputForm ---R hash : % -> SingleInteger latex : % -> String ---R max : (%,%) -> % min : (%,%) -> % ---R negative? : % -> Boolean one? : % -> Boolean ---R positive? : % -> Boolean recip : % -> Union(%,"failed") ---R sample : () -> % sign : % -> Integer ---R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,PositiveInteger) -> % ?^? : (%,NonNegativeInteger) -> % +--R abs : % -> % coerce : Integer -> % +--R coerce : % -> OutputForm hash : % -> SingleInteger +--R latex : % -> String max : (%,%) -> % +--R min : (%,%) -> % negative? : % -> Boolean +--R one? : % -> Boolean positive? : % -> Boolean +--R recip : % -> Union(%,"failed") sample : () -> % +--R sign : % -> Integer zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean --R characteristic : () -> NonNegativeInteger --R subtractIfCan : (%,%) -> Union(%,"failed") --R @@ -40314,22 +40688,20 @@ digraph pic { --R --R------------------------------- Operations -------------------------------- --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ?=? : (%,%) -> Boolean ---R D : (%,List(S)) -> % D : (%,S) -> % ---R 1 : () -> % 0 : () -> % +--R D : (%,S,NonNegativeInteger) -> % D : (%,List(S)) -> % +--R D : (%,S) -> % 1 : () -> % +--R 0 : () -> % ?^? : (%,NonNegativeInteger) -> % --R ?^? : (%,PositiveInteger) -> % coerce : Integer -> % --R coerce : % -> OutputForm differentiate : (%,List(S)) -> % --R differentiate : (%,S) -> % hash : % -> SingleInteger --R latex : % -> String one? : % -> Boolean --R recip : % -> Union(%,"failed") sample : () -> % --R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % --R D : (%,List(S),List(NonNegativeInteger)) -> % ---R D : (%,S,NonNegativeInteger) -> % ---R ?^? : (%,NonNegativeInteger) -> % --R characteristic : () -> NonNegativeInteger --R differentiate : (%,List(S),List(NonNegativeInteger)) -> % --R differentiate : (%,S,NonNegativeInteger) -> % @@ -40592,27 +40964,28 @@ digraph pic { --R Issue )edit bookvol10.2.pamphlet to see algebra source code for PTCAT --R --R------------------------------- Operations -------------------------------- +--R ?*? : (%,R) -> % if R has MONOID ?*? : (R,%) -> % if R has MONOID +--R ?+? : (%,%) -> % if R has ABELSG ?-? : (%,%) -> % if R has ABELGRP --R -? : % -> % if R has ABELGRP concat : List(%) -> % --R concat : (%,%) -> % concat : (R,%) -> % --R concat : (%,R) -> % construct : List(R) -> % --R convert : List(R) -> % copy : % -> % --R cross : (%,%) -> % delete : (%,Integer) -> % ---R dimension : % -> PositiveInteger ?.? : (%,Integer) -> R ---R elt : (%,Integer,R) -> R empty : () -> % ---R empty? : % -> Boolean entries : % -> List(R) ---R eq? : (%,%) -> Boolean extend : (%,List(R)) -> % ---R index? : (Integer,%) -> Boolean indices : % -> List(Integer) ---R insert : (%,%,Integer) -> % insert : (R,%,Integer) -> % +--R dimension : % -> PositiveInteger dot : (%,%) -> R if R has RING +--R ?.? : (%,Integer) -> R elt : (%,Integer,R) -> R +--R empty : () -> % empty? : % -> Boolean +--R entries : % -> List(R) eq? : (%,%) -> Boolean +--R extend : (%,List(R)) -> % index? : (Integer,%) -> Boolean +--R indices : % -> List(Integer) insert : (%,%,Integer) -> % +--R insert : (R,%,Integer) -> % latex : % -> String if R has SETCAT --R map : (((R,R) -> R),%,%) -> % map : ((R -> R),%) -> % +--R max : (%,%) -> % if R has ORDSET min : (%,%) -> % if R has ORDSET --R new : (NonNegativeInteger,R) -> % point : List(R) -> % --R qelt : (%,Integer) -> R reverse : % -> % ---R sample : () -> % +--R sample : () -> % sort : % -> % if R has ORDSET +--R sort : (((R,R) -> Boolean),%) -> % --R #? : % -> NonNegativeInteger if $ has finiteAggregate ---R ?*? : (%,R) -> % if R has MONOID ---R ?*? : (R,%) -> % if R has MONOID --R ?*? : (Integer,%) -> % if R has ABELGRP ---R ?+? : (%,%) -> % if R has ABELSG ---R ?-? : (%,%) -> % if R has ABELGRP --R ? Boolean if R has ORDSET --R ?<=? : (%,%) -> Boolean if R has ORDSET --R ?=? : (%,%) -> Boolean if R has SETCAT @@ -40625,7 +40998,6 @@ digraph pic { --R count : (R,%) -> NonNegativeInteger if R has SETCAT and $ has finiteAggregate --R count : ((R -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate --R delete : (%,UniversalSegment(Integer)) -> % ---R dot : (%,%) -> R if R has RING --R ?.? : (%,UniversalSegment(Integer)) -> % --R entry? : (R,%) -> Boolean if $ has finiteAggregate and R has SETCAT --R eval : (%,List(R),List(R)) -> % if R has EVALAB(R) and R has SETCAT @@ -40637,18 +41009,15 @@ digraph pic { --R find : ((R -> Boolean),%) -> Union(R,"failed") --R first : % -> R if Integer has ORDSET --R hash : % -> SingleInteger if R has SETCAT ---R latex : % -> String if R has SETCAT --R length : % -> R if R has RING and R has RADCAT --R less? : (%,NonNegativeInteger) -> Boolean --R magnitude : % -> R if R has RING and R has RADCAT --R map! : ((R -> R),%) -> % if $ has shallowlyMutable ---R max : (%,%) -> % if R has ORDSET --R maxIndex : % -> Integer if Integer has ORDSET --R member? : (R,%) -> Boolean if R has SETCAT and $ has finiteAggregate --R members : % -> List(R) if $ has finiteAggregate --R merge : (%,%) -> % if R has ORDSET --R merge : (((R,R) -> Boolean),%,%) -> % ---R min : (%,%) -> % if R has ORDSET --R minIndex : % -> Integer if Integer has ORDSET --R more? : (%,NonNegativeInteger) -> Boolean --R outerProduct : (%,%) -> Matrix(R) if R has RING @@ -40668,8 +41037,6 @@ digraph pic { --R setelt : (%,UniversalSegment(Integer),R) -> R if $ has shallowlyMutable --R setelt : (%,Integer,R) -> R if $ has shallowlyMutable --R size? : (%,NonNegativeInteger) -> Boolean ---R sort : % -> % if R has ORDSET ---R sort : (((R,R) -> Boolean),%) -> % --R sort! : % -> % if R has ORDSET and $ has shallowlyMutable --R sort! : (((R,R) -> Boolean),%) -> % if $ has shallowlyMutable --R sorted? : % -> Boolean if R has ORDSET @@ -41004,9 +41371,10 @@ The RectangularMatrix domain is matrices of fixed dimension. --R --R------------------------------- Operations -------------------------------- --R ?*? : (%,R) -> % ?*? : (R,%) -> % ---R ?*? : (Integer,%) -> % ?*? : (PositiveInteger,%) -> % ---R ?+? : (%,%) -> % ?-? : (%,%) -> % ---R -? : % -> % ?=? : (%,%) -> Boolean +--R ?*? : (Integer,%) -> % ?*? : (NonNegativeInteger,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?+? : (%,%) -> % +--R ?-? : (%,%) -> % -? : % -> % +--R ?/? : (%,R) -> % if R has FIELD ?=? : (%,%) -> Boolean --R 0 : () -> % antisymmetric? : % -> Boolean --R coerce : % -> OutputForm column : (%,Integer) -> Col --R copy : % -> % diagonal? : % -> Boolean @@ -41023,8 +41391,6 @@ The RectangularMatrix domain is matrices of fixed dimension. --R square? : % -> Boolean symmetric? : % -> Boolean --R zero? : % -> Boolean ?~=? : (%,%) -> Boolean --R #? : % -> NonNegativeInteger if $ has finiteAggregate ---R ?*? : (NonNegativeInteger,%) -> % ---R ?/? : (%,R) -> % if R has FIELD --R any? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate --R count : ((R -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate --R count : (R,%) -> NonNegativeInteger if R has SETCAT and $ has finiteAggregate @@ -41486,17 +41852,20 @@ digraph pic { --R headReduce : (P,%) -> P headReduced? : % -> Boolean --R headReduced? : (P,%) -> Boolean infRittWu? : (%,%) -> Boolean --R initiallyReduce : (P,%) -> P initiallyReduced? : % -> Boolean ---R initials : % -> List(P) internalAugment : (P,%) -> % ---R intersect : (P,%) -> List(%) invertible? : (P,%) -> Boolean ---R invertibleSet : (P,%) -> List(%) last : % -> Union(P,"failed") ---R latex : % -> String mainVariable? : (V,%) -> Boolean ---R mainVariables : % -> List(V) map : ((P -> P),%) -> % ---R mvar : % -> V normalized? : % -> Boolean ---R normalized? : (P,%) -> Boolean purelyAlgebraic? : % -> Boolean +--R initials : % -> List(P) internalAugment : (List(P),%) -> % +--R internalAugment : (P,%) -> % intersect : (P,List(%)) -> List(%) +--R intersect : (List(P),%) -> List(%) intersect : (P,%) -> List(%) +--R invertible? : (P,%) -> Boolean invertibleSet : (P,%) -> List(%) +--R last : % -> Union(P,"failed") latex : % -> String +--R mainVariable? : (V,%) -> Boolean mainVariables : % -> List(V) +--R map : ((P -> P),%) -> % mvar : % -> V +--R normalized? : % -> Boolean normalized? : (P,%) -> Boolean +--R purelyAlgebraic? : % -> Boolean purelyAlgebraic? : (P,%) -> Boolean --R reduceByQuasiMonic : (P,%) -> P removeZero : (P,%) -> P --R rest : % -> Union(%,"failed") retract : List(P) -> % ---R sample : () -> % stronglyReduce : (P,%) -> P ---R stronglyReduced? : % -> Boolean trivialIdeal? : % -> Boolean +--R sample : () -> % select : (%,V) -> Union(P,"failed") +--R stronglyReduce : (P,%) -> P stronglyReduced? : % -> Boolean +--R stronglyReduced? : (P,%) -> Boolean trivialIdeal? : % -> Boolean --R variables : % -> List(V) zeroSetSplit : List(P) -> List(%) --R ?~=? : (%,%) -> Boolean --R #? : % -> NonNegativeInteger if $ has finiteAggregate @@ -41520,10 +41889,7 @@ digraph pic { --R find : ((P -> Boolean),%) -> Union(P,"failed") --R headRemainder : (P,%) -> Record(num: P,den: R) if R has INTDOM --R initiallyReduced? : (P,%) -> Boolean ---R internalAugment : (List(P),%) -> % ---R intersect : (P,List(%)) -> List(%) --R intersect : (List(P),List(%)) -> List(%) ---R intersect : (List(P),%) -> List(%) --R invertible? : (P,%) -> List(Record(val: Boolean,tower: %)) --R invertibleElseSplit? : (P,%) -> Union(Boolean,List(%)) --R lastSubResultant : (P,P,%) -> List(Record(val: P,tower: %)) @@ -41534,7 +41900,6 @@ digraph pic { --R members : % -> List(P) if $ has finiteAggregate --R more? : (%,NonNegativeInteger) -> Boolean --R parts : % -> List(P) if $ has finiteAggregate ---R purelyAlgebraic? : (P,%) -> Boolean --R purelyAlgebraicLeadingMonomial? : (P,%) -> Boolean --R purelyTranscendental? : (P,%) -> Boolean --R quasiComponent : % -> Record(close: List(P),open: List(P)) @@ -41555,12 +41920,10 @@ digraph pic { --R roughEqualIdeals? : (%,%) -> Boolean if R has INTDOM --R roughSubIdeal? : (%,%) -> Boolean if R has INTDOM --R roughUnitIdeal? : % -> Boolean if R has INTDOM ---R select : (%,V) -> Union(P,"failed") --R select : ((P -> Boolean),%) -> % if $ has finiteAggregate --R size? : (%,NonNegativeInteger) -> Boolean --R sort : (%,V) -> Record(under: %,floor: %,upper: %) --R squareFreePart : (P,%) -> List(Record(val: P,tower: %)) ---R stronglyReduced? : (P,%) -> Boolean --R triangular? : % -> Boolean if R has INTDOM --R zeroSetSplit : (List(P),Boolean) -> List(%) --R zeroSetSplitIntoTriangularSystems : List(P) -> List(Record(close: %,open: List(P))) @@ -41927,15 +42290,15 @@ digraph pic { --R entries : % -> List(Character) eq? : (%,%) -> Boolean --R hash : % -> SingleInteger index? : (Integer,%) -> Boolean --R indices : % -> List(Integer) insert : (%,%,Integer) -> % ---R latex : % -> String leftTrim : (%,Character) -> % ---R lowerCase : % -> % lowerCase! : % -> % ---R prefix? : (%,%) -> Boolean qelt : (%,Integer) -> Character ---R reverse : % -> % rightTrim : (%,Character) -> % ---R sample : () -> % split : (%,Character) -> List(%) ---R string : Integer -> % suffix? : (%,%) -> Boolean ---R trim : (%,CharacterClass) -> % trim : (%,Character) -> % ---R upperCase : % -> % upperCase! : % -> % ---R ?~=? : (%,%) -> Boolean +--R latex : % -> String leftTrim : (%,CharacterClass) -> % +--R leftTrim : (%,Character) -> % lowerCase : % -> % +--R lowerCase! : % -> % prefix? : (%,%) -> Boolean +--R qelt : (%,Integer) -> Character reverse : % -> % +--R rightTrim : (%,Character) -> % sample : () -> % +--R split : (%,Character) -> List(%) string : Integer -> % +--R suffix? : (%,%) -> Boolean trim : (%,CharacterClass) -> % +--R trim : (%,Character) -> % upperCase : % -> % +--R upperCase! : % -> % ?~=? : (%,%) -> Boolean --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R ? Boolean if Character has ORDSET --R ?<=? : (%,%) -> Boolean if Character has ORDSET @@ -41961,7 +42324,6 @@ digraph pic { --R find : ((Character -> Boolean),%) -> Union(Character,"failed") --R first : % -> Character if Integer has ORDSET --R insert : (Character,%,Integer) -> % ---R leftTrim : (%,CharacterClass) -> % --R less? : (%,NonNegativeInteger) -> Boolean --R map : (((Character,Character) -> Character),%,%) -> % --R map : ((Character -> Character),%) -> % @@ -42384,26 +42746,24 @@ digraph pic { --R------------------------------- Operations -------------------------------- --R ?*? : (R,%) -> % ?*? : (%,R) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ?=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % apply : (%,R,R) -> R ---R coefficients : % -> List(R) coerce : R -> % ---R coerce : Integer -> % coerce : % -> OutputForm +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R apply : (%,R,R) -> R coefficients : % -> List(R) +--R coerce : R -> % coerce : Integer -> % +--R coerce : % -> OutputForm content : % -> R if R has GCDDOM --R degree : % -> NonNegativeInteger hash : % -> SingleInteger --R latex : % -> String leadingCoefficient : % -> R --R one? : % -> Boolean recip : % -> Union(%,"failed") --R reductum : % -> % retract : % -> R --R sample : () -> % zero? : % -> Boolean --R ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R ?^? : (%,NonNegativeInteger) -> % --R characteristic : () -> NonNegativeInteger --R coefficient : (%,NonNegativeInteger) -> R --R coerce : Fraction(Integer) -> % if R has RETRACT(FRAC(INT)) ---R content : % -> R if R has GCDDOM --R exquo : (%,R) -> Union(%,"failed") if R has INTDOM --R leftDivide : (%,%) -> Record(quotient: %,remainder: %) if R has FIELD --R leftExactQuotient : (%,%) -> Union(%,"failed") if R has FIELD @@ -42966,19 +43326,17 @@ digraph pic { --R------------------------------- Operations -------------------------------- --R ?*? : (R,%) -> % ?*? : (%,R) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ?=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % coerce : R -> % ---R coerce : Integer -> % coerce : % -> OutputForm ---R hash : % -> SingleInteger latex : % -> String ---R one? : % -> Boolean recip : % -> Union(%,"failed") ---R sample : () -> % zero? : % -> Boolean ---R ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R coerce : R -> % coerce : Integer -> % +--R coerce : % -> OutputForm hash : % -> SingleInteger +--R latex : % -> String one? : % -> Boolean +--R recip : % -> Union(%,"failed") sample : () -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean --R characteristic : () -> NonNegativeInteger --R subtractIfCan : (%,%) -> Union(%,"failed") --R @@ -43189,19 +43547,17 @@ digraph pic { --R------------------------------- Operations -------------------------------- --R ?*? : (R,%) -> % ?*? : (%,R) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ?=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % coerce : R -> % ---R coerce : Integer -> % coerce : % -> OutputForm ---R hash : % -> SingleInteger latex : % -> String ---R one? : % -> Boolean recip : % -> Union(%,"failed") ---R sample : () -> % zero? : % -> Boolean ---R ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R coerce : R -> % coerce : Integer -> % +--R coerce : % -> OutputForm hash : % -> SingleInteger +--R latex : % -> String one? : % -> Boolean +--R recip : % -> Union(%,"failed") sample : () -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean --R characteristic : () -> NonNegativeInteger --R subtractIfCan : (%,%) -> Union(%,"failed") --R @@ -43449,25 +43805,24 @@ digraph pic { --R --R------------------------------- Operations -------------------------------- --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ?=? : (%,%) -> Boolean --R D : % -> % if R has DIFRING D : (%,(R -> R)) -> % --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % coerce : Integer -> % ---R coerce : % -> OutputForm hash : % -> SingleInteger +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R differentiate : (%,(R -> R)) -> % hash : % -> SingleInteger --R latex : % -> String one? : % -> Boolean --R recip : % -> Union(%,"failed") sample : () -> % --R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % --R D : (%,NonNegativeInteger) -> % if R has DIFRING --R D : (%,Symbol) -> % if R has PDRING(SYMBOL) --R D : (%,List(Symbol)) -> % if R has PDRING(SYMBOL) --R D : (%,Symbol,NonNegativeInteger) -> % if R has PDRING(SYMBOL) --R D : (%,List(Symbol),List(NonNegativeInteger)) -> % if R has PDRING(SYMBOL) --R D : (%,(R -> R),NonNegativeInteger) -> % ---R ?^? : (%,NonNegativeInteger) -> % --R characteristic : () -> NonNegativeInteger --R differentiate : % -> % if R has DIFRING --R differentiate : (%,NonNegativeInteger) -> % if R has DIFRING @@ -43476,7 +43831,6 @@ digraph pic { --R differentiate : (%,Symbol,NonNegativeInteger) -> % if R has PDRING(SYMBOL) --R differentiate : (%,List(Symbol),List(NonNegativeInteger)) -> % if R has PDRING(SYMBOL) --R differentiate : (%,(R -> R),NonNegativeInteger) -> % ---R differentiate : (%,(R -> R)) -> % --R subtractIfCan : (%,%) -> Union(%,"failed") --R --E 1 @@ -43738,18 +44092,17 @@ digraph pic { --R --R------------------------------- Operations -------------------------------- --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ?=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % coerce : Integer -> % ---R coerce : % -> OutputForm hash : % -> SingleInteger ---R latex : % -> String one? : % -> Boolean ---R recip : % -> Union(%,"failed") sample : () -> % ---R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R one? : % -> Boolean recip : % -> Union(%,"failed") +--R sample : () -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean --R characteristic : () -> NonNegativeInteger --R reducedSystem : Matrix(%) -> Matrix(Integer) if R has LINEXP(INT) --R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(Integer),vec: Vector(Integer)) if R has LINEXP(INT) @@ -43975,15 +44328,14 @@ digraph pic { --R --R------------------------------- Operations -------------------------------- --R ?*? : (%,R) -> % ?*? : (R,%) -> % ---R ?*? : (Integer,%) -> % ?*? : (PositiveInteger,%) -> % ---R ?+? : (%,%) -> % ?-? : (%,%) -> % ---R -? : % -> % ?=? : (%,%) -> Boolean +--R ?*? : (Integer,%) -> % ?*? : (NonNegativeInteger,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?+? : (%,%) -> % +--R ?-? : (%,%) -> % -? : % -> % +--R ?/? : (%,R) -> % if R has FIELD ?=? : (%,%) -> Boolean --R 0 : () -> % coerce : % -> OutputForm --R construct : (%,%) -> % hash : % -> SingleInteger --R latex : % -> String sample : () -> % --R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?/? : (%,R) -> % if R has FIELD --R subtractIfCan : (%,%) -> Union(%,"failed") --R --E 1 @@ -44169,27 +44521,25 @@ digraph pic { --R------------------------------- Operations -------------------------------- --R ?*? : (A,%) -> % ?*? : (%,A) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ?=? : (%,%) -> Boolean --R D : () -> % 1 : () -> % ---R 0 : () -> % ?^? : (%,PositiveInteger) -> % ---R adjoint : % -> % apply : (%,A,A) -> A ---R coefficients : % -> List(A) coerce : A -> % ---R coerce : Integer -> % coerce : % -> OutputForm +--R 0 : () -> % ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,PositiveInteger) -> % adjoint : % -> % +--R apply : (%,A,A) -> A coefficients : % -> List(A) +--R coerce : A -> % coerce : Integer -> % +--R coerce : % -> OutputForm content : % -> A if A has GCDDOM --R degree : % -> NonNegativeInteger ?.? : (%,A) -> A --R hash : % -> SingleInteger latex : % -> String --R leadingCoefficient : % -> A one? : % -> Boolean --R recip : % -> Union(%,"failed") reductum : % -> % --R retract : % -> A sample : () -> % --R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R ?^? : (%,NonNegativeInteger) -> % --R characteristic : () -> NonNegativeInteger --R coefficient : (%,NonNegativeInteger) -> A --R coerce : Fraction(Integer) -> % if A has RETRACT(FRAC(INT)) ---R content : % -> A if A has GCDDOM --R directSum : (%,%) -> % if A has FIELD --R exquo : (%,A) -> Union(%,"failed") if A has INTDOM --R leftDivide : (%,%) -> Record(quotient: %,remainder: %) if A has FIELD @@ -44591,15 +44941,15 @@ digraph pic { --R------------------------------- Operations -------------------------------- --R ?*? : (R,%) -> % ?*? : (%,R) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % ---R ?+? : (%,%) -> % ?-? : (%,%) -> % ---R -? : % -> % ?=? : (%,%) -> Boolean ---R 0 : () -> % antiCommutator : (%,%) -> % ---R associator : (%,%,%) -> % coerce : % -> OutputForm ---R commutator : (%,%) -> % hash : % -> SingleInteger ---R latex : % -> String sample : () -> % ---R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % +--R ?-? : (%,%) -> % -? : % -> % +--R ?=? : (%,%) -> Boolean 0 : () -> % +--R antiCommutator : (%,%) -> % associator : (%,%,%) -> % +--R coerce : % -> OutputForm commutator : (%,%) -> % +--R hash : % -> SingleInteger latex : % -> String +--R sample : () -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean --R leftPower : (%,PositiveInteger) -> % --R plenaryPower : (%,PositiveInteger) -> % --R rightPower : (%,PositiveInteger) -> % @@ -44813,15 +45163,14 @@ digraph pic { --R --R------------------------------- Operations -------------------------------- --R ?*? : (%,S) -> % ?*? : (S,%) -> % ---R ?*? : (Integer,%) -> % ?*? : (PositiveInteger,%) -> % ---R ?+? : (%,%) -> % ?-? : (%,%) -> % ---R -? : % -> % ?/? : (%,S) -> % ---R ?=? : (%,%) -> Boolean 0 : () -> % ---R coerce : % -> OutputForm dimension : () -> CardinalNumber ---R hash : % -> SingleInteger latex : % -> String ---R sample : () -> % zero? : % -> Boolean ---R ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % +--R ?*? : (Integer,%) -> % ?*? : (NonNegativeInteger,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?+? : (%,%) -> % +--R ?-? : (%,%) -> % -? : % -> % +--R ?/? : (%,S) -> % ?=? : (%,%) -> Boolean +--R 0 : () -> % coerce : % -> OutputForm +--R dimension : () -> CardinalNumber hash : % -> SingleInteger +--R latex : % -> String sample : () -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean --R subtractIfCan : (%,%) -> Union(%,"failed") --R --E 1 @@ -44992,38 +45341,35 @@ digraph pic { --R------------------------------- Operations -------------------------------- --R ?*? : (vl,%) -> % ?*? : (%,R) -> % --R ?*? : (R,%) -> % ?*? : (%,%) -> % ---R ?*? : (Integer,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?*? : (Integer,%) -> % ?*? : (NonNegativeInteger,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,NonNegativeInteger) -> % --R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % --R ?-? : (%,%) -> % -? : % -> % --R ?=? : (%,%) -> Boolean 1 : () -> % ---R 0 : () -> % ?^? : (%,PositiveInteger) -> % ---R coef : (%,%) -> R coerce : vl -> % +--R 0 : () -> % ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,PositiveInteger) -> % coef : (%,%) -> R +--R coerce : vl -> % coerce : OrderedFreeMonoid(vl) -> % --R coerce : R -> % coerce : Integer -> % --R coerce : % -> OutputForm constant : % -> R --R constant? : % -> Boolean hash : % -> SingleInteger --R latex : % -> String lquo : (%,%) -> % --R lquo : (%,vl) -> % map : ((R -> R),%) -> % ---R mirror : % -> % monomial? : % -> Boolean ---R one? : % -> Boolean quasiRegular : % -> % ---R quasiRegular? : % -> Boolean recip : % -> Union(%,"failed") ---R rquo : (%,%) -> % rquo : (%,vl) -> % ---R sample : () -> % varList : % -> List(vl) +--R mindeg : % -> OrderedFreeMonoid(vl) mirror : % -> % +--R monomial? : % -> Boolean one? : % -> Boolean +--R quasiRegular : % -> % quasiRegular? : % -> Boolean +--R recip : % -> Union(%,"failed") rquo : (%,%) -> % +--R rquo : (%,vl) -> % sample : () -> % +--R sh : (%,%) -> % if R has COMRING varList : % -> List(vl) --R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R ?^? : (%,NonNegativeInteger) -> % --R characteristic : () -> NonNegativeInteger --R coef : (%,OrderedFreeMonoid(vl)) -> R ---R coerce : OrderedFreeMonoid(vl) -> % --R lquo : (%,OrderedFreeMonoid(vl)) -> % ---R mindeg : % -> OrderedFreeMonoid(vl) --R mindegTerm : % -> Record(k: OrderedFreeMonoid(vl),c: R) --R monom : (OrderedFreeMonoid(vl),R) -> % --R retract : % -> OrderedFreeMonoid(vl) --R retractIfCan : % -> Union(OrderedFreeMonoid(vl),"failed") --R rquo : (%,OrderedFreeMonoid(vl)) -> % --R sh : (%,NonNegativeInteger) -> % if R has COMRING ---R sh : (%,%) -> % if R has COMRING --R subtractIfCan : (%,%) -> Union(%,"failed") --R --E 1 @@ -45375,27 +45721,28 @@ digraph pic { --R Issue )edit bookvol10.2.pamphlet to see algebra source code for DIRPCAT --R --R------------------------------- Operations -------------------------------- ---R -? : % -> % if R has RING 1 : () -> % if R has MONOID ---R 0 : () -> % if R has CABMON coerce : % -> Vector(R) +--R ?*? : (R,%) -> % if R has MONOID ?*? : (%,R) -> % if R has MONOID +--R ?*? : (%,%) -> % if R has MONOID ?+? : (%,%) -> % if R has ABELSG +--R -? : % -> % if R has RING ?-? : (%,%) -> % if R has RING +--R ?/? : (%,R) -> % if R has FIELD 1 : () -> % if R has MONOID +--R 0 : () -> % if R has CABMON abs : % -> % if R has ORDRING +--R coerce : R -> % if R has SETCAT coerce : % -> Vector(R) --R copy : % -> % directProduct : Vector(R) -> % ---R ?.? : (%,Integer) -> R elt : (%,Integer,R) -> R ---R empty : () -> % empty? : % -> Boolean ---R entries : % -> List(R) eq? : (%,%) -> Boolean ---R index? : (Integer,%) -> Boolean indices : % -> List(Integer) ---R map : ((R -> R),%) -> % qelt : (%,Integer) -> R ---R sample : () -> % +--R dot : (%,%) -> R if R has RING ?.? : (%,Integer) -> R +--R elt : (%,Integer,R) -> R empty : () -> % +--R empty? : % -> Boolean entries : % -> List(R) +--R eq? : (%,%) -> Boolean index? : (Integer,%) -> Boolean +--R indices : % -> List(Integer) latex : % -> String if R has SETCAT +--R map : ((R -> R),%) -> % one? : % -> Boolean if R has MONOID +--R qelt : (%,Integer) -> R random : () -> % if R has FINITE +--R retract : % -> R if R has SETCAT sample : () -> % +--R sup : (%,%) -> % if R has OAMONS --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R ?*? : (PositiveInteger,%) -> % if R has ABELSG --R ?*? : (NonNegativeInteger,%) -> % if R has CABMON ---R ?*? : (R,%) -> % if R has MONOID ---R ?*? : (%,R) -> % if R has MONOID ---R ?*? : (%,%) -> % if R has MONOID --R ?*? : (Integer,%) -> % if R has RING --R ?**? : (%,PositiveInteger) -> % if R has MONOID --R ?**? : (%,NonNegativeInteger) -> % if R has MONOID ---R ?+? : (%,%) -> % if R has ABELSG ---R ?-? : (%,%) -> % if R has RING ---R ?/? : (%,R) -> % if R has FIELD --R ? Boolean if R has ORDRING or R has OAMONS --R ?<=? : (%,%) -> Boolean if R has ORDRING or R has OAMONS --R ?=? : (%,%) -> Boolean if R has SETCAT @@ -45411,10 +45758,8 @@ digraph pic { --R D : % -> % if and(has(R,DifferentialRing),has(R,Ring)) --R ?^? : (%,PositiveInteger) -> % if R has MONOID --R ?^? : (%,NonNegativeInteger) -> % if R has MONOID ---R abs : % -> % if R has ORDRING --R any? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate --R characteristic : () -> NonNegativeInteger if R has RING ---R coerce : R -> % if R has SETCAT --R coerce : Fraction(Integer) -> % if and(has(R,RetractableTo(Fraction(Integer))),has(R,SetCategory)) --R coerce : Integer -> % if and(has(R,RetractableTo(Integer)),has(R,SetCategory)) or R has RING --R coerce : % -> OutputForm if R has SETCAT @@ -45429,7 +45774,6 @@ digraph pic { --R differentiate : (%,NonNegativeInteger) -> % if and(has(R,DifferentialRing),has(R,Ring)) --R differentiate : % -> % if and(has(R,DifferentialRing),has(R,Ring)) --R dimension : () -> CardinalNumber if R has FIELD ---R dot : (%,%) -> R if R has RING --R entry? : (R,%) -> Boolean if $ has finiteAggregate and R has SETCAT --R enumerate : () -> List(%) if R has FINITE --R eval : (%,List(R),List(R)) -> % if R has EVALAB(R) and R has SETCAT @@ -45441,7 +45785,6 @@ digraph pic { --R first : % -> R if Integer has ORDSET --R hash : % -> SingleInteger if R has SETCAT --R index : PositiveInteger -> % if R has FINITE ---R latex : % -> String if R has SETCAT --R less? : (%,NonNegativeInteger) -> Boolean --R lookup : % -> PositiveInteger if R has FINITE --R map! : ((R -> R),%) -> % if $ has shallowlyMutable @@ -45453,17 +45796,14 @@ digraph pic { --R minIndex : % -> Integer if Integer has ORDSET --R more? : (%,NonNegativeInteger) -> Boolean --R negative? : % -> Boolean if R has ORDRING ---R one? : % -> Boolean if R has MONOID --R parts : % -> List(R) if $ has finiteAggregate --R positive? : % -> Boolean if R has ORDRING --R qsetelt! : (%,Integer,R) -> R if $ has shallowlyMutable ---R random : () -> % if R has FINITE --R recip : % -> Union(%,"failed") if R has MONOID --R reducedSystem : Matrix(%) -> Matrix(R) if R has RING --R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(R),vec: Vector(R)) if R has RING --R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(Integer),vec: Vector(Integer)) if and(has(R,LinearlyExplicitRingOver(Integer)),has(R,Ring)) --R reducedSystem : Matrix(%) -> Matrix(Integer) if and(has(R,LinearlyExplicitRingOver(Integer)),has(R,Ring)) ---R retract : % -> R if R has SETCAT --R retract : % -> Fraction(Integer) if and(has(R,RetractableTo(Fraction(Integer))),has(R,SetCategory)) --R retract : % -> Integer if and(has(R,RetractableTo(Integer)),has(R,SetCategory)) --R retractIfCan : % -> Union(R,"failed") if R has SETCAT @@ -45474,7 +45814,6 @@ digraph pic { --R size : () -> NonNegativeInteger if R has FINITE --R size? : (%,NonNegativeInteger) -> Boolean --R subtractIfCan : (%,%) -> Union(%,"failed") if R has CABMON ---R sup : (%,%) -> % if R has OAMONS --R swap! : (%,Integer,Integer) -> Void if $ has shallowlyMutable --R unitVector : PositiveInteger -> % if R has RING --R zero? : % -> Boolean if R has CABMON @@ -46010,20 +46349,19 @@ digraph pic { --R------------------------------- Operations -------------------------------- --R ?*? : (%,Fraction(Integer)) -> % ?*? : (Fraction(Integer),%) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,Integer) -> % ?**? : (%,NonNegativeInteger) -> % --R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % --R ?-? : (%,%) -> % -? : % -> % --R ?=? : (%,%) -> Boolean 1 : () -> % --R 0 : () -> % ?^? : (%,Integer) -> % ---R ?^? : (%,PositiveInteger) -> % coerce : Fraction(Integer) -> % ---R coerce : Integer -> % coerce : % -> OutputForm ---R hash : % -> SingleInteger inv : % -> % ---R latex : % -> String one? : % -> Boolean ---R recip : % -> Union(%,"failed") sample : () -> % ---R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R coerce : Fraction(Integer) -> % coerce : Integer -> % +--R coerce : % -> OutputForm hash : % -> SingleInteger +--R inv : % -> % latex : % -> String +--R one? : % -> Boolean recip : % -> Union(%,"failed") +--R sample : () -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean --R characteristic : () -> NonNegativeInteger --R subtractIfCan : (%,%) -> Union(%,"failed") --R @@ -46253,26 +46591,26 @@ digraph pic { --R------------------------------- Operations -------------------------------- --R ?*? : (R,%) -> % ?*? : (%,R) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % ---R ?+? : (%,%) -> % ?-? : (%,%) -> % ---R -? : % -> % ?=? : (%,%) -> Boolean ---R 0 : () -> % alternative? : () -> Boolean ---R antiAssociative? : () -> Boolean antiCommutative? : () -> Boolean ---R antiCommutator : (%,%) -> % associative? : () -> Boolean ---R associator : (%,%,%) -> % coerce : % -> OutputForm ---R commutative? : () -> Boolean commutator : (%,%) -> % ---R flexible? : () -> Boolean hash : % -> SingleInteger ---R jacobiIdentity? : () -> Boolean jordanAdmissible? : () -> Boolean ---R jordanAlgebra? : () -> Boolean latex : % -> String ---R leftAlternative? : () -> Boolean leftDiscriminant : Vector(%) -> R ---R leftNorm : % -> R leftTrace : % -> R ---R lieAdmissible? : () -> Boolean lieAlgebra? : () -> Boolean ---R powerAssociative? : () -> Boolean rank : () -> PositiveInteger ---R rightAlternative? : () -> Boolean rightNorm : % -> R +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % +--R ?-? : (%,%) -> % -? : % -> % +--R ?=? : (%,%) -> Boolean 0 : () -> % +--R alternative? : () -> Boolean antiAssociative? : () -> Boolean +--R antiCommutative? : () -> Boolean antiCommutator : (%,%) -> % +--R associative? : () -> Boolean associator : (%,%,%) -> % +--R coerce : % -> OutputForm commutative? : () -> Boolean +--R commutator : (%,%) -> % flexible? : () -> Boolean +--R hash : % -> SingleInteger jacobiIdentity? : () -> Boolean +--R jordanAdmissible? : () -> Boolean jordanAlgebra? : () -> Boolean +--R latex : % -> String leftAlternative? : () -> Boolean +--R leftDiscriminant : Vector(%) -> R leftNorm : % -> R +--R leftTrace : % -> R lieAdmissible? : () -> Boolean +--R lieAlgebra? : () -> Boolean powerAssociative? : () -> Boolean +--R rank : () -> PositiveInteger rightAlternative? : () -> Boolean +--R rightDiscriminant : Vector(%) -> R rightNorm : % -> R --R rightTrace : % -> R sample : () -> % --R someBasis : () -> Vector(%) zero? : % -> Boolean --R ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % --R associatorDependence : () -> List(Vector(R)) if R has INTDOM --R conditionsForIdempotents : Vector(%) -> List(Polynomial(R)) --R coordinates : (Vector(%),Vector(%)) -> Matrix(R) @@ -46290,7 +46628,6 @@ digraph pic { --R recip : % -> Union(%,"failed") if R has INTDOM --R represents : (Vector(R),Vector(%)) -> % --R rightCharacteristicPolynomial : % -> SparseUnivariatePolynomial(R) ---R rightDiscriminant : Vector(%) -> R --R rightMinimalPolynomial : % -> SparseUnivariatePolynomial(R) if R has INTDOM --R rightPower : (%,PositiveInteger) -> % --R rightRecip : % -> Union(%,"failed") if R has INTDOM @@ -47280,9 +47617,10 @@ digraph pic { --R --R------------------------------- Operations -------------------------------- --R ?*? : (%,R) -> % ?*? : (R,%) -> % ---R ?*? : (Integer,%) -> % ?*? : (PositiveInteger,%) -> % ---R ?+? : (%,%) -> % ?-? : (%,%) -> % ---R -? : % -> % ?=? : (%,%) -> Boolean +--R ?*? : (Integer,%) -> % ?*? : (NonNegativeInteger,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?+? : (%,%) -> % +--R ?-? : (%,%) -> % -? : % -> % +--R ?/? : (%,R) -> % if R has FIELD ?=? : (%,%) -> Boolean --R LiePoly : LyndonWord(VarSet) -> % 0 : () -> % --R coerce : VarSet -> % coerce : % -> OutputForm --R construct : (%,%) -> % degree : % -> NonNegativeInteger @@ -47290,8 +47628,6 @@ digraph pic { --R latex : % -> String mirror : % -> % --R sample : () -> % varList : % -> List(VarSet) --R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?/? : (%,R) -> % if R has FIELD --R coef : (XRecursivePolynomial(VarSet,R),%) -> R --R coerce : % -> XRecursivePolynomial(VarSet,R) --R coerce : % -> XDistributedPolynomial(VarSet,R) @@ -47532,6 +47868,7 @@ digraph pic { --S 1 of 1 )show IntegralDomain +--R --R IntegralDomain is a category constructor --R Abbreviation for IntegralDomain is INTDOM --R This constructor is exposed in this frame. @@ -47539,20 +47876,19 @@ digraph pic { --R --R------------------------------- Operations -------------------------------- --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ?=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % associates? : (%,%) -> Boolean ---R coerce : % -> % coerce : Integer -> % ---R coerce : % -> OutputForm hash : % -> SingleInteger ---R latex : % -> String one? : % -> Boolean ---R recip : % -> Union(%,"failed") sample : () -> % ---R unit? : % -> Boolean unitCanonical : % -> % ---R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R associates? : (%,%) -> Boolean coerce : % -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R one? : % -> Boolean recip : % -> Union(%,"failed") +--R sample : () -> % unit? : % -> Boolean +--R unitCanonical : % -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean --R characteristic : () -> NonNegativeInteger --R exquo : (%,%) -> Union(%,"failed") --R subtractIfCan : (%,%) -> Union(%,"failed") @@ -47844,23 +48180,21 @@ digraph pic { --R------------------------------- Operations -------------------------------- --R ?*? : (R,%) -> % ?*? : (%,R) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ?=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % coerce : Integer -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R coerce : R -> % if R has COMRING coerce : Integer -> % --R coerce : % -> OutputForm degree : % -> NonNegativeInteger --R hash : % -> SingleInteger latex : % -> String --R leadingCoefficient : % -> R one? : % -> Boolean --R recip : % -> Union(%,"failed") reductum : % -> % --R sample : () -> % zero? : % -> Boolean --R ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R ?^? : (%,NonNegativeInteger) -> % --R characteristic : () -> NonNegativeInteger --R coefficient : (%,NonNegativeInteger) -> R ---R coerce : R -> % if R has COMRING --R minimumDegree : % -> NonNegativeInteger --R monomial : (R,NonNegativeInteger) -> % --R subtractIfCan : (%,%) -> Union(%,"failed") @@ -48129,6 +48463,7 @@ digraph pic { --S 1 of 1 )show OctonionCategory +--R --R OctonionCategory(R: CommutativeRing) is a category constructor --R Abbreviation for OctonionCategory is OC --R This constructor is exposed in this frame. @@ -48137,30 +48472,30 @@ digraph pic { --R------------------------------- Operations -------------------------------- --R ?*? : (R,%) -> % ?*? : (%,R) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ?=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % abs : % -> R if R has RNS ---R coerce : R -> % coerce : Integer -> % ---R coerce : % -> OutputForm conjugate : % -> % ---R hash : % -> SingleInteger imagE : % -> R ---R imagI : % -> R imagJ : % -> R ---R imagK : % -> R imagi : % -> R ---R imagj : % -> R imagk : % -> R ---R inv : % -> % if R has FIELD latex : % -> String ---R map : ((R -> R),%) -> % norm : % -> R ---R octon : (R,R,R,R,R,R,R,R) -> % one? : % -> Boolean +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R abs : % -> R if R has RNS coerce : R -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R conjugate : % -> % hash : % -> SingleInteger +--R imagE : % -> R imagI : % -> R +--R imagJ : % -> R imagK : % -> R +--R imagi : % -> R imagj : % -> R +--R imagk : % -> R inv : % -> % if R has FIELD +--R latex : % -> String map : ((R -> R),%) -> % +--R max : (%,%) -> % if R has ORDSET min : (%,%) -> % if R has ORDSET +--R norm : % -> R octon : (R,R,R,R,R,R,R,R) -> % +--R one? : % -> Boolean random : () -> % if R has FINITE --R real : % -> R recip : % -> Union(%,"failed") --R retract : % -> R sample : () -> % --R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % --R ? Boolean if R has ORDSET --R ?<=? : (%,%) -> Boolean if R has ORDSET --R ?>? : (%,%) -> Boolean if R has ORDSET --R ?>=? : (%,%) -> Boolean if R has ORDSET ---R ?^? : (%,NonNegativeInteger) -> % --R characteristic : () -> NonNegativeInteger --R charthRoot : % -> Union(%,"failed") if R has CHARNZ --R coerce : Fraction(Integer) -> % if R has RETRACT(FRAC(INT)) @@ -48175,9 +48510,6 @@ digraph pic { --R eval : (%,List(R),List(R)) -> % if R has EVALAB(R) --R index : PositiveInteger -> % if R has FINITE --R lookup : % -> PositiveInteger if R has FINITE ---R max : (%,%) -> % if R has ORDSET ---R min : (%,%) -> % if R has ORDSET ---R random : () -> % if R has FINITE --R rational : % -> Fraction(Integer) if R has INS --R rational? : % -> Boolean if R has INS --R rationalIfCan : % -> Union(Fraction(Integer),"failed") if R has INS @@ -48708,27 +49040,28 @@ digraph pic { --R------------------------------- Operations -------------------------------- --R ?*? : (R,%) -> % ?*? : (%,R) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ?=? : (%,%) -> Boolean --R D : (%,(R -> R)) -> % D : % -> % if R has DIFRING --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % abs : % -> R if R has RNS ---R coerce : R -> % coerce : Integer -> % ---R coerce : % -> OutputForm conjugate : % -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R abs : % -> R if R has RNS coerce : R -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R conjugate : % -> % differentiate : (%,(R -> R)) -> % --R hash : % -> SingleInteger imagI : % -> R --R imagJ : % -> R imagK : % -> R --R inv : % -> % if R has FIELD latex : % -> String ---R map : ((R -> R),%) -> % norm : % -> R +--R map : ((R -> R),%) -> % max : (%,%) -> % if R has ORDSET +--R min : (%,%) -> % if R has ORDSET norm : % -> R --R one? : % -> Boolean quatern : (R,R,R,R) -> % --R real : % -> R recip : % -> Union(%,"failed") --R retract : % -> R sample : () -> % --R zero? : % -> Boolean ?~=? : (%,%) -> Boolean --R ?*? : (Fraction(Integer),%) -> % if R has FIELD --R ?*? : (%,Fraction(Integer)) -> % if R has FIELD ---R ?*? : (NonNegativeInteger,%) -> % --R ?**? : (%,Integer) -> % if R has FIELD ---R ?**? : (%,NonNegativeInteger) -> % --R ? Boolean if R has ORDSET --R ?<=? : (%,%) -> Boolean if R has ORDSET --R ?>? : (%,%) -> Boolean if R has ORDSET @@ -48740,12 +49073,10 @@ digraph pic { --R D : (%,Symbol) -> % if R has PDRING(SYMBOL) --R D : (%,NonNegativeInteger) -> % if R has DIFRING --R ?^? : (%,Integer) -> % if R has FIELD ---R ?^? : (%,NonNegativeInteger) -> % --R characteristic : () -> NonNegativeInteger --R charthRoot : % -> Union(%,"failed") if R has CHARNZ --R coerce : Fraction(Integer) -> % if R has FIELD or R has RETRACT(FRAC(INT)) --R convert : % -> InputForm if R has KONVERT(INFORM) ---R differentiate : (%,(R -> R)) -> % --R differentiate : (%,(R -> R),NonNegativeInteger) -> % --R differentiate : (%,List(Symbol),List(NonNegativeInteger)) -> % if R has PDRING(SYMBOL) --R differentiate : (%,Symbol,NonNegativeInteger) -> % if R has PDRING(SYMBOL) @@ -48760,8 +49091,6 @@ digraph pic { --R eval : (%,Equation(R)) -> % if R has EVALAB(R) --R eval : (%,R,R) -> % if R has EVALAB(R) --R eval : (%,List(R),List(R)) -> % if R has EVALAB(R) ---R max : (%,%) -> % if R has ORDSET ---R min : (%,%) -> % if R has ORDSET --R rational : % -> Fraction(Integer) if R has INS --R rational? : % -> Boolean if R has INS --R rationalIfCan : % -> Union(Fraction(Integer),"failed") if R has INS @@ -49274,43 +49603,42 @@ The SquareMatrix domain is for square matrices of fixed dimension. --R ?*? : (Row,%) -> Row ?*? : (%,Col) -> Col --R ?*? : (R,%) -> % ?*? : (%,R) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % ---R -? : % -> % ?=? : (%,%) -> Boolean ---R D : % -> % if R has DIFRING D : (%,(R -> R)) -> % ---R 1 : () -> % 0 : () -> % +--R -? : % -> % ?/? : (%,R) -> % if R has FIELD +--R ?=? : (%,%) -> Boolean D : % -> % if R has DIFRING +--R D : (%,(R -> R)) -> % 1 : () -> % +--R 0 : () -> % ?^? : (%,NonNegativeInteger) -> % --R ?^? : (%,PositiveInteger) -> % antisymmetric? : % -> Boolean --R coerce : R -> % coerce : Integer -> % --R coerce : % -> OutputForm column : (%,Integer) -> Col --R copy : % -> % diagonal : % -> Row --R diagonal? : % -> Boolean diagonalMatrix : List(R) -> % ---R diagonalProduct : % -> R elt : (%,Integer,Integer) -> R ---R elt : (%,Integer,Integer,R) -> R empty : () -> % ---R empty? : % -> Boolean eq? : (%,%) -> Boolean ---R hash : % -> SingleInteger latex : % -> String ---R listOfLists : % -> List(List(R)) map : ((R -> R),%) -> % ---R map : (((R,R) -> R),%,%) -> % matrix : List(List(R)) -> % ---R maxColIndex : % -> Integer maxRowIndex : % -> Integer ---R minColIndex : % -> Integer minRowIndex : % -> Integer ---R ncols : % -> NonNegativeInteger nrows : % -> NonNegativeInteger ---R one? : % -> Boolean qelt : (%,Integer,Integer) -> R ---R recip : % -> Union(%,"failed") retract : % -> R ---R row : (%,Integer) -> Row sample : () -> % ---R scalarMatrix : R -> % square? : % -> Boolean ---R symmetric? : % -> Boolean trace : % -> R ---R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R diagonalProduct : % -> R differentiate : (%,(R -> R)) -> % +--R elt : (%,Integer,Integer) -> R elt : (%,Integer,Integer,R) -> R +--R empty : () -> % empty? : % -> Boolean +--R eq? : (%,%) -> Boolean hash : % -> SingleInteger +--R latex : % -> String listOfLists : % -> List(List(R)) +--R map : ((R -> R),%) -> % map : (((R,R) -> R),%,%) -> % +--R matrix : List(List(R)) -> % maxColIndex : % -> Integer +--R maxRowIndex : % -> Integer minColIndex : % -> Integer +--R minRowIndex : % -> Integer ncols : % -> NonNegativeInteger +--R nrows : % -> NonNegativeInteger one? : % -> Boolean +--R qelt : (%,Integer,Integer) -> R recip : % -> Union(%,"failed") +--R retract : % -> R row : (%,Integer) -> Row +--R sample : () -> % scalarMatrix : R -> % +--R square? : % -> Boolean symmetric? : % -> Boolean +--R trace : % -> R zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean --R #? : % -> NonNegativeInteger if $ has finiteAggregate ---R ?*? : (NonNegativeInteger,%) -> % --R ?**? : (%,Integer) -> % if R has FIELD ---R ?**? : (%,NonNegativeInteger) -> % ---R ?/? : (%,R) -> % if R has FIELD --R D : (%,NonNegativeInteger) -> % if R has DIFRING --R D : (%,Symbol) -> % if R has PDRING(SYMBOL) --R D : (%,List(Symbol)) -> % if R has PDRING(SYMBOL) --R D : (%,Symbol,NonNegativeInteger) -> % if R has PDRING(SYMBOL) --R D : (%,List(Symbol),List(NonNegativeInteger)) -> % if R has PDRING(SYMBOL) --R D : (%,(R -> R),NonNegativeInteger) -> % ---R ?^? : (%,NonNegativeInteger) -> % --R any? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate --R characteristic : () -> NonNegativeInteger --R coerce : Fraction(Integer) -> % if R has RETRACT(FRAC(INT)) @@ -49324,7 +49652,6 @@ The SquareMatrix domain is for square matrices of fixed dimension. --R differentiate : (%,Symbol,NonNegativeInteger) -> % if R has PDRING(SYMBOL) --R differentiate : (%,List(Symbol),List(NonNegativeInteger)) -> % if R has PDRING(SYMBOL) --R differentiate : (%,(R -> R),NonNegativeInteger) -> % ---R differentiate : (%,(R -> R)) -> % --R eval : (%,List(R),List(R)) -> % if R has EVALAB(R) and R has SETCAT --R eval : (%,R,R) -> % if R has EVALAB(R) and R has SETCAT --R eval : (%,Equation(R)) -> % if R has EVALAB(R) and R has SETCAT @@ -49898,40 +50225,36 @@ digraph pic { --R------------------------------- Operations -------------------------------- --R ?*? : (vl,%) -> % ?*? : (%,R) -> % --R ?*? : (R,%) -> % ?*? : (%,%) -> % ---R ?*? : (Integer,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?*? : (Integer,%) -> % ?*? : (NonNegativeInteger,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,NonNegativeInteger) -> % --R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % --R ?-? : (%,%) -> % -? : % -> % --R ?=? : (%,%) -> Boolean 1 : () -> % ---R 0 : () -> % ?^? : (%,PositiveInteger) -> % ---R coef : (%,%) -> R coerce : vl -> % +--R 0 : () -> % ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,PositiveInteger) -> % coef : (%,%) -> R +--R coerce : vl -> % coerce : OrderedFreeMonoid(vl) -> % --R coerce : R -> % coerce : Integer -> % --R coerce : % -> OutputForm constant : % -> R --R constant? : % -> Boolean degree : % -> NonNegativeInteger --R hash : % -> SingleInteger latex : % -> String --R lquo : (%,%) -> % lquo : (%,vl) -> % ---R map : ((R -> R),%) -> % mirror : % -> % +--R map : ((R -> R),%) -> % maxdeg : % -> OrderedFreeMonoid(vl) +--R mindeg : % -> OrderedFreeMonoid(vl) mirror : % -> % --R monomial? : % -> Boolean one? : % -> Boolean --R quasiRegular : % -> % quasiRegular? : % -> Boolean --R recip : % -> Union(%,"failed") rquo : (%,%) -> % --R rquo : (%,vl) -> % sample : () -> % ---R varList : % -> List(vl) zero? : % -> Boolean ---R ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R ?^? : (%,NonNegativeInteger) -> % +--R sh : (%,%) -> % if R has COMRING varList : % -> List(vl) +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean --R characteristic : () -> NonNegativeInteger --R coef : (%,OrderedFreeMonoid(vl)) -> R ---R coerce : OrderedFreeMonoid(vl) -> % --R lquo : (%,OrderedFreeMonoid(vl)) -> % ---R maxdeg : % -> OrderedFreeMonoid(vl) ---R mindeg : % -> OrderedFreeMonoid(vl) --R mindegTerm : % -> Record(k: OrderedFreeMonoid(vl),c: R) --R monom : (OrderedFreeMonoid(vl),R) -> % --R retract : % -> OrderedFreeMonoid(vl) --R retractIfCan : % -> Union(OrderedFreeMonoid(vl),"failed") --R rquo : (%,OrderedFreeMonoid(vl)) -> % --R sh : (%,NonNegativeInteger) -> % if R has COMRING ---R sh : (%,%) -> % if R has COMRING --R subtractIfCan : (%,%) -> Union(%,"failed") --R trunc : (%,NonNegativeInteger) -> % --R @@ -50222,11 +50545,14 @@ digraph pic { --R------------------------------- Operations -------------------------------- --R ?*? : (R,%) -> % ?*? : (%,R) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % ---R -? : % -> % ?=? : (%,%) -> Boolean ---R 1 : () -> % 0 : () -> % +--R -? : % -> % ?/? : (%,R) -> % if R has FIELD +--R ?=? : (%,%) -> Boolean 1 : () -> % +--R 0 : () -> % ?^? : (%,NonNegativeInteger) -> % --R ?^? : (%,PositiveInteger) -> % coefficient : (%,E) -> R +--R coerce : R -> % if R has COMRING coerce : % -> % if R has INTDOM --R coerce : Integer -> % coerce : % -> OutputForm --R degree : % -> E hash : % -> SingleInteger --R latex : % -> String leadingCoefficient : % -> R @@ -50237,15 +50563,9 @@ digraph pic { --R zero? : % -> Boolean ?~=? : (%,%) -> Boolean --R ?*? : (%,Fraction(Integer)) -> % if R has ALGEBRA(FRAC(INT)) --R ?*? : (Fraction(Integer),%) -> % if R has ALGEBRA(FRAC(INT)) ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R ?/? : (%,R) -> % if R has FIELD ---R ?^? : (%,NonNegativeInteger) -> % --R associates? : (%,%) -> Boolean if R has INTDOM --R characteristic : () -> NonNegativeInteger --R charthRoot : % -> Union(%,"failed") if R has CHARNZ ---R coerce : R -> % if R has COMRING ---R coerce : % -> % if R has INTDOM --R coerce : Fraction(Integer) -> % if R has ALGEBRA(FRAC(INT)) --R exquo : (%,%) -> Union(%,"failed") if R has INTDOM --R subtractIfCan : (%,%) -> Union(%,"failed") @@ -50573,6 +50893,7 @@ digraph pic { --S 1 of 1 )show FortranMachineTypeCategory +--R --R FortranMachineTypeCategory is a category constructor --R Abbreviation for FortranMachineTypeCategory is FMTC --R This constructor is exposed in this frame. @@ -50580,24 +50901,23 @@ digraph pic { --R --R------------------------------- Operations -------------------------------- --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ? Boolean --R ?<=? : (%,%) -> Boolean ?=? : (%,%) -> Boolean --R ?>? : (%,%) -> Boolean ?>=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % associates? : (%,%) -> Boolean ---R coerce : Integer -> % coerce : % -> % ---R coerce : Integer -> % coerce : % -> OutputForm ---R hash : % -> SingleInteger latex : % -> String ---R max : (%,%) -> % min : (%,%) -> % ---R one? : % -> Boolean recip : % -> Union(%,"failed") ---R retract : % -> Integer sample : () -> % ---R unit? : % -> Boolean unitCanonical : % -> % ---R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R associates? : (%,%) -> Boolean coerce : Integer -> % +--R coerce : % -> % coerce : Integer -> % +--R coerce : % -> OutputForm hash : % -> SingleInteger +--R latex : % -> String max : (%,%) -> % +--R min : (%,%) -> % one? : % -> Boolean +--R recip : % -> Union(%,"failed") retract : % -> Integer +--R sample : () -> % unit? : % -> Boolean +--R unitCanonical : % -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean --R characteristic : () -> NonNegativeInteger --R exquo : (%,%) -> Union(%,"failed") --R retractIfCan : % -> Union(Integer,"failed") @@ -50852,31 +51172,31 @@ digraph pic { --R------------------------------- Operations -------------------------------- --R ?*? : (R,%) -> % ?*? : (%,R) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % ---R ?+? : (%,%) -> % ?-? : (%,%) -> % ---R -? : % -> % ?=? : (%,%) -> Boolean ---R 0 : () -> % alternative? : () -> Boolean ---R antiAssociative? : () -> Boolean antiCommutative? : () -> Boolean ---R antiCommutator : (%,%) -> % apply : (Matrix(R),%) -> % ---R associative? : () -> Boolean associator : (%,%,%) -> % ---R basis : () -> Vector(%) coerce : % -> OutputForm ---R commutative? : () -> Boolean commutator : (%,%) -> % ---R convert : Vector(R) -> % convert : % -> Vector(R) ---R coordinates : % -> Vector(R) ?.? : (%,Integer) -> R ---R flexible? : () -> Boolean hash : % -> SingleInteger ---R jacobiIdentity? : () -> Boolean jordanAdmissible? : () -> Boolean ---R jordanAlgebra? : () -> Boolean latex : % -> String ---R leftAlternative? : () -> Boolean leftDiscriminant : () -> R ---R leftDiscriminant : Vector(%) -> R leftNorm : % -> R ---R leftTrace : % -> R leftTraceMatrix : () -> Matrix(R) ---R lieAdmissible? : () -> Boolean lieAlgebra? : () -> Boolean ---R powerAssociative? : () -> Boolean rank : () -> PositiveInteger ---R represents : Vector(R) -> % rightAlternative? : () -> Boolean ---R rightDiscriminant : () -> R rightNorm : % -> R +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % +--R ?-? : (%,%) -> % -? : % -> % +--R ?=? : (%,%) -> Boolean 0 : () -> % +--R alternative? : () -> Boolean antiAssociative? : () -> Boolean +--R antiCommutative? : () -> Boolean antiCommutator : (%,%) -> % +--R apply : (Matrix(R),%) -> % associative? : () -> Boolean +--R associator : (%,%,%) -> % basis : () -> Vector(%) +--R coerce : % -> OutputForm commutative? : () -> Boolean +--R commutator : (%,%) -> % convert : Vector(R) -> % +--R convert : % -> Vector(R) coordinates : % -> Vector(R) +--R ?.? : (%,Integer) -> R flexible? : () -> Boolean +--R hash : % -> SingleInteger jacobiIdentity? : () -> Boolean +--R jordanAdmissible? : () -> Boolean jordanAlgebra? : () -> Boolean +--R latex : % -> String leftAlternative? : () -> Boolean +--R leftDiscriminant : () -> R leftDiscriminant : Vector(%) -> R +--R leftNorm : % -> R leftTrace : % -> R +--R leftTraceMatrix : () -> Matrix(R) lieAdmissible? : () -> Boolean +--R lieAlgebra? : () -> Boolean powerAssociative? : () -> Boolean +--R rank : () -> PositiveInteger represents : Vector(R) -> % +--R rightAlternative? : () -> Boolean rightDiscriminant : () -> R +--R rightDiscriminant : Vector(%) -> R rightNorm : % -> R --R rightTrace : % -> R rightTraceMatrix : () -> Matrix(R) --R sample : () -> % someBasis : () -> Vector(%) --R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % --R associatorDependence : () -> List(Vector(R)) if R has INTDOM --R conditionsForIdempotents : () -> List(Polynomial(R)) --R conditionsForIdempotents : Vector(%) -> List(Polynomial(R)) @@ -50898,7 +51218,6 @@ digraph pic { --R recip : % -> Union(%,"failed") if R has INTDOM --R represents : (Vector(R),Vector(%)) -> % --R rightCharacteristicPolynomial : % -> SparseUnivariatePolynomial(R) ---R rightDiscriminant : Vector(%) -> R --R rightMinimalPolynomial : % -> SparseUnivariatePolynomial(R) if R has INTDOM --R rightPower : (%,PositiveInteger) -> % --R rightRankPolynomial : () -> SparseUnivariatePolynomial(Polynomial(R)) if R has FIELD @@ -51539,22 +51858,21 @@ digraph pic { --R --R------------------------------- Operations -------------------------------- --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ?=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % associates? : (%,%) -> Boolean ---R coerce : % -> % coerce : Integer -> % ---R coerce : % -> OutputForm gcd : List(%) -> % ---R gcd : (%,%) -> % hash : % -> SingleInteger ---R latex : % -> String lcm : List(%) -> % ---R lcm : (%,%) -> % one? : % -> Boolean ---R recip : % -> Union(%,"failed") sample : () -> % ---R unit? : % -> Boolean unitCanonical : % -> % ---R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R associates? : (%,%) -> Boolean coerce : % -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R gcd : List(%) -> % gcd : (%,%) -> % +--R hash : % -> SingleInteger latex : % -> String +--R lcm : List(%) -> % lcm : (%,%) -> % +--R one? : % -> Boolean recip : % -> Union(%,"failed") +--R sample : () -> % unit? : % -> Boolean +--R unitCanonical : % -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean --R characteristic : () -> NonNegativeInteger --R exquo : (%,%) -> Union(%,"failed") --R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) @@ -51823,6 +52141,7 @@ digraph pic { --S 1 of 1 )show OrderedIntegralDomain +--R --R OrderedIntegralDomain is a category constructor --R Abbreviation for OrderedIntegralDomain is OINTDOM --R This constructor is exposed in this frame. @@ -51830,25 +52149,24 @@ digraph pic { --R --R------------------------------- Operations -------------------------------- --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ? Boolean --R ?<=? : (%,%) -> Boolean ?=? : (%,%) -> Boolean --R ?>? : (%,%) -> Boolean ?>=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % abs : % -> % ---R associates? : (%,%) -> Boolean coerce : % -> % ---R coerce : Integer -> % coerce : % -> OutputForm ---R hash : % -> SingleInteger latex : % -> String ---R max : (%,%) -> % min : (%,%) -> % ---R negative? : % -> Boolean one? : % -> Boolean ---R positive? : % -> Boolean recip : % -> Union(%,"failed") ---R sample : () -> % sign : % -> Integer ---R unit? : % -> Boolean unitCanonical : % -> % ---R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R abs : % -> % associates? : (%,%) -> Boolean +--R coerce : % -> % coerce : Integer -> % +--R coerce : % -> OutputForm hash : % -> SingleInteger +--R latex : % -> String max : (%,%) -> % +--R min : (%,%) -> % negative? : % -> Boolean +--R one? : % -> Boolean positive? : % -> Boolean +--R recip : % -> Union(%,"failed") sample : () -> % +--R sign : % -> Integer unit? : % -> Boolean +--R unitCanonical : % -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean --R characteristic : () -> NonNegativeInteger --R exquo : (%,%) -> Union(%,"failed") --R subtractIfCan : (%,%) -> Union(%,"failed") @@ -52080,13 +52398,16 @@ digraph pic { --R------------------------------- Operations -------------------------------- --R ?*? : (R,%) -> % ?*? : (%,R) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % ---R -? : % -> % ?=? : (%,%) -> Boolean ---R 1 : () -> % 0 : () -> % +--R -? : % -> % ?/? : (%,R) -> % if R has FIELD +--R ?=? : (%,%) -> Boolean 1 : () -> % +--R 0 : () -> % ?^? : (%,NonNegativeInteger) -> % --R ?^? : (%,PositiveInteger) -> % coefficient : (%,E) -> R --R coefficients : % -> List(R) coerce : R -> % ---R coerce : Integer -> % coerce : % -> OutputForm +--R coerce : % -> % if R has INTDOM coerce : Integer -> % +--R coerce : % -> OutputForm content : % -> R if R has GCDDOM --R degree : % -> E ground : % -> R --R ground? : % -> Boolean hash : % -> SingleInteger --R latex : % -> String leadingCoefficient : % -> R @@ -52099,17 +52420,11 @@ digraph pic { --R zero? : % -> Boolean ?~=? : (%,%) -> Boolean --R ?*? : (%,Fraction(Integer)) -> % if R has ALGEBRA(FRAC(INT)) --R ?*? : (Fraction(Integer),%) -> % if R has ALGEBRA(FRAC(INT)) ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R ?/? : (%,R) -> % if R has FIELD ---R ?^? : (%,NonNegativeInteger) -> % --R associates? : (%,%) -> Boolean if R has INTDOM --R binomThmExpt : (%,%,NonNegativeInteger) -> % if R has COMRING --R characteristic : () -> NonNegativeInteger --R charthRoot : % -> Union(%,"failed") if R has CHARNZ --R coerce : Fraction(Integer) -> % if R has RETRACT(FRAC(INT)) or R has ALGEBRA(FRAC(INT)) ---R coerce : % -> % if R has INTDOM ---R content : % -> R if R has GCDDOM --R exquo : (%,R) -> Union(%,"failed") if R has INTDOM --R exquo : (%,%) -> Union(%,"failed") if R has INTDOM --R numberOfMonomials : % -> NonNegativeInteger @@ -52528,13 +52843,15 @@ digraph pic { --R --R------------------------------- Operations -------------------------------- --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,%) -> % ---R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % ---R ?-? : (%,%) -> % -? : % -> % ---R ? Boolean ?<=? : (%,%) -> Boolean ---R ?=? : (%,%) -> Boolean ?>? : (%,%) -> Boolean ---R ?>=? : (%,%) -> Boolean 1 : () -> % ---R 0 : () -> % ?^? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,Fraction(Integer)) -> % ?**? : (%,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ? Boolean +--R ?<=? : (%,%) -> Boolean ?=? : (%,%) -> Boolean +--R ?>? : (%,%) -> Boolean ?>=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % --R acos : % -> % acosh : % -> % --R acot : % -> % acoth : % -> % --R acsc : % -> % acsch : % -> % @@ -52565,10 +52882,6 @@ digraph pic { --R tanh : % -> % unit? : % -> Boolean --R unitCanonical : % -> % width : % -> R --R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,Fraction(Integer)) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R ?^? : (%,NonNegativeInteger) -> % --R characteristic : () -> NonNegativeInteger --R exquo : (%,%) -> Union(%,"failed") --R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) @@ -52957,11 +53270,13 @@ digraph pic { --R------------------------------- Operations -------------------------------- --R ?*? : (Coef,%) -> % ?*? : (%,Coef) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ?=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % coefficient : (%,Expon) -> Coef +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R coefficient : (%,Expon) -> Coef coerce : % -> % if Coef has INTDOM --R coerce : Integer -> % coerce : % -> OutputForm --R complete : % -> % degree : % -> Expon --R hash : % -> SingleInteger latex : % -> String @@ -52974,15 +53289,11 @@ digraph pic { --R zero? : % -> Boolean ?~=? : (%,%) -> Boolean --R ?*? : (%,Fraction(Integer)) -> % if Coef has ALGEBRA(FRAC(INT)) --R ?*? : (Fraction(Integer),%) -> % if Coef has ALGEBRA(FRAC(INT)) ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % --R ?/? : (%,Coef) -> % if Coef has FIELD ---R ?^? : (%,NonNegativeInteger) -> % --R associates? : (%,%) -> Boolean if Coef has INTDOM --R characteristic : () -> NonNegativeInteger --R charthRoot : % -> Union(%,"failed") if Coef has CHARNZ --R coerce : Coef -> % if Coef has COMRING ---R coerce : % -> % if Coef has INTDOM --R coerce : Fraction(Integer) -> % if Coef has ALGEBRA(FRAC(INT)) --R exquo : (%,%) -> Union(%,"failed") if Coef has INTDOM --R monomial : (%,List(Var),List(Expon)) -> % @@ -53299,22 +53610,21 @@ digraph pic { --R --R------------------------------- Operations -------------------------------- --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ?=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % associates? : (%,%) -> Boolean ---R coerce : % -> % coerce : Integer -> % ---R coerce : % -> OutputForm gcd : List(%) -> % ---R gcd : (%,%) -> % hash : % -> SingleInteger ---R latex : % -> String lcm : List(%) -> % ---R lcm : (%,%) -> % one? : % -> Boolean ---R recip : % -> Union(%,"failed") sample : () -> % ---R unit? : % -> Boolean unitCanonical : % -> % ---R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R associates? : (%,%) -> Boolean coerce : % -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R gcd : List(%) -> % gcd : (%,%) -> % +--R hash : % -> SingleInteger latex : % -> String +--R lcm : List(%) -> % lcm : (%,%) -> % +--R one? : % -> Boolean recip : % -> Union(%,"failed") +--R sample : () -> % unit? : % -> Boolean +--R unitCanonical : % -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean --R characteristic : () -> NonNegativeInteger --R expressIdealMember : (List(%),%) -> Union(List(%),"failed") --R exquo : (%,%) -> Union(%,"failed") @@ -53550,24 +53860,23 @@ digraph pic { --R --R------------------------------- Operations -------------------------------- --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ?=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % associates? : (%,%) -> Boolean ---R coerce : % -> % coerce : Integer -> % ---R coerce : % -> OutputForm factor : % -> Factored(%) ---R gcd : List(%) -> % gcd : (%,%) -> % ---R hash : % -> SingleInteger latex : % -> String ---R lcm : List(%) -> % lcm : (%,%) -> % ---R one? : % -> Boolean prime? : % -> Boolean ---R recip : % -> Union(%,"failed") sample : () -> % ---R squareFree : % -> Factored(%) squareFreePart : % -> % ---R unit? : % -> Boolean unitCanonical : % -> % ---R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R associates? : (%,%) -> Boolean coerce : % -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R factor : % -> Factored(%) gcd : List(%) -> % +--R gcd : (%,%) -> % hash : % -> SingleInteger +--R latex : % -> String lcm : List(%) -> % +--R lcm : (%,%) -> % one? : % -> Boolean +--R prime? : % -> Boolean recip : % -> Union(%,"failed") +--R sample : () -> % squareFree : % -> Factored(%) +--R squareFreePart : % -> % unit? : % -> Boolean +--R unitCanonical : % -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean --R characteristic : () -> NonNegativeInteger --R exquo : (%,%) -> Union(%,"failed") --R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) @@ -53817,23 +54126,23 @@ digraph pic { --R------------------------------- Operations -------------------------------- --R ?*? : (Integer,S) -> % ?*? : (Integer,%) -> % --R ?*? : (%,Integer) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?+? : (S,%) -> % ---R ?+? : (%,%) -> % ?-? : (%,%) -> % ---R -? : % -> % ?<=? : (%,%) -> Boolean ---R ?=? : (%,%) -> Boolean 0 : () -> % ---R coefficient : (S,%) -> Integer coerce : S -> % ---R coerce : % -> OutputForm collect : % -> % ---R concat : (%,%) -> % degree : % -> Integer ---R divOfPole : % -> % divOfZero : % -> % ---R effective? : % -> Boolean hash : % -> SingleInteger ---R incr : % -> % latex : % -> String ---R mapGen : ((S -> S),%) -> % nthCoef : (%,Integer) -> Integer ---R nthFactor : (%,Integer) -> S retract : % -> S ---R sample : () -> % size : % -> NonNegativeInteger ---R split : % -> List(%) supp : % -> List(S) ---R suppOfPole : % -> List(S) suppOfZero : % -> List(S) ---R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?+? : (S,%) -> % ?+? : (%,%) -> % +--R ?-? : (%,%) -> % -? : % -> % +--R ?<=? : (%,%) -> Boolean ?=? : (%,%) -> Boolean +--R 0 : () -> % coefficient : (S,%) -> Integer +--R coerce : S -> % coerce : % -> OutputForm +--R collect : % -> % concat : (%,%) -> % +--R degree : % -> Integer divOfPole : % -> % +--R divOfZero : % -> % effective? : % -> Boolean +--R hash : % -> SingleInteger incr : % -> % +--R latex : % -> String mapGen : ((S -> S),%) -> % +--R nthCoef : (%,Integer) -> Integer nthFactor : (%,Integer) -> S +--R retract : % -> S sample : () -> % +--R size : % -> NonNegativeInteger split : % -> List(%) +--R supp : % -> List(S) suppOfPole : % -> List(S) +--R suppOfZero : % -> List(S) zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean --R highCommonTerms : (%,%) -> % if Integer has OAMON --R mapCoef : ((Integer -> Integer),%) -> % --R retractIfCan : % -> Union(S,"failed") @@ -54074,24 +54383,22 @@ digraph pic { --R --R------------------------------- Operations -------------------------------- --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ?=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % associates? : (%,%) -> Boolean ---R coerce : % -> % coerce : Integer -> % ---R coerce : % -> OutputForm gcd : List(%) -> % ---R gcd : (%,%) -> % hash : % -> SingleInteger ---R latex : % -> String lcm : List(%) -> % ---R lcm : (%,%) -> % one? : % -> Boolean ---R ?quo? : (%,%) -> % recip : % -> Union(%,"failed") ---R ?rem? : (%,%) -> % sample : () -> % ---R sizeLess? : (%,%) -> Boolean unit? : % -> Boolean ---R unitCanonical : % -> % zero? : % -> Boolean ---R ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R associates? : (%,%) -> Boolean coerce : % -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R gcd : List(%) -> % gcd : (%,%) -> % +--R hash : % -> SingleInteger latex : % -> String +--R lcm : List(%) -> % lcm : (%,%) -> % +--R one? : % -> Boolean ?quo? : (%,%) -> % +--R recip : % -> Union(%,"failed") ?rem? : (%,%) -> % +--R sample : () -> % sizeLess? : (%,%) -> Boolean +--R unit? : % -> Boolean unitCanonical : % -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean --R characteristic : () -> NonNegativeInteger --R divide : (%,%) -> Record(quotient: %,remainder: %) --R euclideanSize : % -> NonNegativeInteger @@ -54486,32 +54793,34 @@ digraph pic { --R------------------------------- Operations -------------------------------- --R ?*? : (%,Coef) -> % ?*? : (Coef,%) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ?=? : (%,%) -> Boolean --R D : (%,List(Var)) -> % D : (%,Var) -> % --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % coerce : Integer -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R coerce : % -> % if Coef has INTDOM coerce : Integer -> % --R coerce : % -> OutputForm complete : % -> % ---R differentiate : (%,Var) -> % eval : (%,%,%) -> % ---R eval : (%,Equation(%)) -> % eval : (%,Var,%) -> % ---R hash : % -> SingleInteger latex : % -> String ---R leadingCoefficient : % -> Coef leadingMonomial : % -> % ---R map : ((Coef -> Coef),%) -> % monomial? : % -> Boolean ---R one? : % -> Boolean pole? : % -> Boolean ---R recip : % -> Union(%,"failed") reductum : % -> % ---R sample : () -> % variables : % -> List(Var) ---R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R degree : % -> IndexedExponents(Var) differentiate : (%,List(Var)) -> % +--R differentiate : (%,Var) -> % eval : (%,List(%),List(%)) -> % +--R eval : (%,%,%) -> % eval : (%,Equation(%)) -> % +--R eval : (%,List(Equation(%))) -> % eval : (%,List(Var),List(%)) -> % +--R eval : (%,Var,%) -> % hash : % -> SingleInteger +--R latex : % -> String leadingCoefficient : % -> Coef +--R leadingMonomial : % -> % map : ((Coef -> Coef),%) -> % +--R monomial? : % -> Boolean one? : % -> Boolean +--R pole? : % -> Boolean recip : % -> Union(%,"failed") +--R reductum : % -> % sample : () -> % +--R variables : % -> List(Var) zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean --R ?*? : (Fraction(Integer),%) -> % if Coef has ALGEBRA(FRAC(INT)) --R ?*? : (%,Fraction(Integer)) -> % if Coef has ALGEBRA(FRAC(INT)) ---R ?*? : (NonNegativeInteger,%) -> % --R ?**? : (%,Fraction(Integer)) -> % if Coef has ALGEBRA(FRAC(INT)) --R ?**? : (%,%) -> % if Coef has ALGEBRA(FRAC(INT)) ---R ?**? : (%,NonNegativeInteger) -> % --R ?/? : (%,Coef) -> % if Coef has FIELD --R D : (%,List(Var),List(NonNegativeInteger)) -> % --R D : (%,Var,NonNegativeInteger) -> % ---R ?^? : (%,NonNegativeInteger) -> % --R acos : % -> % if Coef has ALGEBRA(FRAC(INT)) --R acosh : % -> % if Coef has ALGEBRA(FRAC(INT)) --R acot : % -> % if Coef has ALGEBRA(FRAC(INT)) @@ -54531,7 +54840,6 @@ digraph pic { --R coefficient : (%,Var,NonNegativeInteger) -> % --R coefficient : (%,IndexedExponents(Var)) -> Coef --R coerce : Fraction(Integer) -> % if Coef has ALGEBRA(FRAC(INT)) ---R coerce : % -> % if Coef has INTDOM --R coerce : Coef -> % if Coef has COMRING --R cos : % -> % if Coef has ALGEBRA(FRAC(INT)) --R cosh : % -> % if Coef has ALGEBRA(FRAC(INT)) @@ -54539,13 +54847,8 @@ digraph pic { --R coth : % -> % if Coef has ALGEBRA(FRAC(INT)) --R csc : % -> % if Coef has ALGEBRA(FRAC(INT)) --R csch : % -> % if Coef has ALGEBRA(FRAC(INT)) ---R degree : % -> IndexedExponents(Var) --R differentiate : (%,List(Var),List(NonNegativeInteger)) -> % --R differentiate : (%,Var,NonNegativeInteger) -> % ---R differentiate : (%,List(Var)) -> % ---R eval : (%,List(%),List(%)) -> % ---R eval : (%,List(Equation(%))) -> % ---R eval : (%,List(Var),List(%)) -> % --R exp : % -> % if Coef has ALGEBRA(FRAC(INT)) --R exquo : (%,%) -> Union(%,"failed") if Coef has INTDOM --R extend : (%,NonNegativeInteger) -> % @@ -54956,24 +55259,23 @@ digraph pic { --R --R------------------------------- Operations -------------------------------- --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ?=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % associates? : (%,%) -> Boolean ---R coerce : % -> % coerce : Integer -> % ---R coerce : % -> OutputForm factor : % -> Factored(%) ---R gcd : List(%) -> % gcd : (%,%) -> % ---R hash : % -> SingleInteger latex : % -> String ---R lcm : List(%) -> % lcm : (%,%) -> % ---R one? : % -> Boolean prime? : % -> Boolean ---R recip : % -> Union(%,"failed") sample : () -> % ---R squareFree : % -> Factored(%) squareFreePart : % -> % ---R unit? : % -> Boolean unitCanonical : % -> % ---R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R associates? : (%,%) -> Boolean coerce : % -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R factor : % -> Factored(%) gcd : List(%) -> % +--R gcd : (%,%) -> % hash : % -> SingleInteger +--R latex : % -> String lcm : List(%) -> % +--R lcm : (%,%) -> % one? : % -> Boolean +--R prime? : % -> Boolean recip : % -> Union(%,"failed") +--R sample : () -> % squareFree : % -> Factored(%) +--R squareFreePart : % -> % unit? : % -> Boolean +--R unitCanonical : % -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean --R characteristic : () -> NonNegativeInteger --R charthRoot : % -> Union(%,"failed") if $ has CHARNZ --R conditionP : Matrix(%) -> Union(Vector(%),"failed") if $ has CHARNZ @@ -55293,12 +55595,14 @@ digraph pic { --R------------------------------- Operations -------------------------------- --R ?*? : (Coef,%) -> % ?*? : (%,Coef) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ?=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % center : % -> Coef ---R coefficient : (%,Expon) -> Coef coerce : Integer -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R center : % -> Coef coefficient : (%,Expon) -> Coef +--R coerce : % -> % if Coef has INTDOM coerce : Integer -> % --R coerce : % -> OutputForm complete : % -> % --R degree : % -> Expon ?.? : (%,Expon) -> Coef --R extend : (%,Expon) -> % hash : % -> SingleInteger @@ -55313,8 +55617,6 @@ digraph pic { --R zero? : % -> Boolean ?~=? : (%,%) -> Boolean --R ?*? : (%,Fraction(Integer)) -> % if Coef has ALGEBRA(FRAC(INT)) --R ?*? : (Fraction(Integer),%) -> % if Coef has ALGEBRA(FRAC(INT)) ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % --R ?/? : (%,Coef) -> % if Coef has FIELD --R D : % -> % if Coef has *: (Expon,Coef) -> Coef --R D : (%,NonNegativeInteger) -> % if Coef has *: (Expon,Coef) -> Coef @@ -55322,13 +55624,11 @@ digraph pic { --R D : (%,List(Symbol)) -> % if Coef has PDRING(SYMBOL) and Coef has *: (Expon,Coef) -> Coef --R D : (%,Symbol,NonNegativeInteger) -> % if Coef has PDRING(SYMBOL) and Coef has *: (Expon,Coef) -> Coef --R D : (%,List(Symbol),List(NonNegativeInteger)) -> % if Coef has PDRING(SYMBOL) and Coef has *: (Expon,Coef) -> Coef ---R ?^? : (%,NonNegativeInteger) -> % --R approximate : (%,Expon) -> Coef if Coef has **: (Coef,Expon) -> Coef and Coef has coerce: Symbol -> Coef --R associates? : (%,%) -> Boolean if Coef has INTDOM --R characteristic : () -> NonNegativeInteger --R charthRoot : % -> Union(%,"failed") if Coef has CHARNZ --R coerce : Coef -> % if Coef has COMRING ---R coerce : % -> % if Coef has INTDOM --R coerce : Fraction(Integer) -> % if Coef has ALGEBRA(FRAC(INT)) --R differentiate : % -> % if Coef has *: (Expon,Coef) -> Coef --R differentiate : (%,NonNegativeInteger) -> % if Coef has *: (Expon,Coef) -> Coef @@ -55790,28 +56090,27 @@ digraph pic { --R------------------------------- Operations -------------------------------- --R ?*? : (Fraction(Integer),%) -> % ?*? : (%,Fraction(Integer)) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,Integer) -> % ?**? : (%,NonNegativeInteger) -> % --R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % --R ?-? : (%,%) -> % -? : % -> % --R ?/? : (%,%) -> % ?=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % ---R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> % ---R associates? : (%,%) -> Boolean coerce : Fraction(Integer) -> % ---R coerce : % -> % coerce : Integer -> % ---R coerce : % -> OutputForm factor : % -> Factored(%) ---R gcd : List(%) -> % gcd : (%,%) -> % ---R hash : % -> SingleInteger inv : % -> % ---R latex : % -> String lcm : List(%) -> % ---R lcm : (%,%) -> % one? : % -> Boolean ---R prime? : % -> Boolean ?quo? : (%,%) -> % ---R recip : % -> Union(%,"failed") ?rem? : (%,%) -> % ---R sample : () -> % sizeLess? : (%,%) -> Boolean ---R squareFree : % -> Factored(%) squareFreePart : % -> % ---R unit? : % -> Boolean unitCanonical : % -> % ---R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,Integer) -> % ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,PositiveInteger) -> % associates? : (%,%) -> Boolean +--R coerce : Fraction(Integer) -> % coerce : % -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R factor : % -> Factored(%) gcd : List(%) -> % +--R gcd : (%,%) -> % hash : % -> SingleInteger +--R inv : % -> % latex : % -> String +--R lcm : List(%) -> % lcm : (%,%) -> % +--R one? : % -> Boolean prime? : % -> Boolean +--R ?quo? : (%,%) -> % recip : % -> Union(%,"failed") +--R ?rem? : (%,%) -> % sample : () -> % +--R sizeLess? : (%,%) -> Boolean squareFree : % -> Factored(%) +--R squareFreePart : % -> % unit? : % -> Boolean +--R unitCanonical : % -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean --R characteristic : () -> NonNegativeInteger --R divide : (%,%) -> Record(quotient: %,remainder: %) --R euclideanSize : % -> NonNegativeInteger @@ -56128,32 +56427,34 @@ digraph pic { --R --R------------------------------- Operations -------------------------------- --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ? Boolean --R ?<=? : (%,%) -> Boolean ?=? : (%,%) -> Boolean --R ?>? : (%,%) -> Boolean ?>=? : (%,%) -> Boolean --R D : % -> % D : (%,NonNegativeInteger) -> % --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % abs : % -> % ---R addmod : (%,%,%) -> % associates? : (%,%) -> Boolean ---R base : () -> % binomial : (%,%) -> % ---R bit? : (%,%) -> Boolean coerce : Integer -> % ---R coerce : % -> % coerce : Integer -> % ---R coerce : % -> OutputForm convert : % -> DoubleFloat ---R convert : % -> Float convert : % -> Pattern(Integer) ---R convert : % -> InputForm convert : % -> Integer ---R copy : % -> % dec : % -> % ---R differentiate : % -> % even? : % -> Boolean ---R factor : % -> Factored(%) factorial : % -> % ---R gcd : List(%) -> % gcd : (%,%) -> % ---R hash : % -> % hash : % -> SingleInteger ---R inc : % -> % init : () -> % ---R invmod : (%,%) -> % latex : % -> String ---R lcm : List(%) -> % lcm : (%,%) -> % ---R length : % -> % mask : % -> % ---R max : (%,%) -> % min : (%,%) -> % ---R mulmod : (%,%,%) -> % negative? : % -> Boolean +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R abs : % -> % addmod : (%,%,%) -> % +--R associates? : (%,%) -> Boolean base : () -> % +--R binomial : (%,%) -> % bit? : (%,%) -> Boolean +--R coerce : Integer -> % coerce : % -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R convert : % -> DoubleFloat convert : % -> Float +--R convert : % -> Pattern(Integer) convert : % -> InputForm +--R convert : % -> Integer copy : % -> % +--R dec : % -> % differentiate : % -> % +--R even? : % -> Boolean factor : % -> Factored(%) +--R factorial : % -> % gcd : List(%) -> % +--R gcd : (%,%) -> % hash : % -> % +--R hash : % -> SingleInteger inc : % -> % +--R init : () -> % invmod : (%,%) -> % +--R latex : % -> String lcm : List(%) -> % +--R lcm : (%,%) -> % length : % -> % +--R mask : % -> % max : (%,%) -> % +--R min : (%,%) -> % mulmod : (%,%,%) -> % +--R negative? : % -> Boolean nextItem : % -> Union(%,"failed") --R odd? : % -> Boolean one? : % -> Boolean --R permutation : (%,%) -> % positive? : % -> Boolean --R positiveRemainder : (%,%) -> % powmod : (%,%,%) -> % @@ -56168,9 +56469,6 @@ digraph pic { --R symmetricRemainder : (%,%) -> % unit? : % -> Boolean --R unitCanonical : % -> % zero? : % -> Boolean --R ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R ?^? : (%,NonNegativeInteger) -> % --R characteristic : () -> NonNegativeInteger --R differentiate : (%,NonNegativeInteger) -> % --R divide : (%,%) -> Record(quotient: %,remainder: %) @@ -56182,7 +56480,6 @@ digraph pic { --R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) --R lcmCoef : (%,%) -> Record(llcmres: %,coeff1: %,coeff2: %) --R multiEuclidean : (List(%),%) -> Union(List(%),"failed") ---R nextItem : % -> Union(%,"failed") --R patternMatch : (%,Pattern(Integer),PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) --R principalIdeal : List(%) -> Record(coef: List(%),generator: %) --R rationalIfCan : % -> Union(Fraction(Integer),"failed") @@ -56744,57 +57041,54 @@ digraph pic { --R ?*? : (%,K) -> % ?*? : (K,%) -> % --R ?*? : (Fraction(Integer),%) -> % ?*? : (%,Fraction(Integer)) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,Integer) -> % ?**? : (%,NonNegativeInteger) -> % --R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % --R ?-? : (%,%) -> % -? : % -> % ---R ?/? : (%,%) -> % ?=? : (%,%) -> Boolean ---R 1 : () -> % 0 : () -> % ---R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> % +--R ?/? : (%,K) -> % if K has FIELD ?/? : (%,%) -> % +--R ?=? : (%,%) -> Boolean 1 : () -> % +--R 0 : () -> % ?^? : (%,Integer) -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % --R associates? : (%,%) -> Boolean center : % -> K --R coefOfFirstNonZeroTerm : % -> K coefficient : (%,Integer) -> K ---R coerce : Fraction(Integer) -> % coerce : % -> % ---R coerce : Integer -> % coerce : % -> OutputForm ---R complete : % -> % degree : % -> Integer ---R delay : (() -> %) -> % ?.? : (%,Integer) -> K ---R extend : (%,Integer) -> % factor : % -> Factored(%) ---R filterUpTo : (%,Integer) -> % findCoef : (%,Integer) -> K ---R gcd : List(%) -> % gcd : (%,%) -> % ---R hash : % -> SingleInteger inv : % -> % ---R latex : % -> String lcm : List(%) -> % ---R lcm : (%,%) -> % leadingCoefficient : % -> K ---R leadingMonomial : % -> % map : ((K -> K),%) -> % ---R monomial : (K,Integer) -> % monomial? : % -> Boolean ---R one? : % -> Boolean order : % -> Integer ---R order : % -> Integer order : (%,Integer) -> Integer ---R pole? : % -> Boolean posExpnPart : % -> % ---R prime? : % -> Boolean printInfo : () -> Boolean ---R printInfo : Boolean -> Boolean ?quo? : (%,%) -> % ---R recip : % -> Union(%,"failed") reductum : % -> % ---R ?rem? : (%,%) -> % removeFirstZeroes : % -> % ---R removeZeroes : % -> % removeZeroes : (Integer,%) -> % ---R sample : () -> % sbt : (%,%) -> % ---R series : (Integer,K,%) -> % shift : (%,Integer) -> % ---R sizeLess? : (%,%) -> Boolean squareFree : % -> Factored(%) ---R squareFreePart : % -> % truncate : (%,Integer) -> % ---R unit? : % -> Boolean unitCanonical : % -> % ---R variable : % -> Symbol zero? : % -> Boolean ---R ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R ?/? : (%,K) -> % if K has FIELD +--R coerce : K -> % if K has COMRING coerce : Fraction(Integer) -> % +--R coerce : % -> % coerce : Integer -> % +--R coerce : % -> OutputForm complete : % -> % +--R degree : % -> Integer delay : (() -> %) -> % +--R ?.? : (%,Integer) -> K extend : (%,Integer) -> % +--R factor : % -> Factored(%) filterUpTo : (%,Integer) -> % +--R findCoef : (%,Integer) -> K gcd : List(%) -> % +--R gcd : (%,%) -> % hash : % -> SingleInteger +--R inv : % -> % latex : % -> String +--R lcm : List(%) -> % lcm : (%,%) -> % +--R leadingCoefficient : % -> K leadingMonomial : % -> % +--R map : ((K -> K),%) -> % monomial : (K,Integer) -> % +--R monomial? : % -> Boolean one? : % -> Boolean +--R order : % -> Integer order : % -> Integer +--R order : (%,Integer) -> Integer pole? : % -> Boolean +--R posExpnPart : % -> % prime? : % -> Boolean +--R printInfo : () -> Boolean printInfo : Boolean -> Boolean +--R ?quo? : (%,%) -> % recip : % -> Union(%,"failed") +--R reductum : % -> % ?rem? : (%,%) -> % +--R removeFirstZeroes : % -> % removeZeroes : % -> % +--R removeZeroes : (Integer,%) -> % sample : () -> % +--R sbt : (%,%) -> % series : (Integer,K,%) -> % +--R shift : (%,Integer) -> % sizeLess? : (%,%) -> Boolean +--R squareFree : % -> Factored(%) squareFreePart : % -> % +--R truncate : (%,Integer) -> % unit? : % -> Boolean +--R unitCanonical : % -> % variable : % -> Symbol +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean --R D : (%,List(Symbol),List(NonNegativeInteger)) -> % if K has PDRING(SYMBOL) and K has *: (Integer,K) -> K --R D : (%,Symbol,NonNegativeInteger) -> % if K has PDRING(SYMBOL) and K has *: (Integer,K) -> K --R D : (%,List(Symbol)) -> % if K has PDRING(SYMBOL) and K has *: (Integer,K) -> K --R D : (%,Symbol) -> % if K has PDRING(SYMBOL) and K has *: (Integer,K) -> K --R D : (%,NonNegativeInteger) -> % if K has *: (Integer,K) -> K --R D : % -> % if K has *: (Integer,K) -> K ---R ?^? : (%,NonNegativeInteger) -> % --R approximate : (%,Integer) -> K if K has **: (K,Integer) -> K and K has coerce: Symbol -> K --R characteristic : () -> NonNegativeInteger --R charthRoot : % -> Union(%,"failed") if K has CHARNZ --R coerce : % -> Stream(Record(k: Integer,c: K)) --R coerce : Stream(Record(k: Integer,c: K)) -> % ---R coerce : K -> % if K has COMRING --R differentiate : (%,List(Symbol),List(NonNegativeInteger)) -> % if K has PDRING(SYMBOL) and K has *: (Integer,K) -> K --R differentiate : (%,Symbol,NonNegativeInteger) -> % if K has PDRING(SYMBOL) and K has *: (Integer,K) -> K --R differentiate : (%,List(Symbol)) -> % if K has PDRING(SYMBOL) and K has *: (Integer,K) -> K @@ -57212,28 +57506,26 @@ digraph pic { --R --R------------------------------- Operations -------------------------------- --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ?=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % associates? : (%,%) -> Boolean ---R coerce : % -> % coerce : Integer -> % ---R coerce : % -> OutputForm complete : % -> % ---R digits : % -> Stream(Integer) extend : (%,Integer) -> % ---R gcd : List(%) -> % gcd : (%,%) -> % ---R hash : % -> SingleInteger latex : % -> String ---R lcm : List(%) -> % lcm : (%,%) -> % ---R moduloP : % -> Integer modulus : () -> Integer ---R one? : % -> Boolean order : % -> NonNegativeInteger ---R ?quo? : (%,%) -> % quotientByP : % -> % ---R recip : % -> Union(%,"failed") ?rem? : (%,%) -> % ---R sample : () -> % sizeLess? : (%,%) -> Boolean ---R sqrt : (%,Integer) -> % unit? : % -> Boolean ---R unitCanonical : % -> % zero? : % -> Boolean ---R ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R associates? : (%,%) -> Boolean coerce : % -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R complete : % -> % digits : % -> Stream(Integer) +--R extend : (%,Integer) -> % gcd : List(%) -> % +--R gcd : (%,%) -> % hash : % -> SingleInteger +--R latex : % -> String lcm : List(%) -> % +--R lcm : (%,%) -> % moduloP : % -> Integer +--R modulus : () -> Integer one? : % -> Boolean +--R order : % -> NonNegativeInteger ?quo? : (%,%) -> % +--R quotientByP : % -> % recip : % -> Union(%,"failed") +--R ?rem? : (%,%) -> % sample : () -> % +--R sizeLess? : (%,%) -> Boolean sqrt : (%,Integer) -> % +--R unit? : % -> Boolean unitCanonical : % -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean --R approximate : (%,Integer) -> Integer --R characteristic : () -> NonNegativeInteger --R divide : (%,%) -> Record(quotient: %,remainder: %) @@ -57534,41 +57826,44 @@ digraph pic { --R------------------------------- Operations -------------------------------- --R ?*? : (%,R) -> % ?*? : (R,%) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % ---R -? : % -> % ?=? : (%,%) -> Boolean ---R D : (%,List(VarSet)) -> % D : (%,VarSet) -> % ---R 1 : () -> % 0 : () -> % +--R -? : % -> % ?/? : (%,R) -> % if R has FIELD +--R ?=? : (%,%) -> Boolean D : (%,List(VarSet)) -> % +--R D : (%,VarSet) -> % 1 : () -> % +--R 0 : () -> % ?^? : (%,NonNegativeInteger) -> % --R ?^? : (%,PositiveInteger) -> % coefficient : (%,E) -> R ---R coefficients : % -> List(R) coerce : VarSet -> % ---R coerce : R -> % coerce : Integer -> % ---R coerce : % -> OutputForm degree : % -> E +--R coefficients : % -> List(R) coerce : % -> % if R has INTDOM +--R coerce : VarSet -> % coerce : R -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R content : % -> R if R has GCDDOM degree : % -> E --R differentiate : (%,VarSet) -> % eval : (%,VarSet,%) -> % ---R eval : (%,VarSet,R) -> % eval : (%,%,%) -> % ---R eval : (%,Equation(%)) -> % ground : % -> R +--R eval : (%,VarSet,R) -> % eval : (%,List(%),List(%)) -> % +--R eval : (%,%,%) -> % eval : (%,Equation(%)) -> % +--R eval : (%,List(Equation(%))) -> % gcd : (%,%) -> % if R has GCDDOM +--R gcd : List(%) -> % if R has GCDDOM ground : % -> R --R ground? : % -> Boolean hash : % -> SingleInteger ---R latex : % -> String leadingCoefficient : % -> R +--R latex : % -> String lcm : (%,%) -> % if R has GCDDOM +--R lcm : List(%) -> % if R has GCDDOM leadingCoefficient : % -> R --R leadingMonomial : % -> % map : ((R -> R),%) -> % ---R mapExponents : ((E -> E),%) -> % minimumDegree : % -> E +--R mapExponents : ((E -> E),%) -> % max : (%,%) -> % if R has ORDSET +--R min : (%,%) -> % if R has ORDSET minimumDegree : % -> E --R monomial : (R,E) -> % monomial? : % -> Boolean --R monomials : % -> List(%) one? : % -> Boolean ---R pomopo! : (%,R,E,%) -> % recip : % -> Union(%,"failed") ---R reductum : % -> % retract : % -> VarSet ---R retract : % -> R sample : () -> % ---R variables : % -> List(VarSet) zero? : % -> Boolean ---R ?~=? : (%,%) -> Boolean +--R pomopo! : (%,R,E,%) -> % primitiveMonomials : % -> List(%) +--R recip : % -> Union(%,"failed") reductum : % -> % +--R retract : % -> VarSet retract : % -> R +--R sample : () -> % variables : % -> List(VarSet) +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean --R ?*? : (Fraction(Integer),%) -> % if R has ALGEBRA(FRAC(INT)) --R ?*? : (%,Fraction(Integer)) -> % if R has ALGEBRA(FRAC(INT)) ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R ?/? : (%,R) -> % if R has FIELD --R ? Boolean if R has ORDSET --R ?<=? : (%,%) -> Boolean if R has ORDSET --R ?>? : (%,%) -> Boolean if R has ORDSET --R ?>=? : (%,%) -> Boolean if R has ORDSET --R D : (%,List(VarSet),List(NonNegativeInteger)) -> % --R D : (%,VarSet,NonNegativeInteger) -> % ---R ?^? : (%,NonNegativeInteger) -> % --R associates? : (%,%) -> Boolean if R has INTDOM --R binomThmExpt : (%,%,NonNegativeInteger) -> % if R has COMRING --R characteristic : () -> NonNegativeInteger @@ -57576,10 +57871,8 @@ digraph pic { --R coefficient : (%,List(VarSet),List(NonNegativeInteger)) -> % --R coefficient : (%,VarSet,NonNegativeInteger) -> % --R coerce : Fraction(Integer) -> % if R has RETRACT(FRAC(INT)) or R has ALGEBRA(FRAC(INT)) ---R coerce : % -> % if R has INTDOM --R conditionP : Matrix(%) -> Union(Vector(%),"failed") if and(has($,CharacteristicNonZero),has(R,PolynomialFactorizationExplicit)) --R content : (%,VarSet) -> % if R has GCDDOM ---R content : % -> R if R has GCDDOM --R convert : % -> InputForm if VarSet has KONVERT(INFORM) and R has KONVERT(INFORM) --R convert : % -> Pattern(Integer) if VarSet has KONVERT(PATTERN(INT)) and R has KONVERT(PATTERN(INT)) --R convert : % -> Pattern(Float) if VarSet has KONVERT(PATTERN(FLOAT)) and R has KONVERT(PATTERN(FLOAT)) @@ -57591,25 +57884,17 @@ digraph pic { --R discriminant : (%,VarSet) -> % if R has COMRING --R eval : (%,List(VarSet),List(%)) -> % --R eval : (%,List(VarSet),List(R)) -> % ---R eval : (%,List(%),List(%)) -> % ---R eval : (%,List(Equation(%))) -> % --R exquo : (%,%) -> Union(%,"failed") if R has INTDOM --R exquo : (%,R) -> Union(%,"failed") if R has INTDOM --R factor : % -> Factored(%) if R has PFECAT --R factorPolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has PFECAT --R factorSquareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has PFECAT ---R gcd : (%,%) -> % if R has GCDDOM ---R gcd : List(%) -> % if R has GCDDOM --R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) if R has GCDDOM --R isExpt : % -> Union(Record(var: VarSet,exponent: NonNegativeInteger),"failed") --R isPlus : % -> Union(List(%),"failed") --R isTimes : % -> Union(List(%),"failed") ---R lcm : (%,%) -> % if R has GCDDOM ---R lcm : List(%) -> % if R has GCDDOM --R lcmCoef : (%,%) -> Record(llcmres: %,coeff1: %,coeff2: %) if R has GCDDOM --R mainVariable : % -> Union(VarSet,"failed") ---R max : (%,%) -> % if R has ORDSET ---R min : (%,%) -> % if R has ORDSET --R minimumDegree : (%,List(VarSet)) -> List(NonNegativeInteger) --R minimumDegree : (%,VarSet) -> NonNegativeInteger --R monicDivide : (%,%,VarSet) -> Record(quotient: %,remainder: %) @@ -57621,7 +57906,6 @@ digraph pic { --R patternMatch : (%,Pattern(Integer),PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if VarSet has PATMAB(INT) and R has PATMAB(INT) --R patternMatch : (%,Pattern(Float),PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if VarSet has PATMAB(FLOAT) and R has PATMAB(FLOAT) --R prime? : % -> Boolean if R has PFECAT ---R primitiveMonomials : % -> List(%) --R primitivePart : (%,VarSet) -> % if R has GCDDOM --R primitivePart : % -> % if R has GCDDOM --R reducedSystem : Matrix(%) -> Matrix(R) @@ -58593,12 +58877,14 @@ digraph pic { --R------------------------------- Operations -------------------------------- --R ?*? : (Coef,%) -> % ?*? : (%,Coef) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ?=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % center : % -> Coef ---R coefficients : % -> Stream(Coef) coerce : Integer -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R center : % -> Coef coefficients : % -> Stream(Coef) +--R coerce : % -> % if Coef has INTDOM coerce : Integer -> % --R coerce : % -> OutputForm complete : % -> % --R degree : % -> NonNegativeInteger hash : % -> SingleInteger --R latex : % -> String leadingCoefficient : % -> Coef @@ -58611,11 +58897,9 @@ digraph pic { --R zero? : % -> Boolean ?~=? : (%,%) -> Boolean --R ?*? : (%,Fraction(Integer)) -> % if Coef has ALGEBRA(FRAC(INT)) --R ?*? : (Fraction(Integer),%) -> % if Coef has ALGEBRA(FRAC(INT)) ---R ?*? : (NonNegativeInteger,%) -> % --R ?**? : (%,Fraction(Integer)) -> % if Coef has ALGEBRA(FRAC(INT)) --R ?**? : (%,%) -> % if Coef has ALGEBRA(FRAC(INT)) --R ?**? : (%,Coef) -> % if Coef has FIELD ---R ?**? : (%,NonNegativeInteger) -> % --R ?/? : (%,Coef) -> % if Coef has FIELD --R D : % -> % if Coef has *: (NonNegativeInteger,Coef) -> Coef --R D : (%,NonNegativeInteger) -> % if Coef has *: (NonNegativeInteger,Coef) -> Coef @@ -58623,7 +58907,6 @@ digraph pic { --R D : (%,List(Symbol)) -> % if Coef has PDRING(SYMBOL) and Coef has *: (NonNegativeInteger,Coef) -> Coef --R D : (%,Symbol,NonNegativeInteger) -> % if Coef has PDRING(SYMBOL) and Coef has *: (NonNegativeInteger,Coef) -> Coef --R D : (%,List(Symbol),List(NonNegativeInteger)) -> % if Coef has PDRING(SYMBOL) and Coef has *: (NonNegativeInteger,Coef) -> Coef ---R ?^? : (%,NonNegativeInteger) -> % --R acos : % -> % if Coef has ALGEBRA(FRAC(INT)) --R acosh : % -> % if Coef has ALGEBRA(FRAC(INT)) --R acot : % -> % if Coef has ALGEBRA(FRAC(INT)) @@ -58642,7 +58925,6 @@ digraph pic { --R charthRoot : % -> Union(%,"failed") if Coef has CHARNZ --R coefficient : (%,NonNegativeInteger) -> Coef --R coerce : Coef -> % if Coef has COMRING ---R coerce : % -> % if Coef has INTDOM --R coerce : Fraction(Integer) -> % if Coef has ALGEBRA(FRAC(INT)) --R cos : % -> % if Coef has ALGEBRA(FRAC(INT)) --R cosh : % -> % if Coef has ALGEBRA(FRAC(INT)) @@ -59365,7 +59647,7 @@ digraph pic { )set message auto off )clear all ---S 1 of 14 +--S 1 of 15 pi:Polynomial(Integer):=-3*x^3+2*x+13 --R --R @@ -59374,7 +59656,7 @@ pi:Polynomial(Integer):=-3*x^3+2*x+13 --R Type: Polynomial(Integer) --E 1 ---S 2 of 14 +--S 2 of 15 rootOf(pi) --R --R @@ -59382,7 +59664,7 @@ rootOf(pi) --R Type: AlgebraicNumber --E 2 ---S 3 of 14 +--S 3 of 15 rootsOf(pi) --R --R @@ -59390,7 +59672,7 @@ rootsOf(pi) --R Type: List(AlgebraicNumber) --E 3 ---S 4 of 14 +--S 4 of 15 zeroOf(pi) --R --R @@ -59398,7 +59680,7 @@ zeroOf(pi) --R Type: AlgebraicNumber --E 4 ---S 5 of 14 +--S 5 of 15 zerosOf(pi) --R --R @@ -59410,7 +59692,7 @@ zerosOf(pi) --R Type: List(AlgebraicNumber) --E 5 ---S 6 of 14 +--S 6 of 15 sup:SparseUnivariatePolynomial(Integer):=-3*x^3+2*x+13 --R --R @@ -59419,7 +59701,7 @@ sup:SparseUnivariatePolynomial(Integer):=-3*x^3+2*x+13 --R Type: SparseUnivariatePolynomial(Integer) --E 6 ---S 7 of 14 +--S 7 of 15 rootOf(sup) --R --R @@ -59427,7 +59709,7 @@ rootOf(sup) --R Type: AlgebraicNumber --E 7 ---S 8 of 14 +--S 8 of 15 rootOf(sup,x) --R --R @@ -59435,7 +59717,7 @@ rootOf(sup,x) --R Type: AlgebraicNumber --E 8 ---S 9 of 14 +--S 9 of 15 rootsOf(sup) --R --R @@ -59443,7 +59725,7 @@ rootsOf(sup) --R Type: List(AlgebraicNumber) --E 9 ---S 10 of 14 +--S 10 of 15 rootsOf(sup,x) --R --R @@ -59451,7 +59733,7 @@ rootsOf(sup,x) --R Type: List(AlgebraicNumber) --E 10 ---S 11 of 14 +--S 11 of 15 zeroOf(sup) --R --R @@ -59459,7 +59741,7 @@ zeroOf(sup) --R Type: AlgebraicNumber --E 11 ---S 12 of 14 +--S 12 of 15 zeroOf(sup,x) --R --R @@ -59467,7 +59749,7 @@ zeroOf(sup,x) --R Type: AlgebraicNumber --E 12 ---S 13 of 14 +--S 13 of 15 zerosOf(sup) --R --R @@ -59479,7 +59761,7 @@ zerosOf(sup) --R Type: List(AlgebraicNumber) --E 13 ---S 14 of 14 +--S 14 of 15 zerosOf(sup,x) --R --R @@ -59491,6 +59773,65 @@ zerosOf(sup,x) --R Type: List(AlgebraicNumber) --E 14 +--S 15 of 15 +)show AlgebraicallyClosedField +--R +--R AlgebraicallyClosedField is a category constructor +--R Abbreviation for AlgebraicallyClosedField is ACF +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for ACF +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (Fraction(Integer),%) -> % ?*? : (%,Fraction(Integer)) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,Fraction(Integer)) -> % ?**? : (%,Integer) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?/? : (%,%) -> % +--R ?=? : (%,%) -> Boolean 1 : () -> % +--R 0 : () -> % ?^? : (%,Integer) -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R associates? : (%,%) -> Boolean coerce : Fraction(Integer) -> % +--R coerce : % -> % coerce : Integer -> % +--R coerce : % -> OutputForm factor : % -> Factored(%) +--R gcd : List(%) -> % gcd : (%,%) -> % +--R hash : % -> SingleInteger inv : % -> % +--R latex : % -> String lcm : List(%) -> % +--R lcm : (%,%) -> % nthRoot : (%,Integer) -> % +--R one? : % -> Boolean prime? : % -> Boolean +--R ?quo? : (%,%) -> % recip : % -> Union(%,"failed") +--R ?rem? : (%,%) -> % rootOf : Polynomial(%) -> % +--R rootsOf : Polynomial(%) -> List(%) sample : () -> % +--R sizeLess? : (%,%) -> Boolean sqrt : % -> % +--R squareFree : % -> Factored(%) squareFreePart : % -> % +--R unit? : % -> Boolean unitCanonical : % -> % +--R zero? : % -> Boolean zeroOf : Polynomial(%) -> % +--R zerosOf : Polynomial(%) -> List(%) ?~=? : (%,%) -> Boolean +--R characteristic : () -> NonNegativeInteger +--R divide : (%,%) -> Record(quotient: %,remainder: %) +--R euclideanSize : % -> NonNegativeInteger +--R expressIdealMember : (List(%),%) -> Union(List(%),"failed") +--R exquo : (%,%) -> Union(%,"failed") +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) +--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) +--R lcmCoef : (%,%) -> Record(llcmres: %,coeff1: %,coeff2: %) +--R multiEuclidean : (List(%),%) -> Union(List(%),"failed") +--R principalIdeal : List(%) -> Record(coef: List(%),generator: %) +--R rootOf : (SparseUnivariatePolynomial(%),Symbol) -> % +--R rootOf : SparseUnivariatePolynomial(%) -> % +--R rootsOf : (SparseUnivariatePolynomial(%),Symbol) -> List(%) +--R rootsOf : SparseUnivariatePolynomial(%) -> List(%) +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) +--R zeroOf : (SparseUnivariatePolynomial(%),Symbol) -> % +--R zeroOf : SparseUnivariatePolynomial(%) -> % +--R zerosOf : (SparseUnivariatePolynomial(%),Symbol) -> List(%) +--R zerosOf : SparseUnivariatePolynomial(%) -> List(%) +--R +--E 15 + )spool )lisp (bye) \end{chunk} @@ -60027,30 +60368,39 @@ digraph pic { --R------------------------------- Operations -------------------------------- --R ?*? : (%,R) -> % ?*? : (R,%) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % ---R -? : % -> % ?=? : (%,%) -> Boolean ---R D : (%,(R -> R)) -> % D : % -> % if R has DIFRING +--R -? : % -> % ?/? : (%,R) -> % if R has FIELD +--R ?=? : (%,%) -> Boolean D : (%,(R -> R)) -> % +--R D : % -> % if R has DIFRING D : (%,V,NonNegativeInteger) -> % --R D : (%,List(V)) -> % D : (%,V) -> % --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % coefficient : (%,E) -> R ---R coefficients : % -> List(R) coerce : S -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R coefficient : (%,E) -> R coefficients : % -> List(R) +--R coerce : % -> % if R has INTDOM coerce : S -> % --R coerce : V -> % coerce : R -> % --R coerce : Integer -> % coerce : % -> OutputForm ---R degree : % -> E differentiate : (%,List(V)) -> % +--R content : % -> R if R has GCDDOM degree : % -> E +--R differentiate : (%,(R -> R)) -> % differentiate : (%,List(V)) -> % --R differentiate : (%,V) -> % eval : (%,List(V),List(%)) -> % --R eval : (%,V,%) -> % eval : (%,List(V),List(R)) -> % ---R eval : (%,V,R) -> % eval : (%,%,%) -> % ---R eval : (%,Equation(%)) -> % ground : % -> R +--R eval : (%,V,R) -> % eval : (%,List(%),List(%)) -> % +--R eval : (%,%,%) -> % eval : (%,Equation(%)) -> % +--R eval : (%,List(Equation(%))) -> % gcd : (%,%) -> % if R has GCDDOM +--R gcd : List(%) -> % if R has GCDDOM ground : % -> R --R ground? : % -> Boolean hash : % -> SingleInteger --R initial : % -> % isobaric? : % -> Boolean ---R latex : % -> String leader : % -> V +--R latex : % -> String lcm : (%,%) -> % if R has GCDDOM +--R lcm : List(%) -> % if R has GCDDOM leader : % -> V --R leadingCoefficient : % -> R leadingMonomial : % -> % --R map : ((R -> R),%) -> % mapExponents : ((E -> E),%) -> % +--R max : (%,%) -> % if R has ORDSET min : (%,%) -> % if R has ORDSET --R minimumDegree : % -> E monomial : (R,E) -> % --R monomial? : % -> Boolean monomials : % -> List(%) --R one? : % -> Boolean order : % -> NonNegativeInteger ---R pomopo! : (%,R,E,%) -> % recip : % -> Union(%,"failed") +--R order : (%,S) -> NonNegativeInteger pomopo! : (%,R,E,%) -> % +--R primitiveMonomials : % -> List(%) recip : % -> Union(%,"failed") --R reductum : % -> % retract : % -> S --R retract : % -> V retract : % -> R --R sample : () -> % separant : % -> % @@ -60058,9 +60408,6 @@ digraph pic { --R zero? : % -> Boolean ?~=? : (%,%) -> Boolean --R ?*? : (Fraction(Integer),%) -> % if R has ALGEBRA(FRAC(INT)) --R ?*? : (%,Fraction(Integer)) -> % if R has ALGEBRA(FRAC(INT)) ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R ?/? : (%,R) -> % if R has FIELD --R ? Boolean if R has ORDSET --R ?<=? : (%,%) -> Boolean if R has ORDSET --R ?>? : (%,%) -> Boolean if R has ORDSET @@ -60072,19 +60419,15 @@ digraph pic { --R D : (%,Symbol) -> % if R has PDRING(SYMBOL) --R D : (%,NonNegativeInteger) -> % if R has DIFRING --R D : (%,List(V),List(NonNegativeInteger)) -> % ---R D : (%,V,NonNegativeInteger) -> % ---R ?^? : (%,NonNegativeInteger) -> % --R associates? : (%,%) -> Boolean if R has INTDOM --R binomThmExpt : (%,%,NonNegativeInteger) -> % if R has COMRING --R characteristic : () -> NonNegativeInteger --R charthRoot : % -> Union(%,"failed") if and(has($,CharacteristicNonZero),has(R,PolynomialFactorizationExplicit)) or R has CHARNZ --R coefficient : (%,List(V),List(NonNegativeInteger)) -> % --R coefficient : (%,V,NonNegativeInteger) -> % ---R coerce : % -> % if R has INTDOM --R coerce : Fraction(Integer) -> % if R has RETRACT(FRAC(INT)) or R has ALGEBRA(FRAC(INT)) --R conditionP : Matrix(%) -> Union(Vector(%),"failed") if and(has($,CharacteristicNonZero),has(R,PolynomialFactorizationExplicit)) --R content : (%,V) -> % if R has GCDDOM ---R content : % -> R if R has GCDDOM --R convert : % -> InputForm if V has KONVERT(INFORM) and R has KONVERT(INFORM) --R convert : % -> Pattern(Integer) if V has KONVERT(PATTERN(INT)) and R has KONVERT(PATTERN(INT)) --R convert : % -> Pattern(Float) if V has KONVERT(PATTERN(FLOAT)) and R has KONVERT(PATTERN(FLOAT)) @@ -60092,7 +60435,6 @@ digraph pic { --R degree : (%,List(V)) -> List(NonNegativeInteger) --R degree : (%,V) -> NonNegativeInteger --R differentialVariables : % -> List(S) ---R differentiate : (%,(R -> R)) -> % --R differentiate : (%,(R -> R),NonNegativeInteger) -> % --R differentiate : (%,List(Symbol),List(NonNegativeInteger)) -> % if R has PDRING(SYMBOL) --R differentiate : (%,Symbol,NonNegativeInteger) -> % if R has PDRING(SYMBOL) @@ -60107,27 +60449,19 @@ digraph pic { --R eval : (%,S,R) -> % if R has DIFRING --R eval : (%,List(S),List(%)) -> % if R has DIFRING --R eval : (%,S,%) -> % if R has DIFRING ---R eval : (%,List(%),List(%)) -> % ---R eval : (%,List(Equation(%))) -> % --R exquo : (%,%) -> Union(%,"failed") if R has INTDOM --R exquo : (%,R) -> Union(%,"failed") if R has INTDOM --R factor : % -> Factored(%) if R has PFECAT --R factorPolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has PFECAT --R factorSquareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has PFECAT ---R gcd : (%,%) -> % if R has GCDDOM ---R gcd : List(%) -> % if R has GCDDOM --R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) if R has GCDDOM --R isExpt : % -> Union(Record(var: V,exponent: NonNegativeInteger),"failed") --R isPlus : % -> Union(List(%),"failed") --R isTimes : % -> Union(List(%),"failed") ---R lcm : (%,%) -> % if R has GCDDOM ---R lcm : List(%) -> % if R has GCDDOM --R lcmCoef : (%,%) -> Record(llcmres: %,coeff1: %,coeff2: %) if R has GCDDOM --R mainVariable : % -> Union(V,"failed") --R makeVariable : % -> (NonNegativeInteger -> %) if R has DIFRING --R makeVariable : S -> (NonNegativeInteger -> %) ---R max : (%,%) -> % if R has ORDSET ---R min : (%,%) -> % if R has ORDSET --R minimumDegree : (%,List(V)) -> List(NonNegativeInteger) --R minimumDegree : (%,V) -> NonNegativeInteger --R monicDivide : (%,%,V) -> Record(quotient: %,remainder: %) @@ -60136,11 +60470,9 @@ digraph pic { --R multivariate : (SparseUnivariatePolynomial(%),V) -> % --R multivariate : (SparseUnivariatePolynomial(R),V) -> % --R numberOfMonomials : % -> NonNegativeInteger ---R order : (%,S) -> NonNegativeInteger --R patternMatch : (%,Pattern(Integer),PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if V has PATMAB(INT) and R has PATMAB(INT) --R patternMatch : (%,Pattern(Float),PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if V has PATMAB(FLOAT) and R has PATMAB(FLOAT) --R prime? : % -> Boolean if R has PFECAT ---R primitiveMonomials : % -> List(%) --R primitivePart : (%,V) -> % if R has GCDDOM --R primitivePart : % -> % if R has GCDDOM --R reducedSystem : Matrix(%) -> Matrix(R) @@ -60932,29 +61264,27 @@ digraph pic { --R------------------------------- Operations -------------------------------- --R ?*? : (Fraction(Integer),%) -> % ?*? : (%,Fraction(Integer)) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,Integer) -> % ?**? : (%,NonNegativeInteger) -> % --R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % --R ?-? : (%,%) -> % -? : % -> % --R ?/? : (%,%) -> % ?=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % ---R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> % ---R associates? : (%,%) -> Boolean coerce : Fraction(Integer) -> % ---R coerce : % -> % coerce : Integer -> % ---R coerce : % -> OutputForm factor : % -> Factored(%) ---R gcd : List(%) -> % gcd : (%,%) -> % ---R hash : % -> SingleInteger inv : % -> % ---R latex : % -> String lcm : List(%) -> % ---R lcm : (%,%) -> % one? : % -> Boolean ---R prime? : % -> Boolean primeFrobenius : % -> % ---R ?quo? : (%,%) -> % recip : % -> Union(%,"failed") ---R ?rem? : (%,%) -> % sample : () -> % ---R sizeLess? : (%,%) -> Boolean squareFree : % -> Factored(%) ---R squareFreePart : % -> % unit? : % -> Boolean ---R unitCanonical : % -> % zero? : % -> Boolean ---R ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,Integer) -> % ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,PositiveInteger) -> % associates? : (%,%) -> Boolean +--R coerce : Fraction(Integer) -> % coerce : % -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R factor : % -> Factored(%) gcd : List(%) -> % +--R gcd : (%,%) -> % hash : % -> SingleInteger +--R inv : % -> % latex : % -> String +--R lcm : List(%) -> % lcm : (%,%) -> % +--R one? : % -> Boolean prime? : % -> Boolean +--R primeFrobenius : % -> % ?quo? : (%,%) -> % +--R recip : % -> Union(%,"failed") ?rem? : (%,%) -> % +--R sample : () -> % sizeLess? : (%,%) -> Boolean +--R squareFree : % -> Factored(%) squareFreePart : % -> % +--R unit? : % -> Boolean unitCanonical : % -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean --R characteristic : () -> NonNegativeInteger --R charthRoot : % -> Union(%,"failed") --R discreteLog : (%,%) -> Union(NonNegativeInteger,"failed") @@ -61251,11 +61581,13 @@ digraph pic { --R------------------------------- Operations -------------------------------- --R ?*? : (R,%) -> % ?*? : (%,R) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ?=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % coerce : R -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R characteristicPolynomial : % -> UP coerce : R -> % --R coerce : Integer -> % coerce : % -> OutputForm --R discriminant : Vector(%) -> R hash : % -> SingleInteger --R latex : % -> String norm : % -> R @@ -61263,11 +61595,7 @@ digraph pic { --R recip : % -> Union(%,"failed") sample : () -> % --R trace : % -> R zero? : % -> Boolean --R ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R ?^? : (%,NonNegativeInteger) -> % --R characteristic : () -> NonNegativeInteger ---R characteristicPolynomial : % -> UP --R charthRoot : % -> Union(%,"failed") if R has CHARNZ --R coordinates : (Vector(%),Vector(%)) -> Matrix(R) --R coordinates : (%,Vector(%)) -> Vector(R) @@ -61565,61 +61893,63 @@ digraph pic { --R Issue )edit bookvol10.2.pamphlet to see algebra source code for FS --R --R------------------------------- Operations -------------------------------- ---R -? : % -> % if R has ABELGRP ? Boolean ---R ?<=? : (%,%) -> Boolean ?=? : (%,%) -> Boolean ---R ?>? : (%,%) -> Boolean ?>=? : (%,%) -> Boolean +--R ?*? : (%,%) -> % if R has SGROUP ?*? : (%,R) -> % if R has COMRING +--R ?*? : (R,%) -> % if R has COMRING ?+? : (%,%) -> % if R has ABELSG +--R -? : % -> % if R has ABELGRP ?-? : (%,%) -> % if R has ABELGRP +--R ? Boolean ?<=? : (%,%) -> Boolean +--R ?=? : (%,%) -> Boolean ?>? : (%,%) -> Boolean +--R ?>=? : (%,%) -> Boolean D : (%,Symbol) -> % if R has RING --R 1 : () -> % if R has SGROUP 0 : () -> % if R has ABELSG +--R applyQuote : (Symbol,List(%)) -> % applyQuote : (Symbol,%,%,%) -> % --R applyQuote : (Symbol,%,%) -> % applyQuote : (Symbol,%) -> % --R belong? : BasicOperator -> Boolean box : List(%) -> % ---R box : % -> % coerce : R -> % ---R coerce : Symbol -> % coerce : Kernel(%) -> % ---R coerce : % -> OutputForm distribute : (%,%) -> % ---R distribute : % -> % elt : (BasicOperator,%,%) -> % ---R elt : (BasicOperator,%) -> % eval : (%,%,%) -> % ---R eval : (%,Equation(%)) -> % eval : (%,Kernel(%),%) -> % +--R box : % -> % coerce : % -> % if R has INTDOM +--R coerce : R -> % coerce : Symbol -> % +--R coerce : Kernel(%) -> % coerce : % -> OutputForm +--R distribute : (%,%) -> % distribute : % -> % +--R elt : (BasicOperator,List(%)) -> % elt : (BasicOperator,%,%,%) -> % +--R elt : (BasicOperator,%,%) -> % elt : (BasicOperator,%) -> % +--R eval : (%,Symbol,(% -> %)) -> % eval : (%,List(%),List(%)) -> % +--R eval : (%,%,%) -> % eval : (%,Equation(%)) -> % +--R eval : (%,List(Equation(%))) -> % eval : (%,Kernel(%),%) -> % --R freeOf? : (%,Symbol) -> Boolean freeOf? : (%,%) -> Boolean +--R gcd : (%,%) -> % if R has INTDOM gcd : List(%) -> % if R has INTDOM --R ground : % -> R ground? : % -> Boolean --R hash : % -> SingleInteger height : % -> NonNegativeInteger ---R is? : (%,Symbol) -> Boolean kernel : (BasicOperator,%) -> % ---R kernels : % -> List(Kernel(%)) latex : % -> String +--R is? : (%,Symbol) -> Boolean is? : (%,BasicOperator) -> Boolean +--R kernel : (BasicOperator,%) -> % kernels : % -> List(Kernel(%)) +--R latex : % -> String lcm : (%,%) -> % if R has INTDOM +--R lcm : List(%) -> % if R has INTDOM map : ((% -> %),Kernel(%)) -> % --R max : (%,%) -> % min : (%,%) -> % +--R numerator : % -> % if R has RING one? : % -> Boolean if R has SGROUP --R paren : List(%) -> % paren : % -> % --R retract : % -> R retract : % -> Symbol --R retract : % -> Kernel(%) subst : (%,Equation(%)) -> % --R tower : % -> List(Kernel(%)) variables : % -> List(Symbol) --R ?~=? : (%,%) -> Boolean ---R ?*? : (%,%) -> % if R has SGROUP --R ?*? : (PositiveInteger,%) -> % if R has ABELSG --R ?*? : (NonNegativeInteger,%) -> % if R has ABELSG --R ?*? : (Integer,%) -> % if R has ABELGRP ---R ?*? : (%,R) -> % if R has COMRING ---R ?*? : (R,%) -> % if R has COMRING --R ?*? : (%,Fraction(Integer)) -> % if R has INTDOM --R ?*? : (Fraction(Integer),%) -> % if R has INTDOM --R ?**? : (%,PositiveInteger) -> % if R has SGROUP --R ?**? : (%,NonNegativeInteger) -> % if R has SGROUP --R ?**? : (%,Integer) -> % if R has GROUP or R has INTDOM ---R ?+? : (%,%) -> % if R has ABELSG ---R ?-? : (%,%) -> % if R has ABELGRP --R ?/? : (%,%) -> % if R has GROUP or R has INTDOM --R ?/? : (SparseMultivariatePolynomial(R,Kernel(%)),SparseMultivariatePolynomial(R,Kernel(%))) -> % if R has INTDOM ---R D : (%,Symbol) -> % if R has RING --R D : (%,List(Symbol)) -> % if R has RING --R D : (%,Symbol,NonNegativeInteger) -> % if R has RING --R D : (%,List(Symbol),List(NonNegativeInteger)) -> % if R has RING --R ?^? : (%,PositiveInteger) -> % if R has SGROUP --R ?^? : (%,NonNegativeInteger) -> % if R has SGROUP --R ?^? : (%,Integer) -> % if R has GROUP or R has INTDOM ---R applyQuote : (Symbol,List(%)) -> % --R applyQuote : (Symbol,%,%,%,%) -> % ---R applyQuote : (Symbol,%,%,%) -> % --R associates? : (%,%) -> Boolean if R has INTDOM --R characteristic : () -> NonNegativeInteger if R has RING --R charthRoot : % -> Union(%,"failed") if R has CHARNZ --R coerce : Integer -> % if R has RING or R has RETRACT(INT) --R coerce : Fraction(Integer) -> % if R has INTDOM or R has RETRACT(INT) and R has INTDOM or R has RETRACT(FRAC(INT)) --R coerce : Polynomial(R) -> % if R has RING ---R coerce : % -> % if R has INTDOM --R coerce : Fraction(Polynomial(R)) -> % if R has INTDOM --R coerce : Fraction(Polynomial(Fraction(R))) -> % if R has INTDOM --R coerce : Polynomial(Fraction(R)) -> % if R has INTDOM @@ -61639,9 +61969,7 @@ digraph pic { --R differentiate : (%,Symbol,NonNegativeInteger) -> % if R has RING --R differentiate : (%,List(Symbol),List(NonNegativeInteger)) -> % if R has RING --R divide : (%,%) -> Record(quotient: %,remainder: %) if R has INTDOM ---R elt : (BasicOperator,List(%)) -> % --R elt : (BasicOperator,%,%,%,%) -> % ---R elt : (BasicOperator,%,%,%) -> % --R euclideanSize : % -> NonNegativeInteger if R has INTDOM --R eval : (%,Symbol,NonNegativeInteger,(% -> %)) -> % if R has RING --R eval : (%,Symbol,NonNegativeInteger,(List(%) -> %)) -> % if R has RING @@ -61656,12 +61984,9 @@ digraph pic { --R eval : (%,BasicOperator,(List(%) -> %)) -> % --R eval : (%,List(BasicOperator),List((List(%) -> %))) -> % --R eval : (%,List(BasicOperator),List((% -> %))) -> % ---R eval : (%,Symbol,(% -> %)) -> % --R eval : (%,Symbol,(List(%) -> %)) -> % --R eval : (%,List(Symbol),List((List(%) -> %))) -> % --R eval : (%,List(Symbol),List((% -> %))) -> % ---R eval : (%,List(%),List(%)) -> % ---R eval : (%,List(Equation(%))) -> % --R eval : (%,List(Kernel(%)),List(%)) -> % --R even? : % -> Boolean if $ has RETRACT(INT) --R expressIdealMember : (List(%),%) -> Union(List(%),"failed") if R has INTDOM @@ -61669,11 +61994,8 @@ digraph pic { --R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) if R has INTDOM --R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") if R has INTDOM --R factor : % -> Factored(%) if R has INTDOM ---R gcd : (%,%) -> % if R has INTDOM ---R gcd : List(%) -> % if R has INTDOM --R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) if R has INTDOM --R inv : % -> % if R has GROUP or R has INTDOM ---R is? : (%,BasicOperator) -> Boolean --R isExpt : (%,Symbol) -> Union(Record(var: Kernel(%),exponent: Integer),"failed") if R has RING --R isExpt : (%,BasicOperator) -> Union(Record(var: Kernel(%),exponent: Integer),"failed") if R has RING --R isExpt : % -> Union(Record(var: Kernel(%),exponent: Integer),"failed") if R has SGROUP @@ -61682,17 +62004,12 @@ digraph pic { --R isPower : % -> Union(Record(val: %,exponent: Integer),"failed") if R has RING --R isTimes : % -> Union(List(%),"failed") if R has SGROUP --R kernel : (BasicOperator,List(%)) -> % ---R lcm : (%,%) -> % if R has INTDOM ---R lcm : List(%) -> % if R has INTDOM --R lcmCoef : (%,%) -> Record(llcmres: %,coeff1: %,coeff2: %) if R has INTDOM --R mainKernel : % -> Union(Kernel(%),"failed") ---R map : ((% -> %),Kernel(%)) -> % --R minPoly : Kernel(%) -> SparseUnivariatePolynomial(%) if $ has RING --R multiEuclidean : (List(%),%) -> Union(List(%),"failed") if R has INTDOM --R numer : % -> SparseMultivariatePolynomial(R,Kernel(%)) if R has RING ---R numerator : % -> % if R has RING --R odd? : % -> Boolean if $ has RETRACT(INT) ---R one? : % -> Boolean if R has SGROUP --R operator : BasicOperator -> BasicOperator --R operators : % -> List(BasicOperator) --R patternMatch : (%,Pattern(Float),PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if R has PATMAB(FLOAT) @@ -63018,6 +63335,7 @@ digraph pic { --S 1 of 1 )show InfinitlyClosePointCategory +--R --I InfinitlyClosePointCategory(K: Field, --I symb: List Symbol, --I PolyRing: PolynomialCategory(t#1,t#4,OrderedVariableList t#2), @@ -63285,32 +63603,31 @@ digraph pic { --R------------------------------- Operations -------------------------------- --R ?*? : (Fraction(Integer),%) -> % ?*? : (%,Fraction(Integer)) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,Integer) -> % ?**? : (%,NonNegativeInteger) -> % --R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % --R ?-? : (%,%) -> % -? : % -> % --R ?/? : (%,%) -> % ?=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % ---R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> % ---R associates? : (%,%) -> Boolean coerce : Fraction(Integer) -> % ---R coerce : % -> % coerce : Integer -> % ---R coerce : % -> OutputForm conjugate : % -> % ---R extDegree : % -> PositiveInteger factor : % -> Factored(%) ---R fullOutput : % -> OutputForm gcd : List(%) -> % ---R gcd : (%,%) -> % ground? : % -> Boolean ---R hash : % -> SingleInteger inv : % -> % ---R latex : % -> String lcm : List(%) -> % ---R lcm : (%,%) -> % maxTower : List(%) -> % ---R one? : % -> Boolean previousTower : % -> % ---R prime? : % -> Boolean ?quo? : (%,%) -> % ---R recip : % -> Union(%,"failed") ?rem? : (%,%) -> % ---R sample : () -> % setTower! : % -> Void ---R sizeLess? : (%,%) -> Boolean squareFree : % -> Factored(%) ---R squareFreePart : % -> % unit? : % -> Boolean ---R unitCanonical : % -> % vectorise : (%,%) -> Vector(%) ---R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,Integer) -> % ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,PositiveInteger) -> % associates? : (%,%) -> Boolean +--R coerce : Fraction(Integer) -> % coerce : % -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R conjugate : % -> % extDegree : % -> PositiveInteger +--R factor : % -> Factored(%) fullOutput : % -> OutputForm +--R gcd : List(%) -> % gcd : (%,%) -> % +--R ground? : % -> Boolean hash : % -> SingleInteger +--R inv : % -> % latex : % -> String +--R lcm : List(%) -> % lcm : (%,%) -> % +--R maxTower : List(%) -> % one? : % -> Boolean +--R previousTower : % -> % prime? : % -> Boolean +--R ?quo? : (%,%) -> % recip : % -> Union(%,"failed") +--R ?rem? : (%,%) -> % sample : () -> % +--R setTower! : % -> Void sizeLess? : (%,%) -> Boolean +--R squareFree : % -> Factored(%) squareFreePart : % -> % +--R unit? : % -> Boolean unitCanonical : % -> % +--R vectorise : (%,%) -> Vector(%) zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean --R characteristic : () -> NonNegativeInteger --R definingPolynomial : % -> SparseUnivariatePolynomial(%) --R definingPolynomial : () -> SparseUnivariatePolynomial(%) @@ -63664,24 +63981,28 @@ digraph pic { --R ?*? : (%,S) -> % ?*? : (S,%) -> % --R ?*? : (Fraction(Integer),%) -> % ?*? : (%,Fraction(Integer)) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,Integer) -> % ?**? : (%,NonNegativeInteger) -> % --R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % --R ?-? : (%,%) -> % -? : % -> % --R ?/? : (S,S) -> % ?/? : (%,%) -> % --R ?=? : (%,%) -> Boolean D : (%,(S -> S)) -> % --R D : % -> % if S has DIFRING 1 : () -> % --R 0 : () -> % ?^? : (%,Integer) -> % ---R ?^? : (%,PositiveInteger) -> % associates? : (%,%) -> Boolean +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R abs : % -> % if S has OINTDOM associates? : (%,%) -> Boolean --R ceiling : % -> S if S has INS coerce : S -> % --R coerce : Fraction(Integer) -> % coerce : % -> % --R coerce : Integer -> % coerce : % -> OutputForm ---R denom : % -> S denominator : % -> % +--R convert : % -> Float if S has REAL denom : % -> S +--R denominator : % -> % differentiate : (%,(S -> S)) -> % --R factor : % -> Factored(%) floor : % -> S if S has INS --R gcd : List(%) -> % gcd : (%,%) -> % --R hash : % -> SingleInteger init : () -> % if S has STEP --R inv : % -> % latex : % -> String --R lcm : List(%) -> % lcm : (%,%) -> % ---R map : ((S -> S),%) -> % numer : % -> S +--R map : ((S -> S),%) -> % max : (%,%) -> % if S has ORDSET +--R min : (%,%) -> % if S has ORDSET numer : % -> S --R numerator : % -> % one? : % -> Boolean --R prime? : % -> Boolean ?quo? : (%,%) -> % --R random : () -> % if S has INS recip : % -> Union(%,"failed") @@ -63689,9 +64010,8 @@ digraph pic { --R sample : () -> % sizeLess? : (%,%) -> Boolean --R squareFree : % -> Factored(%) squareFreePart : % -> % --R unit? : % -> Boolean unitCanonical : % -> % ---R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % +--R wholePart : % -> S if S has EUCDOM zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean --R ? Boolean if S has ORDSET --R ?<=? : (%,%) -> Boolean if S has ORDSET --R ?>? : (%,%) -> Boolean if S has ORDSET @@ -63702,18 +64022,14 @@ digraph pic { --R D : (%,List(Symbol)) -> % if S has PDRING(SYMBOL) --R D : (%,Symbol) -> % if S has PDRING(SYMBOL) --R D : (%,NonNegativeInteger) -> % if S has DIFRING ---R ?^? : (%,NonNegativeInteger) -> % ---R abs : % -> % if S has OINTDOM --R characteristic : () -> NonNegativeInteger --R charthRoot : % -> Union(%,"failed") if S has CHARNZ or and(has($,CharacteristicNonZero),has(S,PolynomialFactorizationExplicit)) --R coerce : Symbol -> % if S has RETRACT(SYMBOL) --R conditionP : Matrix(%) -> Union(Vector(%),"failed") if and(has($,CharacteristicNonZero),has(S,PolynomialFactorizationExplicit)) --R convert : % -> DoubleFloat if S has REAL ---R convert : % -> Float if S has REAL --R convert : % -> InputForm if S has KONVERT(INFORM) --R convert : % -> Pattern(Float) if S has KONVERT(PATTERN(FLOAT)) --R convert : % -> Pattern(Integer) if S has KONVERT(PATTERN(INT)) ---R differentiate : (%,(S -> S)) -> % --R differentiate : (%,(S -> S),NonNegativeInteger) -> % --R differentiate : (%,List(Symbol),List(NonNegativeInteger)) -> % if S has PDRING(SYMBOL) --R differentiate : (%,Symbol,NonNegativeInteger) -> % if S has PDRING(SYMBOL) @@ -63739,8 +64055,6 @@ digraph pic { --R fractionPart : % -> % if S has EUCDOM --R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) --R lcmCoef : (%,%) -> Record(llcmres: %,coeff1: %,coeff2: %) ---R max : (%,%) -> % if S has ORDSET ---R min : (%,%) -> % if S has ORDSET --R multiEuclidean : (List(%),%) -> Union(List(%),"failed") --R negative? : % -> Boolean if S has OINTDOM --R nextItem : % -> Union(%,"failed") if S has STEP @@ -63764,7 +64078,6 @@ digraph pic { --R squareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if S has PFECAT --R subtractIfCan : (%,%) -> Union(%,"failed") --R unitNormal : % -> Record(unit: %,canonical: %,associate: %) ---R wholePart : % -> S if S has EUCDOM --R --E 1 @@ -64366,14 +64679,16 @@ digraph pic { --R ?*? : (%,Integer) -> % ?*? : (Integer,%) -> % --R ?*? : (%,Fraction(Integer)) -> % ?*? : (Fraction(Integer),%) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % ---R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % ---R ?-? : (%,%) -> % -? : % -> % ---R ?/? : (%,%) -> % ? Boolean ---R ?<=? : (%,%) -> Boolean ?=? : (%,%) -> Boolean ---R ?>? : (%,%) -> Boolean ?>=? : (%,%) -> Boolean ---R 1 : () -> % 0 : () -> % ---R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,Fraction(Integer)) -> % ?**? : (%,Integer) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?/? : (%,%) -> % +--R ? Boolean ?<=? : (%,%) -> Boolean +--R ?=? : (%,%) -> Boolean ?>? : (%,%) -> Boolean +--R ?>=? : (%,%) -> Boolean 1 : () -> % +--R 0 : () -> % ?^? : (%,Integer) -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % --R abs : % -> % associates? : (%,%) -> Boolean --R coerce : Fraction(Integer) -> % coerce : Integer -> % --R coerce : Fraction(Integer) -> % coerce : % -> % @@ -64391,14 +64706,11 @@ digraph pic { --R rename! : (%,OutputForm) -> % retract : % -> Fraction(Integer) --R sample : () -> % sign : % -> Integer --R sizeLess? : (%,%) -> Boolean sqrt : Integer -> % ---R sqrt : Fraction(Integer) -> % sqrt : % -> % ---R squareFree : % -> Factored(%) squareFreePart : % -> % ---R unit? : % -> Boolean unitCanonical : % -> % ---R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,Fraction(Integer)) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R ?^? : (%,NonNegativeInteger) -> % +--R sqrt : Fraction(Integer) -> % sqrt : (%,NonNegativeInteger) -> % +--R sqrt : % -> % squareFree : % -> Factored(%) +--R squareFreePart : % -> % unit? : % -> Boolean +--R unitCanonical : % -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean --R allRootsOf : Polynomial(Integer) -> List(%) --R allRootsOf : Polynomial(Fraction(Integer)) -> List(%) --R allRootsOf : Polynomial(%) -> List(%) @@ -64427,7 +64739,6 @@ digraph pic { --R retractIfCan : % -> Union(Integer,"failed") if Fraction(Integer) has RETRACT(INT) --R rootOf : (SparseUnivariatePolynomial(%),PositiveInteger) -> Union(%,"failed") --R rootOf : (SparseUnivariatePolynomial(%),PositiveInteger,OutputForm) -> Union(%,"failed") ---R sqrt : (%,NonNegativeInteger) -> % --R subtractIfCan : (%,%) -> Union(%,"failed") --R unitNormal : % -> Record(unit: %,canonical: %,associate: %) --R @@ -64915,14 +65226,16 @@ digraph pic { --R------------------------------- Operations -------------------------------- --R ?*? : (Fraction(Integer),%) -> % ?*? : (%,Fraction(Integer)) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % ---R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % ---R ?-? : (%,%) -> % -? : % -> % ---R ?/? : (%,%) -> % ? Boolean ---R ?<=? : (%,%) -> Boolean ?=? : (%,%) -> Boolean ---R ?>? : (%,%) -> Boolean ?>=? : (%,%) -> Boolean ---R 1 : () -> % 0 : () -> % ---R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,Fraction(Integer)) -> % ?**? : (%,Integer) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?/? : (%,%) -> % +--R ? Boolean ?<=? : (%,%) -> Boolean +--R ?=? : (%,%) -> Boolean ?>? : (%,%) -> Boolean +--R ?>=? : (%,%) -> Boolean 1 : () -> % +--R 0 : () -> % ?^? : (%,Integer) -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % --R abs : % -> % associates? : (%,%) -> Boolean --R ceiling : % -> % coerce : Fraction(Integer) -> % --R coerce : Integer -> % coerce : Fraction(Integer) -> % @@ -64947,10 +65260,6 @@ digraph pic { --R truncate : % -> % unit? : % -> Boolean --R unitCanonical : % -> % wholePart : % -> Integer --R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,Fraction(Integer)) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R ?^? : (%,NonNegativeInteger) -> % --R characteristic : () -> NonNegativeInteger --R divide : (%,%) -> Record(quotient: %,remainder: %) --R euclideanSize : % -> NonNegativeInteger @@ -65351,20 +65660,26 @@ digraph pic { --R------------------------------- Operations -------------------------------- --R ?*? : (%,R) -> % ?*? : (R,%) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % ---R -? : % -> % ?=? : (%,%) -> Boolean +--R -? : % -> % ?/? : (%,R) -> % if R has FIELD +--R ?=? : (%,%) -> Boolean D : (%,V,NonNegativeInteger) -> % --R D : (%,List(V)) -> % D : (%,V) -> % --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % coefficient : (%,E) -> R ---R coefficients : % -> List(R) coerce : V -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R coefficient : (%,E) -> R coefficients : % -> List(R) +--R coerce : % -> % if R has INTDOM coerce : V -> % --R coerce : R -> % coerce : Integer -> % ---R coerce : % -> OutputForm deepestInitial : % -> % ---R deepestTail : % -> % degree : % -> E ---R differentiate : (%,List(V)) -> % differentiate : (%,V) -> % ---R eval : (%,List(V),List(%)) -> % eval : (%,V,%) -> % ---R eval : (%,List(V),List(R)) -> % eval : (%,V,R) -> % +--R coerce : % -> OutputForm content : % -> R if R has GCDDOM +--R deepestInitial : % -> % deepestTail : % -> % +--R degree : % -> E differentiate : (%,List(V)) -> % +--R differentiate : (%,V) -> % eval : (%,List(V),List(%)) -> % +--R eval : (%,V,%) -> % eval : (%,List(V),List(R)) -> % +--R eval : (%,V,R) -> % eval : (%,List(%),List(%)) -> % --R eval : (%,%,%) -> % eval : (%,Equation(%)) -> % +--R eval : (%,List(Equation(%))) -> % gcd : (%,%) -> % if R has GCDDOM +--R gcd : List(%) -> % if R has GCDDOM gcd : (R,%) -> R if R has GCDDOM --R ground : % -> R ground? : % -> Boolean --R hash : % -> SingleInteger head : % -> % --R headReduce : (%,%) -> % headReduced? : (%,%) -> Boolean @@ -65372,20 +65687,23 @@ digraph pic { --R initiallyReduce : (%,%) -> % iteratedInitials : % -> List(%) --R latex : % -> String lazyPquo : (%,%,V) -> % --R lazyPquo : (%,%) -> % lazyPrem : (%,%,V) -> % ---R lazyPrem : (%,%) -> % leadingCoefficient : (%,V) -> % +--R lazyPrem : (%,%) -> % lcm : (%,%) -> % if R has GCDDOM +--R lcm : List(%) -> % if R has GCDDOM leadingCoefficient : (%,V) -> % --R leadingCoefficient : % -> R leadingMonomial : % -> % --R leastMonomial : % -> % mainCoefficients : % -> List(%) --R mainMonomial : % -> % mainMonomials : % -> List(%) --R map : ((R -> R),%) -> % mapExponents : ((E -> E),%) -> % ---R mdeg : % -> NonNegativeInteger minimumDegree : % -> E +--R max : (%,%) -> % if R has ORDSET mdeg : % -> NonNegativeInteger +--R min : (%,%) -> % if R has ORDSET minimumDegree : % -> E --R monic? : % -> Boolean monicModulo : (%,%) -> % --R monomial : (R,E) -> % monomial? : % -> Boolean --R monomials : % -> List(%) mvar : % -> V --R normalized? : (%,%) -> Boolean one? : % -> Boolean --R pomopo! : (%,R,E,%) -> % pquo : (%,%,V) -> % --R pquo : (%,%) -> % prem : (%,%,V) -> % ---R prem : (%,%) -> % quasiMonic? : % -> Boolean ---R recip : % -> Union(%,"failed") reduced? : (%,%) -> Boolean +--R prem : (%,%) -> % primitiveMonomials : % -> List(%) +--R quasiMonic? : % -> Boolean recip : % -> Union(%,"failed") +--R reduced? : (%,List(%)) -> Boolean reduced? : (%,%) -> Boolean --R reductum : (%,V) -> % reductum : % -> % --R retract : % -> V retract : % -> R --R sample : () -> % supRittWu? : (%,%) -> Boolean @@ -65393,31 +65711,24 @@ digraph pic { --R zero? : % -> Boolean ?~=? : (%,%) -> Boolean --R ?*? : (Fraction(Integer),%) -> % if R has ALGEBRA(FRAC(INT)) --R ?*? : (%,Fraction(Integer)) -> % if R has ALGEBRA(FRAC(INT)) ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R ?/? : (%,R) -> % if R has FIELD --R ? Boolean if R has ORDSET --R ?<=? : (%,%) -> Boolean if R has ORDSET --R ?>? : (%,%) -> Boolean if R has ORDSET --R ?>=? : (%,%) -> Boolean if R has ORDSET --R D : (%,List(V),List(NonNegativeInteger)) -> % ---R D : (%,V,NonNegativeInteger) -> % --R LazardQuotient : (%,%,NonNegativeInteger) -> % if R has INTDOM --R LazardQuotient2 : (%,%,%,NonNegativeInteger) -> % if R has INTDOM --R RittWuCompare : (%,%) -> Union(Boolean,"failed") ---R ?^? : (%,NonNegativeInteger) -> % --R associates? : (%,%) -> Boolean if R has INTDOM --R binomThmExpt : (%,%,NonNegativeInteger) -> % if R has COMRING --R characteristic : () -> NonNegativeInteger --R charthRoot : % -> Union(%,"failed") if and(has($,CharacteristicNonZero),has(R,PolynomialFactorizationExplicit)) or R has CHARNZ --R coefficient : (%,List(V),List(NonNegativeInteger)) -> % --R coefficient : (%,V,NonNegativeInteger) -> % ---R coerce : % -> % if R has INTDOM --R coerce : Fraction(Integer) -> % if R has RETRACT(FRAC(INT)) or R has ALGEBRA(FRAC(INT)) --R coerce : % -> Polynomial(R) if V has KONVERT(SYMBOL) --R conditionP : Matrix(%) -> Union(Vector(%),"failed") if and(has($,CharacteristicNonZero),has(R,PolynomialFactorizationExplicit)) --R content : (%,V) -> % if R has GCDDOM ---R content : % -> R if R has GCDDOM --R convert : % -> Polynomial(R) if V has KONVERT(SYMBOL) --R convert : % -> String if R has RETRACT(INT) and V has KONVERT(SYMBOL) --R convert : Polynomial(R) -> % if V has KONVERT(SYMBOL) @@ -65431,8 +65742,6 @@ digraph pic { --R differentiate : (%,List(V),List(NonNegativeInteger)) -> % --R differentiate : (%,V,NonNegativeInteger) -> % --R discriminant : (%,V) -> % if R has COMRING ---R eval : (%,List(%),List(%)) -> % ---R eval : (%,List(Equation(%))) -> % --R exactQuotient : (%,%) -> % if R has INTDOM --R exactQuotient : (%,R) -> % if R has INTDOM --R exactQuotient! : (%,%) -> % if R has INTDOM @@ -65443,9 +65752,6 @@ digraph pic { --R factor : % -> Factored(%) if R has PFECAT --R factorPolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has PFECAT --R factorSquareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has PFECAT ---R gcd : (%,%) -> % if R has GCDDOM ---R gcd : List(%) -> % if R has GCDDOM ---R gcd : (R,%) -> R if R has GCDDOM --R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) if R has GCDDOM --R halfExtendedSubResultantGcd1 : (%,%) -> Record(gcd: %,coef1: %) if R has INTDOM --R halfExtendedSubResultantGcd2 : (%,%) -> Record(gcd: %,coef2: %) if R has INTDOM @@ -65461,15 +65767,11 @@ digraph pic { --R lazyPseudoDivide : (%,%,V) -> Record(coef: %,gap: NonNegativeInteger,quotient: %,remainder: %) --R lazyPseudoDivide : (%,%) -> Record(coef: %,gap: NonNegativeInteger,quotient: %,remainder: %) --R lazyResidueClass : (%,%) -> Record(polnum: %,polden: %,power: NonNegativeInteger) ---R lcm : (%,%) -> % if R has GCDDOM ---R lcm : List(%) -> % if R has GCDDOM --R lcmCoef : (%,%) -> Record(llcmres: %,coeff1: %,coeff2: %) if R has GCDDOM --R mainContent : % -> % if R has GCDDOM --R mainPrimitivePart : % -> % if R has GCDDOM --R mainSquareFreePart : % -> % if R has GCDDOM --R mainVariable : % -> Union(V,"failed") ---R max : (%,%) -> % if R has ORDSET ---R min : (%,%) -> % if R has ORDSET --R minimumDegree : (%,List(V)) -> List(NonNegativeInteger) --R minimumDegree : (%,V) -> NonNegativeInteger --R monicDivide : (%,%,V) -> Record(quotient: %,remainder: %) @@ -65485,12 +65787,10 @@ digraph pic { --R primPartElseUnitCanonical : % -> % if R has INTDOM --R primPartElseUnitCanonical! : % -> % if R has INTDOM --R prime? : % -> Boolean if R has PFECAT ---R primitiveMonomials : % -> List(%) --R primitivePart : (%,V) -> % if R has GCDDOM --R primitivePart : % -> % if R has GCDDOM --R primitivePart! : % -> % if R has GCDDOM --R pseudoDivide : (%,%) -> Record(quotient: %,remainder: %) ---R reduced? : (%,List(%)) -> Boolean --R reducedSystem : Matrix(%) -> Matrix(R) --R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(R),vec: Vector(R)) --R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(Integer),vec: Vector(Integer)) if R has LINEXP(INT) @@ -67333,31 +67633,31 @@ digraph pic { --R------------------------------- Operations -------------------------------- --R ?*? : (Coef,%) -> % ?*? : (%,Coef) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ?=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % center : % -> Coef ---R coefficient : (%,Integer) -> Coef coerce : Integer -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R center : % -> Coef coefficient : (%,Integer) -> Coef +--R coerce : % -> % if Coef has INTDOM coerce : Integer -> % --R coerce : % -> OutputForm complete : % -> % --R degree : % -> Integer ?.? : (%,Integer) -> Coef --R extend : (%,Integer) -> % hash : % -> SingleInteger ---R latex : % -> String leadingCoefficient : % -> Coef ---R leadingMonomial : % -> % map : ((Coef -> Coef),%) -> % ---R monomial : (Coef,Integer) -> % monomial? : % -> Boolean ---R one? : % -> Boolean order : (%,Integer) -> Integer ---R order : % -> Integer pole? : % -> Boolean ---R recip : % -> Union(%,"failed") reductum : % -> % ---R sample : () -> % truncate : (%,Integer) -> % ---R variable : % -> Symbol zero? : % -> Boolean ---R ?~=? : (%,%) -> Boolean +--R inv : % -> % if Coef has FIELD latex : % -> String +--R leadingCoefficient : % -> Coef leadingMonomial : % -> % +--R map : ((Coef -> Coef),%) -> % monomial : (Coef,Integer) -> % +--R monomial? : % -> Boolean one? : % -> Boolean +--R order : (%,Integer) -> Integer order : % -> Integer +--R pole? : % -> Boolean recip : % -> Union(%,"failed") +--R reductum : % -> % sample : () -> % +--R truncate : (%,Integer) -> % variable : % -> Symbol +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean --R ?*? : (%,Fraction(Integer)) -> % if Coef has ALGEBRA(FRAC(INT)) --R ?*? : (Fraction(Integer),%) -> % if Coef has ALGEBRA(FRAC(INT)) ---R ?*? : (NonNegativeInteger,%) -> % --R ?**? : (%,Fraction(Integer)) -> % if Coef has ALGEBRA(FRAC(INT)) --R ?**? : (%,%) -> % if Coef has ALGEBRA(FRAC(INT)) --R ?**? : (%,Integer) -> % if Coef has FIELD ---R ?**? : (%,NonNegativeInteger) -> % --R ?/? : (%,%) -> % if Coef has FIELD --R ?/? : (%,Coef) -> % if Coef has FIELD --R D : % -> % if Coef has *: (Integer,Coef) -> Coef @@ -67367,7 +67667,6 @@ digraph pic { --R D : (%,Symbol,NonNegativeInteger) -> % if Coef has PDRING(SYMBOL) and Coef has *: (Integer,Coef) -> Coef --R D : (%,List(Symbol),List(NonNegativeInteger)) -> % if Coef has PDRING(SYMBOL) and Coef has *: (Integer,Coef) -> Coef --R ?^? : (%,Integer) -> % if Coef has FIELD ---R ?^? : (%,NonNegativeInteger) -> % --R acos : % -> % if Coef has ALGEBRA(FRAC(INT)) --R acosh : % -> % if Coef has ALGEBRA(FRAC(INT)) --R acot : % -> % if Coef has ALGEBRA(FRAC(INT)) @@ -67384,7 +67683,6 @@ digraph pic { --R atanh : % -> % if Coef has ALGEBRA(FRAC(INT)) --R characteristic : () -> NonNegativeInteger --R charthRoot : % -> Union(%,"failed") if Coef has CHARNZ ---R coerce : % -> % if Coef has INTDOM --R coerce : Fraction(Integer) -> % if Coef has ALGEBRA(FRAC(INT)) --R coerce : Coef -> % if Coef has COMRING --R cos : % -> % if Coef has ALGEBRA(FRAC(INT)) @@ -67414,7 +67712,6 @@ digraph pic { --R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) if Coef has FIELD --R integrate : (%,Symbol) -> % if Coef has ACFS(INT) and Coef has PRIMCAT and Coef has TRANFUN and Coef has ALGEBRA(FRAC(INT)) or Coef has variables: Coef -> List(Symbol) and Coef has integrate: (Coef,Symbol) -> Coef and Coef has ALGEBRA(FRAC(INT)) --R integrate : % -> % if Coef has ALGEBRA(FRAC(INT)) ---R inv : % -> % if Coef has FIELD --R lcm : (%,%) -> % if Coef has FIELD --R lcm : List(%) -> % if Coef has FIELD --R lcmCoef : (%,%) -> Record(llcmres: %,coeff1: %,coeff2: %) if Coef has FIELD @@ -67988,14 +68285,17 @@ digraph pic { --R------------------------------- Operations -------------------------------- --R ?*? : (Coef,%) -> % ?*? : (%,Coef) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ?=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % center : % -> Coef +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R center : % -> Coef coerce : % -> % if Coef has INTDOM --R coerce : Integer -> % coerce : % -> OutputForm --R complete : % -> % degree : % -> Fraction(Integer) ---R hash : % -> SingleInteger latex : % -> String +--R ?.? : (%,Fraction(Integer)) -> Coef hash : % -> SingleInteger +--R inv : % -> % if Coef has FIELD latex : % -> String --R leadingCoefficient : % -> Coef leadingMonomial : % -> % --R map : ((Coef -> Coef),%) -> % monomial? : % -> Boolean --R one? : % -> Boolean order : % -> Fraction(Integer) @@ -68005,11 +68305,9 @@ digraph pic { --R ?~=? : (%,%) -> Boolean --R ?*? : (%,Fraction(Integer)) -> % if Coef has ALGEBRA(FRAC(INT)) --R ?*? : (Fraction(Integer),%) -> % if Coef has ALGEBRA(FRAC(INT)) ---R ?*? : (NonNegativeInteger,%) -> % --R ?**? : (%,Fraction(Integer)) -> % if Coef has ALGEBRA(FRAC(INT)) --R ?**? : (%,%) -> % if Coef has ALGEBRA(FRAC(INT)) --R ?**? : (%,Integer) -> % if Coef has FIELD ---R ?**? : (%,NonNegativeInteger) -> % --R ?/? : (%,%) -> % if Coef has FIELD --R ?/? : (%,Coef) -> % if Coef has FIELD --R D : % -> % if Coef has *: (Fraction(Integer),Coef) -> Coef @@ -68019,7 +68317,6 @@ digraph pic { --R D : (%,Symbol,NonNegativeInteger) -> % if Coef has PDRING(SYMBOL) and Coef has *: (Fraction(Integer),Coef) -> Coef --R D : (%,List(Symbol),List(NonNegativeInteger)) -> % if Coef has PDRING(SYMBOL) and Coef has *: (Fraction(Integer),Coef) -> Coef --R ?^? : (%,Integer) -> % if Coef has FIELD ---R ?^? : (%,NonNegativeInteger) -> % --R acos : % -> % if Coef has ALGEBRA(FRAC(INT)) --R acosh : % -> % if Coef has ALGEBRA(FRAC(INT)) --R acot : % -> % if Coef has ALGEBRA(FRAC(INT)) @@ -68037,7 +68334,6 @@ digraph pic { --R characteristic : () -> NonNegativeInteger --R charthRoot : % -> Union(%,"failed") if Coef has CHARNZ --R coefficient : (%,Fraction(Integer)) -> Coef ---R coerce : % -> % if Coef has INTDOM --R coerce : Fraction(Integer) -> % if Coef has ALGEBRA(FRAC(INT)) --R coerce : Coef -> % if Coef has COMRING --R cos : % -> % if Coef has ALGEBRA(FRAC(INT)) @@ -68054,7 +68350,6 @@ digraph pic { --R differentiate : (%,List(Symbol),List(NonNegativeInteger)) -> % if Coef has PDRING(SYMBOL) and Coef has *: (Fraction(Integer),Coef) -> Coef --R divide : (%,%) -> Record(quotient: %,remainder: %) if Coef has FIELD --R ?.? : (%,%) -> % if Fraction(Integer) has SGROUP ---R ?.? : (%,Fraction(Integer)) -> Coef --R euclideanSize : % -> NonNegativeInteger if Coef has FIELD --R eval : (%,Coef) -> Stream(Coef) if Coef has **: (Coef,Fraction(Integer)) -> Coef --R exp : % -> % if Coef has ALGEBRA(FRAC(INT)) @@ -68069,7 +68364,6 @@ digraph pic { --R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) if Coef has FIELD --R integrate : (%,Symbol) -> % if Coef has ACFS(INT) and Coef has PRIMCAT and Coef has TRANFUN and Coef has ALGEBRA(FRAC(INT)) or Coef has variables: Coef -> List(Symbol) and Coef has integrate: (Coef,Symbol) -> Coef and Coef has ALGEBRA(FRAC(INT)) --R integrate : % -> % if Coef has ALGEBRA(FRAC(INT)) ---R inv : % -> % if Coef has FIELD --R lcm : (%,%) -> % if Coef has FIELD --R lcm : List(%) -> % if Coef has FIELD --R lcmCoef : (%,%) -> Record(llcmres: %,coeff1: %,coeff2: %) if Coef has FIELD @@ -68602,32 +68896,39 @@ digraph pic { --R------------------------------- Operations -------------------------------- --R ?*? : (%,R) -> % ?*? : (R,%) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % ---R -? : % -> % ?=? : (%,%) -> Boolean ---R D : (%,(R -> R)) -> % D : % -> % ---R D : (%,NonNegativeInteger) -> % 1 : () -> % ---R 0 : () -> % ?^? : (%,PositiveInteger) -> % ---R coefficients : % -> List(R) coerce : R -> % ---R coerce : Integer -> % coerce : % -> OutputForm ---R degree : % -> NonNegativeInteger differentiate : % -> % ---R ?.? : (%,%) -> % ?.? : (%,R) -> R +--R -? : % -> % ?/? : (%,R) -> % if R has FIELD +--R ?=? : (%,%) -> Boolean D : (%,(R -> R)) -> % +--R D : % -> % D : (%,NonNegativeInteger) -> % +--R D : (%,SingletonAsOrderedSet) -> % 1 : () -> % +--R 0 : () -> % ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,PositiveInteger) -> % coefficients : % -> List(R) +--R coerce : % -> % if R has INTDOM coerce : SingletonAsOrderedSet -> % +--R coerce : R -> % coerce : Integer -> % +--R coerce : % -> OutputForm content : % -> R if R has GCDDOM +--R degree : % -> NonNegativeInteger differentiate : (%,(R -> R)) -> % +--R differentiate : % -> % ?.? : (%,%) -> % +--R ?.? : (%,R) -> R eval : (%,List(%),List(%)) -> % --R eval : (%,%,%) -> % eval : (%,Equation(%)) -> % ---R ground : % -> R ground? : % -> Boolean ---R hash : % -> SingleInteger init : () -> % if R has STEP ---R latex : % -> String leadingCoefficient : % -> R ---R leadingMonomial : % -> % map : ((R -> R),%) -> % ---R monomial? : % -> Boolean monomials : % -> List(%) ---R one? : % -> Boolean pseudoRemainder : (%,%) -> % ---R recip : % -> Union(%,"failed") reductum : % -> % +--R eval : (%,List(Equation(%))) -> % gcd : (%,%) -> % if R has GCDDOM +--R gcd : List(%) -> % if R has GCDDOM ground : % -> R +--R ground? : % -> Boolean hash : % -> SingleInteger +--R init : () -> % if R has STEP latex : % -> String +--R lcm : (%,%) -> % if R has GCDDOM lcm : List(%) -> % if R has GCDDOM +--R leadingCoefficient : % -> R leadingMonomial : % -> % +--R map : ((R -> R),%) -> % max : (%,%) -> % if R has ORDSET +--R min : (%,%) -> % if R has ORDSET monomial? : % -> Boolean +--R monomials : % -> List(%) one? : % -> Boolean +--R primitiveMonomials : % -> List(%) pseudoRemainder : (%,%) -> % +--R ?quo? : (%,%) -> % if R has FIELD recip : % -> Union(%,"failed") +--R reductum : % -> % ?rem? : (%,%) -> % if R has FIELD --R retract : % -> R sample : () -> % --R unvectorise : Vector(R) -> % zero? : % -> Boolean --R ?~=? : (%,%) -> Boolean --R ?*? : (Fraction(Integer),%) -> % if R has ALGEBRA(FRAC(INT)) --R ?*? : (%,Fraction(Integer)) -> % if R has ALGEBRA(FRAC(INT)) ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R ?/? : (%,R) -> % if R has FIELD --R ? Boolean if R has ORDSET --R ?<=? : (%,%) -> Boolean if R has ORDSET --R ?>? : (%,%) -> Boolean if R has ORDSET @@ -68640,8 +68941,6 @@ digraph pic { --R D : (%,List(SingletonAsOrderedSet),List(NonNegativeInteger)) -> % --R D : (%,SingletonAsOrderedSet,NonNegativeInteger) -> % --R D : (%,List(SingletonAsOrderedSet)) -> % ---R D : (%,SingletonAsOrderedSet) -> % ---R ?^? : (%,NonNegativeInteger) -> % --R associates? : (%,%) -> Boolean if R has INTDOM --R binomThmExpt : (%,%,NonNegativeInteger) -> % if R has COMRING --R characteristic : () -> NonNegativeInteger @@ -68649,21 +68948,17 @@ digraph pic { --R coefficient : (%,List(SingletonAsOrderedSet),List(NonNegativeInteger)) -> % --R coefficient : (%,SingletonAsOrderedSet,NonNegativeInteger) -> % --R coefficient : (%,NonNegativeInteger) -> R ---R coerce : % -> % if R has INTDOM --R coerce : Fraction(Integer) -> % if R has RETRACT(FRAC(INT)) or R has ALGEBRA(FRAC(INT)) ---R coerce : SingletonAsOrderedSet -> % --R composite : (Fraction(%),%) -> Union(Fraction(%),"failed") if R has INTDOM --R composite : (%,%) -> Union(%,"failed") if R has INTDOM --R conditionP : Matrix(%) -> Union(Vector(%),"failed") if and(has($,CharacteristicNonZero),has(R,PolynomialFactorizationExplicit)) --R content : (%,SingletonAsOrderedSet) -> % if R has GCDDOM ---R content : % -> R if R has GCDDOM --R convert : % -> InputForm if SingletonAsOrderedSet has KONVERT(INFORM) and R has KONVERT(INFORM) --R convert : % -> Pattern(Integer) if SingletonAsOrderedSet has KONVERT(PATTERN(INT)) and R has KONVERT(PATTERN(INT)) --R convert : % -> Pattern(Float) if SingletonAsOrderedSet has KONVERT(PATTERN(FLOAT)) and R has KONVERT(PATTERN(FLOAT)) --R degree : (%,List(SingletonAsOrderedSet)) -> List(NonNegativeInteger) --R degree : (%,SingletonAsOrderedSet) -> NonNegativeInteger --R differentiate : (%,(R -> R),%) -> % ---R differentiate : (%,(R -> R)) -> % --R differentiate : (%,(R -> R),NonNegativeInteger) -> % --R differentiate : (%,List(Symbol),List(NonNegativeInteger)) -> % if R has PDRING(SYMBOL) --R differentiate : (%,Symbol,NonNegativeInteger) -> % if R has PDRING(SYMBOL) @@ -68686,8 +68981,6 @@ digraph pic { --R eval : (%,SingletonAsOrderedSet,%) -> % --R eval : (%,List(SingletonAsOrderedSet),List(R)) -> % --R eval : (%,SingletonAsOrderedSet,R) -> % ---R eval : (%,List(%),List(%)) -> % ---R eval : (%,List(Equation(%))) -> % --R expressIdealMember : (List(%),%) -> Union(List(%),"failed") if R has FIELD --R exquo : (%,%) -> Union(%,"failed") if R has INTDOM --R exquo : (%,R) -> Union(%,"failed") if R has INTDOM @@ -68696,22 +68989,16 @@ digraph pic { --R factor : % -> Factored(%) if R has PFECAT --R factorPolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has PFECAT --R factorSquareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has PFECAT ---R gcd : (%,%) -> % if R has GCDDOM ---R gcd : List(%) -> % if R has GCDDOM --R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) if R has GCDDOM --R integrate : % -> % if R has ALGEBRA(FRAC(INT)) --R isExpt : % -> Union(Record(var: SingletonAsOrderedSet,exponent: NonNegativeInteger),"failed") --R isPlus : % -> Union(List(%),"failed") --R isTimes : % -> Union(List(%),"failed") --R karatsubaDivide : (%,NonNegativeInteger) -> Record(quotient: %,remainder: %) ---R lcm : (%,%) -> % if R has GCDDOM ---R lcm : List(%) -> % if R has GCDDOM --R lcmCoef : (%,%) -> Record(llcmres: %,coeff1: %,coeff2: %) if R has GCDDOM --R mainVariable : % -> Union(SingletonAsOrderedSet,"failed") --R makeSUP : % -> SparseUnivariatePolynomial(R) --R mapExponents : ((NonNegativeInteger -> NonNegativeInteger),%) -> % ---R max : (%,%) -> % if R has ORDSET ---R min : (%,%) -> % if R has ORDSET --R minimumDegree : (%,List(SingletonAsOrderedSet)) -> List(NonNegativeInteger) --R minimumDegree : (%,SingletonAsOrderedSet) -> NonNegativeInteger --R minimumDegree : % -> NonNegativeInteger @@ -68731,18 +69018,15 @@ digraph pic { --R patternMatch : (%,Pattern(Float),PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if SingletonAsOrderedSet has PATMAB(FLOAT) and R has PATMAB(FLOAT) --R pomopo! : (%,R,NonNegativeInteger,%) -> % --R prime? : % -> Boolean if R has PFECAT ---R primitiveMonomials : % -> List(%) --R primitivePart : (%,SingletonAsOrderedSet) -> % if R has GCDDOM --R primitivePart : % -> % if R has GCDDOM --R principalIdeal : List(%) -> Record(coef: List(%),generator: %) if R has FIELD --R pseudoDivide : (%,%) -> Record(coef: R,quotient: %,remainder: %) if R has INTDOM --R pseudoQuotient : (%,%) -> % if R has INTDOM ---R ?quo? : (%,%) -> % if R has FIELD --R reducedSystem : Matrix(%) -> Matrix(R) --R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(R),vec: Vector(R)) --R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(Integer),vec: Vector(Integer)) if R has LINEXP(INT) --R reducedSystem : Matrix(%) -> Matrix(Integer) if R has LINEXP(INT) ---R ?rem? : (%,%) -> % if R has FIELD --R resultant : (%,%) -> R if R has COMRING --R resultant : (%,%,SingletonAsOrderedSet) -> % if R has COMRING --R retract : % -> SingletonAsOrderedSet @@ -69823,43 +70107,52 @@ digraph pic { --R Issue )edit bookvol10.2.pamphlet to see algebra source code for ACFS --R --R------------------------------- Operations -------------------------------- +--R ?*? : (R,%) -> % if R has COMRING ?*? : (%,R) -> % if R has COMRING --R ?*? : (Fraction(Integer),%) -> % ?*? : (%,Fraction(Integer)) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % ---R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % ---R ?-? : (%,%) -> % -? : % -> % ---R ?/? : (%,%) -> % ? Boolean ---R ?<=? : (%,%) -> Boolean ?=? : (%,%) -> Boolean ---R ?>? : (%,%) -> Boolean ?>=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,Fraction(Integer)) -> % ?**? : (%,Integer) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?/? : (%,%) -> % +--R ? Boolean ?<=? : (%,%) -> Boolean +--R ?=? : (%,%) -> Boolean ?>? : (%,%) -> Boolean +--R ?>=? : (%,%) -> Boolean D : (%,Symbol) -> % if R has RING --R 1 : () -> % 0 : () -> % ---R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> % ---R applyQuote : (Symbol,%) -> % applyQuote : (Symbol,%,%) -> % ---R associates? : (%,%) -> Boolean belong? : BasicOperator -> Boolean ---R box : % -> % box : List(%) -> % ---R coerce : Kernel(%) -> % coerce : Symbol -> % ---R coerce : R -> % coerce : Fraction(Integer) -> % ---R coerce : % -> % coerce : Integer -> % ---R coerce : % -> OutputForm distribute : % -> % ---R distribute : (%,%) -> % elt : (BasicOperator,%) -> % ---R elt : (BasicOperator,%,%) -> % eval : (%,Kernel(%),%) -> % +--R ?^? : (%,Integer) -> % ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,PositiveInteger) -> % applyQuote : (Symbol,%) -> % +--R applyQuote : (Symbol,%,%) -> % applyQuote : (Symbol,%,%,%) -> % +--R applyQuote : (Symbol,List(%)) -> % associates? : (%,%) -> Boolean +--R belong? : BasicOperator -> Boolean box : % -> % +--R box : List(%) -> % coerce : Kernel(%) -> % +--R coerce : Symbol -> % coerce : R -> % +--R coerce : Fraction(Integer) -> % coerce : % -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R distribute : % -> % distribute : (%,%) -> % +--R elt : (BasicOperator,%) -> % elt : (BasicOperator,%,%) -> % +--R elt : (BasicOperator,%,%,%) -> % elt : (BasicOperator,List(%)) -> % +--R eval : (%,Kernel(%),%) -> % eval : (%,List(Equation(%))) -> % --R eval : (%,Equation(%)) -> % eval : (%,%,%) -> % +--R eval : (%,List(%),List(%)) -> % eval : (%,Symbol,(% -> %)) -> % --R factor : % -> Factored(%) freeOf? : (%,%) -> Boolean --R freeOf? : (%,Symbol) -> Boolean gcd : List(%) -> % --R gcd : (%,%) -> % ground : % -> R --R ground? : % -> Boolean hash : % -> SingleInteger --R height : % -> NonNegativeInteger inv : % -> % ---R is? : (%,Symbol) -> Boolean kernel : (BasicOperator,%) -> % ---R kernels : % -> List(Kernel(%)) latex : % -> String ---R lcm : List(%) -> % lcm : (%,%) -> % +--R is? : (%,BasicOperator) -> Boolean is? : (%,Symbol) -> Boolean +--R kernel : (BasicOperator,%) -> % kernels : % -> List(Kernel(%)) +--R latex : % -> String lcm : List(%) -> % +--R lcm : (%,%) -> % map : ((% -> %),Kernel(%)) -> % --R max : (%,%) -> % min : (%,%) -> % ---R nthRoot : (%,Integer) -> % one? : % -> Boolean ---R paren : % -> % paren : List(%) -> % ---R prime? : % -> Boolean ?quo? : (%,%) -> % ---R recip : % -> Union(%,"failed") ?rem? : (%,%) -> % ---R retract : % -> Kernel(%) retract : % -> Symbol ---R retract : % -> R rootOf : (%,Symbol) -> % ---R rootOf : % -> % rootOf : Polynomial(%) -> % ---R rootsOf : (%,Symbol) -> List(%) rootsOf : % -> List(%) +--R nthRoot : (%,Integer) -> % numerator : % -> % if R has RING +--R one? : % -> Boolean paren : % -> % +--R paren : List(%) -> % prime? : % -> Boolean +--R ?quo? : (%,%) -> % recip : % -> Union(%,"failed") +--R ?rem? : (%,%) -> % retract : % -> Kernel(%) +--R retract : % -> Symbol retract : % -> R +--R rootOf : (%,Symbol) -> % rootOf : % -> % +--R rootOf : Polynomial(%) -> % rootsOf : (%,Symbol) -> List(%) +--R rootsOf : % -> List(%) rootsOf : Polynomial(%) -> List(%) --R sample : () -> % sizeLess? : (%,%) -> Boolean --R sqrt : % -> % squareFree : % -> Factored(%) --R squareFreePart : % -> % subst : (%,Equation(%)) -> % @@ -69868,21 +70161,12 @@ digraph pic { --R zero? : % -> Boolean zeroOf : (%,Symbol) -> % --R zeroOf : % -> % zeroOf : Polynomial(%) -> % --R zerosOf : (%,Symbol) -> List(%) zerosOf : % -> List(%) ---R ?~=? : (%,%) -> Boolean ---R ?*? : (R,%) -> % if R has COMRING ---R ?*? : (%,R) -> % if R has COMRING ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,Fraction(Integer)) -> % ---R ?**? : (%,NonNegativeInteger) -> % +--R zerosOf : Polynomial(%) -> List(%) ?~=? : (%,%) -> Boolean --R ?/? : (SparseMultivariatePolynomial(R,Kernel(%)),SparseMultivariatePolynomial(R,Kernel(%))) -> % if R has INTDOM --R D : (%,List(Symbol),List(NonNegativeInteger)) -> % if R has RING --R D : (%,Symbol,NonNegativeInteger) -> % if R has RING --R D : (%,List(Symbol)) -> % if R has RING ---R D : (%,Symbol) -> % if R has RING ---R ?^? : (%,NonNegativeInteger) -> % ---R applyQuote : (Symbol,%,%,%) -> % --R applyQuote : (Symbol,%,%,%,%) -> % ---R applyQuote : (Symbol,List(%)) -> % --R characteristic : () -> NonNegativeInteger --R charthRoot : % -> Union(%,"failed") if R has CHARNZ --R coerce : SparseMultivariatePolynomial(R,Kernel(%)) -> % if R has RING @@ -69905,17 +70189,12 @@ digraph pic { --R differentiate : (%,List(Symbol)) -> % if R has RING --R differentiate : (%,Symbol) -> % if R has RING --R divide : (%,%) -> Record(quotient: %,remainder: %) ---R elt : (BasicOperator,%,%,%) -> % --R elt : (BasicOperator,%,%,%,%) -> % ---R elt : (BasicOperator,List(%)) -> % --R euclideanSize : % -> NonNegativeInteger --R eval : (%,List(Kernel(%)),List(%)) -> % ---R eval : (%,List(Equation(%))) -> % ---R eval : (%,List(%),List(%)) -> % --R eval : (%,List(Symbol),List((% -> %))) -> % --R eval : (%,List(Symbol),List((List(%) -> %))) -> % --R eval : (%,Symbol,(List(%) -> %)) -> % ---R eval : (%,Symbol,(% -> %)) -> % --R eval : (%,List(BasicOperator),List((% -> %))) -> % --R eval : (%,List(BasicOperator),List((List(%) -> %))) -> % --R eval : (%,BasicOperator,(List(%) -> %)) -> % @@ -69935,7 +70214,6 @@ digraph pic { --R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") --R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) --R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) ---R is? : (%,BasicOperator) -> Boolean --R isExpt : % -> Union(Record(var: Kernel(%),exponent: Integer),"failed") if R has SGROUP --R isExpt : (%,BasicOperator) -> Union(Record(var: Kernel(%),exponent: Integer),"failed") if R has RING --R isExpt : (%,Symbol) -> Union(Record(var: Kernel(%),exponent: Integer),"failed") if R has RING @@ -69946,11 +70224,9 @@ digraph pic { --R kernel : (BasicOperator,List(%)) -> % --R lcmCoef : (%,%) -> Record(llcmres: %,coeff1: %,coeff2: %) --R mainKernel : % -> Union(Kernel(%),"failed") ---R map : ((% -> %),Kernel(%)) -> % --R minPoly : Kernel(%) -> SparseUnivariatePolynomial(%) if $ has RING --R multiEuclidean : (List(%),%) -> Union(List(%),"failed") --R numer : % -> SparseMultivariatePolynomial(R,Kernel(%)) if R has RING ---R numerator : % -> % if R has RING --R odd? : % -> Boolean if $ has RETRACT(INT) --R operator : BasicOperator -> BasicOperator --R operators : % -> List(BasicOperator) @@ -69976,7 +70252,6 @@ digraph pic { --R rootOf : SparseUnivariatePolynomial(%) -> % --R rootsOf : (SparseUnivariatePolynomial(%),Symbol) -> List(%) --R rootsOf : SparseUnivariatePolynomial(%) -> List(%) ---R rootsOf : Polynomial(%) -> List(%) --R subst : (%,List(Equation(%))) -> % --R subst : (%,List(Kernel(%)),List(%)) -> % --R subtractIfCan : (%,%) -> Union(%,"failed") @@ -69986,7 +70261,6 @@ digraph pic { --R zeroOf : SparseUnivariatePolynomial(%) -> % --R zerosOf : (SparseUnivariatePolynomial(%),Symbol) -> List(%) --R zerosOf : SparseUnivariatePolynomial(%) -> List(%) ---R zerosOf : Polynomial(%) -> List(%) --R --E 1 @@ -70601,12 +70875,14 @@ digraph pic { --R ?*? : (F,%) -> % ?*? : (%,F) -> % --R ?*? : (Fraction(Integer),%) -> % ?*? : (%,Fraction(Integer)) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,Integer) -> % ?**? : (%,NonNegativeInteger) -> % --R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % --R ?-? : (%,%) -> % -? : % -> % --R ?/? : (%,F) -> % ?/? : (%,%) -> % ---R ?=? : (%,%) -> Boolean 1 : () -> % ---R 0 : () -> % ?^? : (%,Integer) -> % +--R ?=? : (%,%) -> Boolean Frobenius : % -> % if F has FINITE +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,Integer) -> % ?^? : (%,NonNegativeInteger) -> % --R ?^? : (%,PositiveInteger) -> % algebraic? : % -> Boolean --R associates? : (%,%) -> Boolean coerce : F -> % --R coerce : Fraction(Integer) -> % coerce : % -> % @@ -70624,11 +70900,7 @@ digraph pic { --R transcendent? : % -> Boolean unit? : % -> Boolean --R unitCanonical : % -> % zero? : % -> Boolean --R ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % --R Frobenius : (%,NonNegativeInteger) -> % if F has FINITE ---R Frobenius : % -> % if F has FINITE ---R ?^? : (%,NonNegativeInteger) -> % --R characteristic : () -> NonNegativeInteger --R charthRoot : % -> Union(%,"failed") if F has CHARNZ or F has FINITE --R degree : % -> OnePointCompletion(PositiveInteger) @@ -71009,23 +71281,25 @@ digraph pic { --R------------------------------- Operations -------------------------------- --R ?*? : (Fraction(Integer),%) -> % ?*? : (%,Fraction(Integer)) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,Integer) -> % ?**? : (%,NonNegativeInteger) -> % --R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % --R ?-? : (%,%) -> % -? : % -> % --R ?/? : (%,%) -> % ?=? : (%,%) -> Boolean --R D : % -> % D : (%,NonNegativeInteger) -> % --R 1 : () -> % 0 : () -> % ---R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> % ---R associates? : (%,%) -> Boolean charthRoot : % -> % ---R coerce : Fraction(Integer) -> % coerce : % -> % ---R coerce : Integer -> % coerce : % -> OutputForm ---R createPrimitiveElement : () -> % differentiate : % -> % ---R enumerate : () -> List(%) factor : % -> Factored(%) ---R gcd : List(%) -> % gcd : (%,%) -> % ---R hash : % -> SingleInteger index : PositiveInteger -> % ---R init : () -> % inv : % -> % ---R latex : % -> String lcm : List(%) -> % ---R lcm : (%,%) -> % lookup : % -> PositiveInteger +--R ?^? : (%,Integer) -> % ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,PositiveInteger) -> % associates? : (%,%) -> Boolean +--R charthRoot : % -> % coerce : Fraction(Integer) -> % +--R coerce : % -> % coerce : Integer -> % +--R coerce : % -> OutputForm createPrimitiveElement : () -> % +--R differentiate : % -> % enumerate : () -> List(%) +--R factor : % -> Factored(%) gcd : List(%) -> % +--R gcd : (%,%) -> % hash : % -> SingleInteger +--R index : PositiveInteger -> % init : () -> % +--R inv : % -> % latex : % -> String +--R lcm : List(%) -> % lcm : (%,%) -> % +--R lookup : % -> PositiveInteger nextItem : % -> Union(%,"failed") --R one? : % -> Boolean order : % -> PositiveInteger --R prime? : % -> Boolean primeFrobenius : % -> % --R primitive? : % -> Boolean primitiveElement : () -> % @@ -71036,9 +71310,6 @@ digraph pic { --R squareFreePart : % -> % unit? : % -> Boolean --R unitCanonical : % -> % zero? : % -> Boolean --R ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R ?^? : (%,NonNegativeInteger) -> % --R characteristic : () -> NonNegativeInteger --R charthRoot : % -> Union(%,"failed") --R conditionP : Matrix(%) -> Union(Vector(%),"failed") @@ -71055,7 +71326,6 @@ digraph pic { --R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) --R lcmCoef : (%,%) -> Record(llcmres: %,coeff1: %,coeff2: %) --R multiEuclidean : (List(%),%) -> Union(List(%),"failed") ---R nextItem : % -> Union(%,"failed") --R order : % -> OnePointCompletion(PositiveInteger) --R primeFrobenius : (%,NonNegativeInteger) -> % --R principalIdeal : List(%) -> Record(coef: List(%),generator: %) @@ -71595,14 +71865,16 @@ digraph pic { --R------------------------------- Operations -------------------------------- --R ?*? : (Fraction(Integer),%) -> % ?*? : (%,Fraction(Integer)) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % ---R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % ---R ?-? : (%,%) -> % -? : % -> % ---R ?/? : (%,%) -> % ? Boolean ---R ?<=? : (%,%) -> Boolean ?=? : (%,%) -> Boolean ---R ?>? : (%,%) -> Boolean ?>=? : (%,%) -> Boolean ---R 1 : () -> % 0 : () -> % ---R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,Fraction(Integer)) -> % ?**? : (%,Integer) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?/? : (%,%) -> % +--R ? Boolean ?<=? : (%,%) -> Boolean +--R ?=? : (%,%) -> Boolean ?>? : (%,%) -> Boolean +--R ?>=? : (%,%) -> Boolean 1 : () -> % +--R 0 : () -> % ?^? : (%,Integer) -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % --R abs : % -> % associates? : (%,%) -> Boolean --R base : () -> PositiveInteger bits : () -> PositiveInteger --R ceiling : % -> % coerce : Fraction(Integer) -> % @@ -71631,10 +71903,6 @@ digraph pic { --R truncate : % -> % unit? : % -> Boolean --R unitCanonical : % -> % wholePart : % -> Integer --R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,Fraction(Integer)) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R ?^? : (%,NonNegativeInteger) -> % --R bits : PositiveInteger -> PositiveInteger if $ has arbitraryPrecision --R characteristic : () -> NonNegativeInteger --R decreasePrecision : Integer -> PositiveInteger if $ has arbitraryPrecision @@ -72086,11 +72354,13 @@ digraph pic { --R------------------------------- Operations -------------------------------- --R ?*? : (R,%) -> % ?*? : (%,R) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ?=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % basis : () -> Vector(%) +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R basis : () -> Vector(%) characteristicPolynomial : % -> UP --R coerce : R -> % coerce : Integer -> % --R coerce : % -> OutputForm convert : Vector(R) -> % --R convert : % -> Vector(R) coordinates : % -> Vector(R) @@ -72101,11 +72371,7 @@ digraph pic { --R represents : Vector(R) -> % sample : () -> % --R trace : % -> R traceMatrix : () -> Matrix(R) --R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R ?^? : (%,NonNegativeInteger) -> % --R characteristic : () -> NonNegativeInteger ---R characteristicPolynomial : % -> UP --R charthRoot : % -> Union(%,"failed") if R has CHARNZ --R coordinates : Vector(%) -> Matrix(R) --R coordinates : (Vector(%),Vector(%)) -> Matrix(R) @@ -72411,26 +72677,28 @@ digraph pic { --R------------------------------- Operations -------------------------------- --R ?*? : (Fraction(Integer),%) -> % ?*? : (%,Fraction(Integer)) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,Integer) -> % ?**? : (%,NonNegativeInteger) -> % --R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % --R ?-? : (%,%) -> % -? : % -> % --R ?/? : (%,%) -> % ?=? : (%,%) -> Boolean --R D : % -> % D : (%,NonNegativeInteger) -> % --R 1 : () -> % 0 : () -> % ---R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> % ---R associates? : (%,%) -> Boolean charthRoot : % -> % ---R coerce : Fraction(Integer) -> % coerce : % -> % ---R coerce : Integer -> % coerce : % -> OutputForm ---R conjugate : % -> % createPrimitiveElement : () -> % ---R differentiate : % -> % enumerate : () -> List(%) ---R extDegree : % -> PositiveInteger factor : % -> Factored(%) ---R fullOutput : % -> OutputForm gcd : List(%) -> % ---R gcd : (%,%) -> % ground? : % -> Boolean ---R hash : % -> SingleInteger index : PositiveInteger -> % ---R init : () -> % inv : % -> % ---R latex : % -> String lcm : List(%) -> % ---R lcm : (%,%) -> % lookup : % -> PositiveInteger ---R maxTower : List(%) -> % one? : % -> Boolean +--R ?^? : (%,Integer) -> % ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,PositiveInteger) -> % associates? : (%,%) -> Boolean +--R charthRoot : % -> % coerce : Fraction(Integer) -> % +--R coerce : % -> % coerce : Integer -> % +--R coerce : % -> OutputForm conjugate : % -> % +--R createPrimitiveElement : () -> % differentiate : % -> % +--R enumerate : () -> List(%) extDegree : % -> PositiveInteger +--R factor : % -> Factored(%) fullOutput : % -> OutputForm +--R gcd : List(%) -> % gcd : (%,%) -> % +--R ground? : % -> Boolean hash : % -> SingleInteger +--R index : PositiveInteger -> % init : () -> % +--R inv : % -> % latex : % -> String +--R lcm : List(%) -> % lcm : (%,%) -> % +--R lookup : % -> PositiveInteger maxTower : List(%) -> % +--R nextItem : % -> Union(%,"failed") one? : % -> Boolean --R order : % -> PositiveInteger previousTower : % -> % --R prime? : % -> Boolean primeFrobenius : % -> % --R primitive? : % -> Boolean primitiveElement : () -> % @@ -72442,9 +72710,6 @@ digraph pic { --R unit? : % -> Boolean unitCanonical : % -> % --R vectorise : (%,%) -> Vector(%) zero? : % -> Boolean --R ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R ?^? : (%,NonNegativeInteger) -> % --R characteristic : () -> NonNegativeInteger --R charthRoot : % -> Union(%,"failed") --R conditionP : Matrix(%) -> Union(Vector(%),"failed") @@ -72468,7 +72733,6 @@ digraph pic { --R multiEuclidean : (List(%),%) -> Union(List(%),"failed") --R newElement : (SparseUnivariatePolynomial(%),%,Symbol) -> % --R newElement : (SparseUnivariatePolynomial(%),Symbol) -> % ---R nextItem : % -> Union(%,"failed") --R order : % -> OnePointCompletion(PositiveInteger) --R primeFrobenius : (%,NonNegativeInteger) -> % --R principalIdeal : List(%) -> Record(coef: List(%),generator: %) @@ -72806,36 +73070,38 @@ digraph pic { --R------------------------------- Operations -------------------------------- --R ?*? : (Coef,%) -> % ?*? : (%,Coef) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ?=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % center : % -> Coef ---R coefficient : (%,Integer) -> Coef coerce : UTS -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R center : % -> Coef coefficient : (%,Integer) -> Coef +--R coerce : % -> % if Coef has INTDOM coerce : UTS -> % --R coerce : Integer -> % coerce : % -> OutputForm --R complete : % -> % degree : % -> Integer ---R ?.? : (%,Integer) -> Coef extend : (%,Integer) -> % ---R hash : % -> SingleInteger latex : % -> String +--R denom : % -> UTS if Coef has FIELD ?.? : (%,Integer) -> Coef +--R extend : (%,Integer) -> % hash : % -> SingleInteger +--R inv : % -> % if Coef has FIELD latex : % -> String --R laurent : (Integer,UTS) -> % leadingCoefficient : % -> Coef --R leadingMonomial : % -> % map : ((Coef -> Coef),%) -> % --R monomial : (Coef,Integer) -> % monomial? : % -> Boolean ---R one? : % -> Boolean order : (%,Integer) -> Integer ---R order : % -> Integer pole? : % -> Boolean ---R recip : % -> Union(%,"failed") reductum : % -> % ---R removeZeroes : (Integer,%) -> % removeZeroes : % -> % ---R retract : % -> UTS sample : () -> % ---R taylor : % -> UTS taylorRep : % -> UTS ---R truncate : (%,Integer) -> % variable : % -> Symbol ---R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R numer : % -> UTS if Coef has FIELD one? : % -> Boolean +--R order : (%,Integer) -> Integer order : % -> Integer +--R pole? : % -> Boolean recip : % -> Union(%,"failed") +--R reductum : % -> % removeZeroes : (Integer,%) -> % +--R removeZeroes : % -> % retract : % -> UTS +--R sample : () -> % taylor : % -> UTS +--R taylorRep : % -> UTS truncate : (%,Integer) -> % +--R variable : % -> Symbol zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean --R ?*? : (%,Fraction(Integer)) -> % if Coef has ALGEBRA(FRAC(INT)) --R ?*? : (Fraction(Integer),%) -> % if Coef has ALGEBRA(FRAC(INT)) --R ?*? : (UTS,%) -> % if Coef has FIELD --R ?*? : (%,UTS) -> % if Coef has FIELD ---R ?*? : (NonNegativeInteger,%) -> % --R ?**? : (%,Fraction(Integer)) -> % if Coef has ALGEBRA(FRAC(INT)) --R ?**? : (%,%) -> % if Coef has ALGEBRA(FRAC(INT)) --R ?**? : (%,Integer) -> % if Coef has FIELD ---R ?**? : (%,NonNegativeInteger) -> % --R ?/? : (UTS,UTS) -> % if Coef has FIELD --R ?/? : (%,%) -> % if Coef has FIELD --R ?/? : (%,Coef) -> % if Coef has FIELD @@ -72852,7 +73118,6 @@ digraph pic { --R D : (%,(UTS -> UTS),NonNegativeInteger) -> % if Coef has FIELD --R D : (%,(UTS -> UTS)) -> % if Coef has FIELD --R ?^? : (%,Integer) -> % if Coef has FIELD ---R ?^? : (%,NonNegativeInteger) -> % --R abs : % -> % if and(has(UTS,OrderedIntegralDomain),has(Coef,Field)) --R acos : % -> % if Coef has ALGEBRA(FRAC(INT)) --R acosh : % -> % if Coef has ALGEBRA(FRAC(INT)) @@ -72871,7 +73136,6 @@ digraph pic { --R ceiling : % -> UTS if and(has(UTS,IntegerNumberSystem),has(Coef,Field)) --R characteristic : () -> NonNegativeInteger --R charthRoot : % -> Union(%,"failed") if and(OR(has(UTS,CharacteristicNonZero),and(has($,CharacteristicNonZero),has(UTS,PolynomialFactorizationExplicit))),has(Coef,Field)) or Coef has CHARNZ ---R coerce : % -> % if Coef has INTDOM --R coerce : Fraction(Integer) -> % if Coef has ALGEBRA(FRAC(INT)) --R coerce : Symbol -> % if and(has(UTS,RetractableTo(Symbol)),has(Coef,Field)) --R coerce : Coef -> % if Coef has COMRING @@ -72887,7 +73151,6 @@ digraph pic { --R coth : % -> % if Coef has ALGEBRA(FRAC(INT)) --R csc : % -> % if Coef has ALGEBRA(FRAC(INT)) --R csch : % -> % if Coef has ALGEBRA(FRAC(INT)) ---R denom : % -> UTS if Coef has FIELD --R denominator : % -> % if Coef has FIELD --R differentiate : (%,Symbol) -> % if and(has(UTS,PartialDifferentialRing(Symbol)),has(Coef,Field)) or Coef has PDRING(SYMBOL) and Coef has *: (Integer,Coef) -> Coef --R differentiate : (%,List(Symbol)) -> % if and(has(UTS,PartialDifferentialRing(Symbol)),has(Coef,Field)) or Coef has PDRING(SYMBOL) and Coef has *: (Integer,Coef) -> Coef @@ -72924,7 +73187,6 @@ digraph pic { --R init : () -> % if and(has(UTS,StepThrough),has(Coef,Field)) --R integrate : (%,Symbol) -> % if Coef has ACFS(INT) and Coef has PRIMCAT and Coef has TRANFUN and Coef has ALGEBRA(FRAC(INT)) or Coef has variables: Coef -> List(Symbol) and Coef has integrate: (Coef,Symbol) -> Coef and Coef has ALGEBRA(FRAC(INT)) --R integrate : % -> % if Coef has ALGEBRA(FRAC(INT)) ---R inv : % -> % if Coef has FIELD --R lcm : (%,%) -> % if Coef has FIELD --R lcm : List(%) -> % if Coef has FIELD --R lcmCoef : (%,%) -> Record(llcmres: %,coeff1: %,coeff2: %) if Coef has FIELD @@ -72940,7 +73202,6 @@ digraph pic { --R negative? : % -> Boolean if and(has(UTS,OrderedIntegralDomain),has(Coef,Field)) --R nextItem : % -> Union(%,"failed") if and(has(UTS,StepThrough),has(Coef,Field)) --R nthRoot : (%,Integer) -> % if Coef has ALGEBRA(FRAC(INT)) ---R numer : % -> UTS if Coef has FIELD --R numerator : % -> % if Coef has FIELD --R patternMatch : (%,Pattern(Integer),PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if and(has(UTS,PatternMatchable(Integer)),has(Coef,Field)) --R patternMatch : (%,Pattern(Float),PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if and(has(UTS,PatternMatchable(Float)),has(Coef,Field)) @@ -73673,14 +73934,17 @@ digraph pic { --R------------------------------- Operations -------------------------------- --R ?*? : (Coef,%) -> % ?*? : (%,Coef) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ?=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % center : % -> Coef +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R center : % -> Coef coerce : % -> % if Coef has INTDOM --R coerce : ULS -> % coerce : Integer -> % --R coerce : % -> OutputForm complete : % -> % ---R degree : % -> Fraction(Integer) hash : % -> SingleInteger +--R degree : % -> Fraction(Integer) ?.? : (%,Fraction(Integer)) -> Coef +--R hash : % -> SingleInteger inv : % -> % if Coef has FIELD --R latex : % -> String laurent : % -> ULS --R laurentRep : % -> ULS leadingCoefficient : % -> Coef --R leadingMonomial : % -> % map : ((Coef -> Coef),%) -> % @@ -73692,11 +73956,9 @@ digraph pic { --R ?~=? : (%,%) -> Boolean --R ?*? : (%,Fraction(Integer)) -> % if Coef has ALGEBRA(FRAC(INT)) --R ?*? : (Fraction(Integer),%) -> % if Coef has ALGEBRA(FRAC(INT)) ---R ?*? : (NonNegativeInteger,%) -> % --R ?**? : (%,Fraction(Integer)) -> % if Coef has ALGEBRA(FRAC(INT)) --R ?**? : (%,%) -> % if Coef has ALGEBRA(FRAC(INT)) --R ?**? : (%,Integer) -> % if Coef has FIELD ---R ?**? : (%,NonNegativeInteger) -> % --R ?/? : (%,%) -> % if Coef has FIELD --R ?/? : (%,Coef) -> % if Coef has FIELD --R D : % -> % if Coef has *: (Fraction(Integer),Coef) -> Coef @@ -73706,7 +73968,6 @@ digraph pic { --R D : (%,Symbol,NonNegativeInteger) -> % if Coef has PDRING(SYMBOL) and Coef has *: (Fraction(Integer),Coef) -> Coef --R D : (%,List(Symbol),List(NonNegativeInteger)) -> % if Coef has PDRING(SYMBOL) and Coef has *: (Fraction(Integer),Coef) -> Coef --R ?^? : (%,Integer) -> % if Coef has FIELD ---R ?^? : (%,NonNegativeInteger) -> % --R acos : % -> % if Coef has ALGEBRA(FRAC(INT)) --R acosh : % -> % if Coef has ALGEBRA(FRAC(INT)) --R acot : % -> % if Coef has ALGEBRA(FRAC(INT)) @@ -73724,7 +73985,6 @@ digraph pic { --R characteristic : () -> NonNegativeInteger --R charthRoot : % -> Union(%,"failed") if Coef has CHARNZ --R coefficient : (%,Fraction(Integer)) -> Coef ---R coerce : % -> % if Coef has INTDOM --R coerce : Fraction(Integer) -> % if Coef has ALGEBRA(FRAC(INT)) --R coerce : Coef -> % if Coef has COMRING --R cos : % -> % if Coef has ALGEBRA(FRAC(INT)) @@ -73741,7 +74001,6 @@ digraph pic { --R differentiate : (%,List(Symbol),List(NonNegativeInteger)) -> % if Coef has PDRING(SYMBOL) and Coef has *: (Fraction(Integer),Coef) -> Coef --R divide : (%,%) -> Record(quotient: %,remainder: %) if Coef has FIELD --R ?.? : (%,%) -> % if Fraction(Integer) has SGROUP ---R ?.? : (%,Fraction(Integer)) -> Coef --R euclideanSize : % -> NonNegativeInteger if Coef has FIELD --R eval : (%,Coef) -> Stream(Coef) if Coef has **: (Coef,Fraction(Integer)) -> Coef --R exp : % -> % if Coef has ALGEBRA(FRAC(INT)) @@ -73756,7 +74015,6 @@ digraph pic { --R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) if Coef has FIELD --R integrate : (%,Symbol) -> % if Coef has ACFS(INT) and Coef has PRIMCAT and Coef has TRANFUN and Coef has ALGEBRA(FRAC(INT)) or Coef has variables: Coef -> List(Symbol) and Coef has integrate: (Coef,Symbol) -> Coef and Coef has ALGEBRA(FRAC(INT)) --R integrate : % -> % if Coef has ALGEBRA(FRAC(INT)) ---R inv : % -> % if Coef has FIELD --R laurentIfCan : % -> Union(ULS,"failed") --R lcm : (%,%) -> % if Coef has FIELD --R lcm : List(%) -> % if Coef has FIELD @@ -74295,13 +74553,15 @@ digraph pic { --R ?*? : (F,%) -> % ?*? : (%,F) -> % --R ?*? : (Fraction(Integer),%) -> % ?*? : (%,Fraction(Integer)) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,Integer) -> % ?**? : (%,NonNegativeInteger) -> % --R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % --R ?-? : (%,%) -> % -? : % -> % --R ?/? : (%,F) -> % ?/? : (%,%) -> % --R ?=? : (%,%) -> Boolean D : % -> % if F has FINITE ---R 1 : () -> % 0 : () -> % ---R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> % +--R Frobenius : % -> % if F has FINITE 1 : () -> % +--R 0 : () -> % ?^? : (%,Integer) -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % --R algebraic? : % -> Boolean associates? : (%,%) -> Boolean --R basis : () -> Vector(%) coerce : F -> % --R coerce : Fraction(Integer) -> % coerce : % -> % @@ -74309,24 +74569,22 @@ digraph pic { --R coordinates : % -> Vector(F) degree : % -> PositiveInteger --R dimension : () -> CardinalNumber factor : % -> Factored(%) --R gcd : List(%) -> % gcd : (%,%) -> % ---R hash : % -> SingleInteger inGroundField? : % -> Boolean +--R generator : () -> % if F has FINITE hash : % -> SingleInteger +--R inGroundField? : % -> Boolean init : () -> % if F has FINITE --R inv : % -> % latex : % -> String --R lcm : List(%) -> % lcm : (%,%) -> % --R norm : % -> F one? : % -> Boolean --R prime? : % -> Boolean ?quo? : (%,%) -> % ---R recip : % -> Union(%,"failed") ?rem? : (%,%) -> % ---R represents : Vector(F) -> % retract : % -> F ---R sample : () -> % sizeLess? : (%,%) -> Boolean ---R squareFree : % -> Factored(%) squareFreePart : % -> % ---R trace : % -> F transcendent? : % -> Boolean ---R unit? : % -> Boolean unitCanonical : % -> % ---R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % +--R random : () -> % if F has FINITE recip : % -> Union(%,"failed") +--R ?rem? : (%,%) -> % represents : Vector(F) -> % +--R retract : % -> F sample : () -> % +--R sizeLess? : (%,%) -> Boolean squareFree : % -> Factored(%) +--R squareFreePart : % -> % trace : % -> F +--R transcendent? : % -> Boolean unit? : % -> Boolean +--R unitCanonical : % -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean --R D : (%,NonNegativeInteger) -> % if F has FINITE --R Frobenius : (%,NonNegativeInteger) -> % if F has FINITE ---R Frobenius : % -> % if F has FINITE ---R ?^? : (%,NonNegativeInteger) -> % --R basis : PositiveInteger -> Vector(%) --R characteristic : () -> NonNegativeInteger --R charthRoot : % -> Union(%,"failed") if F has CHARNZ or F has FINITE @@ -74352,9 +74610,7 @@ digraph pic { --R extensionDegree : () -> OnePointCompletion(PositiveInteger) --R factorsOfCyclicGroupSize : () -> List(Record(factor: Integer,exponent: Integer)) if F has FINITE --R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) ---R generator : () -> % if F has FINITE --R index : PositiveInteger -> % if F has FINITE ---R init : () -> % if F has FINITE --R lcmCoef : (%,%) -> Record(llcmres: %,coeff1: %,coeff2: %) --R linearAssociatedExp : (%,SparseUnivariatePolynomial(F)) -> % if F has FINITE --R linearAssociatedLog : (%,%) -> Union(SparseUnivariatePolynomial(F),"failed") if F has FINITE @@ -74375,7 +74631,6 @@ digraph pic { --R primitive? : % -> Boolean if F has FINITE --R primitiveElement : () -> % if F has FINITE --R principalIdeal : List(%) -> Record(coef: List(%),generator: %) ---R random : () -> % if F has FINITE --R representationType : () -> Union("prime",polynomial,normal,cyclic) if F has FINITE --R retractIfCan : % -> Union(F,"failed") --R size : () -> NonNegativeInteger if F has FINITE @@ -75110,31 +75365,36 @@ digraph pic { --R------------------------------- Operations -------------------------------- --R ?*? : (R,%) -> % ?*? : (%,R) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % ---R -? : % -> % ?=? : (%,%) -> Boolean ---R 1 : () -> % 0 : () -> % +--R -? : % -> % ?/? : (%,%) -> % if R has FIELD +--R ?=? : (%,%) -> Boolean 1 : () -> % +--R 0 : () -> % ?^? : (%,NonNegativeInteger) -> % --R ?^? : (%,PositiveInteger) -> % basis : () -> Vector(%) +--R characteristicPolynomial : % -> UP coerce : % -> % if R has FIELD --R coerce : R -> % coerce : Integer -> % --R coerce : % -> OutputForm convert : UP -> % --R convert : % -> UP convert : Vector(R) -> % --R convert : % -> Vector(R) coordinates : % -> Vector(R) --R definingPolynomial : () -> UP discriminant : () -> R ---R discriminant : Vector(%) -> R generator : () -> % ---R hash : % -> SingleInteger inv : % -> % if R has FIELD ---R latex : % -> String lift : % -> UP ---R norm : % -> R one? : % -> Boolean ---R rank : () -> PositiveInteger recip : % -> Union(%,"failed") ---R reduce : UP -> % represents : Vector(R) -> % +--R discriminant : Vector(%) -> R gcd : (%,%) -> % if R has FIELD +--R gcd : List(%) -> % if R has FIELD generator : () -> % +--R hash : % -> SingleInteger init : () -> % if R has FFIELDC +--R inv : % -> % if R has FIELD latex : % -> String +--R lcm : (%,%) -> % if R has FIELD lcm : List(%) -> % if R has FIELD +--R lift : % -> UP norm : % -> R +--R one? : % -> Boolean ?quo? : (%,%) -> % if R has FIELD +--R random : () -> % if R has FINITE rank : () -> PositiveInteger +--R recip : % -> Union(%,"failed") reduce : UP -> % +--R ?rem? : (%,%) -> % if R has FIELD represents : Vector(R) -> % --R retract : % -> R sample : () -> % --R trace : % -> R traceMatrix : () -> Matrix(R) ---R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R unit? : % -> Boolean if R has FIELD zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean --R ?*? : (%,Fraction(Integer)) -> % if R has FIELD --R ?*? : (Fraction(Integer),%) -> % if R has FIELD ---R ?*? : (NonNegativeInteger,%) -> % --R ?**? : (%,Integer) -> % if R has FIELD ---R ?**? : (%,NonNegativeInteger) -> % ---R ?/? : (%,%) -> % if R has FIELD --R D : (%,(R -> R)) -> % if R has FIELD --R D : (%,(R -> R),NonNegativeInteger) -> % if R has FIELD --R D : (%,List(Symbol),List(NonNegativeInteger)) -> % if and(has(R,PartialDifferentialRing(Symbol)),has(R,Field)) @@ -75144,14 +75404,11 @@ digraph pic { --R D : (%,NonNegativeInteger) -> % if and(has(R,DifferentialRing),has(R,Field)) or R has FFIELDC --R D : % -> % if and(has(R,DifferentialRing),has(R,Field)) or R has FFIELDC --R ?^? : (%,Integer) -> % if R has FIELD ---R ?^? : (%,NonNegativeInteger) -> % --R associates? : (%,%) -> Boolean if R has FIELD --R characteristic : () -> NonNegativeInteger ---R characteristicPolynomial : % -> UP --R charthRoot : % -> Union(%,"failed") if R has CHARNZ --R charthRoot : % -> % if R has FFIELDC --R coerce : Fraction(Integer) -> % if R has FIELD or R has RETRACT(FRAC(INT)) ---R coerce : % -> % if R has FIELD --R conditionP : Matrix(%) -> Union(Vector(%),"failed") if R has FFIELDC --R coordinates : Vector(%) -> Matrix(R) --R coordinates : (Vector(%),Vector(%)) -> Matrix(R) @@ -75177,13 +75434,8 @@ digraph pic { --R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") if R has FIELD --R factor : % -> Factored(%) if R has FIELD --R factorsOfCyclicGroupSize : () -> List(Record(factor: Integer,exponent: Integer)) if R has FFIELDC ---R gcd : (%,%) -> % if R has FIELD ---R gcd : List(%) -> % if R has FIELD --R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) if R has FIELD --R index : PositiveInteger -> % if R has FINITE ---R init : () -> % if R has FFIELDC ---R lcm : (%,%) -> % if R has FIELD ---R lcm : List(%) -> % if R has FIELD --R lcmCoef : (%,%) -> Record(llcmres: %,coeff1: %,coeff2: %) if R has FIELD --R lookup : % -> PositiveInteger if R has FINITE --R minimalPolynomial : % -> UP if R has FIELD @@ -75197,8 +75449,6 @@ digraph pic { --R primitive? : % -> Boolean if R has FFIELDC --R primitiveElement : () -> % if R has FFIELDC --R principalIdeal : List(%) -> Record(coef: List(%),generator: %) if R has FIELD ---R ?quo? : (%,%) -> % if R has FIELD ---R random : () -> % if R has FINITE --R reduce : Fraction(UP) -> Union(%,"failed") if R has FIELD --R reducedSystem : Matrix(%) -> Matrix(R) --R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(R),vec: Vector(R)) @@ -75206,7 +75456,6 @@ digraph pic { --R reducedSystem : Matrix(%) -> Matrix(Integer) if R has LINEXP(INT) --R regularRepresentation : % -> Matrix(R) --R regularRepresentation : (%,Vector(%)) -> Matrix(R) ---R ?rem? : (%,%) -> % if R has FIELD --R representationType : () -> Union("prime",polynomial,normal,cyclic) if R has FFIELDC --R represents : (Vector(R),Vector(%)) -> % --R retract : % -> Fraction(Integer) if R has RETRACT(FRAC(INT)) @@ -75221,7 +75470,6 @@ digraph pic { --R subtractIfCan : (%,%) -> Union(%,"failed") --R tableForDiscreteLogarithm : Integer -> Table(PositiveInteger,NonNegativeInteger) if R has FFIELDC --R traceMatrix : Vector(%) -> Matrix(R) ---R unit? : % -> Boolean if R has FIELD --R unitCanonical : % -> % if R has FIELD --R unitNormal : % -> Record(unit: %,canonical: %,associate: %) if R has FIELD --R @@ -75750,40 +75998,38 @@ digraph pic { --R ?*? : (%,Fraction(Integer)) -> % ?*? : (Fraction(Integer),%) -> % --R ?*? : (Fraction(Integer),%) -> % ?*? : (%,Fraction(Integer)) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,Integer) -> % ?**? : (%,NonNegativeInteger) -> % --R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % --R ?-? : (%,%) -> % -? : % -> % --R ?/? : (%,Fraction(Integer)) -> % ?/? : (%,%) -> % --R ?=? : (%,%) -> Boolean 1 : () -> % --R 0 : () -> % ?^? : (%,Integer) -> % ---R ?^? : (%,PositiveInteger) -> % algebraic? : % -> Boolean ---R associates? : (%,%) -> Boolean coerce : Fraction(Integer) -> % ---R coerce : Fraction(Integer) -> % coerce : Integer -> % ---R coerce : Fraction(Integer) -> % coerce : % -> % ---R coerce : Integer -> % coerce : % -> OutputForm ---R conjugate : % -> % dimension : () -> CardinalNumber ---R extDegree : % -> PositiveInteger factor : % -> Factored(%) ---R fullOutput : % -> OutputForm gcd : List(%) -> % ---R gcd : (%,%) -> % ground? : % -> Boolean ---R hash : % -> SingleInteger inGroundField? : % -> Boolean ---R inv : % -> % latex : % -> String ---R lcm : List(%) -> % lcm : (%,%) -> % ---R maxTower : List(%) -> % one? : % -> Boolean ---R previousTower : % -> % prime? : % -> Boolean ---R ?quo? : (%,%) -> % recip : % -> Union(%,"failed") ---R ?rem? : (%,%) -> % retract : % -> Fraction(Integer) ---R retract : % -> Fraction(Integer) retract : % -> Integer ---R sample : () -> % setTower! : % -> Void ---R sizeLess? : (%,%) -> Boolean squareFree : % -> Factored(%) ---R squareFreePart : % -> % transcendent? : % -> Boolean ---R unit? : % -> Boolean unitCanonical : % -> % ---R vectorise : (%,%) -> Vector(%) zero? : % -> Boolean ---R ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R algebraic? : % -> Boolean associates? : (%,%) -> Boolean +--R coerce : Fraction(Integer) -> % coerce : Fraction(Integer) -> % +--R coerce : Integer -> % coerce : Fraction(Integer) -> % +--R coerce : % -> % coerce : Integer -> % +--R coerce : % -> OutputForm conjugate : % -> % +--R dimension : () -> CardinalNumber extDegree : % -> PositiveInteger +--R factor : % -> Factored(%) fullOutput : % -> OutputForm +--R gcd : List(%) -> % gcd : (%,%) -> % +--R ground? : % -> Boolean hash : % -> SingleInteger +--R inGroundField? : % -> Boolean inv : % -> % +--R latex : % -> String lcm : List(%) -> % +--R lcm : (%,%) -> % maxTower : List(%) -> % +--R one? : % -> Boolean previousTower : % -> % +--R prime? : % -> Boolean ?quo? : (%,%) -> % +--R recip : % -> Union(%,"failed") ?rem? : (%,%) -> % +--R retract : % -> Fraction(Integer) retract : % -> Fraction(Integer) +--R retract : % -> Integer sample : () -> % +--R setTower! : % -> Void sizeLess? : (%,%) -> Boolean +--R squareFree : % -> Factored(%) squareFreePart : % -> % +--R transcendent? : % -> Boolean unit? : % -> Boolean +--R unitCanonical : % -> % vectorise : (%,%) -> Vector(%) +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean --R Frobenius : % -> % if Fraction(Integer) has FINITE --R Frobenius : (%,NonNegativeInteger) -> % if Fraction(Integer) has FINITE ---R ?^? : (%,NonNegativeInteger) -> % --R characteristic : () -> NonNegativeInteger --R charthRoot : % -> Union(%,"failed") if Fraction(Integer) has CHARNZ or Fraction(Integer) has FINITE --R definingPolynomial : % -> SparseUnivariatePolynomial(%) @@ -76150,35 +76396,50 @@ digraph pic { --R------------------------------- Operations -------------------------------- --R ?*? : (R,%) -> % ?*? : (%,R) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % ---R -? : % -> % ?=? : (%,%) -> Boolean ---R D : (%,(R -> R)) -> % 1 : () -> % ---R 0 : () -> % ?^? : (%,PositiveInteger) -> % ---R abs : % -> % if R has RNS basis : () -> Vector(%) ---R coerce : R -> % coerce : Integer -> % ---R coerce : % -> OutputForm complex : (R,R) -> % ---R conjugate : % -> % convert : Vector(R) -> % ---R convert : % -> Vector(R) coordinates : % -> Vector(R) +--R -? : % -> % ?/? : (%,%) -> % if R has FIELD +--R ?=? : (%,%) -> Boolean D : (%,(R -> R)) -> % +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R abs : % -> % if R has RNS acos : % -> % if R has TRANFUN +--R acosh : % -> % if R has TRANFUN acot : % -> % if R has TRANFUN +--R acoth : % -> % if R has TRANFUN acsc : % -> % if R has TRANFUN +--R acsch : % -> % if R has TRANFUN argument : % -> R if R has TRANFUN +--R asec : % -> % if R has TRANFUN asech : % -> % if R has TRANFUN +--R asin : % -> % if R has TRANFUN asinh : % -> % if R has TRANFUN +--R atan : % -> % if R has TRANFUN atanh : % -> % if R has TRANFUN +--R basis : () -> Vector(%) coerce : R -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R complex : (R,R) -> % conjugate : % -> % +--R convert : Vector(R) -> % convert : % -> Vector(R) +--R coordinates : % -> Vector(R) cos : % -> % if R has TRANFUN +--R cosh : % -> % if R has TRANFUN cot : % -> % if R has TRANFUN +--R coth : % -> % if R has TRANFUN csc : % -> % if R has TRANFUN +--R csch : % -> % if R has TRANFUN differentiate : (%,(R -> R)) -> % --R discriminant : () -> R discriminant : Vector(%) -> R ---R generator : () -> % hash : % -> SingleInteger ---R imag : % -> R imaginary : () -> % +--R exp : % -> % if R has TRANFUN generator : () -> % +--R hash : % -> SingleInteger imag : % -> R +--R imaginary : () -> % init : () -> % if R has FFIELDC --R inv : % -> % if R has FIELD latex : % -> String ---R map : ((R -> R),%) -> % norm : % -> R ---R one? : % -> Boolean pi : () -> % if R has TRANFUN +--R log : % -> % if R has TRANFUN map : ((R -> R),%) -> % +--R max : (%,%) -> % if R has ORDSET min : (%,%) -> % if R has ORDSET +--R norm : % -> R one? : % -> Boolean +--R pi : () -> % if R has TRANFUN random : () -> % if R has FINITE --R rank : () -> PositiveInteger real : % -> R --R recip : % -> Union(%,"failed") represents : Vector(R) -> % --R retract : % -> R sample : () -> % +--R sec : % -> % if R has TRANFUN sech : % -> % if R has TRANFUN +--R sin : % -> % if R has TRANFUN sinh : % -> % if R has TRANFUN +--R tan : % -> % if R has TRANFUN tanh : % -> % if R has TRANFUN --R trace : % -> R traceMatrix : () -> Matrix(R) --R zero? : % -> Boolean ?~=? : (%,%) -> Boolean --R ?*? : (%,Fraction(Integer)) -> % if R has FIELD --R ?*? : (Fraction(Integer),%) -> % if R has FIELD ---R ?*? : (NonNegativeInteger,%) -> % --R ?**? : (%,Integer) -> % if R has FIELD --R ?**? : (%,%) -> % if R has TRANFUN --R ?**? : (%,Fraction(Integer)) -> % if R has RADCAT and R has TRANFUN ---R ?**? : (%,NonNegativeInteger) -> % ---R ?/? : (%,%) -> % if R has FIELD --R ? Boolean if R has ORDSET --R ?<=? : (%,%) -> Boolean if R has ORDSET --R ?>? : (%,%) -> Boolean if R has ORDSET @@ -76191,21 +76452,7 @@ digraph pic { --R D : (%,List(Symbol),List(NonNegativeInteger)) -> % if R has PDRING(SYMBOL) --R D : (%,(R -> R),NonNegativeInteger) -> % --R ?^? : (%,Integer) -> % if R has FIELD ---R ?^? : (%,NonNegativeInteger) -> % ---R acos : % -> % if R has TRANFUN ---R acosh : % -> % if R has TRANFUN ---R acot : % -> % if R has TRANFUN ---R acoth : % -> % if R has TRANFUN ---R acsc : % -> % if R has TRANFUN ---R acsch : % -> % if R has TRANFUN ---R argument : % -> R if R has TRANFUN ---R asec : % -> % if R has TRANFUN ---R asech : % -> % if R has TRANFUN ---R asin : % -> % if R has TRANFUN ---R asinh : % -> % if R has TRANFUN --R associates? : (%,%) -> Boolean if R has INTDOM or R has EUCDOM and R has PFECAT ---R atan : % -> % if R has TRANFUN ---R atanh : % -> % if R has TRANFUN --R characteristic : () -> NonNegativeInteger --R characteristicPolynomial : % -> SparseUnivariatePolynomial(R) --R charthRoot : % -> Union(%,"failed") if and(has($,CharacteristicNonZero),AND(has(R,EuclideanDomain),has(R,PolynomialFactorizationExplicit))) or R has CHARNZ @@ -76223,13 +76470,7 @@ digraph pic { --R coordinates : Vector(%) -> Matrix(R) --R coordinates : (Vector(%),Vector(%)) -> Matrix(R) --R coordinates : (%,Vector(%)) -> Vector(R) ---R cos : % -> % if R has TRANFUN ---R cosh : % -> % if R has TRANFUN ---R cot : % -> % if R has TRANFUN ---R coth : % -> % if R has TRANFUN --R createPrimitiveElement : () -> % if R has FFIELDC ---R csc : % -> % if R has TRANFUN ---R csch : % -> % if R has TRANFUN --R definingPolynomial : () -> SparseUnivariatePolynomial(R) --R derivationCoordinates : (Vector(%),(R -> R)) -> Matrix(R) if R has FIELD --R differentiate : % -> % if and(has(R,Field),has(R,DifferentialRing)) or R has DIFRING or and(has(R,DifferentialRing),has(R,Field)) @@ -76238,7 +76479,6 @@ digraph pic { --R differentiate : (%,List(Symbol)) -> % if R has PDRING(SYMBOL) --R differentiate : (%,Symbol,NonNegativeInteger) -> % if R has PDRING(SYMBOL) --R differentiate : (%,List(Symbol),List(NonNegativeInteger)) -> % if R has PDRING(SYMBOL) ---R differentiate : (%,(R -> R)) -> % --R differentiate : (%,(R -> R),NonNegativeInteger) -> % --R discreteLog : (%,%) -> Union(NonNegativeInteger,"failed") if R has FFIELDC --R discreteLog : % -> NonNegativeInteger if R has FFIELDC @@ -76252,7 +76492,6 @@ digraph pic { --R eval : (%,Equation(R)) -> % if R has EVALAB(R) --R eval : (%,R,R) -> % if R has EVALAB(R) --R eval : (%,List(R),List(R)) -> % if R has EVALAB(R) ---R exp : % -> % if R has TRANFUN --R expressIdealMember : (List(%),%) -> Union(List(%),"failed") if R has EUCDOM --R exquo : (%,%) -> Union(%,"failed") if R has INTDOM or R has EUCDOM and R has PFECAT --R exquo : (%,R) -> Union(%,"failed") if R has INTDOM @@ -76266,15 +76505,11 @@ digraph pic { --R gcd : List(%) -> % if R has EUCDOM or R has EUCDOM and R has PFECAT --R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) if R has EUCDOM or R has EUCDOM and R has PFECAT --R index : PositiveInteger -> % if R has FINITE ---R init : () -> % if R has FFIELDC --R lcm : (%,%) -> % if R has EUCDOM or R has EUCDOM and R has PFECAT --R lcm : List(%) -> % if R has EUCDOM or R has EUCDOM and R has PFECAT --R lcmCoef : (%,%) -> Record(llcmres: %,coeff1: %,coeff2: %) if R has EUCDOM or R has EUCDOM and R has PFECAT --R lift : % -> SparseUnivariatePolynomial(R) ---R log : % -> % if R has TRANFUN --R lookup : % -> PositiveInteger if R has FINITE ---R max : (%,%) -> % if R has ORDSET ---R min : (%,%) -> % if R has ORDSET --R minimalPolynomial : % -> SparseUnivariatePolynomial(R) if R has FIELD --R multiEuclidean : (List(%),%) -> Union(List(%),"failed") if R has EUCDOM --R nextItem : % -> Union(%,"failed") if R has FFIELDC @@ -76291,7 +76526,6 @@ digraph pic { --R primitiveElement : () -> % if R has FFIELDC --R principalIdeal : List(%) -> Record(coef: List(%),generator: %) if R has EUCDOM --R ?quo? : (%,%) -> % if R has EUCDOM ---R random : () -> % if R has FINITE --R rational : % -> Fraction(Integer) if R has INS --R rational? : % -> Boolean if R has INS --R rationalIfCan : % -> Union(Fraction(Integer),"failed") if R has INS @@ -76311,10 +76545,6 @@ digraph pic { --R retractIfCan : % -> Union(R,"failed") --R retractIfCan : % -> Union(Fraction(Integer),"failed") if R has RETRACT(FRAC(INT)) --R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT(INT) ---R sec : % -> % if R has TRANFUN ---R sech : % -> % if R has TRANFUN ---R sin : % -> % if R has TRANFUN ---R sinh : % -> % if R has TRANFUN --R size : () -> NonNegativeInteger if R has FINITE --R sizeLess? : (%,%) -> Boolean if R has EUCDOM --R solveLinearPolynomialEquation : (List(SparseUnivariatePolynomial(%)),SparseUnivariatePolynomial(%)) -> Union(List(SparseUnivariatePolynomial(%)),"failed") if R has EUCDOM and R has PFECAT @@ -76324,8 +76554,6 @@ digraph pic { --R squareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has EUCDOM and R has PFECAT --R subtractIfCan : (%,%) -> Union(%,"failed") --R tableForDiscreteLogarithm : Integer -> Table(PositiveInteger,NonNegativeInteger) if R has FFIELDC ---R tan : % -> % if R has TRANFUN ---R tanh : % -> % if R has TRANFUN --R traceMatrix : Vector(%) -> Matrix(R) --R unit? : % -> Boolean if R has INTDOM or R has EUCDOM and R has PFECAT --R unitCanonical : % -> % if R has INTDOM or R has EUCDOM and R has PFECAT @@ -77295,34 +77523,37 @@ digraph pic { --R------------------------------- Operations -------------------------------- --R ?*? : (Fraction(UP),%) -> % ?*? : (%,Fraction(UP)) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ?=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % basis : () -> Vector(%) ---R branchPoint? : UP -> Boolean branchPoint? : F -> Boolean ---R coerce : Fraction(UP) -> % coerce : Integer -> % ---R coerce : % -> OutputForm convert : UPUP -> % ---R convert : % -> UPUP definingPolynomial : () -> UPUP ---R discriminant : () -> Fraction(UP) elt : (%,F,F) -> F +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R basis : () -> Vector(%) branchPoint? : UP -> Boolean +--R branchPoint? : F -> Boolean coerce : Fraction(UP) -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R convert : UPUP -> % convert : % -> UPUP +--R convert : Vector(Fraction(UP)) -> % convert : % -> Vector(Fraction(UP)) +--R definingPolynomial : () -> UPUP discriminant : () -> Fraction(UP) +--R elliptic : () -> Union(UP,"failed") elt : (%,F,F) -> F --R generator : () -> % genus : () -> NonNegativeInteger --R hash : % -> SingleInteger integral? : (%,UP) -> Boolean --R integral? : (%,F) -> Boolean integral? : % -> Boolean ---R integralBasis : () -> Vector(%) latex : % -> String ---R lift : % -> UPUP norm : % -> Fraction(UP) ---R one? : % -> Boolean primitivePart : % -> % ---R ramified? : UP -> Boolean ramified? : F -> Boolean +--R integralAtInfinity? : % -> Boolean integralBasis : () -> Vector(%) +--R latex : % -> String lift : % -> UPUP +--R norm : % -> Fraction(UP) one? : % -> Boolean +--R primitivePart : % -> % ramified? : UP -> Boolean +--R ramified? : F -> Boolean ramifiedAtInfinity? : () -> Boolean --R rank : () -> PositiveInteger rationalPoint? : (F,F) -> Boolean --R recip : % -> Union(%,"failed") reduce : UPUP -> % --R represents : (Vector(UP),UP) -> % retract : % -> Fraction(UP) --R sample : () -> % singular? : UP -> Boolean ---R singular? : F -> Boolean trace : % -> Fraction(UP) ---R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R singular? : F -> Boolean singularAtInfinity? : () -> Boolean +--R trace : % -> Fraction(UP) zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean --R ?*? : (%,Fraction(Integer)) -> % if Fraction(UP) has FIELD --R ?*? : (Fraction(Integer),%) -> % if Fraction(UP) has FIELD ---R ?*? : (NonNegativeInteger,%) -> % --R ?**? : (%,Integer) -> % if Fraction(UP) has FIELD ---R ?**? : (%,NonNegativeInteger) -> % --R ?/? : (%,%) -> % if Fraction(UP) has FIELD --R D : % -> % if and(has(Fraction(UP),Field),has(Fraction(UP),DifferentialRing)) or and(has(Fraction(UP),DifferentialRing),has(Fraction(UP),Field)) or Fraction(UP) has FFIELDC --R D : (%,NonNegativeInteger) -> % if and(has(Fraction(UP),Field),has(Fraction(UP),DifferentialRing)) or and(has(Fraction(UP),DifferentialRing),has(Fraction(UP),Field)) or Fraction(UP) has FFIELDC @@ -77333,7 +77564,6 @@ digraph pic { --R D : (%,(Fraction(UP) -> Fraction(UP))) -> % if Fraction(UP) has FIELD --R D : (%,(Fraction(UP) -> Fraction(UP)),NonNegativeInteger) -> % if Fraction(UP) has FIELD --R ?^? : (%,Integer) -> % if Fraction(UP) has FIELD ---R ?^? : (%,NonNegativeInteger) -> % --R absolutelyIrreducible? : () -> Boolean --R algSplitSimple : (%,(UP -> UP)) -> Record(num: %,den: UP,derivden: UP,gd: UP) --R associates? : (%,%) -> Boolean if Fraction(UP) has FIELD @@ -77346,8 +77576,6 @@ digraph pic { --R coerce : Fraction(Integer) -> % if Fraction(UP) has FIELD or Fraction(UP) has RETRACT(FRAC(INT)) --R complementaryBasis : Vector(%) -> Vector(%) --R conditionP : Matrix(%) -> Union(Vector(%),"failed") if Fraction(UP) has FFIELDC ---R convert : Vector(Fraction(UP)) -> % ---R convert : % -> Vector(Fraction(UP)) --R coordinates : Vector(%) -> Matrix(Fraction(UP)) --R coordinates : % -> Vector(Fraction(UP)) --R coordinates : (Vector(%),Vector(%)) -> Matrix(Fraction(UP)) @@ -77367,7 +77595,6 @@ digraph pic { --R discreteLog : % -> NonNegativeInteger if Fraction(UP) has FFIELDC --R discriminant : Vector(%) -> Fraction(UP) --R divide : (%,%) -> Record(quotient: %,remainder: %) if Fraction(UP) has FIELD ---R elliptic : () -> Union(UP,"failed") --R enumerate : () -> List(%) if Fraction(UP) has FINITE --R euclideanSize : % -> NonNegativeInteger if Fraction(UP) has FIELD --R expressIdealMember : (List(%),%) -> Union(List(%),"failed") if Fraction(UP) has FIELD @@ -77382,7 +77609,6 @@ digraph pic { --R hyperelliptic : () -> Union(UP,"failed") --R index : PositiveInteger -> % if Fraction(UP) has FINITE --R init : () -> % if Fraction(UP) has FFIELDC ---R integralAtInfinity? : % -> Boolean --R integralBasisAtInfinity : () -> Vector(%) --R integralCoordinates : % -> Record(num: Vector(UP),den: UP) --R integralDerivationMatrix : (UP -> UP) -> Record(num: Matrix(UP),den: UP) @@ -77411,7 +77637,6 @@ digraph pic { --R primitiveElement : () -> % if Fraction(UP) has FFIELDC --R principalIdeal : List(%) -> Record(coef: List(%),generator: %) if Fraction(UP) has FIELD --R ?quo? : (%,%) -> % if Fraction(UP) has FIELD ---R ramifiedAtInfinity? : () -> Boolean --R random : () -> % if Fraction(UP) has FINITE --R rationalPoints : () -> List(List(F)) if F has FINITE --R reduce : Fraction(UPUP) -> Union(%,"failed") if Fraction(UP) has FIELD @@ -77431,7 +77656,6 @@ digraph pic { --R retractIfCan : % -> Union(Fraction(UP),"failed") --R retractIfCan : % -> Union(Fraction(Integer),"failed") if Fraction(UP) has RETRACT(FRAC(INT)) --R retractIfCan : % -> Union(Integer,"failed") if Fraction(UP) has RETRACT(INT) ---R singularAtInfinity? : () -> Boolean --R size : () -> NonNegativeInteger if Fraction(UP) has FINITE --R sizeLess? : (%,%) -> Boolean if Fraction(UP) has FIELD --R squareFree : % -> Factored(%) if Fraction(UP) has FIELD @@ -78507,43 +78731,41 @@ digraph pic { --R ?*? : (%,Fraction(Integer)) -> % ?*? : (Fraction(Integer),%) -> % --R ?*? : (Fraction(Integer),%) -> % ?*? : (%,Fraction(Integer)) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,Integer) -> % ?**? : (%,NonNegativeInteger) -> % --R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % --R ?-? : (%,%) -> % -? : % -> % --R ?/? : (%,Fraction(Integer)) -> % ?/? : (%,%) -> % --R ?=? : (%,%) -> Boolean 1 : () -> % --R 0 : () -> % ?^? : (%,Integer) -> % ---R ?^? : (%,PositiveInteger) -> % algebraic? : % -> Boolean ---R associates? : (%,%) -> Boolean coerce : Fraction(Integer) -> % ---R coerce : Fraction(Integer) -> % coerce : Integer -> % ---R coerce : Fraction(Integer) -> % coerce : % -> % ---R coerce : Integer -> % coerce : % -> OutputForm ---R conjugate : % -> % dimension : () -> CardinalNumber ---R extDegree : % -> PositiveInteger factor : % -> Factored(%) ---R fullOutput : % -> OutputForm gcd : List(%) -> % ---R gcd : (%,%) -> % ground? : % -> Boolean ---R hash : % -> SingleInteger inGroundField? : % -> Boolean ---R inv : % -> % latex : % -> String ---R lcm : List(%) -> % lcm : (%,%) -> % ---R maxTower : List(%) -> % one? : % -> Boolean ---R previousTower : % -> % prime? : % -> Boolean ---R ?quo? : (%,%) -> % recip : % -> Union(%,"failed") ---R ?rem? : (%,%) -> % retract : % -> Fraction(Integer) ---R retract : % -> Fraction(Integer) retract : % -> Integer ---R sample : () -> % setTower! : % -> Void ---R sizeLess? : (%,%) -> Boolean squareFree : % -> Factored(%) ---R squareFreePart : % -> % transcendent? : % -> Boolean ---R unit? : % -> Boolean unitCanonical : % -> % ---R vectorise : (%,%) -> Vector(%) zero? : % -> Boolean ---R ?~=? : (%,%) -> Boolean +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R algebraic? : % -> Boolean associates? : (%,%) -> Boolean +--R coerce : Fraction(Integer) -> % coerce : Fraction(Integer) -> % +--R coerce : Integer -> % coerce : Fraction(Integer) -> % +--R coerce : % -> % coerce : Integer -> % +--R coerce : % -> OutputForm conjugate : % -> % +--R dimension : () -> CardinalNumber extDegree : % -> PositiveInteger +--R factor : % -> Factored(%) fullOutput : % -> OutputForm +--R gcd : List(%) -> % gcd : (%,%) -> % +--R ground? : % -> Boolean hash : % -> SingleInteger +--R inGroundField? : % -> Boolean inv : % -> % +--R latex : % -> String lcm : List(%) -> % +--R lcm : (%,%) -> % maxTower : List(%) -> % +--R one? : % -> Boolean previousTower : % -> % +--R prime? : % -> Boolean ?quo? : (%,%) -> % +--R recip : % -> Union(%,"failed") ?rem? : (%,%) -> % +--R retract : % -> Fraction(Integer) retract : % -> Fraction(Integer) +--R retract : % -> Integer sample : () -> % +--R setTower! : % -> Void sizeLess? : (%,%) -> Boolean +--R squareFree : % -> Factored(%) squareFreePart : % -> % +--R transcendent? : % -> Boolean unit? : % -> Boolean +--R unitCanonical : % -> % vectorise : (%,%) -> Vector(%) +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean --R ?*? : (%,PseudoAlgebraicClosureOfRationalNumber) -> % --R ?*? : (PseudoAlgebraicClosureOfRationalNumber,%) -> % ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % --R ?/? : (%,PseudoAlgebraicClosureOfRationalNumber) -> % --R Frobenius : % -> % if PseudoAlgebraicClosureOfRationalNumber has FINITE or Fraction(Integer) has FINITE --R Frobenius : (%,NonNegativeInteger) -> % if PseudoAlgebraicClosureOfRationalNumber has FINITE or Fraction(Integer) has FINITE ---R ?^? : (%,NonNegativeInteger) -> % --R characteristic : () -> NonNegativeInteger --R charthRoot : % -> Union(%,"failed") if PseudoAlgebraicClosureOfRationalNumber has CHARNZ or PseudoAlgebraicClosureOfRationalNumber has FINITE or Fraction(Integer) has CHARNZ or Fraction(Integer) has FINITE --R coerce : PseudoAlgebraicClosureOfRationalNumber -> % diff --git a/books/bookvol10.3.pamphlet b/books/bookvol10.3.pamphlet index 0585c7f..5329aa3 100644 --- a/books/bookvol10.3.pamphlet +++ b/books/bookvol10.3.pamphlet @@ -445,7 +445,7 @@ A Gonshor genetic algebra ([WB], p. 41-42) of dimension 4: The coefficient ring: \begin{chunk}{AlgebraGivenByStructuralConstants.input} ---S 1 of 98 +--S 1 of 99 R := FRAC POLY INT --R --R @@ -457,7 +457,7 @@ R := FRAC POLY INT The following multiplication constants may be chosen arbitrarily (notice that we write ckij for $c_(i,j)^k$): \begin{chunk}{AlgebraGivenByStructuralConstants.input} ---S 2 of 98 +--S 2 of 99 (c100, c101, _ c200, c201, c202, c211, _ c300, c301, c302, c303, c311, c312, c322) : R @@ -465,14 +465,14 @@ c300, c301, c302, c303, c311, c312, c322) : R --R Type: Void --E 2 ---S 3 of 98 +--S 3 of 99 c100 := 1 ; c101 := -1 ; --R --R --R Type: Fraction(Polynomial(Integer)) --E 3 ---S 4 of 98 +--S 4 of 99 c200 := 0 ; c201 := 1 ; c202 := -1 ; c211 := 2 ; --R @@ -480,7 +480,7 @@ c200 := 0 ; c201 := 1 ; c202 := -1 ; --R Type: Fraction(Polynomial(Integer)) --E 4 ---S 5 of 98 +--S 5 of 99 c300 := 1 ; c301 := 0 ; c302 := -1 ; c303 := 1 ; c311 := 1 ; c312 := 0 ; c322 := 2 ; @@ -492,7 +492,7 @@ c300 := 1 ; c301 := 0 ; c302 := -1 ; c303 := 1 ; \end{chunk} The matrices of the multiplication constants: \begin{chunk}{AlgebraGivenByStructuralConstants.input} ---S 6 of 98 +--S 6 of 99 gonshor : List SquareMatrix(4,R) := [matrix [ [1, 0, 0, 0], [0, 0, 0, 0],_ [0, 0, 0, 0], [0, 0, 0, 0] ],_ @@ -507,7 +507,7 @@ gonshor : List SquareMatrix(4,R) := --R Type: List(SquareMatrix(4,Fraction(Polynomial(Integer)))) --E 6 ---S 7 of 98 +--S 7 of 99 basisSymbols : List Symbol := [subscript(e,[i]) for i in 0..3] --R --R @@ -516,7 +516,7 @@ basisSymbols : List Symbol := [subscript(e,[i]) for i in 0..3] --R Type: List(Symbol) --E 7 ---S 8 of 98 +--S 8 of 99 GonshorGenetic := ALGSC(R, 4, basisSymbols, gonshor) --R --R @@ -526,7 +526,7 @@ GonshorGenetic := ALGSC(R, 4, basisSymbols, gonshor) --R Type: Domain --E 8 ---S 9 of 98 +--S 9 of 99 commutative?()$GonshorGenetic --R --R algebra is commutative @@ -535,7 +535,7 @@ commutative?()$GonshorGenetic --R Type: Boolean --E 9 ---S 10 of 98 +--S 10 of 99 associative?()$GonshorGenetic --R --R algebra is not associative @@ -547,28 +547,28 @@ associative?()$GonshorGenetic \end{chunk} The canonical basis: \begin{chunk}{AlgebraGivenByStructuralConstants.input} ---S 11 of 98 +--S 11 of 99 e0 : GonshorGenetic := [1, 0, 0, 0] :: Vector R ; --R --R --RType: AlgebraGivenByStructuralConstants(Fraction(Polynomial(Integer)),4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX]) --E 11 ---S 12 of 98 +--S 12 of 99 e1 : GonshorGenetic := [0, 1, 0, 0] :: Vector R ; --R --R --RType: AlgebraGivenByStructuralConstants(Fraction(Polynomial(Integer)),4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX]) --E 12 ---S 13 of 98 +--S 13 of 99 e2 : GonshorGenetic := [0, 0, 1, 0] :: Vector R ; --R --R --RType: AlgebraGivenByStructuralConstants(Fraction(Polynomial(Integer)),4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX]) --E 13 ---S 14 of 98 +--S 14 of 99 e3 : GonshorGenetic := [0, 0, 0, 1] :: Vector R ; --R --R @@ -578,7 +578,7 @@ e3 : GonshorGenetic := [0, 0, 0, 1] :: Vector R ; \end{chunk} A generic element of the algebra: \begin{chunk}{AlgebraGivenByStructuralConstants.input} ---S 15 of 98 +--S 15 of 99 x : GonshorGenetic := x0*e0 + x1*e1 + x2*e2 + x3*e3 --R --R @@ -590,7 +590,7 @@ x : GonshorGenetic := x0*e0 + x1*e1 + x2*e2 + x3*e3 \end{chunk} The matrix of the left multiplication with x : \begin{chunk}{AlgebraGivenByStructuralConstants.input} ---S 16 of 98 +--S 16 of 99 Lx := leftRegularRepresentation x --R --R @@ -611,7 +611,7 @@ defined by 8(e0) := 1 and 8(ei) := 0 for i = 1,2,3 . The coefficients of the characteristic polynomial of Lx depend only on 8(x) = x0 : \begin{chunk}{AlgebraGivenByStructuralConstants.input} ---S 17 of 98 +--S 17 of 99 p := characteristicPolynomial(Lx,Y) --R --R @@ -623,7 +623,7 @@ p := characteristicPolynomial(Lx,Y) \end{chunk} The left minimal polynomial of x divides Y * p(Y) : \begin{chunk}{AlgebraGivenByStructuralConstants.input} ---S 18 of 98 +--S 18 of 99 leftMinimalPolynomial x --R --R @@ -634,7 +634,7 @@ leftMinimalPolynomial x )clear prop A a b c r s ---S 19 of 98 +--S 19 of 99 A := GonshorGenetic --R --R @@ -644,7 +644,7 @@ A := GonshorGenetic --R Type: Domain --E 19 ---S 20 of 98 +--S 20 of 99 a := x --R --R @@ -653,7 +653,7 @@ a := x --RType: AlgebraGivenByStructuralConstants(Fraction(Polynomial(Integer)),4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX]) --E 20 ---S 21 of 98 +--S 21 of 99 b := (1/4)*e1 + (1/5)*e2 + (3/20)*e3 + (2/5)*e0 --R --R @@ -663,7 +663,7 @@ b := (1/4)*e1 + (1/5)*e2 + (3/20)*e3 + (2/5)*e0 --RType: AlgebraGivenByStructuralConstants(Fraction(Polynomial(Integer)),4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX]) --E 21 ---S 22 of 98 +--S 22 of 99 c := (1/3)*e1 + (1/7)*e2 + (8/21)*e3 + (1/7)*e0 --R --R @@ -673,7 +673,7 @@ c := (1/3)*e1 + (1/7)*e2 + (8/21)*e3 + (1/7)*e0 --RType: AlgebraGivenByStructuralConstants(Fraction(Polynomial(Integer)),4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX]) --E 22 ---S 23 of 98 +--S 23 of 99 r : R := r --R --R @@ -681,7 +681,7 @@ r : R := r --R Type: Fraction(Polynomial(Integer)) --E 23 ---S 24 of 98 +--S 24 of 99 s : R := s --R --R @@ -689,7 +689,7 @@ s : R := s --R Type: Fraction(Polynomial(Integer)) --E 24 ---S 25 of 98 +--S 25 of 99 b*c --R --R @@ -699,7 +699,7 @@ b*c --RType: AlgebraGivenByStructuralConstants(Fraction(Polynomial(Integer)),4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX]) --E 25 ---S 26 of 98 +--S 26 of 99 (b*c)*b --R --R @@ -709,7 +709,7 @@ b*c --RType: AlgebraGivenByStructuralConstants(Fraction(Polynomial(Integer)),4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX]) --E 26 ---S 27 of 98 +--S 27 of 99 b*(c*b) --R --R @@ -726,7 +726,7 @@ r,s : R \begin{chunk}{AlgebraGivenByStructuralConstants.input} )clear prop AP ---S 28 of 98 +--S 28 of 99 AP := ALGPKG(R,A) --R --R @@ -737,7 +737,7 @@ AP := ALGPKG(R,A) --R Type: Domain --E 28 ---S 29 of 98 +--S 29 of 99 r*a --R --R @@ -746,7 +746,7 @@ r*a --RType: AlgebraGivenByStructuralConstants(Fraction(Polynomial(Integer)),4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX]) --E 29 ---S 30 of 98 +--S 30 of 99 a*r --R --R @@ -755,7 +755,7 @@ a*r --RType: AlgebraGivenByStructuralConstants(Fraction(Polynomial(Integer)),4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX]) --E 30 ---S 31 of 98 +--S 31 of 99 a*b --R --R @@ -765,7 +765,7 @@ a*b --RType: AlgebraGivenByStructuralConstants(Fraction(Polynomial(Integer)),4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX]) --E 31 ---S 32 of 98 +--S 32 of 99 b*c --R --R @@ -775,7 +775,7 @@ b*c --RType: AlgebraGivenByStructuralConstants(Fraction(Polynomial(Integer)),4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX]) --E 32 ---S 33 of 98 +--S 33 of 99 12 * c --R --R @@ -785,7 +785,7 @@ b*c --RType: AlgebraGivenByStructuralConstants(Fraction(Polynomial(Integer)),4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX]) --E 32 ---S 34 of 98 +--S 34 of 99 (-3) * a --R --R @@ -794,7 +794,7 @@ b*c --RType: AlgebraGivenByStructuralConstants(Fraction(Polynomial(Integer)),4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX]) --E 34 ---S 35 of 98 +--S 35 of 99 d := a ** 12 --R --R @@ -814,7 +814,7 @@ d := a ** 12 --RType: AlgebraGivenByStructuralConstants(Fraction(Polynomial(Integer)),4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX]) --E 35 ---S 36 of 98 +--S 36 of 99 -d --R --R @@ -834,7 +834,7 @@ d := a ** 12 --RType: AlgebraGivenByStructuralConstants(Fraction(Polynomial(Integer)),4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX]) --E 36 ---S 37 of 98 +--S 37 of 99 a + b --R --R @@ -844,7 +844,7 @@ a + b --RType: AlgebraGivenByStructuralConstants(Fraction(Polynomial(Integer)),4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX]) --E 37 ---S 38 of 98 +--S 38 of 99 d-c --R --R @@ -872,7 +872,7 @@ d-c --RType: AlgebraGivenByStructuralConstants(Fraction(Polynomial(Integer)),4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX]) --E 38 ---S 39 of 98 +--S 39 of 99 (a*(a*a) = leftPower(a,3)) :: Boolean --R --R @@ -880,7 +880,7 @@ d-c --R Type: Boolean --E 39 ---S 40 of 98 +--S 40 of 99 (a ** 11 = (a**8 * a**2) * a) :: Boolean --R --R @@ -888,7 +888,7 @@ d-c --R Type: Boolean --E 40 ---S 41 of 98 +--S 41 of 99 (a ** 11 = a**8 * (a**2 * a)) :: Boolean --R --R @@ -896,7 +896,7 @@ d-c --R Type: Boolean --E 41 ---S 42 of 98 +--S 42 of 99 zero := 0$A --R --R @@ -904,7 +904,7 @@ zero := 0$A --RType: AlgebraGivenByStructuralConstants(Fraction(Polynomial(Integer)),4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX]) --E 42 ---S 43 of 98 +--S 43 of 99 zero : A := 0 --R --R @@ -912,7 +912,7 @@ zero : A := 0 --RType: AlgebraGivenByStructuralConstants(Fraction(Polynomial(Integer)),4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX]) --E 43 ---S 44 of 98 +--S 44 of 99 alternative?()$A --R --R algebra is not left alternative @@ -921,7 +921,7 @@ alternative?()$A --R Type: Boolean --E 44 ---S 45 of 98 +--S 45 of 99 antiCommutative?()$A --R --R algebra is not anti-commutative @@ -930,7 +930,7 @@ antiCommutative?()$A --R Type: Boolean --E 45 ---S 46 of 98 +--S 46 of 99 associative?()$A --R --R algebra is not associative @@ -939,7 +939,7 @@ associative?()$A --R Type: Boolean --E 46 ---S 47 of 98 +--S 47 of 99 commutative?()$A --R --R algebra is commutative @@ -948,7 +948,7 @@ commutative?()$A --R Type: Boolean --E 47 ---S 48 of 98 +--S 48 of 99 commutator(a,b) --R --R @@ -956,7 +956,7 @@ commutator(a,b) --RType: AlgebraGivenByStructuralConstants(Fraction(Polynomial(Integer)),4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX]) --E 48 ---S 49 of 98 +--S 49 of 99 antiCommutator(a,b) --R --R @@ -966,7 +966,7 @@ antiCommutator(a,b) --RType: AlgebraGivenByStructuralConstants(Fraction(Polynomial(Integer)),4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX]) --E 49 ---S 50 of 98 +--S 50 of 99 associator(a,b,c) --R --R @@ -976,7 +976,7 @@ associator(a,b,c) --RType: AlgebraGivenByStructuralConstants(Fraction(Polynomial(Integer)),4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX]) --E 50 ---S 51 of 98 +--S 51 of 99 basis()$A --R --R @@ -985,7 +985,7 @@ basis()$A --RType: Vector(AlgebraGivenByStructuralConstants(Fraction(Polynomial(Integer)),4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])) --E 51 ---S 52 of 98 +--S 52 of 99 n := rank()$A --R --R @@ -993,7 +993,7 @@ n := rank()$A --R Type: PositiveInteger --E 52 ---S 53 of 98 +--S 53 of 99 v : Vector R := [i for i in 1..n] --R --R @@ -1001,7 +1001,7 @@ v : Vector R := [i for i in 1..n] --R Type: Vector(Fraction(Polynomial(Integer))) --E 53 ---S 54 of 98 +--S 54 of 99 g : A := represents v --R --R @@ -1010,7 +1010,7 @@ g : A := represents v --RType: AlgebraGivenByStructuralConstants(Fraction(Polynomial(Integer)),4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX]) --E 54 ---S 55 of 98 +--S 55 of 99 coordinates a --R --R @@ -1018,7 +1018,7 @@ coordinates a --R Type: Vector(Fraction(Polynomial(Integer))) --E 55 ---S 56 of 98 +--S 56 of 99 coordinates [a,b] --R --R @@ -1030,7 +1030,7 @@ coordinates [a,b] --R Type: Matrix(Fraction(Polynomial(Integer))) --E 56 ---S 57 of 98 +--S 57 of 99 a.3 --R --R @@ -1038,7 +1038,7 @@ a.3 --R Type: Fraction(Polynomial(Integer)) --E 57 ---S 58 of 98 +--S 58 of 99 flexible?()$A --R --R algebra is flexible @@ -1047,7 +1047,7 @@ flexible?()$A --R Type: Boolean --E 58 ---S 59 of 98 +--S 59 of 99 leftAlternative?()$A --R --R algebra is not left alternative @@ -1056,7 +1056,7 @@ leftAlternative?()$A --R Type: Boolean --E 59 ---S 60 of 98 +--S 60 of 99 rightAlternative?()$A --R --R algebra is not right alternative @@ -1065,7 +1065,7 @@ rightAlternative?()$A --R Type: Boolean --E 60 ---S 61 of 98 +--S 61 of 99 sB := someBasis()$A --R --R @@ -1074,7 +1074,7 @@ sB := someBasis()$A --RType: Vector(AlgebraGivenByStructuralConstants(Fraction(Polynomial(Integer)),4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])) --E 61 ---S 62 of 98 +--S 62 of 99 zero? a --R --R @@ -1082,7 +1082,7 @@ zero? a --R Type: Boolean --E 62 ---S 63 of 98 +--S 63 of 99 associatorDependence()$A --R --R @@ -1093,7 +1093,7 @@ associatorDependence()$A \end{chunk} ConditionsForIdempotents()\$A \begin{chunk}{AlgebraGivenByStructuralConstants.input} ---S 64 of 98 +--S 64 of 99 jacobiIdentity?()$A --R --R Jacobi identity does not hold @@ -1102,7 +1102,7 @@ jacobiIdentity?()$A --R Type: Boolean --E 64 ---S 65 of 98 +--S 65 of 99 jordanAlgebra?()$A --R --R algebra is commutative @@ -1112,7 +1112,7 @@ jordanAlgebra?()$A --R Type: Boolean --E 65 ---S 66 of 98 +--S 66 of 99 jordanAdmissible?()$A --R --R algebra is not Jordan admissible @@ -1121,7 +1121,7 @@ jordanAdmissible?()$A --R Type: Boolean --E 66 ---S 67 of 98 +--S 67 of 99 lieAdmissible?()$A --R --R algebra is Lie admissible @@ -1133,7 +1133,7 @@ lieAdmissible?()$A \end{chunk} ConditionsForIdempotents \begin{chunk}{AlgebraGivenByStructuralConstants.input} ---S 68 of 98 +--S 68 of 99 b2 := [reduce(+,[sB.i for i in 1..k]) for k in 1..n] --R --R @@ -1142,7 +1142,7 @@ b2 := [reduce(+,[sB.i for i in 1..k]) for k in 1..n] --RType: List(AlgebraGivenByStructuralConstants(Fraction(Polynomial(Integer)),4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])) --E 68 ---S 69 of 98 +--S 69 of 99 coordinates (a ,b2 :: Vector A) --R --R @@ -1150,7 +1150,7 @@ coordinates (a ,b2 :: Vector A) --R Type: Vector(Fraction(Polynomial(Integer))) --E 69 ---S 70 of 98 +--S 70 of 99 coordinates ([a,b] ,bb := (b2 :: Vector A)) --R --R @@ -1162,7 +1162,7 @@ coordinates ([a,b] ,bb := (b2 :: Vector A)) --R Type: Matrix(Fraction(Polynomial(Integer))) --E 70 ---S 71 of 98 +--S 71 of 99 leftMinimalPolynomial a --R --R @@ -1171,7 +1171,7 @@ leftMinimalPolynomial a --R Type: SparseUnivariatePolynomial(Fraction(Polynomial(Integer))) --E 71 ---S 72 of 98 +--S 72 of 99 leftPower (a,10) --R --R @@ -1186,7 +1186,7 @@ leftPower (a,10) --RType: AlgebraGivenByStructuralConstants(Fraction(Polynomial(Integer)),4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX]) --E 72 ---S 73 of 98 +--S 73 of 99 rightPower(a,10) --R --R @@ -1201,7 +1201,7 @@ rightPower(a,10) --RType: AlgebraGivenByStructuralConstants(Fraction(Polynomial(Integer)),4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX]) --E 73 ---S 74 of 98 +--S 74 of 99 leftRegularRepresentation a --R --R @@ -1215,7 +1215,7 @@ leftRegularRepresentation a --R Type: Matrix(Fraction(Polynomial(Integer))) --E 74 ---S 75 of 98 +--S 75 of 99 leftRegularRepresentation (a,bb) --R --R @@ -1229,7 +1229,7 @@ leftRegularRepresentation (a,bb) --R Type: Matrix(Fraction(Polynomial(Integer))) --E 75 ---S 76 of 98 +--S 76 of 99 leftUnit()$A --R --R this algebra has no left unit @@ -1238,7 +1238,7 @@ leftUnit()$A --R Type: Union("failed",...) --E 76 ---S 77 of 98 +--S 77 of 99 represents (v,bb) --R --R @@ -1247,7 +1247,7 @@ represents (v,bb) --RType: AlgebraGivenByStructuralConstants(Fraction(Polynomial(Integer)),4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX]) --E 77 ---S 78 of 98 +--S 78 of 99 rightMinimalPolynomial a --R --R @@ -1256,7 +1256,7 @@ rightMinimalPolynomial a --R Type: SparseUnivariatePolynomial(Fraction(Polynomial(Integer))) --E 78 ---S 79 of 98 +--S 79 of 99 rightRegularRepresentation a --R --R @@ -1270,7 +1270,7 @@ rightRegularRepresentation a --R Type: Matrix(Fraction(Polynomial(Integer))) --E 79 ---S 80 of 98 +--S 80 of 99 rightRegularRepresentation (a,bb) --R --R @@ -1284,7 +1284,7 @@ rightRegularRepresentation (a,bb) --R Type: Matrix(Fraction(Polynomial(Integer))) --E 80 ---S 81 of 98 +--S 81 of 99 rightUnit()$A --R --R this algebra has no right unit @@ -1293,7 +1293,7 @@ rightUnit()$A --R Type: Union("failed",...) --E 81 ---S 82 of 98 +--S 82 of 99 structuralConstants()$A --R --R @@ -1307,7 +1307,7 @@ structuralConstants()$A --R Type: Vector(Matrix(Fraction(Polynomial(Integer)))) --E 82 ---S 83 of 98 +--S 83 of 99 structuralConstants(bb) --R --R @@ -1321,7 +1321,7 @@ structuralConstants(bb) --R Type: Vector(Matrix(Fraction(Polynomial(Integer)))) --E 83 ---S 84 of 98 +--S 84 of 99 unit()$A --R --R this algebra has no unit @@ -1330,7 +1330,7 @@ unit()$A --R Type: Union("failed",...) --E 84 ---S 85 of 98 +--S 85 of 99 biRank a --R --R @@ -1338,7 +1338,7 @@ biRank a --R Type: PositiveInteger --E 85 ---S 86 of 98 +--S 86 of 99 leftRank a --R --R @@ -1346,7 +1346,7 @@ leftRank a --R Type: PositiveInteger --E 86 ---S 87 of 98 +--S 87 of 99 doubleRank a --R --R @@ -1354,7 +1354,7 @@ doubleRank a --R Type: PositiveInteger --E 87 ---S 88 of 98 +--S 88 of 99 rightRank a --R --R @@ -1362,7 +1362,7 @@ rightRank a --R Type: PositiveInteger --E 88 ---S 89 of 98 +--S 89 of 99 weakBiRank a --R --R @@ -1370,7 +1370,7 @@ weakBiRank a --R Type: PositiveInteger --E 89 ---S 90 of 98 +--S 90 of 99 basisOfCenter()$AP --R --R @@ -1379,7 +1379,7 @@ basisOfCenter()$AP --RType: List(AlgebraGivenByStructuralConstants(Fraction(Polynomial(Integer)),4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])) --E 90 ---S 91 of 98 +--S 91 of 99 basisOfLeftNucleus()$AP --R --R @@ -1388,7 +1388,7 @@ basisOfLeftNucleus()$AP --RType: List(AlgebraGivenByStructuralConstants(Fraction(Polynomial(Integer)),4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])) --E 91 ---S 92 of 98 +--S 92 of 99 basisOfNucleus()$AP --R --R @@ -1397,7 +1397,7 @@ basisOfNucleus()$AP --RType: List(AlgebraGivenByStructuralConstants(Fraction(Polynomial(Integer)),4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])) --E 92 ---S 93 of 98 +--S 93 of 99 basisOfRightNucleus()$AP --R --R @@ -1406,7 +1406,7 @@ basisOfRightNucleus()$AP --RType: List(AlgebraGivenByStructuralConstants(Fraction(Polynomial(Integer)),4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])) --E 93 ---S 94 of 98 +--S 94 of 99 basisOfCentroid()$AP --R --R @@ -1420,7 +1420,7 @@ basisOfCentroid()$AP --R Type: List(Matrix(Fraction(Polynomial(Integer)))) --E 94 ---S 95 of 98 +--S 95 of 99 basisOfCommutingElements()$AP --R --R @@ -1429,7 +1429,7 @@ basisOfCommutingElements()$AP --RType: List(AlgebraGivenByStructuralConstants(Fraction(Polynomial(Integer)),4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])) --E 95 ---S 96 of 98 +--S 96 of 99 basisOfLeftNucloid()$AP --R --R @@ -1443,7 +1443,7 @@ basisOfLeftNucloid()$AP --R Type: List(Matrix(Fraction(Polynomial(Integer)))) --E 96 ---S 97 of 98 +--S 97 of 99 basisOfMiddleNucleus()$AP --R --R @@ -1452,7 +1452,7 @@ basisOfMiddleNucleus()$AP --RType: List(AlgebraGivenByStructuralConstants(Fraction(Polynomial(Integer)),4,[*01e0,*01e1,*01e2,*01e3],[MATRIX,MATRIX,MATRIX,MATRIX])) --E 97 ---S 98 of 98 +--S 98 of 99 basisOfRightNucloid()$AP --R --R @@ -1466,6 +1466,80 @@ basisOfRightNucloid()$AP --R Type: List(Matrix(Fraction(Polynomial(Integer)))) --E 98 +--S 99 of 99 +)show AlgebraGivenByStructuralConstants +--R +--R AlgebraGivenByStructuralConstants(R: Field,n: PositiveInteger,ls: List(Symbol),gamma: Vector(Matrix(R))) is a domain constructor +--R Abbreviation for AlgebraGivenByStructuralConstants is ALGSC +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for ALGSC +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (SquareMatrix(n,R),%) -> % ?*? : (R,%) -> % +--R ?*? : (%,R) -> % ?*? : (%,%) -> % +--R ?*? : (Integer,%) -> % ?*? : (NonNegativeInteger,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 0 : () -> % alternative? : () -> Boolean +--R antiAssociative? : () -> Boolean antiCommutative? : () -> Boolean +--R antiCommutator : (%,%) -> % apply : (Matrix(R),%) -> % +--R associative? : () -> Boolean associator : (%,%,%) -> % +--R basis : () -> Vector(%) coerce : Vector(R) -> % +--R coerce : % -> OutputForm commutative? : () -> Boolean +--R commutator : (%,%) -> % convert : Vector(R) -> % +--R convert : % -> Vector(R) coordinates : % -> Vector(R) +--R ?.? : (%,Integer) -> R flexible? : () -> Boolean +--R hash : % -> SingleInteger jacobiIdentity? : () -> Boolean +--R jordanAdmissible? : () -> Boolean jordanAlgebra? : () -> Boolean +--R latex : % -> String leftAlternative? : () -> Boolean +--R leftDiscriminant : () -> R leftDiscriminant : Vector(%) -> R +--R leftNorm : % -> R leftTrace : % -> R +--R leftTraceMatrix : () -> Matrix(R) lieAdmissible? : () -> Boolean +--R lieAlgebra? : () -> Boolean powerAssociative? : () -> Boolean +--R rank : () -> PositiveInteger represents : Vector(R) -> % +--R rightAlternative? : () -> Boolean rightDiscriminant : () -> R +--R rightDiscriminant : Vector(%) -> R rightNorm : % -> R +--R rightTrace : % -> R rightTraceMatrix : () -> Matrix(R) +--R sample : () -> % someBasis : () -> Vector(%) +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R associatorDependence : () -> List(Vector(R)) if R has INTDOM +--R conditionsForIdempotents : () -> List(Polynomial(R)) +--R conditionsForIdempotents : Vector(%) -> List(Polynomial(R)) +--R coordinates : Vector(%) -> Matrix(R) +--R coordinates : (Vector(%),Vector(%)) -> Matrix(R) +--R coordinates : (%,Vector(%)) -> Vector(R) +--R leftCharacteristicPolynomial : % -> SparseUnivariatePolynomial(R) +--R leftMinimalPolynomial : % -> SparseUnivariatePolynomial(R) if R has INTDOM +--R leftPower : (%,PositiveInteger) -> % +--R leftRankPolynomial : () -> SparseUnivariatePolynomial(Polynomial(R)) if R has FIELD +--R leftRecip : % -> Union(%,"failed") if R has INTDOM +--R leftRegularRepresentation : % -> Matrix(R) +--R leftRegularRepresentation : (%,Vector(%)) -> Matrix(R) +--R leftTraceMatrix : Vector(%) -> Matrix(R) +--R leftUnit : () -> Union(%,"failed") if R has INTDOM +--R leftUnits : () -> Union(Record(particular: %,basis: List(%)),"failed") if R has INTDOM +--R noncommutativeJordanAlgebra? : () -> Boolean +--R plenaryPower : (%,PositiveInteger) -> % +--R recip : % -> Union(%,"failed") if R has INTDOM +--R represents : (Vector(R),Vector(%)) -> % +--R rightCharacteristicPolynomial : % -> SparseUnivariatePolynomial(R) +--R rightMinimalPolynomial : % -> SparseUnivariatePolynomial(R) if R has INTDOM +--R rightPower : (%,PositiveInteger) -> % +--R rightRankPolynomial : () -> SparseUnivariatePolynomial(Polynomial(R)) if R has FIELD +--R rightRecip : % -> Union(%,"failed") if R has INTDOM +--R rightRegularRepresentation : % -> Matrix(R) +--R rightRegularRepresentation : (%,Vector(%)) -> Matrix(R) +--R rightTraceMatrix : Vector(%) -> Matrix(R) +--R rightUnit : () -> Union(%,"failed") if R has INTDOM +--R rightUnits : () -> Union(Record(particular: %,basis: List(%)),"failed") if R has INTDOM +--R structuralConstants : () -> Vector(Matrix(R)) +--R structuralConstants : Vector(%) -> Vector(Matrix(R)) +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R unit : () -> Union(%,"failed") if R has INTDOM +--R +--E 99 + )spool )lisp (bye) \end{chunk} @@ -2616,34 +2690,37 @@ AlgebraGivenByStructuralConstants(R:Field, n : PositiveInteger,_ --R------------------------------- Operations -------------------------------- --R ?*? : (Fraction(UP),%) -> % ?*? : (%,Fraction(UP)) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ?=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % basis : () -> Vector(%) ---R branchPoint? : UP -> Boolean branchPoint? : F -> Boolean ---R coerce : Fraction(UP) -> % coerce : Integer -> % ---R coerce : % -> OutputForm convert : UPUP -> % ---R convert : % -> UPUP definingPolynomial : () -> UPUP ---R discriminant : () -> Fraction(UP) elt : (%,F,F) -> F +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R basis : () -> Vector(%) branchPoint? : UP -> Boolean +--R branchPoint? : F -> Boolean coerce : Fraction(UP) -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R convert : UPUP -> % convert : % -> UPUP +--R convert : Vector(Fraction(UP)) -> % convert : % -> Vector(Fraction(UP)) +--R definingPolynomial : () -> UPUP discriminant : () -> Fraction(UP) +--R elliptic : () -> Union(UP,"failed") elt : (%,F,F) -> F --R generator : () -> % genus : () -> NonNegativeInteger --R hash : % -> SingleInteger integral? : (%,UP) -> Boolean --R integral? : (%,F) -> Boolean integral? : % -> Boolean ---R integralBasis : () -> Vector(%) latex : % -> String ---R lift : % -> UPUP norm : % -> Fraction(UP) ---R one? : % -> Boolean primitivePart : % -> % ---R ramified? : UP -> Boolean ramified? : F -> Boolean +--R integralAtInfinity? : % -> Boolean integralBasis : () -> Vector(%) +--R latex : % -> String lift : % -> UPUP +--R norm : % -> Fraction(UP) one? : % -> Boolean +--R primitivePart : % -> % ramified? : UP -> Boolean +--R ramified? : F -> Boolean ramifiedAtInfinity? : () -> Boolean --R rank : () -> PositiveInteger rationalPoint? : (F,F) -> Boolean --R recip : % -> Union(%,"failed") reduce : UPUP -> % --R represents : (Vector(UP),UP) -> % retract : % -> Fraction(UP) --R sample : () -> % singular? : UP -> Boolean ---R singular? : F -> Boolean trace : % -> Fraction(UP) ---R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R singular? : F -> Boolean singularAtInfinity? : () -> Boolean +--R trace : % -> Fraction(UP) zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean --R ?*? : (%,Fraction(Integer)) -> % if Fraction(UP) has FIELD --R ?*? : (Fraction(Integer),%) -> % if Fraction(UP) has FIELD ---R ?*? : (NonNegativeInteger,%) -> % --R ?**? : (%,Integer) -> % if Fraction(UP) has FIELD ---R ?**? : (%,NonNegativeInteger) -> % --R ?/? : (%,%) -> % if Fraction(UP) has FIELD --R D : % -> % if Fraction(UP) has DIFRING and Fraction(UP) has FIELD or Fraction(UP) has FFIELDC --R D : (%,NonNegativeInteger) -> % if Fraction(UP) has DIFRING and Fraction(UP) has FIELD or Fraction(UP) has FFIELDC @@ -2654,7 +2731,6 @@ AlgebraGivenByStructuralConstants(R:Field, n : PositiveInteger,_ --R D : (%,(Fraction(UP) -> Fraction(UP))) -> % if Fraction(UP) has FIELD --R D : (%,(Fraction(UP) -> Fraction(UP)),NonNegativeInteger) -> % if Fraction(UP) has FIELD --R ?^? : (%,Integer) -> % if Fraction(UP) has FIELD ---R ?^? : (%,NonNegativeInteger) -> % --R absolutelyIrreducible? : () -> Boolean --R algSplitSimple : (%,(UP -> UP)) -> Record(num: %,den: UP,derivden: UP,gd: UP) --R associates? : (%,%) -> Boolean if Fraction(UP) has FIELD @@ -2667,8 +2743,6 @@ AlgebraGivenByStructuralConstants(R:Field, n : PositiveInteger,_ --R coerce : Fraction(Integer) -> % if Fraction(UP) has FIELD or Fraction(UP) has RETRACT(FRAC(INT)) --R complementaryBasis : Vector(%) -> Vector(%) --R conditionP : Matrix(%) -> Union(Vector(%),"failed") if Fraction(UP) has FFIELDC ---R convert : Vector(Fraction(UP)) -> % ---R convert : % -> Vector(Fraction(UP)) --R coordinates : Vector(%) -> Matrix(Fraction(UP)) --R coordinates : % -> Vector(Fraction(UP)) --R coordinates : (Vector(%),Vector(%)) -> Matrix(Fraction(UP)) @@ -2688,7 +2762,6 @@ AlgebraGivenByStructuralConstants(R:Field, n : PositiveInteger,_ --R discreteLog : % -> NonNegativeInteger if Fraction(UP) has FFIELDC --R discriminant : Vector(%) -> Fraction(UP) --R divide : (%,%) -> Record(quotient: %,remainder: %) if Fraction(UP) has FIELD ---R elliptic : () -> Union(UP,"failed") --R enumerate : () -> List(%) if Fraction(UP) has FINITE --R euclideanSize : % -> NonNegativeInteger if Fraction(UP) has FIELD --R expressIdealMember : (List(%),%) -> Union(List(%),"failed") if Fraction(UP) has FIELD @@ -2703,7 +2776,6 @@ AlgebraGivenByStructuralConstants(R:Field, n : PositiveInteger,_ --R hyperelliptic : () -> Union(UP,"failed") --R index : PositiveInteger -> % if Fraction(UP) has FINITE --R init : () -> % if Fraction(UP) has FFIELDC ---R integralAtInfinity? : % -> Boolean --R integralBasisAtInfinity : () -> Vector(%) --R integralCoordinates : % -> Record(num: Vector(UP),den: UP) --R integralDerivationMatrix : (UP -> UP) -> Record(num: Matrix(UP),den: UP) @@ -2733,7 +2805,6 @@ AlgebraGivenByStructuralConstants(R:Field, n : PositiveInteger,_ --R primitiveElement : () -> % if Fraction(UP) has FFIELDC --R principalIdeal : List(%) -> Record(coef: List(%),generator: %) if Fraction(UP) has FIELD --R ?quo? : (%,%) -> % if Fraction(UP) has FIELD ---R ramifiedAtInfinity? : () -> Boolean --R random : () -> % if Fraction(UP) has FINITE --R rationalPoints : () -> List(List(F)) if F has FINITE --R reduce : Fraction(UPUP) -> Union(%,"failed") if Fraction(UP) has FIELD @@ -2753,7 +2824,6 @@ AlgebraGivenByStructuralConstants(R:Field, n : PositiveInteger,_ --R retractIfCan : % -> Union(Fraction(UP),"failed") --R retractIfCan : % -> Union(Fraction(Integer),"failed") if Fraction(UP) has RETRACT(FRAC(INT)) --R retractIfCan : % -> Union(Integer,"failed") if Fraction(UP) has RETRACT(INT) ---R singularAtInfinity? : () -> Boolean --R size : () -> NonNegativeInteger if Fraction(UP) has FINITE --R sizeLess? : (%,%) -> Boolean if Fraction(UP) has FIELD --R squareFree : % -> Factored(%) if Fraction(UP) has FIELD @@ -3151,17 +3221,19 @@ AlgebraicFunctionField(F, UP, UPUP, modulus): Exports == Implementation where --R Issue )edit bookvol10.3.pamphlet to see algebra source code for AN --R --R------------------------------- Operations -------------------------------- ---R ?*? : (PositiveInteger,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (%,%) -> % ?*? : (%,Fraction(Integer)) -> % ---R ?*? : (Fraction(Integer),%) -> % ?**? : (%,PositiveInteger) -> % ---R ?**? : (%,Integer) -> % ?+? : (%,%) -> % ---R -? : % -> % ?-? : (%,%) -> % ---R ?/? : (%,%) -> % ? Boolean ---R ?<=? : (%,%) -> Boolean ?=? : (%,%) -> Boolean ---R ?>? : (%,%) -> Boolean ?>=? : (%,%) -> Boolean ---R D : % -> % D : (%,NonNegativeInteger) -> % ---R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % ?^? : (%,Integer) -> % +--R ?*? : (PositiveInteger,%) -> % ?*? : (NonNegativeInteger,%) -> % +--R ?*? : (Integer,%) -> % ?*? : (%,%) -> % +--R ?*? : (%,Fraction(Integer)) -> % ?*? : (Fraction(Integer),%) -> % +--R ?**? : (%,PositiveInteger) -> % ?**? : (%,NonNegativeInteger) -> % +--R ?**? : (%,Integer) -> % ?**? : (%,Fraction(Integer)) -> % +--R ?+? : (%,%) -> % -? : % -> % +--R ?-? : (%,%) -> % ?/? : (%,%) -> % +--R ? Boolean ?<=? : (%,%) -> Boolean +--R ?=? : (%,%) -> Boolean ?>? : (%,%) -> Boolean +--R ?>=? : (%,%) -> Boolean D : % -> % +--R D : (%,NonNegativeInteger) -> % 1 : () -> % +--R 0 : () -> % ?^? : (%,PositiveInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,Integer) -> % --R associates? : (%,%) -> Boolean belong? : BasicOperator -> Boolean --R box : List(%) -> % box : % -> % --R coerce : Integer -> % coerce : % -> % @@ -3169,55 +3241,50 @@ AlgebraicFunctionField(F, UP, UPUP, modulus): Exports == Implementation where --R coerce : % -> OutputForm convert : % -> Complex(Float) --R convert : % -> DoubleFloat convert : % -> Float --R differentiate : % -> % distribute : (%,%) -> % ---R distribute : % -> % elt : (BasicOperator,%,%) -> % ---R elt : (BasicOperator,%) -> % eval : (%,%,%) -> % ---R eval : (%,Equation(%)) -> % eval : (%,Kernel(%),%) -> % ---R factor : % -> Factored(%) freeOf? : (%,Symbol) -> Boolean ---R freeOf? : (%,%) -> Boolean gcd : (%,%) -> % ---R gcd : List(%) -> % hash : % -> SingleInteger ---R height : % -> NonNegativeInteger inv : % -> % ---R is? : (%,Symbol) -> Boolean kernel : (BasicOperator,%) -> % +--R distribute : % -> % elt : (BasicOperator,List(%)) -> % +--R elt : (BasicOperator,%,%,%) -> % elt : (BasicOperator,%,%) -> % +--R elt : (BasicOperator,%) -> % eval : (%,Symbol,(% -> %)) -> % +--R eval : (%,List(%),List(%)) -> % eval : (%,%,%) -> % +--R eval : (%,Equation(%)) -> % eval : (%,List(Equation(%))) -> % +--R eval : (%,Kernel(%),%) -> % factor : % -> Factored(%) +--R freeOf? : (%,Symbol) -> Boolean freeOf? : (%,%) -> Boolean +--R gcd : (%,%) -> % gcd : List(%) -> % +--R hash : % -> SingleInteger height : % -> NonNegativeInteger +--R inv : % -> % is? : (%,Symbol) -> Boolean +--R is? : (%,BasicOperator) -> Boolean kernel : (BasicOperator,%) -> % --R kernels : % -> List(Kernel(%)) latex : % -> String --R lcm : (%,%) -> % lcm : List(%) -> % ---R max : (%,%) -> % min : (%,%) -> % ---R norm : (%,List(Kernel(%))) -> % norm : (%,Kernel(%)) -> % ---R nthRoot : (%,Integer) -> % one? : % -> Boolean ---R paren : List(%) -> % paren : % -> % ---R prime? : % -> Boolean ?quo? : (%,%) -> % ---R recip : % -> Union(%,"failed") reduce : % -> % ---R ?rem? : (%,%) -> % retract : % -> Fraction(Integer) ---R retract : % -> Integer retract : % -> Kernel(%) ---R rootOf : Polynomial(%) -> % sample : () -> % +--R map : ((% -> %),Kernel(%)) -> % max : (%,%) -> % +--R min : (%,%) -> % norm : (%,List(Kernel(%))) -> % +--R norm : (%,Kernel(%)) -> % nthRoot : (%,Integer) -> % +--R one? : % -> Boolean paren : List(%) -> % +--R paren : % -> % prime? : % -> Boolean +--R ?quo? : (%,%) -> % recip : % -> Union(%,"failed") +--R reduce : % -> % ?rem? : (%,%) -> % +--R retract : % -> Fraction(Integer) retract : % -> Integer +--R retract : % -> Kernel(%) rootOf : Polynomial(%) -> % +--R rootsOf : Polynomial(%) -> List(%) sample : () -> % --R sizeLess? : (%,%) -> Boolean sqrt : % -> % --R squareFree : % -> Factored(%) squareFreePart : % -> % --R subst : (%,Equation(%)) -> % tower : % -> List(Kernel(%)) --R unit? : % -> Boolean unitCanonical : % -> % --R zero? : % -> Boolean zeroOf : Polynomial(%) -> % ---R ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R ?**? : (%,Fraction(Integer)) -> % ---R ?^? : (%,NonNegativeInteger) -> % +--R zerosOf : Polynomial(%) -> List(%) ?~=? : (%,%) -> Boolean --R characteristic : () -> NonNegativeInteger --R coerce : SparseMultivariatePolynomial(Integer,Kernel(%)) -> % --R definingPolynomial : % -> % if $ has RING --R denom : % -> SparseMultivariatePolynomial(Integer,Kernel(%)) --R differentiate : (%,NonNegativeInteger) -> % --R divide : (%,%) -> Record(quotient: %,remainder: %) ---R elt : (BasicOperator,List(%)) -> % --R elt : (BasicOperator,%,%,%,%) -> % ---R elt : (BasicOperator,%,%,%) -> % --R euclideanSize : % -> NonNegativeInteger --R eval : (%,BasicOperator,(% -> %)) -> % --R eval : (%,BasicOperator,(List(%) -> %)) -> % --R eval : (%,List(BasicOperator),List((List(%) -> %))) -> % --R eval : (%,List(BasicOperator),List((% -> %))) -> % ---R eval : (%,Symbol,(% -> %)) -> % --R eval : (%,Symbol,(List(%) -> %)) -> % --R eval : (%,List(Symbol),List((List(%) -> %))) -> % --R eval : (%,List(Symbol),List((% -> %))) -> % ---R eval : (%,List(%),List(%)) -> % ---R eval : (%,List(Equation(%))) -> % --R eval : (%,List(Kernel(%)),List(%)) -> % --R even? : % -> Boolean if $ has RETRACT(INT) --R expressIdealMember : (List(%),%) -> Union(List(%),"failed") @@ -3225,11 +3292,9 @@ AlgebraicFunctionField(F, UP, UPUP, modulus): Exports == Implementation where --R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) --R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") --R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) ---R is? : (%,BasicOperator) -> Boolean --R kernel : (BasicOperator,List(%)) -> % --R lcmCoef : (%,%) -> Record(llcmres: %,coeff1: %,coeff2: %) --R mainKernel : % -> Union(Kernel(%),"failed") ---R map : ((% -> %),Kernel(%)) -> % --R minPoly : Kernel(%) -> SparseUnivariatePolynomial(%) if $ has RING --R multiEuclidean : (List(%),%) -> Union(List(%),"failed") --R norm : (SparseUnivariatePolynomial(%),List(Kernel(%))) -> SparseUnivariatePolynomial(%) @@ -3248,7 +3313,6 @@ AlgebraicFunctionField(F, UP, UPUP, modulus): Exports == Implementation where --R retractIfCan : % -> Union(Kernel(%),"failed") --R rootOf : SparseUnivariatePolynomial(%) -> % --R rootOf : (SparseUnivariatePolynomial(%),Symbol) -> % ---R rootsOf : Polynomial(%) -> List(%) --R rootsOf : SparseUnivariatePolynomial(%) -> List(%) --R rootsOf : (SparseUnivariatePolynomial(%),Symbol) -> List(%) --R subst : (%,List(Kernel(%)),List(%)) -> % @@ -3257,7 +3321,6 @@ AlgebraicFunctionField(F, UP, UPUP, modulus): Exports == Implementation where --R unitNormal : % -> Record(unit: %,canonical: %,associate: %) --R zeroOf : SparseUnivariatePolynomial(%) -> % --R zeroOf : (SparseUnivariatePolynomial(%),Symbol) -> % ---R zerosOf : Polynomial(%) -> List(%) --R zerosOf : SparseUnivariatePolynomial(%) -> List(%) --R zerosOf : (SparseUnivariatePolynomial(%),Symbol) -> List(%) --R @@ -3898,6 +3961,7 @@ AlgebraicNumber(): Exports == Implementation where --S 1 of 1 )show AnonymousFunction +--R --R AnonymousFunction is a domain constructor --R Abbreviation for AnonymousFunction is ANON --R This constructor is not exposed in this frame. @@ -3978,14 +4042,16 @@ AnonymousFunction():SetCategory == add --R --R------------------------------- Operations -------------------------------- --R ?*? : (R,%) -> % ?*? : (%,%) -> % ---R ?*? : (Integer,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?*? : (Integer,%) -> % ?*? : (NonNegativeInteger,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,NonNegativeInteger) -> % --R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % --R ?-? : (%,%) -> % -? : % -> % --R ?=? : (%,%) -> Boolean 1 : () -> % ---R 0 : () -> % ?^? : (%,PositiveInteger) -> % ---R coefficient : (%,%) -> R coerce : R -> % ---R coerce : Integer -> % coerce : % -> OutputForm ---R degree : % -> NonNegativeInteger exp : List(Integer) -> % +--R 0 : () -> % ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,PositiveInteger) -> % coefficient : (%,%) -> R +--R coerce : R -> % coerce : Integer -> % +--R coerce : % -> OutputForm degree : % -> NonNegativeInteger +--R exp : List(Integer) -> % generator : NonNegativeInteger -> % --R hash : % -> SingleInteger homogeneous? : % -> Boolean --R latex : % -> String leadingBasisTerm : % -> % --R leadingCoefficient : % -> R map : ((R -> R),%) -> % @@ -3993,11 +4059,7 @@ AnonymousFunction():SetCategory == add --R reductum : % -> % retract : % -> R --R retractable? : % -> Boolean sample : () -> % --R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R ?^? : (%,NonNegativeInteger) -> % --R characteristic : () -> NonNegativeInteger ---R generator : NonNegativeInteger -> % --R retractIfCan : % -> Union(R,"failed") --R subtractIfCan : (%,%) -> Union(%,"failed") --R @@ -4965,8 +5027,8 @@ b := generator()$Sae --R coerce : % -> OutputForm dom : % -> SExpression --R domainOf : % -> OutputForm hash : % -> SingleInteger --R latex : % -> String obj : % -> None ---R objectOf : % -> OutputForm ?~=? : (%,%) -> Boolean ---R showTypeInOutput : Boolean -> String +--R objectOf : % -> OutputForm showTypeInOutput : Boolean -> String +--R ?~=? : (%,%) -> Boolean --R --E 18 @@ -5539,9 +5601,9 @@ latex a --R empty : () -> % empty? : % -> Boolean --R eq? : (%,%) -> Boolean extract! : % -> S --R insert! : (S,%) -> % inspect : % -> S ---R map : ((S -> S),%) -> % pop! : % -> S ---R push! : (S,%) -> S sample : () -> % ---R top : % -> S +--R latex : % -> String if S has SETCAT map : ((S -> S),%) -> % +--R pop! : % -> S push! : (S,%) -> S +--R sample : () -> % top : % -> S --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R ?=? : (%,%) -> Boolean if S has SETCAT --R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate @@ -5554,7 +5616,6 @@ latex a --R eval : (%,List(Equation(S))) -> % if S has EVALAB(S) and S has SETCAT --R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate --R hash : % -> SingleInteger if S has SETCAT ---R latex : % -> String if S has SETCAT --R less? : (%,NonNegativeInteger) -> Boolean --R map! : ((S -> S),%) -> % if $ has shallowlyMutable --R member? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT @@ -6578,13 +6639,12 @@ ArrayStack(S:SetCategory): StackAggregate(S) with --R------------------------------- Operations -------------------------------- --R coerce : FortranCode -> % coerce : List(FortranCode) -> % --R coerce : % -> OutputForm outputAsFortran : % -> Void ---R retract : Polynomial(Float) -> % retract : Expression(Float) -> % +--R retract : Polynomial(Integer) -> % retract : Polynomial(Float) -> % +--R retract : Expression(Integer) -> % retract : Expression(Float) -> % --R coerce : FortranExpression([construct,QUOTEX],[construct],MachineFloat) -> % --R coerce : Record(localSymbols: SymbolTable,code: List(FortranCode)) -> % --R retract : Fraction(Polynomial(Integer)) -> % --R retract : Fraction(Polynomial(Float)) -> % ---R retract : Polynomial(Integer) -> % ---R retract : Expression(Integer) -> % --R retractIfCan : Fraction(Polynomial(Integer)) -> Union(%,"failed") --R retractIfCan : Fraction(Polynomial(Float)) -> Union(%,"failed") --R retractIfCan : Polynomial(Integer) -> Union(%,"failed") @@ -7792,13 +7852,12 @@ Asp20(name): Exports == Implementation where --R------------------------------- Operations -------------------------------- --R coerce : FortranCode -> % coerce : List(FortranCode) -> % --R coerce : % -> OutputForm outputAsFortran : % -> Void ---R retract : Polynomial(Float) -> % retract : Expression(Float) -> % +--R retract : Polynomial(Integer) -> % retract : Polynomial(Float) -> % +--R retract : Expression(Integer) -> % retract : Expression(Float) -> % --R coerce : FortranExpression([construct],[construct,QUOTEXC],MachineFloat) -> % --R coerce : Record(localSymbols: SymbolTable,code: List(FortranCode)) -> % --R retract : Fraction(Polynomial(Integer)) -> % --R retract : Fraction(Polynomial(Float)) -> % ---R retract : Polynomial(Integer) -> % ---R retract : Expression(Integer) -> % --R retractIfCan : Fraction(Polynomial(Integer)) -> Union(%,"failed") --R retractIfCan : Fraction(Polynomial(Float)) -> Union(%,"failed") --R retractIfCan : Polynomial(Integer) -> Union(%,"failed") @@ -7986,9 +8045,9 @@ Asp24(name): Exports == Implementation where --R --R------------------------------- Operations -------------------------------- --R coerce : FortranCode -> % coerce : List(FortranCode) -> % ---R coerce : % -> OutputForm outputAsFortran : % -> Void +--R coerce : Matrix(MachineFloat) -> % coerce : % -> OutputForm +--R outputAsFortran : % -> Void --R coerce : Record(localSymbols: SymbolTable,code: List(FortranCode)) -> % ---R coerce : Matrix(MachineFloat) -> % --R --E 1 @@ -8153,9 +8212,9 @@ Asp27(name): Exports == Implementation where --R --R------------------------------- Operations -------------------------------- --R coerce : FortranCode -> % coerce : List(FortranCode) -> % ---R coerce : % -> OutputForm outputAsFortran : % -> Void +--R coerce : Matrix(MachineFloat) -> % coerce : % -> OutputForm +--R outputAsFortran : % -> Void --R coerce : Record(localSymbols: SymbolTable,code: List(FortranCode)) -> % ---R coerce : Matrix(MachineFloat) -> % --R --E 1 @@ -8678,9 +8737,9 @@ Asp29(name): Exports == Implementation where --R --R------------------------------- Operations -------------------------------- --R coerce : FortranCode -> % coerce : List(FortranCode) -> % ---R coerce : % -> OutputForm outputAsFortran : % -> Void +--R coerce : Matrix(MachineFloat) -> % coerce : % -> OutputForm +--R outputAsFortran : % -> Void --R coerce : Record(localSymbols: SymbolTable,code: List(FortranCode)) -> % ---R coerce : Matrix(MachineFloat) -> % --R --E 1 @@ -9251,9 +9310,9 @@ Asp33(name): Exports == Implementation where --R --R------------------------------- Operations -------------------------------- --R coerce : FortranCode -> % coerce : List(FortranCode) -> % ---R coerce : % -> OutputForm outputAsFortran : % -> Void +--R coerce : Matrix(MachineFloat) -> % coerce : % -> OutputForm +--R outputAsFortran : % -> Void --R coerce : Record(localSymbols: SymbolTable,code: List(FortranCode)) -> % ---R coerce : Matrix(MachineFloat) -> % --R --E 1 @@ -9683,13 +9742,12 @@ Asp35(name): Exports == Implementation where --R------------------------------- Operations -------------------------------- --R coerce : FortranCode -> % coerce : List(FortranCode) -> % --R coerce : % -> OutputForm outputAsFortran : % -> Void ---R retract : Polynomial(Float) -> % retract : Expression(Float) -> % +--R retract : Polynomial(Integer) -> % retract : Polynomial(Float) -> % +--R retract : Expression(Integer) -> % retract : Expression(Float) -> % --R coerce : FortranExpression([construct],[construct,QUOTEX],MachineFloat) -> % --R coerce : Record(localSymbols: SymbolTable,code: List(FortranCode)) -> % --R retract : Fraction(Polynomial(Integer)) -> % --R retract : Fraction(Polynomial(Float)) -> % ---R retract : Polynomial(Integer) -> % ---R retract : Expression(Integer) -> % --R retractIfCan : Fraction(Polynomial(Integer)) -> Union(%,"failed") --R retractIfCan : Fraction(Polynomial(Float)) -> Union(%,"failed") --R retractIfCan : Polynomial(Integer) -> Union(%,"failed") @@ -10534,13 +10592,12 @@ Asp42(nameOne,nameTwo,nameThree): Exports == Implementation where --R------------------------------- Operations -------------------------------- --R coerce : FortranCode -> % coerce : List(FortranCode) -> % --R coerce : % -> OutputForm outputAsFortran : % -> Void ---R retract : Polynomial(Float) -> % retract : Expression(Float) -> % +--R retract : Polynomial(Integer) -> % retract : Polynomial(Float) -> % +--R retract : Expression(Integer) -> % retract : Expression(Float) -> % --R coerce : FortranExpression([construct],[construct,QUOTEX],MachineFloat) -> % --R coerce : Record(localSymbols: SymbolTable,code: List(FortranCode)) -> % --R retract : Fraction(Polynomial(Integer)) -> % --R retract : Fraction(Polynomial(Float)) -> % ---R retract : Polynomial(Integer) -> % ---R retract : Expression(Integer) -> % --R retractIfCan : Fraction(Polynomial(Integer)) -> Union(%,"failed") --R retractIfCan : Fraction(Polynomial(Float)) -> Union(%,"failed") --R retractIfCan : Polynomial(Integer) -> Union(%,"failed") @@ -12709,9 +12766,9 @@ Asp78(name): Exports == Implementation where --R --R------------------------------- Operations -------------------------------- --R coerce : FortranCode -> % coerce : List(FortranCode) -> % ---R coerce : % -> OutputForm outputAsFortran : % -> Void +--R coerce : Vector(MachineFloat) -> % coerce : % -> OutputForm +--R outputAsFortran : % -> Void --R coerce : Record(localSymbols: SymbolTable,code: List(FortranCode)) -> % ---R coerce : Vector(MachineFloat) -> % --R --E 1 @@ -13147,13 +13204,12 @@ Asp80(name): Exports == Implementation where --R------------------------------- Operations -------------------------------- --R coerce : FortranCode -> % coerce : List(FortranCode) -> % --R coerce : % -> OutputForm outputAsFortran : % -> Void ---R retract : Polynomial(Float) -> % retract : Expression(Float) -> % +--R retract : Polynomial(Integer) -> % retract : Polynomial(Float) -> % +--R retract : Expression(Integer) -> % retract : Expression(Float) -> % --R coerce : FortranExpression([construct,QUOTEX],[construct,QUOTEY],MachineFloat) -> % --R coerce : Record(localSymbols: SymbolTable,code: List(FortranCode)) -> % --R retract : Fraction(Polynomial(Integer)) -> % --R retract : Fraction(Polynomial(Float)) -> % ---R retract : Polynomial(Integer) -> % ---R retract : Expression(Integer) -> % --R retractIfCan : Fraction(Polynomial(Integer)) -> Union(%,"failed") --R retractIfCan : Fraction(Polynomial(Float)) -> Union(%,"failed") --R retractIfCan : Polynomial(Integer) -> Union(%,"failed") @@ -13351,16 +13407,16 @@ Asp9(name): Exports == Implementation where --R------------------------------- Operations -------------------------------- --R ?*? : (R,%) -> % ?*? : (%,R) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % ---R ?+? : (%,%) -> % ?-? : (%,%) -> % ---R -? : % -> % ?=? : (%,%) -> Boolean ---R 0 : () -> % antiCommutator : (%,%) -> % ---R associator : (%,%,%) -> % coerce : A -> % ---R coerce : % -> A coerce : % -> OutputForm ---R commutator : (%,%) -> % hash : % -> SingleInteger ---R latex : % -> String sample : () -> % ---R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % +--R ?-? : (%,%) -> % -? : % -> % +--R ?=? : (%,%) -> Boolean 0 : () -> % +--R antiCommutator : (%,%) -> % associator : (%,%,%) -> % +--R coerce : A -> % coerce : % -> A +--R coerce : % -> OutputForm commutator : (%,%) -> % +--R hash : % -> SingleInteger latex : % -> String +--R sample : () -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean --R alternative? : () -> Boolean if A has FINAALG(R) --R antiAssociative? : () -> Boolean if A has FINAALG(R) --R antiCommutative? : () -> Boolean if A has FINAALG(R) @@ -13625,16 +13681,16 @@ AssociatedJordanAlgebra(R:CommutativeRing,A:NonAssociativeAlgebra R): --R------------------------------- Operations -------------------------------- --R ?*? : (R,%) -> % ?*? : (%,R) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % ---R ?+? : (%,%) -> % ?-? : (%,%) -> % ---R -? : % -> % ?=? : (%,%) -> Boolean ---R 0 : () -> % antiCommutator : (%,%) -> % ---R associator : (%,%,%) -> % coerce : A -> % ---R coerce : % -> A coerce : % -> OutputForm ---R commutator : (%,%) -> % hash : % -> SingleInteger ---R latex : % -> String sample : () -> % ---R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % +--R ?-? : (%,%) -> % -? : % -> % +--R ?=? : (%,%) -> Boolean 0 : () -> % +--R antiCommutator : (%,%) -> % associator : (%,%,%) -> % +--R coerce : A -> % coerce : % -> A +--R coerce : % -> OutputForm commutator : (%,%) -> % +--R hash : % -> SingleInteger latex : % -> String +--R sample : () -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean --R alternative? : () -> Boolean if A has FINAALG(R) --R antiAssociative? : () -> Boolean if A has FINAALG(R) --R antiCommutative? : () -> Boolean if A has FINAALG(R) @@ -13883,7 +13939,8 @@ AssociatedLieAlgebra(R:CommutativeRing,A:NonAssociativeAlgebra R): )set message test on )set message auto off )clear all ---S 1 of 10 + +--S 1 of 11 Data := Record(monthsOld : Integer, gender : String) --R --R @@ -13891,13 +13948,13 @@ Data := Record(monthsOld : Integer, gender : String) --R Type: Domain --E 1 ---S 2 of 10 +--S 2 of 11 al : AssociationList(String,Data) --R --R Type: Void --E 2 ---S 3 of 10 +--S 3 of 11 al := table() --R --R @@ -13905,7 +13962,7 @@ al := table() --R Type: AssociationList(String,Record(monthsOld: Integer,gender: String)) --E 3 ---S 4 of 10 +--S 4 of 11 al."bob" := [407,"male"]$Data --R --R @@ -13913,7 +13970,7 @@ al."bob" := [407,"male"]$Data --R Type: Record(monthsOld: Integer,gender: String) --E 4 ---S 5 of 10 +--S 5 of 11 al."judith" := [366,"female"]$Data --R --R @@ -13921,7 +13978,7 @@ al."judith" := [366,"female"]$Data --R Type: Record(monthsOld: Integer,gender: String) --E 5 ---S 6 of 10 +--S 6 of 11 al."katie" := [24,"female"]$Data --R --R @@ -13929,7 +13986,7 @@ al."katie" := [24,"female"]$Data --R Type: Record(monthsOld: Integer,gender: String) --E 6 ---S 7 of 10 +--S 7 of 11 al."smokie" := [200,"female"]$Data --R --R @@ -13937,7 +13994,7 @@ al."smokie" := [200,"female"]$Data --R Type: Record(monthsOld: Integer,gender: String) --E 7 ---S 8 of 10 +--S 8 of 11 al --R --R @@ -13953,7 +14010,7 @@ al --R Type: AssociationList(String,Record(monthsOld: Integer,gender: String)) --E 8 ---S 9 of 10 +--S 9 of 11 al."katie" := [23,"female"]$Data --R --R @@ -13961,7 +14018,7 @@ al."katie" := [23,"female"]$Data --R Type: Record(monthsOld: Integer,gender: String) --E 9 ---S 10 of 10 +--S 10 of 11 delete!(al,1) --R --R @@ -13974,6 +14031,197 @@ delete!(al,1) --R "bob"= [monthsOld= 407,gender= "male"] --R Type: AssociationList(String,Record(monthsOld: Integer,gender: String)) --E 10 + +--S 11 of 11 +)show AssociationList +--R +--R AssociationList(Key: SetCategory,Entry: SetCategory) is a domain constructor +--R Abbreviation for AssociationList is ALIST +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for ALIST +--R +--R------------------------------- Operations -------------------------------- +--R children : % -> List(%) concat : (%,%) -> % +--R concat : List(%) -> % concat! : (%,%) -> % +--R copy : % -> % cycleEntry : % -> % +--R cycleTail : % -> % cyclic? : % -> Boolean +--R delete : (%,Integer) -> % delete! : (%,Integer) -> % +--R dictionary : () -> % distance : (%,%) -> Integer +--R ?.rest : (%,rest) -> % elt : (%,Key,Entry) -> Entry +--R ?.? : (%,Key) -> Entry empty : () -> % +--R empty? : % -> Boolean entries : % -> List(Entry) +--R eq? : (%,%) -> Boolean explicitlyFinite? : % -> Boolean +--R index? : (Integer,%) -> Boolean index? : (Key,%) -> Boolean +--R indices : % -> List(Integer) indices : % -> List(Key) +--R insert : (%,%,Integer) -> % insert! : (%,%,Integer) -> % +--R key? : (Key,%) -> Boolean keys : % -> List(Key) +--R last : (%,NonNegativeInteger) -> % leaf? : % -> Boolean +--R map : ((Entry -> Entry),%) -> % nodes : % -> List(%) +--R possiblyInfinite? : % -> Boolean qelt : (%,Key) -> Entry +--R rest : % -> % rest : (%,NonNegativeInteger) -> % +--R reverse : % -> % sample : () -> % +--R setelt : (%,Key,Entry) -> Entry table : () -> % +--R tail : % -> % +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R ? Boolean if Record(key: Key,entry: Entry) has ORDSET +--R ?<=? : (%,%) -> Boolean if Record(key: Key,entry: Entry) has ORDSET +--R ?=? : (%,%) -> Boolean if Record(key: Key,entry: Entry) has SETCAT or Entry has SETCAT +--R ?>? : (%,%) -> Boolean if Record(key: Key,entry: Entry) has ORDSET +--R ?>=? : (%,%) -> Boolean if Record(key: Key,entry: Entry) has ORDSET +--R any? : ((Record(key: Key,entry: Entry) -> Boolean),%) -> Boolean if $ has finiteAggregate +--R any? : ((Entry -> Boolean),%) -> Boolean if $ has finiteAggregate +--R any? : ((Record(key: Key,entry: Entry) -> Boolean),%) -> Boolean if $ has finiteAggregate +--R assoc : (Key,%) -> Union(Record(key: Key,entry: Entry),"failed") +--R bag : List(Record(key: Key,entry: Entry)) -> % +--R child? : (%,%) -> Boolean if Record(key: Key,entry: Entry) has SETCAT +--R coerce : % -> OutputForm if Record(key: Key,entry: Entry) has SETCAT or Entry has SETCAT +--R concat : (Record(key: Key,entry: Entry),%) -> % +--R concat : (%,Record(key: Key,entry: Entry)) -> % +--R concat! : (%,Record(key: Key,entry: Entry)) -> % +--R construct : List(Record(key: Key,entry: Entry)) -> % +--R construct : List(Record(key: Key,entry: Entry)) -> % +--R convert : % -> InputForm if Record(key: Key,entry: Entry) has KONVERT(INFORM) +--R copyInto! : (%,%,Integer) -> % if $ has shallowlyMutable +--R count : ((Record(key: Key,entry: Entry) -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R count : (Record(key: Key,entry: Entry),%) -> NonNegativeInteger if $ has finiteAggregate and Record(key: Key,entry: Entry) has SETCAT +--R count : ((Entry -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R count : (Entry,%) -> NonNegativeInteger if $ has finiteAggregate and Entry has SETCAT +--R count : (Record(key: Key,entry: Entry),%) -> NonNegativeInteger if $ has finiteAggregate and Record(key: Key,entry: Entry) has SETCAT +--R count : ((Record(key: Key,entry: Entry) -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R cycleLength : % -> NonNegativeInteger +--R cycleSplit! : % -> % if $ has shallowlyMutable +--R delete : (%,UniversalSegment(Integer)) -> % +--R delete! : (%,UniversalSegment(Integer)) -> % +--R dictionary : List(Record(key: Key,entry: Entry)) -> % +--R ?.value : (%,value) -> Record(key: Key,entry: Entry) +--R ?.first : (%,first) -> Record(key: Key,entry: Entry) +--R ?.last : (%,last) -> Record(key: Key,entry: Entry) +--R ?.? : (%,UniversalSegment(Integer)) -> % +--R ?.? : (%,Integer) -> Record(key: Key,entry: Entry) +--R elt : (%,Integer,Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry) +--R entries : % -> List(Record(key: Key,entry: Entry)) +--R entry? : (Record(key: Key,entry: Entry),%) -> Boolean if $ has finiteAggregate and Record(key: Key,entry: Entry) has SETCAT +--R entry? : (Entry,%) -> Boolean if $ has finiteAggregate and Entry has SETCAT +--R eval : (%,List(Equation(Record(key: Key,entry: Entry)))) -> % if Record(key: Key,entry: Entry) has EVALAB(Record(key: Key,entry: Entry)) and Record(key: Key,entry: Entry) has SETCAT +--R eval : (%,Equation(Record(key: Key,entry: Entry))) -> % if Record(key: Key,entry: Entry) has EVALAB(Record(key: Key,entry: Entry)) and Record(key: Key,entry: Entry) has SETCAT +--R eval : (%,Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> % if Record(key: Key,entry: Entry) has EVALAB(Record(key: Key,entry: Entry)) and Record(key: Key,entry: Entry) has SETCAT +--R eval : (%,List(Record(key: Key,entry: Entry)),List(Record(key: Key,entry: Entry))) -> % if Record(key: Key,entry: Entry) has EVALAB(Record(key: Key,entry: Entry)) and Record(key: Key,entry: Entry) has SETCAT +--R eval : (%,List(Equation(Entry))) -> % if Entry has EVALAB(Entry) and Entry has SETCAT +--R eval : (%,Equation(Entry)) -> % if Entry has EVALAB(Entry) and Entry has SETCAT +--R eval : (%,Entry,Entry) -> % if Entry has EVALAB(Entry) and Entry has SETCAT +--R eval : (%,List(Entry),List(Entry)) -> % if Entry has EVALAB(Entry) and Entry has SETCAT +--R eval : (%,List(Record(key: Key,entry: Entry)),List(Record(key: Key,entry: Entry))) -> % if Record(key: Key,entry: Entry) has EVALAB(Record(key: Key,entry: Entry)) and Record(key: Key,entry: Entry) has SETCAT +--R eval : (%,Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> % if Record(key: Key,entry: Entry) has EVALAB(Record(key: Key,entry: Entry)) and Record(key: Key,entry: Entry) has SETCAT +--R eval : (%,Equation(Record(key: Key,entry: Entry))) -> % if Record(key: Key,entry: Entry) has EVALAB(Record(key: Key,entry: Entry)) and Record(key: Key,entry: Entry) has SETCAT +--R eval : (%,List(Equation(Record(key: Key,entry: Entry)))) -> % if Record(key: Key,entry: Entry) has EVALAB(Record(key: Key,entry: Entry)) and Record(key: Key,entry: Entry) has SETCAT +--R every? : ((Record(key: Key,entry: Entry) -> Boolean),%) -> Boolean if $ has finiteAggregate +--R every? : ((Entry -> Boolean),%) -> Boolean if $ has finiteAggregate +--R every? : ((Record(key: Key,entry: Entry) -> Boolean),%) -> Boolean if $ has finiteAggregate +--R extract! : % -> Record(key: Key,entry: Entry) +--R fill! : (%,Record(key: Key,entry: Entry)) -> % if $ has shallowlyMutable +--R fill! : (%,Entry) -> % if $ has shallowlyMutable +--R find : ((Record(key: Key,entry: Entry) -> Boolean),%) -> Union(Record(key: Key,entry: Entry),"failed") +--R find : ((Record(key: Key,entry: Entry) -> Boolean),%) -> Union(Record(key: Key,entry: Entry),"failed") +--R first : % -> Record(key: Key,entry: Entry) +--R first : (%,NonNegativeInteger) -> % +--R first : % -> Entry if Key has ORDSET +--R hash : % -> SingleInteger if Record(key: Key,entry: Entry) has SETCAT or Entry has SETCAT +--R insert : (Record(key: Key,entry: Entry),%,Integer) -> % +--R insert! : (Record(key: Key,entry: Entry),%,Integer) -> % +--R insert! : (Record(key: Key,entry: Entry),%) -> % +--R inspect : % -> Record(key: Key,entry: Entry) +--R last : % -> Record(key: Key,entry: Entry) +--R latex : % -> String if Record(key: Key,entry: Entry) has SETCAT or Entry has SETCAT +--R leaves : % -> List(Record(key: Key,entry: Entry)) +--R less? : (%,NonNegativeInteger) -> Boolean +--R list : Record(key: Key,entry: Entry) -> % +--R map : ((Record(key: Key,entry: Entry) -> Record(key: Key,entry: Entry)),%) -> % +--R map : (((Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry)),%,%) -> % +--R map : (((Entry,Entry) -> Entry),%,%) -> % +--R map : ((Record(key: Key,entry: Entry) -> Record(key: Key,entry: Entry)),%) -> % +--R map! : ((Record(key: Key,entry: Entry) -> Record(key: Key,entry: Entry)),%) -> % if $ has shallowlyMutable +--R map! : ((Entry -> Entry),%) -> % if $ has shallowlyMutable +--R map! : ((Record(key: Key,entry: Entry) -> Record(key: Key,entry: Entry)),%) -> % if $ has shallowlyMutable +--R max : (%,%) -> % if Record(key: Key,entry: Entry) has ORDSET +--R maxIndex : % -> Integer if Integer has ORDSET +--R maxIndex : % -> Key if Key has ORDSET +--R member? : (Record(key: Key,entry: Entry),%) -> Boolean if $ has finiteAggregate and Record(key: Key,entry: Entry) has SETCAT +--R member? : (Entry,%) -> Boolean if $ has finiteAggregate and Entry has SETCAT +--R member? : (Record(key: Key,entry: Entry),%) -> Boolean if $ has finiteAggregate and Record(key: Key,entry: Entry) has SETCAT +--R members : % -> List(Record(key: Key,entry: Entry)) if $ has finiteAggregate +--R members : % -> List(Entry) if $ has finiteAggregate +--R members : % -> List(Record(key: Key,entry: Entry)) if $ has finiteAggregate +--R merge : (%,%) -> % if Record(key: Key,entry: Entry) has ORDSET +--R merge : (((Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> Boolean),%,%) -> % +--R merge! : (%,%) -> % if Record(key: Key,entry: Entry) has ORDSET +--R merge! : (((Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> Boolean),%,%) -> % +--R min : (%,%) -> % if Record(key: Key,entry: Entry) has ORDSET +--R minIndex : % -> Integer if Integer has ORDSET +--R minIndex : % -> Key if Key has ORDSET +--R more? : (%,NonNegativeInteger) -> Boolean +--R new : (NonNegativeInteger,Record(key: Key,entry: Entry)) -> % +--R node? : (%,%) -> Boolean if Record(key: Key,entry: Entry) has SETCAT +--R parts : % -> List(Record(key: Key,entry: Entry)) if $ has finiteAggregate +--R parts : % -> List(Entry) if $ has finiteAggregate +--R parts : % -> List(Record(key: Key,entry: Entry)) if $ has finiteAggregate +--R position : (Record(key: Key,entry: Entry),%,Integer) -> Integer if Record(key: Key,entry: Entry) has SETCAT +--R position : (Record(key: Key,entry: Entry),%) -> Integer if Record(key: Key,entry: Entry) has SETCAT +--R position : ((Record(key: Key,entry: Entry) -> Boolean),%) -> Integer +--R qelt : (%,Integer) -> Record(key: Key,entry: Entry) +--R qsetelt! : (%,Integer,Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry) if $ has shallowlyMutable +--R qsetelt! : (%,Key,Entry) -> Entry if $ has shallowlyMutable +--R reduce : (((Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry)),%) -> Record(key: Key,entry: Entry) if $ has finiteAggregate +--R reduce : (((Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry)),%,Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry) if $ has finiteAggregate +--R reduce : (((Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry)),%,Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry) if $ has finiteAggregate and Record(key: Key,entry: Entry) has SETCAT +--R reduce : (((Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry)),%) -> Record(key: Key,entry: Entry) if $ has finiteAggregate +--R reduce : (((Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry)),%,Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry) if $ has finiteAggregate +--R reduce : (((Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry)),%,Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry) if $ has finiteAggregate and Record(key: Key,entry: Entry) has SETCAT +--R remove : ((Record(key: Key,entry: Entry) -> Boolean),%) -> % if $ has finiteAggregate +--R remove : (Record(key: Key,entry: Entry),%) -> % if $ has finiteAggregate and Record(key: Key,entry: Entry) has SETCAT +--R remove : ((Record(key: Key,entry: Entry) -> Boolean),%) -> % if $ has finiteAggregate +--R remove : (Record(key: Key,entry: Entry),%) -> % if $ has finiteAggregate and Record(key: Key,entry: Entry) has SETCAT +--R remove! : (Record(key: Key,entry: Entry),%) -> % if Record(key: Key,entry: Entry) has SETCAT +--R remove! : ((Record(key: Key,entry: Entry) -> Boolean),%) -> % +--R remove! : (Key,%) -> Union(Entry,"failed") +--R remove! : ((Record(key: Key,entry: Entry) -> Boolean),%) -> % if $ has finiteAggregate +--R remove! : (Record(key: Key,entry: Entry),%) -> % if $ has finiteAggregate +--R removeDuplicates : % -> % if $ has finiteAggregate and Record(key: Key,entry: Entry) has SETCAT +--R removeDuplicates! : % -> % if Record(key: Key,entry: Entry) has SETCAT +--R reverse! : % -> % if $ has shallowlyMutable +--R search : (Key,%) -> Union(Entry,"failed") +--R second : % -> Record(key: Key,entry: Entry) +--R select : ((Record(key: Key,entry: Entry) -> Boolean),%) -> % if $ has finiteAggregate +--R select : ((Record(key: Key,entry: Entry) -> Boolean),%) -> % if $ has finiteAggregate +--R select! : ((Record(key: Key,entry: Entry) -> Boolean),%) -> % +--R select! : ((Record(key: Key,entry: Entry) -> Boolean),%) -> % if $ has finiteAggregate +--R setchildren! : (%,List(%)) -> % if $ has shallowlyMutable +--R setelt : (%,value,Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry) if $ has shallowlyMutable +--R setelt : (%,first,Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry) if $ has shallowlyMutable +--R setelt : (%,rest,%) -> % if $ has shallowlyMutable +--R setelt : (%,last,Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry) if $ has shallowlyMutable +--R setelt : (%,UniversalSegment(Integer),Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry) if $ has shallowlyMutable +--R setelt : (%,Integer,Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry) if $ has shallowlyMutable +--R setfirst! : (%,Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry) if $ has shallowlyMutable +--R setlast! : (%,Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry) if $ has shallowlyMutable +--R setrest! : (%,%) -> % if $ has shallowlyMutable +--R setvalue! : (%,Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry) if $ has shallowlyMutable +--R size? : (%,NonNegativeInteger) -> Boolean +--R sort : % -> % if Record(key: Key,entry: Entry) has ORDSET +--R sort : (((Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> Boolean),%) -> % +--R sort! : % -> % if $ has shallowlyMutable and Record(key: Key,entry: Entry) has ORDSET +--R sort! : (((Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> Boolean),%) -> % if $ has shallowlyMutable +--R sorted? : % -> Boolean if Record(key: Key,entry: Entry) has ORDSET +--R sorted? : (((Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> Boolean),%) -> Boolean +--R split! : (%,Integer) -> % if $ has shallowlyMutable +--R swap! : (%,Integer,Integer) -> Void if $ has shallowlyMutable +--R swap! : (%,Key,Key) -> Void if $ has shallowlyMutable +--R table : List(Record(key: Key,entry: Entry)) -> % +--R third : % -> Record(key: Key,entry: Entry) +--R value : % -> Record(key: Key,entry: Entry) +--R ?~=? : (%,%) -> Boolean if Record(key: Key,entry: Entry) has SETCAT or Entry has SETCAT +--R +--E 11 + )spool )lisp (bye) \end{chunk} @@ -14282,6 +14530,7 @@ AssociationList(Key:SetCategory, Entry:SetCategory): --S 1 of 1 )show AttributeButtons +--R --R AttributeButtons is a domain constructor --R Abbreviation for AttributeButtons is ATTRBUT --R This constructor is exposed in this frame. @@ -14289,12 +14538,11 @@ AssociationList(Key:SetCategory, Entry:SetCategory): --R --R------------------------------- Operations -------------------------------- --R ?=? : (%,%) -> Boolean coerce : % -> OutputForm ---R decrease : String -> Float hash : % -> SingleInteger ---R increase : String -> Float latex : % -> String +--R decrease : String -> Float decrease : (String,String) -> Float +--R hash : % -> SingleInteger increase : String -> Float +--R increase : (String,String) -> Float latex : % -> String --R resetAttributeButtons : () -> Void ?~=? : (%,%) -> Boolean ---R decrease : (String,String) -> Float --R getButtonValue : (String,String) -> Float ---R increase : (String,String) -> Float --R setAttributeButtonStep : Float -> Float --R setButtonValue : (String,String,Float) -> Float --R setButtonValue : (String,Float) -> Float @@ -14588,19 +14836,17 @@ AttributeButtons(): E == I where --R --R------------------------------- Operations -------------------------------- --R ?*? : (%,%) -> % ?**? : (%,Integer) -> % ---R ?**? : (%,PositiveInteger) -> % ?/? : (%,%) -> % ---R ?=? : (%,%) -> Boolean 1 : () -> % ---R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % +--R ?/? : (%,%) -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % ?^? : (%,Integer) -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % --R coerce : % -> OutputForm commutator : (%,%) -> % --R conjugate : (%,%) -> % ?.? : (%,R) -> R --R hash : % -> SingleInteger inv : % -> % ---R latex : % -> String morphism : (R -> R) -> % +--R latex : % -> String morphism : ((R,Integer) -> R) -> % +--R morphism : ((R -> R),(R -> R)) -> % morphism : (R -> R) -> % --R one? : % -> Boolean recip : % -> Union(%,"failed") --R sample : () -> % ?~=? : (%,%) -> Boolean ---R ?**? : (%,NonNegativeInteger) -> % ---R ?^? : (%,NonNegativeInteger) -> % ---R morphism : ((R,Integer) -> R) -> % ---R morphism : ((R -> R),(R -> R)) -> % --R --E 1 @@ -14725,34 +14971,119 @@ Automorphism(R:Ring): Join(Group, Eltable(R, R)) with )set message test on )set message auto off )clear all ---S 1 of 7 + +--S 1 of 8 lm := [3,5,7,11] +--R +--R +--R (1) [3,5,7,11] +--R Type: List(PositiveInteger) --E 1 ---S 2 of 7 +--S 2 of 8 t := balancedBinaryTree(#lm, 0) +--R +--R +--R (2) [[0,0,0],0,[0,0,0]] +--R Type: BalancedBinaryTree(NonNegativeInteger) --E 2 ---S 3 of 7 +--S 3 of 8 setleaves!(t,lm) +--R +--R +--R (3) [[3,0,5],0,[7,0,11]] +--R Type: BalancedBinaryTree(NonNegativeInteger) --E 3 ---S 4 of 7 +--S 4 of 8 mapUp!(t,_*) +--R +--R +--R (4) 1155 +--R Type: PositiveInteger --E 4 ---S 5 of 7 +--S 5 of 8 t +--R +--R +--R (5) [[3,15,5],1155,[7,77,11]] +--R Type: BalancedBinaryTree(NonNegativeInteger) --E 5 ---S 6 of 7 +--S 6 of 8 mapDown!(t,12,_rem) +--R +--R +--R (6) [[0,12,2],12,[5,12,1]] +--R Type: BalancedBinaryTree(NonNegativeInteger) --E 6 ---S 7 of 7 +--S 7 of 8 leaves % +--R +--R +--R (7) [0,2,5,1] +--R Type: List(NonNegativeInteger) --E 7 +--S 8 of 8 +)show BalancedBinaryTree +--R +--R BalancedBinaryTree(S: SetCategory) is a domain constructor +--R Abbreviation for BalancedBinaryTree is BBTREE +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for BBTREE +--R +--R------------------------------- Operations -------------------------------- +--R children : % -> List(%) copy : % -> % +--R cyclic? : % -> Boolean distance : (%,%) -> Integer +--R ?.right : (%,right) -> % ?.left : (%,left) -> % +--R ?.value : (%,value) -> S empty : () -> % +--R empty? : % -> Boolean eq? : (%,%) -> Boolean +--R latex : % -> String if S has SETCAT leaf? : % -> Boolean +--R leaves : % -> List(S) left : % -> % +--R map : ((S -> S),%) -> % mapDown! : (%,S,((S,S) -> S)) -> % +--R mapUp! : (%,((S,S) -> S)) -> S node : (%,S,%) -> % +--R nodes : % -> List(%) right : % -> % +--R sample : () -> % setleaves! : (%,List(S)) -> % +--R value : % -> S +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R ?=? : (%,%) -> Boolean if S has SETCAT +--R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R balancedBinaryTree : (NonNegativeInteger,S) -> % +--R child? : (%,%) -> Boolean if S has SETCAT +--R coerce : % -> OutputForm if S has SETCAT +--R count : (S,%) -> NonNegativeInteger if $ has finiteAggregate and S has SETCAT +--R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R eval : (%,List(S),List(S)) -> % if S has EVALAB(S) and S has SETCAT +--R eval : (%,S,S) -> % if S has EVALAB(S) and S has SETCAT +--R eval : (%,Equation(S)) -> % if S has EVALAB(S) and S has SETCAT +--R eval : (%,List(Equation(S))) -> % if S has EVALAB(S) and S has SETCAT +--R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R hash : % -> SingleInteger if S has SETCAT +--R less? : (%,NonNegativeInteger) -> Boolean +--R map! : ((S -> S),%) -> % if $ has shallowlyMutable +--R mapDown! : (%,S,((S,S,S) -> List(S))) -> % +--R mapUp! : (%,%,((S,S,S,S) -> S)) -> % +--R member? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT +--R members : % -> List(S) if $ has finiteAggregate +--R more? : (%,NonNegativeInteger) -> Boolean +--R node? : (%,%) -> Boolean if S has SETCAT +--R parts : % -> List(S) if $ has finiteAggregate +--R setchildren! : (%,List(%)) -> % if $ has shallowlyMutable +--R setelt : (%,right,%) -> % if $ has shallowlyMutable +--R setelt : (%,left,%) -> % if $ has shallowlyMutable +--R setelt : (%,value,S) -> S if $ has shallowlyMutable +--R setleft! : (%,%) -> % if $ has shallowlyMutable +--R setright! : (%,%) -> % if $ has shallowlyMutable +--R setvalue! : (%,S) -> S if $ has shallowlyMutable +--R size? : (%,NonNegativeInteger) -> Boolean +--R ?~=? : (%,%) -> Boolean if S has SETCAT +--R +--E 8 + )spool )lisp (bye) \end{chunk} @@ -15107,28 +15438,26 @@ BalancedBinaryTree(S: SetCategory): Exports == Implementation where --R --R------------------------------- Operations -------------------------------- --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ?=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % associates? : (%,%) -> Boolean ---R coerce : % -> % coerce : Integer -> % ---R coerce : % -> OutputForm complete : % -> % ---R digits : % -> Stream(Integer) extend : (%,Integer) -> % ---R gcd : List(%) -> % gcd : (%,%) -> % ---R hash : % -> SingleInteger latex : % -> String ---R lcm : List(%) -> % lcm : (%,%) -> % ---R moduloP : % -> Integer modulus : () -> Integer ---R one? : % -> Boolean order : % -> NonNegativeInteger ---R ?quo? : (%,%) -> % quotientByP : % -> % ---R recip : % -> Union(%,"failed") ?rem? : (%,%) -> % ---R sample : () -> % sizeLess? : (%,%) -> Boolean ---R sqrt : (%,Integer) -> % unit? : % -> Boolean ---R unitCanonical : % -> % zero? : % -> Boolean ---R ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R associates? : (%,%) -> Boolean coerce : % -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R complete : % -> % digits : % -> Stream(Integer) +--R extend : (%,Integer) -> % gcd : List(%) -> % +--R gcd : (%,%) -> % hash : % -> SingleInteger +--R latex : % -> String lcm : List(%) -> % +--R lcm : (%,%) -> % moduloP : % -> Integer +--R modulus : () -> Integer one? : % -> Boolean +--R order : % -> NonNegativeInteger ?quo? : (%,%) -> % +--R quotientByP : % -> % recip : % -> Union(%,"failed") +--R ?rem? : (%,%) -> % sample : () -> % +--R sizeLess? : (%,%) -> Boolean sqrt : (%,Integer) -> % +--R unit? : % -> Boolean unitCanonical : % -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean --R approximate : (%,Integer) -> Integer --R characteristic : () -> NonNegativeInteger --R divide : (%,%) -> Record(quotient: %,remainder: %) @@ -15262,31 +15591,31 @@ BalancedPAdicInteger(p:Integer) == InnerPAdicInteger(p,false$Boolean) --R------------------------------- Operations -------------------------------- --R ?*? : (Fraction(Integer),%) -> % ?*? : (%,Fraction(Integer)) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,Integer) -> % ?**? : (%,NonNegativeInteger) -> % --R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % --R ?-? : (%,%) -> % -? : % -> % --R ?/? : (%,%) -> % ?=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % ---R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> % ---R associates? : (%,%) -> Boolean coerce : Fraction(Integer) -> % ---R coerce : % -> % coerce : Integer -> % ---R coerce : % -> OutputForm denominator : % -> % ---R factor : % -> Factored(%) gcd : List(%) -> % ---R gcd : (%,%) -> % hash : % -> SingleInteger ---R inv : % -> % latex : % -> String ---R lcm : List(%) -> % lcm : (%,%) -> % ---R numerator : % -> % one? : % -> Boolean ---R prime? : % -> Boolean ?quo? : (%,%) -> % ---R recip : % -> Union(%,"failed") ?rem? : (%,%) -> % ---R removeZeroes : (Integer,%) -> % removeZeroes : % -> % ---R sample : () -> % sizeLess? : (%,%) -> Boolean ---R squareFree : % -> Factored(%) squareFreePart : % -> % ---R unit? : % -> Boolean unitCanonical : % -> % ---R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?^? : (%,Integer) -> % ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,PositiveInteger) -> % associates? : (%,%) -> Boolean +--R coerce : Fraction(Integer) -> % coerce : % -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R denominator : % -> % factor : % -> Factored(%) +--R gcd : List(%) -> % gcd : (%,%) -> % +--R hash : % -> SingleInteger inv : % -> % +--R latex : % -> String lcm : List(%) -> % +--R lcm : (%,%) -> % numerator : % -> % +--R one? : % -> Boolean prime? : % -> Boolean +--R ?quo? : (%,%) -> % recip : % -> Union(%,"failed") +--R ?rem? : (%,%) -> % removeZeroes : (Integer,%) -> % +--R removeZeroes : % -> % sample : () -> % +--R sizeLess? : (%,%) -> Boolean squareFree : % -> Factored(%) +--R squareFreePart : % -> % unit? : % -> Boolean +--R unitCanonical : % -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean --R ?*? : (%,BalancedPAdicInteger(p)) -> % --R ?*? : (BalancedPAdicInteger(p),%) -> % ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % --R ?/? : (BalancedPAdicInteger(p),BalancedPAdicInteger(p)) -> % --R ? Boolean if BalancedPAdicInteger(p) has ORDSET --R ?<=? : (%,%) -> Boolean if BalancedPAdicInteger(p) has ORDSET @@ -15300,7 +15629,6 @@ BalancedPAdicInteger(p:Integer) == InnerPAdicInteger(p,false$Boolean) --R D : (%,Symbol) -> % if BalancedPAdicInteger(p) has PDRING(SYMBOL) --R D : (%,NonNegativeInteger) -> % if BalancedPAdicInteger(p) has DIFRING --R D : % -> % if BalancedPAdicInteger(p) has DIFRING ---R ?^? : (%,NonNegativeInteger) -> % --R abs : % -> % if BalancedPAdicInteger(p) has OINTDOM --R approximate : (%,Integer) -> Fraction(Integer) --R ceiling : % -> BalancedPAdicInteger(p) if BalancedPAdicInteger(p) has INS @@ -15646,7 +15974,7 @@ BasicFunctions(): E == I where )set message test on )set message auto off )clear all ---S 1 of 18 +--S 1 of 19 y := operator 'y --R --R @@ -15654,7 +15982,7 @@ y := operator 'y --R Type: BasicOperator --E 1 ---S 2 of 18 +--S 2 of 19 deq := D(y x, x, 2) + D(y x, x) + y x = 0 --R --R @@ -15664,7 +15992,7 @@ deq := D(y x, x, 2) + D(y x, x) + y x = 0 --R Type: Equation(Expression(Integer)) --E 2 ---S 3 of 18 +--S 3 of 19 solve(deq, y, x) --R --R @@ -15676,7 +16004,7 @@ solve(deq, y, x) --IType: Union(Record(particular: Expression(Integer),basis: ... --E 3 ---S 4 of 18 +--S 4 of 19 nary? y --R --R @@ -15684,7 +16012,7 @@ nary? y --R Type: Boolean --E 4 ---S 5 of 18 +--S 5 of 19 unary? y --R --R @@ -15692,7 +16020,7 @@ unary? y --R Type: Boolean --E 5 ---S 6 of 18 +--S 6 of 19 opOne := operator('opOne, 1) --R --R @@ -15700,7 +16028,7 @@ opOne := operator('opOne, 1) --R Type: BasicOperator --E 6 ---S 7 of 18 +--S 7 of 19 nary? opOne --R --R @@ -15708,7 +16036,7 @@ nary? opOne --R Type: Boolean --E 7 ---S 8 of 18 +--S 8 of 19 unary? opOne --R --R @@ -15716,7 +16044,7 @@ unary? opOne --R Type: Boolean --E 8 ---S 9 of 18 +--S 9 of 19 arity opOne --R --R @@ -15724,7 +16052,7 @@ arity opOne --R Type: Union(NonNegativeInteger,...) --E 9 ---S 10 of 18 +--S 10 of 19 name opOne --R --R @@ -15732,7 +16060,7 @@ name opOne --R Type: Symbol --E 10 ---S 11 of 18 +--S 11 of 19 is?(opOne, 'z2) --R --R @@ -15740,7 +16068,7 @@ is?(opOne, 'z2) --R Type: Boolean --E 11 ---S 12 of 18 +--S 12 of 19 is?(opOne, "opOne") --R --R @@ -15748,7 +16076,7 @@ is?(opOne, "opOne") --R Type: Boolean --E 12 ---S 13 of 18 +--S 13 of 19 properties y --R --R @@ -15756,7 +16084,7 @@ properties y --R Type: AssociationList(String,None) --E 13 ---S 14 of 18 +--S 14 of 19 setProperty(y, "use", "unknown function" :: None ) --R --R @@ -15764,7 +16092,7 @@ setProperty(y, "use", "unknown function" :: None ) --R Type: BasicOperator --E 14 ---S 15 of 18 +--S 15 of 19 properties y --R --R @@ -15772,7 +16100,7 @@ properties y --R Type: AssociationList(String,None) --E 15 ---S 16 of 18 +--S 16 of 19 property(y, "use") :: None pretend String --R --R @@ -15780,7 +16108,7 @@ property(y, "use") :: None pretend String --R Type: String --E 16 ---S 17 of 18 +--S 17 of 19 deleteProperty!(y, "use") --R --R @@ -15788,13 +16116,51 @@ deleteProperty!(y, "use") --R Type: BasicOperator --E 17 ---S 18 of 18 +--S 18 of 19 properties y --R --R --R (18) table() --R Type: AssociationList(String,None) --E 18 + +--S 19 of 19 +)show BasicOperator +--R +--R BasicOperator is a domain constructor +--R Abbreviation for BasicOperator is BOP +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for BOP +--R +--R------------------------------- Operations -------------------------------- +--R ? Boolean ?<=? : (%,%) -> Boolean +--R ?=? : (%,%) -> Boolean ?>? : (%,%) -> Boolean +--R ?>=? : (%,%) -> Boolean assert : (%,String) -> % +--R coerce : % -> OutputForm copy : % -> % +--R deleteProperty! : (%,String) -> % has? : (%,String) -> Boolean +--R hash : % -> SingleInteger is? : (%,Symbol) -> Boolean +--R latex : % -> String max : (%,%) -> % +--R min : (%,%) -> % name : % -> Symbol +--R nary? : % -> Boolean nullary? : % -> Boolean +--R operator : Symbol -> % setProperty : (%,String,None) -> % +--R unary? : % -> Boolean weight : % -> NonNegativeInteger +--R ?~=? : (%,%) -> Boolean +--R arity : % -> Union(NonNegativeInteger,"failed") +--R comparison : (%,((%,%) -> Boolean)) -> % +--R display : (%,(OutputForm -> OutputForm)) -> % +--R display : (%,(List(OutputForm) -> OutputForm)) -> % +--R display : % -> Union((List(OutputForm) -> OutputForm),"failed") +--R equality : (%,((%,%) -> Boolean)) -> % +--R input : % -> Union((List(InputForm) -> InputForm),"failed") +--R input : (%,(List(InputForm) -> InputForm)) -> % +--R operator : (Symbol,NonNegativeInteger) -> % +--R properties : % -> AssociationList(String,None) +--R property : (%,String) -> Union(None,"failed") +--R setProperties : (%,AssociationList(String,None)) -> % +--R weight : (%,NonNegativeInteger) -> % +--R +--E 19 + )spool )lisp (bye) \end{chunk} @@ -16183,21 +16549,21 @@ BasicOperator(): Exports == Implementation where )set message auto off )clear all ---S 1 of 30 +--S 1 of 31 print copyBSD() --R --R [] --R Type: Void --E 1 ---S 2 of 30 +--S 2 of 31 print copyIto() --R --R table() --R Type: Void --E 2 ---S 3 of 30 +--S 3 of 31 dX:=introduce!(X,dX) -- dX is a new stochastic differential --R --R @@ -16205,21 +16571,21 @@ dX:=introduce!(X,dX) -- dX is a new stochastic differential --R Type: Union(BasicStochasticDifferential,...) --E 3 ---S 4 of 30 +--S 4 of 31 print copyBSD() --R --R [dX] --R Type: Void --E 4 ---S 5 of 30 +--S 5 of 31 print copyIto() --R --R table(X= dX) --R Type: Void --E 5 ---S 6 of 30 +--S 6 of 31 getSmgl(dX) --R --R @@ -16227,42 +16593,42 @@ getSmgl(dX) --R Type: Union(Symbol,...) --E 6 ---S 7 of 30 +--S 7 of 31 print dX --R --R dX --R Type: Void --E 7 ---S 8 of 30 +--S 8 of 31 print domainOf(dX) --R --R BasicStochasticDifferential() --R Type: Void --E 8 ---S 9 of 30 +--S 9 of 31 print d X --R --R dX --R Type: Void --E 9 ---S 10 of 30 +--S 10 of 31 print ((d$BSD) X) --R --R dX --R Type: Void --E 10 ---S 11 of 30 +--S 11 of 31 print domainOf((d$BSD) X) --R --R BasicStochasticDifferential() --R Type: Void --E 11 ---S 12 of 30 +--S 12 of 31 introduce!(t,dt) -- dt is a new stochastic differential --R --R @@ -16270,21 +16636,21 @@ introduce!(t,dt) -- dt is a new stochastic differential --R Type: Union(BasicStochasticDifferential,...) --E 12 ---S 13 of 30 +--S 13 of 31 print copyBSD() --R --R [dX,dt] --R Type: Void --E 13 ---S 14 of 30 +--S 14 of 31 print copyIto() --R --R table(t= dt,X= dX) --R Type: Void --E 14 ---S 15 of 30 +--S 15 of 31 introduce!(t,dt) -- fails (can't repeat an introduction!) --R --R @@ -16292,21 +16658,21 @@ introduce!(t,dt) -- fails (can't repeat an introduction!) --R Type: Union("failed",...) --E 15 ---S 16 of 30 +--S 16 of 31 print copyBSD() --R --R [dX,dt] --R Type: Void --E 16 ---S 17 of 30 +--S 17 of 31 print copyIto() --R --R table(t= dt,X= dX) --R Type: Void --E 17 ---S 18 of 30 +--S 18 of 31 'dZ::BSD -- can fail --R --R dZ is not a stochastic differential @@ -16319,7 +16685,7 @@ print copyIto() --R --E 18 ---S 19 of 30 +--S 19 of 31 dZ::BSD -- fails --R --R dZ is not a stochastic differential @@ -16332,7 +16698,7 @@ dZ::BSD -- fails --R --E 19 ---S 20 of 30 +--S 20 of 31 string(dY)::BSD -- fails --R --R @@ -16343,14 +16709,14 @@ string(dY)::BSD -- fails --R --E 20 ---S 21 of 30 +--S 21 of 31 print domainOf(dt) --R --R Variable(dt) --R Type: Void --E 21 ---S 22 of 30 +--S 22 of 31 dt::BSD -- succeeds! --R --R @@ -16358,7 +16724,7 @@ dt::BSD -- succeeds! --R Type: BasicStochasticDifferential --E 22 ---S 23 of 30 +--S 23 of 31 getSmgl(dt::BSD) --R --R @@ -16366,7 +16732,7 @@ getSmgl(dt::BSD) --R Type: Union(Symbol,...) --E 23 ---S 24 of 30 +--S 24 of 31 dX::Symbol -- succeeds --R --R @@ -16374,7 +16740,7 @@ dX::Symbol -- succeeds --R Type: Symbol --E 24 ---S 25 of 30 +--S 25 of 31 string(dX) -- fails --R --R There are 3 exposed and 1 unexposed library operations named string @@ -16393,7 +16759,7 @@ string(dX) -- fails --R $ to specify which version of the function you need. --E 25 ---S 26 of 30 +--S 26 of 31 string(dX::Symbol) -- succeeds --R --R @@ -16401,7 +16767,7 @@ string(dX::Symbol) -- succeeds --R Type: String --E 26 ---S 27 of 30 +--S 27 of 31 [introduce!(A[i],dA[i]) for i in 1..2] --R --R @@ -16410,7 +16776,7 @@ string(dX::Symbol) -- succeeds --R Type: List(Union(BasicStochasticDifferential,"failed")) --E 27 ---S 28 of 30 +--S 28 of 31 print copyBSD() --R --R [dA ,dA ,dX,dt] @@ -16418,7 +16784,7 @@ print copyBSD() --R Type: Void --E 28 ---S 29 of 30 +--S 29 of 31 print copyIto() --R --R table(A = dA ,A = dA ,t= dt,X= dX) @@ -16426,7 +16792,7 @@ print copyIto() --R Type: Void --E 29 ---S 30 of 30 +--S 30 of 31 [d A[i] for i in 1..2] --R --R @@ -16435,6 +16801,28 @@ print copyIto() --R Type: List(Union(BasicStochasticDifferential,Integer)) --E 30 +--S 31 of 31 +)show BasicStochasticDifferential +--R +--R BasicStochasticDifferential is a domain constructor +--R Abbreviation for BasicStochasticDifferential is BSD +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for BSD +--R +--R------------------------------- Operations -------------------------------- +--R ? Boolean ?<=? : (%,%) -> Boolean +--R ?=? : (%,%) -> Boolean ?>? : (%,%) -> Boolean +--R ?>=? : (%,%) -> Boolean coerce : % -> OutputForm +--R convert : % -> Symbol convert : Symbol -> % +--R copyBSD : () -> List(%) copyIto : () -> Table(Symbol,%) +--R d : Symbol -> Union(%,Integer) hash : % -> SingleInteger +--R latex : % -> String max : (%,%) -> % +--R min : (%,%) -> % ?~=? : (%,%) -> Boolean +--R convertIfCan : Symbol -> Union(%,"failed") +--R getSmgl : % -> Union(Symbol,"failed") +--R introduce! : (Symbol,Symbol) -> Union(%,"failed") +--R +--E 31 )spool )lisp (bye) @@ -16678,7 +17066,8 @@ BasicStochasticDifferential(): category == implementation where )set message test on )set message auto off )clear all ---S 1 of 7 + +--S 1 of 8 r := binary(22/7) --R --R @@ -16687,7 +17076,7 @@ r := binary(22/7) --R Type: BinaryExpansion --E 1 ---S 2 of 7 +--S 2 of 8 r + binary(6/7) --R --R @@ -16695,7 +17084,7 @@ r + binary(6/7) --R Type: BinaryExpansion --E 2 ---S 3 of 7 +--S 3 of 8 [binary(1/i) for i in 102..106] --R --R @@ -16709,7 +17098,7 @@ r + binary(6/7) --R Type: List(BinaryExpansion) --E 3 ---S 4 of 7 +--S 4 of 8 binary(1/1007) --R --R @@ -16726,7 +17115,7 @@ binary(1/1007) --R Type: BinaryExpansion --E 4 ---S 5 of 7 +--S 5 of 8 p := binary(1/4)*x**2 + binary(2/3)*x + binary(4/9) --R --R @@ -16735,7 +17124,7 @@ p := binary(1/4)*x**2 + binary(2/3)*x + binary(4/9) --R Type: Polynomial(BinaryExpansion) --E 5 ---S 6 of 7 +--S 6 of 8 q := D(p, x) --R --R @@ -16744,7 +17133,7 @@ q := D(p, x) --R Type: Polynomial(BinaryExpansion) --E 6 ---S 7 of 7 +--S 7 of 8 g := gcd(p, q) --R --R @@ -16752,6 +17141,126 @@ g := gcd(p, q) --R (7) x + 1.01 --R Type: Polynomial(BinaryExpansion) --E 7 + +--S 8 of 8 +)show BinaryExpansion +--R +--R BinaryExpansion is a domain constructor +--R Abbreviation for BinaryExpansion is BINARY +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for BINARY +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,Integer) -> % ?*? : (Integer,%) -> % +--R ?*? : (Fraction(Integer),%) -> % ?*? : (%,Fraction(Integer)) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,Integer) -> % ?**? : (%,NonNegativeInteger) -> % +--R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % +--R ?-? : (%,%) -> % -? : % -> % +--R ?/? : (Integer,Integer) -> % ?/? : (%,%) -> % +--R ?=? : (%,%) -> Boolean D : (%,(Integer -> Integer)) -> % +--R D : % -> % if Integer has DIFRING 1 : () -> % +--R 0 : () -> % ?^? : (%,Integer) -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R associates? : (%,%) -> Boolean binary : Fraction(Integer) -> % +--R coerce : % -> RadixExpansion(2) coerce : % -> Fraction(Integer) +--R coerce : Integer -> % coerce : Fraction(Integer) -> % +--R coerce : % -> % coerce : Integer -> % +--R coerce : % -> OutputForm denom : % -> Integer +--R denominator : % -> % factor : % -> Factored(%) +--R gcd : List(%) -> % gcd : (%,%) -> % +--R hash : % -> SingleInteger init : () -> % if Integer has STEP +--R inv : % -> % latex : % -> String +--R lcm : List(%) -> % lcm : (%,%) -> % +--R numer : % -> Integer numerator : % -> % +--R one? : % -> Boolean prime? : % -> Boolean +--R ?quo? : (%,%) -> % random : () -> % if Integer has INS +--R recip : % -> Union(%,"failed") ?rem? : (%,%) -> % +--R retract : % -> Integer sample : () -> % +--R sizeLess? : (%,%) -> Boolean squareFree : % -> Factored(%) +--R squareFreePart : % -> % unit? : % -> Boolean +--R unitCanonical : % -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R ? Boolean if Integer has ORDSET +--R ?<=? : (%,%) -> Boolean if Integer has ORDSET +--R ?>? : (%,%) -> Boolean if Integer has ORDSET +--R ?>=? : (%,%) -> Boolean if Integer has ORDSET +--R D : (%,(Integer -> Integer),NonNegativeInteger) -> % +--R D : (%,List(Symbol),List(NonNegativeInteger)) -> % if Integer has PDRING(SYMBOL) +--R D : (%,Symbol,NonNegativeInteger) -> % if Integer has PDRING(SYMBOL) +--R D : (%,List(Symbol)) -> % if Integer has PDRING(SYMBOL) +--R D : (%,Symbol) -> % if Integer has PDRING(SYMBOL) +--R D : (%,NonNegativeInteger) -> % if Integer has DIFRING +--R abs : % -> % if Integer has OINTDOM +--R ceiling : % -> Integer if Integer has INS +--R characteristic : () -> NonNegativeInteger +--R charthRoot : % -> Union(%,"failed") if $ has CHARNZ and Integer has PFECAT or Integer has CHARNZ +--R coerce : Symbol -> % if Integer has RETRACT(SYMBOL) +--R conditionP : Matrix(%) -> Union(Vector(%),"failed") if $ has CHARNZ and Integer has PFECAT +--R convert : % -> DoubleFloat if Integer has REAL +--R convert : % -> Float if Integer has REAL +--R convert : % -> InputForm if Integer has KONVERT(INFORM) +--R convert : % -> Pattern(Float) if Integer has KONVERT(PATTERN(FLOAT)) +--R convert : % -> Pattern(Integer) if Integer has KONVERT(PATTERN(INT)) +--R differentiate : (%,(Integer -> Integer)) -> % +--R differentiate : (%,(Integer -> Integer),NonNegativeInteger) -> % +--R differentiate : (%,List(Symbol),List(NonNegativeInteger)) -> % if Integer has PDRING(SYMBOL) +--R differentiate : (%,Symbol,NonNegativeInteger) -> % if Integer has PDRING(SYMBOL) +--R differentiate : (%,List(Symbol)) -> % if Integer has PDRING(SYMBOL) +--R differentiate : (%,Symbol) -> % if Integer has PDRING(SYMBOL) +--R differentiate : (%,NonNegativeInteger) -> % if Integer has DIFRING +--R differentiate : % -> % if Integer has DIFRING +--R divide : (%,%) -> Record(quotient: %,remainder: %) +--R ?.? : (%,Integer) -> % if Integer has ELTAB(INT,INT) +--R euclideanSize : % -> NonNegativeInteger +--R eval : (%,Symbol,Integer) -> % if Integer has IEVALAB(SYMBOL,INT) +--R eval : (%,List(Symbol),List(Integer)) -> % if Integer has IEVALAB(SYMBOL,INT) +--R eval : (%,List(Equation(Integer))) -> % if Integer has EVALAB(INT) +--R eval : (%,Equation(Integer)) -> % if Integer has EVALAB(INT) +--R eval : (%,Integer,Integer) -> % if Integer has EVALAB(INT) +--R eval : (%,List(Integer),List(Integer)) -> % if Integer has EVALAB(INT) +--R expressIdealMember : (List(%),%) -> Union(List(%),"failed") +--R exquo : (%,%) -> Union(%,"failed") +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) +--R factorPolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if Integer has PFECAT +--R factorSquareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if Integer has PFECAT +--R floor : % -> Integer if Integer has INS +--R fractionPart : % -> Fraction(Integer) +--R fractionPart : % -> % if Integer has EUCDOM +--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) +--R lcmCoef : (%,%) -> Record(llcmres: %,coeff1: %,coeff2: %) +--R map : ((Integer -> Integer),%) -> % +--R max : (%,%) -> % if Integer has ORDSET +--R min : (%,%) -> % if Integer has ORDSET +--R multiEuclidean : (List(%),%) -> Union(List(%),"failed") +--R negative? : % -> Boolean if Integer has OINTDOM +--R nextItem : % -> Union(%,"failed") if Integer has STEP +--R patternMatch : (%,Pattern(Float),PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if Integer has PATMAB(FLOAT) +--R patternMatch : (%,Pattern(Integer),PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if Integer has PATMAB(INT) +--R positive? : % -> Boolean if Integer has OINTDOM +--R principalIdeal : List(%) -> Record(coef: List(%),generator: %) +--R reducedSystem : Matrix(%) -> Matrix(Integer) +--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(Integer),vec: Vector(Integer)) +--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(Integer),vec: Vector(Integer)) if Integer has LINEXP(INT) +--R reducedSystem : Matrix(%) -> Matrix(Integer) if Integer has LINEXP(INT) +--R retract : % -> Integer if Integer has RETRACT(INT) +--R retract : % -> Fraction(Integer) if Integer has RETRACT(INT) +--R retract : % -> Symbol if Integer has RETRACT(SYMBOL) +--R retractIfCan : % -> Union(Integer,"failed") if Integer has RETRACT(INT) +--R retractIfCan : % -> Union(Fraction(Integer),"failed") if Integer has RETRACT(INT) +--R retractIfCan : % -> Union(Symbol,"failed") if Integer has RETRACT(SYMBOL) +--R retractIfCan : % -> Union(Integer,"failed") +--R sign : % -> Integer if Integer has OINTDOM +--R solveLinearPolynomialEquation : (List(SparseUnivariatePolynomial(%)),SparseUnivariatePolynomial(%)) -> Union(List(SparseUnivariatePolynomial(%)),"failed") if Integer has PFECAT +--R squareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if Integer has PFECAT +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) +--R wholePart : % -> Integer if Integer has EUCDOM +--R +--E 8 + )spool )lisp (bye) \end{chunk} @@ -16971,6 +17480,7 @@ BinaryExpansion(): Exports == Implementation where --S 1 of 1 )show BinaryFile +--R --R BinaryFile is a domain constructor --R Abbreviation for BinaryFile is BINFILE --R This constructor is exposed in this frame. @@ -17147,7 +17657,8 @@ BinaryFile: Cat == Def where )set message test on )set message auto off )clear all ---S 1 of 12 + +--S 1 of 13 lv := [8,3,5,4,6,2,1,5,7] --R --R @@ -17155,7 +17666,7 @@ lv := [8,3,5,4,6,2,1,5,7] --R Type: List(PositiveInteger) --E 1 ---S 2 of 12 +--S 2 of 13 t := binarySearchTree lv --R --R @@ -17163,7 +17674,7 @@ t := binarySearchTree lv --R Type: BinarySearchTree(PositiveInteger) --E 2 ---S 3 of 12 +--S 3 of 13 emptybst := empty()$BSTREE(INT) --R --R @@ -17171,7 +17682,7 @@ emptybst := empty()$BSTREE(INT) --R Type: BinarySearchTree(Integer) --E 3 ---S 4 of 12 +--S 4 of 13 t1 := insert!(8,emptybst) --R --R @@ -17179,7 +17690,7 @@ t1 := insert!(8,emptybst) --R Type: BinarySearchTree(Integer) --E 4 ---S 5 of 12 +--S 5 of 13 insert!(3,t1) --R --R @@ -17187,7 +17698,7 @@ insert!(3,t1) --R Type: BinarySearchTree(Integer) --E 5 ---S 6 of 12 +--S 6 of 13 leaves t --R --R @@ -17195,7 +17706,7 @@ leaves t --R Type: List(PositiveInteger) --E 6 ---S 7 of 12 +--S 7 of 13 split(3,t) --R --R @@ -17203,13 +17714,13 @@ split(3,t) --IType: Record(less: BinarySearchTree(PositiveInteger),greater: ... --E 7 ---S 8 of 12 +--S 8 of 13 insertRoot: (INT,BSTREE INT) -> BSTREE INT --R --R Type: Void --E 8 ---S 9 of 12 +--S 9 of 13 insertRoot(x, t) == a := split(x, t) node(a.less, x, a.greater) @@ -17217,13 +17728,13 @@ insertRoot(x, t) == --R Type: Void --E 9 ---S 10 of 12 +--S 10 of 13 buildFromRoot ls == reduce(insertRoot,ls,emptybst) --R --R Type: Void --E 10 ---S 11 of 12 +--S 11 of 13 rt := buildFromRoot reverse lv --R --R Compiling function buildFromRoot with type List(PositiveInteger) -> @@ -17235,13 +17746,68 @@ rt := buildFromRoot reverse lv --R Type: BinarySearchTree(Integer) --E 11 ---S 12 of 12 +--S 12 of 13 (t = rt)@Boolean --R --R --R (12) true --R Type: Boolean --E 12 + +--S 13 of 13 +)show BinarySearchTree +--R +--R BinarySearchTree(S: OrderedSet) is a domain constructor +--R Abbreviation for BinarySearchTree is BSTREE +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for BSTREE +--R +--R------------------------------- Operations -------------------------------- +--R binarySearchTree : List(S) -> % children : % -> List(%) +--R copy : % -> % cyclic? : % -> Boolean +--R distance : (%,%) -> Integer ?.right : (%,right) -> % +--R ?.left : (%,left) -> % ?.value : (%,value) -> S +--R empty : () -> % empty? : % -> Boolean +--R eq? : (%,%) -> Boolean insert! : (S,%) -> % +--R insertRoot! : (S,%) -> % latex : % -> String if S has SETCAT +--R leaf? : % -> Boolean leaves : % -> List(S) +--R left : % -> % map : ((S -> S),%) -> % +--R node : (%,S,%) -> % nodes : % -> List(%) +--R right : % -> % sample : () -> % +--R value : % -> S +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R ?=? : (%,%) -> Boolean if S has SETCAT +--R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R child? : (%,%) -> Boolean if S has SETCAT +--R coerce : % -> OutputForm if S has SETCAT +--R count : (S,%) -> NonNegativeInteger if $ has finiteAggregate and S has SETCAT +--R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R eval : (%,List(S),List(S)) -> % if S has EVALAB(S) and S has SETCAT +--R eval : (%,S,S) -> % if S has EVALAB(S) and S has SETCAT +--R eval : (%,Equation(S)) -> % if S has EVALAB(S) and S has SETCAT +--R eval : (%,List(Equation(S))) -> % if S has EVALAB(S) and S has SETCAT +--R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R hash : % -> SingleInteger if S has SETCAT +--R less? : (%,NonNegativeInteger) -> Boolean +--R map! : ((S -> S),%) -> % if $ has shallowlyMutable +--R member? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT +--R members : % -> List(S) if $ has finiteAggregate +--R more? : (%,NonNegativeInteger) -> Boolean +--R node? : (%,%) -> Boolean if S has SETCAT +--R parts : % -> List(S) if $ has finiteAggregate +--R setchildren! : (%,List(%)) -> % if $ has shallowlyMutable +--R setelt : (%,right,%) -> % if $ has shallowlyMutable +--R setelt : (%,left,%) -> % if $ has shallowlyMutable +--R setelt : (%,value,S) -> S if $ has shallowlyMutable +--R setleft! : (%,%) -> % if $ has shallowlyMutable +--R setright! : (%,%) -> % if $ has shallowlyMutable +--R setvalue! : (%,S) -> S if $ has shallowlyMutable +--R size? : (%,NonNegativeInteger) -> Boolean +--R split : (S,%) -> Record(less: %,greater: %) +--R ?~=? : (%,%) -> Boolean if S has SETCAT +--R +--E 13 + )spool )lisp (bye) \end{chunk} @@ -17512,11 +18078,11 @@ both BinaryTree(S) --R ?.left : (%,left) -> % ?.value : (%,value) -> S --R empty : () -> % empty? : % -> Boolean --R eq? : (%,%) -> Boolean insert! : (S,%) -> % ---R leaf? : % -> Boolean leaves : % -> List(S) ---R left : % -> % map : ((S -> S),%) -> % ---R node : (%,S,%) -> % nodes : % -> List(%) ---R right : % -> % sample : () -> % ---R value : % -> S +--R latex : % -> String if S has SETCAT leaf? : % -> Boolean +--R leaves : % -> List(S) left : % -> % +--R map : ((S -> S),%) -> % node : (%,S,%) -> % +--R nodes : % -> List(%) right : % -> % +--R sample : () -> % value : % -> S --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R ?=? : (%,%) -> Boolean if S has SETCAT --R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate @@ -17530,7 +18096,6 @@ both BinaryTree(S) --R eval : (%,List(Equation(S))) -> % if S has EVALAB(S) and S has SETCAT --R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate --R hash : % -> SingleInteger if S has SETCAT ---R latex : % -> String if S has SETCAT --R less? : (%,NonNegativeInteger) -> Boolean --R map! : ((S -> S),%) -> % if $ has shallowlyMutable --R member? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT @@ -17696,11 +18261,11 @@ BinaryTournament(S: OrderedSet): Exports == Implementation where --R ?.right : (%,right) -> % ?.left : (%,left) -> % --R ?.value : (%,value) -> S empty : () -> % --R empty? : % -> Boolean eq? : (%,%) -> Boolean ---R leaf? : % -> Boolean leaves : % -> List(S) ---R left : % -> % map : ((S -> S),%) -> % ---R node : (%,S,%) -> % nodes : % -> List(%) ---R right : % -> % sample : () -> % ---R value : % -> S +--R latex : % -> String if S has SETCAT leaf? : % -> Boolean +--R leaves : % -> List(S) left : % -> % +--R map : ((S -> S),%) -> % node : (%,S,%) -> % +--R nodes : % -> List(%) right : % -> % +--R sample : () -> % value : % -> S --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R ?=? : (%,%) -> Boolean if S has SETCAT --R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate @@ -17714,7 +18279,6 @@ BinaryTournament(S: OrderedSet): Exports == Implementation where --R eval : (%,List(Equation(S))) -> % if S has EVALAB(S) and S has SETCAT --R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate --R hash : % -> SingleInteger if S has SETCAT ---R latex : % -> String if S has SETCAT --R less? : (%,NonNegativeInteger) -> Boolean --R map! : ((S -> S),%) -> % if $ has shallowlyMutable --R member? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT @@ -17903,14 +18467,14 @@ BinaryTree(S: SetCategory): Exports == Implementation where --R empty : () -> % empty? : % -> Boolean --R entries : % -> List(Boolean) eq? : (%,%) -> Boolean --R hash : % -> SingleInteger index? : (Integer,%) -> Boolean ---R indices : % -> List(Integer) insert : (%,%,Integer) -> % ---R latex : % -> String max : (%,%) -> % ---R min : (%,%) -> % nand : (%,%) -> % ---R nor : (%,%) -> % not? : % -> % ---R ?or? : (%,%) -> % qelt : (%,Integer) -> Boolean ---R reverse : % -> % sample : () -> % ---R xor : (%,%) -> % ~? : % -> % ---R ?~=? : (%,%) -> Boolean +--R indices : % -> List(Integer) insert : (Boolean,%,Integer) -> % +--R insert : (%,%,Integer) -> % latex : % -> String +--R max : (%,%) -> % min : (%,%) -> % +--R nand : (%,%) -> % nor : (%,%) -> % +--R not? : % -> % ?or? : (%,%) -> % +--R qelt : (%,Integer) -> Boolean reverse : % -> % +--R sample : () -> % xor : (%,%) -> % +--R ~? : % -> % ?~=? : (%,%) -> Boolean --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R any? : ((Boolean -> Boolean),%) -> Boolean if $ has finiteAggregate --R bits : (NonNegativeInteger,Boolean) -> % @@ -17930,7 +18494,6 @@ BinaryTree(S: SetCategory): Exports == Implementation where --R fill! : (%,Boolean) -> % if $ has shallowlyMutable --R find : ((Boolean -> Boolean),%) -> Union(Boolean,"failed") --R first : % -> Boolean if Integer has ORDSET ---R insert : (Boolean,%,Integer) -> % --R less? : (%,NonNegativeInteger) -> Boolean --R map : ((Boolean -> Boolean),%) -> % --R map : (((Boolean,Boolean) -> Boolean),%,%) -> % @@ -18320,6 +18883,7 @@ BlowUpWithQuadTrans: Exports == Implementation where --S 1 of 1 )show Boolean +--R --R Boolean is a domain constructor --R Abbreviation for Boolean is BOOLEAN --R This constructor is exposed in this frame. @@ -18497,7 +19061,8 @@ Boolean(): Join(OrderedSet, Finite, Logic, ConvertibleTo InputForm) with )set message test on )set message auto off )clear all ---S 1 of 20 + +--S 1 of 21 c0 := 0 :: CardinalNumber --R --R @@ -18505,7 +19070,7 @@ c0 := 0 :: CardinalNumber --R Type: CardinalNumber --E 1 ---S 2 of 20 +--S 2 of 21 c1 := 1 :: CardinalNumber --R --R @@ -18513,7 +19078,7 @@ c1 := 1 :: CardinalNumber --R Type: CardinalNumber --E 2 ---S 3 of 20 +--S 3 of 21 c2 := 2 :: CardinalNumber --R --R @@ -18521,7 +19086,7 @@ c2 := 2 :: CardinalNumber --R Type: CardinalNumber --E 3 ---S 4 of 20 +--S 4 of 21 c3 := 3 :: CardinalNumber --R --R @@ -18529,7 +19094,7 @@ c3 := 3 :: CardinalNumber --R Type: CardinalNumber --E 4 ---S 5 of 20 +--S 5 of 21 A0 := Aleph 0 --R --R @@ -18537,7 +19102,7 @@ A0 := Aleph 0 --R Type: CardinalNumber --E 5 ---S 6 of 20 +--S 6 of 21 A1 := Aleph 1 --R --R @@ -18545,7 +19110,7 @@ A1 := Aleph 1 --R Type: CardinalNumber --E 6 ---S 7 of 20 +--S 7 of 21 finite? c2 --R --R @@ -18553,7 +19118,7 @@ finite? c2 --R Type: Boolean --E 7 ---S 8 of 20 +--S 8 of 21 finite? A0 --R --R @@ -18561,7 +19126,7 @@ finite? A0 --R Type: Boolean --E 8 ---S 9 of 20 +--S 9 of 21 countable? c2 --R --R @@ -18569,7 +19134,7 @@ countable? c2 --R Type: Boolean --E 9 ---S 10 of 20 +--S 10 of 21 countable? A0 --R --R @@ -18577,7 +19142,7 @@ countable? A0 --R Type: Boolean --E 10 ---S 11 of 20 +--S 11 of 21 countable? A1 --R --R @@ -18585,7 +19150,7 @@ countable? A1 --R Type: Boolean --E 11 ---S 12 of 20 +--S 12 of 21 [c2 + c2, c2 + A1] --R --R @@ -18593,7 +19158,7 @@ countable? A1 --R Type: List(CardinalNumber) --E 12 ---S 13 of 20 +--S 13 of 21 [c0*c2, c1*c2, c2*c2, c0*A1, c1*A1, c2*A1, A0*A1] --R --R @@ -18601,7 +19166,7 @@ countable? A1 --R Type: List(CardinalNumber) --E 13 ---S 14 of 20 +--S 14 of 21 [c2**c0, c2**c1, c2**c2, A1**c0, A1**c1, A1**c2] --R --R @@ -18609,7 +19174,7 @@ countable? A1 --R Type: List(CardinalNumber) --E 14 ---S 15 of 20 +--S 15 of 21 [c2-c1, c2-c2, c2-c3, A1-c2, A1-A0, A1-A1] --R --R @@ -18617,7 +19182,7 @@ countable? A1 --R Type: List(Union(CardinalNumber,"failed")) --E 15 ---S 16 of 20 +--S 16 of 21 generalizedContinuumHypothesisAssumed true --R --R @@ -18625,7 +19190,7 @@ generalizedContinuumHypothesisAssumed true --R Type: Boolean --E 16 ---S 17 of 20 +--S 17 of 21 [c0**A0, c1**A0, c2**A0, A0**A0, A0**A1, A1**A0, A1**A1] --R --R @@ -18633,7 +19198,7 @@ generalizedContinuumHypothesisAssumed true --R Type: List(CardinalNumber) --E 17 ---S 18 of 20 +--S 18 of 21 a := Aleph 0 --R --R @@ -18641,7 +19206,7 @@ a := Aleph 0 --R Type: CardinalNumber --E 18 ---S 19 of 20 +--S 19 of 21 c := 2**a --R --R @@ -18649,13 +19214,45 @@ c := 2**a --R Type: CardinalNumber --E 19 ---S 20 of 20 +--S 20 of 21 f := 2**c --R --R --R (20) Aleph(2) --R Type: CardinalNumber --E 20 + +--S 21 of 21 +)show CardinalNumber +--R +--R CardinalNumber is a domain constructor +--R Abbreviation for CardinalNumber is CARD +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for CARD +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?**? : (%,%) -> % +--R ?**? : (%,PositiveInteger) -> % ?**? : (%,NonNegativeInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> Union(%,"failed") +--R ? Boolean ?<=? : (%,%) -> Boolean +--R ?=? : (%,%) -> Boolean ?>? : (%,%) -> Boolean +--R ?>=? : (%,%) -> Boolean Aleph : NonNegativeInteger -> % +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % ?^? : (%,NonNegativeInteger) -> % +--R coerce : NonNegativeInteger -> % coerce : % -> OutputForm +--R countable? : % -> Boolean finite? : % -> Boolean +--R hash : % -> SingleInteger latex : % -> String +--R max : (%,%) -> % min : (%,%) -> % +--R one? : % -> Boolean recip : % -> Union(%,"failed") +--R retract : % -> NonNegativeInteger sample : () -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R generalizedContinuumHypothesisAssumed : Boolean -> Boolean +--R generalizedContinuumHypothesisAssumed? : () -> Boolean +--R retractIfCan : % -> Union(NonNegativeInteger,"failed") +--R +--E 21 + )spool )lisp (bye) \end{chunk} @@ -19040,7 +19637,8 @@ CardinalNumber: Join(OrderedSet, AbelianMonoid, Monoid, )set message test on )set message auto off )clear all ---S 1 of 48 + +--S 1 of 49 CT := CARTEN(i0 := 1, 2, Integer) --R --R @@ -19048,7 +19646,7 @@ CT := CARTEN(i0 := 1, 2, Integer) --R Type: Domain --E 1 ---S 2 of 48 +--S 2 of 49 t0: CT := 8 --R --R @@ -19056,7 +19654,7 @@ t0: CT := 8 --R Type: CartesianTensor(1,2,Integer) --E 2 ---S 3 of 48 +--S 3 of 49 rank t0 --R --R @@ -19064,7 +19662,7 @@ rank t0 --R Type: NonNegativeInteger --E 3 ---S 4 of 48 +--S 4 of 49 v: DirectProduct(2, Integer) := directProduct [3,4] --R --R @@ -19072,7 +19670,7 @@ v: DirectProduct(2, Integer) := directProduct [3,4] --R Type: DirectProduct(2,Integer) --E 4 ---S 5 of 48 +--S 5 of 49 Tv: CT := v --R --R @@ -19080,7 +19678,7 @@ Tv: CT := v --R Type: CartesianTensor(1,2,Integer) --E 5 ---S 6 of 48 +--S 6 of 49 m: SquareMatrix(2, Integer) := matrix [ [1,2],[4,5] ] --R --R @@ -19090,7 +19688,7 @@ m: SquareMatrix(2, Integer) := matrix [ [1,2],[4,5] ] --R Type: SquareMatrix(2,Integer) --E 6 ---S 7 of 48 +--S 7 of 49 Tm: CT := m --R --R @@ -19100,7 +19698,7 @@ Tm: CT := m --R Type: CartesianTensor(1,2,Integer) --E 7 ---S 8 of 48 +--S 8 of 49 n: SquareMatrix(2, Integer) := matrix [ [2,3],[0,1] ] --R --R @@ -19110,7 +19708,7 @@ n: SquareMatrix(2, Integer) := matrix [ [2,3],[0,1] ] --R Type: SquareMatrix(2,Integer) --E 8 ---S 9 of 48 +--S 9 of 49 Tn: CT := n --R --R @@ -19120,7 +19718,7 @@ Tn: CT := n --R Type: CartesianTensor(1,2,Integer) --E 9 ---S 10 of 48 +--S 10 of 49 t1: CT := [2, 3] --R --R @@ -19128,7 +19726,7 @@ t1: CT := [2, 3] --R Type: CartesianTensor(1,2,Integer) --E 10 ---S 11 of 48 +--S 11 of 49 rank t1 --R --R @@ -19136,7 +19734,7 @@ rank t1 --R Type: PositiveInteger --E 11 ---S 12 of 48 +--S 12 of 49 t2: CT := [t1, t1] --R --R @@ -19146,7 +19744,7 @@ t2: CT := [t1, t1] --R Type: CartesianTensor(1,2,Integer) --E 12 ---S 13 of 48 +--S 13 of 49 t3: CT := [t2, t2] --R --R @@ -19156,7 +19754,7 @@ t3: CT := [t2, t2] --R Type: CartesianTensor(1,2,Integer) --E 13 ---S 14 of 48 +--S 14 of 49 tt: CT := [t3, t3]; tt := [tt, tt] --R --R @@ -19170,7 +19768,7 @@ tt: CT := [t3, t3]; tt := [tt, tt] --R Type: CartesianTensor(1,2,Integer) --E 14 ---S 15 of 48 +--S 15 of 49 rank tt --R --R @@ -19178,7 +19776,7 @@ rank tt --R Type: PositiveInteger --E 15 ---S 16 of 48 +--S 16 of 49 Tmn := product(Tm, Tn) --R --R @@ -19192,7 +19790,7 @@ Tmn := product(Tm, Tn) --R Type: CartesianTensor(1,2,Integer) --E 16 ---S 17 of 48 +--S 17 of 49 Tmv := contract(Tm,2,Tv,1) --R --R @@ -19200,7 +19798,7 @@ Tmv := contract(Tm,2,Tv,1) --R Type: CartesianTensor(1,2,Integer) --E 17 ---S 18 of 48 +--S 18 of 49 Tm*Tv --R --R @@ -19208,7 +19806,7 @@ Tm*Tv --R Type: CartesianTensor(1,2,Integer) --E 18 ---S 19 of 48 +--S 19 of 49 Tmv = m * v --R --R @@ -19216,7 +19814,7 @@ Tmv = m * v --R Type: Equation(CartesianTensor(1,2,Integer)) --E 19 ---S 20 of 48 +--S 20 of 49 t0() --R --R @@ -19224,7 +19822,7 @@ t0() --R Type: PositiveInteger --E 20 ---S 21 of 48 +--S 21 of 49 t1(1+1) --R --R @@ -19232,7 +19830,7 @@ t1(1+1) --R Type: PositiveInteger --E 21 ---S 22 of 48 +--S 22 of 49 t2(2,1) --R --R @@ -19240,7 +19838,7 @@ t2(2,1) --R Type: PositiveInteger --E 22 ---S 23 of 48 +--S 23 of 49 t3(2,1,2) --R --R @@ -19248,7 +19846,7 @@ t3(2,1,2) --R Type: PositiveInteger --E 23 ---S 24 of 48 +--S 24 of 49 Tmn(2,1,2,1) --R --R @@ -19256,7 +19854,7 @@ Tmn(2,1,2,1) --R Type: NonNegativeInteger --E 24 ---S 25 of 48 +--S 25 of 49 t0[] --R --R @@ -19264,7 +19862,7 @@ t0[] --R Type: PositiveInteger --E 25 ---S 26 of 48 +--S 26 of 49 t1[2] --R --R @@ -19272,7 +19870,7 @@ t1[2] --R Type: PositiveInteger --E 26 ---S 27 of 48 +--S 27 of 49 t2[2,1] --R --R @@ -19280,7 +19878,7 @@ t2[2,1] --R Type: PositiveInteger --E 27 ---S 28 of 48 +--S 28 of 49 t3[2,1,2] --R --R @@ -19288,7 +19886,7 @@ t3[2,1,2] --R Type: PositiveInteger --E 28 ---S 29 of 48 +--S 29 of 49 Tmn[2,1,2,1] --R --R @@ -19296,7 +19894,7 @@ Tmn[2,1,2,1] --R Type: NonNegativeInteger --E 29 ---S 30 of 48 +--S 30 of 49 cTmn := contract(Tmn,1,2) --R --R @@ -19306,7 +19904,7 @@ cTmn := contract(Tmn,1,2) --R Type: CartesianTensor(1,2,Integer) --E 30 ---S 31 of 48 +--S 31 of 49 trace(m) * n --R --R @@ -19316,7 +19914,7 @@ trace(m) * n --R Type: SquareMatrix(2,Integer) --E 31 ---S 32 of 48 +--S 32 of 49 contract(Tmn,1,2) = trace(m) * n --R --R @@ -19326,7 +19924,7 @@ contract(Tmn,1,2) = trace(m) * n --R Type: Equation(CartesianTensor(1,2,Integer)) --E 32 ---S 33 of 48 +--S 33 of 49 contract(Tmn,1,3) = transpose(m) * n --R --R @@ -19336,7 +19934,7 @@ contract(Tmn,1,3) = transpose(m) * n --R Type: Equation(CartesianTensor(1,2,Integer)) --E 33 ---S 34 of 48 +--S 34 of 49 contract(Tmn,1,4) = transpose(m) * transpose(n) --R --R @@ -19346,7 +19944,7 @@ contract(Tmn,1,4) = transpose(m) * transpose(n) --R Type: Equation(CartesianTensor(1,2,Integer)) --E 34 ---S 35 of 48 +--S 35 of 49 contract(Tmn,2,3) = m * n --R --R @@ -19356,7 +19954,7 @@ contract(Tmn,2,3) = m * n --R Type: Equation(CartesianTensor(1,2,Integer)) --E 35 ---S 36 of 48 +--S 36 of 49 contract(Tmn,2,4) = m * transpose(n) --R --R @@ -19366,7 +19964,7 @@ contract(Tmn,2,4) = m * transpose(n) --R Type: Equation(CartesianTensor(1,2,Integer)) --E 36 ---S 37 of 48 +--S 37 of 49 contract(Tmn,3,4) = trace(n) * m --R --R @@ -19376,7 +19974,7 @@ contract(Tmn,3,4) = trace(n) * m --R Type: Equation(CartesianTensor(1,2,Integer)) --E 37 ---S 38 of 48 +--S 38 of 49 tTmn := transpose(Tmn,1,3) --R --R @@ -19390,7 +19988,7 @@ tTmn := transpose(Tmn,1,3) --R Type: CartesianTensor(1,2,Integer) --E 38 ---S 39 of 48 +--S 39 of 49 transpose Tmn --R --R @@ -19404,7 +20002,7 @@ transpose Tmn --R Type: CartesianTensor(1,2,Integer) --E 39 ---S 40 of 48 +--S 40 of 49 transpose Tm = transpose m --R --R @@ -19414,7 +20012,7 @@ transpose Tm = transpose m --R Type: Equation(CartesianTensor(1,2,Integer)) --E 40 ---S 41 of 48 +--S 41 of 49 rTmn := reindex(Tmn, [1,4,2,3]) --R --R @@ -19428,7 +20026,7 @@ rTmn := reindex(Tmn, [1,4,2,3]) --R Type: CartesianTensor(1,2,Integer) --E 41 ---S 42 of 48 +--S 42 of 49 tt := transpose(Tm)*Tn - Tn*transpose(Tm) --R --R @@ -19438,7 +20036,7 @@ tt := transpose(Tm)*Tn - Tn*transpose(Tm) --R Type: CartesianTensor(1,2,Integer) --E 42 ---S 43 of 48 +--S 43 of 49 Tv*(tt+Tn) --R --R @@ -19446,7 +20044,7 @@ Tv*(tt+Tn) --R Type: CartesianTensor(1,2,Integer) --E 43 ---S 44 of 48 +--S 44 of 49 reindex(product(Tn,Tn),[4,3,2,1])+3*Tn*product(Tm,Tm) --R --R @@ -19460,7 +20058,7 @@ reindex(product(Tn,Tn),[4,3,2,1])+3*Tn*product(Tm,Tm) --R Type: CartesianTensor(1,2,Integer) --E 44 ---S 45 of 48 +--S 45 of 49 delta: CT := kroneckerDelta() --R --R @@ -19470,7 +20068,7 @@ delta: CT := kroneckerDelta() --R Type: CartesianTensor(1,2,Integer) --E 45 ---S 46 of 48 +--S 46 of 49 contract(Tmn, 2, delta, 1) = reindex(Tmn, [1,3,4,2]) --R --R @@ -19484,7 +20082,7 @@ contract(Tmn, 2, delta, 1) = reindex(Tmn, [1,3,4,2]) --R Type: Equation(CartesianTensor(1,2,Integer)) --E 46 ---S 47 of 48 +--S 47 of 49 epsilon:CT := leviCivitaSymbol() --R --R @@ -19494,13 +20092,50 @@ epsilon:CT := leviCivitaSymbol() --R Type: CartesianTensor(1,2,Integer) --E 47 ---S 48 of 48 +--S 48 of 49 contract(epsilon*Tm*epsilon, 1,2) = 2 * determinant m --R --R --R (48) - 6= - 6 --R Type: Equation(CartesianTensor(1,2,Integer)) --E 48 + +--S 49 of 49 +)show CartesianTensor +--R +--R CartesianTensor(minix: Integer,dim: NonNegativeInteger,R: CommutativeRing) is a domain constructor +--R Abbreviation for CartesianTensor is CARTEN +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for CARTEN +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (%,Integer) -> % ?*? : (%,R) -> % +--R ?*? : (R,%) -> % ?+? : (%,%) -> % +--R ?-? : (%,%) -> % -? : % -> % +--R ?=? : (%,%) -> Boolean 1 : () -> % +--R 0 : () -> % coerce : List(%) -> % +--R coerce : List(R) -> % coerce : SquareMatrix(dim,R) -> % +--R coerce : DirectProduct(dim,R) -> % coerce : R -> % +--R coerce : % -> OutputForm degree : % -> NonNegativeInteger +--R ?.? : (%,List(Integer)) -> R elt : (%,Integer,Integer) -> R +--R ?.? : (%,Integer) -> R elt : % -> R +--R hash : % -> SingleInteger kroneckerDelta : () -> % +--R latex : % -> String leviCivitaSymbol : () -> % +--R product : (%,%) -> % rank : % -> NonNegativeInteger +--R ravel : % -> List(R) reindex : (%,List(Integer)) -> % +--R retract : % -> R sample : () -> % +--R transpose : % -> % unravel : List(R) -> % +--R ?~=? : (%,%) -> Boolean +--R contract : (%,Integer,Integer) -> % +--R contract : (%,Integer,%,Integer) -> % +--R elt : (%,Integer,Integer,Integer,Integer) -> R +--R elt : (%,Integer,Integer,Integer) -> R +--R retractIfCan : % -> Union(R,"failed") +--R transpose : (%,Integer,Integer) -> % +--R +--E 49 + )spool )lisp (bye) \end{chunk} @@ -20632,6 +21267,21 @@ CartesianTensor(minix, dim, R): Exports == Implementation where --S 1 of 1 )show Cell +--R +--R Cell(TheField: RealClosedField) is a domain constructor +--R Abbreviation for Cell is CELL +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for CELL +--R +--R------------------------------- Operations -------------------------------- +--R coerce : % -> OutputForm dimension : % -> NonNegativeInteger +--R mainVariableOf : % -> Symbol samplePoint : % -> List(TheField) +--R variablesOf : % -> List(Symbol) +--R hasDimension? : (%,Symbol) -> Boolean +--R makeCell : (SimpleCell(TheField,SparseUnivariatePolynomial(TheField)),%) -> % +--R makeCell : List(SimpleCell(TheField,SparseUnivariatePolynomial(TheField))) -> % +--R projection : % -> Union(%,"failed") +--R --E 1 )spool @@ -20757,7 +21407,7 @@ Cell(TheField) : PUB == PRIV where )set message test on )set message auto off )clear all ---S 1 of 13 +--S 1 of 14 chars := [char "a", char "A", char "X", char "8", char "+"] --R --R @@ -20765,7 +21415,7 @@ chars := [char "a", char "A", char "X", char "8", char "+"] --R Type: List(Character) --E 1 ---S 2 of 13 +--S 2 of 14 space() --R --R @@ -20773,7 +21423,7 @@ space() --R Type: Character --E 2 ---S 3 of 13 +--S 3 of 14 quote() --R --R @@ -20781,7 +21431,7 @@ quote() --R Type: Character --E 3 ---S 4 of 13 +--S 4 of 14 escape() --R --R @@ -20789,7 +21439,7 @@ escape() --R Type: Character --E 4 ---S 5 of 13 +--S 5 of 14 [ord c for c in chars] --R --R @@ -20797,7 +21447,7 @@ escape() --R Type: List(Integer) --E 5 ---S 6 of 13 +--S 6 of 14 [upperCase c for c in chars] --R --R @@ -20805,7 +21455,7 @@ escape() --R Type: List(Character) --E 6 ---S 7 of 13 +--S 7 of 14 [lowerCase c for c in chars] --R --R @@ -20813,7 +21463,7 @@ escape() --R Type: List(Character) --E 7 ---S 8 of 13 +--S 8 of 14 [alphabetic? c for c in chars] --R --R @@ -20821,7 +21471,7 @@ escape() --R Type: List(Boolean) --E 8 ---S 9 of 13 +--S 9 of 14 [upperCase? c for c in chars] --R --R @@ -20829,7 +21479,7 @@ escape() --R Type: List(Boolean) --E 9 ---S 10 of 13 +--S 10 of 14 [lowerCase? c for c in chars] --R --R @@ -20837,7 +21487,7 @@ escape() --R Type: List(Boolean) --E 10 ---S 11 of 13 +--S 11 of 14 [digit? c for c in chars] --R --R @@ -20845,7 +21495,7 @@ escape() --R Type: List(Boolean) --E 11 ---S 12 of 13 +--S 12 of 14 [hexDigit? c for c in chars] --R --R @@ -20853,13 +21503,41 @@ escape() --R Type: List(Boolean) --E 12 ---S 13 of 13 +--S 13 of 14 [alphanumeric? c for c in chars] --R --R --R (13) [true,true,true,true,false] --R Type: List(Boolean) --E 13 + +--S 14 of 14 +)show Character +--R +--R Character is a domain constructor +--R Abbreviation for Character is CHAR +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for CHAR +--R +--R------------------------------- Operations -------------------------------- +--R ? Boolean ?<=? : (%,%) -> Boolean +--R ?=? : (%,%) -> Boolean ?>? : (%,%) -> Boolean +--R ?>=? : (%,%) -> Boolean alphabetic? : % -> Boolean +--R alphanumeric? : % -> Boolean char : String -> % +--R char : Integer -> % coerce : % -> OutputForm +--R digit? : % -> Boolean enumerate : () -> List(%) +--R escape : () -> % hash : % -> SingleInteger +--R hexDigit? : % -> Boolean index : PositiveInteger -> % +--R latex : % -> String lookup : % -> PositiveInteger +--R lowerCase : % -> % lowerCase? : % -> Boolean +--R max : (%,%) -> % min : (%,%) -> % +--R ord : % -> Integer quote : () -> % +--R random : () -> % size : () -> NonNegativeInteger +--R space : () -> % upperCase : % -> % +--R upperCase? : % -> Boolean ?~=? : (%,%) -> Boolean +--R +--E 14 + )spool )lisp (bye) \end{chunk} @@ -21140,7 +21818,8 @@ Character: OrderedFinite() with )set message test on )set message auto off )clear all ---S 1 of 16 + +--S 1 of 17 cl1:=charClass[char "a",char "e",char "i",char "o",char "u",char "y"] --R --R @@ -21148,7 +21827,7 @@ cl1:=charClass[char "a",char "e",char "i",char "o",char "u",char "y"] --R Type: CharacterClass --E 1 ---S 2 of 16 +--S 2 of 17 cl2 := charClass "bcdfghjklmnpqrstvwxyz" --R --R @@ -21156,7 +21835,7 @@ cl2 := charClass "bcdfghjklmnpqrstvwxyz" --R Type: CharacterClass --E 2 ---S 3 of 16 +--S 3 of 17 digit() --R --R @@ -21164,7 +21843,7 @@ digit() --R Type: CharacterClass --E 3 ---S 4 of 16 +--S 4 of 17 hexDigit() --R --R @@ -21172,7 +21851,7 @@ hexDigit() --R Type: CharacterClass --E 4 ---S 5 of 16 +--S 5 of 17 upperCase() --R --R @@ -21180,7 +21859,7 @@ upperCase() --R Type: CharacterClass --E 5 ---S 6 of 16 +--S 6 of 17 lowerCase() --R --R @@ -21188,7 +21867,7 @@ lowerCase() --R Type: CharacterClass --E 6 ---S 7 of 16 +--S 7 of 17 alphabetic() --R --R @@ -21196,7 +21875,7 @@ alphabetic() --R Type: CharacterClass --E 7 ---S 8 of 16 +--S 8 of 17 alphanumeric() --R --R @@ -21204,7 +21883,7 @@ alphanumeric() --R Type: CharacterClass --E 8 ---S 9 of 16 +--S 9 of 17 member?(char "a", cl1) --R --R @@ -21212,7 +21891,7 @@ member?(char "a", cl1) --R Type: Boolean --E 9 ---S 10 of 16 +--S 10 of 17 member?(char "a", cl2) --R --R @@ -21220,7 +21899,7 @@ member?(char "a", cl2) --R Type: Boolean --E 10 ---S 11 of 16 +--S 11 of 17 intersect(cl1, cl2) --R --R @@ -21228,7 +21907,7 @@ intersect(cl1, cl2) --R Type: CharacterClass --E 11 ---S 12 of 16 +--S 12 of 17 union(cl1,cl2) --R --R @@ -21236,7 +21915,7 @@ union(cl1,cl2) --R Type: CharacterClass --E 12 ---S 13 of 16 +--S 13 of 17 difference(cl1,cl2) --R --R @@ -21244,7 +21923,7 @@ difference(cl1,cl2) --R Type: CharacterClass --E 13 ---S 14 of 16 +--S 14 of 17 intersect(complement(cl1),cl2) --R --R @@ -21252,7 +21931,7 @@ intersect(complement(cl1),cl2) --R Type: CharacterClass --E 14 ---S 15 of 16 +--S 15 of 17 insert!(char "a", cl2) --R --R @@ -21260,13 +21939,85 @@ insert!(char "a", cl2) --R Type: CharacterClass --E 15 ---S 16 of 16 +--S 16 of 17 remove!(char "b", cl2) --R --R --R (16) "acdfghjklmnpqrstvwxyz" --R Type: CharacterClass --E 16 + +--S 17 of 17 +)show CharacterClass +--R +--R CharacterClass is a domain constructor +--R Abbreviation for CharacterClass is CCLASS +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for CCLASS +--R +--R------------------------------- Operations -------------------------------- +--R ? Boolean ?=? : (%,%) -> Boolean +--R alphabetic : () -> % alphanumeric : () -> % +--R bag : List(Character) -> % brace : List(Character) -> % +--R brace : () -> % charClass : List(Character) -> % +--R charClass : String -> % coerce : % -> OutputForm +--R construct : List(Character) -> % convert : % -> List(Character) +--R convert : % -> String copy : % -> % +--R dictionary : () -> % dictionary : List(Character) -> % +--R difference : (%,Character) -> % difference : (%,%) -> % +--R digit : () -> % empty : () -> % +--R empty? : % -> Boolean eq? : (%,%) -> Boolean +--R extract! : % -> Character hash : % -> SingleInteger +--R hexDigit : () -> % insert! : (Character,%) -> % +--R inspect : % -> Character intersect : (%,%) -> % +--R latex : % -> String lowerCase : () -> % +--R sample : () -> % set : List(Character) -> % +--R set : () -> % subset? : (%,%) -> Boolean +--R symmetricDifference : (%,%) -> % union : (Character,%) -> % +--R union : (%,Character) -> % union : (%,%) -> % +--R upperCase : () -> % ?~=? : (%,%) -> Boolean +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R any? : ((Character -> Boolean),%) -> Boolean if $ has finiteAggregate +--R cardinality : % -> NonNegativeInteger +--R complement : % -> % if Character has FINITE +--R convert : % -> InputForm if Character has KONVERT(INFORM) +--R count : ((Character -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R count : (Character,%) -> NonNegativeInteger if $ has finiteAggregate and Character has SETCAT +--R enumerate : () -> List(%) if Character has FINITE +--R eval : (%,List(Equation(Character))) -> % if Character has EVALAB(CHAR) and Character has SETCAT +--R eval : (%,Equation(Character)) -> % if Character has EVALAB(CHAR) and Character has SETCAT +--R eval : (%,Character,Character) -> % if Character has EVALAB(CHAR) and Character has SETCAT +--R eval : (%,List(Character),List(Character)) -> % if Character has EVALAB(CHAR) and Character has SETCAT +--R every? : ((Character -> Boolean),%) -> Boolean if $ has finiteAggregate +--R find : ((Character -> Boolean),%) -> Union(Character,"failed") +--R index : PositiveInteger -> % if Character has FINITE +--R less? : (%,NonNegativeInteger) -> Boolean +--R lookup : % -> PositiveInteger if Character has FINITE +--R map : ((Character -> Character),%) -> % +--R map! : ((Character -> Character),%) -> % if $ has shallowlyMutable +--R max : % -> Character if Character has ORDSET +--R member? : (Character,%) -> Boolean if $ has finiteAggregate and Character has SETCAT +--R members : % -> List(Character) if $ has finiteAggregate +--R min : % -> Character if Character has ORDSET +--R more? : (%,NonNegativeInteger) -> Boolean +--R parts : % -> List(Character) if $ has finiteAggregate +--R random : () -> % if Character has FINITE +--R reduce : (((Character,Character) -> Character),%,Character,Character) -> Character if $ has finiteAggregate and Character has SETCAT +--R reduce : (((Character,Character) -> Character),%,Character) -> Character if $ has finiteAggregate +--R reduce : (((Character,Character) -> Character),%) -> Character if $ has finiteAggregate +--R remove : (Character,%) -> % if $ has finiteAggregate and Character has SETCAT +--R remove : ((Character -> Boolean),%) -> % if $ has finiteAggregate +--R remove! : (Character,%) -> % if $ has finiteAggregate +--R remove! : ((Character -> Boolean),%) -> % if $ has finiteAggregate +--R removeDuplicates : % -> % if $ has finiteAggregate and Character has SETCAT +--R select : ((Character -> Boolean),%) -> % if $ has finiteAggregate +--R select! : ((Character -> Boolean),%) -> % if $ has finiteAggregate +--R size : () -> NonNegativeInteger if Character has FINITE +--R size? : (%,NonNegativeInteger) -> Boolean +--R universe : () -> % if Character has FINITE +--R +--E 17 + )spool )lisp (bye) \end{chunk} @@ -21746,7 +22497,8 @@ $\mathbb{R}_{m,m}$ & --------$>$ & $\mathbb{R}^{4^m}$ \\ )set message test on )set message auto off )clear all ---S 1 of 36 + +--S 1 of 37 K := Fraction Polynomial Integer --R --R @@ -21754,7 +22506,7 @@ K := Fraction Polynomial Integer --R Type: Domain --E 1 ---S 2 of 36 +--S 2 of 37 m := matrix [ [-1] ] --R --R @@ -21762,7 +22514,7 @@ m := matrix [ [-1] ] --R Type: Matrix(Integer) --E 2 ---S 3 of 36 +--S 3 of 37 C := CliffordAlgebra(1, K, quadraticForm m) --R --R @@ -21770,7 +22522,7 @@ C := CliffordAlgebra(1, K, quadraticForm m) --R Type: Domain --E 3 ---S 4 of 36 +--S 4 of 37 i: C := e(1) --R --R @@ -21779,7 +22531,7 @@ i: C := e(1) --R Type: CliffordAlgebra(1,Fraction(Polynomial(Integer)),[[-1]]) --E 4 ---S 5 of 36 +--S 5 of 37 x := a + b * i --R --R @@ -21788,7 +22540,7 @@ x := a + b * i --R Type: CliffordAlgebra(1,Fraction(Polynomial(Integer)),[[-1]]) --E 5 ---S 6 of 36 +--S 6 of 37 y := c + d * i --R --R @@ -21797,7 +22549,7 @@ y := c + d * i --R Type: CliffordAlgebra(1,Fraction(Polynomial(Integer)),[[-1]]) --E 6 ---S 7 of 36 +--S 7 of 37 x * y --R --R @@ -21807,7 +22559,7 @@ x * y --E 7 )clear all ---S 8 of 36 +--S 8 of 37 K := Fraction Polynomial Integer --R --R @@ -21815,7 +22567,7 @@ K := Fraction Polynomial Integer --R Type: Domain --E 8 ---S 9 of 36 +--S 9 of 37 m := matrix [ [-1,0],[0,-1] ] --R --R @@ -21825,7 +22577,7 @@ m := matrix [ [-1,0],[0,-1] ] --R Type: Matrix(Integer) --E 9 ---S 10 of 36 +--S 10 of 37 H := CliffordAlgebra(2, K, quadraticForm m) --R --R @@ -21833,7 +22585,7 @@ H := CliffordAlgebra(2, K, quadraticForm m) --R Type: Domain --E 10 ---S 11 of 36 +--S 11 of 37 i: H := e(1) --R --R @@ -21842,7 +22594,7 @@ i: H := e(1) --R Type: CliffordAlgebra(2,Fraction(Polynomial(Integer)),[[-1,0],[0,-1]]) --E 11 ---S 12 of 36 +--S 12 of 37 j: H := e(2) --R --R @@ -21851,7 +22603,7 @@ j: H := e(2) --R Type: CliffordAlgebra(2,Fraction(Polynomial(Integer)),[[-1,0],[0,-1]]) --E 12 ---S 13 of 36 +--S 13 of 37 k: H := i * j --R --R @@ -21860,7 +22612,7 @@ k: H := i * j --R Type: CliffordAlgebra(2,Fraction(Polynomial(Integer)),[[-1,0],[0,-1]]) --E 13 ---S 14 of 36 +--S 14 of 37 x := a + b * i + c * j + d * k --R --R @@ -21869,7 +22621,7 @@ x := a + b * i + c * j + d * k --R Type: CliffordAlgebra(2,Fraction(Polynomial(Integer)),[[-1,0],[0,-1]]) --E 14 ---S 15 of 36 +--S 15 of 37 y := e + f * i + g * j + h * k --R --R @@ -21878,7 +22630,7 @@ y := e + f * i + g * j + h * k --R Type: CliffordAlgebra(2,Fraction(Polynomial(Integer)),[[-1,0],[0,-1]]) --E 15 ---S 16 of 36 +--S 16 of 37 x + y --R --R @@ -21887,7 +22639,7 @@ x + y --R Type: CliffordAlgebra(2,Fraction(Polynomial(Integer)),[[-1,0],[0,-1]]) --E 16 ---S 17 of 36 +--S 17 of 37 x * y --R --R @@ -21900,7 +22652,7 @@ x * y --R Type: CliffordAlgebra(2,Fraction(Polynomial(Integer)),[[-1,0],[0,-1]]) --E 17 ---S 18 of 36 +--S 18 of 37 y * x --R --R @@ -21914,7 +22666,7 @@ y * x --E 18 )clear all ---S 19 of 36 +--S 19 of 37 K := Fraction Polynomial Integer --R --R @@ -21922,7 +22674,7 @@ K := Fraction Polynomial Integer --R Type: Domain --E 19 ---S 20 of 36 +--S 20 of 37 Ext := CliffordAlgebra(3, K, quadraticForm 0) --R --R @@ -21931,7 +22683,7 @@ Ext := CliffordAlgebra(3, K, quadraticForm 0) --R Type: Domain --E 20 ---S 21 of 36 +--S 21 of 37 i: Ext := e(1) --R --R @@ -21940,7 +22692,7 @@ i: Ext := e(1) --RType: CliffordAlgebra(3,Fraction(Polynomial(Integer)),[[0,0,0],[0,0,0],[0,0,0]]) --E 21 ---S 22 of 36 +--S 22 of 37 j: Ext := e(2) --R --R @@ -21949,7 +22701,7 @@ j: Ext := e(2) --RType: CliffordAlgebra(3,Fraction(Polynomial(Integer)),[[0,0,0],[0,0,0],[0,0,0]]) --E 22 ---S 23 of 36 +--S 23 of 37 k: Ext := e(3) --R --R @@ -21958,7 +22710,7 @@ k: Ext := e(3) --RType: CliffordAlgebra(3,Fraction(Polynomial(Integer)),[[0,0,0],[0,0,0],[0,0,0]]) --E 23 ---S 24 of 36 +--S 24 of 37 x := x1*i + x2*j + x3*k --R --R @@ -21967,7 +22719,7 @@ x := x1*i + x2*j + x3*k --RType: CliffordAlgebra(3,Fraction(Polynomial(Integer)),[[0,0,0],[0,0,0],[0,0,0]]) --E 24 ---S 25 of 36 +--S 25 of 37 y := y1*i + y2*j + y3*k --R --R @@ -21976,7 +22728,7 @@ y := y1*i + y2*j + y3*k --RType: CliffordAlgebra(3,Fraction(Polynomial(Integer)),[[0,0,0],[0,0,0],[0,0,0]]) --E 25 ---S 26 of 36 +--S 26 of 37 x + y --R --R @@ -21985,7 +22737,7 @@ x + y --RType: CliffordAlgebra(3,Fraction(Polynomial(Integer)),[[0,0,0],[0,0,0],[0,0,0]]) --E 26 ---S 27 of 36 +--S 27 of 37 x * y + y * x --R --R @@ -21993,13 +22745,13 @@ x * y + y * x --RType: CliffordAlgebra(3,Fraction(Polynomial(Integer)),[[0,0,0],[0,0,0],[0,0,0]]) --E 27 ---S 28 of 36 +--S 28 of 37 dual2 a == coefficient(a,[2,3]) * i + coefficient(a,[3,1]) * j + coefficient(a,[1,2]) * k --R --R Type: Void --E 28 ---S 29 of 36 +--S 29 of 37 dual2(x*y) --R --R Compiling function dual2 with type CliffordAlgebra(3,Fraction( @@ -22013,7 +22765,7 @@ dual2(x*y) --E 29 )clear all ---S 30 of 36 +--S 30 of 37 K := Fraction Integer --R --R @@ -22021,7 +22773,7 @@ K := Fraction Integer --R Type: Domain --E 30 ---S 31 of 36 +--S 31 of 37 g := matrix [ [1,0,0,0], [0,-1,0,0], [0,0,-1,0], [0,0,0,-1] ] --R --R @@ -22035,7 +22787,7 @@ g := matrix [ [1,0,0,0], [0,-1,0,0], [0,0,-1,0], [0,0,0,-1] ] --R Type: Matrix(Integer) --E 31 ---S 32 of 36 +--S 32 of 37 D := CliffordAlgebra(4,K, quadraticForm g) --R --R @@ -22045,7 +22797,7 @@ D := CliffordAlgebra(4,K, quadraticForm g) --R Type: Domain --E 32 ---S 33 of 36 +--S 33 of 37 gam := [e(i)$D for i in 1..4] --R --R @@ -22054,14 +22806,14 @@ gam := [e(i)$D for i in 1..4] --RType: List(CliffordAlgebra(4,Fraction(Integer),[[1,0,0,0],[0,-1,0,0],[0,0,-1,0],[0,0,0,-1]])) --E 33 ---S 34 of 36 +--S 34 of 37 m := 1; n:= 2; r := 3; s := 4; --R --R --R Type: PositiveInteger --E 34 ---S 35 of 36 +--S 35 of 37 lhs := reduce(+, [reduce(+, [ g(l,t)*gam(l)*gam(m)*gam(n)*gam(r)*gam(s)*gam(t) for l in 1..4]) for t in 1..4]) --R --R @@ -22070,7 +22822,7 @@ lhs := reduce(+, [reduce(+, [ g(l,t)*gam(l)*gam(m)*gam(n)*gam(r)*gam(s)*gam(t) f --RType: CliffordAlgebra(4,Fraction(Integer),[[1,0,0,0],[0,-1,0,0],[0,0,-1,0],[0,0,0,-1]]) --E 35 ---S 36 of 36 +--S 36 of 37 rhs := 2*(gam s * gam m*gam n*gam r + gam r*gam n*gam m*gam s) --R --R @@ -22078,6 +22830,38 @@ rhs := 2*(gam s * gam m*gam n*gam r + gam r*gam n*gam m*gam s) --R 1 2 3 4 --RType: CliffordAlgebra(4,Fraction(Integer),[[1,0,0,0],[0,-1,0,0],[0,0,-1,0],[0,0,0,-1]]) --E 36 + +--S 37 of 37 +)show CliffordAlgebra +--R +--R CliffordAlgebra(n: PositiveInteger,K: Field,Q: QuadraticForm(n,K)) is a domain constructor +--R Abbreviation for CliffordAlgebra is CLIF +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for CLIF +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,K) -> % ?*? : (K,%) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?/? : (%,K) -> % +--R ?=? : (%,%) -> Boolean 1 : () -> % +--R 0 : () -> % ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,PositiveInteger) -> % coerce : K -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R dimension : () -> CardinalNumber e : PositiveInteger -> % +--R hash : % -> SingleInteger latex : % -> String +--R one? : % -> Boolean recip : % -> Union(%,"failed") +--R sample : () -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R characteristic : () -> NonNegativeInteger +--R coefficient : (%,List(PositiveInteger)) -> K +--R monomial : (K,List(PositiveInteger)) -> % +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R +--E 37 + )spool )lisp (bye) \end{chunk} @@ -22610,6 +23394,7 @@ CliffordAlgebra(n, K, Q): T == Impl where --S 1 of 1 )show Color +--R --R Color is a domain constructor --R Abbreviation for Color is COLOR --R This constructor is exposed in this frame. @@ -22621,9 +23406,9 @@ CliffordAlgebra(n, K, Q): T == Impl where --R blue : () -> % coerce : % -> OutputForm --R color : Integer -> % green : () -> % --R hash : % -> SingleInteger hue : % -> Integer ---R latex : % -> String red : () -> % ---R yellow : () -> % ?~=? : (%,%) -> Boolean ---R numberOfHues : () -> PositiveInteger +--R latex : % -> String numberOfHues : () -> PositiveInteger +--R red : () -> % yellow : () -> % +--R ?~=? : (%,%) -> Boolean --R --E 1 @@ -22773,6 +23558,7 @@ Color(): Exports == Implementation where --S 1 of 1 )show Commutator +--R --R Commutator is a domain constructor --R Abbreviation for Commutator is COMM --R This constructor is exposed in this frame. @@ -22877,7 +23663,8 @@ Commutator: Export == Implement where )set message test on )set message auto off )clear all ---S 1 of 16 + +--S 1 of 17 a := complex(4/3,5/2) --R --R @@ -22887,7 +23674,7 @@ a := complex(4/3,5/2) --R Type: Complex(Fraction(Integer)) --E 1 ---S 2 of 16 +--S 2 of 17 b := complex(4/3,-5/2) --R --R @@ -22897,7 +23684,7 @@ b := complex(4/3,-5/2) --R Type: Complex(Fraction(Integer)) --E 2 ---S 3 of 16 +--S 3 of 17 a + b --R --R @@ -22907,7 +23694,7 @@ a + b --R Type: Complex(Fraction(Integer)) --E 3 ---S 4 of 16 +--S 4 of 17 a - b --R --R @@ -22915,7 +23702,7 @@ a - b --R Type: Complex(Fraction(Integer)) --E 4 ---S 5 of 16 +--S 5 of 17 a * b --R --R @@ -22925,7 +23712,7 @@ a * b --R Type: Complex(Fraction(Integer)) --E 5 ---S 6 of 16 +--S 6 of 17 a / b --R --R @@ -22935,7 +23722,7 @@ a / b --R Type: Complex(Fraction(Integer)) --E 6 ---S 7 of 16 +--S 7 of 17 % :: Fraction Complex Integer --R --R @@ -22945,7 +23732,7 @@ a / b --R Type: Fraction(Complex(Integer)) --E 7 ---S 8 of 16 +--S 8 of 17 3.4 + 6.7 * %i --R --R @@ -22953,7 +23740,7 @@ a / b --R Type: Complex(Float) --E 8 ---S 9 of 16 +--S 9 of 17 conjugate a --R --R @@ -22963,7 +23750,7 @@ conjugate a --R Type: Complex(Fraction(Integer)) --E 9 ---S 10 of 16 +--S 10 of 17 norm a --R --R @@ -22973,7 +23760,7 @@ norm a --R Type: Fraction(Integer) --E 10 ---S 11 of 16 +--S 11 of 17 real a --R --R @@ -22983,7 +23770,7 @@ real a --R Type: Fraction(Integer) --E 11 ---S 12 of 16 +--S 12 of 17 imag a --R --R @@ -22993,7 +23780,7 @@ imag a --R Type: Fraction(Integer) --E 12 ---S 13 of 16 +--S 13 of 17 gcd(13 - 13*%i,31 + 27*%i) --R --R @@ -23001,7 +23788,7 @@ gcd(13 - 13*%i,31 + 27*%i) --R Type: Complex(Integer) --E 13 ---S 14 of 16 +--S 14 of 17 lcm(13 - 13*%i,31 + 27*%i) --R --R @@ -23009,7 +23796,7 @@ lcm(13 - 13*%i,31 + 27*%i) --R Type: Complex(Integer) --E 14 ---S 15 of 16 +--S 15 of 17 factor(13 - 13*%i) --R --R @@ -23017,7 +23804,7 @@ factor(13 - 13*%i) --R Type: Factored(Complex(Integer)) --E 15 ---S 16 of 16 +--S 16 of 17 factor complex(2,0) --R --R @@ -23025,6 +23812,184 @@ factor complex(2,0) --R (16) - %i (1 + %i) --R Type: Factored(Complex(Integer)) --E 16 + +--S 17 of 17 +)show Complex +--R +--R Complex(R: CommutativeRing) is a domain constructor +--R Abbreviation for Complex is COMPLEX +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for COMPLEX +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (R,%) -> % ?*? : (%,R) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?/? : (%,%) -> % if R has FIELD +--R ?=? : (%,%) -> Boolean D : % -> % if R has DIFRING +--R D : (%,(R -> R)) -> % OMwrite : % -> String if R has OM +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R abs : % -> % if R has RNS acos : % -> % if R has TRANFUN +--R acosh : % -> % if R has TRANFUN acot : % -> % if R has TRANFUN +--R acoth : % -> % if R has TRANFUN acsc : % -> % if R has TRANFUN +--R acsch : % -> % if R has TRANFUN argument : % -> R if R has TRANFUN +--R asec : % -> % if R has TRANFUN asech : % -> % if R has TRANFUN +--R asin : % -> % if R has TRANFUN asinh : % -> % if R has TRANFUN +--R atan : % -> % if R has TRANFUN atanh : % -> % if R has TRANFUN +--R basis : () -> Vector(%) coerce : R -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R complex : (R,R) -> % conjugate : % -> % +--R convert : Vector(R) -> % convert : % -> Vector(R) +--R coordinates : % -> Vector(R) cos : % -> % if R has TRANFUN +--R cosh : % -> % if R has TRANFUN cot : % -> % if R has TRANFUN +--R coth : % -> % if R has TRANFUN csc : % -> % if R has TRANFUN +--R csch : % -> % if R has TRANFUN differentiate : (%,(R -> R)) -> % +--R discriminant : () -> R discriminant : Vector(%) -> R +--R exp : % -> % if R has TRANFUN gcd : (%,%) -> % if R has EUCDOM +--R gcd : List(%) -> % if R has EUCDOM generator : () -> % +--R hash : % -> SingleInteger imag : % -> R +--R imaginary : () -> % init : () -> % if R has FFIELDC +--R inv : % -> % if R has FIELD latex : % -> String +--R lcm : (%,%) -> % if R has EUCDOM lcm : List(%) -> % if R has EUCDOM +--R log : % -> % if R has TRANFUN map : ((R -> R),%) -> % +--R max : (%,%) -> % if R has ORDSET min : (%,%) -> % if R has ORDSET +--R norm : % -> R one? : % -> Boolean +--R pi : () -> % if R has TRANFUN random : () -> % if R has FINITE +--R rank : () -> PositiveInteger real : % -> R +--R recip : % -> Union(%,"failed") represents : Vector(R) -> % +--R retract : % -> R sample : () -> % +--R sec : % -> % if R has TRANFUN sech : % -> % if R has TRANFUN +--R sin : % -> % if R has TRANFUN sinh : % -> % if R has TRANFUN +--R tan : % -> % if R has TRANFUN tanh : % -> % if R has TRANFUN +--R trace : % -> R traceMatrix : () -> Matrix(R) +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (%,Fraction(Integer)) -> % if R has FIELD +--R ?*? : (Fraction(Integer),%) -> % if R has FIELD +--R ?**? : (%,Integer) -> % if R has FIELD +--R ?**? : (%,%) -> % if R has TRANFUN +--R ?**? : (%,Fraction(Integer)) -> % if R has RADCAT and R has TRANFUN +--R ? Boolean if R has ORDSET +--R ?<=? : (%,%) -> Boolean if R has ORDSET +--R ?>? : (%,%) -> Boolean if R has ORDSET +--R ?>=? : (%,%) -> Boolean if R has ORDSET +--R D : (%,NonNegativeInteger) -> % if R has DIFRING +--R D : (%,Symbol) -> % if R has PDRING(SYMBOL) +--R D : (%,List(Symbol)) -> % if R has PDRING(SYMBOL) +--R D : (%,Symbol,NonNegativeInteger) -> % if R has PDRING(SYMBOL) +--R D : (%,List(Symbol),List(NonNegativeInteger)) -> % if R has PDRING(SYMBOL) +--R D : (%,(R -> R),NonNegativeInteger) -> % +--R OMwrite : (OpenMathDevice,%,Boolean) -> Void if R has OM +--R OMwrite : (OpenMathDevice,%) -> Void if R has OM +--R OMwrite : (%,Boolean) -> String if R has OM +--R ?^? : (%,Integer) -> % if R has FIELD +--R associates? : (%,%) -> Boolean if R has EUCDOM and R has PFECAT or R has INTDOM +--R characteristic : () -> NonNegativeInteger +--R characteristicPolynomial : % -> SparseUnivariatePolynomial(R) +--R charthRoot : % -> Union(%,"failed") if $ has CHARNZ and R has EUCDOM and R has PFECAT or R has CHARNZ +--R charthRoot : % -> % if R has FFIELDC +--R coerce : % -> % if R has EUCDOM and R has PFECAT or R has INTDOM +--R coerce : Fraction(Integer) -> % if R has FIELD or R has RETRACT(FRAC(INT)) +--R conditionP : Matrix(%) -> Union(Vector(%),"failed") if $ has CHARNZ and R has EUCDOM and R has PFECAT or R has FFIELDC +--R convert : % -> InputForm if R has KONVERT(INFORM) +--R convert : % -> Complex(DoubleFloat) if R has REAL +--R convert : % -> Complex(Float) if R has REAL +--R convert : % -> Pattern(Float) if R has KONVERT(PATTERN(FLOAT)) +--R convert : % -> Pattern(Integer) if R has KONVERT(PATTERN(INT)) +--R convert : SparseUnivariatePolynomial(R) -> % +--R convert : % -> SparseUnivariatePolynomial(R) +--R coordinates : Vector(%) -> Matrix(R) +--R coordinates : (Vector(%),Vector(%)) -> Matrix(R) +--R coordinates : (%,Vector(%)) -> Vector(R) +--R createPrimitiveElement : () -> % if R has FFIELDC +--R definingPolynomial : () -> SparseUnivariatePolynomial(R) +--R derivationCoordinates : (Vector(%),(R -> R)) -> Matrix(R) if R has FIELD +--R differentiate : % -> % if R has DIFRING +--R differentiate : (%,NonNegativeInteger) -> % if R has DIFRING +--R differentiate : (%,Symbol) -> % if R has PDRING(SYMBOL) +--R differentiate : (%,List(Symbol)) -> % if R has PDRING(SYMBOL) +--R differentiate : (%,Symbol,NonNegativeInteger) -> % if R has PDRING(SYMBOL) +--R differentiate : (%,List(Symbol),List(NonNegativeInteger)) -> % if R has PDRING(SYMBOL) +--R differentiate : (%,(R -> R),NonNegativeInteger) -> % +--R discreteLog : (%,%) -> Union(NonNegativeInteger,"failed") if R has FFIELDC +--R discreteLog : % -> NonNegativeInteger if R has FFIELDC +--R divide : (%,%) -> Record(quotient: %,remainder: %) if R has EUCDOM +--R ?.? : (%,R) -> % if R has ELTAB(R,R) +--R enumerate : () -> List(%) if R has FINITE +--R euclideanSize : % -> NonNegativeInteger if R has EUCDOM +--R eval : (%,Symbol,R) -> % if R has IEVALAB(SYMBOL,R) +--R eval : (%,List(Symbol),List(R)) -> % if R has IEVALAB(SYMBOL,R) +--R eval : (%,List(Equation(R))) -> % if R has EVALAB(R) +--R eval : (%,Equation(R)) -> % if R has EVALAB(R) +--R eval : (%,R,R) -> % if R has EVALAB(R) +--R eval : (%,List(R),List(R)) -> % if R has EVALAB(R) +--R expressIdealMember : (List(%),%) -> Union(List(%),"failed") if R has EUCDOM +--R exquo : (%,%) -> Union(%,"failed") if R has EUCDOM and R has PFECAT or R has INTDOM +--R exquo : (%,R) -> Union(%,"failed") if R has INTDOM +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) if R has EUCDOM +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") if R has EUCDOM +--R factor : % -> Factored(%) if R has EUCDOM and R has PFECAT or R has FIELD +--R factorPolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has EUCDOM and R has PFECAT +--R factorSquareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has EUCDOM and R has PFECAT +--R factorsOfCyclicGroupSize : () -> List(Record(factor: Integer,exponent: Integer)) if R has FFIELDC +--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) if R has EUCDOM +--R index : PositiveInteger -> % if R has FINITE +--R lcmCoef : (%,%) -> Record(llcmres: %,coeff1: %,coeff2: %) if R has EUCDOM +--R lift : % -> SparseUnivariatePolynomial(R) +--R lookup : % -> PositiveInteger if R has FINITE +--R minimalPolynomial : % -> SparseUnivariatePolynomial(R) if R has FIELD +--R multiEuclidean : (List(%),%) -> Union(List(%),"failed") if R has EUCDOM +--R nextItem : % -> Union(%,"failed") if R has FFIELDC +--R nthRoot : (%,Integer) -> % if R has RADCAT and R has TRANFUN +--R order : % -> OnePointCompletion(PositiveInteger) if R has FFIELDC +--R order : % -> PositiveInteger if R has FFIELDC +--R patternMatch : (%,Pattern(Float),PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if R has PATMAB(FLOAT) +--R patternMatch : (%,Pattern(Integer),PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if R has PATMAB(INT) +--R polarCoordinates : % -> Record(r: R,phi: R) if R has RNS and R has TRANFUN +--R prime? : % -> Boolean if R has EUCDOM and R has PFECAT or R has FIELD +--R primeFrobenius : % -> % if R has FFIELDC +--R primeFrobenius : (%,NonNegativeInteger) -> % if R has FFIELDC +--R primitive? : % -> Boolean if R has FFIELDC +--R primitiveElement : () -> % if R has FFIELDC +--R principalIdeal : List(%) -> Record(coef: List(%),generator: %) if R has EUCDOM +--R ?quo? : (%,%) -> % if R has EUCDOM +--R rational : % -> Fraction(Integer) if R has INS +--R rational? : % -> Boolean if R has INS +--R rationalIfCan : % -> Union(Fraction(Integer),"failed") if R has INS +--R reduce : Fraction(SparseUnivariatePolynomial(R)) -> Union(%,"failed") if R has FIELD +--R reduce : SparseUnivariatePolynomial(R) -> % +--R reducedSystem : Matrix(%) -> Matrix(R) +--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(R),vec: Vector(R)) +--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(Integer),vec: Vector(Integer)) if R has LINEXP(INT) +--R reducedSystem : Matrix(%) -> Matrix(Integer) if R has LINEXP(INT) +--R regularRepresentation : % -> Matrix(R) +--R regularRepresentation : (%,Vector(%)) -> Matrix(R) +--R ?rem? : (%,%) -> % if R has EUCDOM +--R representationType : () -> Union("prime",polynomial,normal,cyclic) if R has FFIELDC +--R represents : (Vector(R),Vector(%)) -> % +--R retract : % -> Fraction(Integer) if R has RETRACT(FRAC(INT)) +--R retract : % -> Integer if R has RETRACT(INT) +--R retractIfCan : % -> Union(R,"failed") +--R retractIfCan : % -> Union(Fraction(Integer),"failed") if R has RETRACT(FRAC(INT)) +--R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT(INT) +--R size : () -> NonNegativeInteger if R has FINITE +--R sizeLess? : (%,%) -> Boolean if R has EUCDOM +--R solveLinearPolynomialEquation : (List(SparseUnivariatePolynomial(%)),SparseUnivariatePolynomial(%)) -> Union(List(SparseUnivariatePolynomial(%)),"failed") if R has EUCDOM and R has PFECAT +--R sqrt : % -> % if R has RADCAT and R has TRANFUN +--R squareFree : % -> Factored(%) if R has EUCDOM and R has PFECAT or R has FIELD +--R squareFreePart : % -> % if R has EUCDOM and R has PFECAT or R has FIELD +--R squareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has EUCDOM and R has PFECAT +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R tableForDiscreteLogarithm : Integer -> Table(PositiveInteger,NonNegativeInteger) if R has FFIELDC +--R traceMatrix : Vector(%) -> Matrix(R) +--R unit? : % -> Boolean if R has EUCDOM and R has PFECAT or R has INTDOM +--R unitCanonical : % -> % if R has EUCDOM and R has PFECAT or R has INTDOM +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) if R has EUCDOM and R has PFECAT or R has INTDOM +--R +--E 17 + )spool )lisp (bye) \end{chunk} @@ -23398,25 +24363,25 @@ Complex(R:CommutativeRing): ComplexCategory(R) with --R --R------------------------------- Operations -------------------------------- --R ?*? : (Integer,%) -> % ?*? : (%,%) -> % ---R ?+? : (%,%) -> % -? : % -> % ---R ?-? : (%,%) -> % antisymmetric? : % -> Boolean ---R copy : % -> % diagonal? : % -> Boolean ---R diagonalMatrix : List(%) -> % empty : () -> % ---R empty? : % -> Boolean eq? : (%,%) -> Boolean ---R horizConcat : (%,%) -> % maxColIndex : % -> Integer ---R maxRowIndex : % -> Integer minColIndex : % -> Integer ---R minRowIndex : % -> Integer ncols : % -> NonNegativeInteger ---R nrows : % -> NonNegativeInteger qnew : (Integer,Integer) -> % ---R sample : () -> % square? : % -> Boolean ---R squareTop : % -> % symmetric? : % -> Boolean ---R transpose : % -> % vertConcat : (%,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?+? : (%,%) -> % +--R -? : % -> % ?-? : (%,%) -> % +--R antisymmetric? : % -> Boolean copy : % -> % +--R diagonal? : % -> Boolean diagonalMatrix : List(%) -> % +--R empty : () -> % empty? : % -> Boolean +--R eq? : (%,%) -> Boolean horizConcat : (%,%) -> % +--R maxColIndex : % -> Integer maxRowIndex : % -> Integer +--R minColIndex : % -> Integer minRowIndex : % -> Integer +--R ncols : % -> NonNegativeInteger nrows : % -> NonNegativeInteger +--R qnew : (Integer,Integer) -> % sample : () -> % +--R square? : % -> Boolean squareTop : % -> % +--R symmetric? : % -> Boolean transpose : % -> % +--R vertConcat : (%,%) -> % --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R ?*? : (ComplexDoubleFloatVector,%) -> ComplexDoubleFloatVector --R ?*? : (%,ComplexDoubleFloatVector) -> ComplexDoubleFloatVector --R ?*? : (%,Complex(DoubleFloat)) -> % --R ?*? : (Complex(DoubleFloat),%) -> % --R ?**? : (%,Integer) -> % if Complex(DoubleFloat) has FIELD ---R ?**? : (%,NonNegativeInteger) -> % --R ?/? : (%,Complex(DoubleFloat)) -> % if Complex(DoubleFloat) has FIELD --R ?=? : (%,%) -> Boolean if Complex(DoubleFloat) has SETCAT --R any? : ((Complex(DoubleFloat) -> Boolean),%) -> Boolean if $ has finiteAggregate @@ -24028,7 +24993,8 @@ ComplexDoubleFloatVector : VectorCategory Complex DoubleFloat with )set message test on )set message auto off )clear all ---S 1 of 22 + +--S 1 of 23 c := continuedFraction(314159/100000) --R --R @@ -24038,7 +25004,7 @@ c := continuedFraction(314159/100000) --R Type: ContinuedFraction(Integer) --E 1 ---S 2 of 22 +--S 2 of 23 partialQuotients c --R --R @@ -24046,7 +25012,7 @@ partialQuotients c --R Type: Stream(Integer) --E 2 ---S 3 of 22 +--S 3 of 23 convergents c --R --R @@ -24056,7 +25022,7 @@ convergents c --R Type: Stream(Fraction(Integer)) --E 3 ---S 4 of 22 +--S 4 of 23 approximants c --R --R @@ -24067,7 +25033,7 @@ approximants c --R Type: Stream(Fraction(Integer)) --E 4 ---S 5 of 22 +--S 5 of 23 pq := partialQuotients(1/c) --R --R @@ -24075,7 +25041,7 @@ pq := partialQuotients(1/c) --R Type: Stream(Integer) --E 5 ---S 6 of 22 +--S 6 of 23 continuedFraction(first pq,repeating [1],rest pq) --R --R @@ -24085,7 +25051,7 @@ continuedFraction(first pq,repeating [1],rest pq) --R Type: ContinuedFraction(Integer) --E 6 ---S 7 of 22 +--S 7 of 23 z:=continuedFraction(3,repeating [1],repeating [3,6]) --R --R @@ -24100,7 +25066,7 @@ z:=continuedFraction(3,repeating [1],repeating [3,6]) --R Type: ContinuedFraction(Integer) --E 7 ---S 8 of 22 +--S 8 of 23 dens:Stream Integer := cons(1,generate((x+->x+4),6)) --R --R @@ -24108,7 +25074,7 @@ dens:Stream Integer := cons(1,generate((x+->x+4),6)) --R Type: Stream(Integer) --E 8 ---S 9 of 22 +--S 9 of 23 cf := continuedFraction(0,repeating [1],dens) --R --R @@ -24123,7 +25089,7 @@ cf := continuedFraction(0,repeating [1],dens) --R Type: ContinuedFraction(Integer) --E 9 ---S 10 of 22 +--S 10 of 23 ccf := convergents cf --R --R @@ -24133,7 +25099,7 @@ ccf := convergents cf --R Type: Stream(Fraction(Integer)) --E 10 ---S 11 of 22 +--S 11 of 23 eConvergents := [2*e + 1 for e in ccf] --R --R @@ -24143,7 +25109,7 @@ eConvergents := [2*e + 1 for e in ccf] --R Type: Stream(Fraction(Integer)) --E 11 ---S 12 of 22 +--S 12 of 23 eConvergents :: Stream Float --R --R @@ -24155,7 +25121,7 @@ eConvergents :: Stream Float --R Type: Stream(Float) --E 12 ---S 13 of 22 +--S 13 of 23 exp 1.0 --R --R @@ -24163,7 +25129,7 @@ exp 1.0 --R Type: Float --E 13 ---S 14 of 22 +--S 14 of 23 cf := continuedFraction(1,[(2*i+1)**2 for i in 0..],repeating [2]) --R --R @@ -24178,7 +25144,7 @@ cf := continuedFraction(1,[(2*i+1)**2 for i in 0..],repeating [2]) --R Type: ContinuedFraction(Integer) --E 14 ---S 15 of 22 +--S 15 of 23 ccf := convergents cf --R --R @@ -24188,7 +25154,7 @@ ccf := convergents cf --R Type: Stream(Fraction(Integer)) --E 15 ---S 16 of 22 +--S 16 of 23 piConvergents := [4/p for p in ccf] --R --R @@ -24198,7 +25164,7 @@ piConvergents := [4/p for p in ccf] --R Type: Stream(Fraction(Integer)) --E 16 ---S 17 of 22 +--S 17 of 23 piConvergents :: Stream Float --R --R @@ -24210,7 +25176,7 @@ piConvergents :: Stream Float --R Type: Stream(Float) --E 17 ---S 18 of 22 +--S 18 of 23 continuedFraction((- 122 + 597*%i)/(4 - 4*%i)) --R --R @@ -24220,13 +25186,13 @@ continuedFraction((- 122 + 597*%i)/(4 - 4*%i)) --R Type: ContinuedFraction(Complex(Integer)) --E 18 ---S 19 of 22 +--S 19 of 23 r : Fraction UnivariatePolynomial(x,Fraction Integer) --R --R Type: Void --E 19 ---S 20 of 22 +--S 20 of 23 r := ((x - 1) * (x - 2)) / ((x-3) * (x-4)) --R --R @@ -24238,7 +25204,7 @@ r := ((x - 1) * (x - 2)) / ((x-3) * (x-4)) --R Type: Fraction(UnivariatePolynomial(x,Fraction(Integer))) --E 20 ---S 21 of 22 +--S 21 of 23 continuedFraction r --R --R @@ -24250,7 +25216,7 @@ continuedFraction r --R Type: ContinuedFraction(UnivariatePolynomial(x,Fraction(Integer))) --E 21 ---S 22 of 22 +--S 22 of 23 [i*i for i in convergents(z) :: Stream Float] --R --R @@ -24261,6 +25227,68 @@ continuedFraction r --R ...] --R Type: Stream(Float) --E 22 + +--S 23 of 23 +)show ContinuedFraction +--R +--R ContinuedFraction(R: EuclideanDomain) is a domain constructor +--R Abbreviation for ContinuedFraction is CONTFRAC +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for CONTFRAC +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,Fraction(Integer)) -> % ?*? : (Fraction(Integer),%) -> % +--R ?*? : (%,Fraction(R)) -> % ?*? : (Fraction(R),%) -> % +--R ?*? : (R,%) -> % ?*? : (%,R) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,Integer) -> % ?**? : (%,NonNegativeInteger) -> % +--R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % +--R ?-? : (%,%) -> % -? : % -> % +--R ?/? : (%,%) -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,Integer) -> % ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,PositiveInteger) -> % associates? : (%,%) -> Boolean +--R coerce : % -> % coerce : Fraction(Integer) -> % +--R coerce : Fraction(R) -> % coerce : R -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R complete : % -> % denominators : % -> Stream(R) +--R extend : (%,Integer) -> % factor : % -> Factored(%) +--R gcd : (%,%) -> % gcd : List(%) -> % +--R hash : % -> SingleInteger inv : % -> % +--R latex : % -> String lcm : (%,%) -> % +--R lcm : List(%) -> % numerators : % -> Stream(R) +--R one? : % -> Boolean partialNumerators : % -> Stream(R) +--R partialQuotients : % -> Stream(R) prime? : % -> Boolean +--R ?quo? : (%,%) -> % recip : % -> Union(%,"failed") +--R reducedForm : % -> % ?rem? : (%,%) -> % +--R sample : () -> % sizeLess? : (%,%) -> Boolean +--R squareFree : % -> Factored(%) squareFreePart : % -> % +--R unit? : % -> Boolean unitCanonical : % -> % +--R wholePart : % -> R zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R approximants : % -> Stream(Fraction(R)) +--R characteristic : () -> NonNegativeInteger +--R continuedFraction : (R,Stream(R),Stream(R)) -> % +--R continuedFraction : Fraction(R) -> % +--R convergents : % -> Stream(Fraction(R)) +--R divide : (%,%) -> Record(quotient: %,remainder: %) +--R euclideanSize : % -> NonNegativeInteger +--R expressIdealMember : (List(%),%) -> Union(List(%),"failed") +--R exquo : (%,%) -> Union(%,"failed") +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") +--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) +--R lcmCoef : (%,%) -> Record(llcmres: %,coeff1: %,coeff2: %) +--R multiEuclidean : (List(%),%) -> Union(List(%),"failed") +--R partialDenominators : % -> Stream(R) +--R principalIdeal : List(%) -> Record(coef: List(%),generator: %) +--R reducedContinuedFraction : (R,Stream(R)) -> % +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) +--R +--E 23 + )spool )lisp (bye) \end{chunk} @@ -24968,8 +25996,8 @@ ContinuedFraction(R): Exports == Implementation where --S 1 of 1 )show Database --R ---R Database(S) where ---R S: OrderedSet with +--R Database(S)where +--R S: OrderedSetwith --R ?.? : (%,Symbol) -> String --R display : % -> Void --R fullDisplay : % -> Void is a domain constructor @@ -25123,15 +26151,19 @@ Database(S): Exports == Implementation where --R index? : (Integer,%) -> Boolean indices : % -> List(Integer) --R insert : (S,%,Integer) -> % insert : (%,%,Integer) -> % --R insert! : (S,%,Integer) -> % insert! : (%,%,Integer) -> % ---R last : % -> S leaf? : % -> Boolean +--R last : (%,NonNegativeInteger) -> % last : % -> S +--R latex : % -> String if S has SETCAT leaf? : % -> Boolean --R leaves : % -> List(S) list : S -> % --R map : (((S,S) -> S),%,%) -> % map : ((S -> S),%) -> % +--R max : (%,%) -> % if S has ORDSET min : (%,%) -> % if S has ORDSET --R new : (NonNegativeInteger,S) -> % nodes : % -> List(%) --R possiblyInfinite? : % -> Boolean qelt : (%,Integer) -> S +--R remove! : ((S -> Boolean),%) -> % rest : (%,NonNegativeInteger) -> % --R rest : % -> % reverse : % -> % --R sample : () -> % second : % -> S ---R tail : % -> % third : % -> S ---R value : % -> S +--R select! : ((S -> Boolean),%) -> % sort : (((S,S) -> Boolean),%) -> % +--R sort : % -> % if S has ORDSET tail : % -> % +--R third : % -> S value : % -> S --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R ? Boolean if S has ORDSET --R ?<=? : (%,%) -> Boolean if S has ORDSET @@ -25161,11 +26193,8 @@ Database(S): Exports == Implementation where --R find : ((S -> Boolean),%) -> Union(S,"failed") --R first : (%,NonNegativeInteger) -> % --R hash : % -> SingleInteger if S has SETCAT ---R last : (%,NonNegativeInteger) -> % ---R latex : % -> String if S has SETCAT --R less? : (%,NonNegativeInteger) -> Boolean --R map! : ((S -> S),%) -> % if $ has shallowlyMutable ---R max : (%,%) -> % if S has ORDSET --R maxIndex : % -> Integer if Integer has ORDSET --R member? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT --R members : % -> List(S) if $ has finiteAggregate @@ -25173,7 +26202,6 @@ Database(S): Exports == Implementation where --R merge : (%,%) -> % if S has ORDSET --R merge! : (((S,S) -> Boolean),%,%) -> % --R merge! : (%,%) -> % if S has ORDSET ---R min : (%,%) -> % if S has ORDSET --R minIndex : % -> Integer if Integer has ORDSET --R more? : (%,NonNegativeInteger) -> Boolean --R node? : (%,%) -> Boolean if S has SETCAT @@ -25187,14 +26215,11 @@ Database(S): Exports == Implementation where --R reduce : (((S,S) -> S),%) -> S if $ has finiteAggregate --R remove : (S,%) -> % if $ has finiteAggregate and S has SETCAT --R remove : ((S -> Boolean),%) -> % if $ has finiteAggregate ---R remove! : ((S -> Boolean),%) -> % --R remove! : (S,%) -> % if S has SETCAT --R removeDuplicates : % -> % if $ has finiteAggregate and S has SETCAT --R removeDuplicates! : % -> % if S has SETCAT ---R rest : (%,NonNegativeInteger) -> % --R reverse! : % -> % if $ has shallowlyMutable --R select : ((S -> Boolean),%) -> % if $ has finiteAggregate ---R select! : ((S -> Boolean),%) -> % --R setchildren! : (%,List(%)) -> % if $ has shallowlyMutable --R setelt : (%,Integer,S) -> S if $ has shallowlyMutable --R setelt : (%,UniversalSegment(Integer),S) -> S if $ has shallowlyMutable @@ -25207,8 +26232,6 @@ Database(S): Exports == Implementation where --R setrest! : (%,%) -> % if $ has shallowlyMutable --R setvalue! : (%,S) -> S if $ has shallowlyMutable --R size? : (%,NonNegativeInteger) -> Boolean ---R sort : (((S,S) -> Boolean),%) -> % ---R sort : % -> % if S has ORDSET --R sort! : (((S,S) -> Boolean),%) -> % if $ has shallowlyMutable --R sort! : % -> % if $ has shallowlyMutable and S has ORDSET --R sorted? : (((S,S) -> Boolean),%) -> Boolean @@ -25397,7 +26420,8 @@ DataList(S:OrderedSet) : Exports == Implementation where )set message test on )set message auto off )clear all ---S 1 of 7 + +--S 1 of 8 r := decimal(22/7) --R --R @@ -25406,7 +26430,7 @@ r := decimal(22/7) --R Type: DecimalExpansion --E 1 ---S 2 of 7 +--S 2 of 8 r + decimal(6/7) --R --R @@ -25414,7 +26438,7 @@ r + decimal(6/7) --R Type: DecimalExpansion --E 2 ---S 3 of 7 +--S 3 of 8 [decimal(1/i) for i in 350..354] --R --R @@ -25426,7 +26450,7 @@ r + decimal(6/7) --R Type: List(DecimalExpansion) --E 3 ---S 4 of 7 +--S 4 of 8 decimal(1/2049) --R --R @@ -25441,7 +26465,7 @@ decimal(1/2049) --R Type: DecimalExpansion --E 4 ---S 5 of 7 +--S 5 of 8 p := decimal(1/4)*x**2 + decimal(2/3)*x + decimal(4/9) --R --R @@ -25450,7 +26474,7 @@ p := decimal(1/4)*x**2 + decimal(2/3)*x + decimal(4/9) --R Type: Polynomial(DecimalExpansion) --E 5 ---S 6 of 7 +--S 6 of 8 q := differentiate(p, x) --R --R @@ -25459,7 +26483,7 @@ q := differentiate(p, x) --R Type: Polynomial(DecimalExpansion) --E 6 ---S 7 of 7 +--S 7 of 8 g := gcd(p, q) --R --R @@ -25467,6 +26491,125 @@ g := gcd(p, q) --R (7) x + 1.3 --R Type: Polynomial(DecimalExpansion) --E 7 + +--S 8 of 8 +)show DecimalExpansion + DecimalExpansion is a domain constructor + Abbreviation for DecimalExpansion is DECIMAL + This constructor is exposed in this frame. + Issue )edit bookvol10.3.pamphlet to see algebra source code for DECIMAL + +------------------------------- Operations -------------------------------- + ?*? : (%,Integer) -> % ?*? : (Integer,%) -> % + ?*? : (Fraction(Integer),%) -> % ?*? : (%,Fraction(Integer)) -> % + ?*? : (%,%) -> % ?*? : (Integer,%) -> % + ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % + ?**? : (%,Integer) -> % ?**? : (%,NonNegativeInteger) -> % + ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % + ?-? : (%,%) -> % -? : % -> % + ?/? : (Integer,Integer) -> % ?/? : (%,%) -> % + ?=? : (%,%) -> Boolean D : (%,(Integer -> Integer)) -> % + D : % -> % if Integer has DIFRING 1 : () -> % + 0 : () -> % ?^? : (%,Integer) -> % + ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % + associates? : (%,%) -> Boolean coerce : % -> RadixExpansion(10) + coerce : % -> Fraction(Integer) coerce : Integer -> % + coerce : Fraction(Integer) -> % coerce : % -> % + coerce : Integer -> % coerce : % -> OutputForm + decimal : Fraction(Integer) -> % denom : % -> Integer + denominator : % -> % factor : % -> Factored(%) + gcd : List(%) -> % gcd : (%,%) -> % + hash : % -> SingleInteger init : () -> % if Integer has STEP + inv : % -> % latex : % -> String + lcm : List(%) -> % lcm : (%,%) -> % + numer : % -> Integer numerator : % -> % + one? : % -> Boolean prime? : % -> Boolean + ?quo? : (%,%) -> % random : () -> % if Integer has INS + recip : % -> Union(%,"failed") ?rem? : (%,%) -> % + retract : % -> Integer sample : () -> % + sizeLess? : (%,%) -> Boolean squareFree : % -> Factored(%) + squareFreePart : % -> % unit? : % -> Boolean + unitCanonical : % -> % zero? : % -> Boolean + ?~=? : (%,%) -> Boolean + ? Boolean if Integer has ORDSET + ?<=? : (%,%) -> Boolean if Integer has ORDSET + ?>? : (%,%) -> Boolean if Integer has ORDSET + ?>=? : (%,%) -> Boolean if Integer has ORDSET + D : (%,(Integer -> Integer),NonNegativeInteger) -> % + D : (%,List(Symbol),List(NonNegativeInteger)) -> % if Integer has PDRING(SYMBOL) + D : (%,Symbol,NonNegativeInteger) -> % if Integer has PDRING(SYMBOL) + D : (%,List(Symbol)) -> % if Integer has PDRING(SYMBOL) + D : (%,Symbol) -> % if Integer has PDRING(SYMBOL) + D : (%,NonNegativeInteger) -> % if Integer has DIFRING + abs : % -> % if Integer has OINTDOM + ceiling : % -> Integer if Integer has INS + characteristic : () -> NonNegativeInteger + charthRoot : % -> Union(%,"failed") if $ has CHARNZ and Integer has PFECAT or Integer has CHARNZ + coerce : Symbol -> % if Integer has RETRACT(SYMBOL) + conditionP : Matrix(%) -> Union(Vector(%),"failed") if $ has CHARNZ and Integer has PFECAT + convert : % -> DoubleFloat if Integer has REAL + convert : % -> Float if Integer has REAL + convert : % -> InputForm if Integer has KONVERT(INFORM) + convert : % -> Pattern(Float) if Integer has KONVERT(PATTERN(FLOAT)) + convert : % -> Pattern(Integer) if Integer has KONVERT(PATTERN(INT)) + differentiate : (%,(Integer -> Integer)) -> % + differentiate : (%,(Integer -> Integer),NonNegativeInteger) -> % + differentiate : (%,List(Symbol),List(NonNegativeInteger)) -> % if Integer has PDRING(SYMBOL) + differentiate : (%,Symbol,NonNegativeInteger) -> % if Integer has PDRING(SYMBOL) + differentiate : (%,List(Symbol)) -> % if Integer has PDRING(SYMBOL) + differentiate : (%,Symbol) -> % if Integer has PDRING(SYMBOL) + differentiate : (%,NonNegativeInteger) -> % if Integer has DIFRING + differentiate : % -> % if Integer has DIFRING + divide : (%,%) -> Record(quotient: %,remainder: %) + ?.? : (%,Integer) -> % if Integer has ELTAB(INT,INT) + euclideanSize : % -> NonNegativeInteger + eval : (%,Symbol,Integer) -> % if Integer has IEVALAB(SYMBOL,INT) + eval : (%,List(Symbol),List(Integer)) -> % if Integer has IEVALAB(SYMBOL,INT) + eval : (%,List(Equation(Integer))) -> % if Integer has EVALAB(INT) + eval : (%,Equation(Integer)) -> % if Integer has EVALAB(INT) + eval : (%,Integer,Integer) -> % if Integer has EVALAB(INT) + eval : (%,List(Integer),List(Integer)) -> % if Integer has EVALAB(INT) + expressIdealMember : (List(%),%) -> Union(List(%),"failed") + exquo : (%,%) -> Union(%,"failed") + extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") + extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) + factorPolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if Integer has PFECAT + factorSquareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if Integer has PFECAT + floor : % -> Integer if Integer has INS + fractionPart : % -> Fraction(Integer) + fractionPart : % -> % if Integer has EUCDOM + gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) + lcmCoef : (%,%) -> Record(llcmres: %,coeff1: %,coeff2: %) + map : ((Integer -> Integer),%) -> % + max : (%,%) -> % if Integer has ORDSET + min : (%,%) -> % if Integer has ORDSET + multiEuclidean : (List(%),%) -> Union(List(%),"failed") + negative? : % -> Boolean if Integer has OINTDOM + nextItem : % -> Union(%,"failed") if Integer has STEP + patternMatch : (%,Pattern(Float),PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if Integer has PATMAB(FLOAT) + patternMatch : (%,Pattern(Integer),PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if Integer has PATMAB(INT) + positive? : % -> Boolean if Integer has OINTDOM + principalIdeal : List(%) -> Record(coef: List(%),generator: %) + reducedSystem : Matrix(%) -> Matrix(Integer) + reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(Integer),vec: Vector(Integer)) + reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(Integer),vec: Vector(Integer)) if Integer has LINEXP(INT) + reducedSystem : Matrix(%) -> Matrix(Integer) if Integer has LINEXP(INT) + retract : % -> Integer if Integer has RETRACT(INT) + retract : % -> Fraction(Integer) if Integer has RETRACT(INT) + retract : % -> Symbol if Integer has RETRACT(SYMBOL) + retractIfCan : % -> Union(Integer,"failed") if Integer has RETRACT(INT) + retractIfCan : % -> Union(Fraction(Integer),"failed") if Integer has RETRACT(INT) + retractIfCan : % -> Union(Symbol,"failed") if Integer has RETRACT(SYMBOL) + retractIfCan : % -> Union(Integer,"failed") + sign : % -> Integer if Integer has OINTDOM + solveLinearPolynomialEquation : (List(SparseUnivariatePolynomial(%)),SparseUnivariatePolynomial(%)) -> Union(List(SparseUnivariatePolynomial(%)),"failed") if Integer has PFECAT + squareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if Integer has PFECAT + subtractIfCan : (%,%) -> Union(%,"failed") + unitNormal : % -> Record(unit: %,canonical: %,associate: %) + wholePart : % -> Integer if Integer has EUCDOM + +--E 8 + )spool )lisp (bye) \end{chunk} @@ -27264,6 +28407,84 @@ description is in terms of a vector and angle of rotation. --S 1 of 1 )show DenavitHartenbergMatrix +--R +--R DenavitHartenbergMatrix(R: Join(Field,TranscendentalFunctionCategory)) is a domain constructor +--R Abbreviation for DenavitHartenbergMatrix is DHMATRIX +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for DHMATRIX +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,Point(R)) -> Point(R) ?*? : (Vector(R),%) -> Vector(R) +--R ?*? : (%,Vector(R)) -> Vector(R) ?*? : (Integer,%) -> % +--R ?*? : (%,R) -> % ?*? : (R,%) -> % +--R ?*? : (%,%) -> % ?**? : (%,NonNegativeInteger) -> % +--R ?+? : (%,%) -> % -? : % -> % +--R ?-? : (%,%) -> % ?/? : (%,R) -> % if R has FIELD +--R antisymmetric? : % -> Boolean coerce : Vector(R) -> % +--R column : (%,Integer) -> Vector(R) copy : % -> % +--R diagonal? : % -> Boolean diagonalMatrix : List(%) -> % +--R diagonalMatrix : List(R) -> % elt : (%,Integer,Integer,R) -> R +--R elt : (%,Integer,Integer) -> R empty : () -> % +--R empty? : % -> Boolean eq? : (%,%) -> Boolean +--R fill! : (%,R) -> % horizConcat : (%,%) -> % +--R identity : () -> % latex : % -> String if R has SETCAT +--R listOfLists : % -> List(List(R)) map : (((R,R) -> R),%,%,R) -> % +--R map : (((R,R) -> R),%,%) -> % map : ((R -> R),%) -> % +--R map! : ((R -> R),%) -> % matrix : List(List(R)) -> % +--R maxColIndex : % -> Integer maxRowIndex : % -> Integer +--R minColIndex : % -> Integer minRowIndex : % -> Integer +--R ncols : % -> NonNegativeInteger nrows : % -> NonNegativeInteger +--R parts : % -> List(R) pfaffian : % -> R if R has COMRING +--R qelt : (%,Integer,Integer) -> R rotatex : R -> % +--R rotatey : R -> % rotatez : R -> % +--R row : (%,Integer) -> Vector(R) sample : () -> % +--R scale : (R,R,R) -> % setelt : (%,Integer,Integer,R) -> R +--R square? : % -> Boolean squareTop : % -> % +--R symmetric? : % -> Boolean translate : (R,R,R) -> % +--R transpose : % -> % transpose : Vector(R) -> % +--R vertConcat : (%,%) -> % +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R ?**? : (%,Integer) -> % if R has FIELD +--R ?=? : (%,%) -> Boolean if R has SETCAT +--R any? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate +--R coerce : % -> OutputForm if R has SETCAT +--R columnSpace : % -> List(Vector(R)) if R has EUCDOM +--R count : (R,%) -> NonNegativeInteger if $ has finiteAggregate and R has SETCAT +--R count : ((R -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R determinant : % -> R if R has commutative(*) +--R elt : (%,List(Integer),List(Integer)) -> % +--R eval : (%,List(R),List(R)) -> % if R has EVALAB(R) and R has SETCAT +--R eval : (%,R,R) -> % if R has EVALAB(R) and R has SETCAT +--R eval : (%,Equation(R)) -> % if R has EVALAB(R) and R has SETCAT +--R eval : (%,List(Equation(R))) -> % if R has EVALAB(R) and R has SETCAT +--R every? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate +--R exquo : (%,R) -> Union(%,"failed") if R has INTDOM +--R hash : % -> SingleInteger if R has SETCAT +--R inverse : % -> Union(%,"failed") if R has FIELD +--R less? : (%,NonNegativeInteger) -> Boolean +--R matrix : (NonNegativeInteger,NonNegativeInteger,((Integer,Integer) -> R)) -> % +--R member? : (R,%) -> Boolean if $ has finiteAggregate and R has SETCAT +--R members : % -> List(R) if $ has finiteAggregate +--R minordet : % -> R if R has commutative(*) +--R more? : (%,NonNegativeInteger) -> Boolean +--R new : (NonNegativeInteger,NonNegativeInteger,R) -> % +--R nullSpace : % -> List(Vector(R)) if R has INTDOM +--R nullity : % -> NonNegativeInteger if R has INTDOM +--R qsetelt! : (%,Integer,Integer,R) -> R +--R rank : % -> NonNegativeInteger if R has INTDOM +--R rowEchelon : % -> % if R has EUCDOM +--R scalarMatrix : (NonNegativeInteger,R) -> % +--R setColumn! : (%,Integer,Vector(R)) -> % +--R setRow! : (%,Integer,Vector(R)) -> % +--R setelt : (%,List(Integer),List(Integer),%) -> % +--R setsubMatrix! : (%,Integer,Integer,%) -> % +--R size? : (%,NonNegativeInteger) -> Boolean +--R subMatrix : (%,Integer,Integer,Integer,Integer) -> % +--R swapColumns! : (%,Integer,Integer) -> % +--R swapRows! : (%,Integer,Integer) -> % +--R zero : (NonNegativeInteger,NonNegativeInteger) -> % +--R ?~=? : (%,%) -> Boolean if R has SETCAT +--R --E 1 )spool @@ -28689,11 +29910,12 @@ latex a --R extractTop! : % -> S front : % -> S --R height : % -> NonNegativeInteger insert! : (S,%) -> % --R insertBottom! : (S,%) -> S insertTop! : (S,%) -> S ---R inspect : % -> S length : % -> NonNegativeInteger ---R map : ((S -> S),%) -> % pop! : % -> S ---R push! : (S,%) -> S reverse! : % -> % ---R rotate! : % -> % sample : () -> % ---R top : % -> S top! : % -> S +--R inspect : % -> S latex : % -> String if S has SETCAT +--R length : % -> NonNegativeInteger map : ((S -> S),%) -> % +--R pop! : % -> S push! : (S,%) -> S +--R reverse! : % -> % rotate! : % -> % +--R sample : () -> % top : % -> S +--R top! : % -> S --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R ?=? : (%,%) -> Boolean if S has SETCAT --R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate @@ -28706,7 +29928,6 @@ latex a --R eval : (%,List(Equation(S))) -> % if S has EVALAB(S) and S has SETCAT --R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate --R hash : % -> SingleInteger if S has SETCAT ---R latex : % -> String if S has SETCAT --R less? : (%,NonNegativeInteger) -> Boolean --R map! : ((S -> S),%) -> % if $ has shallowlyMutable --R member? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT @@ -29377,7 +30598,7 @@ Dequeue(S:SetCategory): DequeueAggregate S with )set message auto off )clear all ---S 1 of 148 +--S 1 of 149 coefRing := Integer --R --R @@ -29385,7 +30606,7 @@ coefRing := Integer --R Type: Domain --E 1 ---S 2 of 148 +--S 2 of 149 lv : List Symbol := [x,y,z] --R --R @@ -29393,7 +30614,7 @@ lv : List Symbol := [x,y,z] --R Type: List(Symbol) --E 2 ---S 3 of 148 +--S 3 of 149 der := DERHAM(coefRing,lv) --R --R @@ -29401,7 +30622,7 @@ der := DERHAM(coefRing,lv) --R Type: Domain --E 3 ---S 4 of 148 +--S 4 of 149 R := Expression coefRing --R --R @@ -29409,7 +30630,7 @@ R := Expression coefRing --R Type: Domain --E 4 ---S 5 of 148 +--S 5 of 149 f : R := x**2*y*z-5*x**3*y**2*z**5 --R --R @@ -29418,7 +30639,7 @@ f : R := x**2*y*z-5*x**3*y**2*z**5 --R Type: Expression(Integer) --E 5 ---S 6 of 148 +--S 6 of 149 g : R := z**2*y*cos(z)-7*sin(x**3*y**2)*z**2 --R --R @@ -29427,7 +30648,7 @@ g : R := z**2*y*cos(z)-7*sin(x**3*y**2)*z**2 --R Type: Expression(Integer) --E 6 ---S 7 of 148 +--S 7 of 149 h : R :=x*y*z-2*x**3*y*z**2 --R --R @@ -29436,7 +30657,7 @@ h : R :=x*y*z-2*x**3*y*z**2 --R Type: Expression(Integer) --E 7 ---S 8 of 148 +--S 8 of 149 dx : der := generator(1) --R --R @@ -29444,7 +30665,7 @@ dx : der := generator(1) --R Type: DeRhamComplex(Integer,[x,y,z]) --E 8 ---S 9 of 148 +--S 9 of 149 dy : der := generator(2) --R --R @@ -29452,7 +30673,7 @@ dy : der := generator(2) --R Type: DeRhamComplex(Integer,[x,y,z]) --E 9 ---S 10 of 148 +--S 10 of 149 dz : der := generator(3) --R --R @@ -29460,7 +30681,7 @@ dz : der := generator(3) --R Type: DeRhamComplex(Integer,[x,y,z]) --E 10 ---S 11 of 148 +--S 11 of 149 [dx,dy,dz] := [generator(i)$der for i in 1..3] --R --R @@ -29468,7 +30689,7 @@ dz : der := generator(3) --R Type: List(DeRhamComplex(Integer,[x,y,z])) --E 11 ---S 12 of 148 +--S 12 of 149 alpha : der := f*dx + g*dy + h*dz --R --R @@ -29481,7 +30702,7 @@ alpha : der := f*dx + g*dy + h*dz --R Type: DeRhamComplex(Integer,[x,y,z]) --E 12 ---S 13 of 148 +--S 13 of 149 beta : der := cos(tan(x*y*z)+x*y*z)*dx + x*dy --R --R @@ -29489,7 +30710,7 @@ beta : der := cos(tan(x*y*z)+x*y*z)*dx + x*dy --R Type: DeRhamComplex(Integer,[x,y,z]) --E 13 ---S 14 of 148 +--S 14 of 149 m1:=exteriorDifferential alpha --R --R @@ -29505,7 +30726,7 @@ m1:=exteriorDifferential alpha --R Type: DeRhamComplex(Integer,[x,y,z]) --E 14 ---S 15 of 148 +--S 15 of 149 exteriorDifferential m1 --R --R @@ -29513,7 +30734,7 @@ exteriorDifferential m1 --R Type: DeRhamComplex(Integer,[x,y,z]) --E 15 ---S 16 of 148 +--S 16 of 149 gamma := alpha * beta --R --R @@ -29526,7 +30747,7 @@ gamma := alpha * beta --R Type: DeRhamComplex(Integer,[x,y,z]) --E 16 ---S 17 of 148 +--S 17 of 149 exteriorDifferential(gamma) - (exteriorDifferential(alpha)*beta - _ alpha * exteriorDifferential(beta)) --R @@ -29535,7 +30756,7 @@ exteriorDifferential(gamma) - (exteriorDifferential(alpha)*beta - _ --R Type: DeRhamComplex(Integer,[x,y,z]) --E 17 ---S 18 of 148 +--S 18 of 149 a : BOP := operator('a) --R --R @@ -29543,7 +30764,7 @@ a : BOP := operator('a) --R Type: BasicOperator --E 18 ---S 19 of 148 +--S 19 of 149 b : BOP := operator('b) --R --R @@ -29551,7 +30772,7 @@ b : BOP := operator('b) --R Type: BasicOperator --E 19 ---S 20 of 148 +--S 20 of 149 c : BOP := operator('c) --R --R @@ -29559,7 +30780,7 @@ c : BOP := operator('c) --R Type: BasicOperator --E 20 ---S 21 of 148 +--S 21 of 149 sigma := a(x,y,z) * dx + b(x,y,z) * dy + c(x,y,z) * dz --R --R @@ -29567,7 +30788,7 @@ sigma := a(x,y,z) * dx + b(x,y,z) * dy + c(x,y,z) * dz --R Type: DeRhamComplex(Integer,[x,y,z]) --E 21 ---S 22 of 148 +--S 22 of 149 theta := a(x,y,z) * dx * dy + b(x,y,z) * dx * dz + c(x,y,z) * dy * dz --R --R @@ -29575,7 +30796,7 @@ theta := a(x,y,z) * dx * dy + b(x,y,z) * dx * dz + c(x,y,z) * dy * dz --R Type: DeRhamComplex(Integer,[x,y,z]) --E 22 ---S 23 of 148 +--S 23 of 149 totalDifferential(a(x,y,z))$der --R --R @@ -29584,7 +30805,7 @@ totalDifferential(a(x,y,z))$der --R Type: DeRhamComplex(Integer,[x,y,z]) --E 23 ---S 24 of 148 +--S 24 of 149 exteriorDifferential sigma --R --R @@ -29597,7 +30818,7 @@ exteriorDifferential sigma --R Type: DeRhamComplex(Integer,[x,y,z]) --E 24 ---S 25 of 148 +--S 25 of 149 exteriorDifferential theta --R --R @@ -29606,7 +30827,7 @@ exteriorDifferential theta --R Type: DeRhamComplex(Integer,[x,y,z]) --E 25 ---S 26 of 148 +--S 26 of 149 one : der := 1 --R --R @@ -29614,7 +30835,7 @@ one : der := 1 --R Type: DeRhamComplex(Integer,[x,y,z]) --E 26 ---S 27 of 148 +--S 27 of 149 g1 : der := a([x,t,y,u,v,z,e]) * one --R --R @@ -29622,7 +30843,7 @@ g1 : der := a([x,t,y,u,v,z,e]) * one --R Type: DeRhamComplex(Integer,[x,y,z]) --E 27 ---S 28 of 148 +--S 28 of 149 h1 : der := a([x,y,x,t,x,z,y,r,u,x]) * one --R --R @@ -29630,7 +30851,7 @@ h1 : der := a([x,y,x,t,x,z,y,r,u,x]) * one --R Type: DeRhamComplex(Integer,[x,y,z]) --E 28 ---S 29 of 148 +--S 29 of 149 exteriorDifferential g1 --R --R @@ -29639,7 +30860,7 @@ exteriorDifferential g1 --R Type: DeRhamComplex(Integer,[x,y,z]) --E 29 ---S 30 of 148 +--S 30 of 149 exteriorDifferential h1 --R --R @@ -29660,7 +30881,7 @@ exteriorDifferential h1 --R Type: DeRhamComplex(Integer,[x,y,z]) --E 30 ---S 31 of 148 +--S 31 of 149 coefficient(gamma, dx*dy) --R --R @@ -29669,7 +30890,7 @@ coefficient(gamma, dx*dy) --R Type: Expression(Integer) --E 31 ---S 32 of 148 +--S 32 of 149 coefficient(gamma, one) --R --R @@ -29677,7 +30898,7 @@ coefficient(gamma, one) --R Type: Expression(Integer) --E 32 ---S 33 of 148 +--S 33 of 149 coefficient(g1,one) --R --R @@ -29685,7 +30906,7 @@ coefficient(g1,one) --R Type: Expression(Integer) --E 33 ---S 34 of 148 +--S 34 of 149 gamma := alpha * beta --R --R @@ -29698,7 +30919,7 @@ gamma := alpha * beta --R Type: DeRhamComplex(Integer,[x,y,z]) --E 34 ---S 35 of 148 +--S 35 of 149 t1:=generator(1)$der --R --R @@ -29706,7 +30927,7 @@ t1:=generator(1)$der --R Type: DeRhamComplex(Integer,[x,y,z]) --E 35 ---S 36 of 148 +--S 36 of 149 degree(t1) --R --R @@ -29716,7 +30937,7 @@ degree(t1) )clear all ---S 37 of 148 +--S 37 of 149 X:=DERHAM(Integer,[x,y,z]) --R --R @@ -29724,7 +30945,7 @@ X:=DERHAM(Integer,[x,y,z]) --R Type: Domain --E 37 ---S 38 of 148 +--S 38 of 149 [dx,dy,dz]:=[generator(i)$X for i in 1..3] --R --R @@ -29732,7 +30953,7 @@ X:=DERHAM(Integer,[x,y,z]) --R Type: List(DeRhamComplex(Integer,[x,y,z])) --E 38 ---S 39 of 148 +--S 39 of 149 f:BOP:=operator('f) --R --R @@ -29740,7 +30961,7 @@ f:BOP:=operator('f) --R Type: BasicOperator --E 39 ---S 40 of 148 +--S 40 of 149 g:BOP:=operator('g) --R --R @@ -29748,7 +30969,7 @@ g:BOP:=operator('g) --R Type: BasicOperator --E 40 ---S 41 of 148 +--S 41 of 149 h:BOP:=operator('h) --R --R @@ -29756,7 +30977,7 @@ h:BOP:=operator('h) --R Type: BasicOperator --E 41 ---S 42 of 148 +--S 42 of 149 a:BOP:=operator('a) --R --R @@ -29764,7 +30985,7 @@ a:BOP:=operator('a) --R Type: BasicOperator --E 42 ---S 43 of 148 +--S 43 of 149 b:BOP:=operator('b) --R --R @@ -29772,7 +30993,7 @@ b:BOP:=operator('b) --R Type: BasicOperator --E 43 ---S 44 of 148 +--S 44 of 149 c:BOP:=operator('c) --R --R @@ -29780,7 +31001,7 @@ c:BOP:=operator('c) --R Type: BasicOperator --E 44 ---S 45 of 148 +--S 45 of 149 sigma:=f(x,y,z)*dx + g(x,y,z)*dy + h(x,y,z)*dz --R --R @@ -29788,7 +31009,7 @@ sigma:=f(x,y,z)*dx + g(x,y,z)*dy + h(x,y,z)*dz --R Type: DeRhamComplex(Integer,[x,y,z]) --E 45 ---S 46 of 148 +--S 46 of 149 theta:=a(x,y,z)*dx*dy + b(x,y,z)*dx*dz + c(x,y,z)*dy*dz --R --R @@ -29796,13 +31017,13 @@ theta:=a(x,y,z)*dx*dy + b(x,y,z)*dx*dz + c(x,y,z)*dy*dz --R Type: DeRhamComplex(Integer,[x,y,z]) --E 46 ---S 47 of 148 +--S 47 of 149 d ==> exteriorDifferential --R --R Type: Void --E 47 ---S 48 of 148 +--S 48 of 149 leadingCoefficient sigma --R --R @@ -29810,7 +31031,7 @@ leadingCoefficient sigma --R Type: Expression(Integer) --E 48 ---S 49 of 148 +--S 49 of 149 leadingBasisTerm sigma --R --R @@ -29818,7 +31039,7 @@ leadingBasisTerm sigma --R Type: DeRhamComplex(Integer,[x,y,z]) --E 49 ---S 50 of 148 +--S 50 of 149 reductum sigma --R --R @@ -29826,7 +31047,7 @@ reductum sigma --R Type: DeRhamComplex(Integer,[x,y,z]) --E 50 ---S 51 of 148 +--S 51 of 149 coefficient(sigma,dz) --R --R @@ -29834,7 +31055,7 @@ coefficient(sigma,dz) --R Type: Expression(Integer) --E 51 ---S 52 of 148 +--S 52 of 149 homogeneous? sigma --R --R @@ -29842,7 +31063,7 @@ homogeneous? sigma --R Type: Boolean --E 52 ---S 53 of 148 +--S 53 of 149 homogeneous? (sigma+theta) --R --R @@ -29850,7 +31071,7 @@ homogeneous? (sigma+theta) --R Type: Boolean --E 53 ---S 54 of 148 +--S 54 of 149 retractable? sigma --R --R @@ -29858,7 +31079,7 @@ retractable? sigma --R Type: Boolean --E 54 ---S 55 of 148 +--S 55 of 149 retractable? (1::X) --R --R @@ -29866,7 +31087,7 @@ retractable? (1::X) --R Type: Boolean --E 55 ---S 56 of 148 +--S 56 of 149 [degree x for x in [sigma,theta,1::X]] --R --R @@ -29874,7 +31095,7 @@ retractable? (1::X) --R Type: List(NonNegativeInteger) --E 56 ---S 57 of 148 +--S 57 of 149 R:=Expression(Integer) --R --R @@ -29882,19 +31103,19 @@ R:=Expression(Integer) --R Type: Domain --E 57 ---S 58 of 148 +--S 58 of 149 T:R->R --R --R Type: Void --E 58 ---S 59 of 148 +--S 59 of 149 T(x)==x^2 --R --R Type: Void --E 59 ---S 60 of 148 +--S 60 of 149 map(T,sigma) --R --R Compiling function T with type Expression(Integer) -> Expression( @@ -29905,7 +31126,7 @@ map(T,sigma) --R Type: DeRhamComplex(Integer,[x,y,z]) --E 60 ---S 61 of 148 +--S 61 of 149 exteriorDifferential sigma --R --R @@ -29918,7 +31139,7 @@ exteriorDifferential sigma --R Type: DeRhamComplex(Integer,[x,y,z]) --E 61 ---S 62 of 148 +--S 62 of 149 d theta --R --R @@ -29927,7 +31148,7 @@ d theta --R Type: DeRhamComplex(Integer,[x,y,z]) --E 62 ---S 63 of 148 +--S 63 of 149 F:=operator 'F --R --R @@ -29935,7 +31156,7 @@ F:=operator 'F --R Type: BasicOperator --E 63 ---S 64 of 148 +--S 64 of 149 nullForm:=F(x,y,z)*(1::X) --R --R @@ -29943,7 +31164,7 @@ nullForm:=F(x,y,z)*(1::X) --R Type: DeRhamComplex(Integer,[x,y,z]) --E 64 ---S 65 of 148 +--S 65 of 149 d nullForm --R --R @@ -29952,7 +31173,7 @@ d nullForm --R Type: DeRhamComplex(Integer,[x,y,z]) --E 65 ---S 66 of 148 +--S 66 of 149 totalDifferential(x^2+y^2+sin(x)*z^2)$X --R --R @@ -29961,7 +31182,7 @@ totalDifferential(x^2+y^2+sin(x)*z^2)$X --R Type: DeRhamComplex(Integer,[x,y,z]) --E 66 ---S 67 of 148 +--S 67 of 149 d(d sigma) --R --R @@ -29976,7 +31197,7 @@ d(d sigma) --R Type: DeRhamComplex(Integer,[x,y,z]) --E 67 ---S 68 of 148 +--S 68 of 149 d(d theta) --R --R @@ -29984,7 +31205,7 @@ d(d theta) --R Type: DeRhamComplex(Integer,[x,y,z]) --E 68 ---S 69 of 148 +--S 69 of 149 sigma*theta --R --R @@ -29992,7 +31213,7 @@ sigma*theta --R Type: DeRhamComplex(Integer,[x,y,z]) --E 69 ---S 70 of 148 +--S 70 of 149 dx*dy+dy*dx --R --R @@ -30000,7 +31221,7 @@ dx*dy+dy*dx --R Type: DeRhamComplex(Integer,[x,y,z]) --E 70 ---S 71 of 148 +--S 71 of 149 sigma+dz --R --R @@ -30008,7 +31229,7 @@ sigma+dz --R Type: DeRhamComplex(Integer,[x,y,z]) --E 71 ---S 72 of 148 +--S 72 of 149 theta-(2/3)*sigma+%pi*dx --R --R @@ -30021,7 +31242,7 @@ theta-(2/3)*sigma+%pi*dx --R Type: DeRhamComplex(Integer,[x,y,z]) --E 72 ---S 73 of 148 +--S 73 of 149 G:=diagonalMatrix([1,1,1]) --R --R @@ -30033,7 +31254,7 @@ G:=diagonalMatrix([1,1,1]) --R Type: Matrix(Integer) --E 73 ---S 74 of 148 +--S 74 of 149 dot(sigma,sigma,G) --R --R @@ -30042,7 +31263,7 @@ dot(sigma,sigma,G) --R Type: Expression(Integer) --E 74 ---S 75 of 148 +--S 75 of 149 hodgeStar(sigma,G) --R --R @@ -30050,7 +31271,7 @@ hodgeStar(sigma,G) --R Type: DeRhamComplex(Integer,[x,y,z]) --E 75 ---S 76 of 148 +--S 76 of 149 A:=dot(sigma,sigma,G)*sqrt(abs(determinant(G))) --R --R @@ -30059,7 +31280,7 @@ A:=dot(sigma,sigma,G)*sqrt(abs(determinant(G))) --R Type: Expression(Integer) --E 76 ---S 77 of 148 +--S 77 of 149 B:=sigma*hodgeStar(sigma,G) --R --R @@ -30068,7 +31289,7 @@ B:=sigma*hodgeStar(sigma,G) --R Type: DeRhamComplex(Integer,[x,y,z]) --E 77 ---S 78 of 148 +--S 78 of 149 test(A*dx*dy*dz=B) --R --R @@ -30076,7 +31297,7 @@ test(A*dx*dy*dz=B) --R Type: Boolean --E 78 ---S 79 of 148 +--S 79 of 149 hodgeStar(dx,G) --R --R @@ -30084,7 +31305,7 @@ hodgeStar(dx,G) --R Type: DeRhamComplex(Integer,[x,y,z]) --E 79 ---S 80 of 148 +--S 80 of 149 hodgeStar(dy,G) --R --R @@ -30092,7 +31313,7 @@ hodgeStar(dy,G) --R Type: DeRhamComplex(Integer,[x,y,z]) --E 80 ---S 81 of 148 +--S 81 of 149 d hodgeStar(d nullForm,G) --- = Laplace(F) ? --R --R @@ -30101,7 +31322,7 @@ d hodgeStar(d nullForm,G) --- = Laplace(F) ? --R Type: DeRhamComplex(Integer,[x,y,z]) --E 81 ---S 82 of 148 +--S 82 of 149 H:=diagonalMatrix([1+x^2,z^2+exp(-y^2),1/z^2]) --R --R @@ -30119,7 +31340,7 @@ H:=diagonalMatrix([1+x^2,z^2+exp(-y^2),1/z^2]) --R Type: Matrix(Expression(Integer)) --E 82 ---S 83 of 148 +--S 83 of 149 hodgeStar(dy,H) --R --R @@ -30137,7 +31358,7 @@ hodgeStar(dy,H) --R Type: DeRhamComplex(Integer,[x,y,z]) --E 83 ---S 84 of 148 +--S 84 of 149 hodgeStar(sigma,H) --R --R @@ -30175,7 +31396,7 @@ hodgeStar(sigma,H) --R Type: DeRhamComplex(Integer,[x,y,z]) --E 84 ---S 85 of 148 +--S 85 of 149 VolH:=sqrt(abs(determinant(H)))*dx*dy*dz --R --R @@ -30189,7 +31410,7 @@ VolH:=sqrt(abs(determinant(H)))*dx*dy*dz --R Type: DeRhamComplex(Integer,[x,y,z]) --E 85 ---S 86 of 148 +--S 86 of 149 AA:=dot(sigma,sigma,H)*VolH --R --R @@ -30217,7 +31438,7 @@ AA:=dot(sigma,sigma,H)*VolH --R Type: DeRhamComplex(Integer,[x,y,z]) --E 86 ---S 87 of 148 +--S 87 of 149 BB:=sigma*hodgeStar(sigma,H) --R --R @@ -30245,7 +31466,7 @@ BB:=sigma*hodgeStar(sigma,H) --R Type: DeRhamComplex(Integer,[x,y,z]) --E 87 ---S 88 of 148 +--S 88 of 149 test(AA=BB) --R --R @@ -30253,7 +31474,7 @@ test(AA=BB) --R Type: Boolean --E 88 ---S 89 of 148 +--S 89 of 149 M:=DERHAM(Integer,[t,x,y,z]) --R --R @@ -30261,7 +31482,7 @@ M:=DERHAM(Integer,[t,x,y,z]) --R Type: Domain --E 89 ---S 90 of 148 +--S 90 of 149 [dt,dx,dy,dz]:=[generator(i)$M for i in 1..4] --R --R @@ -30269,7 +31490,7 @@ M:=DERHAM(Integer,[t,x,y,z]) --R Type: List(DeRhamComplex(Integer,[t,x,y,z])) --E 90 ---S 91 of 148 +--S 91 of 149 L:=diagonalMatrix([1,-1,-1,-1]) --R --R @@ -30283,7 +31504,7 @@ L:=diagonalMatrix([1,-1,-1,-1]) --R Type: Matrix(Integer) --E 91 ---S 92 of 148 +--S 92 of 149 hodgeStar(dt,L) --R --R @@ -30291,7 +31512,7 @@ hodgeStar(dt,L) --R Type: DeRhamComplex(Integer,[t,x,y,z]) --E 92 ---S 93 of 148 +--S 93 of 149 hodgeStar(dx,L) --R --R @@ -30299,7 +31520,7 @@ hodgeStar(dx,L) --R Type: DeRhamComplex(Integer,[t,x,y,z]) --E 93 ---S 94 of 148 +--S 94 of 149 hodgeStar(dy,L) --R --R @@ -30307,7 +31528,7 @@ hodgeStar(dy,L) --R Type: DeRhamComplex(Integer,[t,x,y,z]) --E 94 ---S 95 of 148 +--S 95 of 149 hodgeStar(dz,L) --R --R @@ -30315,7 +31536,7 @@ hodgeStar(dz,L) --R Type: DeRhamComplex(Integer,[t,x,y,z]) --E 95 ---S 96 of 148 +--S 96 of 149 hodgeStar(dt*dz,L) --R --R @@ -30323,7 +31544,7 @@ hodgeStar(dt*dz,L) --R Type: DeRhamComplex(Integer,[t,x,y,z]) --E 96 ---S 97 of 148 +--S 97 of 149 P:=a(t,x,y,z)*(dx+dy+dz-dt) --R --R @@ -30331,7 +31552,7 @@ P:=a(t,x,y,z)*(dx+dy+dz-dt) --R Type: DeRhamComplex(Integer,[t,x,y,z]) --E 97 ---S 98 of 148 +--S 98 of 149 dot(P,P,L) --R --R @@ -30340,7 +31561,7 @@ dot(P,P,L) --R Type: Expression(Integer) --E 98 ---S 99 of 148 +--S 99 of 149 P*P --R --R @@ -30348,7 +31569,7 @@ P*P --R Type: DeRhamComplex(Integer,[t,x,y,z]) --E 99 ---S 100 of 148 +--S 100 of 149 d P --R --R @@ -30366,7 +31587,7 @@ d P )clear all ---S 101 of 148 +--S 101 of 149 coefRing := Integer --R --R @@ -30374,7 +31595,7 @@ coefRing := Integer --R Type: Domain --E 101 ---S 102 of 148 +--S 102 of 149 R3 : List Symbol := [x,y,z] --R --R @@ -30382,7 +31603,7 @@ R3 : List Symbol := [x,y,z] --R Type: List(Symbol) --E 102 ---S 103 of 148 +--S 103 of 149 X := DERHAM(coefRing,R3) --R --R @@ -30390,7 +31611,7 @@ X := DERHAM(coefRing,R3) --R Type: Domain --E 103 ---S 104 of 148 +--S 104 of 149 [dx,dy,dz] := [generator(i)$X for i in 1..3] --R --R @@ -30398,7 +31619,7 @@ X := DERHAM(coefRing,R3) --R Type: List(DeRhamComplex(Integer,[x,y,z])) --E 104 ---S 105 of 148 +--S 105 of 149 f : BOP := operator('f) --R --R @@ -30406,7 +31627,7 @@ f : BOP := operator('f) --R Type: BasicOperator --E 105 ---S 106 of 148 +--S 106 of 149 g : BOP := operator('g) --R --R @@ -30414,7 +31635,7 @@ g : BOP := operator('g) --R Type: BasicOperator --E 106 ---S 107 of 148 +--S 107 of 149 h : BOP := operator('h) --R --R @@ -30422,7 +31643,7 @@ h : BOP := operator('h) --R Type: BasicOperator --E 107 ---S 108 of 148 +--S 108 of 149 a : BOP := operator('a) --R --R @@ -30430,7 +31651,7 @@ a : BOP := operator('a) --R Type: BasicOperator --E 108 ---S 109 of 148 +--S 109 of 149 b : BOP := operator('b) --R --R @@ -30438,7 +31659,7 @@ b : BOP := operator('b) --R Type: BasicOperator --E 109 ---S 110 of 148 +--S 110 of 149 c : BOP := operator('c) --R --R @@ -30446,7 +31667,7 @@ c : BOP := operator('c) --R Type: BasicOperator --E 110 ---S 111 of 148 +--S 111 of 149 U : BOP := operator('U) --R --R @@ -30454,7 +31675,7 @@ U : BOP := operator('U) --R Type: BasicOperator --E 111 ---S 112 of 148 +--S 112 of 149 V : BOP := operator('V) --R --R @@ -30462,7 +31683,7 @@ V : BOP := operator('V) --R Type: BasicOperator --E 112 ---S 113 of 148 +--S 113 of 149 W : BOP := operator('W) --R --R @@ -30470,7 +31691,7 @@ W : BOP := operator('W) --R Type: BasicOperator --E 113 ---S 114 of 148 +--S 114 of 149 v := vector[U(x,y,z),V(x,y,z),W(x,y,z)] --R --R @@ -30478,7 +31699,7 @@ v := vector[U(x,y,z),V(x,y,z),W(x,y,z)] --R Type: Vector(Expression(Integer)) --E 114 ---S 115 of 148 +--S 115 of 149 sigma := f(x,y,z) * dx + g(x,y,z) * dy + h(x,y,z) * dz --R --R @@ -30486,7 +31707,7 @@ sigma := f(x,y,z) * dx + g(x,y,z) * dy + h(x,y,z) * dz --R Type: DeRhamComplex(Integer,[x,y,z]) --E 115 ---S 116 of 148 +--S 116 of 149 theta := a(x,y,z) * dx * dy + b(x,y,z) * dx * dz + c(x,y,z) * dy * dz --R --R @@ -30494,13 +31715,13 @@ theta := a(x,y,z) * dx * dy + b(x,y,z) * dx * dz + c(x,y,z) * dy * dz --R Type: DeRhamComplex(Integer,[x,y,z]) --E 116 ---S 117 of 148 +--S 117 of 149 d ==> exteriorDifferential --R --R Type: Void --E 117 ---S 118 of 148 +--S 118 of 149 G := diagonalMatrix([1,1,1]) --R --R @@ -30512,7 +31733,7 @@ G := diagonalMatrix([1,1,1]) --R Type: Matrix(Integer) --E 118 ---S 119 of 148 +--S 119 of 149 interiorProduct(v,sigma,G) --R --R @@ -30520,7 +31741,7 @@ interiorProduct(v,sigma,G) --R Type: DeRhamComplex(Integer,[x,y,z]) --E 119 ---S 120 of 148 +--S 120 of 149 interiorProduct(v,theta,G) --R --R @@ -30533,7 +31754,7 @@ interiorProduct(v,theta,G) --R Type: DeRhamComplex(Integer,[x,y,z]) --E 120 ---S 121 of 148 +--S 121 of 149 t1 := d interiorProduct(v,dz*dy*dz,G) --R --R @@ -30541,7 +31762,7 @@ t1 := d interiorProduct(v,dz*dy*dz,G) --R Type: DeRhamComplex(Integer,[x,y,z]) --E 121 ---S 122 of 148 +--S 122 of 149 hodgeStar(t1,G) -- should be div(v) --R --R @@ -30549,7 +31770,7 @@ hodgeStar(t1,G) -- should be div(v) --R Type: DeRhamComplex(Integer,[x,y,z]) --E 122 ---S 123 of 148 +--S 123 of 149 eta := lieDerivative(v,theta,G) --R --R @@ -30595,7 +31816,7 @@ eta := lieDerivative(v,theta,G) --R Type: DeRhamComplex(Integer,[x,y,z]) --E 123 ---S 124 of 148 +--S 124 of 149 proj(dx+dy*dz+dx*dy*dz,2) --R --R @@ -30603,7 +31824,7 @@ proj(dx+dy*dz+dx*dy*dz,2) --R Type: DeRhamComplex(Integer,[x,y,z]) --E 124 ---S 125 of 148 +--S 125 of 149 proj(sigma+theta,1) --R --R @@ -30611,7 +31832,7 @@ proj(sigma+theta,1) --R Type: DeRhamComplex(Integer,[x,y,z]) --E 125 ---S 126 of 148 +--S 126 of 149 dim(sigma) --R --R @@ -30619,7 +31840,7 @@ dim(sigma) --R Type: PositiveInteger --E 126 ---S 127 of 148 +--S 127 of 149 degree(sigma) --R --R @@ -30630,7 +31851,7 @@ degree(sigma) -- Laplace Operator for $S^2:\delta F := \star d \star dF$ )clear all ---S 128 of 148 +--S 128 of 149 coefRing := Integer --R --R @@ -30638,7 +31859,7 @@ coefRing := Integer --R Type: Domain --E 128 ---S 129 of 148 +--S 129 of 149 S2 : List Symbol := [r,theta] --R --R @@ -30646,7 +31867,7 @@ S2 : List Symbol := [r,theta] --R Type: List(Symbol) --E 129 ---S 130 of 148 +--S 130 of 149 Y := DERHAM(coefRing,S2) --R --R @@ -30654,7 +31875,7 @@ Y := DERHAM(coefRing,S2) --R Type: Domain --E 130 ---S 131 of 148 +--S 131 of 149 g := diagonalMatrix([1,r^2]) --R --R @@ -30665,7 +31886,7 @@ g := diagonalMatrix([1,r^2]) --R Type: Matrix(Polynomial(Integer)) --E 131 ---S 132 of 148 +--S 132 of 149 F := operator 'F --R --R @@ -30673,13 +31894,13 @@ F := operator 'F --R Type: BasicOperator --E 132 ---S 133 of 148 +--S 133 of 149 d ==> exteriorDifferential --R --R Type: Void --E 133 ---S 134 of 148 +--S 134 of 149 [dr,dtheta] := [generator(i)$Y for i in 1..2] --R --R @@ -30687,7 +31908,7 @@ d ==> exteriorDifferential --R Type: List(DeRhamComplex(Integer,[r,theta])) --E 134 ---S 135 of 148 +--S 135 of 149 F0 := F(r,theta)*1::Y --R --R @@ -30695,7 +31916,7 @@ F0 := F(r,theta)*1::Y --R Type: DeRhamComplex(Integer,[r,theta]) --E 135 ---S 136 of 148 +--S 136 of 149 F1 := d F0 --R --R @@ -30704,7 +31925,7 @@ F1 := d F0 --R Type: DeRhamComplex(Integer,[r,theta]) --E 136 ---S 137 of 148 +--S 137 of 149 F2 := hodgeStar(F1,g) --R --R @@ -30718,7 +31939,7 @@ F2 := hodgeStar(F1,g) --R Type: DeRhamComplex(Integer,[r,theta]) --E 137 ---S 138 of 148 +--S 138 of 149 F3 := d F2 --R --R @@ -30735,7 +31956,7 @@ F3 := d F2 --R Type: DeRhamComplex(Integer,[r,theta]) --E 138 ---S 139 of 148 +--S 139 of 149 LaplaceF := hodgeStar(F3,g) --R --R @@ -30749,7 +31970,7 @@ LaplaceF := hodgeStar(F3,g) --R Type: DeRhamComplex(Integer,[r,theta]) --E 139 ---S 140 of 148 +--S 140 of 149 LapF := LaplaceF::Expression(Integer) --R --R @@ -30763,7 +31984,7 @@ LapF := LaplaceF::Expression(Integer) --R Type: Expression(Integer) --E 140 ---S 141 of 148 +--S 141 of 149 subst(LapF,abs(r^2)=r^2) --R --R @@ -30778,7 +31999,7 @@ subst(LapF,abs(r^2)=r^2) -- Internal representation ---S 142 of 148 +--S 142 of 149 R := Expression(Integer) --R --R @@ -30786,7 +32007,7 @@ R := Expression(Integer) --R Type: Domain --E 142 ---S 143 of 148 +--S 143 of 149 Y := DERHAM(coefRing,S2) --R --R @@ -30794,19 +32015,19 @@ Y := DERHAM(coefRing,S2) --R Type: Domain --E 143 ---S 144 of 148 +--S 144 of 149 terms : Y -> List Record(k : EAB, c : R) --R --R Type: Void --E 144 ---S 145 of 148 +--S 145 of 149 terms(a) == a pretend List Record(k : EAB, c : R) --R --R Type: Void --E 145 ---S 146 of 148 +--S 146 of 149 terms(dr) --R --R Compiling function terms with type DeRhamComplex(Integer,[r,theta]) @@ -30816,7 +32037,7 @@ terms(dr) --R Type: List(Record(k: ExtAlgBasis,c: Expression(Integer))) --E 146 ---S 147 of 148 +--S 147 of 149 terms(dtheta) --R --R @@ -30824,7 +32045,7 @@ terms(dtheta) --R Type: List(Record(k: ExtAlgBasis,c: Expression(Integer))) --E 147 ---S 148 of 148 +--S 148 of 149 terms(F1) --R --R @@ -30833,6 +32054,46 @@ terms(F1) --R Type: List(Record(k: ExtAlgBasis,c: Expression(Integer))) --E 148 +--S 149 of 149 +)show DeRhamComplex +--R +--R DeRhamComplex(CoefRing: Join(Ring,OrderedSet),listIndVar: List(Symbol)) is a domain constructor +--R Abbreviation for DeRhamComplex is DERHAM +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for DERHAM +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R coerce : Expression(CoefRing) -> % coerce : Integer -> % +--R coerce : % -> OutputForm degree : % -> NonNegativeInteger +--R dim : % -> NonNegativeInteger exteriorDifferential : % -> % +--R generator : NonNegativeInteger -> % hash : % -> SingleInteger +--R homogeneous? : % -> Boolean latex : % -> String +--R leadingBasisTerm : % -> % one? : % -> Boolean +--R proj : (%,NonNegativeInteger) -> % recip : % -> Union(%,"failed") +--R reductum : % -> % retract : % -> Expression(CoefRing) +--R retractable? : % -> Boolean sample : () -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (Expression(CoefRing),%) -> % +--R characteristic : () -> NonNegativeInteger +--R coefficient : (%,%) -> Expression(CoefRing) +--R dot : (%,%,SquareMatrix(#(listIndVar),Expression(CoefRing))) -> Expression(CoefRing) +--R hodgeStar : (%,SquareMatrix(#(listIndVar),Expression(CoefRing))) -> % +--R interiorProduct : (Vector(Expression(CoefRing)),%,SquareMatrix(#(listIndVar),Expression(CoefRing))) -> % +--R leadingCoefficient : % -> Expression(CoefRing) +--R lieDerivative : (Vector(Expression(CoefRing)),%,SquareMatrix(#(listIndVar),Expression(CoefRing))) -> % +--R map : ((Expression(CoefRing) -> Expression(CoefRing)),%) -> % +--R retractIfCan : % -> Union(Expression(CoefRing),"failed") +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R totalDifferential : Expression(CoefRing) -> % +--R +--E 149 )spool )lisp (bye) @@ -32988,11 +34249,11 @@ DeRhamComplex(CoefRing,listIndVar:List Symbol): Export == Implement where --R empty? : % -> Boolean encode : % -> String --R eq? : (%,%) -> Boolean fullOut : % -> OutputForm --R fullOutput : () -> Boolean fullOutput : Boolean -> Boolean ---R leaf? : % -> Boolean leaves : % -> List(S) ---R map : ((S -> S),%) -> % nodes : % -> List(%) ---R sample : () -> % tree : List(S) -> % ---R tree : S -> % tree : (S,List(%)) -> % ---R value : % -> S +--R latex : % -> String if S has SETCAT leaf? : % -> Boolean +--R leaves : % -> List(S) map : ((S -> S),%) -> % +--R nodes : % -> List(%) sample : () -> % +--R tree : List(S) -> % tree : S -> % +--R tree : (S,List(%)) -> % value : % -> S --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R ?=? : (%,%) -> Boolean if S has SETCAT --R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate @@ -33006,7 +34267,6 @@ DeRhamComplex(CoefRing,listIndVar:List Symbol): Export == Implement where --R eval : (%,List(Equation(S))) -> % if S has EVALAB(S) and S has SETCAT --R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate --R hash : % -> SingleInteger if S has SETCAT ---R latex : % -> String if S has SETCAT --R less? : (%,NonNegativeInteger) -> Boolean --R map! : ((S -> S),%) -> % if $ has shallowlyMutable --R member? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT @@ -33185,27 +34445,36 @@ DesingTree(S: SetCategory): T==C where --R------------------------------- Operations -------------------------------- --R ?*? : (%,R) -> % ?*? : (R,%) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % ---R -? : % -> % ?=? : (%,%) -> Boolean ---R D : (%,(R -> R)) -> % D : % -> % if R has DIFRING +--R -? : % -> % ?/? : (%,R) -> % if R has FIELD +--R ?=? : (%,%) -> Boolean D : (%,(R -> R)) -> % +--R D : % -> % if R has DIFRING D : (%,V,NonNegativeInteger) -> % --R D : (%,List(V)) -> % D : (%,V) -> % --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % coefficients : % -> List(R) +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R coefficients : % -> List(R) coerce : % -> % if R has INTDOM --R coerce : S -> % coerce : V -> % --R coerce : R -> % coerce : Integer -> % ---R coerce : % -> OutputForm degree : % -> IndexedExponents(V) +--R coerce : % -> OutputForm content : % -> R if R has GCDDOM +--R degree : % -> IndexedExponents(V) differentiate : (%,(R -> R)) -> % --R differentiate : (%,List(V)) -> % differentiate : (%,V) -> % --R eval : (%,List(V),List(%)) -> % eval : (%,V,%) -> % --R eval : (%,List(V),List(R)) -> % eval : (%,V,R) -> % ---R eval : (%,%,%) -> % eval : (%,Equation(%)) -> % +--R eval : (%,List(%),List(%)) -> % eval : (%,%,%) -> % +--R eval : (%,Equation(%)) -> % eval : (%,List(Equation(%))) -> % +--R gcd : (%,%) -> % if R has GCDDOM gcd : List(%) -> % if R has GCDDOM --R ground : % -> R ground? : % -> Boolean --R hash : % -> SingleInteger initial : % -> % --R isobaric? : % -> Boolean latex : % -> String +--R lcm : (%,%) -> % if R has GCDDOM lcm : List(%) -> % if R has GCDDOM --R leader : % -> V leadingCoefficient : % -> R --R leadingMonomial : % -> % map : ((R -> R),%) -> % +--R max : (%,%) -> % if R has ORDSET min : (%,%) -> % if R has ORDSET --R monomial? : % -> Boolean monomials : % -> List(%) --R one? : % -> Boolean order : % -> NonNegativeInteger +--R order : (%,S) -> NonNegativeInteger primitiveMonomials : % -> List(%) --R recip : % -> Union(%,"failed") reductum : % -> % --R retract : % -> S retract : % -> V --R retract : % -> R sample : () -> % @@ -33214,9 +34483,6 @@ DesingTree(S: SetCategory): T==C where --R ?~=? : (%,%) -> Boolean --R ?*? : (Fraction(Integer),%) -> % if R has ALGEBRA(FRAC(INT)) --R ?*? : (%,Fraction(Integer)) -> % if R has ALGEBRA(FRAC(INT)) ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R ?/? : (%,R) -> % if R has FIELD --R ? Boolean if R has ORDSET --R ?<=? : (%,%) -> Boolean if R has ORDSET --R ?>? : (%,%) -> Boolean if R has ORDSET @@ -33228,8 +34494,6 @@ DesingTree(S: SetCategory): T==C where --R D : (%,Symbol) -> % if R has PDRING(SYMBOL) --R D : (%,NonNegativeInteger) -> % if R has DIFRING --R D : (%,List(V),List(NonNegativeInteger)) -> % ---R D : (%,V,NonNegativeInteger) -> % ---R ?^? : (%,NonNegativeInteger) -> % --R associates? : (%,%) -> Boolean if R has INTDOM --R binomThmExpt : (%,%,NonNegativeInteger) -> % if R has COMRING --R characteristic : () -> NonNegativeInteger @@ -33237,12 +34501,10 @@ DesingTree(S: SetCategory): T==C where --R coefficient : (%,List(V),List(NonNegativeInteger)) -> % --R coefficient : (%,V,NonNegativeInteger) -> % --R coefficient : (%,IndexedExponents(V)) -> R ---R coerce : % -> % if R has INTDOM --R coerce : Fraction(Integer) -> % if R has ALGEBRA(FRAC(INT)) or R has RETRACT(FRAC(INT)) --R coerce : SparseMultivariatePolynomial(R,S) -> % --R conditionP : Matrix(%) -> Union(Vector(%),"failed") if $ has CHARNZ and R has PFECAT --R content : (%,V) -> % if R has GCDDOM ---R content : % -> R if R has GCDDOM --R convert : % -> InputForm if R has KONVERT(INFORM) and V has KONVERT(INFORM) --R convert : % -> Pattern(Integer) if R has KONVERT(PATTERN(INT)) and V has KONVERT(PATTERN(INT)) --R convert : % -> Pattern(Float) if R has KONVERT(PATTERN(FLOAT)) and V has KONVERT(PATTERN(FLOAT)) @@ -33250,7 +34512,6 @@ DesingTree(S: SetCategory): T==C where --R degree : (%,List(V)) -> List(NonNegativeInteger) --R degree : (%,V) -> NonNegativeInteger --R differentialVariables : % -> List(S) ---R differentiate : (%,(R -> R)) -> % --R differentiate : (%,(R -> R),NonNegativeInteger) -> % --R differentiate : (%,List(Symbol),List(NonNegativeInteger)) -> % if R has PDRING(SYMBOL) --R differentiate : (%,Symbol,NonNegativeInteger) -> % if R has PDRING(SYMBOL) @@ -33265,28 +34526,20 @@ DesingTree(S: SetCategory): T==C where --R eval : (%,S,R) -> % if R has DIFRING --R eval : (%,List(S),List(%)) -> % if R has DIFRING --R eval : (%,S,%) -> % if R has DIFRING ---R eval : (%,List(%),List(%)) -> % ---R eval : (%,List(Equation(%))) -> % --R exquo : (%,%) -> Union(%,"failed") if R has INTDOM --R exquo : (%,R) -> Union(%,"failed") if R has INTDOM --R factor : % -> Factored(%) if R has PFECAT --R factorPolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has PFECAT --R factorSquareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has PFECAT ---R gcd : (%,%) -> % if R has GCDDOM ---R gcd : List(%) -> % if R has GCDDOM --R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) if R has GCDDOM --R isExpt : % -> Union(Record(var: V,exponent: NonNegativeInteger),"failed") --R isPlus : % -> Union(List(%),"failed") --R isTimes : % -> Union(List(%),"failed") ---R lcm : (%,%) -> % if R has GCDDOM ---R lcm : List(%) -> % if R has GCDDOM --R lcmCoef : (%,%) -> Record(llcmres: %,coeff1: %,coeff2: %) if R has GCDDOM --R mainVariable : % -> Union(V,"failed") --R makeVariable : % -> (NonNegativeInteger -> %) if R has DIFRING --R makeVariable : S -> (NonNegativeInteger -> %) --R mapExponents : ((IndexedExponents(V) -> IndexedExponents(V)),%) -> % ---R max : (%,%) -> % if R has ORDSET ---R min : (%,%) -> % if R has ORDSET --R minimumDegree : (%,List(V)) -> List(NonNegativeInteger) --R minimumDegree : (%,V) -> NonNegativeInteger --R minimumDegree : % -> IndexedExponents(V) @@ -33297,12 +34550,10 @@ DesingTree(S: SetCategory): T==C where --R multivariate : (SparseUnivariatePolynomial(%),V) -> % --R multivariate : (SparseUnivariatePolynomial(R),V) -> % --R numberOfMonomials : % -> NonNegativeInteger ---R order : (%,S) -> NonNegativeInteger --R patternMatch : (%,Pattern(Integer),PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if R has PATMAB(INT) and V has PATMAB(INT) --R patternMatch : (%,Pattern(Float),PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if R has PATMAB(FLOAT) and V has PATMAB(FLOAT) --R pomopo! : (%,R,IndexedExponents(V),%) -> % --R prime? : % -> Boolean if R has PFECAT ---R primitiveMonomials : % -> List(%) --R primitivePart : (%,V) -> % if R has GCDDOM --R primitivePart : % -> % if R has GCDDOM --R reducedSystem : Matrix(%) -> Matrix(R) @@ -33516,33 +34767,35 @@ DifferentialSparseMultivariatePolynomial(R, S, V): --S 1 of 1 )show DirectProduct +--R --R DirectProduct(dim: NonNegativeInteger,R: Type) is a domain constructor --R Abbreviation for DirectProduct is DIRPROD --R This constructor is not exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for DIRPROD --R --R------------------------------- Operations -------------------------------- ---R -? : % -> % if R has RING 1 : () -> % if R has MONOID ---R 0 : () -> % if R has CABMON coerce : % -> Vector(R) +--R ?*? : (R,%) -> % if R has MONOID ?*? : (%,R) -> % if R has MONOID +--R ?*? : (%,%) -> % if R has MONOID ?+? : (%,%) -> % if R has ABELSG +--R -? : % -> % if R has RING ?-? : (%,%) -> % if R has RING +--R ?/? : (%,R) -> % if R has FIELD 1 : () -> % if R has MONOID +--R 0 : () -> % if R has CABMON abs : % -> % if R has ORDRING +--R coerce : R -> % if R has SETCAT coerce : % -> Vector(R) --R copy : % -> % directProduct : Vector(R) -> % ---R ?.? : (%,Integer) -> R elt : (%,Integer,R) -> R ---R empty : () -> % empty? : % -> Boolean ---R entries : % -> List(R) eq? : (%,%) -> Boolean ---R index? : (Integer,%) -> Boolean indices : % -> List(Integer) ---R map : ((R -> R),%) -> % qelt : (%,Integer) -> R ---R sample : () -> % +--R dot : (%,%) -> R if R has RING ?.? : (%,Integer) -> R +--R elt : (%,Integer,R) -> R empty : () -> % +--R empty? : % -> Boolean entries : % -> List(R) +--R eq? : (%,%) -> Boolean index? : (Integer,%) -> Boolean +--R indices : % -> List(Integer) latex : % -> String if R has SETCAT +--R map : ((R -> R),%) -> % one? : % -> Boolean if R has MONOID +--R qelt : (%,Integer) -> R random : () -> % if R has FINITE +--R retract : % -> R if R has SETCAT sample : () -> % +--R sup : (%,%) -> % if R has OAMONS --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R ?*? : (PositiveInteger,%) -> % if R has ABELSG --R ?*? : (NonNegativeInteger,%) -> % if R has CABMON ---R ?*? : (R,%) -> % if R has MONOID ---R ?*? : (%,R) -> % if R has MONOID ---R ?*? : (%,%) -> % if R has MONOID --R ?*? : (Integer,%) -> % if R has RING --R ?**? : (%,PositiveInteger) -> % if R has MONOID --R ?**? : (%,NonNegativeInteger) -> % if R has MONOID ---R ?+? : (%,%) -> % if R has ABELSG ---R ?-? : (%,%) -> % if R has RING ---R ?/? : (%,R) -> % if R has FIELD --R ? Boolean if R has OAMONS or R has ORDRING --R ?<=? : (%,%) -> Boolean if R has OAMONS or R has ORDRING --R ?=? : (%,%) -> Boolean if R has SETCAT @@ -33558,10 +34811,8 @@ DifferentialSparseMultivariatePolynomial(R, S, V): --R D : % -> % if R has DIFRING and R has RING --R ?^? : (%,PositiveInteger) -> % if R has MONOID --R ?^? : (%,NonNegativeInteger) -> % if R has MONOID ---R abs : % -> % if R has ORDRING --R any? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate --R characteristic : () -> NonNegativeInteger if R has RING ---R coerce : R -> % if R has SETCAT --R coerce : Fraction(Integer) -> % if R has RETRACT(FRAC(INT)) and R has SETCAT --R coerce : Integer -> % if R has RETRACT(INT) and R has SETCAT or R has RING --R coerce : % -> OutputForm if R has SETCAT @@ -33576,7 +34827,6 @@ DifferentialSparseMultivariatePolynomial(R, S, V): --R differentiate : (%,NonNegativeInteger) -> % if R has DIFRING and R has RING --R differentiate : % -> % if R has DIFRING and R has RING --R dimension : () -> CardinalNumber if R has FIELD ---R dot : (%,%) -> R if R has RING --R entry? : (R,%) -> Boolean if $ has finiteAggregate and R has SETCAT --R enumerate : () -> List(%) if R has FINITE --R eval : (%,List(R),List(R)) -> % if R has EVALAB(R) and R has SETCAT @@ -33588,7 +34838,6 @@ DifferentialSparseMultivariatePolynomial(R, S, V): --R first : % -> R if Integer has ORDSET --R hash : % -> SingleInteger if R has SETCAT --R index : PositiveInteger -> % if R has FINITE ---R latex : % -> String if R has SETCAT --R less? : (%,NonNegativeInteger) -> Boolean --R lookup : % -> PositiveInteger if R has FINITE --R map! : ((R -> R),%) -> % if $ has shallowlyMutable @@ -33600,17 +34849,14 @@ DifferentialSparseMultivariatePolynomial(R, S, V): --R minIndex : % -> Integer if Integer has ORDSET --R more? : (%,NonNegativeInteger) -> Boolean --R negative? : % -> Boolean if R has ORDRING ---R one? : % -> Boolean if R has MONOID --R parts : % -> List(R) if $ has finiteAggregate --R positive? : % -> Boolean if R has ORDRING --R qsetelt! : (%,Integer,R) -> R if $ has shallowlyMutable ---R random : () -> % if R has FINITE --R recip : % -> Union(%,"failed") if R has MONOID --R reducedSystem : Matrix(%) -> Matrix(R) if R has RING --R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(R),vec: Vector(R)) if R has RING --R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(Integer),vec: Vector(Integer)) if R has LINEXP(INT) and R has RING --R reducedSystem : Matrix(%) -> Matrix(Integer) if R has LINEXP(INT) and R has RING ---R retract : % -> R if R has SETCAT --R retract : % -> Fraction(Integer) if R has RETRACT(FRAC(INT)) and R has SETCAT --R retract : % -> Integer if R has RETRACT(INT) and R has SETCAT --R retractIfCan : % -> Union(R,"failed") if R has SETCAT @@ -33621,7 +34867,6 @@ DifferentialSparseMultivariatePolynomial(R, S, V): --R size : () -> NonNegativeInteger if R has FINITE --R size? : (%,NonNegativeInteger) -> Boolean --R subtractIfCan : (%,%) -> Union(%,"failed") if R has CABMON ---R sup : (%,%) -> % if R has OAMONS --R swap! : (%,Integer,Integer) -> Void if $ has shallowlyMutable --R unitVector : PositiveInteger -> % if R has RING --R zero? : % -> Boolean if R has CABMON @@ -33846,34 +35091,36 @@ DirectProduct(dim:NonNegativeInteger, R:Type): --S 1 of 1 )show DirectProductMatrixModule +--R --R DirectProductMatrixModule(n: PositiveInteger,R: Ring,M: SquareMatrixCategory(n,R,DirectProduct(n,R),DirectProduct(n,R)),S: LeftModule(R)) is a domain constructor --R Abbreviation for DirectProductMatrixModule is DPMM --R This constructor is not exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for DPMM --R --R------------------------------- Operations -------------------------------- +--R ?*? : (S,%) -> % if S has MONOID ?*? : (%,S) -> % if S has MONOID --R ?*? : (M,%) -> % ?*? : (PositiveInteger,%) -> % ---R ?*? : (Integer,%) -> % ?*? : (R,%) -> % ---R ?+? : (%,%) -> % -? : % -> % ---R ?-? : (%,%) -> % ?=? : (%,%) -> Boolean ---R 0 : () -> % coerce : % -> OutputForm +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (R,%) -> % ?+? : (%,%) -> % +--R -? : % -> % ?-? : (%,%) -> % +--R ?/? : (%,S) -> % if S has FIELD ?=? : (%,%) -> Boolean +--R 0 : () -> % abs : % -> % if S has ORDRING +--R coerce : S -> % if S has SETCAT coerce : % -> OutputForm --R coerce : % -> Vector(S) copy : % -> % ---R directProduct : Vector(S) -> % ?.? : (%,Integer) -> S ---R elt : (%,Integer,S) -> S empty : () -> % ---R empty? : % -> Boolean entries : % -> List(S) ---R eq? : (%,%) -> Boolean hash : % -> SingleInteger ---R index? : (Integer,%) -> Boolean indices : % -> List(Integer) ---R latex : % -> String map : ((S -> S),%) -> % ---R qelt : (%,Integer) -> S sample : () -> % +--R directProduct : Vector(S) -> % dot : (%,%) -> S if S has RING +--R ?.? : (%,Integer) -> S elt : (%,Integer,S) -> S +--R empty : () -> % empty? : % -> Boolean +--R entries : % -> List(S) eq? : (%,%) -> Boolean +--R hash : % -> SingleInteger index? : (Integer,%) -> Boolean +--R indices : % -> List(Integer) latex : % -> String +--R map : ((S -> S),%) -> % qelt : (%,Integer) -> S +--R random : () -> % if S has FINITE retract : % -> S if S has SETCAT +--R sample : () -> % sup : (%,%) -> % if S has OAMONS --R zero? : % -> Boolean ?~=? : (%,%) -> Boolean --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R ?*? : (%,%) -> % if S has DIFRING and S has RING or S has LINEXP(INT) and S has RING or S has MONOID or S has PDRING(SYMBOL) and S has RING ---R ?*? : (S,%) -> % if S has MONOID ---R ?*? : (%,S) -> % if S has MONOID ---R ?*? : (NonNegativeInteger,%) -> % --R ?**? : (%,PositiveInteger) -> % if S has DIFRING and S has RING or S has LINEXP(INT) and S has RING or S has MONOID or S has PDRING(SYMBOL) and S has RING --R ?**? : (%,NonNegativeInteger) -> % if S has DIFRING and S has RING or S has LINEXP(INT) and S has RING or S has MONOID or S has PDRING(SYMBOL) and S has RING ---R ?/? : (%,S) -> % if S has FIELD --R ? Boolean if S has OAMONS or S has ORDRING --R ?<=? : (%,%) -> Boolean if S has OAMONS or S has ORDRING --R ?>? : (%,%) -> Boolean if S has OAMONS or S has ORDRING @@ -33889,12 +35136,10 @@ DirectProduct(dim:NonNegativeInteger, R:Type): --R 1 : () -> % if S has DIFRING and S has RING or S has LINEXP(INT) and S has RING or S has MONOID or S has PDRING(SYMBOL) and S has RING --R ?^? : (%,PositiveInteger) -> % if S has DIFRING and S has RING or S has LINEXP(INT) and S has RING or S has MONOID or S has PDRING(SYMBOL) and S has RING --R ?^? : (%,NonNegativeInteger) -> % if S has DIFRING and S has RING or S has LINEXP(INT) and S has RING or S has MONOID or S has PDRING(SYMBOL) and S has RING ---R abs : % -> % if S has ORDRING --R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate --R characteristic : () -> NonNegativeInteger if S has RING --R coerce : Fraction(Integer) -> % if S has RETRACT(FRAC(INT)) and S has SETCAT --R coerce : Integer -> % if S has RETRACT(INT) and S has SETCAT or S has RING ---R coerce : S -> % if S has SETCAT --R count : (S,%) -> NonNegativeInteger if $ has finiteAggregate and S has SETCAT --R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate --R differentiate : % -> % if S has DIFRING and S has RING @@ -33906,7 +35151,6 @@ DirectProduct(dim:NonNegativeInteger, R:Type): --R differentiate : (%,(S -> S)) -> % if S has RING --R differentiate : (%,(S -> S),NonNegativeInteger) -> % if S has RING --R dimension : () -> CardinalNumber if S has FIELD ---R dot : (%,%) -> S if S has RING --R entry? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT --R enumerate : () -> List(%) if S has FINITE --R eval : (%,List(S),List(S)) -> % if S has EVALAB(S) and S has SETCAT @@ -33932,7 +35176,6 @@ DirectProduct(dim:NonNegativeInteger, R:Type): --R parts : % -> List(S) if $ has finiteAggregate --R positive? : % -> Boolean if S has ORDRING --R qsetelt! : (%,Integer,S) -> S if $ has shallowlyMutable ---R random : () -> % if S has FINITE --R recip : % -> Union(%,"failed") if S has DIFRING and S has RING or S has LINEXP(INT) and S has RING or S has MONOID or S has PDRING(SYMBOL) and S has RING --R reducedSystem : Matrix(%) -> Matrix(Integer) if S has LINEXP(INT) and S has RING --R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(Integer),vec: Vector(Integer)) if S has LINEXP(INT) and S has RING @@ -33940,7 +35183,6 @@ DirectProduct(dim:NonNegativeInteger, R:Type): --R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(S),vec: Vector(S)) if S has RING --R retract : % -> Fraction(Integer) if S has RETRACT(FRAC(INT)) and S has SETCAT --R retract : % -> Integer if S has RETRACT(INT) and S has SETCAT ---R retract : % -> S if S has SETCAT --R retractIfCan : % -> Union(Fraction(Integer),"failed") if S has RETRACT(FRAC(INT)) and S has SETCAT --R retractIfCan : % -> Union(Integer,"failed") if S has RETRACT(INT) and S has SETCAT --R retractIfCan : % -> Union(S,"failed") if S has SETCAT @@ -33949,7 +35191,6 @@ DirectProduct(dim:NonNegativeInteger, R:Type): --R size : () -> NonNegativeInteger if S has FINITE --R size? : (%,NonNegativeInteger) -> Boolean --R subtractIfCan : (%,%) -> Union(%,"failed") ---R sup : (%,%) -> % if S has OAMONS --R swap! : (%,Integer,Integer) -> Void if $ has shallowlyMutable --R unitVector : PositiveInteger -> % if S has RING --R @@ -34101,34 +35342,36 @@ DirectProductMatrixModule(n, R, M, S): DPcategory == DPcapsule where --S 1 of 1 )show DirectProductModule +--R --R DirectProductModule(n: NonNegativeInteger,R: Ring,S: LeftModule(R)) is a domain constructor --R Abbreviation for DirectProductModule is DPMO --R This constructor is not exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for DPMO --R --R------------------------------- Operations -------------------------------- ---R ?*? : (PositiveInteger,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (R,%) -> % ?+? : (%,%) -> % ---R -? : % -> % ?-? : (%,%) -> % +--R ?*? : (S,%) -> % if S has MONOID ?*? : (%,S) -> % if S has MONOID +--R ?*? : (PositiveInteger,%) -> % ?*? : (NonNegativeInteger,%) -> % +--R ?*? : (Integer,%) -> % ?*? : (R,%) -> % +--R ?+? : (%,%) -> % -? : % -> % +--R ?-? : (%,%) -> % ?/? : (%,S) -> % if S has FIELD --R ?=? : (%,%) -> Boolean 0 : () -> % +--R abs : % -> % if S has ORDRING coerce : S -> % if S has SETCAT --R coerce : % -> OutputForm coerce : % -> Vector(S) --R copy : % -> % directProduct : Vector(S) -> % ---R ?.? : (%,Integer) -> S elt : (%,Integer,S) -> S ---R empty : () -> % empty? : % -> Boolean ---R entries : % -> List(S) eq? : (%,%) -> Boolean ---R hash : % -> SingleInteger index? : (Integer,%) -> Boolean ---R indices : % -> List(Integer) latex : % -> String ---R map : ((S -> S),%) -> % qelt : (%,Integer) -> S ---R sample : () -> % zero? : % -> Boolean +--R dot : (%,%) -> S if S has RING ?.? : (%,Integer) -> S +--R elt : (%,Integer,S) -> S empty : () -> % +--R empty? : % -> Boolean entries : % -> List(S) +--R eq? : (%,%) -> Boolean hash : % -> SingleInteger +--R index? : (Integer,%) -> Boolean indices : % -> List(Integer) +--R latex : % -> String map : ((S -> S),%) -> % +--R qelt : (%,Integer) -> S random : () -> % if S has FINITE +--R retract : % -> S if S has SETCAT sample : () -> % +--R sup : (%,%) -> % if S has OAMONS zero? : % -> Boolean --R ?~=? : (%,%) -> Boolean --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R ?*? : (%,%) -> % if S has DIFRING and S has RING or S has LINEXP(INT) and S has RING or S has MONOID or S has PDRING(SYMBOL) and S has RING ---R ?*? : (S,%) -> % if S has MONOID ---R ?*? : (%,S) -> % if S has MONOID ---R ?*? : (NonNegativeInteger,%) -> % --R ?**? : (%,PositiveInteger) -> % if S has DIFRING and S has RING or S has LINEXP(INT) and S has RING or S has MONOID or S has PDRING(SYMBOL) and S has RING --R ?**? : (%,NonNegativeInteger) -> % if S has DIFRING and S has RING or S has LINEXP(INT) and S has RING or S has MONOID or S has PDRING(SYMBOL) and S has RING ---R ?/? : (%,S) -> % if S has FIELD --R ? Boolean if S has OAMONS or S has ORDRING --R ?<=? : (%,%) -> Boolean if S has OAMONS or S has ORDRING --R ?>? : (%,%) -> Boolean if S has OAMONS or S has ORDRING @@ -34144,12 +35387,10 @@ DirectProductMatrixModule(n, R, M, S): DPcategory == DPcapsule where --R 1 : () -> % if S has DIFRING and S has RING or S has LINEXP(INT) and S has RING or S has MONOID or S has PDRING(SYMBOL) and S has RING --R ?^? : (%,PositiveInteger) -> % if S has DIFRING and S has RING or S has LINEXP(INT) and S has RING or S has MONOID or S has PDRING(SYMBOL) and S has RING --R ?^? : (%,NonNegativeInteger) -> % if S has DIFRING and S has RING or S has LINEXP(INT) and S has RING or S has MONOID or S has PDRING(SYMBOL) and S has RING ---R abs : % -> % if S has ORDRING --R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate --R characteristic : () -> NonNegativeInteger if S has RING --R coerce : Fraction(Integer) -> % if S has RETRACT(FRAC(INT)) and S has SETCAT --R coerce : Integer -> % if S has RETRACT(INT) and S has SETCAT or S has RING ---R coerce : S -> % if S has SETCAT --R count : (S,%) -> NonNegativeInteger if $ has finiteAggregate and S has SETCAT --R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate --R differentiate : % -> % if S has DIFRING and S has RING @@ -34161,7 +35402,6 @@ DirectProductMatrixModule(n, R, M, S): DPcategory == DPcapsule where --R differentiate : (%,(S -> S)) -> % if S has RING --R differentiate : (%,(S -> S),NonNegativeInteger) -> % if S has RING --R dimension : () -> CardinalNumber if S has FIELD ---R dot : (%,%) -> S if S has RING --R entry? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT --R enumerate : () -> List(%) if S has FINITE --R eval : (%,List(S),List(S)) -> % if S has EVALAB(S) and S has SETCAT @@ -34187,7 +35427,6 @@ DirectProductMatrixModule(n, R, M, S): DPcategory == DPcapsule where --R parts : % -> List(S) if $ has finiteAggregate --R positive? : % -> Boolean if S has ORDRING --R qsetelt! : (%,Integer,S) -> S if $ has shallowlyMutable ---R random : () -> % if S has FINITE --R recip : % -> Union(%,"failed") if S has DIFRING and S has RING or S has LINEXP(INT) and S has RING or S has MONOID or S has PDRING(SYMBOL) and S has RING --R reducedSystem : Matrix(%) -> Matrix(Integer) if S has LINEXP(INT) and S has RING --R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(Integer),vec: Vector(Integer)) if S has LINEXP(INT) and S has RING @@ -34195,7 +35434,6 @@ DirectProductMatrixModule(n, R, M, S): DPcategory == DPcapsule where --R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(S),vec: Vector(S)) if S has RING --R retract : % -> Fraction(Integer) if S has RETRACT(FRAC(INT)) and S has SETCAT --R retract : % -> Integer if S has RETRACT(INT) and S has SETCAT ---R retract : % -> S if S has SETCAT --R retractIfCan : % -> Union(Fraction(Integer),"failed") if S has RETRACT(FRAC(INT)) and S has SETCAT --R retractIfCan : % -> Union(Integer,"failed") if S has RETRACT(INT) and S has SETCAT --R retractIfCan : % -> Union(S,"failed") if S has SETCAT @@ -34204,7 +35442,6 @@ DirectProductMatrixModule(n, R, M, S): DPcategory == DPcapsule where --R size : () -> NonNegativeInteger if S has FINITE --R size? : (%,NonNegativeInteger) -> Boolean --R subtractIfCan : (%,%) -> Union(%,"failed") ---R sup : (%,%) -> % if S has OAMONS --R swap! : (%,Integer,Integer) -> Void if $ has shallowlyMutable --R unitVector : PositiveInteger -> % if S has RING --R @@ -34542,22 +35779,21 @@ reduce(_and,[(x = y)@Boolean for x in t9 for y in t10]) --R --R------------------------------- Operations -------------------------------- --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ?=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % coerce : % -> Stream(Coef) ---R coerce : Stream(Coef) -> % coerce : Integer -> % ---R coerce : % -> OutputForm ?.? : (%,PositiveInteger) -> Coef ---R hash : % -> SingleInteger latex : % -> String ---R one? : % -> Boolean recip : % -> Union(%,"failed") ---R sample : () -> % zero? : % -> Boolean ---R zeta : () -> % ?~=? : (%,%) -> Boolean +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R coerce : % -> Stream(Coef) coerce : Stream(Coef) -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R ?.? : (%,PositiveInteger) -> Coef hash : % -> SingleInteger +--R latex : % -> String one? : % -> Boolean +--R recip : % -> Union(%,"failed") sample : () -> % +--R zero? : % -> Boolean zeta : () -> % +--R ?~=? : (%,%) -> Boolean --R ?*? : (%,Coef) -> % if Coef has COMRING --R ?*? : (Coef,%) -> % if Coef has COMRING ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R ?^? : (%,NonNegativeInteger) -> % --R additive? : (%,PositiveInteger) -> Boolean --R associates? : (%,%) -> Boolean if Coef has COMRING --R characteristic : () -> NonNegativeInteger @@ -34775,13 +36011,14 @@ DirichletRing(Coef: Ring): )set message test on )set message auto off )clear all ---S 1 of 10 + +--S 1 of 11 (d1,d2,d3) : DMP([z,y,x],FRAC INT) --R --R Type: Void --E 1 ---S 2 of 10 +--S 2 of 11 d1 := -4*z + 4*y**2*x + 16*x**2 + 1 --R --R @@ -34790,7 +36027,7 @@ d1 := -4*z + 4*y**2*x + 16*x**2 + 1 --R Type: DistributedMultivariatePolynomial([z,y,x],Fraction(Integer)) --E 2 ---S 3 of 10 +--S 3 of 11 d2 := 2*z*y**2 + 4*x + 1 --R --R @@ -34799,7 +36036,7 @@ d2 := 2*z*y**2 + 4*x + 1 --R Type: DistributedMultivariatePolynomial([z,y,x],Fraction(Integer)) --E 3 ---S 4 of 10 +--S 4 of 11 d3 := 2*z*x**2 - 2*y**2 - x --R --R @@ -34808,7 +36045,7 @@ d3 := 2*z*x**2 - 2*y**2 - x --R Type: DistributedMultivariatePolynomial([z,y,x],Fraction(Integer)) --E 4 ---S 5 of 10 +--S 5 of 11 groebner [d1,d2,d3] --R --R @@ -34825,13 +36062,13 @@ groebner [d1,d2,d3] --R Type: List(DistributedMultivariatePolynomial([z,y,x],Fraction(Integer))) --E 5 ---S 6 of 10 +--S 6 of 11 (n1,n2,n3) : HDMP([z,y,x],FRAC INT) --R --R Type: Void --E 6 ---S 7 of 10 +--S 7 of 11 n1 := d1 --R --R @@ -34840,7 +36077,7 @@ n1 := d1 --RType: HomogeneousDistributedMultivariatePolynomial([z,y,x],Fraction(Integer)) --E 7 ---S 8 of 10 +--S 8 of 11 n2 := d2 --R --R @@ -34849,7 +36086,7 @@ n2 := d2 --RType: HomogeneousDistributedMultivariatePolynomial([z,y,x],Fraction(Integer)) --E 8 ---S 9 of 10 +--S 9 of 11 n3 := d3 --R --R @@ -34858,7 +36095,7 @@ n3 := d3 --RType: HomogeneousDistributedMultivariatePolynomial([z,y,x],Fraction(Integer)) --E 9 ---S 10 of 10 +--S 10 of 11 groebner [n1,n2,n3] --R --R @@ -34874,6 +36111,134 @@ groebner [n1,n2,n3] --R 4 2 --RType: List(HomogeneousDistributedMultivariatePolynomial([z,y,x],Fraction(Integer))) --E 10 + +--S 11 of 11 +)show DistributedMultivariatePolynomial +--R +--R DistributedMultivariatePolynomial(vl: List(Symbol),R: Ring) is a domain constructor +--R Abbreviation for DistributedMultivariatePolynomial is DMP +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for DMP +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,R) -> % ?*? : (R,%) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?/? : (%,R) -> % if R has FIELD +--R ?=? : (%,%) -> Boolean 1 : () -> % +--R 0 : () -> % ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,PositiveInteger) -> % coefficients : % -> List(R) +--R coerce : % -> % if R has INTDOM coerce : R -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R content : % -> R if R has GCDDOM eval : (%,List(%),List(%)) -> % +--R eval : (%,%,%) -> % eval : (%,Equation(%)) -> % +--R eval : (%,List(Equation(%))) -> % gcd : (%,%) -> % if R has GCDDOM +--R gcd : List(%) -> % if R has GCDDOM ground : % -> R +--R ground? : % -> Boolean hash : % -> SingleInteger +--R latex : % -> String lcm : (%,%) -> % if R has GCDDOM +--R lcm : List(%) -> % if R has GCDDOM leadingCoefficient : % -> R +--R leadingMonomial : % -> % map : ((R -> R),%) -> % +--R max : (%,%) -> % if R has ORDSET min : (%,%) -> % if R has ORDSET +--R monomial? : % -> Boolean monomials : % -> List(%) +--R one? : % -> Boolean primitiveMonomials : % -> List(%) +--R recip : % -> Union(%,"failed") reductum : % -> % +--R reorder : (%,List(Integer)) -> % retract : % -> R +--R sample : () -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R ?*? : (Fraction(Integer),%) -> % if R has ALGEBRA(FRAC(INT)) +--R ?*? : (%,Fraction(Integer)) -> % if R has ALGEBRA(FRAC(INT)) +--R ? Boolean if R has ORDSET +--R ?<=? : (%,%) -> Boolean if R has ORDSET +--R ?>? : (%,%) -> Boolean if R has ORDSET +--R ?>=? : (%,%) -> Boolean if R has ORDSET +--R D : (%,List(OrderedVariableList(vl)),List(NonNegativeInteger)) -> % +--R D : (%,OrderedVariableList(vl),NonNegativeInteger) -> % +--R D : (%,List(OrderedVariableList(vl))) -> % +--R D : (%,OrderedVariableList(vl)) -> % +--R associates? : (%,%) -> Boolean if R has INTDOM +--R binomThmExpt : (%,%,NonNegativeInteger) -> % if R has COMRING +--R characteristic : () -> NonNegativeInteger +--R charthRoot : % -> Union(%,"failed") if $ has CHARNZ and R has PFECAT or R has CHARNZ +--R coefficient : (%,List(OrderedVariableList(vl)),List(NonNegativeInteger)) -> % +--R coefficient : (%,OrderedVariableList(vl),NonNegativeInteger) -> % +--R coefficient : (%,DirectProduct(#(vl),NonNegativeInteger)) -> R +--R coerce : Fraction(Integer) -> % if R has ALGEBRA(FRAC(INT)) or R has RETRACT(FRAC(INT)) +--R coerce : OrderedVariableList(vl) -> % +--R conditionP : Matrix(%) -> Union(Vector(%),"failed") if $ has CHARNZ and R has PFECAT +--R content : (%,OrderedVariableList(vl)) -> % if R has GCDDOM +--R convert : % -> InputForm if OrderedVariableList(vl) has KONVERT(INFORM) and R has KONVERT(INFORM) +--R convert : % -> Pattern(Integer) if OrderedVariableList(vl) has KONVERT(PATTERN(INT)) and R has KONVERT(PATTERN(INT)) +--R convert : % -> Pattern(Float) if OrderedVariableList(vl) has KONVERT(PATTERN(FLOAT)) and R has KONVERT(PATTERN(FLOAT)) +--R degree : (%,List(OrderedVariableList(vl))) -> List(NonNegativeInteger) +--R degree : (%,OrderedVariableList(vl)) -> NonNegativeInteger +--R degree : % -> DirectProduct(#(vl),NonNegativeInteger) +--R differentiate : (%,List(OrderedVariableList(vl)),List(NonNegativeInteger)) -> % +--R differentiate : (%,OrderedVariableList(vl),NonNegativeInteger) -> % +--R differentiate : (%,List(OrderedVariableList(vl))) -> % +--R differentiate : (%,OrderedVariableList(vl)) -> % +--R discriminant : (%,OrderedVariableList(vl)) -> % if R has COMRING +--R eval : (%,List(OrderedVariableList(vl)),List(%)) -> % +--R eval : (%,OrderedVariableList(vl),%) -> % +--R eval : (%,List(OrderedVariableList(vl)),List(R)) -> % +--R eval : (%,OrderedVariableList(vl),R) -> % +--R exquo : (%,%) -> Union(%,"failed") if R has INTDOM +--R exquo : (%,R) -> Union(%,"failed") if R has INTDOM +--R factor : % -> Factored(%) if R has PFECAT +--R factorPolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has PFECAT +--R factorSquareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has PFECAT +--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) if R has GCDDOM +--R isExpt : % -> Union(Record(var: OrderedVariableList(vl),exponent: NonNegativeInteger),"failed") +--R isPlus : % -> Union(List(%),"failed") +--R isTimes : % -> Union(List(%),"failed") +--R lcmCoef : (%,%) -> Record(llcmres: %,coeff1: %,coeff2: %) if R has GCDDOM +--R mainVariable : % -> Union(OrderedVariableList(vl),"failed") +--R mapExponents : ((DirectProduct(#(vl),NonNegativeInteger) -> DirectProduct(#(vl),NonNegativeInteger)),%) -> % +--R minimumDegree : (%,List(OrderedVariableList(vl))) -> List(NonNegativeInteger) +--R minimumDegree : (%,OrderedVariableList(vl)) -> NonNegativeInteger +--R minimumDegree : % -> DirectProduct(#(vl),NonNegativeInteger) +--R monicDivide : (%,%,OrderedVariableList(vl)) -> Record(quotient: %,remainder: %) +--R monomial : (%,List(OrderedVariableList(vl)),List(NonNegativeInteger)) -> % +--R monomial : (%,OrderedVariableList(vl),NonNegativeInteger) -> % +--R monomial : (R,DirectProduct(#(vl),NonNegativeInteger)) -> % +--R multivariate : (SparseUnivariatePolynomial(%),OrderedVariableList(vl)) -> % +--R multivariate : (SparseUnivariatePolynomial(R),OrderedVariableList(vl)) -> % +--R numberOfMonomials : % -> NonNegativeInteger +--R patternMatch : (%,Pattern(Integer),PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if OrderedVariableList(vl) has PATMAB(INT) and R has PATMAB(INT) +--R patternMatch : (%,Pattern(Float),PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if OrderedVariableList(vl) has PATMAB(FLOAT) and R has PATMAB(FLOAT) +--R pomopo! : (%,R,DirectProduct(#(vl),NonNegativeInteger),%) -> % +--R prime? : % -> Boolean if R has PFECAT +--R primitivePart : (%,OrderedVariableList(vl)) -> % if R has GCDDOM +--R primitivePart : % -> % if R has GCDDOM +--R reducedSystem : Matrix(%) -> Matrix(R) +--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(R),vec: Vector(R)) +--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(Integer),vec: Vector(Integer)) if R has LINEXP(INT) +--R reducedSystem : Matrix(%) -> Matrix(Integer) if R has LINEXP(INT) +--R resultant : (%,%,OrderedVariableList(vl)) -> % if R has COMRING +--R retract : % -> OrderedVariableList(vl) +--R retract : % -> Integer if R has RETRACT(INT) +--R retract : % -> Fraction(Integer) if R has RETRACT(FRAC(INT)) +--R retractIfCan : % -> Union(OrderedVariableList(vl),"failed") +--R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT(INT) +--R retractIfCan : % -> Union(Fraction(Integer),"failed") if R has RETRACT(FRAC(INT)) +--R retractIfCan : % -> Union(R,"failed") +--R solveLinearPolynomialEquation : (List(SparseUnivariatePolynomial(%)),SparseUnivariatePolynomial(%)) -> Union(List(SparseUnivariatePolynomial(%)),"failed") if R has PFECAT +--R squareFree : % -> Factored(%) if R has GCDDOM +--R squareFreePart : % -> % if R has GCDDOM +--R squareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has PFECAT +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R totalDegree : (%,List(OrderedVariableList(vl))) -> NonNegativeInteger +--R totalDegree : % -> NonNegativeInteger +--R unit? : % -> Boolean if R has INTDOM +--R unitCanonical : % -> % if R has INTDOM +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) if R has INTDOM +--R univariate : % -> SparseUnivariatePolynomial(R) +--R univariate : (%,OrderedVariableList(vl)) -> SparseUnivariatePolynomial(%) +--R variables : % -> List(OrderedVariableList(vl)) +--R +--E 11 + )spool )lisp (bye) \end{chunk} @@ -35127,24 +36492,23 @@ DistributedMultivariatePolynomial(vl,R): public == private where --R------------------------------- Operations -------------------------------- --R ?*? : (Integer,S) -> % ?*? : (Integer,%) -> % --R ?*? : (%,Integer) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?+? : (S,%) -> % ---R ?+? : (%,%) -> % ?-? : (%,%) -> % ---R -? : % -> % ?<=? : (%,%) -> Boolean ---R ?=? : (%,%) -> Boolean 0 : () -> % ---R coefficient : (S,%) -> Integer coerce : S -> % ---R coerce : % -> OutputForm collect : % -> % ---R concat : (%,%) -> % degree : % -> Integer ---R divOfPole : % -> % divOfZero : % -> % ---R effective? : % -> Boolean hash : % -> SingleInteger ---R incr : % -> % latex : % -> String ---R mapGen : ((S -> S),%) -> % nthCoef : (%,Integer) -> Integer ---R nthFactor : (%,Integer) -> S reductum : % -> % ---R retract : % -> S sample : () -> % ---R size : % -> NonNegativeInteger split : % -> List(%) ---R supp : % -> List(S) suppOfPole : % -> List(S) ---R suppOfZero : % -> List(S) zero? : % -> Boolean ---R ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?+? : (S,%) -> % ?+? : (%,%) -> % +--R ?-? : (%,%) -> % -? : % -> % +--R ?<=? : (%,%) -> Boolean ?=? : (%,%) -> Boolean +--R 0 : () -> % coefficient : (S,%) -> Integer +--R coerce : S -> % coerce : % -> OutputForm +--R collect : % -> % concat : (%,%) -> % +--R degree : % -> Integer divOfPole : % -> % +--R divOfZero : % -> % effective? : % -> Boolean +--R hash : % -> SingleInteger incr : % -> % +--R latex : % -> String mapGen : ((S -> S),%) -> % +--R nthCoef : (%,Integer) -> Integer nthFactor : (%,Integer) -> S +--R reductum : % -> % retract : % -> S +--R sample : () -> % size : % -> NonNegativeInteger +--R split : % -> List(%) supp : % -> List(S) +--R suppOfPole : % -> List(S) suppOfZero : % -> List(S) +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean --R head : % -> Record(gen: S,exp: Integer) --R highCommonTerms : (%,%) -> % if Integer has OAMON --R mapCoef : ((Integer -> Integer),%) -> % @@ -35526,7 +36890,7 @@ which just returns a list of the multiple values from the )set message auto off )clear all ---S 1 of 13 +--S 1 of 14 2.71828 --R --R @@ -35534,7 +36898,7 @@ which just returns a list of the multiple values from the --R Type: Float --E 1 ---S 2 of 13 +--S 2 of 14 2.71828@DoubleFloat --R --R @@ -35542,7 +36906,7 @@ which just returns a list of the multiple values from the --R Type: DoubleFloat --E 2 ---S 3 of 13 +--S 3 of 14 2.71828 :: DoubleFloat --R --R @@ -35550,7 +36914,7 @@ which just returns a list of the multiple values from the --R Type: DoubleFloat --E 3 ---S 4 of 13 +--S 4 of 14 eApprox : DoubleFloat := 2.71828 --R --R @@ -35558,13 +36922,13 @@ eApprox : DoubleFloat := 2.71828 --R Type: DoubleFloat --E 4 ---S 5 of 13 +--S 5 of 14 avg : List DoubleFloat -> DoubleFloat --R --R Type: Void --E 5 ---S 6 of 13 +--S 6 of 14 avg l == empty? l => 0 :: DoubleFloat reduce(_+,l) / #l @@ -35572,7 +36936,7 @@ avg l == --R Type: Void --E 6 ---S 7 of 13 +--S 7 of 14 avg [] --R --R Compiling function avg with type List(DoubleFloat) -> DoubleFloat @@ -35581,7 +36945,7 @@ avg [] --R Type: DoubleFloat --E 7 ---S 8 of 13 +--S 8 of 14 avg [3.4,9.7,-6.8] --R --R @@ -35589,7 +36953,7 @@ avg [3.4,9.7,-6.8] --R Type: DoubleFloat --E 8 ---S 9 of 13 +--S 9 of 14 cos(3.1415926)$DoubleFloat --R --R @@ -35597,7 +36961,7 @@ cos(3.1415926)$DoubleFloat --R Type: DoubleFloat --E 9 ---S 10 of 13 +--S 10 of 14 cos(3.1415926 :: DoubleFloat) --R --R @@ -35605,7 +36969,7 @@ cos(3.1415926 :: DoubleFloat) --R Type: DoubleFloat --E 10 ---S 11 of 13 +--S 11 of 14 a:DFLOAT := -1.0/3.0 --R --R @@ -35613,7 +36977,7 @@ a:DFLOAT := -1.0/3.0 --R Type: DoubleFloat --E 11 ---S 12 of 13 +--S 12 of 14 integerDecode a --R --R @@ -35621,7 +36985,7 @@ integerDecode a --R Type: List(Integer) --E 12 ---S 13 of 13 +--S 13 of 14 machineFraction a --R --R @@ -35631,6 +36995,115 @@ machineFraction a --R Type: Fraction(Integer) --E 13 +--S 14 of 14 +)show DoubleFloat +--R +--R DoubleFloat is a domain constructor +--R Abbreviation for DoubleFloat is DFLOAT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for DFLOAT +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (Fraction(Integer),%) -> % ?*? : (%,Fraction(Integer)) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,%) -> % ?**? : (%,Fraction(Integer)) -> % +--R ?**? : (%,Integer) -> % ?**? : (%,NonNegativeInteger) -> % +--R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % +--R ?-? : (%,%) -> % -? : % -> % +--R ?/? : (%,Integer) -> % ?/? : (%,%) -> % +--R ? Boolean ?<=? : (%,%) -> Boolean +--R ?=? : (%,%) -> Boolean ?>? : (%,%) -> Boolean +--R ?>=? : (%,%) -> Boolean Beta : (%,%) -> % +--R D : % -> % D : (%,NonNegativeInteger) -> % +--R Gamma : (%,%) -> % Gamma : % -> % +--R OMwrite : (%,Boolean) -> String OMwrite : % -> String +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,Integer) -> % ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,PositiveInteger) -> % abs : % -> % +--R acos : % -> % acosh : % -> % +--R acot : % -> % acoth : % -> % +--R acsc : % -> % acsch : % -> % +--R airyAi : % -> % airyBi : % -> % +--R asec : % -> % asech : % -> % +--R asin : % -> % asinh : % -> % +--R associates? : (%,%) -> Boolean atan : (%,%) -> % +--R atan : % -> % atanh : % -> % +--R base : () -> PositiveInteger besselI : (%,%) -> % +--R besselJ : (%,%) -> % besselK : (%,%) -> % +--R besselY : (%,%) -> % bits : () -> PositiveInteger +--R ceiling : % -> % coerce : Fraction(Integer) -> % +--R coerce : Integer -> % coerce : Fraction(Integer) -> % +--R coerce : % -> % coerce : Integer -> % +--R coerce : % -> OutputForm convert : % -> InputForm +--R convert : % -> Pattern(Float) convert : % -> DoubleFloat +--R convert : % -> Float cos : % -> % +--R cosh : % -> % cot : % -> % +--R coth : % -> % csc : % -> % +--R csch : % -> % differentiate : % -> % +--R digamma : % -> % digits : () -> PositiveInteger +--R doubleFloatFormat : String -> String exp : % -> % +--R exp1 : () -> % exponent : % -> Integer +--R factor : % -> Factored(%) float : (Integer,Integer) -> % +--R floor : % -> % fractionPart : % -> % +--R gcd : List(%) -> % gcd : (%,%) -> % +--R hash : % -> Integer hash : % -> SingleInteger +--R integerDecode : % -> List(Integer) inv : % -> % +--R latex : % -> String lcm : List(%) -> % +--R lcm : (%,%) -> % log : % -> % +--R log10 : % -> % log2 : % -> % +--R mantissa : % -> Integer max : (%,%) -> % +--R min : (%,%) -> % negative? : % -> Boolean +--R norm : % -> % nthRoot : (%,Integer) -> % +--R one? : % -> Boolean order : % -> Integer +--R pi : () -> % polygamma : (%,%) -> % +--R positive? : % -> Boolean precision : () -> PositiveInteger +--R prime? : % -> Boolean ?quo? : (%,%) -> % +--R recip : % -> Union(%,"failed") ?rem? : (%,%) -> % +--R retract : % -> Fraction(Integer) retract : % -> Integer +--R round : % -> % sample : () -> % +--R sec : % -> % sech : % -> % +--R sign : % -> Integer sin : % -> % +--R sinh : % -> % sizeLess? : (%,%) -> Boolean +--R sqrt : % -> % squareFree : % -> Factored(%) +--R squareFreePart : % -> % tan : % -> % +--R tanh : % -> % truncate : % -> % +--R unit? : % -> Boolean unitCanonical : % -> % +--R wholePart : % -> Integer zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R OMwrite : (OpenMathDevice,%,Boolean) -> Void +--R OMwrite : (OpenMathDevice,%) -> Void +--R bits : PositiveInteger -> PositiveInteger if $ has arbitraryPrecision +--R characteristic : () -> NonNegativeInteger +--R decreasePrecision : Integer -> PositiveInteger if $ has arbitraryPrecision +--R differentiate : (%,NonNegativeInteger) -> % +--R digits : PositiveInteger -> PositiveInteger if $ has arbitraryPrecision +--R divide : (%,%) -> Record(quotient: %,remainder: %) +--R euclideanSize : % -> NonNegativeInteger +--R expressIdealMember : (List(%),%) -> Union(List(%),"failed") +--R exquo : (%,%) -> Union(%,"failed") +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) +--R float : (Integer,Integer,PositiveInteger) -> % +--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) +--R increasePrecision : Integer -> PositiveInteger if $ has arbitraryPrecision +--R lcmCoef : (%,%) -> Record(llcmres: %,coeff1: %,coeff2: %) +--R machineFraction : % -> Fraction(Integer) +--R max : () -> % if not(has($,arbitraryExponent)) and not(has($,arbitraryPrecision)) +--R min : () -> % if not(has($,arbitraryExponent)) and not(has($,arbitraryPrecision)) +--R multiEuclidean : (List(%),%) -> Union(List(%),"failed") +--R patternMatch : (%,Pattern(Float),PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) +--R precision : PositiveInteger -> PositiveInteger if $ has arbitraryPrecision +--R principalIdeal : List(%) -> Record(coef: List(%),generator: %) +--R rationalApproximation : (%,NonNegativeInteger,NonNegativeInteger) -> Fraction(Integer) +--R rationalApproximation : (%,NonNegativeInteger) -> Fraction(Integer) +--R retractIfCan : % -> Union(Fraction(Integer),"failed") +--R retractIfCan : % -> Union(Integer,"failed") +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) +--R +--E 14 + )spool )lisp (bye) @@ -36255,25 +37728,25 @@ DoubleFloat(): Join(FloatingPointSystem, DifferentialRing, OpenMath, --R------------------------------- Operations -------------------------------- --R ?*? : (Integer,%) -> % ?*? : (%,DoubleFloat) -> % --R ?*? : (DoubleFloat,%) -> % ?*? : (%,%) -> % ---R ?+? : (%,%) -> % -? : % -> % ---R ?-? : (%,%) -> % antisymmetric? : % -> Boolean ---R coerce : DoubleFloatVector -> % copy : % -> % ---R diagonal? : % -> Boolean diagonalMatrix : List(%) -> % ---R empty : () -> % empty? : % -> Boolean ---R eq? : (%,%) -> Boolean fill! : (%,DoubleFloat) -> % ---R horizConcat : (%,%) -> % maxColIndex : % -> Integer ---R maxRowIndex : % -> Integer minColIndex : % -> Integer ---R minRowIndex : % -> Integer ncols : % -> NonNegativeInteger ---R nrows : % -> NonNegativeInteger parts : % -> List(DoubleFloat) ---R qnew : (Integer,Integer) -> % sample : () -> % ---R square? : % -> Boolean squareTop : % -> % ---R symmetric? : % -> Boolean transpose : % -> % +--R ?**? : (%,NonNegativeInteger) -> % ?+? : (%,%) -> % +--R -? : % -> % ?-? : (%,%) -> % +--R antisymmetric? : % -> Boolean coerce : DoubleFloatVector -> % +--R copy : % -> % diagonal? : % -> Boolean +--R diagonalMatrix : List(%) -> % empty : () -> % +--R empty? : % -> Boolean eq? : (%,%) -> Boolean +--R fill! : (%,DoubleFloat) -> % horizConcat : (%,%) -> % +--R maxColIndex : % -> Integer maxRowIndex : % -> Integer +--R minColIndex : % -> Integer minRowIndex : % -> Integer +--R ncols : % -> NonNegativeInteger nrows : % -> NonNegativeInteger +--R parts : % -> List(DoubleFloat) qnew : (Integer,Integer) -> % +--R sample : () -> % square? : % -> Boolean +--R squareTop : % -> % symmetric? : % -> Boolean +--R transpose : % -> % transpose : DoubleFloatVector -> % --R vertConcat : (%,%) -> % --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R ?*? : (DoubleFloatVector,%) -> DoubleFloatVector --R ?*? : (%,DoubleFloatVector) -> DoubleFloatVector --R ?**? : (%,Integer) -> % if DoubleFloat has FIELD ---R ?**? : (%,NonNegativeInteger) -> % --R ?/? : (%,DoubleFloat) -> % if DoubleFloat has FIELD --R ?=? : (%,%) -> Boolean if DoubleFloat has SETCAT --R any? : ((DoubleFloat -> Boolean),%) -> Boolean if $ has finiteAggregate @@ -36327,7 +37800,6 @@ DoubleFloat(): Join(FloatingPointSystem, DifferentialRing, OpenMath, --R subMatrix : (%,Integer,Integer,Integer,Integer) -> % --R swapColumns! : (%,Integer,Integer) -> % --R swapRows! : (%,Integer,Integer) -> % ---R transpose : DoubleFloatVector -> % --R zero : (NonNegativeInteger,NonNegativeInteger) -> % --R ?~=? : (%,%) -> Boolean if DoubleFloat has SETCAT --R @@ -36581,13 +38053,14 @@ DoubleFloatMatrix : MatrixCategory(DoubleFloat, --R------------------------------- Operations -------------------------------- --R concat : List(%) -> % concat : (%,%) -> % --R concat : (DoubleFloat,%) -> % concat : (%,DoubleFloat) -> % ---R copy : % -> % delete : (%,Integer) -> % ---R ?.? : (%,Integer) -> DoubleFloat empty : () -> % ---R empty? : % -> Boolean entries : % -> List(DoubleFloat) ---R eq? : (%,%) -> Boolean index? : (Integer,%) -> Boolean ---R indices : % -> List(Integer) insert : (%,%,Integer) -> % ---R qelt : (%,Integer) -> DoubleFloat qnew : Integer -> % ---R reverse : % -> % sample : () -> % +--R construct : List(DoubleFloat) -> % copy : % -> % +--R delete : (%,Integer) -> % ?.? : (%,Integer) -> DoubleFloat +--R empty : () -> % empty? : % -> Boolean +--R entries : % -> List(DoubleFloat) eq? : (%,%) -> Boolean +--R index? : (Integer,%) -> Boolean indices : % -> List(Integer) +--R insert : (%,%,Integer) -> % qelt : (%,Integer) -> DoubleFloat +--R qnew : Integer -> % reverse : % -> % +--R sample : () -> % --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R ?*? : (%,DoubleFloat) -> % if DoubleFloat has MONOID --R ?*? : (DoubleFloat,%) -> % if DoubleFloat has MONOID @@ -36602,7 +38075,6 @@ DoubleFloatMatrix : MatrixCategory(DoubleFloat, --R ?>=? : (%,%) -> Boolean if DoubleFloat has ORDSET --R any? : ((DoubleFloat -> Boolean),%) -> Boolean if $ has finiteAggregate --R coerce : % -> OutputForm if DoubleFloat has SETCAT ---R construct : List(DoubleFloat) -> % --R convert : % -> InputForm if DoubleFloat has KONVERT(INFORM) --R copyInto! : (%,%,Integer) -> % if $ has shallowlyMutable --R count : (DoubleFloat,%) -> NonNegativeInteger if $ has finiteAggregate and DoubleFloat has SETCAT @@ -36896,11 +38368,11 @@ DoubleFloatVector : VectorCategory DoubleFloat with --R curveColor : Float -> % hash : % -> SingleInteger --R latex : % -> String pointColor : Palette -> % --R pointColor : Float -> % range : List(Segment(Float)) -> % ---R style : String -> % title : String -> % ---R toScale : Boolean -> % tubePoints : PositiveInteger -> % ---R tubeRadius : Float -> % unit : List(Float) -> % ---R var1Steps : PositiveInteger -> % var2Steps : PositiveInteger -> % ---R ?~=? : (%,%) -> Boolean +--R ranges : List(Segment(Float)) -> % style : String -> % +--R title : String -> % toScale : Boolean -> % +--R tubePoints : PositiveInteger -> % tubeRadius : Float -> % +--R unit : List(Float) -> % var1Steps : PositiveInteger -> % +--R var2Steps : PositiveInteger -> % ?~=? : (%,%) -> Boolean --R colorFunction : ((DoubleFloat,DoubleFloat,DoubleFloat) -> DoubleFloat) -> % --R colorFunction : ((DoubleFloat,DoubleFloat) -> DoubleFloat) -> % --R colorFunction : (DoubleFloat -> DoubleFloat) -> % @@ -36909,7 +38381,6 @@ DoubleFloatVector : VectorCategory DoubleFloat with --R option : (List(%),Symbol) -> Union(Any,"failed") --R option? : (List(%),Symbol) -> Boolean --R range : List(Segment(Fraction(Integer))) -> % ---R ranges : List(Segment(Float)) -> % --R space : ThreeSpace(DoubleFloat) -> % --R viewpoint : Record(theta: DoubleFloat,phi: DoubleFloat,scale: DoubleFloat,scaleX: DoubleFloat,scaleY: DoubleFloat,scaleZ: DoubleFloat,deltaX: DoubleFloat,deltaY: DoubleFloat) -> % --R @@ -39675,6 +41146,55 @@ d03fafAnnaType():PartialDifferentialEquationsSolverCategory == Result add --S 1 of 1 )show ElementaryFunctionsUnivariateLaurentSeries +--R +--R ElementaryFunctionsUnivariateLaurentSeries(Coef: Algebra(Fraction(Integer)),UTS: UnivariateTaylorSeriesCategory(Coef),ULS: UnivariateLaurentSeriesConstructorCategory(Coef,UTS)) is a domain constructor +--R Abbreviation for ElementaryFunctionsUnivariateLaurentSeries is EFULS +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for EFULS +--R +--R------------------------------- Operations -------------------------------- +--R acos : ULS -> ULS acosh : ULS -> ULS +--R acot : ULS -> ULS acoth : ULS -> ULS +--R acsc : ULS -> ULS acsch : ULS -> ULS +--R asec : ULS -> ULS asech : ULS -> ULS +--R asin : ULS -> ULS asinh : ULS -> ULS +--R atan : ULS -> ULS atanh : ULS -> ULS +--R cos : ULS -> ULS cosh : ULS -> ULS +--R cot : ULS -> ULS coth : ULS -> ULS +--R csc : ULS -> ULS csch : ULS -> ULS +--R exp : ULS -> ULS log : ULS -> ULS +--R sec : ULS -> ULS sech : ULS -> ULS +--R sin : ULS -> ULS sinh : ULS -> ULS +--R tan : ULS -> ULS tanh : ULS -> ULS +--R ?**? : (ULS,Fraction(Integer)) -> ULS if Coef has FIELD +--R acosIfCan : ULS -> Union(ULS,"failed") +--R acoshIfCan : ULS -> Union(ULS,"failed") +--R acotIfCan : ULS -> Union(ULS,"failed") +--R acothIfCan : ULS -> Union(ULS,"failed") +--R acscIfCan : ULS -> Union(ULS,"failed") +--R acschIfCan : ULS -> Union(ULS,"failed") +--R asecIfCan : ULS -> Union(ULS,"failed") +--R asechIfCan : ULS -> Union(ULS,"failed") +--R asinIfCan : ULS -> Union(ULS,"failed") +--R asinhIfCan : ULS -> Union(ULS,"failed") +--R atanIfCan : ULS -> Union(ULS,"failed") +--R atanhIfCan : ULS -> Union(ULS,"failed") +--R cosIfCan : ULS -> Union(ULS,"failed") +--R coshIfCan : ULS -> Union(ULS,"failed") +--R cotIfCan : ULS -> Union(ULS,"failed") +--R cothIfCan : ULS -> Union(ULS,"failed") +--R cscIfCan : ULS -> Union(ULS,"failed") +--R cschIfCan : ULS -> Union(ULS,"failed") +--R expIfCan : ULS -> Union(ULS,"failed") +--R logIfCan : ULS -> Union(ULS,"failed") +--R nthRootIfCan : (ULS,NonNegativeInteger) -> Union(ULS,"failed") +--R secIfCan : ULS -> Union(ULS,"failed") +--R sechIfCan : ULS -> Union(ULS,"failed") +--R sinIfCan : ULS -> Union(ULS,"failed") +--R sinhIfCan : ULS -> Union(ULS,"failed") +--R tanIfCan : ULS -> Union(ULS,"failed") +--R tanhIfCan : ULS -> Union(ULS,"failed") +--R --E 1 )spool @@ -40120,6 +41640,55 @@ ElementaryFunctionsUnivariateLaurentSeries(Coef,UTS,ULS):_ --S 1 of 1 )show ElementaryFunctionsUnivariatePuiseuxSeries +--R +--R ElementaryFunctionsUnivariatePuiseuxSeries(Coef: Algebra(Fraction(Integer)),ULS: UnivariateLaurentSeriesCategory(Coef),UPXS: UnivariatePuiseuxSeriesConstructorCategory(Coef,ULS),EFULS: PartialTranscendentalFunctions(ULS)) is a domain constructor +--R Abbreviation for ElementaryFunctionsUnivariatePuiseuxSeries is EFUPXS +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for EFUPXS +--R +--R------------------------------- Operations -------------------------------- +--R acos : UPXS -> UPXS acosh : UPXS -> UPXS +--R acot : UPXS -> UPXS acoth : UPXS -> UPXS +--R acsc : UPXS -> UPXS acsch : UPXS -> UPXS +--R asec : UPXS -> UPXS asech : UPXS -> UPXS +--R asin : UPXS -> UPXS asinh : UPXS -> UPXS +--R atan : UPXS -> UPXS atanh : UPXS -> UPXS +--R cos : UPXS -> UPXS cosh : UPXS -> UPXS +--R cot : UPXS -> UPXS coth : UPXS -> UPXS +--R csc : UPXS -> UPXS csch : UPXS -> UPXS +--R exp : UPXS -> UPXS log : UPXS -> UPXS +--R sec : UPXS -> UPXS sech : UPXS -> UPXS +--R sin : UPXS -> UPXS sinh : UPXS -> UPXS +--R tan : UPXS -> UPXS tanh : UPXS -> UPXS +--R ?**? : (UPXS,Fraction(Integer)) -> UPXS if Coef has FIELD +--R acosIfCan : UPXS -> Union(UPXS,"failed") +--R acoshIfCan : UPXS -> Union(UPXS,"failed") +--R acotIfCan : UPXS -> Union(UPXS,"failed") +--R acothIfCan : UPXS -> Union(UPXS,"failed") +--R acscIfCan : UPXS -> Union(UPXS,"failed") +--R acschIfCan : UPXS -> Union(UPXS,"failed") +--R asecIfCan : UPXS -> Union(UPXS,"failed") +--R asechIfCan : UPXS -> Union(UPXS,"failed") +--R asinIfCan : UPXS -> Union(UPXS,"failed") +--R asinhIfCan : UPXS -> Union(UPXS,"failed") +--R atanIfCan : UPXS -> Union(UPXS,"failed") +--R atanhIfCan : UPXS -> Union(UPXS,"failed") +--R cosIfCan : UPXS -> Union(UPXS,"failed") +--R coshIfCan : UPXS -> Union(UPXS,"failed") +--R cotIfCan : UPXS -> Union(UPXS,"failed") +--R cothIfCan : UPXS -> Union(UPXS,"failed") +--R cscIfCan : UPXS -> Union(UPXS,"failed") +--R cschIfCan : UPXS -> Union(UPXS,"failed") +--R expIfCan : UPXS -> Union(UPXS,"failed") +--R logIfCan : UPXS -> Union(UPXS,"failed") +--R nthRootIfCan : (UPXS,NonNegativeInteger) -> Union(UPXS,"failed") +--R secIfCan : UPXS -> Union(UPXS,"failed") +--R sechIfCan : UPXS -> Union(UPXS,"failed") +--R sinIfCan : UPXS -> Union(UPXS,"failed") +--R sinhIfCan : UPXS -> Union(UPXS,"failed") +--R tanIfCan : UPXS -> Union(UPXS,"failed") +--R tanhIfCan : UPXS -> Union(UPXS,"failed") +--R --E 1 )spool @@ -40478,7 +42047,8 @@ ElementaryFunctionsUnivariatePuiseuxSeries(Coef,ULS,UPXS,EFULS):_ )set message test on )set message auto off )clear all ---S 1 of 12 + +--S 1 of 13 eq1 := 3*x + 4*y = 5 --R --R @@ -40486,7 +42056,7 @@ eq1 := 3*x + 4*y = 5 --R Type: Equation(Polynomial(Integer)) --E 1 ---S 2 of 12 +--S 2 of 13 eq2 := 2*x + 2*y = 3 --R --R @@ -40494,7 +42064,7 @@ eq2 := 2*x + 2*y = 3 --R Type: Equation(Polynomial(Integer)) --E 2 ---S 3 of 12 +--S 3 of 13 lhs eq1 --R --R @@ -40502,7 +42072,7 @@ lhs eq1 --R Type: Polynomial(Integer) --E 3 ---S 4 of 12 +--S 4 of 13 rhs eq1 --R --R @@ -40510,7 +42080,7 @@ rhs eq1 --R Type: Polynomial(Integer) --E 4 ---S 5 of 12 +--S 5 of 13 eq1 + eq2 --R --R @@ -40518,7 +42088,7 @@ eq1 + eq2 --R Type: Equation(Polynomial(Integer)) --E 5 ---S 6 of 12 +--S 6 of 13 eq1 * eq2 --R --R @@ -40527,7 +42097,7 @@ eq1 * eq2 --R Type: Equation(Polynomial(Integer)) --E 6 ---S 7 of 12 +--S 7 of 13 2*eq2 - eq1 --R --R @@ -40535,7 +42105,7 @@ eq1 * eq2 --R Type: Equation(Polynomial(Integer)) --E 7 ---S 8 of 12 +--S 8 of 13 eq1**2 --R --R @@ -40544,7 +42114,7 @@ eq1**2 --R Type: Equation(Polynomial(Integer)) --E 8 ---S 9 of 12 +--S 9 of 13 if x+1 = y then "equal" else "unequal" --R --R @@ -40552,7 +42122,7 @@ if x+1 = y then "equal" else "unequal" --R Type: String --E 9 ---S 10 of 12 +--S 10 of 13 eqpol := x+1 = y --R --R @@ -40560,7 +42130,7 @@ eqpol := x+1 = y --R Type: Equation(Polynomial(Integer)) --E 10 ---S 11 of 12 +--S 11 of 13 if eqpol then "equal" else "unequal" --R --R @@ -40568,13 +42138,78 @@ if eqpol then "equal" else "unequal" --R Type: String --E 11 ---S 12 of 12 +--S 12 of 13 eqpol::Boolean --R --R --R (12) false --R Type: Boolean --E 12 + +--S 13 of 13 +)show Equation +--R +--R Equation(S: Type) is a domain constructor +--R Abbreviation for Equation is EQ +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for EQ +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,%) -> % if S has SGROUP ?*? : (S,%) -> % if S has SGROUP +--R ?*? : (%,S) -> % if S has SGROUP ?+? : (%,%) -> % if S has ABELSG +--R ?+? : (%,S) -> % if S has ABELSG ?+? : (S,%) -> % if S has ABELSG +--R -? : % -> % if S has ABELGRP ?-? : (%,%) -> % if S has ABELGRP +--R ?-? : (%,S) -> % if S has ABELGRP ?-? : (S,%) -> % if S has ABELGRP +--R ?/? : (%,S) -> % if S has FIELD ?=? : (S,S) -> % +--R 1 : () -> % if S has MONOID 0 : () -> % if S has ABELGRP +--R coerce : Integer -> % if S has RING equation : (S,S) -> % +--R latex : % -> String if S has SETCAT leftZero : % -> % if S has ABELGRP +--R lhs : % -> S map : ((S -> S),%) -> % +--R one? : % -> Boolean if S has MONOID rhs : % -> S +--R subst : (%,%) -> % if S has ES swap : % -> % +--R ?*? : (PositiveInteger,%) -> % if S has ABELSG +--R ?*? : (NonNegativeInteger,%) -> % if S has ABELGRP +--R ?*? : (Integer,%) -> % if S has ABELGRP +--R ?**? : (%,PositiveInteger) -> % if S has SGROUP +--R ?**? : (%,NonNegativeInteger) -> % if S has MONOID +--R ?**? : (%,Integer) -> % if S has GROUP +--R ?/? : (%,%) -> % if S has FIELD or S has GROUP +--R ?=? : (%,%) -> Boolean if S has SETCAT +--R D : (%,Symbol) -> % if S has PDRING(SYMBOL) +--R D : (%,List(Symbol)) -> % if S has PDRING(SYMBOL) +--R D : (%,Symbol,NonNegativeInteger) -> % if S has PDRING(SYMBOL) +--R D : (%,List(Symbol),List(NonNegativeInteger)) -> % if S has PDRING(SYMBOL) +--R ?^? : (%,PositiveInteger) -> % if S has SGROUP +--R ?^? : (%,NonNegativeInteger) -> % if S has MONOID +--R ?^? : (%,Integer) -> % if S has GROUP +--R characteristic : () -> NonNegativeInteger if S has RING +--R coerce : % -> OutputForm if S has SETCAT +--R coerce : % -> Boolean if S has SETCAT +--R commutator : (%,%) -> % if S has GROUP +--R conjugate : (%,%) -> % if S has GROUP +--R differentiate : (%,Symbol) -> % if S has PDRING(SYMBOL) +--R differentiate : (%,List(Symbol)) -> % if S has PDRING(SYMBOL) +--R differentiate : (%,Symbol,NonNegativeInteger) -> % if S has PDRING(SYMBOL) +--R differentiate : (%,List(Symbol),List(NonNegativeInteger)) -> % if S has PDRING(SYMBOL) +--R dimension : () -> CardinalNumber if S has FIELD +--R eval : (%,List(Symbol),List(S)) -> % if S has IEVALAB(SYMBOL,S) +--R eval : (%,Symbol,S) -> % if S has IEVALAB(SYMBOL,S) +--R eval : (%,List(%)) -> % if S has EVALAB(S) and S has SETCAT +--R eval : (%,%) -> % if S has EVALAB(S) and S has SETCAT +--R factorAndSplit : % -> List(%) if S has INTDOM +--R hash : % -> SingleInteger if S has SETCAT +--R inv : % -> % if S has FIELD or S has GROUP +--R leftOne : % -> Union(%,"failed") if S has MONOID +--R recip : % -> Union(%,"failed") if S has MONOID +--R rightOne : % -> Union(%,"failed") if S has MONOID +--R rightZero : % -> % if S has ABELGRP +--R sample : () -> % if S has ABELGRP or S has MONOID +--R subtractIfCan : (%,%) -> Union(%,"failed") if S has ABELGRP +--R zero? : % -> Boolean if S has ABELGRP +--R ?~=? : (%,%) -> Boolean if S has SETCAT +--R +--E 13 + )spool )lisp (bye) \end{chunk} @@ -40929,7 +42564,8 @@ Equation(S: Type): public == private where )set message test on )set message auto off )clear all ---S 1 of 6 + +--S 1 of 7 e: EqTable(List Integer, Integer) := table() --R --R @@ -40937,7 +42573,7 @@ e: EqTable(List Integer, Integer) := table() --R Type: EqTable(List(Integer),Integer) --E 1 ---S 2 of 6 +--S 2 of 7 l1 := [1,2,3] --R --R @@ -40945,7 +42581,7 @@ l1 := [1,2,3] --R Type: List(PositiveInteger) --E 2 ---S 3 of 6 +--S 3 of 7 l2 := [1,2,3] --R --R @@ -40953,7 +42589,7 @@ l2 := [1,2,3] --R Type: List(PositiveInteger) --E 3 ---S 4 of 6 +--S 4 of 7 e.l1 := 111 --R --R @@ -40961,7 +42597,7 @@ e.l1 := 111 --R Type: PositiveInteger --E 4 ---S 5 of 6 +--S 5 of 7 e.l2 := 222 --R --R @@ -40969,13 +42605,98 @@ e.l2 := 222 --R Type: PositiveInteger --E 5 ---S 6 of 6 +--S 6 of 7 e.l1 --R --R --R (6) 111 --R Type: PositiveInteger --E 6 + +--S 7 of 7 +)show EqTable +--R +--R EqTable(Key: SetCategory,Entry: SetCategory) is a domain constructor +--R Abbreviation for EqTable is EQTBL +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for EQTBL +--R +--R------------------------------- Operations -------------------------------- +--R copy : % -> % dictionary : () -> % +--R elt : (%,Key,Entry) -> Entry ?.? : (%,Key) -> Entry +--R empty : () -> % empty? : % -> Boolean +--R entries : % -> List(Entry) eq? : (%,%) -> Boolean +--R index? : (Key,%) -> Boolean indices : % -> List(Key) +--R key? : (Key,%) -> Boolean keys : % -> List(Key) +--R map : ((Entry -> Entry),%) -> % qelt : (%,Key) -> Entry +--R sample : () -> % setelt : (%,Key,Entry) -> Entry +--R table : () -> % +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R ?=? : (%,%) -> Boolean if Record(key: Key,entry: Entry) has SETCAT or Entry has SETCAT +--R any? : ((Entry -> Boolean),%) -> Boolean if $ has finiteAggregate +--R any? : ((Record(key: Key,entry: Entry) -> Boolean),%) -> Boolean if $ has finiteAggregate +--R bag : List(Record(key: Key,entry: Entry)) -> % +--R coerce : % -> OutputForm if Record(key: Key,entry: Entry) has SETCAT or Entry has SETCAT +--R construct : List(Record(key: Key,entry: Entry)) -> % +--R convert : % -> InputForm if Record(key: Key,entry: Entry) has KONVERT(INFORM) +--R count : ((Entry -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R count : (Entry,%) -> NonNegativeInteger if $ has finiteAggregate and Entry has SETCAT +--R count : (Record(key: Key,entry: Entry),%) -> NonNegativeInteger if $ has finiteAggregate and Record(key: Key,entry: Entry) has SETCAT +--R count : ((Record(key: Key,entry: Entry) -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R dictionary : List(Record(key: Key,entry: Entry)) -> % +--R entry? : (Entry,%) -> Boolean if $ has finiteAggregate and Entry has SETCAT +--R eval : (%,List(Equation(Entry))) -> % if Entry has EVALAB(Entry) and Entry has SETCAT +--R eval : (%,Equation(Entry)) -> % if Entry has EVALAB(Entry) and Entry has SETCAT +--R eval : (%,Entry,Entry) -> % if Entry has EVALAB(Entry) and Entry has SETCAT +--R eval : (%,List(Entry),List(Entry)) -> % if Entry has EVALAB(Entry) and Entry has SETCAT +--R eval : (%,List(Record(key: Key,entry: Entry)),List(Record(key: Key,entry: Entry))) -> % if Record(key: Key,entry: Entry) has EVALAB(Record(key: Key,entry: Entry)) and Record(key: Key,entry: Entry) has SETCAT +--R eval : (%,Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> % if Record(key: Key,entry: Entry) has EVALAB(Record(key: Key,entry: Entry)) and Record(key: Key,entry: Entry) has SETCAT +--R eval : (%,Equation(Record(key: Key,entry: Entry))) -> % if Record(key: Key,entry: Entry) has EVALAB(Record(key: Key,entry: Entry)) and Record(key: Key,entry: Entry) has SETCAT +--R eval : (%,List(Equation(Record(key: Key,entry: Entry)))) -> % if Record(key: Key,entry: Entry) has EVALAB(Record(key: Key,entry: Entry)) and Record(key: Key,entry: Entry) has SETCAT +--R every? : ((Entry -> Boolean),%) -> Boolean if $ has finiteAggregate +--R every? : ((Record(key: Key,entry: Entry) -> Boolean),%) -> Boolean if $ has finiteAggregate +--R extract! : % -> Record(key: Key,entry: Entry) +--R fill! : (%,Entry) -> % if $ has shallowlyMutable +--R find : ((Record(key: Key,entry: Entry) -> Boolean),%) -> Union(Record(key: Key,entry: Entry),"failed") +--R first : % -> Entry if Key has ORDSET +--R hash : % -> SingleInteger if Record(key: Key,entry: Entry) has SETCAT or Entry has SETCAT +--R insert! : (Record(key: Key,entry: Entry),%) -> % +--R inspect : % -> Record(key: Key,entry: Entry) +--R latex : % -> String if Record(key: Key,entry: Entry) has SETCAT or Entry has SETCAT +--R less? : (%,NonNegativeInteger) -> Boolean +--R map : (((Entry,Entry) -> Entry),%,%) -> % +--R map : ((Record(key: Key,entry: Entry) -> Record(key: Key,entry: Entry)),%) -> % +--R map! : ((Entry -> Entry),%) -> % if $ has shallowlyMutable +--R map! : ((Record(key: Key,entry: Entry) -> Record(key: Key,entry: Entry)),%) -> % if $ has shallowlyMutable +--R maxIndex : % -> Key if Key has ORDSET +--R member? : (Entry,%) -> Boolean if $ has finiteAggregate and Entry has SETCAT +--R member? : (Record(key: Key,entry: Entry),%) -> Boolean if $ has finiteAggregate and Record(key: Key,entry: Entry) has SETCAT +--R members : % -> List(Entry) if $ has finiteAggregate +--R members : % -> List(Record(key: Key,entry: Entry)) if $ has finiteAggregate +--R minIndex : % -> Key if Key has ORDSET +--R more? : (%,NonNegativeInteger) -> Boolean +--R parts : % -> List(Entry) if $ has finiteAggregate +--R parts : % -> List(Record(key: Key,entry: Entry)) if $ has finiteAggregate +--R qsetelt! : (%,Key,Entry) -> Entry if $ has shallowlyMutable +--R reduce : (((Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry)),%) -> Record(key: Key,entry: Entry) if $ has finiteAggregate +--R reduce : (((Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry)),%,Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry) if $ has finiteAggregate +--R reduce : (((Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry)),%,Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry) if $ has finiteAggregate and Record(key: Key,entry: Entry) has SETCAT +--R remove : ((Record(key: Key,entry: Entry) -> Boolean),%) -> % if $ has finiteAggregate +--R remove : (Record(key: Key,entry: Entry),%) -> % if $ has finiteAggregate and Record(key: Key,entry: Entry) has SETCAT +--R remove! : (Key,%) -> Union(Entry,"failed") +--R remove! : ((Record(key: Key,entry: Entry) -> Boolean),%) -> % if $ has finiteAggregate +--R remove! : (Record(key: Key,entry: Entry),%) -> % if $ has finiteAggregate +--R removeDuplicates : % -> % if $ has finiteAggregate and Record(key: Key,entry: Entry) has SETCAT +--R search : (Key,%) -> Union(Entry,"failed") +--R select : ((Record(key: Key,entry: Entry) -> Boolean),%) -> % if $ has finiteAggregate +--R select! : ((Record(key: Key,entry: Entry) -> Boolean),%) -> % if $ has finiteAggregate +--R size? : (%,NonNegativeInteger) -> Boolean +--R swap! : (%,Key,Key) -> Void if $ has shallowlyMutable +--R table : List(Record(key: Key,entry: Entry)) -> % +--R ?~=? : (%,%) -> Boolean if Record(key: Key,entry: Entry) has SETCAT or Entry has SETCAT +--R +--E 7 + )spool )lisp (bye) \end{chunk} @@ -41136,26 +42857,25 @@ EqTable(Key: SetCategory, Entry: SetCategory) == --R --R------------------------------- Operations -------------------------------- --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ?=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % associates? : (%,%) -> Boolean ---R coerce : % -> R coerce : % -> % ---R coerce : Integer -> % coerce : % -> OutputForm ---R ?.? : (%,R) -> R gcd : List(%) -> % ---R gcd : (%,%) -> % hash : % -> SingleInteger ---R inv : % -> % latex : % -> String ---R lcm : List(%) -> % lcm : (%,%) -> % ---R modulus : % -> Mod one? : % -> Boolean ---R ?quo? : (%,%) -> % recip : % -> Union(%,"failed") ---R reduce : (R,Mod) -> % ?rem? : (%,%) -> % ---R sample : () -> % sizeLess? : (%,%) -> Boolean ---R unit? : % -> Boolean unitCanonical : % -> % ---R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R associates? : (%,%) -> Boolean coerce : % -> R +--R coerce : % -> % coerce : Integer -> % +--R coerce : % -> OutputForm ?.? : (%,R) -> R +--R gcd : List(%) -> % gcd : (%,%) -> % +--R hash : % -> SingleInteger inv : % -> % +--R latex : % -> String lcm : List(%) -> % +--R lcm : (%,%) -> % modulus : % -> Mod +--R one? : % -> Boolean ?quo? : (%,%) -> % +--R recip : % -> Union(%,"failed") reduce : (R,Mod) -> % +--R ?rem? : (%,%) -> % sample : () -> % +--R sizeLess? : (%,%) -> Boolean unit? : % -> Boolean +--R unitCanonical : % -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean --R characteristic : () -> NonNegativeInteger --R divide : (%,%) -> Record(quotient: %,remainder: %) --R euclideanSize : % -> NonNegativeInteger @@ -41364,7 +43084,8 @@ EuclideanModularRing(S,R,Mod,reduction:(R,Mod) -> R, )set message test on )set message auto off )clear all ---S 1 + +--S 1 of 7 n := 0 --R --R @@ -41372,7 +43093,7 @@ n := 0 --R Type: NonNegativeInteger --E 1 ---S 2 +--S 2 of 7 gasp(): Exit == free n n := n + 1 @@ -41382,7 +43103,7 @@ gasp(): Exit == --R Type: Void --E 2 ---S 3 +--S 3 of 7 half(k) == if odd? k then gasp() else k quo 2 @@ -41390,7 +43111,7 @@ half(k) == --R Type: Void --E 3 ---S 4 +--S 4 of 7 half 4 --R --R Compiling function gasp with type () -> Exit @@ -41400,7 +43121,7 @@ half 4 --R Type: PositiveInteger --E 4 ---S 5 +--S 5 of 7 half 3 --R --R @@ -41409,13 +43130,29 @@ half 3 --R Oh no! --E 5 ---S 6 +--S 6 of 7 n --R --R --R (5) 1 --R Type: NonNegativeInteger --E 6 + +--S 7 of 7 +)show Exit +--R +--R Exit is a domain constructor +--R Abbreviation for Exit is EXIT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for EXIT +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R ?~=? : (%,%) -> Boolean +--R +--E 7 + )spool )lisp (bye) \end{chunk} @@ -41518,30 +43255,30 @@ Exit: SetCategory == add --R------------------------------- Operations -------------------------------- --R ?*? : (Fraction(Integer),%) -> % ?*? : (%,Fraction(Integer)) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,Integer) -> % ?**? : (%,NonNegativeInteger) -> % --R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % --R ?-? : (%,%) -> % -? : % -> % --R ?/? : (%,%) -> % ?=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % ---R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> % ---R associates? : (%,%) -> Boolean coerce : Fraction(Integer) -> % ---R coerce : % -> % coerce : Integer -> % ---R coerce : % -> OutputForm denominator : % -> % ---R factor : % -> Factored(%) gcd : List(%) -> % ---R gcd : (%,%) -> % hash : % -> SingleInteger ---R inv : % -> % latex : % -> String ---R lcm : List(%) -> % lcm : (%,%) -> % ---R numerator : % -> % one? : % -> Boolean ---R prime? : % -> Boolean ?quo? : (%,%) -> % ---R recip : % -> Union(%,"failed") ?rem? : (%,%) -> % ---R sample : () -> % sizeLess? : (%,%) -> Boolean ---R squareFree : % -> Factored(%) squareFreePart : % -> % ---R unit? : % -> Boolean unitCanonical : % -> % ---R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?^? : (%,Integer) -> % ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,PositiveInteger) -> % associates? : (%,%) -> Boolean +--R coerce : Fraction(Integer) -> % coerce : % -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R denominator : % -> % factor : % -> Factored(%) +--R gcd : List(%) -> % gcd : (%,%) -> % +--R hash : % -> SingleInteger inv : % -> % +--R latex : % -> String lcm : List(%) -> % +--R lcm : (%,%) -> % numerator : % -> % +--R one? : % -> Boolean prime? : % -> Boolean +--R ?quo? : (%,%) -> % recip : % -> Union(%,"failed") +--R ?rem? : (%,%) -> % sample : () -> % +--R sizeLess? : (%,%) -> Boolean squareFree : % -> Factored(%) +--R squareFreePart : % -> % unit? : % -> Boolean +--R unitCanonical : % -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean --R ?*? : (%,UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen)) -> % --R ?*? : (UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen),%) -> % ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % --R ?/? : (UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen),UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen)) -> % --R ? Boolean if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has ORDSET --R ?<=? : (%,%) -> Boolean if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has ORDSET @@ -41555,7 +43292,6 @@ Exit: SetCategory == add --R D : (%,Symbol) -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has PDRING(SYMBOL) --R D : (%,NonNegativeInteger) -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has DIFRING --R D : % -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has DIFRING ---R ?^? : (%,NonNegativeInteger) -> % --R abs : % -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has OINTDOM --R ceiling : % -> UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has INS --R characteristic : () -> NonNegativeInteger @@ -41899,7 +43635,8 @@ ExponentialExpansion(R,FE,var,cen): Exports == Implementation where )set message test on )set message auto off )clear all ---S 1 of 23 + +--S 1 of 24 sin(x) + 3*cos(x)**2 --R --R @@ -41908,7 +43645,7 @@ sin(x) + 3*cos(x)**2 --R Type: Expression(Integer) --E 1 ---S 2 of 23 +--S 2 of 24 tan(x) - 3.45*x --R --R @@ -41916,7 +43653,7 @@ tan(x) - 3.45*x --R Type: Expression(Float) --E 2 ---S 3 of 23 +--S 3 of 24 (tan sqrt 7 - sin sqrt 11)**2 / (4 - cos(x - y)) --R --R @@ -41927,7 +43664,7 @@ tan(x) - 3.45*x --R Type: Expression(Integer) --E 3 ---S 4 of 23 +--S 4 of 24 log(exp x)@Expression(Integer) --R --R @@ -41935,7 +43672,7 @@ log(exp x)@Expression(Integer) --R Type: Expression(Integer) --E 4 ---S 5 of 23 +--S 5 of 24 log(exp x)@Expression(Complex Integer) --R --R @@ -41944,7 +43681,7 @@ log(exp x)@Expression(Complex Integer) --R Type: Expression(Complex(Integer)) --E 5 ---S 6 of 23 +--S 6 of 24 sqrt 3 + sqrt(2 + sqrt(-5)) --R --R @@ -41954,7 +43691,7 @@ sqrt 3 + sqrt(2 + sqrt(-5)) --R Type: AlgebraicNumber --E 6 ---S 7 of 23 +--S 7 of 24 % :: Expression Integer --R --R @@ -41964,7 +43701,7 @@ sqrt 3 + sqrt(2 + sqrt(-5)) --R Type: Expression(Integer) --E 7 ---S 8 of 23 +--S 8 of 24 height mainKernel sin(x + 4) --R --R @@ -41972,7 +43709,7 @@ height mainKernel sin(x + 4) --R Type: PositiveInteger --E 8 ---S 9 of 23 +--S 9 of 24 e := (sin(x) - 4)**2 / ( 1 - 2*y*sqrt(- y) ) --R --R @@ -41984,7 +43721,7 @@ e := (sin(x) - 4)**2 / ( 1 - 2*y*sqrt(- y) ) --R Type: Expression(Integer) --E 9 ---S 10 of 23 +--S 10 of 24 numer e --R --R @@ -41993,7 +43730,7 @@ numer e --R Type: SparseMultivariatePolynomial(Integer,Kernel(Expression(Integer))) --E 10 ---S 11 of 23 +--S 11 of 24 denom e --R --R @@ -42002,7 +43739,7 @@ denom e --R Type: SparseMultivariatePolynomial(Integer,Kernel(Expression(Integer))) --E 11 ---S 12 of 23 +--S 12 of 24 D(e, x) --R --R @@ -42014,7 +43751,7 @@ D(e, x) --R Type: Expression(Integer) --E 12 ---S 13 of 23 +--S 13 of 24 D(e, [x, y], [1, 2]) --R --R @@ -42036,7 +43773,7 @@ D(e, [x, y], [1, 2]) --R Type: Expression(Integer) --E 13 ---S 14 of 23 +--S 14 of 24 complexNumeric(cos(2 - 3*%i)) --R --R @@ -42044,7 +43781,7 @@ complexNumeric(cos(2 - 3*%i)) --R Type: Complex(Float) --E 14 ---S 15 of 23 +--S 15 of 24 numeric(tan 3.8) --R --R @@ -42052,7 +43789,7 @@ numeric(tan 3.8) --R Type: Float --E 15 ---S 16 of 23 +--S 16 of 24 e2 := cos(x**2 - y + 3) --R --R @@ -42061,7 +43798,7 @@ e2 := cos(x**2 - y + 3) --R Type: Expression(Integer) --E 16 ---S 17 of 23 +--S 17 of 24 e3 := asin(e2) - %pi/2 --R --R @@ -42070,7 +43807,7 @@ e3 := asin(e2) - %pi/2 --R Type: Expression(Integer) --E 17 ---S 18 of 23 +--S 18 of 24 e3 :: Polynomial Integer --R --R @@ -42079,7 +43816,7 @@ e3 :: Polynomial Integer --R Type: Polynomial(Integer) --E 18 ---S 19 of 23 +--S 19 of 24 e3 :: DMP([x, y], Integer) --R --R @@ -42088,7 +43825,7 @@ e3 :: DMP([x, y], Integer) --R Type: DistributedMultivariatePolynomial([x,y],Integer) --E 19 ---S 20 of 23 +--S 20 of 24 sin %pi --R --R @@ -42096,7 +43833,7 @@ sin %pi --R Type: Expression(Integer) --E 20 ---S 21 of 23 +--S 21 of 24 cos(%pi / 4) --R --R @@ -42107,7 +43844,7 @@ cos(%pi / 4) --R Type: Expression(Integer) --E 21 ---S 22 of 23 +--S 22 of 24 tan(x)**6 + 3*tan(x)**4 + 3*tan(x)**2 + 1 --R --R @@ -42116,7 +43853,7 @@ tan(x)**6 + 3*tan(x)**4 + 3*tan(x)**2 + 1 --R Type: Expression(Integer) --E 22 ---S 23 of 23 +--S 23 of 24 simplify % --R --R @@ -42126,6 +43863,242 @@ simplify % --R cos(x) --R Type: Expression(Integer) --E 23 + +--S 24 of 24 +)show Expression +--R +--R Expression(R: OrderedSet) is a domain constructor +--R Abbreviation for Expression is EXPR +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for EXPR +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,R) -> % if R has COMRING ?*? : (R,%) -> % if R has COMRING +--R ?**? : (%,%) -> % if R has INTDOM ? Boolean +--R ?<=? : (%,%) -> Boolean ?=? : (%,%) -> Boolean +--R ?>? : (%,%) -> Boolean ?>=? : (%,%) -> Boolean +--R Beta : (%,%) -> % if R has INTDOM Ci : % -> % if R has INTDOM +--R D : (%,Symbol) -> % if R has RING Ei : % -> % if R has INTDOM +--R Gamma : % -> % if R has INTDOM Si : % -> % if R has INTDOM +--R abs : % -> % if R has INTDOM acos : % -> % if R has INTDOM +--R acosh : % -> % if R has INTDOM acot : % -> % if R has INTDOM +--R acoth : % -> % if R has INTDOM acsc : % -> % if R has INTDOM +--R acsch : % -> % if R has INTDOM airyAi : % -> % if R has INTDOM +--R airyBi : % -> % if R has INTDOM applyQuote : (Symbol,List(%)) -> % +--R applyQuote : (Symbol,%,%,%) -> % applyQuote : (Symbol,%,%) -> % +--R applyQuote : (Symbol,%) -> % asec : % -> % if R has INTDOM +--R asech : % -> % if R has INTDOM asin : % -> % if R has INTDOM +--R asinh : % -> % if R has INTDOM atan : % -> % if R has INTDOM +--R atanh : % -> % if R has INTDOM belong? : BasicOperator -> Boolean +--R box : List(%) -> % box : % -> % +--R coerce : % -> % if R has INTDOM coerce : R -> % +--R coerce : Symbol -> % coerce : Kernel(%) -> % +--R coerce : % -> OutputForm cos : % -> % if R has INTDOM +--R cosh : % -> % if R has INTDOM cot : % -> % if R has INTDOM +--R coth : % -> % if R has INTDOM csc : % -> % if R has INTDOM +--R csch : % -> % if R has INTDOM digamma : % -> % if R has INTDOM +--R dilog : % -> % if R has INTDOM distribute : (%,%) -> % +--R distribute : % -> % elt : (BasicOperator,List(%)) -> % +--R elt : (BasicOperator,%,%,%) -> % elt : (BasicOperator,%,%) -> % +--R elt : (BasicOperator,%) -> % erf : % -> % if R has INTDOM +--R eval : (%,Symbol,(% -> %)) -> % eval : (%,List(%),List(%)) -> % +--R eval : (%,%,%) -> % eval : (%,Equation(%)) -> % +--R eval : (%,List(Equation(%))) -> % eval : (%,Kernel(%),%) -> % +--R exp : % -> % if R has INTDOM factorial : % -> % if R has INTDOM +--R freeOf? : (%,Symbol) -> Boolean freeOf? : (%,%) -> Boolean +--R fresnelC : % -> % if R has INTDOM fresnelS : % -> % if R has INTDOM +--R gcd : (%,%) -> % if R has INTDOM gcd : List(%) -> % if R has INTDOM +--R ground : % -> R ground? : % -> Boolean +--R hash : % -> SingleInteger height : % -> NonNegativeInteger +--R is? : (%,Symbol) -> Boolean is? : (%,BasicOperator) -> Boolean +--R kernel : (BasicOperator,%) -> % kernels : % -> List(Kernel(%)) +--R latex : % -> String lcm : (%,%) -> % if R has INTDOM +--R lcm : List(%) -> % if R has INTDOM li : % -> % if R has INTDOM +--R log : % -> % if R has INTDOM map : ((% -> %),Kernel(%)) -> % +--R max : (%,%) -> % min : (%,%) -> % +--R numerator : % -> % if R has RING paren : List(%) -> % +--R paren : % -> % pi : () -> % if R has INTDOM +--R reduce : % -> % if R has INTDOM retract : % -> R +--R retract : % -> Symbol retract : % -> Kernel(%) +--R rootOf : % -> % if R has INTDOM sec : % -> % if R has INTDOM +--R sech : % -> % if R has INTDOM sin : % -> % if R has INTDOM +--R sinh : % -> % if R has INTDOM sqrt : % -> % if R has INTDOM +--R subst : (%,Equation(%)) -> % tan : % -> % if R has INTDOM +--R tanh : % -> % if R has INTDOM tower : % -> List(Kernel(%)) +--R variables : % -> List(Symbol) zeroOf : % -> % if R has INTDOM +--R ?~=? : (%,%) -> Boolean +--R ?*? : (PositiveInteger,%) -> % if R has ABELSG or R has LINEXP(INT) and R has RING +--R ?*? : (NonNegativeInteger,%) -> % if R has ABELSG or R has LINEXP(INT) and R has RING +--R ?*? : (Integer,%) -> % if R has ABELGRP or R has LINEXP(INT) and R has RING +--R ?*? : (%,%) -> % if R has LINEXP(INT) and R has RING or R has SGROUP +--R ?*? : (%,Fraction(Integer)) -> % if R has INTDOM +--R ?*? : (Fraction(Integer),%) -> % if R has INTDOM +--R ?**? : (%,PositiveInteger) -> % if R has LINEXP(INT) and R has RING or R has SGROUP +--R ?**? : (%,NonNegativeInteger) -> % if R has LINEXP(INT) and R has RING or R has SGROUP +--R ?**? : (%,Integer) -> % if R has GROUP or R has INTDOM +--R ?**? : (%,Fraction(Integer)) -> % if R has INTDOM +--R ?+? : (%,%) -> % if R has ABELSG or R has LINEXP(INT) and R has RING +--R -? : % -> % if R has ABELGRP or R has LINEXP(INT) and R has RING +--R ?-? : (%,%) -> % if R has ABELGRP or R has LINEXP(INT) and R has RING +--R ?/? : (%,%) -> % if R has GROUP or R has INTDOM +--R ?/? : (SparseMultivariatePolynomial(R,Kernel(%)),SparseMultivariatePolynomial(R,Kernel(%))) -> % if R has INTDOM +--R D : (%,List(Symbol)) -> % if R has RING +--R D : (%,Symbol,NonNegativeInteger) -> % if R has RING +--R D : (%,List(Symbol),List(NonNegativeInteger)) -> % if R has RING +--R Gamma : (%,%) -> % if R has INTDOM +--R 1 : () -> % if R has LINEXP(INT) and R has RING or R has SGROUP +--R 0 : () -> % if R has ABELSG or R has LINEXP(INT) and R has RING +--R ?^? : (%,PositiveInteger) -> % if R has LINEXP(INT) and R has RING or R has SGROUP +--R ?^? : (%,NonNegativeInteger) -> % if R has LINEXP(INT) and R has RING or R has SGROUP +--R ?^? : (%,Integer) -> % if R has GROUP or R has INTDOM +--R applyQuote : (Symbol,%,%,%,%) -> % +--R associates? : (%,%) -> Boolean if R has INTDOM +--R besselI : (%,%) -> % if R has INTDOM +--R besselJ : (%,%) -> % if R has INTDOM +--R besselK : (%,%) -> % if R has INTDOM +--R besselY : (%,%) -> % if R has INTDOM +--R binomial : (%,%) -> % if R has INTDOM +--R characteristic : () -> NonNegativeInteger if R has RING +--R charthRoot : % -> Union(%,"failed") if R has CHARNZ +--R coerce : Integer -> % if R has RETRACT(INT) or R has RING +--R coerce : Fraction(Integer) -> % if R has INTDOM or R has RETRACT(FRAC(INT)) +--R coerce : Polynomial(R) -> % if R has RING +--R coerce : Fraction(Polynomial(R)) -> % if R has INTDOM +--R coerce : Fraction(Polynomial(Fraction(R))) -> % if R has INTDOM +--R coerce : Polynomial(Fraction(R)) -> % if R has INTDOM +--R coerce : Fraction(R) -> % if R has INTDOM +--R coerce : SparseMultivariatePolynomial(R,Kernel(%)) -> % if R has RING +--R coerce : AlgebraicNumber -> % if R has INTDOM and R has RETRACT(INT) +--R commutator : (%,%) -> % if R has GROUP +--R conjugate : (%,%) -> % if R has GROUP +--R convert : % -> InputForm if R has KONVERT(INFORM) +--R convert : Factored(%) -> % if R has INTDOM +--R convert : % -> Pattern(Float) if R has KONVERT(PATTERN(FLOAT)) +--R convert : % -> Pattern(Integer) if R has KONVERT(PATTERN(INT)) +--R definingPolynomial : % -> % if $ has RING +--R denom : % -> SparseMultivariatePolynomial(R,Kernel(%)) if R has INTDOM +--R denominator : % -> % if R has INTDOM +--R differentiate : (%,Symbol) -> % if R has RING +--R differentiate : (%,List(Symbol)) -> % if R has RING +--R differentiate : (%,Symbol,NonNegativeInteger) -> % if R has RING +--R differentiate : (%,List(Symbol),List(NonNegativeInteger)) -> % if R has RING +--R divide : (%,%) -> Record(quotient: %,remainder: %) if R has INTDOM +--R elt : (BasicOperator,%,%,%,%) -> % +--R euclideanSize : % -> NonNegativeInteger if R has INTDOM +--R eval : (%,Symbol,NonNegativeInteger,(% -> %)) -> % if R has RING +--R eval : (%,Symbol,NonNegativeInteger,(List(%) -> %)) -> % if R has RING +--R eval : (%,List(Symbol),List(NonNegativeInteger),List((List(%) -> %))) -> % if R has RING +--R eval : (%,List(Symbol),List(NonNegativeInteger),List((% -> %))) -> % if R has RING +--R eval : (%,List(BasicOperator),List(%),Symbol) -> % if R has KONVERT(INFORM) +--R eval : (%,BasicOperator,%,Symbol) -> % if R has KONVERT(INFORM) +--R eval : % -> % if R has KONVERT(INFORM) +--R eval : (%,List(Symbol)) -> % if R has KONVERT(INFORM) +--R eval : (%,Symbol) -> % if R has KONVERT(INFORM) +--R eval : (%,BasicOperator,(% -> %)) -> % +--R eval : (%,BasicOperator,(List(%) -> %)) -> % +--R eval : (%,List(BasicOperator),List((List(%) -> %))) -> % +--R eval : (%,List(BasicOperator),List((% -> %))) -> % +--R eval : (%,Symbol,(List(%) -> %)) -> % +--R eval : (%,List(Symbol),List((List(%) -> %))) -> % +--R eval : (%,List(Symbol),List((% -> %))) -> % +--R eval : (%,List(Kernel(%)),List(%)) -> % +--R even? : % -> Boolean if $ has RETRACT(INT) +--R expressIdealMember : (List(%),%) -> Union(List(%),"failed") if R has INTDOM +--R exquo : (%,%) -> Union(%,"failed") if R has INTDOM +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) if R has INTDOM +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") if R has INTDOM +--R factor : % -> Factored(%) if R has INTDOM +--R factorPolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has GCDDOM and R has INTDOM +--R factorials : % -> % if R has INTDOM +--R factorials : (%,Symbol) -> % if R has INTDOM +--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) if R has INTDOM +--R integral : (%,SegmentBinding(%)) -> % if R has INTDOM +--R integral : (%,Symbol) -> % if R has INTDOM +--R inv : % -> % if R has GROUP or R has INTDOM +--R isExpt : (%,Symbol) -> Union(Record(var: Kernel(%),exponent: Integer),"failed") if R has RING +--R isExpt : (%,BasicOperator) -> Union(Record(var: Kernel(%),exponent: Integer),"failed") if R has RING +--R isExpt : % -> Union(Record(var: Kernel(%),exponent: Integer),"failed") if R has SGROUP +--R isMult : % -> Union(Record(coef: Integer,var: Kernel(%)),"failed") if R has ABELSG +--R isPlus : % -> Union(List(%),"failed") if R has ABELSG +--R isPower : % -> Union(Record(val: %,exponent: Integer),"failed") if R has RING +--R isTimes : % -> Union(List(%),"failed") if R has SGROUP +--R kernel : (BasicOperator,List(%)) -> % +--R lcmCoef : (%,%) -> Record(llcmres: %,coeff1: %,coeff2: %) if R has INTDOM +--R mainKernel : % -> Union(Kernel(%),"failed") +--R minPoly : Kernel(%) -> SparseUnivariatePolynomial(%) if $ has RING +--R multiEuclidean : (List(%),%) -> Union(List(%),"failed") if R has INTDOM +--R nthRoot : (%,Integer) -> % if R has INTDOM +--R number? : % -> Boolean if R has INTDOM +--R numer : % -> SparseMultivariatePolynomial(R,Kernel(%)) if R has RING +--R odd? : % -> Boolean if $ has RETRACT(INT) +--R one? : % -> Boolean if R has LINEXP(INT) and R has RING or R has SGROUP +--R operator : BasicOperator -> BasicOperator +--R operators : % -> List(BasicOperator) +--R patternMatch : (%,Pattern(Float),PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if R has PATMAB(FLOAT) +--R patternMatch : (%,Pattern(Integer),PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if R has PATMAB(INT) +--R permutation : (%,%) -> % if R has INTDOM +--R polygamma : (%,%) -> % if R has INTDOM +--R prime? : % -> Boolean if R has INTDOM +--R principalIdeal : List(%) -> Record(coef: List(%),generator: %) if R has INTDOM +--R product : (%,Symbol) -> % if R has INTDOM +--R product : (%,SegmentBinding(%)) -> % if R has INTDOM +--R ?quo? : (%,%) -> % if R has INTDOM +--R recip : % -> Union(%,"failed") if R has LINEXP(INT) and R has RING or R has SGROUP +--R reducedSystem : Matrix(%) -> Matrix(Integer) if R has LINEXP(INT) and R has RING +--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(Integer),vec: Vector(Integer)) if R has LINEXP(INT) and R has RING +--R reducedSystem : Matrix(%) -> Matrix(R) if R has RING +--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(R),vec: Vector(R)) if R has RING +--R ?rem? : (%,%) -> % if R has INTDOM +--R retract : % -> Fraction(Integer) if R has INTDOM and R has RETRACT(INT) or R has RETRACT(FRAC(INT)) +--R retract : % -> Polynomial(R) if R has RING +--R retract : % -> Fraction(Polynomial(R)) if R has INTDOM +--R retract : % -> Integer if R has RETRACT(INT) +--R retract : % -> AlgebraicNumber if R has INTDOM and R has RETRACT(INT) +--R retractIfCan : % -> Union(Fraction(Integer),"failed") if R has INTDOM and R has RETRACT(INT) or R has RETRACT(FRAC(INT)) +--R retractIfCan : % -> Union(Polynomial(R),"failed") if R has RING +--R retractIfCan : % -> Union(Fraction(Polynomial(R)),"failed") if R has INTDOM +--R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT(INT) +--R retractIfCan : % -> Union(AlgebraicNumber,"failed") if R has INTDOM and R has RETRACT(INT) +--R retractIfCan : % -> Union(R,"failed") +--R retractIfCan : % -> Union(Symbol,"failed") +--R retractIfCan : % -> Union(Kernel(%),"failed") +--R rootOf : Polynomial(%) -> % if R has INTDOM +--R rootOf : SparseUnivariatePolynomial(%) -> % if R has INTDOM +--R rootOf : (SparseUnivariatePolynomial(%),Symbol) -> % if R has INTDOM +--R rootOf : (%,Symbol) -> % if R has INTDOM +--R rootsOf : Polynomial(%) -> List(%) if R has INTDOM +--R rootsOf : SparseUnivariatePolynomial(%) -> List(%) if R has INTDOM +--R rootsOf : (SparseUnivariatePolynomial(%),Symbol) -> List(%) if R has INTDOM +--R rootsOf : % -> List(%) if R has INTDOM +--R rootsOf : (%,Symbol) -> List(%) if R has INTDOM +--R sample : () -> % if R has ABELSG or R has LINEXP(INT) and R has RING or R has SGROUP +--R simplifyPower : (%,Integer) -> % if R has INTDOM +--R sizeLess? : (%,%) -> Boolean if R has INTDOM +--R squareFree : % -> Factored(%) if R has INTDOM +--R squareFreePart : % -> % if R has INTDOM +--R squareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has GCDDOM and R has INTDOM +--R subst : (%,List(Kernel(%)),List(%)) -> % +--R subst : (%,List(Equation(%))) -> % +--R subtractIfCan : (%,%) -> Union(%,"failed") if R has ABELGRP or R has LINEXP(INT) and R has RING +--R summation : (%,Symbol) -> % if R has INTDOM +--R summation : (%,SegmentBinding(%)) -> % if R has INTDOM +--R unit? : % -> Boolean if R has INTDOM +--R unitCanonical : % -> % if R has INTDOM +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) if R has INTDOM +--R univariate : (%,Kernel(%)) -> Fraction(SparseUnivariatePolynomial(%)) if R has INTDOM +--R zero? : % -> Boolean if R has ABELSG or R has LINEXP(INT) and R has RING +--R zeroOf : Polynomial(%) -> % if R has INTDOM +--R zeroOf : SparseUnivariatePolynomial(%) -> % if R has INTDOM +--R zeroOf : (SparseUnivariatePolynomial(%),Symbol) -> % if R has INTDOM +--R zeroOf : (%,Symbol) -> % if R has INTDOM +--R zerosOf : Polynomial(%) -> List(%) if R has INTDOM +--R zerosOf : SparseUnivariatePolynomial(%) -> List(%) if R has INTDOM +--R zerosOf : (SparseUnivariatePolynomial(%),Symbol) -> List(%) if R has INTDOM +--R zerosOf : % -> List(%) if R has INTDOM +--R zerosOf : (%,Symbol) -> List(%) if R has INTDOM +--R +--E 24 + )spool )lisp (bye) \end{chunk} @@ -42989,34 +44962,35 @@ Expression(R:OrderedSet): Exports == Implementation where --R------------------------------- Operations -------------------------------- --R ?*? : (FE,%) -> % ?*? : (%,FE) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % ---R -? : % -> % ? Boolean +--R -? : % -> % ?/? : (%,%) -> % if FE has FIELD +--R ?/? : (%,FE) -> % if FE has FIELD ? Boolean --R ?<=? : (%,%) -> Boolean ?=? : (%,%) -> Boolean --R ?>? : (%,%) -> Boolean ?>=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % center : % -> FE ---R coerce : Integer -> % coerce : % -> OutputForm ---R complete : % -> % degree : % -> Fraction(Integer) ---R ?.? : (%,Fraction(Integer)) -> FE hash : % -> SingleInteger ---R inv : % -> % if FE has FIELD latex : % -> String ---R leadingCoefficient : % -> FE leadingMonomial : % -> % ---R map : ((FE -> FE),%) -> % max : (%,%) -> % ---R min : (%,%) -> % monomial? : % -> Boolean ---R one? : % -> Boolean order : % -> Fraction(Integer) ---R pole? : % -> Boolean recip : % -> Union(%,"failed") ---R reductum : % -> % sample : () -> % ---R variable : % -> Symbol zero? : % -> Boolean ---R ?~=? : (%,%) -> Boolean +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R center : % -> FE coerce : % -> % if FE has INTDOM +--R coerce : FE -> % if FE has COMRING coerce : Integer -> % +--R coerce : % -> OutputForm complete : % -> % +--R degree : % -> Fraction(Integer) ?.? : (%,Fraction(Integer)) -> FE +--R gcd : (%,%) -> % if FE has FIELD gcd : List(%) -> % if FE has FIELD +--R hash : % -> SingleInteger inv : % -> % if FE has FIELD +--R latex : % -> String lcm : (%,%) -> % if FE has FIELD +--R lcm : List(%) -> % if FE has FIELD leadingCoefficient : % -> FE +--R leadingMonomial : % -> % map : ((FE -> FE),%) -> % +--R max : (%,%) -> % min : (%,%) -> % +--R monomial? : % -> Boolean one? : % -> Boolean +--R order : % -> Fraction(Integer) pole? : % -> Boolean +--R recip : % -> Union(%,"failed") reductum : % -> % +--R sample : () -> % variable : % -> Symbol +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean --R ?*? : (%,Fraction(Integer)) -> % if FE has ALGEBRA(FRAC(INT)) --R ?*? : (Fraction(Integer),%) -> % if FE has ALGEBRA(FRAC(INT)) ---R ?*? : (NonNegativeInteger,%) -> % --R ?**? : (%,Fraction(Integer)) -> % if FE has ALGEBRA(FRAC(INT)) --R ?**? : (%,%) -> % if FE has ALGEBRA(FRAC(INT)) --R ?**? : (%,Integer) -> % if FE has FIELD ---R ?**? : (%,NonNegativeInteger) -> % ---R ?/? : (%,%) -> % if FE has FIELD ---R ?/? : (%,FE) -> % if FE has FIELD --R D : % -> % if FE has *: (Fraction(Integer),FE) -> FE --R D : (%,NonNegativeInteger) -> % if FE has *: (Fraction(Integer),FE) -> FE --R D : (%,Symbol) -> % if FE has *: (Fraction(Integer),FE) -> FE and FE has PDRING(SYMBOL) @@ -43024,7 +44998,6 @@ Expression(R:OrderedSet): Exports == Implementation where --R D : (%,Symbol,NonNegativeInteger) -> % if FE has *: (Fraction(Integer),FE) -> FE and FE has PDRING(SYMBOL) --R D : (%,List(Symbol),List(NonNegativeInteger)) -> % if FE has *: (Fraction(Integer),FE) -> FE and FE has PDRING(SYMBOL) --R ?^? : (%,Integer) -> % if FE has FIELD ---R ?^? : (%,NonNegativeInteger) -> % --R acos : % -> % if FE has ALGEBRA(FRAC(INT)) --R acosh : % -> % if FE has ALGEBRA(FRAC(INT)) --R acot : % -> % if FE has ALGEBRA(FRAC(INT)) @@ -43042,9 +45015,7 @@ Expression(R:OrderedSet): Exports == Implementation where --R characteristic : () -> NonNegativeInteger --R charthRoot : % -> Union(%,"failed") if FE has CHARNZ --R coefficient : (%,Fraction(Integer)) -> FE ---R coerce : % -> % if FE has INTDOM --R coerce : Fraction(Integer) -> % if FE has ALGEBRA(FRAC(INT)) ---R coerce : FE -> % if FE has COMRING --R cos : % -> % if FE has ALGEBRA(FRAC(INT)) --R cosh : % -> % if FE has ALGEBRA(FRAC(INT)) --R cot : % -> % if FE has ALGEBRA(FRAC(INT)) @@ -43071,13 +45042,9 @@ Expression(R:OrderedSet): Exports == Implementation where --R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) if FE has FIELD --R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") if FE has FIELD --R factor : % -> Factored(%) if FE has FIELD ---R gcd : (%,%) -> % if FE has FIELD ---R gcd : List(%) -> % if FE has FIELD --R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) if FE has FIELD --R integrate : (%,Symbol) -> % if FE has integrate: (FE,Symbol) -> FE and FE has variables: FE -> List(Symbol) and FE has ALGEBRA(FRAC(INT)) or FE has ACFS(INT) and FE has ALGEBRA(FRAC(INT)) and FE has PRIMCAT and FE has TRANFUN --R integrate : % -> % if FE has ALGEBRA(FRAC(INT)) ---R lcm : (%,%) -> % if FE has FIELD ---R lcm : List(%) -> % if FE has FIELD --R lcmCoef : (%,%) -> Record(llcmres: %,coeff1: %,coeff2: %) if FE has FIELD --R log : % -> % if FE has ALGEBRA(FRAC(INT)) --R monomial : (%,List(SingletonAsOrderedSet),List(Fraction(Integer))) -> % @@ -44659,7 +46626,8 @@ e04ucfAnnaType(): NumericalOptimizationCategory == Result add )set message test on )set message auto off )clear all ---S 1 of 38 + +--S 1 of 39 g := factor(4312) --R --R @@ -44668,7 +46636,7 @@ g := factor(4312) --R Type: Factored(Integer) --E 1 ---S 2 of 38 +--S 2 of 39 unit(g) --R --R @@ -44676,7 +46644,7 @@ unit(g) --R Type: PositiveInteger --E 2 ---S 3 of 38 +--S 3 of 39 numberOfFactors(g) --R --R @@ -44684,7 +46652,7 @@ numberOfFactors(g) --R Type: PositiveInteger --E 3 ---S 4 of 38 +--S 4 of 39 [nthFactor(g,i) for i in 1..numberOfFactors(g)] --R --R @@ -44692,7 +46660,7 @@ numberOfFactors(g) --R Type: List(Integer) --E 4 ---S 5 of 38 +--S 5 of 39 [nthExponent(g,i) for i in 1..numberOfFactors(g)] --R --R @@ -44700,7 +46668,7 @@ numberOfFactors(g) --R Type: List(Integer) --E 5 ---S 6 of 38 +--S 6 of 39 [nthFlag(g,i) for i in 1..numberOfFactors(g)] --R --R @@ -44708,7 +46676,7 @@ numberOfFactors(g) --R Type: List(Union("nil","sqfr","irred","prime")) --E 6 ---S 7 of 38 +--S 7 of 39 factorList(g) --R --R @@ -44718,7 +46686,7 @@ factorList(g) --RType: List(Record(flg: Union("nil","sqfr","irred","prime"),fctr: Integer,xpnt: Integer)) --E 7 ---S 8 of 38 +--S 8 of 39 factors(g) --R --R @@ -44727,7 +46695,7 @@ factors(g) --R Type: List(Record(factor: Integer,exponent: Integer)) --E 8 ---S 9 of 38 +--S 9 of 39 first(%).factor --R --R @@ -44735,7 +46703,7 @@ first(%).factor --R Type: PositiveInteger --E 9 ---S 10 of 38 +--S 10 of 39 g := factor(4312) --R --R @@ -44744,7 +46712,7 @@ g := factor(4312) --R Type: Factored(Integer) --E 10 ---S 11 of 38 +--S 11 of 39 expand(g) --R --R @@ -44752,7 +46720,7 @@ expand(g) --R Type: PositiveInteger --E 11 ---S 12 of 38 +--S 12 of 39 reduce(*,[t.factor for t in factors(g)]) --R --R @@ -44760,7 +46728,7 @@ reduce(*,[t.factor for t in factors(g)]) --R Type: PositiveInteger --E 12 ---S 13 of 38 +--S 13 of 39 g := factor(4312) --R --R @@ -44769,7 +46737,7 @@ g := factor(4312) --R Type: Factored(Integer) --E 13 ---S 14 of 38 +--S 14 of 39 f := factor(246960) --R --R @@ -44778,7 +46746,7 @@ f := factor(246960) --R Type: Factored(Integer) --E 14 ---S 15 of 38 +--S 15 of 39 f * g --R --R @@ -44787,7 +46755,7 @@ f * g --R Type: Factored(Integer) --E 15 ---S 16 of 38 +--S 16 of 39 f**500 --R --R @@ -44796,7 +46764,7 @@ f**500 --R Type: Factored(Integer) --E 16 ---S 17 of 38 +--S 17 of 39 gcd(f,g) --R --R @@ -44805,7 +46773,7 @@ gcd(f,g) --R Type: Factored(Integer) --E 17 ---S 18 of 38 +--S 18 of 39 lcm(f,g) --R --R @@ -44814,7 +46782,7 @@ lcm(f,g) --R Type: Factored(Integer) --E 18 ---S 19 of 38 +--S 19 of 39 f + g --R --R @@ -44823,7 +46791,7 @@ f + g --R Type: Factored(Integer) --E 19 ---S 20 of 38 +--S 20 of 39 f - g --R --R @@ -44832,7 +46800,7 @@ f - g --R Type: Factored(Integer) --E 20 ---S 21 of 38 +--S 21 of 39 zero?(factor(0)) --R --R @@ -44840,7 +46808,7 @@ zero?(factor(0)) --R Type: Boolean --E 21 ---S 22 of 38 +--S 22 of 39 zero?(g) --R --R @@ -44848,7 +46816,7 @@ zero?(g) --R Type: Boolean --E 22 ---S 23 of 38 +--S 23 of 39 one?(factor(1)) --R --R @@ -44856,7 +46824,7 @@ one?(factor(1)) --R Type: Boolean --E 23 ---S 24 of 38 +--S 24 of 39 one?(f) --R --R @@ -44864,7 +46832,7 @@ one?(f) --R Type: Boolean --E 24 ---S 25 of 38 +--S 25 of 39 0$Factored(Integer) --R --R @@ -44872,7 +46840,7 @@ one?(f) --R Type: Factored(Integer) --E 25 ---S 26 of 38 +--S 26 of 39 1$Factored(Integer) --R --R @@ -44880,7 +46848,7 @@ one?(f) --R Type: Factored(Integer) --E 26 ---S 27 of 38 +--S 27 of 39 nilFactor(24,2) --R --R @@ -44889,7 +46857,7 @@ nilFactor(24,2) --R Type: Factored(Integer) --E 27 ---S 28 of 38 +--S 28 of 39 nthFlag(%,1) --R --R @@ -44897,7 +46865,7 @@ nthFlag(%,1) --R Type: Union("nil",...) --E 28 ---S 29 of 38 +--S 29 of 39 sqfrFactor(30,2) --R --R @@ -44906,7 +46874,7 @@ sqfrFactor(30,2) --R Type: Factored(Integer) --E 29 ---S 30 of 38 +--S 30 of 39 irreducibleFactor(13,10) --R --R @@ -44915,7 +46883,7 @@ irreducibleFactor(13,10) --R Type: Factored(Integer) --E 30 ---S 31 of 38 +--S 31 of 39 primeFactor(11,5) --R --R @@ -44924,7 +46892,7 @@ primeFactor(11,5) --R Type: Factored(Integer) --E 31 ---S 32 of 38 +--S 32 of 39 h := factor(-720) --R --R @@ -44933,7 +46901,7 @@ h := factor(-720) --R Type: Factored(Integer) --E 32 ---S 33 of 38 +--S 33 of 39 h - makeFR(unit(h),factorList(h)) --R --R @@ -44941,7 +46909,7 @@ h - makeFR(unit(h),factorList(h)) --R Type: Factored(Integer) --E 33 ---S 34 of 38 +--S 34 of 39 p := (4*x*x-12*x+9)*y*y + (4*x*x-12*x+9)*y + 28*x*x - 84*x + 63 --R --R @@ -44950,7 +46918,7 @@ p := (4*x*x-12*x+9)*y*y + (4*x*x-12*x+9)*y + 28*x*x - 84*x + 63 --R Type: Polynomial(Integer) --E 34 ---S 35 of 38 +--S 35 of 39 fp := factor(p) --R --R @@ -44959,7 +46927,7 @@ fp := factor(p) --R Type: Factored(Polynomial(Integer)) --E 35 ---S 36 of 38 +--S 36 of 39 D(p,x) --R --R @@ -44968,7 +46936,7 @@ D(p,x) --R Type: Polynomial(Integer) --E 36 ---S 37 of 38 +--S 37 of 39 D(fp,x) --R --R @@ -44977,13 +46945,106 @@ D(fp,x) --R Type: Factored(Polynomial(Integer)) --E 37 ---S 38 of 38 +--S 38 of 39 numberOfFactors(%) --R --R --R (38) 3 --R Type: PositiveInteger --E 38 + +--S 39 of 39 +)show Factored +--R +--R Factored(R: IntegralDomain) is a domain constructor +--R Abbreviation for Factored is FR +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for FR +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,R) -> % ?*? : (R,%) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R D : (%,(R -> R)) -> % D : % -> % if R has DIFRING +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R associates? : (%,%) -> Boolean coerce : R -> % +--R coerce : % -> % coerce : Integer -> % +--R coerce : % -> OutputForm convert : % -> Float if R has REAL +--R differentiate : (%,(R -> R)) -> % expand : % -> R +--R exponent : % -> Integer gcd : (%,%) -> % if R has GCDDOM +--R gcd : List(%) -> % if R has GCDDOM hash : % -> SingleInteger +--R latex : % -> String lcm : (%,%) -> % if R has GCDDOM +--R lcm : List(%) -> % if R has GCDDOM map : ((R -> R),%) -> % +--R nilFactor : (R,Integer) -> % nthFactor : (%,Integer) -> R +--R one? : % -> Boolean prime? : % -> Boolean if R has UFD +--R primeFactor : (R,Integer) -> % recip : % -> Union(%,"failed") +--R retract : % -> R sample : () -> % +--R sqfrFactor : (R,Integer) -> % unit : % -> R +--R unit? : % -> Boolean unitCanonical : % -> % +--R unitNormalize : % -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R D : (%,(R -> R),NonNegativeInteger) -> % +--R D : (%,List(Symbol),List(NonNegativeInteger)) -> % if R has PDRING(SYMBOL) +--R D : (%,Symbol,NonNegativeInteger) -> % if R has PDRING(SYMBOL) +--R D : (%,List(Symbol)) -> % if R has PDRING(SYMBOL) +--R D : (%,Symbol) -> % if R has PDRING(SYMBOL) +--R D : (%,NonNegativeInteger) -> % if R has DIFRING +--R characteristic : () -> NonNegativeInteger +--R coerce : Fraction(Integer) -> % if R has RETRACT(FRAC(INT)) +--R convert : % -> DoubleFloat if R has REAL +--R convert : % -> InputForm if R has KONVERT(INFORM) +--R differentiate : (%,(R -> R),NonNegativeInteger) -> % +--R differentiate : (%,List(Symbol),List(NonNegativeInteger)) -> % if R has PDRING(SYMBOL) +--R differentiate : (%,Symbol,NonNegativeInteger) -> % if R has PDRING(SYMBOL) +--R differentiate : (%,List(Symbol)) -> % if R has PDRING(SYMBOL) +--R differentiate : (%,Symbol) -> % if R has PDRING(SYMBOL) +--R differentiate : (%,NonNegativeInteger) -> % if R has DIFRING +--R differentiate : % -> % if R has DIFRING +--R ?.? : (%,%) -> % if R has ELTAB($,$) +--R ?.? : (%,R) -> % if R has ELTAB(R,R) +--R eval : (%,List(%),List(%)) -> % if R has EVALAB($) +--R eval : (%,%,%) -> % if R has EVALAB($) +--R eval : (%,Equation(%)) -> % if R has EVALAB($) +--R eval : (%,List(Equation(%))) -> % if R has EVALAB($) +--R eval : (%,List(Symbol),List(%)) -> % if R has IEVALAB(SYMBOL,$) +--R eval : (%,Symbol,%) -> % if R has IEVALAB(SYMBOL,$) +--R eval : (%,Symbol,R) -> % if R has IEVALAB(SYMBOL,R) +--R eval : (%,List(Symbol),List(R)) -> % if R has IEVALAB(SYMBOL,R) +--R eval : (%,List(Equation(R))) -> % if R has EVALAB(R) +--R eval : (%,Equation(R)) -> % if R has EVALAB(R) +--R eval : (%,R,R) -> % if R has EVALAB(R) +--R eval : (%,List(R),List(R)) -> % if R has EVALAB(R) +--R exquo : (%,%) -> Union(%,"failed") +--R factor : % -> Factored(%) if R has UFD +--R factorList : % -> List(Record(flg: Union("nil","sqfr","irred","prime"),fctr: R,xpnt: Integer)) +--R factors : % -> List(Record(factor: R,exponent: Integer)) +--R flagFactor : (R,Integer,Union("nil","sqfr","irred","prime")) -> % +--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) if R has GCDDOM +--R irreducibleFactor : (R,Integer) -> % +--R lcmCoef : (%,%) -> Record(llcmres: %,coeff1: %,coeff2: %) if R has GCDDOM +--R makeFR : (R,List(Record(flg: Union("nil","sqfr","irred","prime"),fctr: R,xpnt: Integer))) -> % +--R nthExponent : (%,Integer) -> Integer +--R nthFlag : (%,Integer) -> Union("nil","sqfr","irred","prime") +--R numberOfFactors : % -> NonNegativeInteger +--R rational : % -> Fraction(Integer) if R has INS +--R rational? : % -> Boolean if R has INS +--R rationalIfCan : % -> Union(Fraction(Integer),"failed") if R has INS +--R retract : % -> Fraction(Integer) if R has RETRACT(FRAC(INT)) +--R retract : % -> Integer if R has RETRACT(INT) +--R retractIfCan : % -> Union(R,"failed") +--R retractIfCan : % -> Union(Fraction(Integer),"failed") if R has RETRACT(FRAC(INT)) +--R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT(INT) +--R squareFree : % -> Factored(%) if R has UFD +--R squareFreePart : % -> % if R has UFD +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) +--R +--E 39 + )spool )lisp (bye) \end{chunk} @@ -45890,7 +47951,8 @@ Factored(R: IntegralDomain): Exports == Implementation where )set message test on )set message auto off )clear all ---S 1 of 12 + +--S 1 of 13 ifile:File List Integer:=open("jazz1","output") --R --R @@ -45898,7 +47960,7 @@ ifile:File List Integer:=open("jazz1","output") --R Type: File(List(Integer)) --E 1 ---S 2 of 12 +--S 2 of 13 write!(ifile, [-1,2,3]) --R --R @@ -45906,7 +47968,7 @@ write!(ifile, [-1,2,3]) --R Type: List(Integer) --E 2 ---S 3 of 12 +--S 3 of 13 write!(ifile, [10,-10,0,111]) --R --R @@ -45914,7 +47976,7 @@ write!(ifile, [10,-10,0,111]) --R Type: List(Integer) --E 3 ---S 4 of 12 +--S 4 of 13 write!(ifile, [7]) --R --R @@ -45922,7 +47984,7 @@ write!(ifile, [7]) --R Type: List(Integer) --E 4 ---S 5 of 12 +--S 5 of 13 reopen!(ifile, "input") --R --R @@ -45930,7 +47992,7 @@ reopen!(ifile, "input") --R Type: File(List(Integer)) --E 5 ---S 6 of 12 +--S 6 of 13 read! ifile --R --R @@ -45938,7 +48000,7 @@ read! ifile --R Type: List(Integer) --E 6 ---S 7 of 12 +--S 7 of 13 read! ifile --R --R @@ -45946,7 +48008,7 @@ read! ifile --R Type: List(Integer) --E 7 ---S 8 of 12 +--S 8 of 13 readIfCan! ifile --R --R @@ -45954,7 +48016,7 @@ readIfCan! ifile --R Type: Union(List(Integer),...) --E 8 ---S 9 of 12 +--S 9 of 13 readIfCan! ifile --R --R @@ -45962,7 +48024,7 @@ readIfCan! ifile --R Type: Union("failed",...) --E 9 ---S 10 of 12 +--S 10 of 13 iomode ifile --R --R @@ -45970,7 +48032,7 @@ iomode ifile --R Type: String --E 10 ---S 11 of 12 +--S 11 of 13 name ifile --R --R @@ -45978,13 +48040,34 @@ name ifile --R Type: FileName --E 11 ---S 12 of 12 +--S 12 of 13 close! ifile --R --R --R (12) "jazz1" --R Type: File(List(Integer)) --E 12 + +--S 13 of 13 +)show File +--R +--R File(S: SetCategory) is a domain constructor +--R Abbreviation for File is FILE +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for FILE +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean close! : % -> % +--R coerce : % -> OutputForm flush : % -> Void +--R hash : % -> SingleInteger iomode : % -> String +--R latex : % -> String name : % -> FileName +--R open : (FileName,String) -> % open : FileName -> % +--R read! : % -> S readIfCan! : % -> Union(S,"failed") +--R reopen! : (%,String) -> % write! : (%,S) -> S +--R ?~=? : (%,%) -> Boolean +--R +--E 13 + )system rm jazz1 )spool )lisp (bye) @@ -46201,13 +48284,14 @@ File(S:SetCategory): FileCategory(FileName, S) with )set message test on )set message auto off )clear all ---S 1 of 18 + +--S 1 of 19 fn: FileName --R --R Type: Void --E 1 ---S 2 of 18 +--S 2 of 19 fn := "fname.input" --R --R @@ -46215,7 +48299,7 @@ fn := "fname.input" --R Type: FileName --E 2 ---S 3 of 18 +--S 3 of 19 directory fn --R --R @@ -46223,7 +48307,7 @@ directory fn --R Type: String --E 3 ---S 4 of 18 +--S 4 of 19 name fn --R --R @@ -46231,7 +48315,7 @@ name fn --R Type: String --E 4 ---S 5 of 18 +--S 5 of 19 extension fn --R --R @@ -46239,7 +48323,7 @@ extension fn --R Type: String --E 5 ---S 6 of 18 +--S 6 of 19 fn := filename("/tmp", "fname", "input") --R --R @@ -46247,7 +48331,7 @@ fn := filename("/tmp", "fname", "input") --R Type: FileName --E 6 ---S 7 of 18 +--S 7 of 19 objdir := "/tmp" --R --R @@ -46255,7 +48339,7 @@ objdir := "/tmp" --R Type: String --E 7 ---S 8 of 18 +--S 8 of 19 fn := filename(objdir, "table", "spad") --R --R @@ -46263,7 +48347,7 @@ fn := filename(objdir, "table", "spad") --R Type: FileName --E 8 ---S 9 of 18 +--S 9 of 19 fn := filename("", "letter", "") --R --R @@ -46271,7 +48355,7 @@ fn := filename("", "letter", "") --R Type: FileName --E 9 ---S 10 of 18 +--S 10 of 19 exists? "/etc/passwd" --R --R @@ -46279,7 +48363,7 @@ exists? "/etc/passwd" --R Type: Boolean --E 10 ---S 11 of 18 +--S 11 of 19 readable? "/etc/passwd" --R --R @@ -46287,7 +48371,7 @@ readable? "/etc/passwd" --R Type: Boolean --E 11 ---S 12 of 18 +--S 12 of 19 readable? "/etc/security/passwd" --R --R @@ -46295,7 +48379,7 @@ readable? "/etc/security/passwd" --R Type: Boolean --E 12 ---S 13 of 18 +--S 13 of 19 readable? "/ect/passwd" --R --R @@ -46303,7 +48387,7 @@ readable? "/ect/passwd" --R Type: Boolean --E 13 ---S 14 of 18 +--S 14 of 19 writable? "/etc/passwd" --R --R @@ -46311,7 +48395,7 @@ writable? "/etc/passwd" --R Type: Boolean --E 14 ---S 15 of 18 +--S 15 of 19 writable? "/dev/null" --R --R @@ -46319,7 +48403,7 @@ writable? "/dev/null" --R Type: Boolean --E 15 ---S 16 of 18 +--S 16 of 19 writable? "/etc/DoesNotExist" --R --R @@ -46327,7 +48411,7 @@ writable? "/etc/DoesNotExist" --R Type: Boolean --E 16 ---S 17 of 18 +--S 17 of 19 writable? "/tmp/DoesNotExist" --R --R @@ -46335,13 +48419,34 @@ writable? "/tmp/DoesNotExist" --R Type: Boolean --E 17 ---S 18 of 18 +--S 18 of 19 fn := new(objdir, "xxx", "yy") --R --R --I (18) "/tmp/xxx1419.yy" --R Type: FileName --E 18 + +--S 19 of 19 +)show FileName +--R +--R FileName is a domain constructor +--R Abbreviation for FileName is FNAME +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for FNAME +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean coerce : % -> String +--R coerce : String -> % coerce : % -> OutputForm +--R directory : % -> String exists? : % -> Boolean +--R extension : % -> String hash : % -> SingleInteger +--R latex : % -> String name : % -> String +--R new : (String,String,String) -> % readable? : % -> Boolean +--R writable? : % -> Boolean ?~=? : (%,%) -> Boolean +--R filename : (String,String,String) -> % +--R +--E 19 + )spool )lisp (bye) \end{chunk} @@ -46548,21 +48653,20 @@ FileName(): FileNameCategory == add --R Issue )edit bookvol10.3.pamphlet to see algebra source code for FDIV --R --R------------------------------- Operations -------------------------------- ---R ?*? : (Integer,%) -> % ?*? : (PositiveInteger,%) -> % ---R ?+? : (%,%) -> % ?-? : (%,%) -> % ---R -? : % -> % ?=? : (%,%) -> Boolean ---R 0 : () -> % coerce : % -> OutputForm ---R divisor : (R,UP,UP,UP,F) -> % divisor : (F,F,Integer) -> % ---R divisor : (F,F) -> % divisor : R -> % ---R finiteBasis : % -> Vector(R) hash : % -> SingleInteger +--R ?*? : (Integer,%) -> % ?*? : (NonNegativeInteger,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?+? : (%,%) -> % +--R ?-? : (%,%) -> % -? : % -> % +--R ?=? : (%,%) -> Boolean 0 : () -> % +--R coerce : % -> OutputForm divisor : (R,UP,UP,UP,F) -> % +--R divisor : (F,F,Integer) -> % divisor : (F,F) -> % +--R divisor : R -> % finiteBasis : % -> Vector(R) +--R generator : % -> Union(R,"failed") hash : % -> SingleInteger --R lSpaceBasis : % -> Vector(R) latex : % -> String --R principal? : % -> Boolean reduce : % -> % --R sample : () -> % zero? : % -> Boolean --R ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % --R decompose : % -> Record(id: FractionalIdeal(UP,Fraction(UP),UPUP,R),principalPart: R) --R divisor : FractionalIdeal(UP,Fraction(UP),UPUP,R) -> % ---R generator : % -> Union(R,"failed") --R ideal : % -> FractionalIdeal(UP,Fraction(UP),UPUP,R) --R subtractIfCan : (%,%) -> Union(%,"failed") --R @@ -46773,38 +48877,36 @@ FiniteDivisor(F, UP, UPUP, R): Exports == Implementation where --R ?*? : (PrimeField(p),%) -> % ?*? : (%,PrimeField(p)) -> % --R ?*? : (Fraction(Integer),%) -> % ?*? : (%,Fraction(Integer)) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,Integer) -> % ?**? : (%,NonNegativeInteger) -> % --R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % --R ?-? : (%,%) -> % -? : % -> % --R ?/? : (%,PrimeField(p)) -> % ?/? : (%,%) -> % --R ?=? : (%,%) -> Boolean 1 : () -> % --R 0 : () -> % ?^? : (%,Integer) -> % ---R ?^? : (%,PositiveInteger) -> % algebraic? : % -> Boolean ---R associates? : (%,%) -> Boolean basis : () -> Vector(%) ---R coerce : PrimeField(p) -> % coerce : Fraction(Integer) -> % ---R coerce : % -> % coerce : Integer -> % ---R coerce : % -> OutputForm degree : % -> PositiveInteger ---R dimension : () -> CardinalNumber factor : % -> Factored(%) ---R gcd : List(%) -> % gcd : (%,%) -> % ---R hash : % -> SingleInteger inGroundField? : % -> Boolean ---R inv : % -> % latex : % -> String ---R lcm : List(%) -> % lcm : (%,%) -> % ---R norm : % -> PrimeField(p) one? : % -> Boolean ---R prime? : % -> Boolean ?quo? : (%,%) -> % ---R recip : % -> Union(%,"failed") ?rem? : (%,%) -> % ---R retract : % -> PrimeField(p) sample : () -> % ---R sizeLess? : (%,%) -> Boolean squareFree : % -> Factored(%) ---R squareFreePart : % -> % trace : % -> PrimeField(p) ---R transcendent? : % -> Boolean unit? : % -> Boolean ---R unitCanonical : % -> % zero? : % -> Boolean ---R ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R algebraic? : % -> Boolean associates? : (%,%) -> Boolean +--R basis : () -> Vector(%) coerce : PrimeField(p) -> % +--R coerce : Fraction(Integer) -> % coerce : % -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R degree : % -> PositiveInteger dimension : () -> CardinalNumber +--R factor : % -> Factored(%) gcd : List(%) -> % +--R gcd : (%,%) -> % hash : % -> SingleInteger +--R inGroundField? : % -> Boolean inv : % -> % +--R latex : % -> String lcm : List(%) -> % +--R lcm : (%,%) -> % norm : % -> PrimeField(p) +--R one? : % -> Boolean prime? : % -> Boolean +--R ?quo? : (%,%) -> % recip : % -> Union(%,"failed") +--R ?rem? : (%,%) -> % retract : % -> PrimeField(p) +--R sample : () -> % sizeLess? : (%,%) -> Boolean +--R squareFree : % -> Factored(%) squareFreePart : % -> % +--R trace : % -> PrimeField(p) transcendent? : % -> Boolean +--R unit? : % -> Boolean unitCanonical : % -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean --R D : (%,NonNegativeInteger) -> % if PrimeField(p) has FINITE --R D : % -> % if PrimeField(p) has FINITE --R Frobenius : (%,NonNegativeInteger) -> % if PrimeField(p) has FINITE --R Frobenius : % -> % if PrimeField(p) has FINITE ---R ?^? : (%,NonNegativeInteger) -> % --R basis : PositiveInteger -> Vector(%) --R characteristic : () -> NonNegativeInteger --R charthRoot : % -> Union(%,"failed") if PrimeField(p) has CHARNZ or PrimeField(p) has FINITE @@ -47034,38 +49136,36 @@ FiniteField(p:PositiveInteger, n:PositiveInteger): _ --R ?*? : (PrimeField(p),%) -> % ?*? : (%,PrimeField(p)) -> % --R ?*? : (Fraction(Integer),%) -> % ?*? : (%,Fraction(Integer)) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,Integer) -> % ?**? : (%,NonNegativeInteger) -> % --R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % --R ?-? : (%,%) -> % -? : % -> % --R ?/? : (%,PrimeField(p)) -> % ?/? : (%,%) -> % --R ?=? : (%,%) -> Boolean 1 : () -> % --R 0 : () -> % ?^? : (%,Integer) -> % ---R ?^? : (%,PositiveInteger) -> % algebraic? : % -> Boolean ---R associates? : (%,%) -> Boolean basis : () -> Vector(%) ---R coerce : PrimeField(p) -> % coerce : Fraction(Integer) -> % ---R coerce : % -> % coerce : Integer -> % ---R coerce : % -> OutputForm degree : % -> PositiveInteger ---R dimension : () -> CardinalNumber factor : % -> Factored(%) ---R gcd : List(%) -> % gcd : (%,%) -> % ---R hash : % -> SingleInteger inGroundField? : % -> Boolean ---R inv : % -> % latex : % -> String ---R lcm : List(%) -> % lcm : (%,%) -> % ---R norm : % -> PrimeField(p) one? : % -> Boolean ---R prime? : % -> Boolean ?quo? : (%,%) -> % ---R recip : % -> Union(%,"failed") ?rem? : (%,%) -> % ---R retract : % -> PrimeField(p) sample : () -> % ---R sizeLess? : (%,%) -> Boolean squareFree : % -> Factored(%) ---R squareFreePart : % -> % trace : % -> PrimeField(p) ---R transcendent? : % -> Boolean unit? : % -> Boolean ---R unitCanonical : % -> % zero? : % -> Boolean ---R ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R algebraic? : % -> Boolean associates? : (%,%) -> Boolean +--R basis : () -> Vector(%) coerce : PrimeField(p) -> % +--R coerce : Fraction(Integer) -> % coerce : % -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R degree : % -> PositiveInteger dimension : () -> CardinalNumber +--R factor : % -> Factored(%) gcd : List(%) -> % +--R gcd : (%,%) -> % hash : % -> SingleInteger +--R inGroundField? : % -> Boolean inv : % -> % +--R latex : % -> String lcm : List(%) -> % +--R lcm : (%,%) -> % norm : % -> PrimeField(p) +--R one? : % -> Boolean prime? : % -> Boolean +--R ?quo? : (%,%) -> % recip : % -> Union(%,"failed") +--R ?rem? : (%,%) -> % retract : % -> PrimeField(p) +--R sample : () -> % sizeLess? : (%,%) -> Boolean +--R squareFree : % -> Factored(%) squareFreePart : % -> % +--R trace : % -> PrimeField(p) transcendent? : % -> Boolean +--R unit? : % -> Boolean unitCanonical : % -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean --R D : (%,NonNegativeInteger) -> % if PrimeField(p) has FINITE --R D : % -> % if PrimeField(p) has FINITE --R Frobenius : (%,NonNegativeInteger) -> % if PrimeField(p) has FINITE --R Frobenius : % -> % if PrimeField(p) has FINITE ---R ?^? : (%,NonNegativeInteger) -> % --R basis : PositiveInteger -> Vector(%) --R characteristic : () -> NonNegativeInteger --R charthRoot : % -> Union(%,"failed") if PrimeField(p) has CHARNZ or PrimeField(p) has FINITE @@ -47309,38 +49409,38 @@ FiniteFieldCyclicGroup(p,extdeg):_ --R ?*? : (GF,%) -> % ?*? : (%,GF) -> % --R ?*? : (Fraction(Integer),%) -> % ?*? : (%,Fraction(Integer)) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,Integer) -> % ?**? : (%,NonNegativeInteger) -> % --R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % --R ?-? : (%,%) -> % -? : % -> % --R ?/? : (%,GF) -> % ?/? : (%,%) -> % --R ?=? : (%,%) -> Boolean D : % -> % if GF has FINITE --R 1 : () -> % 0 : () -> % ---R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> % ---R algebraic? : % -> Boolean associates? : (%,%) -> Boolean ---R basis : () -> Vector(%) coerce : GF -> % ---R coerce : Fraction(Integer) -> % coerce : % -> % ---R coerce : Integer -> % coerce : % -> OutputForm ---R coordinates : % -> Vector(GF) degree : % -> PositiveInteger ---R dimension : () -> CardinalNumber factor : % -> Factored(%) ---R gcd : List(%) -> % gcd : (%,%) -> % ---R hash : % -> SingleInteger inGroundField? : % -> Boolean +--R ?^? : (%,Integer) -> % ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,PositiveInteger) -> % algebraic? : % -> Boolean +--R associates? : (%,%) -> Boolean basis : () -> Vector(%) +--R coerce : GF -> % coerce : Fraction(Integer) -> % +--R coerce : % -> % coerce : Integer -> % +--R coerce : % -> OutputForm coordinates : % -> Vector(GF) +--R degree : % -> PositiveInteger dimension : () -> CardinalNumber +--R factor : % -> Factored(%) gcd : List(%) -> % +--R gcd : (%,%) -> % hash : % -> SingleInteger +--R inGroundField? : % -> Boolean init : () -> % if GF has FINITE --R inv : % -> % latex : % -> String --R lcm : List(%) -> % lcm : (%,%) -> % --R norm : % -> GF one? : % -> Boolean --R prime? : % -> Boolean ?quo? : (%,%) -> % ---R recip : % -> Union(%,"failed") ?rem? : (%,%) -> % ---R represents : Vector(GF) -> % retract : % -> GF ---R sample : () -> % sizeLess? : (%,%) -> Boolean ---R squareFree : % -> Factored(%) squareFreePart : % -> % ---R trace : % -> GF transcendent? : % -> Boolean ---R unit? : % -> Boolean unitCanonical : % -> % ---R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % +--R random : () -> % if GF has FINITE recip : % -> Union(%,"failed") +--R ?rem? : (%,%) -> % represents : Vector(GF) -> % +--R retract : % -> GF sample : () -> % +--R sizeLess? : (%,%) -> Boolean squareFree : % -> Factored(%) +--R squareFreePart : % -> % trace : % -> GF +--R transcendent? : % -> Boolean unit? : % -> Boolean +--R unitCanonical : % -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean --R D : (%,NonNegativeInteger) -> % if GF has FINITE --R Frobenius : (%,NonNegativeInteger) -> % if GF has FINITE --R Frobenius : % -> % if GF has FINITE ---R ?^? : (%,NonNegativeInteger) -> % --R basis : PositiveInteger -> Vector(%) --R characteristic : () -> NonNegativeInteger --R charthRoot : % -> Union(%,"failed") if GF has CHARNZ or GF has FINITE @@ -47369,7 +49469,6 @@ FiniteFieldCyclicGroup(p,extdeg):_ --R generator : () -> % if GF has FINITE --R getZechTable : () -> PrimitiveArray(SingleInteger) --R index : PositiveInteger -> % if GF has FINITE ---R init : () -> % if GF has FINITE --R lcmCoef : (%,%) -> Record(llcmres: %,coeff1: %,coeff2: %) --R linearAssociatedExp : (%,SparseUnivariatePolynomial(GF)) -> % if GF has FINITE --R linearAssociatedLog : (%,%) -> Union(SparseUnivariatePolynomial(GF),"failed") if GF has FINITE @@ -47390,7 +49489,6 @@ FiniteFieldCyclicGroup(p,extdeg):_ --R primitive? : % -> Boolean if GF has FINITE --R primitiveElement : () -> % if GF has FINITE --R principalIdeal : List(%) -> Record(coef: List(%),generator: %) ---R random : () -> % if GF has FINITE --R representationType : () -> Union("prime",polynomial,normal,cyclic) if GF has FINITE --R retractIfCan : % -> Union(GF,"failed") --R size : () -> NonNegativeInteger if GF has FINITE @@ -47584,38 +49682,38 @@ FiniteFieldCyclicGroupExtension(GF,extdeg):_ --R ?*? : (GF,%) -> % ?*? : (%,GF) -> % --R ?*? : (Fraction(Integer),%) -> % ?*? : (%,Fraction(Integer)) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,Integer) -> % ?**? : (%,NonNegativeInteger) -> % --R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % --R ?-? : (%,%) -> % -? : % -> % --R ?/? : (%,GF) -> % ?/? : (%,%) -> % --R ?=? : (%,%) -> Boolean D : % -> % if GF has FINITE --R 1 : () -> % 0 : () -> % ---R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> % ---R algebraic? : % -> Boolean associates? : (%,%) -> Boolean ---R basis : () -> Vector(%) coerce : GF -> % ---R coerce : Fraction(Integer) -> % coerce : % -> % ---R coerce : Integer -> % coerce : % -> OutputForm ---R coordinates : % -> Vector(GF) degree : % -> PositiveInteger ---R dimension : () -> CardinalNumber factor : % -> Factored(%) ---R gcd : List(%) -> % gcd : (%,%) -> % ---R hash : % -> SingleInteger inGroundField? : % -> Boolean +--R ?^? : (%,Integer) -> % ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,PositiveInteger) -> % algebraic? : % -> Boolean +--R associates? : (%,%) -> Boolean basis : () -> Vector(%) +--R coerce : GF -> % coerce : Fraction(Integer) -> % +--R coerce : % -> % coerce : Integer -> % +--R coerce : % -> OutputForm coordinates : % -> Vector(GF) +--R degree : % -> PositiveInteger dimension : () -> CardinalNumber +--R factor : % -> Factored(%) gcd : List(%) -> % +--R gcd : (%,%) -> % hash : % -> SingleInteger +--R inGroundField? : % -> Boolean init : () -> % if GF has FINITE --R inv : % -> % latex : % -> String --R lcm : List(%) -> % lcm : (%,%) -> % --R norm : % -> GF one? : % -> Boolean --R prime? : % -> Boolean ?quo? : (%,%) -> % ---R recip : % -> Union(%,"failed") ?rem? : (%,%) -> % ---R represents : Vector(GF) -> % retract : % -> GF ---R sample : () -> % sizeLess? : (%,%) -> Boolean ---R squareFree : % -> Factored(%) squareFreePart : % -> % ---R trace : % -> GF transcendent? : % -> Boolean ---R unit? : % -> Boolean unitCanonical : % -> % ---R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % +--R random : () -> % if GF has FINITE recip : % -> Union(%,"failed") +--R ?rem? : (%,%) -> % represents : Vector(GF) -> % +--R retract : % -> GF sample : () -> % +--R sizeLess? : (%,%) -> Boolean squareFree : % -> Factored(%) +--R squareFreePart : % -> % trace : % -> GF +--R transcendent? : % -> Boolean unit? : % -> Boolean +--R unitCanonical : % -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean --R D : (%,NonNegativeInteger) -> % if GF has FINITE --R Frobenius : (%,NonNegativeInteger) -> % if GF has FINITE --R Frobenius : % -> % if GF has FINITE ---R ?^? : (%,NonNegativeInteger) -> % --R basis : PositiveInteger -> Vector(%) --R characteristic : () -> NonNegativeInteger --R charthRoot : % -> Union(%,"failed") if GF has CHARNZ or GF has FINITE @@ -47644,7 +49742,6 @@ FiniteFieldCyclicGroupExtension(GF,extdeg):_ --R generator : () -> % if GF has FINITE --R getZechTable : () -> PrimitiveArray(SingleInteger) --R index : PositiveInteger -> % if GF has FINITE ---R init : () -> % if GF has FINITE --R lcmCoef : (%,%) -> Record(llcmres: %,coeff1: %,coeff2: %) --R linearAssociatedExp : (%,SparseUnivariatePolynomial(GF)) -> % if GF has FINITE --R linearAssociatedLog : (%,%) -> Union(SparseUnivariatePolynomial(GF),"failed") if GF has FINITE @@ -47665,7 +49762,6 @@ FiniteFieldCyclicGroupExtension(GF,extdeg):_ --R primitive? : % -> Boolean if GF has FINITE --R primitiveElement : () -> % if GF has FINITE --R principalIdeal : List(%) -> Record(coef: List(%),generator: %) ---R random : () -> % if GF has FINITE --R representationType : () -> Union("prime",polynomial,normal,cyclic) if GF has FINITE --R retractIfCan : % -> Union(GF,"failed") --R size : () -> NonNegativeInteger if GF has FINITE @@ -48126,38 +50222,38 @@ FiniteFieldCyclicGroupExtensionByPolynomial(GF,defpol):_ --R ?*? : (GF,%) -> % ?*? : (%,GF) -> % --R ?*? : (Fraction(Integer),%) -> % ?*? : (%,Fraction(Integer)) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,Integer) -> % ?**? : (%,NonNegativeInteger) -> % --R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % --R ?-? : (%,%) -> % -? : % -> % --R ?/? : (%,GF) -> % ?/? : (%,%) -> % --R ?=? : (%,%) -> Boolean D : % -> % if GF has FINITE --R 1 : () -> % 0 : () -> % ---R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> % ---R algebraic? : % -> Boolean associates? : (%,%) -> Boolean ---R basis : () -> Vector(%) coerce : GF -> % ---R coerce : Fraction(Integer) -> % coerce : % -> % ---R coerce : Integer -> % coerce : % -> OutputForm ---R coordinates : % -> Vector(GF) degree : % -> PositiveInteger ---R dimension : () -> CardinalNumber factor : % -> Factored(%) ---R gcd : List(%) -> % gcd : (%,%) -> % ---R hash : % -> SingleInteger inGroundField? : % -> Boolean +--R ?^? : (%,Integer) -> % ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,PositiveInteger) -> % algebraic? : % -> Boolean +--R associates? : (%,%) -> Boolean basis : () -> Vector(%) +--R coerce : GF -> % coerce : Fraction(Integer) -> % +--R coerce : % -> % coerce : Integer -> % +--R coerce : % -> OutputForm coordinates : % -> Vector(GF) +--R degree : % -> PositiveInteger dimension : () -> CardinalNumber +--R factor : % -> Factored(%) gcd : List(%) -> % +--R gcd : (%,%) -> % hash : % -> SingleInteger +--R inGroundField? : % -> Boolean init : () -> % if GF has FINITE --R inv : % -> % latex : % -> String --R lcm : List(%) -> % lcm : (%,%) -> % --R norm : % -> GF one? : % -> Boolean --R prime? : % -> Boolean ?quo? : (%,%) -> % ---R recip : % -> Union(%,"failed") ?rem? : (%,%) -> % ---R represents : Vector(GF) -> % retract : % -> GF ---R sample : () -> % sizeLess? : (%,%) -> Boolean ---R squareFree : % -> Factored(%) squareFreePart : % -> % ---R trace : % -> GF transcendent? : % -> Boolean ---R unit? : % -> Boolean unitCanonical : % -> % ---R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % +--R random : () -> % if GF has FINITE recip : % -> Union(%,"failed") +--R ?rem? : (%,%) -> % represents : Vector(GF) -> % +--R retract : % -> GF sample : () -> % +--R sizeLess? : (%,%) -> Boolean squareFree : % -> Factored(%) +--R squareFreePart : % -> % trace : % -> GF +--R transcendent? : % -> Boolean unit? : % -> Boolean +--R unitCanonical : % -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean --R D : (%,NonNegativeInteger) -> % if GF has FINITE --R Frobenius : (%,NonNegativeInteger) -> % if GF has FINITE --R Frobenius : % -> % if GF has FINITE ---R ?^? : (%,NonNegativeInteger) -> % --R basis : PositiveInteger -> Vector(%) --R characteristic : () -> NonNegativeInteger --R charthRoot : % -> Union(%,"failed") if GF has CHARNZ or GF has FINITE @@ -48185,7 +50281,6 @@ FiniteFieldCyclicGroupExtensionByPolynomial(GF,defpol):_ --R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) --R generator : () -> % if GF has FINITE --R index : PositiveInteger -> % if GF has FINITE ---R init : () -> % if GF has FINITE --R lcmCoef : (%,%) -> Record(llcmres: %,coeff1: %,coeff2: %) --R linearAssociatedExp : (%,SparseUnivariatePolynomial(GF)) -> % if GF has FINITE --R linearAssociatedLog : (%,%) -> Union(SparseUnivariatePolynomial(GF),"failed") if GF has FINITE @@ -48206,7 +50301,6 @@ FiniteFieldCyclicGroupExtensionByPolynomial(GF,defpol):_ --R primitive? : % -> Boolean if GF has FINITE --R primitiveElement : () -> % if GF has FINITE --R principalIdeal : List(%) -> Record(coef: List(%),generator: %) ---R random : () -> % if GF has FINITE --R representationType : () -> Union("prime",polynomial,normal,cyclic) if GF has FINITE --R retractIfCan : % -> Union(GF,"failed") --R size : () -> NonNegativeInteger if GF has FINITE @@ -48388,38 +50482,38 @@ FiniteFieldExtension(GF, n): Exports == Implementation where --R ?*? : (GF,%) -> % ?*? : (%,GF) -> % --R ?*? : (Fraction(Integer),%) -> % ?*? : (%,Fraction(Integer)) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,Integer) -> % ?**? : (%,NonNegativeInteger) -> % --R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % --R ?-? : (%,%) -> % -? : % -> % --R ?/? : (%,GF) -> % ?/? : (%,%) -> % --R ?=? : (%,%) -> Boolean D : % -> % if GF has FINITE --R 1 : () -> % 0 : () -> % ---R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> % ---R algebraic? : % -> Boolean associates? : (%,%) -> Boolean ---R basis : () -> Vector(%) coerce : GF -> % ---R coerce : Fraction(Integer) -> % coerce : % -> % ---R coerce : Integer -> % coerce : % -> OutputForm ---R coordinates : % -> Vector(GF) degree : % -> PositiveInteger ---R dimension : () -> CardinalNumber factor : % -> Factored(%) ---R gcd : List(%) -> % gcd : (%,%) -> % ---R hash : % -> SingleInteger inGroundField? : % -> Boolean +--R ?^? : (%,Integer) -> % ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,PositiveInteger) -> % algebraic? : % -> Boolean +--R associates? : (%,%) -> Boolean basis : () -> Vector(%) +--R coerce : GF -> % coerce : Fraction(Integer) -> % +--R coerce : % -> % coerce : Integer -> % +--R coerce : % -> OutputForm coordinates : % -> Vector(GF) +--R degree : % -> PositiveInteger dimension : () -> CardinalNumber +--R factor : % -> Factored(%) gcd : List(%) -> % +--R gcd : (%,%) -> % hash : % -> SingleInteger +--R inGroundField? : % -> Boolean init : () -> % if GF has FINITE --R inv : % -> % latex : % -> String --R lcm : List(%) -> % lcm : (%,%) -> % --R norm : % -> GF one? : % -> Boolean --R prime? : % -> Boolean ?quo? : (%,%) -> % ---R recip : % -> Union(%,"failed") ?rem? : (%,%) -> % ---R represents : Vector(GF) -> % retract : % -> GF ---R sample : () -> % sizeLess? : (%,%) -> Boolean ---R squareFree : % -> Factored(%) squareFreePart : % -> % ---R trace : % -> GF transcendent? : % -> Boolean ---R unit? : % -> Boolean unitCanonical : % -> % ---R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % +--R random : () -> % if GF has FINITE recip : % -> Union(%,"failed") +--R ?rem? : (%,%) -> % represents : Vector(GF) -> % +--R retract : % -> GF sample : () -> % +--R sizeLess? : (%,%) -> Boolean squareFree : % -> Factored(%) +--R squareFreePart : % -> % trace : % -> GF +--R transcendent? : % -> Boolean unit? : % -> Boolean +--R unitCanonical : % -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean --R D : (%,NonNegativeInteger) -> % if GF has FINITE --R Frobenius : (%,NonNegativeInteger) -> % if GF has FINITE --R Frobenius : % -> % if GF has FINITE ---R ?^? : (%,NonNegativeInteger) -> % --R basis : PositiveInteger -> Vector(%) --R characteristic : () -> NonNegativeInteger --R charthRoot : % -> Union(%,"failed") if GF has CHARNZ or GF has FINITE @@ -48447,7 +50541,6 @@ FiniteFieldExtension(GF, n): Exports == Implementation where --R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) --R generator : () -> % if GF has FINITE --R index : PositiveInteger -> % if GF has FINITE ---R init : () -> % if GF has FINITE --R lcmCoef : (%,%) -> Record(llcmres: %,coeff1: %,coeff2: %) --R linearAssociatedExp : (%,SparseUnivariatePolynomial(GF)) -> % if GF has FINITE --R linearAssociatedLog : (%,%) -> Union(SparseUnivariatePolynomial(GF),"failed") if GF has FINITE @@ -48468,7 +50561,6 @@ FiniteFieldExtension(GF, n): Exports == Implementation where --R primitive? : % -> Boolean if GF has FINITE --R primitiveElement : () -> % if GF has FINITE --R principalIdeal : List(%) -> Record(coef: List(%),generator: %) ---R random : () -> % if GF has FINITE --R representationType : () -> Union("prime",polynomial,normal,cyclic) if GF has FINITE --R retractIfCan : % -> Union(GF,"failed") --R size : () -> NonNegativeInteger if GF has FINITE @@ -48850,38 +50942,36 @@ FiniteFieldExtensionByPolynomial(GF:FiniteFieldCategory,_ --R ?*? : (PrimeField(p),%) -> % ?*? : (%,PrimeField(p)) -> % --R ?*? : (Fraction(Integer),%) -> % ?*? : (%,Fraction(Integer)) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,Integer) -> % ?**? : (%,NonNegativeInteger) -> % --R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % --R ?-? : (%,%) -> % -? : % -> % --R ?/? : (%,PrimeField(p)) -> % ?/? : (%,%) -> % --R ?=? : (%,%) -> Boolean 1 : () -> % --R 0 : () -> % ?^? : (%,Integer) -> % ---R ?^? : (%,PositiveInteger) -> % algebraic? : % -> Boolean ---R associates? : (%,%) -> Boolean basis : () -> Vector(%) ---R coerce : PrimeField(p) -> % coerce : Fraction(Integer) -> % ---R coerce : % -> % coerce : Integer -> % ---R coerce : % -> OutputForm degree : % -> PositiveInteger ---R dimension : () -> CardinalNumber factor : % -> Factored(%) ---R gcd : List(%) -> % gcd : (%,%) -> % ---R hash : % -> SingleInteger inGroundField? : % -> Boolean ---R inv : % -> % latex : % -> String ---R lcm : List(%) -> % lcm : (%,%) -> % ---R norm : % -> PrimeField(p) one? : % -> Boolean ---R prime? : % -> Boolean ?quo? : (%,%) -> % ---R recip : % -> Union(%,"failed") ?rem? : (%,%) -> % ---R retract : % -> PrimeField(p) sample : () -> % ---R sizeLess? : (%,%) -> Boolean squareFree : % -> Factored(%) ---R squareFreePart : % -> % trace : % -> PrimeField(p) ---R transcendent? : % -> Boolean unit? : % -> Boolean ---R unitCanonical : % -> % zero? : % -> Boolean ---R ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R algebraic? : % -> Boolean associates? : (%,%) -> Boolean +--R basis : () -> Vector(%) coerce : PrimeField(p) -> % +--R coerce : Fraction(Integer) -> % coerce : % -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R degree : % -> PositiveInteger dimension : () -> CardinalNumber +--R factor : % -> Factored(%) gcd : List(%) -> % +--R gcd : (%,%) -> % hash : % -> SingleInteger +--R inGroundField? : % -> Boolean inv : % -> % +--R latex : % -> String lcm : List(%) -> % +--R lcm : (%,%) -> % norm : % -> PrimeField(p) +--R one? : % -> Boolean prime? : % -> Boolean +--R ?quo? : (%,%) -> % recip : % -> Union(%,"failed") +--R ?rem? : (%,%) -> % retract : % -> PrimeField(p) +--R sample : () -> % sizeLess? : (%,%) -> Boolean +--R squareFree : % -> Factored(%) squareFreePart : % -> % +--R trace : % -> PrimeField(p) transcendent? : % -> Boolean +--R unit? : % -> Boolean unitCanonical : % -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean --R D : (%,NonNegativeInteger) -> % if PrimeField(p) has FINITE --R D : % -> % if PrimeField(p) has FINITE --R Frobenius : (%,NonNegativeInteger) -> % if PrimeField(p) has FINITE --R Frobenius : % -> % if PrimeField(p) has FINITE ---R ?^? : (%,NonNegativeInteger) -> % --R basis : PositiveInteger -> Vector(%) --R characteristic : () -> NonNegativeInteger --R charthRoot : % -> Union(%,"failed") if PrimeField(p) has CHARNZ or PrimeField(p) has FINITE @@ -49137,38 +51227,38 @@ FiniteFieldNormalBasis(p,extdeg):_ --R ?*? : (GF,%) -> % ?*? : (%,GF) -> % --R ?*? : (Fraction(Integer),%) -> % ?*? : (%,Fraction(Integer)) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,Integer) -> % ?**? : (%,NonNegativeInteger) -> % --R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % --R ?-? : (%,%) -> % -? : % -> % --R ?/? : (%,GF) -> % ?/? : (%,%) -> % --R ?=? : (%,%) -> Boolean D : % -> % if GF has FINITE --R 1 : () -> % 0 : () -> % ---R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> % ---R algebraic? : % -> Boolean associates? : (%,%) -> Boolean ---R basis : () -> Vector(%) coerce : GF -> % ---R coerce : Fraction(Integer) -> % coerce : % -> % ---R coerce : Integer -> % coerce : % -> OutputForm ---R coordinates : % -> Vector(GF) degree : % -> PositiveInteger ---R dimension : () -> CardinalNumber factor : % -> Factored(%) ---R gcd : List(%) -> % gcd : (%,%) -> % ---R hash : % -> SingleInteger inGroundField? : % -> Boolean +--R ?^? : (%,Integer) -> % ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,PositiveInteger) -> % algebraic? : % -> Boolean +--R associates? : (%,%) -> Boolean basis : () -> Vector(%) +--R coerce : GF -> % coerce : Fraction(Integer) -> % +--R coerce : % -> % coerce : Integer -> % +--R coerce : % -> OutputForm coordinates : % -> Vector(GF) +--R degree : % -> PositiveInteger dimension : () -> CardinalNumber +--R factor : % -> Factored(%) gcd : List(%) -> % +--R gcd : (%,%) -> % hash : % -> SingleInteger +--R inGroundField? : % -> Boolean init : () -> % if GF has FINITE --R inv : % -> % latex : % -> String --R lcm : List(%) -> % lcm : (%,%) -> % --R norm : % -> GF one? : % -> Boolean --R prime? : % -> Boolean ?quo? : (%,%) -> % ---R recip : % -> Union(%,"failed") ?rem? : (%,%) -> % ---R represents : Vector(GF) -> % retract : % -> GF ---R sample : () -> % sizeLess? : (%,%) -> Boolean ---R squareFree : % -> Factored(%) squareFreePart : % -> % ---R trace : % -> GF transcendent? : % -> Boolean ---R unit? : % -> Boolean unitCanonical : % -> % ---R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % +--R random : () -> % if GF has FINITE recip : % -> Union(%,"failed") +--R ?rem? : (%,%) -> % represents : Vector(GF) -> % +--R retract : % -> GF sample : () -> % +--R sizeLess? : (%,%) -> Boolean squareFree : % -> Factored(%) +--R squareFreePart : % -> % trace : % -> GF +--R transcendent? : % -> Boolean unit? : % -> Boolean +--R unitCanonical : % -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean --R D : (%,NonNegativeInteger) -> % if GF has FINITE --R Frobenius : (%,NonNegativeInteger) -> % if GF has FINITE --R Frobenius : % -> % if GF has FINITE ---R ?^? : (%,NonNegativeInteger) -> % --R basis : PositiveInteger -> Vector(%) --R characteristic : () -> NonNegativeInteger --R charthRoot : % -> Union(%,"failed") if GF has CHARNZ or GF has FINITE @@ -49198,7 +51288,6 @@ FiniteFieldNormalBasis(p,extdeg):_ --R getMultiplicationMatrix : () -> Matrix(GF) --R getMultiplicationTable : () -> Vector(List(Record(value: GF,index: SingleInteger))) --R index : PositiveInteger -> % if GF has FINITE ---R init : () -> % if GF has FINITE --R lcmCoef : (%,%) -> Record(llcmres: %,coeff1: %,coeff2: %) --R linearAssociatedExp : (%,SparseUnivariatePolynomial(GF)) -> % if GF has FINITE --R linearAssociatedLog : (%,%) -> Union(SparseUnivariatePolynomial(GF),"failed") if GF has FINITE @@ -49219,7 +51308,6 @@ FiniteFieldNormalBasis(p,extdeg):_ --R primitive? : % -> Boolean if GF has FINITE --R primitiveElement : () -> % if GF has FINITE --R principalIdeal : List(%) -> Record(coef: List(%),generator: %) ---R random : () -> % if GF has FINITE --R representationType : () -> Union("prime",polynomial,normal,cyclic) if GF has FINITE --R retractIfCan : % -> Union(GF,"failed") --R size : () -> NonNegativeInteger if GF has FINITE @@ -49423,38 +51511,38 @@ FiniteFieldNormalBasisExtension(GF,extdeg):_ --R ?*? : (GF,%) -> % ?*? : (%,GF) -> % --R ?*? : (Fraction(Integer),%) -> % ?*? : (%,Fraction(Integer)) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,Integer) -> % ?**? : (%,NonNegativeInteger) -> % --R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % --R ?-? : (%,%) -> % -? : % -> % --R ?/? : (%,GF) -> % ?/? : (%,%) -> % --R ?=? : (%,%) -> Boolean D : % -> % if GF has FINITE --R 1 : () -> % 0 : () -> % ---R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> % ---R algebraic? : % -> Boolean associates? : (%,%) -> Boolean ---R basis : () -> Vector(%) coerce : GF -> % ---R coerce : Fraction(Integer) -> % coerce : % -> % ---R coerce : Integer -> % coerce : % -> OutputForm ---R coordinates : % -> Vector(GF) degree : % -> PositiveInteger ---R dimension : () -> CardinalNumber factor : % -> Factored(%) ---R gcd : List(%) -> % gcd : (%,%) -> % ---R hash : % -> SingleInteger inGroundField? : % -> Boolean +--R ?^? : (%,Integer) -> % ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,PositiveInteger) -> % algebraic? : % -> Boolean +--R associates? : (%,%) -> Boolean basis : () -> Vector(%) +--R coerce : GF -> % coerce : Fraction(Integer) -> % +--R coerce : % -> % coerce : Integer -> % +--R coerce : % -> OutputForm coordinates : % -> Vector(GF) +--R degree : % -> PositiveInteger dimension : () -> CardinalNumber +--R factor : % -> Factored(%) gcd : List(%) -> % +--R gcd : (%,%) -> % hash : % -> SingleInteger +--R inGroundField? : % -> Boolean init : () -> % if GF has FINITE --R inv : % -> % latex : % -> String --R lcm : List(%) -> % lcm : (%,%) -> % --R norm : % -> GF one? : % -> Boolean --R prime? : % -> Boolean ?quo? : (%,%) -> % ---R recip : % -> Union(%,"failed") ?rem? : (%,%) -> % ---R represents : Vector(GF) -> % retract : % -> GF ---R sample : () -> % sizeLess? : (%,%) -> Boolean ---R squareFree : % -> Factored(%) squareFreePart : % -> % ---R trace : % -> GF transcendent? : % -> Boolean ---R unit? : % -> Boolean unitCanonical : % -> % ---R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % +--R random : () -> % if GF has FINITE recip : % -> Union(%,"failed") +--R ?rem? : (%,%) -> % represents : Vector(GF) -> % +--R retract : % -> GF sample : () -> % +--R sizeLess? : (%,%) -> Boolean squareFree : % -> Factored(%) +--R squareFreePart : % -> % trace : % -> GF +--R transcendent? : % -> Boolean unit? : % -> Boolean +--R unitCanonical : % -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean --R D : (%,NonNegativeInteger) -> % if GF has FINITE --R Frobenius : (%,NonNegativeInteger) -> % if GF has FINITE --R Frobenius : % -> % if GF has FINITE ---R ?^? : (%,NonNegativeInteger) -> % --R basis : PositiveInteger -> Vector(%) --R characteristic : () -> NonNegativeInteger --R charthRoot : % -> Union(%,"failed") if GF has CHARNZ or GF has FINITE @@ -49484,7 +51572,6 @@ FiniteFieldNormalBasisExtension(GF,extdeg):_ --R getMultiplicationMatrix : () -> Matrix(GF) --R getMultiplicationTable : () -> Vector(List(Record(value: GF,index: SingleInteger))) --R index : PositiveInteger -> % if GF has FINITE ---R init : () -> % if GF has FINITE --R lcmCoef : (%,%) -> Record(llcmres: %,coeff1: %,coeff2: %) --R linearAssociatedExp : (%,SparseUnivariatePolynomial(GF)) -> % if GF has FINITE --R linearAssociatedLog : (%,%) -> Union(SparseUnivariatePolynomial(GF),"failed") if GF has FINITE @@ -49505,7 +51592,6 @@ FiniteFieldNormalBasisExtension(GF,extdeg):_ --R primitive? : % -> Boolean if GF has FINITE --R primitiveElement : () -> % if GF has FINITE --R principalIdeal : List(%) -> Record(coef: List(%),generator: %) ---R random : () -> % if GF has FINITE --R representationType : () -> Union("prime",polynomial,normal,cyclic) if GF has FINITE --R retractIfCan : % -> Union(GF,"failed") --R size : () -> NonNegativeInteger if GF has FINITE @@ -50007,7 +52093,8 @@ divisor of the order of the multiplicative group" )set message test on )set message auto off )clear all ---S 1 of 16 + +--S 1 of 17 flexibleArray [i for i in 1..6] --R --R @@ -50015,7 +52102,7 @@ flexibleArray [i for i in 1..6] --R Type: FlexibleArray(PositiveInteger) --E 1 ---S 2 of 16 +--S 2 of 17 f : FARRAY INT := new(6,0) --R --R @@ -50023,7 +52110,7 @@ f : FARRAY INT := new(6,0) --R Type: FlexibleArray(Integer) --E 2 ---S 3 of 16 +--S 3 of 17 for i in 1..6 repeat f.i := i; f --R --R @@ -50031,7 +52118,7 @@ for i in 1..6 repeat f.i := i; f --R Type: FlexibleArray(Integer) --E 3 ---S 4 of 16 +--S 4 of 17 physicalLength f --R --R @@ -50039,7 +52126,7 @@ physicalLength f --R Type: PositiveInteger --E 4 ---S 5 of 16 +--S 5 of 17 concat!(f,11) --R --R @@ -50047,7 +52134,7 @@ concat!(f,11) --R Type: FlexibleArray(Integer) --E 5 ---S 6 of 16 +--S 6 of 17 physicalLength f --R --R @@ -50055,7 +52142,7 @@ physicalLength f --R Type: PositiveInteger --E 6 ---S 7 of 16 +--S 7 of 17 physicalLength!(f,15) --R --R @@ -50063,7 +52150,7 @@ physicalLength!(f,15) --R Type: FlexibleArray(Integer) --E 7 ---S 8 of 16 +--S 8 of 17 concat!(f,f) --R --R @@ -50071,7 +52158,7 @@ concat!(f,f) --R Type: FlexibleArray(Integer) --E 8 ---S 9 of 16 +--S 9 of 17 insert!(22,f,1) --R --R @@ -50079,7 +52166,7 @@ insert!(22,f,1) --R Type: FlexibleArray(Integer) --E 9 ---S 10 of 16 +--S 10 of 17 g := f(10..) --R --R @@ -50087,7 +52174,7 @@ g := f(10..) --R Type: FlexibleArray(Integer) --E 10 ---S 11 of 16 +--S 11 of 17 insert!(g,f,1) --R --R @@ -50095,7 +52182,7 @@ insert!(g,f,1) --R Type: FlexibleArray(Integer) --E 11 ---S 12 of 16 +--S 12 of 17 merge!(sort! f, sort! g) --R --R @@ -50103,7 +52190,7 @@ merge!(sort! f, sort! g) --R Type: FlexibleArray(Integer) --E 12 ---S 13 of 16 +--S 13 of 17 removeDuplicates! f --R --R @@ -50111,7 +52198,7 @@ removeDuplicates! f --R Type: FlexibleArray(Integer) --E 13 ---S 14 of 16 +--S 14 of 17 select!(i +-> even? i,f) --R --R @@ -50119,7 +52206,7 @@ select!(i +-> even? i,f) --R Type: FlexibleArray(Integer) --E 14 ---S 15 of 16 +--S 15 of 17 physicalLength f --R --R @@ -50127,13 +52214,105 @@ physicalLength f --R Type: PositiveInteger --E 15 ---S 16 of 16 +--S 16 of 17 shrinkable(false)$FlexibleArray(Integer) --R --R --R (16) true --R Type: Boolean --E 16 + +--S 17 of 17 +)show FlexibleArray + FlexibleArray(S: Type) is a domain constructor + Abbreviation for FlexibleArray is FARRAY + This constructor is exposed in this frame. + Issue )edit bookvol10.3.pamphlet to see algebra source code for FARRAY + +------------------------------- Operations -------------------------------- + concat : List(%) -> % concat : (%,%) -> % + concat : (S,%) -> % concat : (%,S) -> % + concat! : (%,S) -> % concat! : (%,%) -> % + construct : List(S) -> % copy : % -> % + delete : (%,Integer) -> % delete! : (%,Integer) -> % + ?.? : (%,Integer) -> S elt : (%,Integer,S) -> S + empty : () -> % empty? : % -> Boolean + entries : % -> List(S) eq? : (%,%) -> Boolean + flexibleArray : List(S) -> % index? : (Integer,%) -> Boolean + indices : % -> List(Integer) insert : (%,%,Integer) -> % + insert : (S,%,Integer) -> % insert! : (S,%,Integer) -> % + insert! : (%,%,Integer) -> % latex : % -> String if S has SETCAT + map : (((S,S) -> S),%,%) -> % map : ((S -> S),%) -> % + max : (%,%) -> % if S has ORDSET min : (%,%) -> % if S has ORDSET + new : (NonNegativeInteger,S) -> % physicalLength! : (%,Integer) -> % + qelt : (%,Integer) -> S remove! : ((S -> Boolean),%) -> % + reverse : % -> % sample : () -> % + select! : ((S -> Boolean),%) -> % shrinkable : Boolean -> Boolean + sort : % -> % if S has ORDSET sort : (((S,S) -> Boolean),%) -> % + #? : % -> NonNegativeInteger if $ has finiteAggregate + ? Boolean if S has ORDSET + ?<=? : (%,%) -> Boolean if S has ORDSET + ?=? : (%,%) -> Boolean if S has SETCAT + ?>? : (%,%) -> Boolean if S has ORDSET + ?>=? : (%,%) -> Boolean if S has ORDSET + any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate + coerce : % -> OutputForm if S has SETCAT + convert : % -> InputForm if S has KONVERT(INFORM) + copyInto! : (%,%,Integer) -> % if $ has shallowlyMutable + count : (S,%) -> NonNegativeInteger if $ has finiteAggregate and S has SETCAT + count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate + delete : (%,UniversalSegment(Integer)) -> % + delete! : (%,UniversalSegment(Integer)) -> % + ?.? : (%,UniversalSegment(Integer)) -> % + entry? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT + eval : (%,List(S),List(S)) -> % if S has EVALAB(S) and S has SETCAT + eval : (%,S,S) -> % if S has EVALAB(S) and S has SETCAT + eval : (%,Equation(S)) -> % if S has EVALAB(S) and S has SETCAT + eval : (%,List(Equation(S))) -> % if S has EVALAB(S) and S has SETCAT + every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate + fill! : (%,S) -> % if $ has shallowlyMutable + find : ((S -> Boolean),%) -> Union(S,"failed") + first : % -> S if Integer has ORDSET + hash : % -> SingleInteger if S has SETCAT + less? : (%,NonNegativeInteger) -> Boolean + map! : ((S -> S),%) -> % if $ has shallowlyMutable + maxIndex : % -> Integer if Integer has ORDSET + member? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT + members : % -> List(S) if $ has finiteAggregate + merge : (%,%) -> % if S has ORDSET + merge : (((S,S) -> Boolean),%,%) -> % + merge! : (((S,S) -> Boolean),%,%) -> % + merge! : (%,%) -> % if S has ORDSET + minIndex : % -> Integer if Integer has ORDSET + more? : (%,NonNegativeInteger) -> Boolean + parts : % -> List(S) if $ has finiteAggregate + physicalLength : % -> NonNegativeInteger + position : (S,%,Integer) -> Integer if S has SETCAT + position : (S,%) -> Integer if S has SETCAT + position : ((S -> Boolean),%) -> Integer + qsetelt! : (%,Integer,S) -> S if $ has shallowlyMutable + reduce : (((S,S) -> S),%) -> S if $ has finiteAggregate + reduce : (((S,S) -> S),%,S) -> S if $ has finiteAggregate + reduce : (((S,S) -> S),%,S,S) -> S if $ has finiteAggregate and S has SETCAT + remove : ((S -> Boolean),%) -> % if $ has finiteAggregate + remove : (S,%) -> % if $ has finiteAggregate and S has SETCAT + remove! : (S,%) -> % if S has SETCAT + removeDuplicates : % -> % if $ has finiteAggregate and S has SETCAT + removeDuplicates! : % -> % if S has SETCAT + reverse! : % -> % if $ has shallowlyMutable + select : ((S -> Boolean),%) -> % if $ has finiteAggregate + setelt : (%,UniversalSegment(Integer),S) -> S if $ has shallowlyMutable + setelt : (%,Integer,S) -> S if $ has shallowlyMutable + size? : (%,NonNegativeInteger) -> Boolean + sort! : % -> % if $ has shallowlyMutable and S has ORDSET + sort! : (((S,S) -> Boolean),%) -> % if $ has shallowlyMutable + sorted? : % -> Boolean if S has ORDSET + sorted? : (((S,S) -> Boolean),%) -> Boolean + swap! : (%,Integer,Integer) -> Void if $ has shallowlyMutable + ?~=? : (%,%) -> Boolean if S has SETCAT + +--E 17 + )spool )lisp (bye) \end{chunk} @@ -50417,7 +52596,8 @@ parts of Axiom. )set message test on )set message auto off )clear all ---S 1 of 64 + +--S 1 of 65 1.234 --R --R @@ -50425,7 +52605,7 @@ parts of Axiom. --R Type: Float --E 1 ---S 2 of 64 +--S 2 of 65 1.234E2 --R --R @@ -50433,7 +52613,7 @@ parts of Axiom. --R Type: Float --E 2 ---S 3 of 64 +--S 3 of 65 sqrt(1.2 + 2.3 / 3.4 ** 4.5) --R --R @@ -50441,7 +52621,7 @@ sqrt(1.2 + 2.3 / 3.4 ** 4.5) --R Type: Float --E 3 ---S 4 of 64 +--S 4 of 65 i := 3 :: Float --R --R @@ -50449,7 +52629,7 @@ i := 3 :: Float --R Type: Float --E 4 ---S 5 of 64 +--S 5 of 65 i :: Integer --R --R @@ -50457,7 +52637,7 @@ i :: Integer --R Type: Integer --E 5 ---S 6 of 64 +--S 6 of 65 i :: Fraction Integer --R --R @@ -50465,7 +52645,7 @@ i :: Fraction Integer --R Type: Fraction(Integer) --E 6 ---S 7 of 64 +--S 7 of 65 r := 3/7 :: Float --R --R @@ -50473,7 +52653,7 @@ r := 3/7 :: Float --R Type: Float --E 7 ---S 8 of 64 +--S 8 of 65 r :: Fraction Integer --R --R @@ -50483,7 +52663,7 @@ r :: Fraction Integer --R Type: Fraction(Integer) --E 8 ---S 9 of 64 +--S 9 of 65 r :: Integer --R --R @@ -50493,7 +52673,7 @@ r :: Integer --R --E 9 ---S 10 of 64 +--S 10 of 65 truncate 3.6 --R --R @@ -50501,7 +52681,7 @@ truncate 3.6 --R Type: Float --E 10 ---S 11 of 64 +--S 11 of 65 round 3.6 --R --R @@ -50509,7 +52689,7 @@ round 3.6 --R Type: Float --E 11 ---S 12 of 64 +--S 12 of 65 truncate(-3.6) --R --R @@ -50517,7 +52697,7 @@ truncate(-3.6) --R Type: Float --E 12 ---S 13 of 64 +--S 13 of 65 round(-3.6) --R --R @@ -50525,7 +52705,7 @@ round(-3.6) --R Type: Float --E 13 ---S 14 of 64 +--S 14 of 65 fractionPart 3.6 --R --R @@ -50533,7 +52713,7 @@ fractionPart 3.6 --R Type: Float --E 14 ---S 15 of 64 +--S 15 of 65 digits 40 --R --R @@ -50541,7 +52721,7 @@ digits 40 --R Type: PositiveInteger --E 15 ---S 16 of 64 +--S 16 of 65 sqrt 0.2 --R --R @@ -50549,7 +52729,7 @@ sqrt 0.2 --R Type: Float --E 16 ---S 17 of 64 +--S 17 of 65 pi()$Float --R --R @@ -50557,7 +52737,7 @@ pi()$Float --R Type: Float --E 17 ---S 18 of 64 +--S 18 of 65 digits 500 --R --R @@ -50565,7 +52745,7 @@ digits 500 --R Type: PositiveInteger --E 18 ---S 19 of 64 +--S 19 of 65 pi()$Float --R --R @@ -50581,7 +52761,7 @@ pi()$Float --R Type: Float --E 19 ---S 20 of 64 +--S 20 of 65 digits 20 --R --R @@ -50589,7 +52769,7 @@ digits 20 --R Type: PositiveInteger --E 20 ---S 21 of 64 +--S 21 of 65 outputSpacing 0; x := sqrt 0.2 --R --R @@ -50597,7 +52777,7 @@ outputSpacing 0; x := sqrt 0.2 --R Type: Float --E 21 ---S 22 of 64 +--S 22 of 65 outputSpacing 5; x --R --R @@ -50605,7 +52785,7 @@ outputSpacing 5; x --R Type: Float --E 22 ---S 23 of 64 +--S 23 of 65 y := x/10**10 --R --R @@ -50613,7 +52793,7 @@ y := x/10**10 --R Type: Float --E 23 ---S 24 of 64 +--S 24 of 65 outputFloating(); x --R --R @@ -50621,7 +52801,7 @@ outputFloating(); x --R Type: Float --E 24 ---S 25 of 64 +--S 25 of 65 outputFixed(); y --R --R @@ -50629,7 +52809,7 @@ outputFixed(); y --R Type: Float --E 25 ---S 26 of 64 +--S 26 of 65 outputFloating 2; y --R --R @@ -50637,7 +52817,7 @@ outputFloating 2; y --R Type: Float --E 26 ---S 27 of 64 +--S 27 of 65 outputFixed 2; x --R --R @@ -50645,13 +52825,13 @@ outputFixed 2; x --R Type: Float --E 27 ---S 28 of 64 +--S 28 of 65 outputGeneral() --R --R Type: Void --E 28 ---S 29 of 64 +--S 29 of 65 a: Matrix Fraction Integer := matrix [ [1/(i+j+1) for j in 0..9] for i in 0..9] --R --R @@ -50697,7 +52877,7 @@ a: Matrix Fraction Integer := matrix [ [1/(i+j+1) for j in 0..9] for i in 0..9] --R Type: Matrix(Fraction(Integer)) --E 29 ---S 30 of 64 +--S 30 of 65 d:= determinant a --R --R @@ -50707,7 +52887,7 @@ d:= determinant a --R Type: Fraction(Integer) --E 30 ---S 31 of 64 +--S 31 of 65 d :: Float --R --R @@ -50715,7 +52895,7 @@ d :: Float --R Type: Float --E 31 ---S 32 of 64 +--S 32 of 65 b: Matrix DoubleFloat := matrix [ [1/(i+j+1$DoubleFloat) for j in 0..9] for i in 0..9] --R --R @@ -50775,7 +52955,7 @@ b: Matrix DoubleFloat := matrix [ [1/(i+j+1$DoubleFloat) for j in 0..9] for i in --R Type: Matrix(DoubleFloat) --E 32 ---S 33 of 64 +--S 33 of 65 determinant b --R --R @@ -50783,7 +52963,7 @@ determinant b --R Type: DoubleFloat --E 33 ---S 34 of 64 +--S 34 of 65 digits 40 --R --R @@ -50791,7 +52971,7 @@ digits 40 --R Type: PositiveInteger --E 34 ---S 35 of 64 +--S 35 of 65 c: Matrix Float := matrix [ [1/(i+j+1$Float) for j in 0..9] for i in 0..9] --R --R @@ -50885,7 +53065,7 @@ c: Matrix Float := matrix [ [1/(i+j+1$Float) for j in 0..9] for i in 0..9] --R Type: Matrix(Float) --E 35 ---S 36 of 64 +--S 36 of 65 determinant c --R --R @@ -50893,7 +53073,7 @@ determinant c --R Type: Float --E 36 ---S 37 of 64 +--S 37 of 65 digits 20 --R --R @@ -50903,13 +53083,13 @@ digits 20 )clear all ---S 38 of 64 +--S 38 of 65 outputFixed() --R --R Type: Void --E 38 ---S 39 of 64 +--S 39 of 65 a:=3.0 --R --R @@ -50917,7 +53097,7 @@ a:=3.0 --R Type: Float --E 39 ---S 40 of 64 +--S 40 of 65 b:=3.1 --R --R @@ -50925,7 +53105,7 @@ b:=3.1 --R Type: Float --E 40 ---S 41 of 64 +--S 41 of 65 c:=numeric pi() --R --R @@ -50933,7 +53113,7 @@ c:=numeric pi() --R Type: Float --E 41 ---S 42 of 64 +--S 42 of 65 d:=0.0 --R --R @@ -50941,13 +53121,13 @@ d:=0.0 --R Type: Float --E 42 ---S 43 of 64 +--S 43 of 65 outputFixed 2 --R --R Type: Void --E 43 ---S 44 of 64 +--S 44 of 65 a --R --R @@ -50955,7 +53135,7 @@ a --R Type: Float --E 44 ---S 45 of 64 +--S 45 of 65 b --R --R @@ -50963,7 +53143,7 @@ b --R Type: Float --E 45 ---S 46 of 64 +--S 46 of 65 c --R --R @@ -50971,7 +53151,7 @@ c --R Type: Float --E 46 ---S 47 of 64 +--S 47 of 65 d --R --R @@ -50979,13 +53159,13 @@ d --R Type: Float --E 47 ---S 48 of 64 +--S 48 of 65 outputFixed 0 --R --R Type: Void --E 48 ---S 49 of 64 +--S 49 of 65 a --R --R @@ -50993,7 +53173,7 @@ a --R Type: Float --E 49 ---S 50 of 64 +--S 50 of 65 b --R --R @@ -51001,7 +53181,7 @@ b --R Type: Float --E 50 ---S 51 of 64 +--S 51 of 65 c --R --R @@ -51009,7 +53189,7 @@ c --R Type: Float --E 51 ---S 52 of 64 +--S 52 of 65 31.1 --R --R @@ -51017,7 +53197,7 @@ c --R Type: Float --E 52 ---S 53 of 64 +--S 53 of 65 310.1 --R --R @@ -51025,7 +53205,7 @@ c --R Type: Float --E 53 ---S 54 of 64 +--S 54 of 65 d --R --R @@ -51033,68 +53213,178 @@ d --R Type: Float --E 54 ---S 55 of 64 +--S 55 of 65 outputFixed(0) --R Type: Void --E 55 ---S 56 of 64 +--S 56 of 65 1.1 --R --R (19) 1. --R Type: Float --E 56 ---S 57 of 64 +--S 57 of 65 3111.1 --R --R (20) 3111. --R Type: Float --E 57 ---S 58 of 64 +--S 58 of 65 1234567890.1 --R --R (21) 12345 67890. --R Type: Float --E 58 ---S 59 of 64 +--S 59 of 65 outputFixed(12) --R Type: Void --E 59 ---S 60 of 64 +--S 60 of 65 1234567890.1 --R --R (23) 12345 67890.09999 99999 99 --R Type: Float --E 60 ---S 61 of 64 +--S 61 of 65 outputFixed(15) --R Type: Void --E 61 ---S 62 of 64 +--S 62 of 65 1234567890.1 --R --R (25) 12345 67890.09999 99999 98545 --R Type: Float --E 62 ---S 63 of 64 +--S 63 of 65 outputFixed(2) --R Type: Void --E 63 ---S 64 of 64 +--S 64 of 65 1234567890.1 --R --R (27) 12345 67890.10 --R Type: Float --E 64 +--S 65 of 65 +)show Float +--R +--R Float is a domain constructor +--R Abbreviation for Float is FLOAT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for FLOAT +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (Fraction(Integer),%) -> % ?*? : (%,Fraction(Integer)) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,%) -> % ?**? : (%,Fraction(Integer)) -> % +--R ?**? : (%,Integer) -> % ?**? : (%,NonNegativeInteger) -> % +--R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % +--R ?-? : (%,%) -> % -? : % -> % +--R ?/? : (%,Integer) -> % ?/? : (%,%) -> % +--R ? Boolean ?<=? : (%,%) -> Boolean +--R ?=? : (%,%) -> Boolean ?>? : (%,%) -> Boolean +--R ?>=? : (%,%) -> Boolean D : % -> % +--R D : (%,NonNegativeInteger) -> % OMwrite : (%,Boolean) -> String +--R OMwrite : % -> String 1 : () -> % +--R 0 : () -> % ?^? : (%,Integer) -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R abs : % -> % acos : % -> % +--R acosh : % -> % acot : % -> % +--R acoth : % -> % acsc : % -> % +--R acsch : % -> % asec : % -> % +--R asech : % -> % asin : % -> % +--R asinh : % -> % associates? : (%,%) -> Boolean +--R atan : (%,%) -> % atan : % -> % +--R atanh : % -> % base : () -> PositiveInteger +--R bits : () -> PositiveInteger ceiling : % -> % +--R coerce : % -> DoubleFloat coerce : Fraction(Integer) -> % +--R coerce : Integer -> % coerce : Fraction(Integer) -> % +--R coerce : % -> % coerce : Integer -> % +--R coerce : % -> OutputForm convert : DoubleFloat -> % +--R convert : % -> InputForm convert : % -> String +--R convert : % -> Pattern(Float) convert : % -> DoubleFloat +--R convert : % -> Float cos : % -> % +--R cosh : % -> % cot : % -> % +--R coth : % -> % csc : % -> % +--R csch : % -> % differentiate : % -> % +--R digits : () -> PositiveInteger exp : % -> % +--R exp1 : () -> % exponent : % -> Integer +--R factor : % -> Factored(%) float : (Integer,Integer) -> % +--R floor : % -> % fractionPart : % -> % +--R gcd : List(%) -> % gcd : (%,%) -> % +--R hash : % -> SingleInteger inv : % -> % +--R latex : % -> String lcm : List(%) -> % +--R lcm : (%,%) -> % log : % -> % +--R log10 : % -> % log10 : () -> % +--R log2 : % -> % log2 : () -> % +--R mantissa : % -> Integer max : (%,%) -> % +--R min : (%,%) -> % negative? : % -> Boolean +--R norm : % -> % normalize : % -> % +--R nthRoot : (%,Integer) -> % one? : % -> Boolean +--R order : % -> Integer outputFixed : () -> Void +--R outputFloating : () -> Void outputGeneral : () -> Void +--R pi : () -> % positive? : % -> Boolean +--R precision : () -> PositiveInteger prime? : % -> Boolean +--R ?quo? : (%,%) -> % recip : % -> Union(%,"failed") +--R relerror : (%,%) -> Integer ?rem? : (%,%) -> % +--R retract : % -> Fraction(Integer) retract : % -> Integer +--R round : % -> % sample : () -> % +--R sec : % -> % sech : % -> % +--R shift : (%,Integer) -> % sign : % -> Integer +--R sin : % -> % sinh : % -> % +--R sizeLess? : (%,%) -> Boolean sqrt : % -> % +--R squareFree : % -> Factored(%) squareFreePart : % -> % +--R tan : % -> % tanh : % -> % +--R truncate : % -> % unit? : % -> Boolean +--R unitCanonical : % -> % wholePart : % -> Integer +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R OMwrite : (OpenMathDevice,%,Boolean) -> Void +--R OMwrite : (OpenMathDevice,%) -> Void +--R bits : PositiveInteger -> PositiveInteger if $ has arbitraryPrecision +--R characteristic : () -> NonNegativeInteger +--R decreasePrecision : Integer -> PositiveInteger if $ has arbitraryPrecision +--R differentiate : (%,NonNegativeInteger) -> % +--R digits : PositiveInteger -> PositiveInteger if $ has arbitraryPrecision +--R divide : (%,%) -> Record(quotient: %,remainder: %) +--R euclideanSize : % -> NonNegativeInteger +--R expressIdealMember : (List(%),%) -> Union(List(%),"failed") +--R exquo : (%,%) -> Union(%,"failed") +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) +--R float : (Integer,Integer,PositiveInteger) -> % +--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) +--R increasePrecision : Integer -> PositiveInteger if $ has arbitraryPrecision +--R lcmCoef : (%,%) -> Record(llcmres: %,coeff1: %,coeff2: %) +--R max : () -> % if not(has($,arbitraryExponent)) and not(has($,arbitraryPrecision)) +--R min : () -> % if not(has($,arbitraryExponent)) and not(has($,arbitraryPrecision)) +--R multiEuclidean : (List(%),%) -> Union(List(%),"failed") +--R outputFixed : NonNegativeInteger -> Void +--R outputFloating : NonNegativeInteger -> Void +--R outputGeneral : NonNegativeInteger -> Void +--R outputSpacing : NonNegativeInteger -> Void +--R patternMatch : (%,Pattern(Float),PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) +--R precision : PositiveInteger -> PositiveInteger if $ has arbitraryPrecision +--R principalIdeal : List(%) -> Record(coef: List(%),generator: %) +--R rationalApproximation : (%,NonNegativeInteger,NonNegativeInteger) -> Fraction(Integer) +--R rationalApproximation : (%,NonNegativeInteger) -> Fraction(Integer) +--R retractIfCan : % -> Union(Fraction(Integer),"failed") +--R retractIfCan : % -> Union(Integer,"failed") +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) +--R +--E 65 + )spool )lisp (bye) \end{chunk} @@ -52552,14 +54842,15 @@ Float(): --R ?=? : (%,%) -> Boolean assign : (Symbol,String) -> % --R block : List(%) -> % call : String -> % --R coerce : % -> OutputForm comment : List(String) -> % ---R comment : String -> % cond : (Switch,%,%) -> % ---R cond : (Switch,%) -> % continue : SingleInteger -> % ---R getCode : % -> SExpression goto : SingleInteger -> % ---R hash : % -> SingleInteger latex : % -> String ---R printCode : % -> Void returns : Expression(Float) -> % ---R returns : () -> % save : () -> % ---R stop : () -> % whileLoop : (Switch,%) -> % ---R ?~=? : (%,%) -> Boolean +--R comment : String -> % common : (Symbol,List(Symbol)) -> % +--R cond : (Switch,%,%) -> % cond : (Switch,%) -> % +--R continue : SingleInteger -> % getCode : % -> SExpression +--R goto : SingleInteger -> % hash : % -> SingleInteger +--R latex : % -> String printCode : % -> Void +--R repeatUntilLoop : (Switch,%) -> % returns : Expression(Integer) -> % +--R returns : Expression(Float) -> % returns : () -> % +--R save : () -> % stop : () -> % +--R whileLoop : (Switch,%) -> % ?~=? : (%,%) -> Boolean --R assign : (Symbol,List(Polynomial(Integer)),Expression(Complex(Float))) -> % --R assign : (Symbol,List(Polynomial(Integer)),Expression(Float)) -> % --R assign : (Symbol,List(Polynomial(Integer)),Expression(Integer)) -> % @@ -52591,14 +54882,11 @@ Float(): --R assign : (Symbol,Expression(MachineFloat)) -> % --R assign : (Symbol,Expression(MachineInteger)) -> % --R code : % -> Union(nullBranch: null,assignmentBranch: Record(var: Symbol,arrayIndex: List(Polynomial(Integer)),rand: Record(ints2Floats?: Boolean,expr: OutputForm)),arrayAssignmentBranch: Record(var: Symbol,rand: OutputForm,ints2Floats?: Boolean),conditionalBranch: Record(switch: Switch,thenClause: %,elseClause: %),returnBranch: Record(empty?: Boolean,value: Record(ints2Floats?: Boolean,expr: OutputForm)),blockBranch: List(%),commentBranch: List(String),callBranch: String,forBranch: Record(range: SegmentBinding(Polynomial(Integer)),span: Polynomial(Integer),body: %),labelBranch: SingleInteger,loopBranch: Record(switch: Switch,body: %),commonBranch: Record(name: Symbol,contents: List(Symbol)),printBranch: List(OutputForm)) ---R common : (Symbol,List(Symbol)) -> % --R forLoop : (SegmentBinding(Polynomial(Integer)),Polynomial(Integer),%) -> % --R forLoop : (SegmentBinding(Polynomial(Integer)),%) -> % --R operation : % -> Union(Null: null,Assignment: assignment,Conditional: conditional,Return: return,Block: block,Comment: comment,Call: call,For: for,While: while,Repeat: repeat,Goto: goto,Continue: continue,ArrayAssignment: arrayAssignment,Save: save,Stop: stop,Common: common,Print: print) --R printStatement : List(OutputForm) -> % ---R repeatUntilLoop : (Switch,%) -> % --R returns : Expression(Complex(Float)) -> % ---R returns : Expression(Integer) -> % --R returns : Expression(MachineComplex) -> % --R returns : Expression(MachineInteger) -> % --R returns : Expression(MachineFloat) -> % @@ -53269,32 +55557,37 @@ FortranCode(): public == private where --R Issue )edit bookvol10.3.pamphlet to see algebra source code for FEXPR --R --R------------------------------- Operations -------------------------------- ---R ?*? : (PositiveInteger,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (%,%) -> % ?*? : (%,R) -> % ---R ?*? : (R,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (PositiveInteger,%) -> % ?*? : (NonNegativeInteger,%) -> % +--R ?*? : (Integer,%) -> % ?*? : (%,%) -> % +--R ?*? : (%,R) -> % ?*? : (R,%) -> % +--R ?**? : (%,PositiveInteger) -> % ?**? : (%,NonNegativeInteger) -> % --R ?+? : (%,%) -> % -? : % -> % --R ?-? : (%,%) -> % ? Boolean --R ?<=? : (%,%) -> Boolean ?=? : (%,%) -> Boolean --R ?>? : (%,%) -> Boolean ?>=? : (%,%) -> Boolean --R D : (%,Symbol) -> % D : (%,List(Symbol)) -> % --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % abs : % -> % ---R acos : % -> % asin : % -> % ---R atan : % -> % belong? : BasicOperator -> Boolean ---R box : List(%) -> % box : % -> % ---R coerce : % -> Expression(R) coerce : Integer -> % ---R coerce : R -> % coerce : Kernel(%) -> % ---R coerce : % -> OutputForm cos : % -> % ---R cosh : % -> % differentiate : (%,Symbol) -> % ---R distribute : (%,%) -> % distribute : % -> % ---R elt : (BasicOperator,%,%) -> % elt : (BasicOperator,%) -> % ---R eval : (%,%,%) -> % eval : (%,Equation(%)) -> % +--R ?^? : (%,PositiveInteger) -> % ?^? : (%,NonNegativeInteger) -> % +--R abs : % -> % acos : % -> % +--R asin : % -> % atan : % -> % +--R belong? : BasicOperator -> Boolean box : List(%) -> % +--R box : % -> % coerce : % -> Expression(R) +--R coerce : Integer -> % coerce : R -> % +--R coerce : Kernel(%) -> % coerce : % -> OutputForm +--R cos : % -> % cosh : % -> % +--R differentiate : (%,Symbol) -> % distribute : (%,%) -> % +--R distribute : % -> % elt : (BasicOperator,List(%)) -> % +--R elt : (BasicOperator,%,%,%) -> % elt : (BasicOperator,%,%) -> % +--R elt : (BasicOperator,%) -> % eval : (%,Symbol,(% -> %)) -> % +--R eval : (%,List(%),List(%)) -> % eval : (%,%,%) -> % +--R eval : (%,Equation(%)) -> % eval : (%,List(Equation(%))) -> % --R eval : (%,Kernel(%),%) -> % exp : % -> % --R freeOf? : (%,Symbol) -> Boolean freeOf? : (%,%) -> Boolean --R hash : % -> SingleInteger height : % -> NonNegativeInteger ---R is? : (%,Symbol) -> Boolean kernel : (BasicOperator,%) -> % ---R kernels : % -> List(Kernel(%)) latex : % -> String ---R log : % -> % log10 : % -> % +--R is? : (%,Symbol) -> Boolean is? : (%,BasicOperator) -> Boolean +--R kernel : (BasicOperator,%) -> % kernels : % -> List(Kernel(%)) +--R latex : % -> String log : % -> % +--R log10 : % -> % map : ((% -> %),Kernel(%)) -> % --R max : (%,%) -> % min : (%,%) -> % --R one? : % -> Boolean paren : List(%) -> % --R paren : % -> % pi : () -> % @@ -53304,38 +55597,28 @@ FortranCode(): public == private where --R sin : % -> % sinh : % -> % --R sqrt : % -> % subst : (%,Equation(%)) -> % --R tan : % -> % tanh : % -> % ---R tower : % -> List(Kernel(%)) useNagFunctions : () -> Boolean ---R variables : % -> List(Symbol) zero? : % -> Boolean ---R ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % +--R tower : % -> List(Kernel(%)) useNagFunctions : Boolean -> Boolean +--R useNagFunctions : () -> Boolean variables : % -> List(Symbol) +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean --R D : (%,Symbol,NonNegativeInteger) -> % --R D : (%,List(Symbol),List(NonNegativeInteger)) -> % ---R ?^? : (%,NonNegativeInteger) -> % --R characteristic : () -> NonNegativeInteger --R definingPolynomial : % -> % if $ has RING --R differentiate : (%,List(Symbol)) -> % --R differentiate : (%,Symbol,NonNegativeInteger) -> % --R differentiate : (%,List(Symbol),List(NonNegativeInteger)) -> % ---R elt : (BasicOperator,List(%)) -> % --R elt : (BasicOperator,%,%,%,%) -> % ---R elt : (BasicOperator,%,%,%) -> % --R eval : (%,BasicOperator,(% -> %)) -> % --R eval : (%,BasicOperator,(List(%) -> %)) -> % --R eval : (%,List(BasicOperator),List((List(%) -> %))) -> % --R eval : (%,List(BasicOperator),List((% -> %))) -> % ---R eval : (%,Symbol,(% -> %)) -> % --R eval : (%,Symbol,(List(%) -> %)) -> % --R eval : (%,List(Symbol),List((List(%) -> %))) -> % --R eval : (%,List(Symbol),List((% -> %))) -> % ---R eval : (%,List(%),List(%)) -> % ---R eval : (%,List(Equation(%))) -> % --R eval : (%,List(Kernel(%)),List(%)) -> % --R even? : % -> Boolean if $ has RETRACT(INT) ---R is? : (%,BasicOperator) -> Boolean --R kernel : (BasicOperator,List(%)) -> % --R mainKernel : % -> Union(Kernel(%),"failed") ---R map : ((% -> %),Kernel(%)) -> % --R minPoly : Kernel(%) -> SparseUnivariatePolynomial(%) if $ has RING --R odd? : % -> Boolean if $ has RETRACT(INT) --R operator : BasicOperator -> BasicOperator @@ -53359,7 +55642,6 @@ FortranCode(): public == private where --R subst : (%,List(Kernel(%)),List(%)) -> % --R subst : (%,List(Equation(%))) -> % --R subtractIfCan : (%,%) -> Union(%,"failed") ---R useNagFunctions : Boolean -> Boolean --R --E 1 @@ -54112,6 +56394,7 @@ FortranProgram(name,returnType,arguments,symbols): Exports == Implement where --S 1 of 1 )show FortranScalarType +--R --R FortranScalarType is a domain constructor --R Abbreviation for FortranScalarType is FST --R This constructor is exposed in this frame. @@ -54330,6 +56613,7 @@ FortranScalarType() : exports == implementation where --S 1 of 1 )show FortranTemplate +--R --R FortranTemplate is a domain constructor --R Abbreviation for FortranTemplate is FTEM --R This constructor is exposed in this frame. @@ -54339,12 +56623,12 @@ FortranScalarType() : exports == implementation where --R ?=? : (%,%) -> Boolean close! : % -> % --R coerce : % -> OutputForm flush : % -> Void --R fortranCarriageReturn : () -> Void fortranLiteral : String -> Void ---R hash : % -> SingleInteger iomode : % -> String ---R latex : % -> String name : % -> FileName ---R open : (FileName,String) -> % open : FileName -> % ---R read! : % -> String reopen! : (%,String) -> % ---R write! : (%,String) -> String ?~=? : (%,%) -> Boolean ---R fortranLiteralLine : String -> Void +--R fortranLiteralLine : String -> Void hash : % -> SingleInteger +--R iomode : % -> String latex : % -> String +--R name : % -> FileName open : (FileName,String) -> % +--R open : FileName -> % read! : % -> String +--R reopen! : (%,String) -> % write! : (%,String) -> String +--R ?~=? : (%,%) -> Boolean --R processTemplate : FileName -> FileName --R processTemplate : (FileName,FileName) -> FileName --R @@ -54808,20 +57092,19 @@ FourierComponent(E:OrderedSet): --R------------------------------- Operations -------------------------------- --R ?*? : (R,%) -> % ?*? : (%,R) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ?=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % coerce : FourierComponent(E) -> % ---R coerce : R -> % coerce : Integer -> % ---R coerce : % -> OutputForm hash : % -> SingleInteger ---R latex : % -> String makeCos : (E,R) -> % ---R makeSin : (E,R) -> % one? : % -> Boolean ---R recip : % -> Union(%,"failed") sample : () -> % ---R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R coerce : FourierComponent(E) -> % coerce : R -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R makeCos : (E,R) -> % makeSin : (E,R) -> % +--R one? : % -> Boolean recip : % -> Union(%,"failed") +--R sample : () -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean --R characteristic : () -> NonNegativeInteger --R subtractIfCan : (%,%) -> Union(%,"failed") --R @@ -54957,7 +57240,8 @@ FourierSeries(R:Join(CommutativeRing,Algebra(Fraction Integer)), )set message test on )set message auto off )clear all ---S 1 of 12 + +--S 1 of 13 a := 11/12 --R --R @@ -54967,7 +57251,7 @@ a := 11/12 --R Type: Fraction(Integer) --E 1 ---S 2 of 12 +--S 2 of 13 b := 23/24 --R --R @@ -54977,7 +57261,7 @@ b := 23/24 --R Type: Fraction(Integer) --E 2 ---S 3 of 12 +--S 3 of 13 3 - a*b**2 + a + b/a --R --R @@ -54987,7 +57271,7 @@ b := 23/24 --R Type: Fraction(Integer) --E 3 ---S 4 of 12 +--S 4 of 13 numer(a) --R --R @@ -54995,7 +57279,7 @@ numer(a) --R Type: PositiveInteger --E 4 ---S 5 of 12 +--S 5 of 13 denom(b) --R --R @@ -55003,7 +57287,7 @@ denom(b) --R Type: PositiveInteger --E 5 ---S 6 of 12 +--S 6 of 13 r := (x**2 + 2*x + 1)/(x**2 - 2*x + 1) --R --R @@ -55015,7 +57299,7 @@ r := (x**2 + 2*x + 1)/(x**2 - 2*x + 1) --R Type: Fraction(Polynomial(Integer)) --E 6 ---S 7 of 12 +--S 7 of 13 factor(r) --R --R @@ -55027,7 +57311,7 @@ factor(r) --R Type: Factored(Fraction(Polynomial(Integer))) --E 7 ---S 8 of 12 +--S 8 of 13 map(factor,r) --R --R @@ -55039,7 +57323,7 @@ map(factor,r) --R Type: Fraction(Factored(Polynomial(Integer))) --E 8 ---S 9 of 12 +--S 9 of 13 continuedFraction(7/12) --R --R @@ -55049,7 +57333,7 @@ continuedFraction(7/12) --R Type: ContinuedFraction(Integer) --E 9 ---S 10 of 12 +--S 10 of 13 partialFraction(7,12) --R --R @@ -55060,7 +57344,7 @@ partialFraction(7,12) --R Type: PartialFraction(Integer) --E 10 ---S 11 of 12 +--S 11 of 13 g := 2/3 + 4/5*%i --R --R @@ -55070,7 +57354,7 @@ g := 2/3 + 4/5*%i --R Type: Complex(Fraction(Integer)) --E 11 ---S 12 of 12 +--S 12 of 13 g :: FRAC COMPLEX INT --R --R @@ -55080,6 +57364,122 @@ g :: FRAC COMPLEX INT --R Type: Fraction(Complex(Integer)) --E 12 +--S 13 of 13 +)show Fraction +--R +--R Fraction(S: IntegralDomain) is a domain constructor +--R Abbreviation for Fraction is FRAC +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for FRAC +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,S) -> % ?*? : (S,%) -> % +--R ?*? : (Fraction(Integer),%) -> % ?*? : (%,Fraction(Integer)) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,Integer) -> % ?**? : (%,NonNegativeInteger) -> % +--R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % +--R ?-? : (%,%) -> % -? : % -> % +--R ?/? : (S,S) -> % ?/? : (%,%) -> % +--R ?=? : (%,%) -> Boolean D : (%,(S -> S)) -> % +--R D : % -> % if S has DIFRING 1 : () -> % +--R 0 : () -> % ?^? : (%,Integer) -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R abs : % -> % if S has OINTDOM associates? : (%,%) -> Boolean +--R ceiling : % -> S if S has INS coerce : S -> % +--R coerce : Fraction(Integer) -> % coerce : % -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R convert : % -> Float if S has REAL denom : % -> S +--R denominator : % -> % differentiate : (%,(S -> S)) -> % +--R factor : % -> Factored(%) floor : % -> S if S has INS +--R gcd : List(%) -> % gcd : (%,%) -> % +--R hash : % -> SingleInteger init : () -> % if S has STEP +--R inv : % -> % latex : % -> String +--R lcm : List(%) -> % lcm : (%,%) -> % +--R map : ((S -> S),%) -> % max : (%,%) -> % if S has ORDSET +--R min : (%,%) -> % if S has ORDSET numer : % -> S +--R numerator : % -> % one? : % -> Boolean +--R prime? : % -> Boolean ?quo? : (%,%) -> % +--R random : () -> % if S has INS recip : % -> Union(%,"failed") +--R ?rem? : (%,%) -> % retract : % -> S +--R sample : () -> % sizeLess? : (%,%) -> Boolean +--R squareFree : % -> Factored(%) squareFreePart : % -> % +--R unit? : % -> Boolean unitCanonical : % -> % +--R wholePart : % -> S if S has EUCDOM zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R ? Boolean if S has ORDSET +--R ?<=? : (%,%) -> Boolean if S has ORDSET +--R ?>? : (%,%) -> Boolean if S has ORDSET +--R ?>=? : (%,%) -> Boolean if S has ORDSET +--R D : (%,(S -> S),NonNegativeInteger) -> % +--R D : (%,List(Symbol),List(NonNegativeInteger)) -> % if S has PDRING(SYMBOL) +--R D : (%,Symbol,NonNegativeInteger) -> % if S has PDRING(SYMBOL) +--R D : (%,List(Symbol)) -> % if S has PDRING(SYMBOL) +--R D : (%,Symbol) -> % if S has PDRING(SYMBOL) +--R D : (%,NonNegativeInteger) -> % if S has DIFRING +--R OMwrite : (OpenMathDevice,%,Boolean) -> Void if S has INS and S has OM +--R OMwrite : (OpenMathDevice,%) -> Void if S has INS and S has OM +--R OMwrite : (%,Boolean) -> String if S has INS and S has OM +--R OMwrite : % -> String if S has INS and S has OM +--R characteristic : () -> NonNegativeInteger +--R charthRoot : % -> Union(%,"failed") if $ has CHARNZ and S has PFECAT or S has CHARNZ +--R coerce : Symbol -> % if S has RETRACT(SYMBOL) +--R conditionP : Matrix(%) -> Union(Vector(%),"failed") if $ has CHARNZ and S has PFECAT +--R convert : % -> DoubleFloat if S has REAL +--R convert : % -> InputForm if S has KONVERT(INFORM) +--R convert : % -> Pattern(Float) if S has KONVERT(PATTERN(FLOAT)) +--R convert : % -> Pattern(Integer) if S has KONVERT(PATTERN(INT)) +--R differentiate : (%,(S -> S),NonNegativeInteger) -> % +--R differentiate : (%,List(Symbol),List(NonNegativeInteger)) -> % if S has PDRING(SYMBOL) +--R differentiate : (%,Symbol,NonNegativeInteger) -> % if S has PDRING(SYMBOL) +--R differentiate : (%,List(Symbol)) -> % if S has PDRING(SYMBOL) +--R differentiate : (%,Symbol) -> % if S has PDRING(SYMBOL) +--R differentiate : (%,NonNegativeInteger) -> % if S has DIFRING +--R differentiate : % -> % if S has DIFRING +--R divide : (%,%) -> Record(quotient: %,remainder: %) +--R ?.? : (%,S) -> % if S has ELTAB(S,S) +--R euclideanSize : % -> NonNegativeInteger +--R eval : (%,Symbol,S) -> % if S has IEVALAB(SYMBOL,S) +--R eval : (%,List(Symbol),List(S)) -> % if S has IEVALAB(SYMBOL,S) +--R eval : (%,List(Equation(S))) -> % if S has EVALAB(S) +--R eval : (%,Equation(S)) -> % if S has EVALAB(S) +--R eval : (%,S,S) -> % if S has EVALAB(S) +--R eval : (%,List(S),List(S)) -> % if S has EVALAB(S) +--R expressIdealMember : (List(%),%) -> Union(List(%),"failed") +--R exquo : (%,%) -> Union(%,"failed") +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) +--R factorPolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if S has PFECAT +--R factorSquareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if S has PFECAT +--R fractionPart : % -> % if S has EUCDOM +--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) +--R lcmCoef : (%,%) -> Record(llcmres: %,coeff1: %,coeff2: %) +--R multiEuclidean : (List(%),%) -> Union(List(%),"failed") +--R negative? : % -> Boolean if S has OINTDOM +--R nextItem : % -> Union(%,"failed") if S has STEP +--R patternMatch : (%,Pattern(Float),PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if S has PATMAB(FLOAT) +--R patternMatch : (%,Pattern(Integer),PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if S has PATMAB(INT) +--R positive? : % -> Boolean if S has OINTDOM +--R principalIdeal : List(%) -> Record(coef: List(%),generator: %) +--R reducedSystem : Matrix(%) -> Matrix(S) +--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(S),vec: Vector(S)) +--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(Integer),vec: Vector(Integer)) if S has LINEXP(INT) +--R reducedSystem : Matrix(%) -> Matrix(Integer) if S has LINEXP(INT) +--R retract : % -> Integer if S has RETRACT(INT) +--R retract : % -> Fraction(Integer) if S has RETRACT(INT) +--R retract : % -> Symbol if S has RETRACT(SYMBOL) +--R retractIfCan : % -> Union(Integer,"failed") if S has RETRACT(INT) +--R retractIfCan : % -> Union(Fraction(Integer),"failed") if S has RETRACT(INT) +--R retractIfCan : % -> Union(Symbol,"failed") if S has RETRACT(SYMBOL) +--R retractIfCan : % -> Union(S,"failed") +--R sign : % -> Integer if S has OINTDOM +--R solveLinearPolynomialEquation : (List(SparseUnivariatePolynomial(%)),SparseUnivariatePolynomial(%)) -> Union(List(SparseUnivariatePolynomial(%)),"failed") if S has PFECAT +--R squareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if S has PFECAT +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) +--R +--E 13 + )spool )lisp (bye) \end{chunk} @@ -55645,9 +58045,10 @@ Fraction(S: IntegralDomain): QuotientFieldCategory S with --R --R------------------------------- Operations -------------------------------- --R ?*? : (%,%) -> % ?**? : (%,Integer) -> % ---R ?**? : (%,PositiveInteger) -> % ?/? : (%,%) -> % ---R ?=? : (%,%) -> Boolean 1 : () -> % ---R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % +--R ?/? : (%,%) -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % ?^? : (%,Integer) -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % --R basis : % -> Vector(A) coerce : % -> OutputForm --R commutator : (%,%) -> % conjugate : (%,%) -> % --R denom : % -> R hash : % -> SingleInteger @@ -55656,8 +58057,6 @@ Fraction(S: IntegralDomain): QuotientFieldCategory S with --R norm : % -> F numer : % -> Vector(A) --R one? : % -> Boolean recip : % -> Union(%,"failed") --R sample : () -> % ?~=? : (%,%) -> Boolean ---R ?**? : (%,NonNegativeInteger) -> % ---R ?^? : (%,NonNegativeInteger) -> % --R randomLC : (NonNegativeInteger,Vector(A)) -> A --R --E 1 @@ -55907,16 +58306,15 @@ FractionalIdeal(R, F, UP, A): Exports == Implementation where --R Issue )edit bookvol10.3.pamphlet to see algebra source code for FRMOD --R --R------------------------------- Operations -------------------------------- ---R ?*? : (%,%) -> % ?**? : (%,PositiveInteger) -> % ---R ?=? : (%,%) -> Boolean 1 : () -> % +--R ?*? : (%,%) -> % ?**? : (%,NonNegativeInteger) -> % +--R ?**? : (%,PositiveInteger) -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % ?^? : (%,NonNegativeInteger) -> % --R ?^? : (%,PositiveInteger) -> % basis : % -> Vector(A) --R coerce : % -> OutputForm hash : % -> SingleInteger --R latex : % -> String module : Vector(A) -> % --R norm : % -> F one? : % -> Boolean --R recip : % -> Union(%,"failed") sample : () -> % --R ?~=? : (%,%) -> Boolean ---R ?**? : (%,NonNegativeInteger) -> % ---R ?^? : (%,NonNegativeInteger) -> % --R module : FractionalIdeal(R,F,UP,A) -> % if A has RETRACT(F) --R --E 1 @@ -56095,26 +58493,24 @@ FramedModule(R, F, UP, A, ibasis): Exports == Implementation where --R --R------------------------------- Operations -------------------------------- --R ?*? : (Integer,S) -> % ?*? : (%,Integer) -> % ---R ?*? : (Integer,%) -> % ?*? : (PositiveInteger,%) -> % ---R ?+? : (S,%) -> % ?+? : (%,%) -> % ---R ?-? : (%,%) -> % -? : % -> % ---R ?=? : (%,%) -> Boolean 0 : () -> % ---R coefficient : (S,%) -> Integer coerce : S -> % ---R coerce : % -> OutputForm hash : % -> SingleInteger ---R latex : % -> String mapGen : ((S -> S),%) -> % ---R nthCoef : (%,Integer) -> Integer nthFactor : (%,Integer) -> S ---R retract : % -> S sample : () -> % ---R size : % -> NonNegativeInteger zero? : % -> Boolean ---R ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % +--R ?*? : (Integer,%) -> % ?*? : (NonNegativeInteger,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?+? : (S,%) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 0 : () -> % coefficient : (S,%) -> Integer +--R coerce : S -> % coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R mapGen : ((S -> S),%) -> % max : (%,%) -> % if S has ORDSET +--R min : (%,%) -> % if S has ORDSET nthCoef : (%,Integer) -> Integer +--R nthFactor : (%,Integer) -> S retract : % -> S +--R sample : () -> % size : % -> NonNegativeInteger +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean --R ? Boolean if S has ORDSET --R ?<=? : (%,%) -> Boolean if S has ORDSET --R ?>? : (%,%) -> Boolean if S has ORDSET --R ?>=? : (%,%) -> Boolean if S has ORDSET --R highCommonTerms : (%,%) -> % if Integer has OAMON --R mapCoef : ((Integer -> Integer),%) -> % ---R max : (%,%) -> % if S has ORDSET ---R min : (%,%) -> % if S has ORDSET --R retractIfCan : % -> Union(S,"failed") --R subtractIfCan : (%,%) -> Union(%,"failed") --R terms : % -> List(Record(gen: S,exp: Integer)) @@ -56253,16 +58649,15 @@ FreeAbelianGroup(S:SetCategory): Exports == Implementation where --R Issue )edit bookvol10.3.pamphlet to see algebra source code for FAMONOID --R --R------------------------------- Operations -------------------------------- ---R ?*? : (NonNegativeInteger,S) -> % ?*? : (PositiveInteger,%) -> % ---R ?+? : (S,%) -> % ?+? : (%,%) -> % ---R ?=? : (%,%) -> Boolean 0 : () -> % ---R coerce : S -> % coerce : % -> OutputForm ---R hash : % -> SingleInteger latex : % -> String ---R mapGen : ((S -> S),%) -> % nthFactor : (%,Integer) -> S ---R retract : % -> S sample : () -> % ---R size : % -> NonNegativeInteger zero? : % -> Boolean ---R ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % +--R ?*? : (NonNegativeInteger,S) -> % ?*? : (NonNegativeInteger,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?+? : (S,%) -> % +--R ?+? : (%,%) -> % ?=? : (%,%) -> Boolean +--R 0 : () -> % coerce : S -> % +--R coerce : % -> OutputForm hash : % -> SingleInteger +--R latex : % -> String mapGen : ((S -> S),%) -> % +--R nthFactor : (%,Integer) -> S retract : % -> S +--R sample : () -> % size : % -> NonNegativeInteger +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean --R coefficient : (S,%) -> NonNegativeInteger --R highCommonTerms : (%,%) -> % if NonNegativeInteger has OAMON --R mapCoef : ((NonNegativeInteger -> NonNegativeInteger),%) -> % @@ -56369,9 +58764,10 @@ FreeAbelianMonoid(S: SetCategory): --R------------------------------- Operations -------------------------------- --R ?*? : (%,S) -> % ?*? : (S,%) -> % --R ?*? : (%,%) -> % ?**? : (S,Integer) -> % ---R ?**? : (%,Integer) -> % ?**? : (%,PositiveInteger) -> % ---R ?/? : (%,%) -> % ?=? : (%,%) -> Boolean ---R 1 : () -> % ?^? : (%,Integer) -> % +--R ?**? : (%,Integer) -> % ?**? : (%,NonNegativeInteger) -> % +--R ?**? : (%,PositiveInteger) -> % ?/? : (%,%) -> % +--R ?=? : (%,%) -> Boolean 1 : () -> % +--R ?^? : (%,Integer) -> % ?^? : (%,NonNegativeInteger) -> % --R ?^? : (%,PositiveInteger) -> % coerce : S -> % --R coerce : % -> OutputForm commutator : (%,%) -> % --R conjugate : (%,%) -> % hash : % -> SingleInteger @@ -56381,8 +58777,6 @@ FreeAbelianMonoid(S: SetCategory): --R recip : % -> Union(%,"failed") retract : % -> S --R sample : () -> % size : % -> NonNegativeInteger --R ?~=? : (%,%) -> Boolean ---R ?**? : (%,NonNegativeInteger) -> % ---R ?^? : (%,NonNegativeInteger) -> % --R factors : % -> List(Record(gen: S,exp: Integer)) --R mapExpon : ((Integer -> Integer),%) -> % --R retractIfCan : % -> Union(S,"failed") @@ -56528,6 +58922,7 @@ FreeGroup(S: SetCategory): Join(Group, RetractableTo S) with --S 1 of 1 )show FreeModule +--R --R FreeModule(R: Ring,S: OrderedSet) is a domain constructor --R Abbreviation for FreeModule is FM --R This constructor is not exposed in this frame. @@ -56535,16 +58930,16 @@ FreeGroup(S: SetCategory): Join(Group, RetractableTo S) with --R --R------------------------------- Operations -------------------------------- --R ?*? : (%,R) -> % ?*? : (R,%) -> % ---R ?*? : (Integer,%) -> % ?*? : (PositiveInteger,%) -> % ---R ?+? : (%,%) -> % ?-? : (%,%) -> % ---R -? : % -> % ?=? : (%,%) -> Boolean ---R 0 : () -> % coerce : % -> OutputForm ---R hash : % -> SingleInteger latex : % -> String ---R leadingCoefficient : % -> R leadingSupport : % -> S ---R map : ((R -> R),%) -> % monomial : (R,S) -> % ---R reductum : % -> % sample : () -> % ---R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % +--R ?*? : (Integer,%) -> % ?*? : (NonNegativeInteger,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?+? : (%,%) -> % +--R ?-? : (%,%) -> % -? : % -> % +--R ?=? : (%,%) -> Boolean 0 : () -> % +--R coerce : % -> OutputForm hash : % -> SingleInteger +--R latex : % -> String leadingCoefficient : % -> R +--R leadingSupport : % -> S map : ((R -> R),%) -> % +--R monomial : (R,S) -> % reductum : % -> % +--R sample : () -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean --R subtractIfCan : (%,%) -> Union(%,"failed") --R --E 1 @@ -56684,19 +59079,19 @@ FreeModule(R:Ring,S:OrderedSet): --R------------------------------- Operations -------------------------------- --R ?*? : (S,R) -> % ?*? : (R,S) -> % --R ?*? : (%,R) -> % ?*? : (R,%) -> % ---R ?*? : (Integer,%) -> % ?*? : (PositiveInteger,%) -> % ---R ?+? : (%,%) -> % ?-? : (%,%) -> % ---R -? : % -> % ?=? : (%,%) -> Boolean ---R 0 : () -> % coefficient : (%,S) -> R ---R coefficients : % -> List(R) coerce : S -> % ---R coerce : % -> OutputForm hash : % -> SingleInteger ---R latex : % -> String leadingCoefficient : % -> R ---R leadingMonomial : % -> S map : ((R -> R),%) -> % ---R monom : (S,R) -> % monomial? : % -> Boolean ---R monomials : % -> List(%) reductum : % -> % ---R retract : % -> S sample : () -> % ---R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % +--R ?*? : (Integer,%) -> % ?*? : (NonNegativeInteger,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?+? : (%,%) -> % +--R ?-? : (%,%) -> % -? : % -> % +--R ?=? : (%,%) -> Boolean 0 : () -> % +--R coefficient : (%,S) -> R coefficients : % -> List(R) +--R coerce : S -> % coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R leadingCoefficient : % -> R leadingMonomial : % -> S +--R map : ((R -> R),%) -> % monom : (S,R) -> % +--R monomial? : % -> Boolean monomials : % -> List(%) +--R reductum : % -> % retract : % -> S +--R sample : () -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean --R leadingTerm : % -> Record(k: S,c: R) --R listOfTerms : % -> List(Record(k: S,c: R)) --R numberOfMonomials : % -> NonNegativeInteger @@ -56878,33 +59273,29 @@ FreeModule1(R:Ring,S:OrderedSet): FMcat == FMdef where --R --R------------------------------- Operations -------------------------------- --R ?*? : (%,S) -> % ?*? : (S,%) -> % ---R ?*? : (%,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (%,%) -> % ?**? : (S,NonNegativeInteger) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?=? : (%,%) -> Boolean 1 : () -> % ---R ?^? : (%,PositiveInteger) -> % coerce : S -> % ---R coerce : % -> OutputForm hash : % -> SingleInteger ---R hclf : (%,%) -> % hcrf : (%,%) -> % ---R latex : % -> String mapGen : ((S -> S),%) -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R coerce : S -> % coerce : % -> OutputForm +--R hash : % -> SingleInteger hclf : (%,%) -> % +--R hcrf : (%,%) -> % latex : % -> String +--R lquo : (%,%) -> Union(%,"failed") mapGen : ((S -> S),%) -> % +--R max : (%,%) -> % if S has ORDSET min : (%,%) -> % if S has ORDSET --R nthFactor : (%,Integer) -> S one? : % -> Boolean --R recip : % -> Union(%,"failed") retract : % -> S ---R sample : () -> % size : % -> NonNegativeInteger ---R ?~=? : (%,%) -> Boolean ---R ?**? : (S,NonNegativeInteger) -> % ---R ?**? : (%,NonNegativeInteger) -> % +--R rquo : (%,%) -> Union(%,"failed") sample : () -> % +--R size : % -> NonNegativeInteger ?~=? : (%,%) -> Boolean --R ? Boolean if S has ORDSET --R ?<=? : (%,%) -> Boolean if S has ORDSET --R ?>? : (%,%) -> Boolean if S has ORDSET --R ?>=? : (%,%) -> Boolean if S has ORDSET ---R ?^? : (%,NonNegativeInteger) -> % --R divide : (%,%) -> Union(Record(lm: %,rm: %),"failed") --R factors : % -> List(Record(gen: S,exp: NonNegativeInteger)) ---R lquo : (%,%) -> Union(%,"failed") --R mapExpon : ((NonNegativeInteger -> NonNegativeInteger),%) -> % ---R max : (%,%) -> % if S has ORDSET ---R min : (%,%) -> % if S has ORDSET --R nthExpon : (%,Integer) -> NonNegativeInteger --R overlap : (%,%) -> Record(lm: %,mm: %,rm: %) --R retractIfCan : % -> Union(S,"failed") ---R rquo : (%,%) -> Union(%,"failed") --R --E 1 @@ -57174,6 +59565,7 @@ FreeMonoid(S: SetCategory): FMcategory == FMdefinition where --S 1 of 1 )show FreeNilpotentLie +--R --R FreeNilpotentLie(n: NonNegativeInteger,class: NonNegativeInteger,R: CommutativeRing) is a domain constructor --R Abbreviation for FreeNilpotentLie is FNLA --R This constructor is exposed in this frame. @@ -57182,18 +59574,17 @@ FreeMonoid(S: SetCategory): FMcategory == FMdefinition where --R------------------------------- Operations -------------------------------- --R ?*? : (R,%) -> % ?*? : (%,R) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % ---R ?+? : (%,%) -> % ?-? : (%,%) -> % ---R -? : % -> % ?=? : (%,%) -> Boolean ---R 0 : () -> % antiCommutator : (%,%) -> % ---R associator : (%,%,%) -> % coerce : % -> OutputForm ---R commutator : (%,%) -> % deepExpand : % -> OutputForm ---R hash : % -> SingleInteger latex : % -> String ---R sample : () -> % shallowExpand : % -> OutputForm ---R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R dimension : () -> NonNegativeInteger ---R generator : NonNegativeInteger -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % +--R ?-? : (%,%) -> % -? : % -> % +--R ?=? : (%,%) -> Boolean 0 : () -> % +--R antiCommutator : (%,%) -> % associator : (%,%,%) -> % +--R coerce : % -> OutputForm commutator : (%,%) -> % +--R deepExpand : % -> OutputForm dimension : () -> NonNegativeInteger +--R generator : NonNegativeInteger -> % hash : % -> SingleInteger +--R latex : % -> String sample : () -> % +--R shallowExpand : % -> OutputForm zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean --R leftPower : (%,PositiveInteger) -> % --R plenaryPower : (%,PositiveInteger) -> % --R rightPower : (%,PositiveInteger) -> % @@ -57381,7 +59772,8 @@ FreeNilpotentLie(n:NNI,class:NNI,R: CommutativeRing): Export == Implement where )set message test on )set message auto off )clear all ---S 1 of 16 + +--S 1 of 17 Fx := FRAC UP(x, FRAC INT) --R --R @@ -57389,7 +59781,7 @@ Fx := FRAC UP(x, FRAC INT) --R Type: Domain --E 1 ---S 2 of 16 +--S 2 of 17 f : Fx := 36 / (x**5-2*x**4-2*x**3+4*x**2+x-2) --R --R @@ -57400,7 +59792,7 @@ f : Fx := 36 / (x**5-2*x**4-2*x**3+4*x**2+x-2) --R Type: Fraction(UnivariatePolynomial(x,Fraction(Integer))) --E 2 ---S 3 of 16 +--S 3 of 17 g := fullPartialFraction f --R --R @@ -57412,7 +59804,7 @@ g := fullPartialFraction f --RType: FullPartialFractionExpansion(Fraction(Integer),UnivariatePolynomial(x,Fraction(Integer))) --E 3 ---S 4 of 16 +--S 4 of 17 g :: Fx --R --R @@ -57423,7 +59815,7 @@ g :: Fx --R Type: Fraction(UnivariatePolynomial(x,Fraction(Integer))) --E 4 ---S 5 of 16 +--S 5 of 17 g5 := D(g, 5) --R --R @@ -57435,7 +59827,7 @@ g5 := D(g, 5) --RType: FullPartialFractionExpansion(Fraction(Integer),UnivariatePolynomial(x,Fraction(Integer))) --E 5 ---S 6 of 16 +--S 6 of 17 f5 := D(f, 5) --R --R @@ -57457,7 +59849,7 @@ f5 := D(f, 5) --R Type: Fraction(UnivariatePolynomial(x,Fraction(Integer))) --E 6 ---S 7 of 16 +--S 7 of 17 g5::Fx - f5 --R --R @@ -57465,7 +59857,7 @@ g5::Fx - f5 --R Type: Fraction(UnivariatePolynomial(x,Fraction(Integer))) --E 7 ---S 8 of 16 +--S 8 of 17 f : Fx := (x**5 * (x-1)) / ((x**2 + x + 1)**2 * (x-2)**3) --R --R @@ -57477,7 +59869,7 @@ f : Fx := (x**5 * (x-1)) / ((x**2 + x + 1)**2 * (x-2)**3) --R Type: Fraction(UnivariatePolynomial(x,Fraction(Integer))) --E 8 ---S 9 of 16 +--S 9 of 17 g := fullPartialFraction f --R --R @@ -57500,7 +59892,7 @@ g := fullPartialFraction f --RType: FullPartialFractionExpansion(Fraction(Integer),UnivariatePolynomial(x,Fraction(Integer))) --E 9 ---S 10 of 16 +--S 10 of 17 g :: Fx - f --R --R @@ -57508,7 +59900,7 @@ g :: Fx - f --R Type: Fraction(UnivariatePolynomial(x,Fraction(Integer))) --E 10 ---S 11 of 16 +--S 11 of 17 f : Fx := (2*x**7-7*x**5+26*x**3+8*x) / (x**8-5*x**6+6*x**4+4*x**2-8) --R --R @@ -57520,7 +59912,7 @@ f : Fx := (2*x**7-7*x**5+26*x**3+8*x) / (x**8-5*x**6+6*x**4+4*x**2-8) --R Type: Fraction(UnivariatePolynomial(x,Fraction(Integer))) --E 11 ---S 12 of 16 +--S 12 of 17 g := fullPartialFraction f --R --R @@ -57534,7 +59926,7 @@ g := fullPartialFraction f --RType: FullPartialFractionExpansion(Fraction(Integer),UnivariatePolynomial(x,Fraction(Integer))) --E 12 ---S 13 of 16 +--S 13 of 17 g :: Fx - f --R --R @@ -57542,7 +59934,7 @@ g :: Fx - f --R Type: Fraction(UnivariatePolynomial(x,Fraction(Integer))) --E 13 ---S 14 of 16 +--S 14 of 17 f:Fx := x**3 / (x**21 + 2*x**20 + 4*x**19 + 7*x**18 + 10*x**17 + 17*x**16 + 22*x**15 + 30*x**14 + 36*x**13 + 40*x**12 + 47*x**11 + 46*x**10 + 49*x**9 + 43*x**8 + 38*x**7 + 32*x**6 + 23*x**5 + 19*x**4 + 10*x**3 + 7*x**2 + 2*x + 1) --R --R @@ -57560,7 +59952,7 @@ f:Fx := x**3 / (x**21 + 2*x**20 + 4*x**19 + 7*x**18 + 10*x**17 + 17*x**16 + 22*x --R Type: Fraction(UnivariatePolynomial(x,Fraction(Integer))) --E 14 ---S 15 of 16 +--S 15 of 17 g := fullPartialFraction f --R --R @@ -57619,13 +60011,36 @@ g := fullPartialFraction f --RType: FullPartialFractionExpansion(Fraction(Integer),UnivariatePolynomial(x,Fraction(Integer))) --E 15 ---S 16 of 16 +--S 16 of 17 g :: Fx - f --R --R --R (16) 0 --R Type: Fraction(UnivariatePolynomial(x,Fraction(Integer))) --E 16 + +--S 17 of 17 +)show FullPartialFractionExpansion +--R +--R FullPartialFractionExpansion(F: Join(Field,CharacteristicZero),UP: UnivariatePolynomialCategory(F)) is a domain constructor +--R Abbreviation for FullPartialFractionExpansion is FPARFRAC +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for FPARFRAC +--R +--R------------------------------- Operations -------------------------------- +--R ?+? : (UP,%) -> % ?=? : (%,%) -> Boolean +--R D : (%,NonNegativeInteger) -> % D : % -> % +--R coerce : % -> OutputForm convert : % -> Fraction(UP) +--R differentiate : % -> % hash : % -> SingleInteger +--R latex : % -> String polyPart : % -> UP +--R ?~=? : (%,%) -> Boolean +--R construct : List(Record(exponent: NonNegativeInteger,center: UP,num: UP)) -> % +--R differentiate : (%,NonNegativeInteger) -> % +--R fracPart : % -> List(Record(exponent: NonNegativeInteger,center: UP,num: UP)) +--R fullPartialFraction : Fraction(UP) -> % +--R +--E 17 + )spool )lisp (bye) \end{chunk} @@ -58141,13 +60556,14 @@ FunctionCalled(f:Symbol): SetCategory with )set message test on )set message auto off )clear all ---S 1 of 10 + +--S 1 of 11 (d1,d2,d3) : DMP([z,y,x],FRAC INT) --R --R Type: Void --E 1 ---S 2 of 10 +--S 2 of 11 d1 := -4*z + 4*y**2*x + 16*x**2 + 1 --R --R @@ -58156,7 +60572,7 @@ d1 := -4*z + 4*y**2*x + 16*x**2 + 1 --R Type: DistributedMultivariatePolynomial([z,y,x],Fraction(Integer)) --E 2 ---S 3 of 10 +--S 3 of 11 d2 := 2*z*y**2 + 4*x + 1 --R --R @@ -58165,7 +60581,7 @@ d2 := 2*z*y**2 + 4*x + 1 --R Type: DistributedMultivariatePolynomial([z,y,x],Fraction(Integer)) --E 3 ---S 4 of 10 +--S 4 of 11 d3 := 2*z*x**2 - 2*y**2 - x --R --R @@ -58174,7 +60590,7 @@ d3 := 2*z*x**2 - 2*y**2 - x --R Type: DistributedMultivariatePolynomial([z,y,x],Fraction(Integer)) --E 4 ---S 5 of 10 +--S 5 of 11 groebner [d1,d2,d3] --R --R @@ -58191,13 +60607,13 @@ groebner [d1,d2,d3] --R Type: List(DistributedMultivariatePolynomial([z,y,x],Fraction(Integer))) --E 5 ---S 6 of 10 +--S 6 of 11 (n1,n2,n3) : HDMP([z,y,x],FRAC INT) --R --R Type: Void --E 6 ---S 7 of 10 +--S 7 of 11 n1 := d1 --R --R @@ -58206,7 +60622,7 @@ n1 := d1 --RType: HomogeneousDistributedMultivariatePolynomial([z,y,x],Fraction(Integer)) --E 7 ---S 8 of 10 +--S 8 of 11 n2 := d2 --R --R @@ -58215,7 +60631,7 @@ n2 := d2 --RType: HomogeneousDistributedMultivariatePolynomial([z,y,x],Fraction(Integer)) --E 8 ---S 9 of 10 +--S 9 of 11 n3 := d3 --R --R @@ -58224,7 +60640,7 @@ n3 := d3 --RType: HomogeneousDistributedMultivariatePolynomial([z,y,x],Fraction(Integer)) --E 9 ---S 10 of 10 +--S 10 of 11 groebner [n1,n2,n3] --R --R @@ -58240,6 +60656,131 @@ groebner [n1,n2,n3] --R 4 2 --RType: List(HomogeneousDistributedMultivariatePolynomial([z,y,x],Fraction(Integer))) --E 10 + +--S 11 of 11 +)show GeneralDistributedMultivariatePolynomial +--R +--R GeneralDistributedMultivariatePolynomial(vl: List(Symbol),R: Ring,E: DirectProductCategory(#(vl),NonNegativeInteger)) is a domain constructor +--R Abbreviation for GeneralDistributedMultivariatePolynomial is GDMP +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for GDMP +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,R) -> % ?*? : (R,%) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?/? : (%,R) -> % if R has FIELD +--R ?=? : (%,%) -> Boolean 1 : () -> % +--R 0 : () -> % ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,PositiveInteger) -> % coefficient : (%,E) -> R +--R coefficients : % -> List(R) coerce : % -> % if R has INTDOM +--R coerce : R -> % coerce : Integer -> % +--R coerce : % -> OutputForm content : % -> R if R has GCDDOM +--R degree : % -> E eval : (%,List(%),List(%)) -> % +--R eval : (%,%,%) -> % eval : (%,Equation(%)) -> % +--R eval : (%,List(Equation(%))) -> % gcd : (%,%) -> % if R has GCDDOM +--R gcd : List(%) -> % if R has GCDDOM ground : % -> R +--R ground? : % -> Boolean hash : % -> SingleInteger +--R latex : % -> String lcm : (%,%) -> % if R has GCDDOM +--R lcm : List(%) -> % if R has GCDDOM leadingCoefficient : % -> R +--R leadingMonomial : % -> % map : ((R -> R),%) -> % +--R mapExponents : ((E -> E),%) -> % max : (%,%) -> % if R has ORDSET +--R min : (%,%) -> % if R has ORDSET minimumDegree : % -> E +--R monomial : (R,E) -> % monomial? : % -> Boolean +--R monomials : % -> List(%) one? : % -> Boolean +--R pomopo! : (%,R,E,%) -> % primitiveMonomials : % -> List(%) +--R recip : % -> Union(%,"failed") reductum : % -> % +--R reorder : (%,List(Integer)) -> % retract : % -> R +--R sample : () -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R ?*? : (Fraction(Integer),%) -> % if R has ALGEBRA(FRAC(INT)) +--R ?*? : (%,Fraction(Integer)) -> % if R has ALGEBRA(FRAC(INT)) +--R ? Boolean if R has ORDSET +--R ?<=? : (%,%) -> Boolean if R has ORDSET +--R ?>? : (%,%) -> Boolean if R has ORDSET +--R ?>=? : (%,%) -> Boolean if R has ORDSET +--R D : (%,List(OrderedVariableList(vl)),List(NonNegativeInteger)) -> % +--R D : (%,OrderedVariableList(vl),NonNegativeInteger) -> % +--R D : (%,List(OrderedVariableList(vl))) -> % +--R D : (%,OrderedVariableList(vl)) -> % +--R associates? : (%,%) -> Boolean if R has INTDOM +--R binomThmExpt : (%,%,NonNegativeInteger) -> % if R has COMRING +--R characteristic : () -> NonNegativeInteger +--R charthRoot : % -> Union(%,"failed") if $ has CHARNZ and R has PFECAT or R has CHARNZ +--R coefficient : (%,List(OrderedVariableList(vl)),List(NonNegativeInteger)) -> % +--R coefficient : (%,OrderedVariableList(vl),NonNegativeInteger) -> % +--R coerce : Fraction(Integer) -> % if R has ALGEBRA(FRAC(INT)) or R has RETRACT(FRAC(INT)) +--R coerce : OrderedVariableList(vl) -> % +--R conditionP : Matrix(%) -> Union(Vector(%),"failed") if $ has CHARNZ and R has PFECAT +--R content : (%,OrderedVariableList(vl)) -> % if R has GCDDOM +--R convert : % -> InputForm if OrderedVariableList(vl) has KONVERT(INFORM) and R has KONVERT(INFORM) +--R convert : % -> Pattern(Integer) if OrderedVariableList(vl) has KONVERT(PATTERN(INT)) and R has KONVERT(PATTERN(INT)) +--R convert : % -> Pattern(Float) if OrderedVariableList(vl) has KONVERT(PATTERN(FLOAT)) and R has KONVERT(PATTERN(FLOAT)) +--R degree : (%,List(OrderedVariableList(vl))) -> List(NonNegativeInteger) +--R degree : (%,OrderedVariableList(vl)) -> NonNegativeInteger +--R differentiate : (%,List(OrderedVariableList(vl)),List(NonNegativeInteger)) -> % +--R differentiate : (%,OrderedVariableList(vl),NonNegativeInteger) -> % +--R differentiate : (%,List(OrderedVariableList(vl))) -> % +--R differentiate : (%,OrderedVariableList(vl)) -> % +--R discriminant : (%,OrderedVariableList(vl)) -> % if R has COMRING +--R eval : (%,List(OrderedVariableList(vl)),List(%)) -> % +--R eval : (%,OrderedVariableList(vl),%) -> % +--R eval : (%,List(OrderedVariableList(vl)),List(R)) -> % +--R eval : (%,OrderedVariableList(vl),R) -> % +--R exquo : (%,%) -> Union(%,"failed") if R has INTDOM +--R exquo : (%,R) -> Union(%,"failed") if R has INTDOM +--R factor : % -> Factored(%) if R has PFECAT +--R factorPolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has PFECAT +--R factorSquareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has PFECAT +--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) if R has GCDDOM +--R isExpt : % -> Union(Record(var: OrderedVariableList(vl),exponent: NonNegativeInteger),"failed") +--R isPlus : % -> Union(List(%),"failed") +--R isTimes : % -> Union(List(%),"failed") +--R lcmCoef : (%,%) -> Record(llcmres: %,coeff1: %,coeff2: %) if R has GCDDOM +--R mainVariable : % -> Union(OrderedVariableList(vl),"failed") +--R minimumDegree : (%,List(OrderedVariableList(vl))) -> List(NonNegativeInteger) +--R minimumDegree : (%,OrderedVariableList(vl)) -> NonNegativeInteger +--R monicDivide : (%,%,OrderedVariableList(vl)) -> Record(quotient: %,remainder: %) +--R monomial : (%,List(OrderedVariableList(vl)),List(NonNegativeInteger)) -> % +--R monomial : (%,OrderedVariableList(vl),NonNegativeInteger) -> % +--R multivariate : (SparseUnivariatePolynomial(%),OrderedVariableList(vl)) -> % +--R multivariate : (SparseUnivariatePolynomial(R),OrderedVariableList(vl)) -> % +--R numberOfMonomials : % -> NonNegativeInteger +--R patternMatch : (%,Pattern(Integer),PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if OrderedVariableList(vl) has PATMAB(INT) and R has PATMAB(INT) +--R patternMatch : (%,Pattern(Float),PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if OrderedVariableList(vl) has PATMAB(FLOAT) and R has PATMAB(FLOAT) +--R prime? : % -> Boolean if R has PFECAT +--R primitivePart : (%,OrderedVariableList(vl)) -> % if R has GCDDOM +--R primitivePart : % -> % if R has GCDDOM +--R reducedSystem : Matrix(%) -> Matrix(R) +--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(R),vec: Vector(R)) +--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(Integer),vec: Vector(Integer)) if R has LINEXP(INT) +--R reducedSystem : Matrix(%) -> Matrix(Integer) if R has LINEXP(INT) +--R resultant : (%,%,OrderedVariableList(vl)) -> % if R has COMRING +--R retract : % -> OrderedVariableList(vl) +--R retract : % -> Integer if R has RETRACT(INT) +--R retract : % -> Fraction(Integer) if R has RETRACT(FRAC(INT)) +--R retractIfCan : % -> Union(OrderedVariableList(vl),"failed") +--R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT(INT) +--R retractIfCan : % -> Union(Fraction(Integer),"failed") if R has RETRACT(FRAC(INT)) +--R retractIfCan : % -> Union(R,"failed") +--R solveLinearPolynomialEquation : (List(SparseUnivariatePolynomial(%)),SparseUnivariatePolynomial(%)) -> Union(List(SparseUnivariatePolynomial(%)),"failed") if R has PFECAT +--R squareFree : % -> Factored(%) if R has GCDDOM +--R squareFreePart : % -> % if R has GCDDOM +--R squareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has PFECAT +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R totalDegree : (%,List(OrderedVariableList(vl))) -> NonNegativeInteger +--R totalDegree : % -> NonNegativeInteger +--R unit? : % -> Boolean if R has INTDOM +--R unitCanonical : % -> % if R has INTDOM +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) if R has INTDOM +--R univariate : % -> SparseUnivariatePolynomial(R) +--R univariate : (%,OrderedVariableList(vl)) -> SparseUnivariatePolynomial(%) +--R variables : % -> List(OrderedVariableList(vl)) +--R +--E 11 + )spool )lisp (bye) \end{chunk} @@ -58706,17 +61247,17 @@ GeneralDistributedMultivariatePolynomial(vl,R,E): public == private where --R------------------------------- Operations -------------------------------- --R ?*? : (R,%) -> % ?*? : (%,R) -> % --R ?*? : (%,P) -> % ?*? : (P,%) -> % ---R ?*? : (Integer,%) -> % ?*? : (PositiveInteger,%) -> % ---R ?+? : (%,%) -> % ?-? : (%,%) -> % ---R -? : % -> % ?=? : (%,%) -> Boolean ---R 0 : () -> % build : (R,IS,E) -> % ---R coerce : % -> OutputForm hash : % -> SingleInteger ---R latex : % -> String leadingCoefficient : % -> R ---R leadingExponent : % -> E leadingIndex : % -> IS ---R multMonom : (R,E,%) -> % reductum : % -> % ---R sample : () -> % unitVector : IS -> % ---R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % +--R ?*? : (Integer,%) -> % ?*? : (NonNegativeInteger,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?+? : (%,%) -> % +--R ?-? : (%,%) -> % -? : % -> % +--R ?=? : (%,%) -> Boolean 0 : () -> % +--R build : (R,IS,E) -> % coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R leadingCoefficient : % -> R leadingExponent : % -> E +--R leadingIndex : % -> IS multMonom : (R,E,%) -> % +--R reductum : % -> % sample : () -> % +--R unitVector : IS -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean --R leadingMonomial : % -> ModuleMonomial(IS,E,ff) --R monomial : (R,ModuleMonomial(IS,E,ff)) -> % --R subtractIfCan : (%,%) -> Union(%,"failed") @@ -58870,15 +61411,16 @@ GeneralModulePolynomial(vl, R, IS, E, ff, P): public == private where --R --R------------------------------- Operations -------------------------------- --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % ---R ?+? : (%,%) -> % ?-? : (%,%) -> % ---R -? : % -> % ?=? : (%,%) -> Boolean ---R 0 : () -> % alternative? : () -> Boolean ---R antiAssociative? : () -> Boolean antiCommutative? : () -> Boolean ---R antiCommutator : (%,%) -> % associative? : () -> Boolean ---R associator : (%,%,%) -> % basis : () -> Vector(%) ---R coerce : % -> OutputForm commutative? : () -> Boolean ---R commutator : (%,%) -> % flexible? : () -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % +--R ?-? : (%,%) -> % -? : % -> % +--R ?=? : (%,%) -> Boolean 0 : () -> % +--R alternative? : () -> Boolean antiAssociative? : () -> Boolean +--R antiCommutative? : () -> Boolean antiCommutator : (%,%) -> % +--R associative? : () -> Boolean associator : (%,%,%) -> % +--R basis : () -> Vector(%) coerce : % -> OutputForm +--R commutative? : () -> Boolean commutator : (%,%) -> % +--R flexible? : () -> Boolean generic : (Symbol,Vector(%)) -> % --R generic : Vector(%) -> % generic : Vector(Symbol) -> % --R generic : Symbol -> % generic : () -> % --R hash : % -> SingleInteger jacobiIdentity? : () -> Boolean @@ -58892,7 +61434,6 @@ GeneralModulePolynomial(vl, R, IS, E, ff, P): public == private where --R ?*? : (SquareMatrix(n,Fraction(Polynomial(R))),%) -> % --R ?*? : (Fraction(Polynomial(R)),%) -> % --R ?*? : (%,Fraction(Polynomial(R))) -> % ---R ?*? : (NonNegativeInteger,%) -> % --R apply : (Matrix(Fraction(Polynomial(R))),%) -> % --R associatorDependence : () -> List(Vector(Fraction(Polynomial(R)))) if Fraction(Polynomial(R)) has INTDOM --R coerce : Vector(Fraction(Polynomial(R))) -> % @@ -58908,7 +61449,6 @@ GeneralModulePolynomial(vl, R, IS, E, ff, P): public == private where --R coordinates : (%,Vector(%)) -> Vector(Fraction(Polynomial(R))) --R ?.? : (%,Integer) -> Fraction(Polynomial(R)) --R generic : (Vector(Symbol),Vector(%)) -> % ---R generic : (Symbol,Vector(%)) -> % --R genericLeftDiscriminant : () -> Fraction(Polynomial(R)) if R has INTDOM --R genericLeftMinimalPolynomial : % -> SparseUnivariatePolynomial(Fraction(Polynomial(R))) if R has INTDOM --R genericLeftNorm : % -> Fraction(Polynomial(R)) if R has INTDOM @@ -59611,33 +62151,119 @@ GeneralPolynomialSet(R,E,VarSet,P) : Exports == Implementation where )set message auto off )set break resume )clear all ---S 1 of 7 + +--S 1 of 8 patrons: GeneralSparseTable(String, Integer, KeyedAccessFile(Integer), 0) := table() ; --E 1 ---S 2 of 7 +--S 2 of 8 patrons."Smith" := 10500 --E 2 ---S 3 of 7 +--S 3 of 8 patrons."Jones" := 22000 --E 3 ---S 4 of 7 +--S 4 of 8 patrons."Jones" --E 4 ---S 5 of 7 +--S 5 of 8 patrons."Stingy" --E 5 ---S 6 of 7 +--S 6 of 8 reduce(+, entries patrons) --E 6 ---S 7 of 7 +--S 7 of 8 )system rm -r kaf*.sdata --E 7 + +--S 8 of 8 +)show GeneralSparseTable +--R +--R GeneralSparseTable(Key: SetCategory,Entry: SetCategory,Tbl: TableAggregate(Key,Entry),dent: Entry) is a domain constructor +--R Abbreviation for GeneralSparseTable is GSTBL +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for GSTBL +--R +--R------------------------------- Operations -------------------------------- +--R copy : % -> % dictionary : () -> % +--R elt : (%,Key,Entry) -> Entry ?.? : (%,Key) -> Entry +--R empty : () -> % empty? : % -> Boolean +--R entries : % -> List(Entry) eq? : (%,%) -> Boolean +--R index? : (Key,%) -> Boolean indices : % -> List(Key) +--R key? : (Key,%) -> Boolean keys : % -> List(Key) +--R map : ((Entry -> Entry),%) -> % qelt : (%,Key) -> Entry +--R sample : () -> % setelt : (%,Key,Entry) -> Entry +--R table : () -> % +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R ?=? : (%,%) -> Boolean if Record(key: Key,entry: Entry) has SETCAT or Entry has SETCAT +--R any? : ((Entry -> Boolean),%) -> Boolean if $ has finiteAggregate +--R any? : ((Record(key: Key,entry: Entry) -> Boolean),%) -> Boolean if $ has finiteAggregate +--R bag : List(Record(key: Key,entry: Entry)) -> % +--R coerce : % -> OutputForm if Record(key: Key,entry: Entry) has SETCAT or Entry has SETCAT +--R construct : List(Record(key: Key,entry: Entry)) -> % +--R convert : % -> InputForm if Record(key: Key,entry: Entry) has KONVERT(INFORM) +--R count : ((Entry -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R count : (Entry,%) -> NonNegativeInteger if $ has finiteAggregate and Entry has SETCAT +--R count : (Record(key: Key,entry: Entry),%) -> NonNegativeInteger if $ has finiteAggregate and Record(key: Key,entry: Entry) has SETCAT +--R count : ((Record(key: Key,entry: Entry) -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R dictionary : List(Record(key: Key,entry: Entry)) -> % +--R entry? : (Entry,%) -> Boolean if $ has finiteAggregate and Entry has SETCAT +--R eval : (%,List(Equation(Entry))) -> % if Entry has EVALAB(Entry) and Entry has SETCAT +--R eval : (%,Equation(Entry)) -> % if Entry has EVALAB(Entry) and Entry has SETCAT +--R eval : (%,Entry,Entry) -> % if Entry has EVALAB(Entry) and Entry has SETCAT +--R eval : (%,List(Entry),List(Entry)) -> % if Entry has EVALAB(Entry) and Entry has SETCAT +--R eval : (%,List(Record(key: Key,entry: Entry)),List(Record(key: Key,entry: Entry))) -> % if Record(key: Key,entry: Entry) has EVALAB(Record(key: Key,entry: Entry)) and Record(key: Key,entry: Entry) has SETCAT +--R eval : (%,Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> % if Record(key: Key,entry: Entry) has EVALAB(Record(key: Key,entry: Entry)) and Record(key: Key,entry: Entry) has SETCAT +--R eval : (%,Equation(Record(key: Key,entry: Entry))) -> % if Record(key: Key,entry: Entry) has EVALAB(Record(key: Key,entry: Entry)) and Record(key: Key,entry: Entry) has SETCAT +--R eval : (%,List(Equation(Record(key: Key,entry: Entry)))) -> % if Record(key: Key,entry: Entry) has EVALAB(Record(key: Key,entry: Entry)) and Record(key: Key,entry: Entry) has SETCAT +--R every? : ((Entry -> Boolean),%) -> Boolean if $ has finiteAggregate +--R every? : ((Record(key: Key,entry: Entry) -> Boolean),%) -> Boolean if $ has finiteAggregate +--R extract! : % -> Record(key: Key,entry: Entry) +--R fill! : (%,Entry) -> % if $ has shallowlyMutable +--R find : ((Record(key: Key,entry: Entry) -> Boolean),%) -> Union(Record(key: Key,entry: Entry),"failed") +--R first : % -> Entry if Key has ORDSET +--R hash : % -> SingleInteger if Record(key: Key,entry: Entry) has SETCAT or Entry has SETCAT +--R insert! : (Record(key: Key,entry: Entry),%) -> % +--R inspect : % -> Record(key: Key,entry: Entry) +--R latex : % -> String if Record(key: Key,entry: Entry) has SETCAT or Entry has SETCAT +--R less? : (%,NonNegativeInteger) -> Boolean +--R map : (((Entry,Entry) -> Entry),%,%) -> % +--R map : ((Record(key: Key,entry: Entry) -> Record(key: Key,entry: Entry)),%) -> % +--R map! : ((Entry -> Entry),%) -> % if $ has shallowlyMutable +--R map! : ((Record(key: Key,entry: Entry) -> Record(key: Key,entry: Entry)),%) -> % if $ has shallowlyMutable +--R maxIndex : % -> Key if Key has ORDSET +--R member? : (Entry,%) -> Boolean if $ has finiteAggregate and Entry has SETCAT +--R member? : (Record(key: Key,entry: Entry),%) -> Boolean if $ has finiteAggregate and Record(key: Key,entry: Entry) has SETCAT +--R members : % -> List(Entry) if $ has finiteAggregate +--R members : % -> List(Record(key: Key,entry: Entry)) if $ has finiteAggregate +--R minIndex : % -> Key if Key has ORDSET +--R more? : (%,NonNegativeInteger) -> Boolean +--R parts : % -> List(Entry) if $ has finiteAggregate +--R parts : % -> List(Record(key: Key,entry: Entry)) if $ has finiteAggregate +--R qsetelt! : (%,Key,Entry) -> Entry if $ has shallowlyMutable +--R reduce : (((Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry)),%) -> Record(key: Key,entry: Entry) if $ has finiteAggregate +--R reduce : (((Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry)),%,Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry) if $ has finiteAggregate +--R reduce : (((Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry)),%,Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry) if $ has finiteAggregate and Record(key: Key,entry: Entry) has SETCAT +--R remove : ((Record(key: Key,entry: Entry) -> Boolean),%) -> % if $ has finiteAggregate +--R remove : (Record(key: Key,entry: Entry),%) -> % if $ has finiteAggregate and Record(key: Key,entry: Entry) has SETCAT +--R remove! : (Key,%) -> Union(Entry,"failed") +--R remove! : ((Record(key: Key,entry: Entry) -> Boolean),%) -> % if $ has finiteAggregate +--R remove! : (Record(key: Key,entry: Entry),%) -> % if $ has finiteAggregate +--R removeDuplicates : % -> % if $ has finiteAggregate and Record(key: Key,entry: Entry) has SETCAT +--R search : (Key,%) -> Union(Entry,"failed") +--R select : ((Record(key: Key,entry: Entry) -> Boolean),%) -> % if $ has finiteAggregate +--R select! : ((Record(key: Key,entry: Entry) -> Boolean),%) -> % if $ has finiteAggregate +--R size? : (%,NonNegativeInteger) -> Boolean +--R swap! : (%,Key,Key) -> Void if $ has shallowlyMutable +--R table : List(Record(key: Key,entry: Entry)) -> % +--R ?~=? : (%,%) -> Boolean if Record(key: Key,entry: Entry) has SETCAT or Entry has SETCAT +--R +--E 8 + )spool )lisp (bye) \end{chunk} @@ -59831,7 +62457,8 @@ GeneralSparseTable(Key, Entry, Tbl, dent): TableAggregate(Key, Entry) == Impl --R normalized? : (P,%) -> Boolean reduceByQuasiMonic : (P,%) -> P --R removeZero : (P,%) -> P rest : % -> Union(%,"failed") --R retract : List(P) -> % sample : () -> % ---R stronglyReduce : (P,%) -> P stronglyReduced? : % -> Boolean +--R select : (%,V) -> Union(P,"failed") stronglyReduce : (P,%) -> P +--R stronglyReduced? : % -> Boolean stronglyReduced? : (P,%) -> Boolean --R trivialIdeal? : % -> Boolean variables : % -> List(V) --R zeroSetSplit : List(P) -> List(%) ?~=? : (%,%) -> Boolean --R #? : % -> NonNegativeInteger if $ has finiteAggregate @@ -59876,11 +62503,9 @@ GeneralSparseTable(Key, Entry, Tbl, dent): TableAggregate(Key, Entry) == Impl --R roughEqualIdeals? : (%,%) -> Boolean if R has INTDOM --R roughSubIdeal? : (%,%) -> Boolean if R has INTDOM --R roughUnitIdeal? : % -> Boolean if R has INTDOM ---R select : (%,V) -> Union(P,"failed") --R select : ((P -> Boolean),%) -> % if $ has finiteAggregate --R size? : (%,NonNegativeInteger) -> Boolean --R sort : (%,V) -> Record(under: %,floor: %,upper: %) ---R stronglyReduced? : (P,%) -> Boolean --R triangular? : % -> Boolean if R has INTDOM --R zeroSetSplitIntoTriangularSystems : List(P) -> List(Record(close: %,open: List(P))) --R @@ -60127,14 +62752,17 @@ GeneralTriangularSet(R,E,V,P) : Exports == Implementation where --R------------------------------- Operations -------------------------------- --R ?*? : (Coef,%) -> % ?*? : (%,Coef) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ?=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % center : % -> Coef +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R center : % -> Coef coerce : % -> % if Coef has INTDOM --R coerce : Variable(var) -> % coerce : Integer -> % --R coerce : % -> OutputForm complete : % -> % ---R degree : % -> Fraction(Integer) hash : % -> SingleInteger +--R degree : % -> Fraction(Integer) ?.? : (%,Fraction(Integer)) -> Coef +--R hash : % -> SingleInteger inv : % -> % if Coef has FIELD --R latex : % -> String leadingCoefficient : % -> Coef --R leadingMonomial : % -> % map : ((Coef -> Coef),%) -> % --R monomial? : % -> Boolean one? : % -> Boolean @@ -60144,11 +62772,9 @@ GeneralTriangularSet(R,E,V,P) : Exports == Implementation where --R zero? : % -> Boolean ?~=? : (%,%) -> Boolean --R ?*? : (%,Fraction(Integer)) -> % if Coef has ALGEBRA(FRAC(INT)) --R ?*? : (Fraction(Integer),%) -> % if Coef has ALGEBRA(FRAC(INT)) ---R ?*? : (NonNegativeInteger,%) -> % --R ?**? : (%,Fraction(Integer)) -> % if Coef has ALGEBRA(FRAC(INT)) --R ?**? : (%,%) -> % if Coef has ALGEBRA(FRAC(INT)) --R ?**? : (%,Integer) -> % if Coef has FIELD ---R ?**? : (%,NonNegativeInteger) -> % --R ?/? : (%,%) -> % if Coef has FIELD --R ?/? : (%,Coef) -> % if Coef has FIELD --R D : % -> % if Coef has *: (Fraction(Integer),Coef) -> Coef @@ -60158,7 +62784,6 @@ GeneralTriangularSet(R,E,V,P) : Exports == Implementation where --R D : (%,Symbol,NonNegativeInteger) -> % if Coef has *: (Fraction(Integer),Coef) -> Coef and Coef has PDRING(SYMBOL) --R D : (%,List(Symbol),List(NonNegativeInteger)) -> % if Coef has *: (Fraction(Integer),Coef) -> Coef and Coef has PDRING(SYMBOL) --R ?^? : (%,Integer) -> % if Coef has FIELD ---R ?^? : (%,NonNegativeInteger) -> % --R acos : % -> % if Coef has ALGEBRA(FRAC(INT)) --R acosh : % -> % if Coef has ALGEBRA(FRAC(INT)) --R acot : % -> % if Coef has ALGEBRA(FRAC(INT)) @@ -60176,7 +62801,6 @@ GeneralTriangularSet(R,E,V,P) : Exports == Implementation where --R characteristic : () -> NonNegativeInteger --R charthRoot : % -> Union(%,"failed") if Coef has CHARNZ --R coefficient : (%,Fraction(Integer)) -> Coef ---R coerce : % -> % if Coef has INTDOM --R coerce : Fraction(Integer) -> % if Coef has ALGEBRA(FRAC(INT)) --R coerce : UnivariatePuiseuxSeries(Coef,var,cen) -> % --R coerce : Coef -> % if Coef has COMRING @@ -60195,7 +62819,6 @@ GeneralTriangularSet(R,E,V,P) : Exports == Implementation where --R differentiate : (%,List(Symbol),List(NonNegativeInteger)) -> % if Coef has *: (Fraction(Integer),Coef) -> Coef and Coef has PDRING(SYMBOL) --R divide : (%,%) -> Record(quotient: %,remainder: %) if Coef has FIELD --R ?.? : (%,%) -> % if Fraction(Integer) has SGROUP ---R ?.? : (%,Fraction(Integer)) -> Coef --R euclideanSize : % -> NonNegativeInteger if Coef has FIELD --R eval : (%,Coef) -> Stream(Coef) if Coef has **: (Coef,Fraction(Integer)) -> Coef --R exp : % -> % if Coef has ALGEBRA(FRAC(INT)) @@ -60211,7 +62834,6 @@ GeneralTriangularSet(R,E,V,P) : Exports == Implementation where --R integrate : (%,Variable(var)) -> % if Coef has ALGEBRA(FRAC(INT)) --R integrate : (%,Symbol) -> % if Coef has integrate: (Coef,Symbol) -> Coef and Coef has variables: Coef -> List(Symbol) and Coef has ALGEBRA(FRAC(INT)) or Coef has ACFS(INT) and Coef has ALGEBRA(FRAC(INT)) and Coef has PRIMCAT and Coef has TRANFUN --R integrate : % -> % if Coef has ALGEBRA(FRAC(INT)) ---R inv : % -> % if Coef has FIELD --R lcm : (%,%) -> % if Coef has FIELD --R lcm : List(%) -> % if Coef has FIELD --R lcmCoef : (%,%) -> Record(llcmres: %,coeff1: %,coeff2: %) if Coef has FIELD @@ -60506,8 +63128,8 @@ GeneralUnivariatePowerSeries(Coef,var,cen): Exports == Implementation where --R ?=? : (%,%) -> Boolean coerce : % -> OutputForm --R graphImage : () -> % hash : % -> SingleInteger --R key : % -> Integer latex : % -> String ---R makeGraphImage : % -> % units : % -> List(Float) ---R ?~=? : (%,%) -> Boolean +--R makeGraphImage : % -> % ranges : % -> List(Segment(Float)) +--R units : % -> List(Float) ?~=? : (%,%) -> Boolean --R appendPoint : (%,Point(DoubleFloat)) -> Void --R coerce : List(List(Point(DoubleFloat))) -> % --R component : (%,Point(DoubleFloat),Palette,Palette,PositiveInteger) -> Void @@ -60521,7 +63143,6 @@ GeneralUnivariatePowerSeries(Coef,var,cen): Exports == Implementation where --R pointLists : % -> List(List(Point(DoubleFloat))) --R putColorInfo : (List(List(Point(DoubleFloat))),List(Palette)) -> List(List(Point(DoubleFloat))) --R ranges : (%,List(Segment(Float))) -> List(Segment(Float)) ---R ranges : % -> List(Segment(Float)) --R units : (%,List(Float)) -> List(Float) --R --E 1 @@ -61258,14 +63879,14 @@ GuessOption(): Exports == Implementation where --R --R------------------------------- Operations -------------------------------- --R ?=? : (%,%) -> Boolean coerce : % -> OutputForm ---R hash : % -> SingleInteger latex : % -> String ---R one : List(GuessOption) -> Boolean ?~=? : (%,%) -> Boolean +--R debug : List(GuessOption) -> Boolean hash : % -> SingleInteger +--R latex : % -> String one : List(GuessOption) -> Boolean +--R ?~=? : (%,%) -> Boolean --R Somos : List(GuessOption) -> Union(PositiveInteger,Boolean) --R allDegrees : List(GuessOption) -> Boolean --R check : List(GuessOption) -> Union(skip,MonteCarlo,deterministic) --R checkExtraValues : List(GuessOption) -> Boolean --R checkOptions : List(GuessOption) -> Void ---R debug : List(GuessOption) -> Boolean --R displayAsGF : List(GuessOption) -> Boolean --R functionName : List(GuessOption) -> Symbol --R homogeneous : List(GuessOption) -> Union(PositiveInteger,Boolean) @@ -62192,9 +64813,10 @@ coerce a --R empty : () -> % empty? : % -> Boolean --R eq? : (%,%) -> Boolean extract! : % -> S --R heap : List(S) -> % insert! : (S,%) -> % ---R inspect : % -> S map : ((S -> S),%) -> % ---R max : % -> S merge : (%,%) -> % ---R merge! : (%,%) -> % sample : () -> % +--R inspect : % -> S latex : % -> String if S has SETCAT +--R map : ((S -> S),%) -> % max : % -> S +--R merge : (%,%) -> % merge! : (%,%) -> % +--R sample : () -> % --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R ?=? : (%,%) -> Boolean if S has SETCAT --R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate @@ -62207,7 +64829,6 @@ coerce a --R eval : (%,List(Equation(S))) -> % if S has EVALAB(S) and S has SETCAT --R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate --R hash : % -> SingleInteger if S has SETCAT ---R latex : % -> String if S has SETCAT --R less? : (%,NonNegativeInteger) -> Boolean --R map! : ((S -> S),%) -> % if $ has shallowlyMutable --R member? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT @@ -62709,7 +65330,8 @@ Heap(S:OrderedSet): Exports == Implementation where )set message test on )set message auto off )clear all ---S 1 of 7 + +--S 1 of 8 r := hex(22/7) --R --R @@ -62718,7 +65340,7 @@ r := hex(22/7) --R Type: HexadecimalExpansion --E 1 ---S 2 of 7 +--S 2 of 8 r + hex(6/7) --R --R @@ -62726,7 +65348,7 @@ r + hex(6/7) --R Type: HexadecimalExpansion --E 2 ---S 3 of 7 +--S 3 of 8 [hex(1/i) for i in 350..354] --R --R @@ -62738,7 +65360,7 @@ r + hex(6/7) --R Type: List(HexadecimalExpansion) --E 3 ---S 4 of 7 +--S 4 of 8 hex(1/1007) --R --R @@ -62750,7 +65372,7 @@ hex(1/1007) --R Type: HexadecimalExpansion --E 4 ---S 5 of 7 +--S 5 of 8 p := hex(1/4)*x**2 + hex(2/3)*x + hex(4/9) --R --R @@ -62759,7 +65381,7 @@ p := hex(1/4)*x**2 + hex(2/3)*x + hex(4/9) --R Type: Polynomial(HexadecimalExpansion) --E 5 ---S 6 of 7 +--S 6 of 8 q := D(p, x) --R --R @@ -62768,7 +65390,7 @@ q := D(p, x) --R Type: Polynomial(HexadecimalExpansion) --E 6 ---S 7 of 7 +--S 7 of 8 g := gcd(p, q) --R --R @@ -62776,6 +65398,126 @@ g := gcd(p, q) --R (7) x + 1.5 --R Type: Polynomial(HexadecimalExpansion) --E 7 + +--S 8 of 8 +)show HexadecimalExpansion +--R +--R HexadecimalExpansion is a domain constructor +--R Abbreviation for HexadecimalExpansion is HEXADEC +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for HEXADEC +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,Integer) -> % ?*? : (Integer,%) -> % +--R ?*? : (Fraction(Integer),%) -> % ?*? : (%,Fraction(Integer)) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,Integer) -> % ?**? : (%,NonNegativeInteger) -> % +--R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % +--R ?-? : (%,%) -> % -? : % -> % +--R ?/? : (Integer,Integer) -> % ?/? : (%,%) -> % +--R ?=? : (%,%) -> Boolean D : (%,(Integer -> Integer)) -> % +--R D : % -> % if Integer has DIFRING 1 : () -> % +--R 0 : () -> % ?^? : (%,Integer) -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R associates? : (%,%) -> Boolean coerce : % -> RadixExpansion(16) +--R coerce : % -> Fraction(Integer) coerce : Integer -> % +--R coerce : Fraction(Integer) -> % coerce : % -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R denom : % -> Integer denominator : % -> % +--R factor : % -> Factored(%) gcd : List(%) -> % +--R gcd : (%,%) -> % hash : % -> SingleInteger +--R hex : Fraction(Integer) -> % init : () -> % if Integer has STEP +--R inv : % -> % latex : % -> String +--R lcm : List(%) -> % lcm : (%,%) -> % +--R numer : % -> Integer numerator : % -> % +--R one? : % -> Boolean prime? : % -> Boolean +--R ?quo? : (%,%) -> % random : () -> % if Integer has INS +--R recip : % -> Union(%,"failed") ?rem? : (%,%) -> % +--R retract : % -> Integer sample : () -> % +--R sizeLess? : (%,%) -> Boolean squareFree : % -> Factored(%) +--R squareFreePart : % -> % toint : String -> Integer +--R unit? : % -> Boolean unitCanonical : % -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ? Boolean if Integer has ORDSET +--R ?<=? : (%,%) -> Boolean if Integer has ORDSET +--R ?>? : (%,%) -> Boolean if Integer has ORDSET +--R ?>=? : (%,%) -> Boolean if Integer has ORDSET +--R D : (%,(Integer -> Integer),NonNegativeInteger) -> % +--R D : (%,List(Symbol),List(NonNegativeInteger)) -> % if Integer has PDRING(SYMBOL) +--R D : (%,Symbol,NonNegativeInteger) -> % if Integer has PDRING(SYMBOL) +--R D : (%,List(Symbol)) -> % if Integer has PDRING(SYMBOL) +--R D : (%,Symbol) -> % if Integer has PDRING(SYMBOL) +--R D : (%,NonNegativeInteger) -> % if Integer has DIFRING +--R abs : % -> % if Integer has OINTDOM +--R ceiling : % -> Integer if Integer has INS +--R characteristic : () -> NonNegativeInteger +--R charthRoot : % -> Union(%,"failed") if $ has CHARNZ and Integer has PFECAT or Integer has CHARNZ +--R coerce : Symbol -> % if Integer has RETRACT(SYMBOL) +--R conditionP : Matrix(%) -> Union(Vector(%),"failed") if $ has CHARNZ and Integer has PFECAT +--R convert : % -> DoubleFloat if Integer has REAL +--R convert : % -> Float if Integer has REAL +--R convert : % -> InputForm if Integer has KONVERT(INFORM) +--R convert : % -> Pattern(Float) if Integer has KONVERT(PATTERN(FLOAT)) +--R convert : % -> Pattern(Integer) if Integer has KONVERT(PATTERN(INT)) +--R differentiate : (%,(Integer -> Integer)) -> % +--R differentiate : (%,(Integer -> Integer),NonNegativeInteger) -> % +--R differentiate : (%,List(Symbol),List(NonNegativeInteger)) -> % if Integer has PDRING(SYMBOL) +--R differentiate : (%,Symbol,NonNegativeInteger) -> % if Integer has PDRING(SYMBOL) +--R differentiate : (%,List(Symbol)) -> % if Integer has PDRING(SYMBOL) +--R differentiate : (%,Symbol) -> % if Integer has PDRING(SYMBOL) +--R differentiate : (%,NonNegativeInteger) -> % if Integer has DIFRING +--R differentiate : % -> % if Integer has DIFRING +--R divide : (%,%) -> Record(quotient: %,remainder: %) +--R ?.? : (%,Integer) -> % if Integer has ELTAB(INT,INT) +--R euclideanSize : % -> NonNegativeInteger +--R eval : (%,Symbol,Integer) -> % if Integer has IEVALAB(SYMBOL,INT) +--R eval : (%,List(Symbol),List(Integer)) -> % if Integer has IEVALAB(SYMBOL,INT) +--R eval : (%,List(Equation(Integer))) -> % if Integer has EVALAB(INT) +--R eval : (%,Equation(Integer)) -> % if Integer has EVALAB(INT) +--R eval : (%,Integer,Integer) -> % if Integer has EVALAB(INT) +--R eval : (%,List(Integer),List(Integer)) -> % if Integer has EVALAB(INT) +--R expressIdealMember : (List(%),%) -> Union(List(%),"failed") +--R exquo : (%,%) -> Union(%,"failed") +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) +--R factorPolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if Integer has PFECAT +--R factorSquareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if Integer has PFECAT +--R floor : % -> Integer if Integer has INS +--R fractionPart : % -> Fraction(Integer) +--R fractionPart : % -> % if Integer has EUCDOM +--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) +--R lcmCoef : (%,%) -> Record(llcmres: %,coeff1: %,coeff2: %) +--R map : ((Integer -> Integer),%) -> % +--R max : (%,%) -> % if Integer has ORDSET +--R min : (%,%) -> % if Integer has ORDSET +--R multiEuclidean : (List(%),%) -> Union(List(%),"failed") +--R negative? : % -> Boolean if Integer has OINTDOM +--R nextItem : % -> Union(%,"failed") if Integer has STEP +--R patternMatch : (%,Pattern(Float),PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if Integer has PATMAB(FLOAT) +--R patternMatch : (%,Pattern(Integer),PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if Integer has PATMAB(INT) +--R positive? : % -> Boolean if Integer has OINTDOM +--R principalIdeal : List(%) -> Record(coef: List(%),generator: %) +--R reducedSystem : Matrix(%) -> Matrix(Integer) +--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(Integer),vec: Vector(Integer)) +--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(Integer),vec: Vector(Integer)) if Integer has LINEXP(INT) +--R reducedSystem : Matrix(%) -> Matrix(Integer) if Integer has LINEXP(INT) +--R retract : % -> Integer if Integer has RETRACT(INT) +--R retract : % -> Fraction(Integer) if Integer has RETRACT(INT) +--R retract : % -> Symbol if Integer has RETRACT(SYMBOL) +--R retractIfCan : % -> Union(Integer,"failed") if Integer has RETRACT(INT) +--R retractIfCan : % -> Union(Fraction(Integer),"failed") if Integer has RETRACT(INT) +--R retractIfCan : % -> Union(Symbol,"failed") if Integer has RETRACT(SYMBOL) +--R retractIfCan : % -> Union(Integer,"failed") +--R sign : % -> Integer if Integer has OINTDOM +--R solveLinearPolynomialEquation : (List(SparseUnivariatePolynomial(%)),SparseUnivariatePolynomial(%)) -> Union(List(SparseUnivariatePolynomial(%)),"failed") if Integer has PFECAT +--R squareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if Integer has PFECAT +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) +--R wholePart : % -> Integer if Integer has EUCDOM +--R +--E 8 + )spool )lisp (bye) \end{chunk} @@ -63170,6 +65912,7 @@ information. --S 1 of 9 )show HTMLFormat +--R --R HTMLFormat is a domain constructor --R Abbreviation for HTMLFormat is HTMLFORM --R This constructor is exposed in this frame. @@ -64242,33 +66985,35 @@ HTMLFormat(): public == private where --S 1 of 1 )show HomogeneousDirectProduct +--R --R HomogeneousDirectProduct(dim: NonNegativeInteger,S: OrderedAbelianMonoidSup) is a domain constructor --R Abbreviation for HomogeneousDirectProduct is HDP --R This constructor is not exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for HDP --R --R------------------------------- Operations -------------------------------- ---R -? : % -> % if S has RING 1 : () -> % if S has MONOID ---R 0 : () -> % if S has CABMON coerce : % -> Vector(S) +--R ?*? : (S,%) -> % if S has MONOID ?*? : (%,S) -> % if S has MONOID +--R ?*? : (%,%) -> % if S has MONOID ?+? : (%,%) -> % if S has ABELSG +--R -? : % -> % if S has RING ?-? : (%,%) -> % if S has RING +--R ?/? : (%,S) -> % if S has FIELD 1 : () -> % if S has MONOID +--R 0 : () -> % if S has CABMON abs : % -> % if S has ORDRING +--R coerce : S -> % if S has SETCAT coerce : % -> Vector(S) --R copy : % -> % directProduct : Vector(S) -> % ---R ?.? : (%,Integer) -> S elt : (%,Integer,S) -> S ---R empty : () -> % empty? : % -> Boolean ---R entries : % -> List(S) eq? : (%,%) -> Boolean ---R index? : (Integer,%) -> Boolean indices : % -> List(Integer) ---R map : ((S -> S),%) -> % qelt : (%,Integer) -> S ---R sample : () -> % +--R dot : (%,%) -> S if S has RING ?.? : (%,Integer) -> S +--R elt : (%,Integer,S) -> S empty : () -> % +--R empty? : % -> Boolean entries : % -> List(S) +--R eq? : (%,%) -> Boolean index? : (Integer,%) -> Boolean +--R indices : % -> List(Integer) latex : % -> String if S has SETCAT +--R map : ((S -> S),%) -> % one? : % -> Boolean if S has MONOID +--R qelt : (%,Integer) -> S random : () -> % if S has FINITE +--R retract : % -> S if S has SETCAT sample : () -> % +--R sup : (%,%) -> % if S has OAMONS --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R ?*? : (PositiveInteger,%) -> % if S has ABELSG --R ?*? : (NonNegativeInteger,%) -> % if S has CABMON ---R ?*? : (S,%) -> % if S has MONOID ---R ?*? : (%,S) -> % if S has MONOID ---R ?*? : (%,%) -> % if S has MONOID --R ?*? : (Integer,%) -> % if S has RING --R ?**? : (%,PositiveInteger) -> % if S has MONOID --R ?**? : (%,NonNegativeInteger) -> % if S has MONOID ---R ?+? : (%,%) -> % if S has ABELSG ---R ?-? : (%,%) -> % if S has RING ---R ?/? : (%,S) -> % if S has FIELD --R ? Boolean if S has OAMONS or S has ORDRING --R ?<=? : (%,%) -> Boolean if S has OAMONS or S has ORDRING --R ?=? : (%,%) -> Boolean if S has SETCAT @@ -64284,10 +67029,8 @@ HTMLFormat(): public == private where --R D : % -> % if S has DIFRING and S has RING --R ?^? : (%,PositiveInteger) -> % if S has MONOID --R ?^? : (%,NonNegativeInteger) -> % if S has MONOID ---R abs : % -> % if S has ORDRING --R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate --R characteristic : () -> NonNegativeInteger if S has RING ---R coerce : S -> % if S has SETCAT --R coerce : Fraction(Integer) -> % if S has RETRACT(FRAC(INT)) and S has SETCAT --R coerce : Integer -> % if S has RETRACT(INT) and S has SETCAT or S has RING --R coerce : % -> OutputForm if S has SETCAT @@ -64302,7 +67045,6 @@ HTMLFormat(): public == private where --R differentiate : (%,NonNegativeInteger) -> % if S has DIFRING and S has RING --R differentiate : % -> % if S has DIFRING and S has RING --R dimension : () -> CardinalNumber if S has FIELD ---R dot : (%,%) -> S if S has RING --R entry? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT --R enumerate : () -> List(%) if S has FINITE --R eval : (%,List(S),List(S)) -> % if S has EVALAB(S) and S has SETCAT @@ -64314,7 +67056,6 @@ HTMLFormat(): public == private where --R first : % -> S if Integer has ORDSET --R hash : % -> SingleInteger if S has SETCAT --R index : PositiveInteger -> % if S has FINITE ---R latex : % -> String if S has SETCAT --R less? : (%,NonNegativeInteger) -> Boolean --R lookup : % -> PositiveInteger if S has FINITE --R map! : ((S -> S),%) -> % if $ has shallowlyMutable @@ -64326,17 +67067,14 @@ HTMLFormat(): public == private where --R minIndex : % -> Integer if Integer has ORDSET --R more? : (%,NonNegativeInteger) -> Boolean --R negative? : % -> Boolean if S has ORDRING ---R one? : % -> Boolean if S has MONOID --R parts : % -> List(S) if $ has finiteAggregate --R positive? : % -> Boolean if S has ORDRING --R qsetelt! : (%,Integer,S) -> S if $ has shallowlyMutable ---R random : () -> % if S has FINITE --R recip : % -> Union(%,"failed") if S has MONOID --R reducedSystem : Matrix(%) -> Matrix(S) if S has RING --R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(S),vec: Vector(S)) if S has RING --R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(Integer),vec: Vector(Integer)) if S has LINEXP(INT) and S has RING --R reducedSystem : Matrix(%) -> Matrix(Integer) if S has LINEXP(INT) and S has RING ---R retract : % -> S if S has SETCAT --R retract : % -> Fraction(Integer) if S has RETRACT(FRAC(INT)) and S has SETCAT --R retract : % -> Integer if S has RETRACT(INT) and S has SETCAT --R retractIfCan : % -> Union(S,"failed") if S has SETCAT @@ -64347,7 +67085,6 @@ HTMLFormat(): public == private where --R size : () -> NonNegativeInteger if S has FINITE --R size? : (%,NonNegativeInteger) -> Boolean --R subtractIfCan : (%,%) -> Union(%,"failed") if S has CABMON ---R sup : (%,%) -> % if S has OAMONS --R swap! : (%,Integer,Integer) -> Void if $ has shallowlyMutable --R unitVector : PositiveInteger -> % if S has RING --R zero? : % -> Boolean if S has CABMON @@ -64507,13 +67244,14 @@ HomogeneousDirectProduct(dim,S) : T == C where )set message test on )set message auto off )clear all ---S 1 of 10 + +--S 1 of 11 (d1,d2,d3) : DMP([z,y,x],FRAC INT) --R --R Type: Void --E 1 ---S 2 of 10 +--S 2 of 11 d1 := -4*z + 4*y**2*x + 16*x**2 + 1 --R --R @@ -64522,7 +67260,7 @@ d1 := -4*z + 4*y**2*x + 16*x**2 + 1 --R Type: DistributedMultivariatePolynomial([z,y,x],Fraction(Integer)) --E 2 ---S 3 of 10 +--S 3 of 11 d2 := 2*z*y**2 + 4*x + 1 --R --R @@ -64531,7 +67269,7 @@ d2 := 2*z*y**2 + 4*x + 1 --R Type: DistributedMultivariatePolynomial([z,y,x],Fraction(Integer)) --E 3 ---S 4 of 10 +--S 4 of 11 d3 := 2*z*x**2 - 2*y**2 - x --R --R @@ -64540,7 +67278,7 @@ d3 := 2*z*x**2 - 2*y**2 - x --R Type: DistributedMultivariatePolynomial([z,y,x],Fraction(Integer)) --E 4 ---S 5 of 10 +--S 5 of 11 groebner [d1,d2,d3] --R --R @@ -64557,13 +67295,13 @@ groebner [d1,d2,d3] --R Type: List(DistributedMultivariatePolynomial([z,y,x],Fraction(Integer))) --E 5 ---S 6 of 10 +--S 6 of 11 (n1,n2,n3) : HDMP([z,y,x],FRAC INT) --R --R Type: Void --E 6 ---S 7 of 10 +--S 7 of 11 n1 := d1 --R --R @@ -64572,7 +67310,7 @@ n1 := d1 --RType: HomogeneousDistributedMultivariatePolynomial([z,y,x],Fraction(Integer)) --E 7 ---S 8 of 10 +--S 8 of 11 n2 := d2 --R --R @@ -64581,7 +67319,7 @@ n2 := d2 --RType: HomogeneousDistributedMultivariatePolynomial([z,y,x],Fraction(Integer)) --E 8 ---S 9 of 10 +--S 9 of 11 n3 := d3 --R --R @@ -64590,7 +67328,7 @@ n3 := d3 --RType: HomogeneousDistributedMultivariatePolynomial([z,y,x],Fraction(Integer)) --E 9 ---S 10 of 10 +--S 10 of 11 groebner [n1,n2,n3] --R --R @@ -64606,6 +67344,134 @@ groebner [n1,n2,n3] --R 4 2 --RType: List(HomogeneousDistributedMultivariatePolynomial([z,y,x],Fraction(Integer))) --E 10 + +--S 11 of 11 +)show HomogeneousDistributedMultivariatePolynomial +--R +--R HomogeneousDistributedMultivariatePolynomial(vl: List(Symbol),R: Ring) is a domain constructor +--R Abbreviation for HomogeneousDistributedMultivariatePolynomial is HDMP +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for HDMP +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,R) -> % ?*? : (R,%) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?/? : (%,R) -> % if R has FIELD +--R ?=? : (%,%) -> Boolean 1 : () -> % +--R 0 : () -> % ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,PositiveInteger) -> % coefficients : % -> List(R) +--R coerce : % -> % if R has INTDOM coerce : R -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R content : % -> R if R has GCDDOM eval : (%,List(%),List(%)) -> % +--R eval : (%,%,%) -> % eval : (%,Equation(%)) -> % +--R eval : (%,List(Equation(%))) -> % gcd : (%,%) -> % if R has GCDDOM +--R gcd : List(%) -> % if R has GCDDOM ground : % -> R +--R ground? : % -> Boolean hash : % -> SingleInteger +--R latex : % -> String lcm : (%,%) -> % if R has GCDDOM +--R lcm : List(%) -> % if R has GCDDOM leadingCoefficient : % -> R +--R leadingMonomial : % -> % map : ((R -> R),%) -> % +--R max : (%,%) -> % if R has ORDSET min : (%,%) -> % if R has ORDSET +--R monomial? : % -> Boolean monomials : % -> List(%) +--R one? : % -> Boolean primitiveMonomials : % -> List(%) +--R recip : % -> Union(%,"failed") reductum : % -> % +--R reorder : (%,List(Integer)) -> % retract : % -> R +--R sample : () -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R ?*? : (Fraction(Integer),%) -> % if R has ALGEBRA(FRAC(INT)) +--R ?*? : (%,Fraction(Integer)) -> % if R has ALGEBRA(FRAC(INT)) +--R ? Boolean if R has ORDSET +--R ?<=? : (%,%) -> Boolean if R has ORDSET +--R ?>? : (%,%) -> Boolean if R has ORDSET +--R ?>=? : (%,%) -> Boolean if R has ORDSET +--R D : (%,List(OrderedVariableList(vl)),List(NonNegativeInteger)) -> % +--R D : (%,OrderedVariableList(vl),NonNegativeInteger) -> % +--R D : (%,List(OrderedVariableList(vl))) -> % +--R D : (%,OrderedVariableList(vl)) -> % +--R associates? : (%,%) -> Boolean if R has INTDOM +--R binomThmExpt : (%,%,NonNegativeInteger) -> % if R has COMRING +--R characteristic : () -> NonNegativeInteger +--R charthRoot : % -> Union(%,"failed") if $ has CHARNZ and R has PFECAT or R has CHARNZ +--R coefficient : (%,List(OrderedVariableList(vl)),List(NonNegativeInteger)) -> % +--R coefficient : (%,OrderedVariableList(vl),NonNegativeInteger) -> % +--R coefficient : (%,HomogeneousDirectProduct(#(vl),NonNegativeInteger)) -> R +--R coerce : Fraction(Integer) -> % if R has ALGEBRA(FRAC(INT)) or R has RETRACT(FRAC(INT)) +--R coerce : OrderedVariableList(vl) -> % +--R conditionP : Matrix(%) -> Union(Vector(%),"failed") if $ has CHARNZ and R has PFECAT +--R content : (%,OrderedVariableList(vl)) -> % if R has GCDDOM +--R convert : % -> InputForm if OrderedVariableList(vl) has KONVERT(INFORM) and R has KONVERT(INFORM) +--R convert : % -> Pattern(Integer) if OrderedVariableList(vl) has KONVERT(PATTERN(INT)) and R has KONVERT(PATTERN(INT)) +--R convert : % -> Pattern(Float) if OrderedVariableList(vl) has KONVERT(PATTERN(FLOAT)) and R has KONVERT(PATTERN(FLOAT)) +--R degree : (%,List(OrderedVariableList(vl))) -> List(NonNegativeInteger) +--R degree : (%,OrderedVariableList(vl)) -> NonNegativeInteger +--R degree : % -> HomogeneousDirectProduct(#(vl),NonNegativeInteger) +--R differentiate : (%,List(OrderedVariableList(vl)),List(NonNegativeInteger)) -> % +--R differentiate : (%,OrderedVariableList(vl),NonNegativeInteger) -> % +--R differentiate : (%,List(OrderedVariableList(vl))) -> % +--R differentiate : (%,OrderedVariableList(vl)) -> % +--R discriminant : (%,OrderedVariableList(vl)) -> % if R has COMRING +--R eval : (%,List(OrderedVariableList(vl)),List(%)) -> % +--R eval : (%,OrderedVariableList(vl),%) -> % +--R eval : (%,List(OrderedVariableList(vl)),List(R)) -> % +--R eval : (%,OrderedVariableList(vl),R) -> % +--R exquo : (%,%) -> Union(%,"failed") if R has INTDOM +--R exquo : (%,R) -> Union(%,"failed") if R has INTDOM +--R factor : % -> Factored(%) if R has PFECAT +--R factorPolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has PFECAT +--R factorSquareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has PFECAT +--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) if R has GCDDOM +--R isExpt : % -> Union(Record(var: OrderedVariableList(vl),exponent: NonNegativeInteger),"failed") +--R isPlus : % -> Union(List(%),"failed") +--R isTimes : % -> Union(List(%),"failed") +--R lcmCoef : (%,%) -> Record(llcmres: %,coeff1: %,coeff2: %) if R has GCDDOM +--R mainVariable : % -> Union(OrderedVariableList(vl),"failed") +--R mapExponents : ((HomogeneousDirectProduct(#(vl),NonNegativeInteger) -> HomogeneousDirectProduct(#(vl),NonNegativeInteger)),%) -> % +--R minimumDegree : (%,List(OrderedVariableList(vl))) -> List(NonNegativeInteger) +--R minimumDegree : (%,OrderedVariableList(vl)) -> NonNegativeInteger +--R minimumDegree : % -> HomogeneousDirectProduct(#(vl),NonNegativeInteger) +--R monicDivide : (%,%,OrderedVariableList(vl)) -> Record(quotient: %,remainder: %) +--R monomial : (%,List(OrderedVariableList(vl)),List(NonNegativeInteger)) -> % +--R monomial : (%,OrderedVariableList(vl),NonNegativeInteger) -> % +--R monomial : (R,HomogeneousDirectProduct(#(vl),NonNegativeInteger)) -> % +--R multivariate : (SparseUnivariatePolynomial(%),OrderedVariableList(vl)) -> % +--R multivariate : (SparseUnivariatePolynomial(R),OrderedVariableList(vl)) -> % +--R numberOfMonomials : % -> NonNegativeInteger +--R patternMatch : (%,Pattern(Integer),PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if OrderedVariableList(vl) has PATMAB(INT) and R has PATMAB(INT) +--R patternMatch : (%,Pattern(Float),PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if OrderedVariableList(vl) has PATMAB(FLOAT) and R has PATMAB(FLOAT) +--R pomopo! : (%,R,HomogeneousDirectProduct(#(vl),NonNegativeInteger),%) -> % +--R prime? : % -> Boolean if R has PFECAT +--R primitivePart : (%,OrderedVariableList(vl)) -> % if R has GCDDOM +--R primitivePart : % -> % if R has GCDDOM +--R reducedSystem : Matrix(%) -> Matrix(R) +--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(R),vec: Vector(R)) +--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(Integer),vec: Vector(Integer)) if R has LINEXP(INT) +--R reducedSystem : Matrix(%) -> Matrix(Integer) if R has LINEXP(INT) +--R resultant : (%,%,OrderedVariableList(vl)) -> % if R has COMRING +--R retract : % -> OrderedVariableList(vl) +--R retract : % -> Integer if R has RETRACT(INT) +--R retract : % -> Fraction(Integer) if R has RETRACT(FRAC(INT)) +--R retractIfCan : % -> Union(OrderedVariableList(vl),"failed") +--R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT(INT) +--R retractIfCan : % -> Union(Fraction(Integer),"failed") if R has RETRACT(FRAC(INT)) +--R retractIfCan : % -> Union(R,"failed") +--R solveLinearPolynomialEquation : (List(SparseUnivariatePolynomial(%)),SparseUnivariatePolynomial(%)) -> Union(List(SparseUnivariatePolynomial(%)),"failed") if R has PFECAT +--R squareFree : % -> Factored(%) if R has GCDDOM +--R squareFreePart : % -> % if R has GCDDOM +--R squareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has PFECAT +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R totalDegree : (%,List(OrderedVariableList(vl))) -> NonNegativeInteger +--R totalDegree : % -> NonNegativeInteger +--R unit? : % -> Boolean if R has INTDOM +--R unitCanonical : % -> % if R has INTDOM +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) if R has INTDOM +--R univariate : % -> SparseUnivariatePolynomial(R) +--R univariate : (%,OrderedVariableList(vl)) -> SparseUnivariatePolynomial(%) +--R variables : % -> List(OrderedVariableList(vl)) +--R +--E 11 + )spool )lisp (bye) \end{chunk} @@ -64858,20 +67724,19 @@ HomogeneousDistributedMultivariatePolynomial(vl,R): public == private where --R Issue )edit bookvol10.3.pamphlet to see algebra source code for HELLFDIV --R --R------------------------------- Operations -------------------------------- ---R ?*? : (Integer,%) -> % ?*? : (PositiveInteger,%) -> % ---R ?+? : (%,%) -> % ?-? : (%,%) -> % ---R -? : % -> % ?=? : (%,%) -> Boolean ---R 0 : () -> % coerce : % -> OutputForm ---R divisor : (R,UP,UP,UP,F) -> % divisor : (F,F,Integer) -> % ---R divisor : (F,F) -> % divisor : R -> % +--R ?*? : (Integer,%) -> % ?*? : (NonNegativeInteger,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?+? : (%,%) -> % +--R ?-? : (%,%) -> % -? : % -> % +--R ?=? : (%,%) -> Boolean 0 : () -> % +--R coerce : % -> OutputForm divisor : (R,UP,UP,UP,F) -> % +--R divisor : (F,F,Integer) -> % divisor : (F,F) -> % +--R divisor : R -> % generator : % -> Union(R,"failed") --R hash : % -> SingleInteger latex : % -> String --R principal? : % -> Boolean reduce : % -> % --R sample : () -> % zero? : % -> Boolean --R ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % --R decompose : % -> Record(id: FractionalIdeal(UP,Fraction(UP),UPUP,R),principalPart: R) --R divisor : FractionalIdeal(UP,Fraction(UP),UPUP,R) -> % ---R generator : % -> Union(R,"failed") --R ideal : % -> FractionalIdeal(UP,Fraction(UP),UPUP,R) --R subtractIfCan : (%,%) -> Union(%,"failed") --R @@ -65112,6 +67977,7 @@ HyperellipticFiniteDivisor(F, UP, UPUP, R): Exports == Implementation where --S 1 of 1 )show InfClsPt +--R --R InfClsPt(K: Field,symb: List(Symbol),BLMET: BlowUpMethodCategory) is a domain constructor --R Abbreviation for InfClsPt is ICP --R This constructor is exposed in this frame. @@ -65120,16 +67986,17 @@ HyperellipticFiniteDivisor(F, UP, UPUP, R): Exports == Implementation where --R------------------------------- Operations -------------------------------- --R ?=? : (%,%) -> Boolean actualExtensionV : % -> K --R chartV : % -> BLMET coerce : % -> OutputForm ---R degree : % -> PositiveInteger fullOut : % -> OutputForm ---R fullOutput : () -> Boolean fullOutput : Boolean -> Boolean ---R hash : % -> SingleInteger latex : % -> String ---R localPointV : % -> AffinePlane(K) multV : % -> NonNegativeInteger ---R pointV : % -> ProjectivePlane(K) setchart! : (%,BLMET) -> BLMET ---R symbNameV : % -> Symbol ?~=? : (%,%) -> Boolean +--R degree : % -> PositiveInteger excpDivV : % -> Divisor(Places(K)) +--R fullOut : % -> OutputForm fullOutput : () -> Boolean +--R fullOutput : Boolean -> Boolean hash : % -> SingleInteger +--R latex : % -> String localPointV : % -> AffinePlane(K) +--R multV : % -> NonNegativeInteger pointV : % -> ProjectivePlane(K) +--R setchart! : (%,BLMET) -> BLMET setsymbName! : (%,Symbol) -> Symbol +--R subMultV : % -> NonNegativeInteger symbNameV : % -> Symbol +--R ?~=? : (%,%) -> Boolean --R create : (ProjectivePlane(K),DistributedMultivariatePolynomial(symb,K)) -> % --R create : (ProjectivePlane(K),DistributedMultivariatePolynomial([construct,QUOTEX,QUOTEY],K),AffinePlane(K),NonNegativeInteger,BLMET,NonNegativeInteger,Divisor(Places(K)),K,Symbol) -> % --R curveV : % -> DistributedMultivariatePolynomial([construct,QUOTEX,QUOTEY],K) ---R excpDivV : % -> Divisor(Places(K)) --R localParamV : % -> List(NeitherSparseOrDensePowerSeries(K)) --R setcurve! : (%,DistributedMultivariatePolynomial([construct,QUOTEX,QUOTEY],K)) -> DistributedMultivariatePolynomial([construct,QUOTEX,QUOTEY],K) --R setexcpDiv! : (%,Divisor(Places(K))) -> Divisor(Places(K)) @@ -65138,8 +68005,6 @@ HyperellipticFiniteDivisor(F, UP, UPUP, R): Exports == Implementation where --R setmult! : (%,NonNegativeInteger) -> NonNegativeInteger --R setpoint! : (%,ProjectivePlane(K)) -> ProjectivePlane(K) --R setsubmult! : (%,NonNegativeInteger) -> NonNegativeInteger ---R setsymbName! : (%,Symbol) -> Symbol ---R subMultV : % -> NonNegativeInteger --R --E 1 @@ -65251,6 +68116,7 @@ InfClsPt(K,symb,BLMET):Exports == Implementation where --S 1 of 1 )show IndexCard +--R --R IndexCard is a domain constructor --R Abbreviation for IndexCard is ICARD --R This constructor is exposed in this frame. @@ -65384,7 +68250,8 @@ IndexCard() : Exports == Implementation where )set message test on )set message auto off )clear all ---S 1 of 13 + +--S 1 of 14 a:IBITS(32):=new(32,false) --R --R @@ -65392,7 +68259,7 @@ a:IBITS(32):=new(32,false) --R Type: IndexedBits(32) --E 1 ---S 2 of 13 +--S 2 of 14 b:IBITS(32):=new(32,true) --R --R @@ -65400,7 +68267,7 @@ b:IBITS(32):=new(32,true) --R Type: IndexedBits(32) --E 2 ---S 3 of 13 +--S 3 of 14 elt(a,3) --R --R @@ -65408,7 +68275,7 @@ elt(a,3) --R Type: Boolean --E 3 ---S 4 of 13 +--S 4 of 14 setelt(a,3,true) --R --R @@ -65416,7 +68283,7 @@ setelt(a,3,true) --R Type: Boolean --E 4 ---S 5 of 13 +--S 5 of 14 a --R --R @@ -65424,7 +68291,7 @@ a --R Type: IndexedBits(32) --E 5 ---S 6 of 13 +--S 6 of 14 #a --R --R @@ -65432,7 +68299,7 @@ a --R Type: PositiveInteger --E 6 ---S 7 of 13 +--S 7 of 14 (a=a)$IBITS(32) --R --R @@ -65440,7 +68307,7 @@ a --R Type: Boolean --E 7 ---S 8 of 13 +--S 8 of 14 (a=b)$IBITS(32) --R --R @@ -65448,7 +68315,7 @@ a --R Type: Boolean --E 8 ---S 9 of 13 +--S 9 of 14 (a ~= b) --R --R @@ -65456,7 +68323,7 @@ a --R Type: Boolean --E 9 ---S 10 of 13 +--S 10 of 14 Or(a,b) --R --R @@ -65464,7 +68331,7 @@ Or(a,b) --R Type: IndexedBits(32) --E 10 ---S 11 of 13 +--S 11 of 14 And(a,b) --R --R @@ -65472,7 +68339,7 @@ And(a,b) --R Type: IndexedBits(32) --E 11 ---S 12 of 13 +--S 12 of 14 Not(a) --R --R @@ -65480,13 +68347,101 @@ Not(a) --R Type: IndexedBits(32) --E 12 ---S 13 of 13 +--S 13 of 14 c:=copy a --R --R --R (13) "00000000000000000000000000000100" --R Type: IndexedBits(32) --E 13 + +--S 14 of 14 +)show IndexedBits +--R +--R IndexedBits(mn: Integer) is a domain constructor +--R Abbreviation for IndexedBits is IBITS +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for IBITS +--R +--R------------------------------- Operations -------------------------------- +--R ?/\? : (%,%) -> % ? Boolean +--R ?<=? : (%,%) -> Boolean ?=? : (%,%) -> Boolean +--R ?>? : (%,%) -> Boolean ?>=? : (%,%) -> Boolean +--R And : (%,%) -> % Not : % -> % +--R Or : (%,%) -> % ?\/? : (%,%) -> % +--R ^? : % -> % ?and? : (%,%) -> % +--R coerce : % -> OutputForm concat : (%,Boolean) -> % +--R concat : (Boolean,%) -> % concat : (%,%) -> % +--R concat : List(%) -> % construct : List(Boolean) -> % +--R copy : % -> % delete : (%,Integer) -> % +--R ?.? : (%,Integer) -> Boolean empty : () -> % +--R empty? : % -> Boolean entries : % -> List(Boolean) +--R eq? : (%,%) -> Boolean hash : % -> SingleInteger +--R index? : (Integer,%) -> Boolean indices : % -> List(Integer) +--R insert : (Boolean,%,Integer) -> % insert : (%,%,Integer) -> % +--R latex : % -> String max : (%,%) -> % +--R min : (%,%) -> % nand : (%,%) -> % +--R nor : (%,%) -> % not? : % -> % +--R ?or? : (%,%) -> % qelt : (%,Integer) -> Boolean +--R reverse : % -> % sample : () -> % +--R xor : (%,%) -> % ~? : % -> % +--R ?~=? : (%,%) -> Boolean +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R any? : ((Boolean -> Boolean),%) -> Boolean if $ has finiteAggregate +--R convert : % -> InputForm if Boolean has KONVERT(INFORM) +--R copyInto! : (%,%,Integer) -> % if $ has shallowlyMutable +--R count : ((Boolean -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R count : (Boolean,%) -> NonNegativeInteger if $ has finiteAggregate and Boolean has SETCAT +--R delete : (%,UniversalSegment(Integer)) -> % +--R elt : (%,Integer,Boolean) -> Boolean +--R ?.? : (%,UniversalSegment(Integer)) -> % +--R entry? : (Boolean,%) -> Boolean if $ has finiteAggregate and Boolean has SETCAT +--R eval : (%,List(Equation(Boolean))) -> % if Boolean has EVALAB(BOOLEAN) and Boolean has SETCAT +--R eval : (%,Equation(Boolean)) -> % if Boolean has EVALAB(BOOLEAN) and Boolean has SETCAT +--R eval : (%,Boolean,Boolean) -> % if Boolean has EVALAB(BOOLEAN) and Boolean has SETCAT +--R eval : (%,List(Boolean),List(Boolean)) -> % if Boolean has EVALAB(BOOLEAN) and Boolean has SETCAT +--R every? : ((Boolean -> Boolean),%) -> Boolean if $ has finiteAggregate +--R fill! : (%,Boolean) -> % if $ has shallowlyMutable +--R find : ((Boolean -> Boolean),%) -> Union(Boolean,"failed") +--R first : % -> Boolean if Integer has ORDSET +--R less? : (%,NonNegativeInteger) -> Boolean +--R map : ((Boolean -> Boolean),%) -> % +--R map : (((Boolean,Boolean) -> Boolean),%,%) -> % +--R map! : ((Boolean -> Boolean),%) -> % if $ has shallowlyMutable +--R maxIndex : % -> Integer if Integer has ORDSET +--R member? : (Boolean,%) -> Boolean if $ has finiteAggregate and Boolean has SETCAT +--R members : % -> List(Boolean) if $ has finiteAggregate +--R merge : (((Boolean,Boolean) -> Boolean),%,%) -> % +--R merge : (%,%) -> % if Boolean has ORDSET +--R minIndex : % -> Integer if Integer has ORDSET +--R more? : (%,NonNegativeInteger) -> Boolean +--R new : (NonNegativeInteger,Boolean) -> % +--R parts : % -> List(Boolean) if $ has finiteAggregate +--R position : ((Boolean -> Boolean),%) -> Integer +--R position : (Boolean,%) -> Integer if Boolean has SETCAT +--R position : (Boolean,%,Integer) -> Integer if Boolean has SETCAT +--R qsetelt! : (%,Integer,Boolean) -> Boolean if $ has shallowlyMutable +--R reduce : (((Boolean,Boolean) -> Boolean),%,Boolean,Boolean) -> Boolean if $ has finiteAggregate and Boolean has SETCAT +--R reduce : (((Boolean,Boolean) -> Boolean),%,Boolean) -> Boolean if $ has finiteAggregate +--R reduce : (((Boolean,Boolean) -> Boolean),%) -> Boolean if $ has finiteAggregate +--R remove : (Boolean,%) -> % if $ has finiteAggregate and Boolean has SETCAT +--R remove : ((Boolean -> Boolean),%) -> % if $ has finiteAggregate +--R removeDuplicates : % -> % if $ has finiteAggregate and Boolean has SETCAT +--R reverse! : % -> % if $ has shallowlyMutable +--R select : ((Boolean -> Boolean),%) -> % if $ has finiteAggregate +--R setelt : (%,Integer,Boolean) -> Boolean if $ has shallowlyMutable +--R setelt : (%,UniversalSegment(Integer),Boolean) -> Boolean if $ has shallowlyMutable +--R size? : (%,NonNegativeInteger) -> Boolean +--R sort : (((Boolean,Boolean) -> Boolean),%) -> % +--R sort : % -> % if Boolean has ORDSET +--R sort! : (((Boolean,Boolean) -> Boolean),%) -> % if $ has shallowlyMutable +--R sort! : % -> % if $ has shallowlyMutable and Boolean has ORDSET +--R sorted? : (((Boolean,Boolean) -> Boolean),%) -> Boolean +--R sorted? : % -> Boolean if Boolean has ORDSET +--R swap! : (%,Integer,Integer) -> Void if $ has shallowlyMutable +--R +--E 14 + )spool )lisp (bye) \end{chunk} @@ -65701,22 +68656,23 @@ IndexedBits(mn:Integer): BitAggregate() with --S 1 of 1 )show IndexedDirectProductAbelianGroup +--R --R IndexedDirectProductAbelianGroup(A: AbelianGroup,S: OrderedSet) is a domain constructor --R Abbreviation for IndexedDirectProductAbelianGroup is IDPAG --R This constructor is not exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for IDPAG --R --R------------------------------- Operations -------------------------------- ---R ?*? : (Integer,%) -> % ?*? : (PositiveInteger,%) -> % ---R ?+? : (%,%) -> % ?-? : (%,%) -> % ---R -? : % -> % ?=? : (%,%) -> Boolean ---R 0 : () -> % coerce : % -> OutputForm ---R hash : % -> SingleInteger latex : % -> String ---R leadingCoefficient : % -> A leadingSupport : % -> S ---R map : ((A -> A),%) -> % monomial : (A,S) -> % ---R reductum : % -> % sample : () -> % ---R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % +--R ?*? : (Integer,%) -> % ?*? : (NonNegativeInteger,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?+? : (%,%) -> % +--R ?-? : (%,%) -> % -? : % -> % +--R ?=? : (%,%) -> Boolean 0 : () -> % +--R coerce : % -> OutputForm hash : % -> SingleInteger +--R latex : % -> String leadingCoefficient : % -> A +--R leadingSupport : % -> S map : ((A -> A),%) -> % +--R monomial : (A,S) -> % reductum : % -> % +--R sample : () -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean --R subtractIfCan : (%,%) -> Union(%,"failed") --R --E 1 @@ -65859,21 +68815,21 @@ IndexedDirectProductAbelianGroup(A:AbelianGroup,S:OrderedSet): --S 1 of 1 )show IndexedDirectProductAbelianMonoid +--R --R IndexedDirectProductAbelianMonoid(A: AbelianMonoid,S: OrderedSet) is a domain constructor --R Abbreviation for IndexedDirectProductAbelianMonoid is IDPAM --R This constructor is not exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for IDPAM --R --R------------------------------- Operations -------------------------------- ---R ?*? : (PositiveInteger,%) -> % ?+? : (%,%) -> % ---R ?=? : (%,%) -> Boolean 0 : () -> % ---R coerce : % -> OutputForm hash : % -> SingleInteger ---R latex : % -> String leadingCoefficient : % -> A ---R leadingSupport : % -> S map : ((A -> A),%) -> % ---R monomial : (A,S) -> % reductum : % -> % ---R sample : () -> % zero? : % -> Boolean ---R ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?+? : (%,%) -> % ?=? : (%,%) -> Boolean +--R 0 : () -> % coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R leadingCoefficient : % -> A leadingSupport : % -> S +--R map : ((A -> A),%) -> % monomial : (A,S) -> % +--R reductum : % -> % sample : () -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean --R --E 1 @@ -66023,6 +68979,7 @@ IndexedDirectProductAbelianMonoid(A:AbelianMonoid,S:OrderedSet): --S 1 of 1 )show IndexedDirectProductObject +--R --R IndexedDirectProductObject(A: SetCategory,S: OrderedSet) is a domain constructor --R Abbreviation for IndexedDirectProductObject is IDPO --R This constructor is not exposed in this frame. @@ -66140,24 +69097,24 @@ IndexedDirectProductObject(A:SetCategory,S:OrderedSet): _ --S 1 of 1 )show IndexedDirectProductOrderedAbelianMonoid +--R --R IndexedDirectProductOrderedAbelianMonoid(A: OrderedAbelianMonoid,S: OrderedSet) is a domain constructor --R Abbreviation for IndexedDirectProductOrderedAbelianMonoid is IDPOAM --R This constructor is not exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for IDPOAM --R --R------------------------------- Operations -------------------------------- ---R ?*? : (PositiveInteger,%) -> % ?+? : (%,%) -> % ---R ? Boolean ?<=? : (%,%) -> Boolean ---R ?=? : (%,%) -> Boolean ?>? : (%,%) -> Boolean ---R ?>=? : (%,%) -> Boolean 0 : () -> % ---R coerce : % -> OutputForm hash : % -> SingleInteger ---R latex : % -> String leadingCoefficient : % -> A ---R leadingSupport : % -> S map : ((A -> A),%) -> % ---R max : (%,%) -> % min : (%,%) -> % ---R monomial : (A,S) -> % reductum : % -> % ---R sample : () -> % zero? : % -> Boolean ---R ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?+? : (%,%) -> % ? Boolean +--R ?<=? : (%,%) -> Boolean ?=? : (%,%) -> Boolean +--R ?>? : (%,%) -> Boolean ?>=? : (%,%) -> Boolean +--R 0 : () -> % coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R leadingCoefficient : % -> A leadingSupport : % -> S +--R map : ((A -> A),%) -> % max : (%,%) -> % +--R min : (%,%) -> % monomial : (A,S) -> % +--R reductum : % -> % sample : () -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean --R --E 1 @@ -66256,24 +69213,25 @@ IndexedDirectProductOrderedAbelianMonoid(A:OrderedAbelianMonoid,S:OrderedSet): --S 1 of 1 )show IndexedDirectProductOrderedAbelianMonoidSup +--R --R IndexedDirectProductOrderedAbelianMonoidSup(A: OrderedAbelianMonoidSup,S: OrderedSet) is a domain constructor --R Abbreviation for IndexedDirectProductOrderedAbelianMonoidSup is IDPOAMS --R This constructor is not exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for IDPOAMS --R --R------------------------------- Operations -------------------------------- ---R ?*? : (PositiveInteger,%) -> % ?+? : (%,%) -> % ---R ? Boolean ?<=? : (%,%) -> Boolean ---R ?=? : (%,%) -> Boolean ?>? : (%,%) -> Boolean ---R ?>=? : (%,%) -> Boolean 0 : () -> % ---R coerce : % -> OutputForm hash : % -> SingleInteger ---R latex : % -> String leadingCoefficient : % -> A ---R leadingSupport : % -> S map : ((A -> A),%) -> % ---R max : (%,%) -> % min : (%,%) -> % ---R monomial : (A,S) -> % reductum : % -> % ---R sample : () -> % sup : (%,%) -> % ---R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?+? : (%,%) -> % ? Boolean +--R ?<=? : (%,%) -> Boolean ?=? : (%,%) -> Boolean +--R ?>? : (%,%) -> Boolean ?>=? : (%,%) -> Boolean +--R 0 : () -> % coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R leadingCoefficient : % -> A leadingSupport : % -> S +--R map : ((A -> A),%) -> % max : (%,%) -> % +--R min : (%,%) -> % monomial : (A,S) -> % +--R reductum : % -> % sample : () -> % +--R sup : (%,%) -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean --R subtractIfCan : (%,%) -> Union(%,"failed") --R --E 1 @@ -66398,17 +69356,16 @@ IndexedDirectProductOrderedAbelianMonoidSup(A:OrderedAbelianMonoidSup,S:OrderedS --R Issue )edit bookvol10.3.pamphlet to see algebra source code for INDE --R --R------------------------------- Operations -------------------------------- ---R ?*? : (PositiveInteger,%) -> % ?+? : (%,%) -> % ---R ? Boolean ?<=? : (%,%) -> Boolean ---R ?=? : (%,%) -> Boolean ?>? : (%,%) -> Boolean ---R ?>=? : (%,%) -> Boolean 0 : () -> % ---R coerce : % -> OutputForm hash : % -> SingleInteger ---R latex : % -> String leadingSupport : % -> Varset ---R max : (%,%) -> % min : (%,%) -> % ---R reductum : % -> % sample : () -> % ---R sup : (%,%) -> % zero? : % -> Boolean ---R ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?+? : (%,%) -> % ? Boolean +--R ?<=? : (%,%) -> Boolean ?=? : (%,%) -> Boolean +--R ?>? : (%,%) -> Boolean ?>=? : (%,%) -> Boolean +--R 0 : () -> % coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R leadingSupport : % -> Varset max : (%,%) -> % +--R min : (%,%) -> % reductum : % -> % +--R sample : () -> % sup : (%,%) -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean --R leadingCoefficient : % -> NonNegativeInteger --R map : ((NonNegativeInteger -> NonNegativeInteger),%) -> % --R monomial : (NonNegativeInteger,Varset) -> % @@ -66529,10 +69486,14 @@ IndexedExponents(Varset:OrderedSet): C == T where --R flexibleArray : List(S) -> % index? : (Integer,%) -> Boolean --R indices : % -> List(Integer) insert : (%,%,Integer) -> % --R insert : (S,%,Integer) -> % insert! : (S,%,Integer) -> % ---R insert! : (%,%,Integer) -> % map : (((S,S) -> S),%,%) -> % ---R map : ((S -> S),%) -> % new : (NonNegativeInteger,S) -> % ---R qelt : (%,Integer) -> S reverse : % -> % ---R sample : () -> % shrinkable : Boolean -> Boolean +--R insert! : (%,%,Integer) -> % latex : % -> String if S has SETCAT +--R map : (((S,S) -> S),%,%) -> % map : ((S -> S),%) -> % +--R max : (%,%) -> % if S has ORDSET min : (%,%) -> % if S has ORDSET +--R new : (NonNegativeInteger,S) -> % physicalLength! : (%,Integer) -> % +--R qelt : (%,Integer) -> S remove! : ((S -> Boolean),%) -> % +--R reverse : % -> % sample : () -> % +--R select! : ((S -> Boolean),%) -> % shrinkable : Boolean -> Boolean +--R sort : % -> % if S has ORDSET sort : (((S,S) -> Boolean),%) -> % --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R ? Boolean if S has ORDSET --R ?<=? : (%,%) -> Boolean if S has ORDSET @@ -66558,10 +69519,8 @@ IndexedExponents(Varset:OrderedSet): C == T where --R find : ((S -> Boolean),%) -> Union(S,"failed") --R first : % -> S if Integer has ORDSET --R hash : % -> SingleInteger if S has SETCAT ---R latex : % -> String if S has SETCAT --R less? : (%,NonNegativeInteger) -> Boolean --R map! : ((S -> S),%) -> % if $ has shallowlyMutable ---R max : (%,%) -> % if S has ORDSET --R maxIndex : % -> Integer if Integer has ORDSET --R member? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT --R members : % -> List(S) if $ has finiteAggregate @@ -66569,12 +69528,10 @@ IndexedExponents(Varset:OrderedSet): C == T where --R merge : (((S,S) -> Boolean),%,%) -> % --R merge! : (((S,S) -> Boolean),%,%) -> % --R merge! : (%,%) -> % if S has ORDSET ---R min : (%,%) -> % if S has ORDSET --R minIndex : % -> Integer if Integer has ORDSET --R more? : (%,NonNegativeInteger) -> Boolean --R parts : % -> List(S) if $ has finiteAggregate --R physicalLength : % -> NonNegativeInteger ---R physicalLength! : (%,Integer) -> % --R position : (S,%,Integer) -> Integer if S has SETCAT --R position : (S,%) -> Integer if S has SETCAT --R position : ((S -> Boolean),%) -> Integer @@ -66584,18 +69541,14 @@ IndexedExponents(Varset:OrderedSet): C == T where --R reduce : (((S,S) -> S),%,S,S) -> S if $ has finiteAggregate and S has SETCAT --R remove : ((S -> Boolean),%) -> % if $ has finiteAggregate --R remove : (S,%) -> % if $ has finiteAggregate and S has SETCAT ---R remove! : ((S -> Boolean),%) -> % --R remove! : (S,%) -> % if S has SETCAT --R removeDuplicates : % -> % if $ has finiteAggregate and S has SETCAT --R removeDuplicates! : % -> % if S has SETCAT --R reverse! : % -> % if $ has shallowlyMutable --R select : ((S -> Boolean),%) -> % if $ has finiteAggregate ---R select! : ((S -> Boolean),%) -> % --R setelt : (%,UniversalSegment(Integer),S) -> S if $ has shallowlyMutable --R setelt : (%,Integer,S) -> S if $ has shallowlyMutable --R size? : (%,NonNegativeInteger) -> Boolean ---R sort : % -> % if S has ORDSET ---R sort : (((S,S) -> Boolean),%) -> % --R sort! : % -> % if $ has shallowlyMutable and S has ORDSET --R sort! : (((S,S) -> Boolean),%) -> % if $ has shallowlyMutable --R sorted? : % -> Boolean if S has ORDSET @@ -67000,15 +69953,20 @@ IndexedFlexibleArray(S:Type, mn: Integer): Exports == Implementation where --R first : % -> S index? : (Integer,%) -> Boolean --R indices : % -> List(Integer) insert : (S,%,Integer) -> % --R insert : (%,%,Integer) -> % insert! : (S,%,Integer) -> % ---R insert! : (%,%,Integer) -> % last : % -> S +--R insert! : (%,%,Integer) -> % last : (%,NonNegativeInteger) -> % +--R last : % -> S latex : % -> String if S has SETCAT --R leaf? : % -> Boolean leaves : % -> List(S) --R list : S -> % map : (((S,S) -> S),%,%) -> % ---R map : ((S -> S),%) -> % new : (NonNegativeInteger,S) -> % +--R map : ((S -> S),%) -> % max : (%,%) -> % if S has ORDSET +--R min : (%,%) -> % if S has ORDSET new : (NonNegativeInteger,S) -> % --R nodes : % -> List(%) possiblyInfinite? : % -> Boolean ---R qelt : (%,Integer) -> S rest : % -> % +--R qelt : (%,Integer) -> S remove! : ((S -> Boolean),%) -> % +--R rest : (%,NonNegativeInteger) -> % rest : % -> % --R reverse : % -> % sample : () -> % ---R second : % -> S tail : % -> % ---R third : % -> S value : % -> S +--R second : % -> S select! : ((S -> Boolean),%) -> % +--R sort : (((S,S) -> Boolean),%) -> % sort : % -> % if S has ORDSET +--R tail : % -> % third : % -> S +--R value : % -> S --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R ? Boolean if S has ORDSET --R ?<=? : (%,%) -> Boolean if S has ORDSET @@ -67037,11 +69995,8 @@ IndexedFlexibleArray(S:Type, mn: Integer): Exports == Implementation where --R find : ((S -> Boolean),%) -> Union(S,"failed") --R first : (%,NonNegativeInteger) -> % --R hash : % -> SingleInteger if S has SETCAT ---R last : (%,NonNegativeInteger) -> % ---R latex : % -> String if S has SETCAT --R less? : (%,NonNegativeInteger) -> Boolean --R map! : ((S -> S),%) -> % if $ has shallowlyMutable ---R max : (%,%) -> % if S has ORDSET --R maxIndex : % -> Integer if Integer has ORDSET --R member? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT --R members : % -> List(S) if $ has finiteAggregate @@ -67049,7 +70004,6 @@ IndexedFlexibleArray(S:Type, mn: Integer): Exports == Implementation where --R merge : (%,%) -> % if S has ORDSET --R merge! : (((S,S) -> Boolean),%,%) -> % --R merge! : (%,%) -> % if S has ORDSET ---R min : (%,%) -> % if S has ORDSET --R minIndex : % -> Integer if Integer has ORDSET --R more? : (%,NonNegativeInteger) -> Boolean --R node? : (%,%) -> Boolean if S has SETCAT @@ -67063,14 +70017,11 @@ IndexedFlexibleArray(S:Type, mn: Integer): Exports == Implementation where --R reduce : (((S,S) -> S),%) -> S if $ has finiteAggregate --R remove : (S,%) -> % if $ has finiteAggregate and S has SETCAT --R remove : ((S -> Boolean),%) -> % if $ has finiteAggregate ---R remove! : ((S -> Boolean),%) -> % --R remove! : (S,%) -> % if S has SETCAT --R removeDuplicates : % -> % if $ has finiteAggregate and S has SETCAT --R removeDuplicates! : % -> % if S has SETCAT ---R rest : (%,NonNegativeInteger) -> % --R reverse! : % -> % if $ has shallowlyMutable --R select : ((S -> Boolean),%) -> % if $ has finiteAggregate ---R select! : ((S -> Boolean),%) -> % --R setchildren! : (%,List(%)) -> % if $ has shallowlyMutable --R setelt : (%,Integer,S) -> S if $ has shallowlyMutable --R setelt : (%,UniversalSegment(Integer),S) -> S if $ has shallowlyMutable @@ -67083,8 +70034,6 @@ IndexedFlexibleArray(S:Type, mn: Integer): Exports == Implementation where --R setrest! : (%,%) -> % if $ has shallowlyMutable --R setvalue! : (%,S) -> S if $ has shallowlyMutable --R size? : (%,NonNegativeInteger) -> Boolean ---R sort : (((S,S) -> Boolean),%) -> % ---R sort : % -> % if S has ORDSET --R sort! : (((S,S) -> Boolean),%) -> % if $ has shallowlyMutable --R sort! : % -> % if $ has shallowlyMutable and S has ORDSET --R sorted? : (((S,S) -> Boolean),%) -> Boolean @@ -67427,6 +70376,7 @@ IndexedList(S:Type, mn:Integer): Exports == Implementation where --S 1 of 1 )show IndexedMatrix +--R --R IndexedMatrix(R: Ring,mnRow: Integer,mnCol: Integer) is a domain constructor --R Abbreviation for IndexedMatrix is IMATRIX --R This constructor is not exposed in this frame. @@ -67435,30 +70385,30 @@ IndexedList(S:Type, mn:Integer): Exports == Implementation where --R------------------------------- Operations -------------------------------- --R ?*? : (Integer,%) -> % ?*? : (%,R) -> % --R ?*? : (R,%) -> % ?*? : (%,%) -> % ---R ?+? : (%,%) -> % -? : % -> % ---R ?-? : (%,%) -> % antisymmetric? : % -> Boolean +--R ?**? : (%,NonNegativeInteger) -> % ?+? : (%,%) -> % +--R -? : % -> % ?-? : (%,%) -> % +--R ?/? : (%,R) -> % if R has FIELD antisymmetric? : % -> Boolean --R copy : % -> % diagonal? : % -> Boolean --R diagonalMatrix : List(%) -> % diagonalMatrix : List(R) -> % --R elt : (%,Integer,Integer,R) -> R elt : (%,Integer,Integer) -> R --R empty : () -> % empty? : % -> Boolean --R eq? : (%,%) -> Boolean fill! : (%,R) -> % ---R horizConcat : (%,%) -> % listOfLists : % -> List(List(R)) ---R map : (((R,R) -> R),%,%,R) -> % map : (((R,R) -> R),%,%) -> % ---R map : ((R -> R),%) -> % map! : ((R -> R),%) -> % ---R matrix : List(List(R)) -> % maxColIndex : % -> Integer ---R maxRowIndex : % -> Integer minColIndex : % -> Integer ---R minRowIndex : % -> Integer ncols : % -> NonNegativeInteger ---R nrows : % -> NonNegativeInteger parts : % -> List(R) +--R horizConcat : (%,%) -> % latex : % -> String if R has SETCAT +--R listOfLists : % -> List(List(R)) map : (((R,R) -> R),%,%,R) -> % +--R map : (((R,R) -> R),%,%) -> % map : ((R -> R),%) -> % +--R map! : ((R -> R),%) -> % matrix : List(List(R)) -> % +--R maxColIndex : % -> Integer maxRowIndex : % -> Integer +--R minColIndex : % -> Integer minRowIndex : % -> Integer +--R ncols : % -> NonNegativeInteger nrows : % -> NonNegativeInteger +--R parts : % -> List(R) pfaffian : % -> R if R has COMRING --R qelt : (%,Integer,Integer) -> R sample : () -> % ---R square? : % -> Boolean squareTop : % -> % ---R symmetric? : % -> Boolean transpose : % -> % ---R vertConcat : (%,%) -> % +--R setelt : (%,Integer,Integer,R) -> R square? : % -> Boolean +--R squareTop : % -> % symmetric? : % -> Boolean +--R transpose : % -> % vertConcat : (%,%) -> % --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R ?*? : (IndexedVector(R,mnCol),%) -> IndexedVector(R,mnCol) --R ?*? : (%,IndexedVector(R,mnRow)) -> IndexedVector(R,mnRow) --R ?**? : (%,Integer) -> % if R has FIELD ---R ?**? : (%,NonNegativeInteger) -> % ---R ?/? : (%,R) -> % if R has FIELD --R ?=? : (%,%) -> Boolean if R has SETCAT --R any? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate --R coerce : IndexedVector(R,mnRow) -> % @@ -67477,7 +70427,6 @@ IndexedList(S:Type, mn:Integer): Exports == Implementation where --R exquo : (%,R) -> Union(%,"failed") if R has INTDOM --R hash : % -> SingleInteger if R has SETCAT --R inverse : % -> Union(%,"failed") if R has FIELD ---R latex : % -> String if R has SETCAT --R less? : (%,NonNegativeInteger) -> Boolean --R matrix : (NonNegativeInteger,NonNegativeInteger,((Integer,Integer) -> R)) -> % --R member? : (R,%) -> Boolean if $ has finiteAggregate and R has SETCAT @@ -67487,7 +70436,6 @@ IndexedList(S:Type, mn:Integer): Exports == Implementation where --R new : (NonNegativeInteger,NonNegativeInteger,R) -> % --R nullSpace : % -> List(IndexedVector(R,mnRow)) if R has INTDOM --R nullity : % -> NonNegativeInteger if R has INTDOM ---R pfaffian : % -> R if R has COMRING --R qsetelt! : (%,Integer,Integer,R) -> R --R rank : % -> NonNegativeInteger if R has INTDOM --R row : (%,Integer) -> IndexedVector(R,mnCol) @@ -67496,7 +70444,6 @@ IndexedList(S:Type, mn:Integer): Exports == Implementation where --R setColumn! : (%,Integer,IndexedVector(R,mnRow)) -> % --R setRow! : (%,Integer,IndexedVector(R,mnCol)) -> % --R setelt : (%,List(Integer),List(Integer),%) -> % ---R setelt : (%,Integer,Integer,R) -> R --R setsubMatrix! : (%,Integer,Integer,%) -> % --R size? : (%,NonNegativeInteger) -> Boolean --R subMatrix : (%,Integer,Integer,Integer,Integer) -> % @@ -67707,10 +70654,12 @@ IndexedMatrix(R,mnRow,mnCol): Exports == Implementation where --R empty? : % -> Boolean entries : % -> List(S) --R eq? : (%,%) -> Boolean index? : (Integer,%) -> Boolean --R indices : % -> List(Integer) insert : (%,%,Integer) -> % ---R insert : (S,%,Integer) -> % map : (((S,S) -> S),%,%) -> % ---R map : ((S -> S),%) -> % new : (NonNegativeInteger,S) -> % ---R qelt : (%,Integer) -> S reverse : % -> % ---R sample : () -> % +--R insert : (S,%,Integer) -> % latex : % -> String if S has SETCAT +--R map : (((S,S) -> S),%,%) -> % map : ((S -> S),%) -> % +--R max : (%,%) -> % if S has ORDSET min : (%,%) -> % if S has ORDSET +--R new : (NonNegativeInteger,S) -> % qelt : (%,Integer) -> S +--R reverse : % -> % sample : () -> % +--R sort : % -> % if S has ORDSET sort : (((S,S) -> Boolean),%) -> % --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R ? Boolean if S has ORDSET --R ?<=? : (%,%) -> Boolean if S has ORDSET @@ -67735,16 +70684,13 @@ IndexedMatrix(R,mnRow,mnCol): Exports == Implementation where --R find : ((S -> Boolean),%) -> Union(S,"failed") --R first : % -> S if Integer has ORDSET --R hash : % -> SingleInteger if S has SETCAT ---R latex : % -> String if S has SETCAT --R less? : (%,NonNegativeInteger) -> Boolean --R map! : ((S -> S),%) -> % if $ has shallowlyMutable ---R max : (%,%) -> % if S has ORDSET --R maxIndex : % -> Integer if Integer has ORDSET --R member? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT --R members : % -> List(S) if $ has finiteAggregate --R merge : (%,%) -> % if S has ORDSET --R merge : (((S,S) -> Boolean),%,%) -> % ---R min : (%,%) -> % if S has ORDSET --R minIndex : % -> Integer if Integer has ORDSET --R more? : (%,NonNegativeInteger) -> Boolean --R parts : % -> List(S) if $ has finiteAggregate @@ -67763,8 +70709,6 @@ IndexedMatrix(R,mnRow,mnCol): Exports == Implementation where --R setelt : (%,UniversalSegment(Integer),S) -> S if $ has shallowlyMutable --R setelt : (%,Integer,S) -> S if $ has shallowlyMutable --R size? : (%,NonNegativeInteger) -> Boolean ---R sort : % -> % if S has ORDSET ---R sort : (((S,S) -> Boolean),%) -> % --R sort! : % -> % if $ has shallowlyMutable and S has ORDSET --R sort! : (((S,S) -> Boolean),%) -> % if $ has shallowlyMutable --R sorted? : % -> Boolean if S has ORDSET @@ -68004,13 +70948,14 @@ IndexedOneDimensionalArray(S:Type, mn:Integer): --R entries : % -> List(Character) eq? : (%,%) -> Boolean --R hash : % -> Integer index? : (Integer,%) -> Boolean --R indices : % -> List(Integer) insert : (%,%,Integer) -> % ---R leftTrim : (%,Character) -> % lowerCase : % -> % ---R lowerCase! : % -> % prefix? : (%,%) -> Boolean ---R qelt : (%,Integer) -> Character reverse : % -> % ---R rightTrim : (%,Character) -> % sample : () -> % ---R split : (%,Character) -> List(%) suffix? : (%,%) -> Boolean ---R trim : (%,CharacterClass) -> % trim : (%,Character) -> % ---R upperCase : % -> % upperCase! : % -> % +--R leftTrim : (%,CharacterClass) -> % leftTrim : (%,Character) -> % +--R lowerCase : % -> % lowerCase! : % -> % +--R prefix? : (%,%) -> Boolean qelt : (%,Integer) -> Character +--R reverse : % -> % rightTrim : (%,Character) -> % +--R sample : () -> % split : (%,Character) -> List(%) +--R suffix? : (%,%) -> Boolean trim : (%,CharacterClass) -> % +--R trim : (%,Character) -> % upperCase : % -> % +--R upperCase! : % -> % --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R ? Boolean if Character has ORDSET --R ?<=? : (%,%) -> Boolean if Character has ORDSET @@ -68038,7 +70983,6 @@ IndexedOneDimensionalArray(S:Type, mn:Integer): --R hash : % -> SingleInteger if Character has SETCAT --R insert : (Character,%,Integer) -> % --R latex : % -> String if Character has SETCAT ---R leftTrim : (%,CharacterClass) -> % --R less? : (%,NonNegativeInteger) -> Boolean --R map : (((Character,Character) -> Character),%,%) -> % --R map : ((Character -> Character),%) -> % @@ -68422,13 +71366,14 @@ first column in an array and vice versa. --R copy : % -> % elt : (%,Integer,Integer,R) -> R --R elt : (%,Integer,Integer) -> R empty : () -> % --R empty? : % -> Boolean eq? : (%,%) -> Boolean ---R fill! : (%,R) -> % map : (((R,R) -> R),%,%,R) -> % ---R map : (((R,R) -> R),%,%) -> % map : ((R -> R),%) -> % ---R map! : ((R -> R),%) -> % maxColIndex : % -> Integer ---R maxRowIndex : % -> Integer minColIndex : % -> Integer ---R minRowIndex : % -> Integer ncols : % -> NonNegativeInteger ---R nrows : % -> NonNegativeInteger parts : % -> List(R) ---R qelt : (%,Integer,Integer) -> R sample : () -> % +--R fill! : (%,R) -> % latex : % -> String if R has SETCAT +--R map : (((R,R) -> R),%,%,R) -> % map : (((R,R) -> R),%,%) -> % +--R map : ((R -> R),%) -> % map! : ((R -> R),%) -> % +--R maxColIndex : % -> Integer maxRowIndex : % -> Integer +--R minColIndex : % -> Integer minRowIndex : % -> Integer +--R ncols : % -> NonNegativeInteger nrows : % -> NonNegativeInteger +--R parts : % -> List(R) qelt : (%,Integer,Integer) -> R +--R sample : () -> % setelt : (%,Integer,Integer,R) -> R --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R ?=? : (%,%) -> Boolean if R has SETCAT --R any? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate @@ -68442,7 +71387,6 @@ first column in an array and vice versa. --R eval : (%,List(Equation(R))) -> % if R has EVALAB(R) and R has SETCAT --R every? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate --R hash : % -> SingleInteger if R has SETCAT ---R latex : % -> String if R has SETCAT --R less? : (%,NonNegativeInteger) -> Boolean --R member? : (R,%) -> Boolean if $ has finiteAggregate and R has SETCAT --R members : % -> List(R) if $ has finiteAggregate @@ -68452,7 +71396,6 @@ first column in an array and vice versa. --R row : (%,Integer) -> IndexedOneDimensionalArray(R,mnCol) --R setColumn! : (%,Integer,IndexedOneDimensionalArray(R,mnRow)) -> % --R setRow! : (%,Integer,IndexedOneDimensionalArray(R,mnCol)) -> % ---R setelt : (%,Integer,Integer,R) -> R --R size? : (%,NonNegativeInteger) -> Boolean --R ?~=? : (%,%) -> Boolean if R has SETCAT --R @@ -68569,24 +71512,26 @@ IndexedTwoDimensionalArray(R,mnRow,mnCol):Exports == Implementation where --R Issue )edit bookvol10.3.pamphlet to see algebra source code for IVECTOR --R --R------------------------------- Operations -------------------------------- +--R ?*? : (%,R) -> % if R has MONOID ?*? : (R,%) -> % if R has MONOID +--R ?+? : (%,%) -> % if R has ABELSG ?-? : (%,%) -> % if R has ABELGRP --R -? : % -> % if R has ABELGRP concat : List(%) -> % --R concat : (%,%) -> % concat : (R,%) -> % --R concat : (%,R) -> % construct : List(R) -> % ---R copy : % -> % delete : (%,Integer) -> % +--R copy : % -> % cross : (%,%) -> % if R has RING +--R delete : (%,Integer) -> % dot : (%,%) -> R if R has RING --R ?.? : (%,Integer) -> R elt : (%,Integer,R) -> R --R empty : () -> % empty? : % -> Boolean --R entries : % -> List(R) eq? : (%,%) -> Boolean --R index? : (Integer,%) -> Boolean indices : % -> List(Integer) --R insert : (%,%,Integer) -> % insert : (R,%,Integer) -> % ---R map : (((R,R) -> R),%,%) -> % map : ((R -> R),%) -> % ---R new : (NonNegativeInteger,R) -> % qelt : (%,Integer) -> R ---R reverse : % -> % sample : () -> % +--R latex : % -> String if R has SETCAT map : (((R,R) -> R),%,%) -> % +--R map : ((R -> R),%) -> % max : (%,%) -> % if R has ORDSET +--R min : (%,%) -> % if R has ORDSET new : (NonNegativeInteger,R) -> % +--R qelt : (%,Integer) -> R reverse : % -> % +--R sample : () -> % sort : % -> % if R has ORDSET +--R sort : (((R,R) -> Boolean),%) -> % --R #? : % -> NonNegativeInteger if $ has finiteAggregate ---R ?*? : (%,R) -> % if R has MONOID ---R ?*? : (R,%) -> % if R has MONOID --R ?*? : (Integer,%) -> % if R has ABELGRP ---R ?+? : (%,%) -> % if R has ABELSG ---R ?-? : (%,%) -> % if R has ABELGRP --R ? Boolean if R has ORDSET --R ?<=? : (%,%) -> Boolean if R has ORDSET --R ?=? : (%,%) -> Boolean if R has SETCAT @@ -68598,9 +71543,7 @@ IndexedTwoDimensionalArray(R,mnRow,mnCol):Exports == Implementation where --R copyInto! : (%,%,Integer) -> % if $ has shallowlyMutable --R count : (R,%) -> NonNegativeInteger if $ has finiteAggregate and R has SETCAT --R count : ((R -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate ---R cross : (%,%) -> % if R has RING --R delete : (%,UniversalSegment(Integer)) -> % ---R dot : (%,%) -> R if R has RING --R ?.? : (%,UniversalSegment(Integer)) -> % --R entry? : (R,%) -> Boolean if $ has finiteAggregate and R has SETCAT --R eval : (%,List(R),List(R)) -> % if R has EVALAB(R) and R has SETCAT @@ -68612,18 +71555,15 @@ IndexedTwoDimensionalArray(R,mnRow,mnCol):Exports == Implementation where --R find : ((R -> Boolean),%) -> Union(R,"failed") --R first : % -> R if Integer has ORDSET --R hash : % -> SingleInteger if R has SETCAT ---R latex : % -> String if R has SETCAT --R length : % -> R if R has RADCAT and R has RING --R less? : (%,NonNegativeInteger) -> Boolean --R magnitude : % -> R if R has RADCAT and R has RING --R map! : ((R -> R),%) -> % if $ has shallowlyMutable ---R max : (%,%) -> % if R has ORDSET --R maxIndex : % -> Integer if Integer has ORDSET --R member? : (R,%) -> Boolean if $ has finiteAggregate and R has SETCAT --R members : % -> List(R) if $ has finiteAggregate --R merge : (%,%) -> % if R has ORDSET --R merge : (((R,R) -> Boolean),%,%) -> % ---R min : (%,%) -> % if R has ORDSET --R minIndex : % -> Integer if Integer has ORDSET --R more? : (%,NonNegativeInteger) -> Boolean --R outerProduct : (%,%) -> Matrix(R) if R has RING @@ -68643,8 +71583,6 @@ IndexedTwoDimensionalArray(R,mnRow,mnCol):Exports == Implementation where --R setelt : (%,UniversalSegment(Integer),R) -> R if $ has shallowlyMutable --R setelt : (%,Integer,R) -> R if $ has shallowlyMutable --R size? : (%,NonNegativeInteger) -> Boolean ---R sort : % -> % if R has ORDSET ---R sort : (((R,R) -> Boolean),%) -> % --R sort! : % -> % if $ has shallowlyMutable and R has ORDSET --R sort! : (((R,R) -> Boolean),%) -> % if $ has shallowlyMutable --R sorted? : % -> Boolean if R has ORDSET @@ -68895,6 +71833,7 @@ InfiniteTuple(S:Type): Exports == Implementation where --R localParamV : % -> List(PCS) localPointV : % -> AffinePlane(K) --R multV : % -> NonNegativeInteger pointV : % -> ProjPt --R setchart! : (%,BLMET) -> BLMET setpoint! : (%,ProjPt) -> ProjPt +--R setsymbName! : (%,Symbol) -> Symbol subMultV : % -> NonNegativeInteger --R symbNameV : % -> Symbol ?~=? : (%,%) -> Boolean --R create : (ProjPt,DistributedMultivariatePolynomial([construct,QUOTEX,QUOTEY],K),AffinePlane(K),NonNegativeInteger,BLMET,NonNegativeInteger,DIVISOR,K,Symbol) -> % --R curveV : % -> DistributedMultivariatePolynomial([construct,QUOTEX,QUOTEY],K) @@ -68904,10 +71843,9 @@ InfiniteTuple(S:Type): Exports == Implementation where --R setlocalPoint! : (%,AffinePlane(K)) -> AffinePlane(K) --R setmult! : (%,NonNegativeInteger) -> NonNegativeInteger --R setsubmult! : (%,NonNegativeInteger) -> NonNegativeInteger ---R setsymbName! : (%,Symbol) -> Symbol ---R subMultV : % -> NonNegativeInteger --R --E 1 + )spool )lisp (bye) @@ -69162,7 +72100,8 @@ InfinitlyClosePoint(K,symb,PolyRing,E,ProjPt,PCS,Plc,DIVISOR,BLMET):Exports == I --R fullOut : % -> OutputForm fullOutput : () -> Boolean --R fullOutput : Boolean -> Boolean hash : % -> SingleInteger --R latex : % -> String multV : % -> NonNegativeInteger ---R setchart! : (%,BLMET) -> BLMET symbNameV : % -> Symbol +--R setchart! : (%,BLMET) -> BLMET setsymbName! : (%,Symbol) -> Symbol +--R subMultV : % -> NonNegativeInteger symbNameV : % -> Symbol --R ?~=? : (%,%) -> Boolean --R actualExtensionV : % -> PseudoAlgebraicClosureOfFiniteField(K) --R create : (ProjectivePlaneOverPseudoAlgebraicClosureOfFiniteField(K),DistributedMultivariatePolynomial(symb,PseudoAlgebraicClosureOfFiniteField(K))) -> % @@ -69179,8 +72118,6 @@ InfinitlyClosePoint(K,symb,PolyRing,E,ProjPt,PCS,Plc,DIVISOR,BLMET):Exports == I --R setmult! : (%,NonNegativeInteger) -> NonNegativeInteger --R setpoint! : (%,ProjectivePlaneOverPseudoAlgebraicClosureOfFiniteField(K)) -> ProjectivePlaneOverPseudoAlgebraicClosureOfFiniteField(K) --R setsubmult! : (%,NonNegativeInteger) -> NonNegativeInteger ---R setsymbName! : (%,Symbol) -> Symbol ---R subMultV : % -> NonNegativeInteger --R --E 1 @@ -69300,17 +72237,19 @@ InfinitlyClosePointOverPseudoAlgebraicClosureOfFiniteField(K,symb,BLMET):_ --R Issue )edit bookvol10.3.pamphlet to see algebra source code for IAN --R --R------------------------------- Operations -------------------------------- ---R ?*? : (PositiveInteger,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (%,%) -> % ?*? : (%,Fraction(Integer)) -> % ---R ?*? : (Fraction(Integer),%) -> % ?**? : (%,PositiveInteger) -> % ---R ?**? : (%,Integer) -> % ?+? : (%,%) -> % ---R -? : % -> % ?-? : (%,%) -> % ---R ?/? : (%,%) -> % ? Boolean ---R ?<=? : (%,%) -> Boolean ?=? : (%,%) -> Boolean ---R ?>? : (%,%) -> Boolean ?>=? : (%,%) -> Boolean ---R D : % -> % D : (%,NonNegativeInteger) -> % ---R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % ?^? : (%,Integer) -> % +--R ?*? : (PositiveInteger,%) -> % ?*? : (NonNegativeInteger,%) -> % +--R ?*? : (Integer,%) -> % ?*? : (%,%) -> % +--R ?*? : (%,Fraction(Integer)) -> % ?*? : (Fraction(Integer),%) -> % +--R ?**? : (%,PositiveInteger) -> % ?**? : (%,NonNegativeInteger) -> % +--R ?**? : (%,Integer) -> % ?**? : (%,Fraction(Integer)) -> % +--R ?+? : (%,%) -> % -? : % -> % +--R ?-? : (%,%) -> % ?/? : (%,%) -> % +--R ? Boolean ?<=? : (%,%) -> Boolean +--R ?=? : (%,%) -> Boolean ?>? : (%,%) -> Boolean +--R ?>=? : (%,%) -> Boolean D : % -> % +--R D : (%,NonNegativeInteger) -> % 1 : () -> % +--R 0 : () -> % ?^? : (%,PositiveInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,Integer) -> % --R associates? : (%,%) -> Boolean belong? : BasicOperator -> Boolean --R box : List(%) -> % box : % -> % --R coerce : Integer -> % coerce : % -> % @@ -69318,55 +72257,51 @@ InfinitlyClosePointOverPseudoAlgebraicClosureOfFiniteField(K,symb,BLMET):_ --R coerce : % -> OutputForm convert : % -> Complex(Float) --R convert : % -> DoubleFloat convert : % -> Float --R differentiate : % -> % distribute : (%,%) -> % ---R distribute : % -> % elt : (BasicOperator,%,%) -> % ---R elt : (BasicOperator,%) -> % eval : (%,%,%) -> % ---R eval : (%,Equation(%)) -> % eval : (%,Kernel(%),%) -> % ---R factor : % -> Factored(%) freeOf? : (%,Symbol) -> Boolean ---R freeOf? : (%,%) -> Boolean gcd : (%,%) -> % ---R gcd : List(%) -> % hash : % -> SingleInteger ---R height : % -> NonNegativeInteger inv : % -> % ---R is? : (%,Symbol) -> Boolean kernel : (BasicOperator,%) -> % +--R distribute : % -> % elt : (BasicOperator,List(%)) -> % +--R elt : (BasicOperator,%,%,%) -> % elt : (BasicOperator,%,%) -> % +--R elt : (BasicOperator,%) -> % eval : (%,Symbol,(% -> %)) -> % +--R eval : (%,List(%),List(%)) -> % eval : (%,%,%) -> % +--R eval : (%,Equation(%)) -> % eval : (%,List(Equation(%))) -> % +--R eval : (%,Kernel(%),%) -> % factor : % -> Factored(%) +--R freeOf? : (%,Symbol) -> Boolean freeOf? : (%,%) -> Boolean +--R gcd : (%,%) -> % gcd : List(%) -> % +--R hash : % -> SingleInteger height : % -> NonNegativeInteger +--R inv : % -> % is? : (%,Symbol) -> Boolean +--R is? : (%,BasicOperator) -> Boolean kernel : (BasicOperator,%) -> % --R kernels : % -> List(Kernel(%)) latex : % -> String --R lcm : (%,%) -> % lcm : List(%) -> % ---R max : (%,%) -> % min : (%,%) -> % ---R norm : (%,List(Kernel(%))) -> % norm : (%,Kernel(%)) -> % ---R nthRoot : (%,Integer) -> % one? : % -> Boolean ---R paren : List(%) -> % paren : % -> % ---R prime? : % -> Boolean ?quo? : (%,%) -> % ---R recip : % -> Union(%,"failed") reduce : % -> % ---R ?rem? : (%,%) -> % retract : % -> Fraction(Integer) ---R retract : % -> Integer retract : % -> Kernel(%) ---R rootOf : Polynomial(%) -> % sample : () -> % +--R map : ((% -> %),Kernel(%)) -> % max : (%,%) -> % +--R min : (%,%) -> % norm : (%,List(Kernel(%))) -> % +--R norm : (%,Kernel(%)) -> % nthRoot : (%,Integer) -> % +--R one? : % -> Boolean paren : List(%) -> % +--R paren : % -> % prime? : % -> Boolean +--R ?quo? : (%,%) -> % recip : % -> Union(%,"failed") +--R reduce : % -> % ?rem? : (%,%) -> % +--R retract : % -> Fraction(Integer) retract : % -> Integer +--R retract : % -> Kernel(%) rootOf : Polynomial(%) -> % +--R rootsOf : Polynomial(%) -> List(%) sample : () -> % --R sizeLess? : (%,%) -> Boolean sqrt : % -> % --R squareFree : % -> Factored(%) squareFreePart : % -> % --R subst : (%,Equation(%)) -> % tower : % -> List(Kernel(%)) --R trueEqual : (%,%) -> Boolean unit? : % -> Boolean --R unitCanonical : % -> % zero? : % -> Boolean ---R zeroOf : Polynomial(%) -> % ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R ?**? : (%,Fraction(Integer)) -> % ---R ?^? : (%,NonNegativeInteger) -> % +--R zeroOf : Polynomial(%) -> % zerosOf : Polynomial(%) -> List(%) +--R ?~=? : (%,%) -> Boolean --R characteristic : () -> NonNegativeInteger --R coerce : SparseMultivariatePolynomial(Integer,Kernel(%)) -> % --R definingPolynomial : % -> % if $ has RING --R denom : % -> SparseMultivariatePolynomial(Integer,Kernel(%)) --R differentiate : (%,NonNegativeInteger) -> % --R divide : (%,%) -> Record(quotient: %,remainder: %) ---R elt : (BasicOperator,List(%)) -> % --R elt : (BasicOperator,%,%,%,%) -> % ---R elt : (BasicOperator,%,%,%) -> % --R euclideanSize : % -> NonNegativeInteger --R eval : (%,BasicOperator,(% -> %)) -> % --R eval : (%,BasicOperator,(List(%) -> %)) -> % --R eval : (%,List(BasicOperator),List((List(%) -> %))) -> % --R eval : (%,List(BasicOperator),List((% -> %))) -> % ---R eval : (%,Symbol,(% -> %)) -> % --R eval : (%,Symbol,(List(%) -> %)) -> % --R eval : (%,List(Symbol),List((List(%) -> %))) -> % --R eval : (%,List(Symbol),List((% -> %))) -> % ---R eval : (%,List(%),List(%)) -> % ---R eval : (%,List(Equation(%))) -> % --R eval : (%,List(Kernel(%)),List(%)) -> % --R even? : % -> Boolean if $ has RETRACT(INT) --R expressIdealMember : (List(%),%) -> Union(List(%),"failed") @@ -69374,11 +72309,9 @@ InfinitlyClosePointOverPseudoAlgebraicClosureOfFiniteField(K,symb,BLMET):_ --R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) --R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") --R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) ---R is? : (%,BasicOperator) -> Boolean --R kernel : (BasicOperator,List(%)) -> % --R lcmCoef : (%,%) -> Record(llcmres: %,coeff1: %,coeff2: %) --R mainKernel : % -> Union(Kernel(%),"failed") ---R map : ((% -> %),Kernel(%)) -> % --R minPoly : Kernel(%) -> SparseUnivariatePolynomial(%) if $ has RING --R multiEuclidean : (List(%),%) -> Union(List(%),"failed") --R norm : (SparseUnivariatePolynomial(%),List(Kernel(%))) -> SparseUnivariatePolynomial(%) @@ -69397,7 +72330,6 @@ InfinitlyClosePointOverPseudoAlgebraicClosureOfFiniteField(K,symb,BLMET):_ --R retractIfCan : % -> Union(Kernel(%),"failed") --R rootOf : SparseUnivariatePolynomial(%) -> % --R rootOf : (SparseUnivariatePolynomial(%),Symbol) -> % ---R rootsOf : Polynomial(%) -> List(%) --R rootsOf : SparseUnivariatePolynomial(%) -> List(%) --R rootsOf : (SparseUnivariatePolynomial(%),Symbol) -> List(%) --R subst : (%,List(Kernel(%)),List(%)) -> % @@ -69406,7 +72338,6 @@ InfinitlyClosePointOverPseudoAlgebraicClosureOfFiniteField(K,symb,BLMET):_ --R unitNormal : % -> Record(unit: %,canonical: %,associate: %) --R zeroOf : SparseUnivariatePolynomial(%) -> % --R zeroOf : (SparseUnivariatePolynomial(%),Symbol) -> % ---R zerosOf : Polynomial(%) -> List(%) --R zerosOf : SparseUnivariatePolynomial(%) -> List(%) --R zerosOf : (SparseUnivariatePolynomial(%),Symbol) -> List(%) --R @@ -69695,14 +72626,17 @@ InnerAlgebraicNumber(): Exports == Implementation where --R Issue )edit bookvol10.3.pamphlet to see algebra source code for IFF --R --R------------------------------- Operations -------------------------------- +--R ?*? : (InnerPrimeField(p),%) -> % ?*? : (%,InnerPrimeField(p)) -> % --R ?*? : (Fraction(Integer),%) -> % ?*? : (%,Fraction(Integer)) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,Integer) -> % ?**? : (%,NonNegativeInteger) -> % --R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % --R ?-? : (%,%) -> % -? : % -> % ---R ?/? : (%,%) -> % ?=? : (%,%) -> Boolean ---R 1 : () -> % 0 : () -> % ---R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> % +--R ?/? : (%,InnerPrimeField(p)) -> % ?/? : (%,%) -> % +--R ?=? : (%,%) -> Boolean 1 : () -> % +--R 0 : () -> % ?^? : (%,Integer) -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % --R algebraic? : % -> Boolean associates? : (%,%) -> Boolean --R basis : () -> Vector(%) coerce : InnerPrimeField(p) -> % --R coerce : Fraction(Integer) -> % coerce : % -> % @@ -69721,16 +72655,10 @@ InnerAlgebraicNumber(): Exports == Implementation where --R trace : % -> InnerPrimeField(p) transcendent? : % -> Boolean --R unit? : % -> Boolean unitCanonical : % -> % --R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (InnerPrimeField(p),%) -> % ---R ?*? : (%,InnerPrimeField(p)) -> % ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R ?/? : (%,InnerPrimeField(p)) -> % --R D : (%,NonNegativeInteger) -> % if InnerPrimeField(p) has FINITE --R D : % -> % if InnerPrimeField(p) has FINITE --R Frobenius : (%,NonNegativeInteger) -> % if InnerPrimeField(p) has FINITE --R Frobenius : % -> % if InnerPrimeField(p) has FINITE ---R ?^? : (%,NonNegativeInteger) -> % --R basis : PositiveInteger -> Vector(%) --R characteristic : () -> NonNegativeInteger --R charthRoot : % -> Union(%,"failed") if InnerPrimeField(p) has CHARNZ or InnerPrimeField(p) has FINITE @@ -69951,17 +72879,17 @@ InnerFiniteField(p:PositiveInteger, n:PositiveInteger) == --R Issue )edit bookvol10.3.pamphlet to see algebra source code for IFAMON --R --R------------------------------- Operations -------------------------------- ---R ?*? : (E,S) -> % ?*? : (PositiveInteger,%) -> % ---R ?+? : (S,%) -> % ?+? : (%,%) -> % ---R ?=? : (%,%) -> Boolean 0 : () -> % ---R coefficient : (S,%) -> E coerce : S -> % ---R coerce : % -> OutputForm hash : % -> SingleInteger ---R latex : % -> String mapCoef : ((E -> E),%) -> % ---R mapGen : ((S -> S),%) -> % nthCoef : (%,Integer) -> E ---R nthFactor : (%,Integer) -> S retract : % -> S ---R sample : () -> % size : % -> NonNegativeInteger ---R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % +--R ?*? : (E,S) -> % ?*? : (NonNegativeInteger,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?+? : (S,%) -> % +--R ?+? : (%,%) -> % ?=? : (%,%) -> Boolean +--R 0 : () -> % coefficient : (S,%) -> E +--R coerce : S -> % coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R mapCoef : ((E -> E),%) -> % mapGen : ((S -> S),%) -> % +--R nthCoef : (%,Integer) -> E nthFactor : (%,Integer) -> S +--R retract : % -> S sample : () -> % +--R size : % -> NonNegativeInteger zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean --R highCommonTerms : (%,%) -> % if E has OAMON --R retractIfCan : % -> Union(S,"failed") --R subtractIfCan : (%,%) -> Union(%,"failed") @@ -70088,14 +73016,15 @@ This is an internal type which provides an implementation of --R elt : (%,Integer,Integer,R) -> R elt : (%,Integer,Integer) -> R --R empty : () -> % empty? : % -> Boolean --R eq? : (%,%) -> Boolean fill! : (%,R) -> % ---R map : (((R,R) -> R),%,%,R) -> % map : (((R,R) -> R),%,%) -> % ---R map : ((R -> R),%) -> % map! : ((R -> R),%) -> % ---R maxColIndex : % -> Integer maxRowIndex : % -> Integer ---R minColIndex : % -> Integer minRowIndex : % -> Integer ---R ncols : % -> NonNegativeInteger nrows : % -> NonNegativeInteger ---R parts : % -> List(R) qelt : (%,Integer,Integer) -> R ---R row : (%,Integer) -> Row sample : () -> % ---R setRow! : (%,Integer,Row) -> % +--R latex : % -> String if R has SETCAT map : (((R,R) -> R),%,%,R) -> % +--R map : (((R,R) -> R),%,%) -> % map : ((R -> R),%) -> % +--R map! : ((R -> R),%) -> % maxColIndex : % -> Integer +--R maxRowIndex : % -> Integer minColIndex : % -> Integer +--R minRowIndex : % -> Integer ncols : % -> NonNegativeInteger +--R nrows : % -> NonNegativeInteger parts : % -> List(R) +--R qelt : (%,Integer,Integer) -> R row : (%,Integer) -> Row +--R sample : () -> % setColumn! : (%,Integer,Col) -> % +--R setRow! : (%,Integer,Row) -> % setelt : (%,Integer,Integer,R) -> R --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R ?=? : (%,%) -> Boolean if R has SETCAT --R any? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate @@ -70108,15 +73037,12 @@ This is an internal type which provides an implementation of --R eval : (%,List(Equation(R))) -> % if R has EVALAB(R) and R has SETCAT --R every? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate --R hash : % -> SingleInteger if R has SETCAT ---R latex : % -> String if R has SETCAT --R less? : (%,NonNegativeInteger) -> Boolean --R member? : (R,%) -> Boolean if $ has finiteAggregate and R has SETCAT --R members : % -> List(R) if $ has finiteAggregate --R more? : (%,NonNegativeInteger) -> Boolean --R new : (NonNegativeInteger,NonNegativeInteger,R) -> % --R qsetelt! : (%,Integer,Integer,R) -> R ---R setColumn! : (%,Integer,Col) -> % ---R setelt : (%,Integer,Integer,R) -> R --R size? : (%,NonNegativeInteger) -> Boolean --R ?~=? : (%,%) -> Boolean if R has SETCAT --R @@ -70301,28 +73227,26 @@ InnerIndexedTwoDimensionalArray(R,mnRow,mnCol,Row,Col):_ --R --R------------------------------- Operations -------------------------------- --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ?=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % associates? : (%,%) -> Boolean ---R coerce : % -> % coerce : Integer -> % ---R coerce : % -> OutputForm complete : % -> % ---R digits : % -> Stream(Integer) extend : (%,Integer) -> % ---R gcd : List(%) -> % gcd : (%,%) -> % ---R hash : % -> SingleInteger latex : % -> String ---R lcm : List(%) -> % lcm : (%,%) -> % ---R moduloP : % -> Integer modulus : () -> Integer ---R one? : % -> Boolean order : % -> NonNegativeInteger ---R ?quo? : (%,%) -> % quotientByP : % -> % ---R recip : % -> Union(%,"failed") ?rem? : (%,%) -> % ---R sample : () -> % sizeLess? : (%,%) -> Boolean ---R sqrt : (%,Integer) -> % unit? : % -> Boolean ---R unitCanonical : % -> % zero? : % -> Boolean ---R ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R associates? : (%,%) -> Boolean coerce : % -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R complete : % -> % digits : % -> Stream(Integer) +--R extend : (%,Integer) -> % gcd : List(%) -> % +--R gcd : (%,%) -> % hash : % -> SingleInteger +--R latex : % -> String lcm : List(%) -> % +--R lcm : (%,%) -> % moduloP : % -> Integer +--R modulus : () -> Integer one? : % -> Boolean +--R order : % -> NonNegativeInteger ?quo? : (%,%) -> % +--R quotientByP : % -> % recip : % -> Union(%,"failed") +--R ?rem? : (%,%) -> % sample : () -> % +--R sizeLess? : (%,%) -> Boolean sqrt : (%,Integer) -> % +--R unit? : % -> Boolean unitCanonical : % -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean --R approximate : (%,Integer) -> Integer --R characteristic : () -> NonNegativeInteger --R divide : (%,%) -> Record(quotient: %,remainder: %) @@ -70689,13 +73613,15 @@ InnerPAdicInteger(p,unBalanced?): Exports == Implementation where --R------------------------------- Operations -------------------------------- --R ?*? : (Fraction(Integer),%) -> % ?*? : (%,Fraction(Integer)) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,Integer) -> % ?**? : (%,NonNegativeInteger) -> % --R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % --R ?-? : (%,%) -> % -? : % -> % --R ?/? : (%,%) -> % ?=? : (%,%) -> Boolean --R D : % -> % D : (%,NonNegativeInteger) -> % ---R 1 : () -> % 0 : () -> % ---R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> % +--R Frobenius : % -> % if $ has FINITE 1 : () -> % +--R 0 : () -> % ?^? : (%,Integer) -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % --R algebraic? : % -> Boolean associates? : (%,%) -> Boolean --R basis : () -> Vector(%) charthRoot : % -> % --R coerce : Fraction(Integer) -> % coerce : % -> % @@ -70705,11 +73631,12 @@ InnerPAdicInteger(p,unBalanced?): Exports == Implementation where --R differentiate : % -> % dimension : () -> CardinalNumber --R enumerate : () -> List(%) factor : % -> Factored(%) --R gcd : List(%) -> % gcd : (%,%) -> % ---R hash : % -> SingleInteger inGroundField? : % -> Boolean ---R index : PositiveInteger -> % init : () -> % ---R inv : % -> % latex : % -> String ---R lcm : List(%) -> % lcm : (%,%) -> % ---R lookup : % -> PositiveInteger norm : % -> % +--R generator : () -> % if $ has FINITE hash : % -> SingleInteger +--R inGroundField? : % -> Boolean index : PositiveInteger -> % +--R init : () -> % inv : % -> % +--R latex : % -> String lcm : List(%) -> % +--R lcm : (%,%) -> % lookup : % -> PositiveInteger +--R nextItem : % -> Union(%,"failed") norm : % -> % --R one? : % -> Boolean order : % -> PositiveInteger --R prime? : % -> Boolean primeFrobenius : % -> % --R primitive? : % -> Boolean primitiveElement : () -> % @@ -70722,11 +73649,7 @@ InnerPAdicInteger(p,unBalanced?): Exports == Implementation where --R transcendent? : % -> Boolean unit? : % -> Boolean --R unitCanonical : % -> % zero? : % -> Boolean --R ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R Frobenius : % -> % if $ has FINITE --R Frobenius : (%,NonNegativeInteger) -> % if $ has FINITE ---R ?^? : (%,NonNegativeInteger) -> % --R basis : PositiveInteger -> Vector(%) --R characteristic : () -> NonNegativeInteger --R charthRoot : % -> Union(%,"failed") @@ -70748,7 +73671,6 @@ InnerPAdicInteger(p,unBalanced?): Exports == Implementation where --R extensionDegree : () -> PositiveInteger --R factorsOfCyclicGroupSize : () -> List(Record(factor: Integer,exponent: Integer)) --R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) ---R generator : () -> % if $ has FINITE --R lcmCoef : (%,%) -> Record(llcmres: %,coeff1: %,coeff2: %) --R linearAssociatedExp : (%,SparseUnivariatePolynomial(%)) -> % if $ has FINITE --R linearAssociatedLog : % -> SparseUnivariatePolynomial(%) if $ has FINITE @@ -70757,7 +73679,6 @@ InnerPAdicInteger(p,unBalanced?): Exports == Implementation where --R minimalPolynomial : % -> SparseUnivariatePolynomial(%) --R minimalPolynomial : (%,PositiveInteger) -> SparseUnivariatePolynomial(%) if $ has FINITE --R multiEuclidean : (List(%),%) -> Union(List(%),"failed") ---R nextItem : % -> Union(%,"failed") --R norm : (%,PositiveInteger) -> % if $ has FINITE --R normal? : % -> Boolean if $ has FINITE --R normalElement : () -> % if $ has FINITE @@ -71089,12 +74010,14 @@ InnerPrimeField(p:PositiveInteger): Exports == Implementation where --R------------------------------- Operations -------------------------------- --R ?*? : (Coef,%) -> % ?*? : (%,Coef) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ?=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % center : % -> Coef ---R coefficient : (%,Integer) -> Coef coerce : Integer -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R center : % -> Coef coefficient : (%,Integer) -> Coef +--R coerce : % -> % if Coef has INTDOM coerce : Integer -> % --R coerce : % -> OutputForm complete : % -> % --R degree : % -> Integer ?.? : (%,Integer) -> Coef --R extend : (%,Integer) -> % hash : % -> SingleInteger @@ -71110,8 +74033,6 @@ InnerPrimeField(p:PositiveInteger): Exports == Implementation where --R ?~=? : (%,%) -> Boolean --R ?*? : (%,Fraction(Integer)) -> % if Coef has ALGEBRA(FRAC(INT)) --R ?*? : (Fraction(Integer),%) -> % if Coef has ALGEBRA(FRAC(INT)) ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % --R ?/? : (%,Coef) -> % if Coef has FIELD --R D : % -> % if Coef has *: (Integer,Coef) -> Coef --R D : (%,NonNegativeInteger) -> % if Coef has *: (Integer,Coef) -> Coef @@ -71119,7 +74040,6 @@ InnerPrimeField(p:PositiveInteger): Exports == Implementation where --R D : (%,List(Symbol)) -> % if Coef has *: (Integer,Coef) -> Coef and Coef has PDRING(SYMBOL) --R D : (%,Symbol,NonNegativeInteger) -> % if Coef has *: (Integer,Coef) -> Coef and Coef has PDRING(SYMBOL) --R D : (%,List(Symbol),List(NonNegativeInteger)) -> % if Coef has *: (Integer,Coef) -> Coef and Coef has PDRING(SYMBOL) ---R ?^? : (%,NonNegativeInteger) -> % --R approximate : (%,Integer) -> Coef if Coef has **: (Coef,Integer) -> Coef and Coef has coerce: Symbol -> Coef --R associates? : (%,%) -> Boolean if Coef has INTDOM --R cAcos : % -> % if Coef has ALGEBRA(FRAC(INT)) @@ -71153,7 +74073,6 @@ InnerPrimeField(p:PositiveInteger): Exports == Implementation where --R characteristic : () -> NonNegativeInteger --R charthRoot : % -> Union(%,"failed") if Coef has CHARNZ --R coerce : Coef -> % if Coef has COMRING ---R coerce : % -> % if Coef has INTDOM --R coerce : Fraction(Integer) -> % if Coef has ALGEBRA(FRAC(INT)) --R differentiate : % -> % if Coef has *: (Integer,Coef) -> Coef --R differentiate : (%,NonNegativeInteger) -> % if Coef has *: (Integer,Coef) -> Coef @@ -72395,8 +75314,8 @@ InnerSparseUnivariatePowerSeries(Coef): Exports == Implementation where --S 1 of 1 )show InnerTable --R ---R InnerTable(Key: SetCategory,Entry: SetCategory,addDom) where ---R addDom: TableAggregate(Key,Entry) with +--R InnerTable(Key: SetCategory,Entry: SetCategory,addDom)where +--R addDom: TableAggregate(Key,Entry)with --R finiteAggregate is a domain constructor --R Abbreviation for InnerTable is INTABL --R This constructor is not exposed in this frame. @@ -72609,24 +75528,22 @@ InnerTable(Key: SetCategory, Entry: SetCategory, addDom):Exports == Implementati --R------------------------------- Operations -------------------------------- --R ?*? : (%,Integer) -> % ?*? : (%,Coef) -> % --R ?*? : (Coef,%) -> % ?*? : (%,%) -> % ---R ?*? : (Integer,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?*? : (Integer,%) -> % ?*? : (NonNegativeInteger,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,NonNegativeInteger) -> % --R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % --R ?-? : (%,%) -> % -? : % -> % --R ?=? : (%,%) -> Boolean 1 : () -> % ---R 0 : () -> % ?^? : (%,PositiveInteger) -> % ---R coefficients : % -> Stream(Coef) coerce : Integer -> % +--R 0 : () -> % ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,PositiveInteger) -> % coefficients : % -> Stream(Coef) +--R coerce : % -> % if Coef has INTDOM coerce : Integer -> % --R coerce : % -> OutputForm hash : % -> SingleInteger --R latex : % -> String one? : % -> Boolean --R order : % -> NonNegativeInteger pole? : % -> Boolean --R recip : % -> Union(%,"failed") sample : () -> % --R series : Stream(Coef) -> % zero? : % -> Boolean --R ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R ?^? : (%,NonNegativeInteger) -> % --R associates? : (%,%) -> Boolean if Coef has INTDOM --R characteristic : () -> NonNegativeInteger ---R coerce : % -> % if Coef has INTDOM --R exquo : (%,%) -> Union(%,"failed") if Coef has INTDOM --R order : (%,NonNegativeInteger) -> NonNegativeInteger --R subtractIfCan : (%,%) -> Union(%,"failed") @@ -72850,29 +75767,29 @@ InnerTaylorSeries(Coef): Exports == Implementation where --R --R------------------------------- Operations -------------------------------- --R #? : % -> Integer ?*? : (%,%) -> % ---R ?**? : (%,Integer) -> % ?+? : (%,%) -> % ---R ?/? : (%,%) -> % ?=? : (%,%) -> Boolean ---R 1 : () -> % 0 : () -> % ---R atom? : % -> Boolean binary : (%,List(%)) -> % ---R car : % -> % cdr : % -> % ---R coerce : % -> OutputForm convert : SExpression -> % ---R convert : % -> SExpression convert : OutputForm -> % ---R convert : DoubleFloat -> % convert : Integer -> % ---R convert : Symbol -> % convert : String -> % ---R convert : List(%) -> % declare : List(%) -> Symbol ---R destruct : % -> List(%) ?.? : (%,List(Integer)) -> % ---R ?.? : (%,Integer) -> % eq : (%,%) -> Boolean ---R expr : % -> OutputForm flatten : % -> % ---R float : % -> DoubleFloat float? : % -> Boolean ---R hash : % -> SingleInteger integer : % -> Integer ---R integer? : % -> Boolean interpret : % -> Any ---R lambda : (%,List(Symbol)) -> % latex : % -> String ---R list? : % -> Boolean null? : % -> Boolean ---R pair? : % -> Boolean parse : String -> % ---R string : % -> String string? : % -> Boolean ---R symbol : % -> Symbol symbol? : % -> Boolean ---R unparse : % -> String ?~=? : (%,%) -> Boolean ---R ?**? : (%,NonNegativeInteger) -> % +--R ?**? : (%,Integer) -> % ?**? : (%,NonNegativeInteger) -> % +--R ?+? : (%,%) -> % ?/? : (%,%) -> % +--R ?=? : (%,%) -> Boolean 1 : () -> % +--R 0 : () -> % atom? : % -> Boolean +--R binary : (%,List(%)) -> % car : % -> % +--R cdr : % -> % coerce : % -> OutputForm +--R convert : SExpression -> % convert : % -> SExpression +--R convert : OutputForm -> % convert : DoubleFloat -> % +--R convert : Integer -> % convert : Symbol -> % +--R convert : String -> % convert : List(%) -> % +--R declare : List(%) -> Symbol destruct : % -> List(%) +--R ?.? : (%,List(Integer)) -> % ?.? : (%,Integer) -> % +--R eq : (%,%) -> Boolean expr : % -> OutputForm +--R flatten : % -> % float : % -> DoubleFloat +--R float? : % -> Boolean hash : % -> SingleInteger +--R integer : % -> Integer integer? : % -> Boolean +--R interpret : % -> Any lambda : (%,List(Symbol)) -> % +--R latex : % -> String list? : % -> Boolean +--R null? : % -> Boolean pair? : % -> Boolean +--R parse : String -> % string : % -> String +--R string? : % -> Boolean symbol : % -> Symbol +--R symbol? : % -> Boolean unparse : % -> String +--R ?~=? : (%,%) -> Boolean --R compile : (Symbol,List(%)) -> Symbol --R function : (%,List(Symbol),Symbol) -> % --R @@ -73148,7 +76065,8 @@ Common Lisp and is not defined in Common Lisp. )set message test on )set message auto off )clear all ---S 1 of 42 + +--S 1 of 43 2**(5678 - 4856 + 2 * 17) --R --R @@ -73160,7 +76078,7 @@ Common Lisp and is not defined in Common Lisp. --R Type: PositiveInteger --E 1 ---S 2 of 42 +--S 2 of 43 x := -101 --R --R @@ -73168,7 +76086,7 @@ x := -101 --R Type: Integer --E 2 ---S 3 of 42 +--S 3 of 43 abs(x) --R --R @@ -73176,7 +76094,7 @@ abs(x) --R Type: PositiveInteger --E 3 ---S 4 of 42 +--S 4 of 43 sign(x) --R --R @@ -73184,7 +76102,7 @@ sign(x) --R Type: Integer --E 4 ---S 5 of 42 +--S 5 of 43 x < 0 --R --R @@ -73192,7 +76110,7 @@ x < 0 --R Type: Boolean --E 5 ---S 6 of 42 +--S 6 of 43 x <= -1 --R --R @@ -73200,7 +76118,7 @@ x <= -1 --R Type: Boolean --E 6 ---S 7 of 42 +--S 7 of 43 negative?(x) --R --R @@ -73208,7 +76126,7 @@ negative?(x) --R Type: Boolean --E 7 ---S 8 of 42 +--S 8 of 43 x > 0 --R --R @@ -73216,7 +76134,7 @@ x > 0 --R Type: Boolean --E 8 ---S 9 of 42 +--S 9 of 43 x >= 1 --R --R @@ -73224,7 +76142,7 @@ x >= 1 --R Type: Boolean --E 9 ---S 10 of 42 +--S 10 of 43 positive?(x) --R --R @@ -73232,7 +76150,7 @@ positive?(x) --R Type: Boolean --E 10 ---S 11 of 42 +--S 11 of 43 zero?(x) --R --R @@ -73240,7 +76158,7 @@ zero?(x) --R Type: Boolean --E 11 ---S 12 of 42 +--S 12 of 43 one?(x) --R --R @@ -73248,7 +76166,7 @@ one?(x) --R Type: Boolean --E 12 ---S 13 of 42 +--S 13 of 43 (x = -101)@Boolean --R --R @@ -73256,7 +76174,7 @@ one?(x) --R Type: Boolean --E 13 ---S 14 of 42 +--S 14 of 43 odd?(x) --R --R @@ -73264,7 +76182,7 @@ odd?(x) --R Type: Boolean --E 14 ---S 15 of 42 +--S 15 of 43 even?(x) --R --R @@ -73272,7 +76190,7 @@ even?(x) --R Type: Boolean --E 15 ---S 16 of 42 +--S 16 of 43 gcd(56788,43688) --R --R @@ -73280,7 +76198,7 @@ gcd(56788,43688) --R Type: PositiveInteger --E 16 ---S 17 of 42 +--S 17 of 43 lcm(56788,43688) --R --R @@ -73288,7 +76206,7 @@ lcm(56788,43688) --R Type: PositiveInteger --E 17 ---S 18 of 42 +--S 18 of 43 max(678,567) --R --R @@ -73296,7 +76214,7 @@ max(678,567) --R Type: PositiveInteger --E 18 ---S 19 of 42 +--S 19 of 43 min(678,567) --R --R @@ -73304,7 +76222,7 @@ min(678,567) --R Type: PositiveInteger --E 19 ---S 20 of 42 +--S 20 of 43 reduce(max,[2,45,-89,78,100,-45]) --R --R @@ -73312,7 +76230,7 @@ reduce(max,[2,45,-89,78,100,-45]) --R Type: PositiveInteger --E 20 ---S 21 of 42 +--S 21 of 43 reduce(min,[2,45,-89,78,100,-45]) --R --R @@ -73320,7 +76238,7 @@ reduce(min,[2,45,-89,78,100,-45]) --R Type: Integer --E 21 ---S 22 of 42 +--S 22 of 43 reduce(gcd,[2,45,-89,78,100,-45]) --R --R @@ -73328,7 +76246,7 @@ reduce(gcd,[2,45,-89,78,100,-45]) --R Type: PositiveInteger --E 22 ---S 23 of 42 +--S 23 of 43 reduce(lcm,[2,45,-89,78,100,-45]) --R --R @@ -73336,7 +76254,7 @@ reduce(lcm,[2,45,-89,78,100,-45]) --R Type: PositiveInteger --E 23 ---S 24 of 42 +--S 24 of 43 13 / 4 --R --R @@ -73346,7 +76264,7 @@ reduce(lcm,[2,45,-89,78,100,-45]) --R Type: Fraction(Integer) --E 24 ---S 25 of 42 +--S 25 of 43 13 quo 4 --R --R @@ -73354,7 +76272,7 @@ reduce(lcm,[2,45,-89,78,100,-45]) --R Type: PositiveInteger --E 25 ---S 26 of 42 +--S 26 of 43 13 rem 4 --R --R @@ -73362,7 +76280,7 @@ reduce(lcm,[2,45,-89,78,100,-45]) --R Type: PositiveInteger --E 26 ---S 27 of 42 +--S 27 of 43 zero?(167604736446952 rem 2003644) --R --R @@ -73370,7 +76288,7 @@ zero?(167604736446952 rem 2003644) --R Type: Boolean --E 27 ---S 28 of 42 +--S 28 of 43 d := divide(13,4) --R --R @@ -73378,7 +76296,7 @@ d := divide(13,4) --R Type: Record(quotient: Integer,remainder: Integer) --E 28 ---S 29 of 42 +--S 29 of 43 d.quotient --R --R @@ -73386,7 +76304,7 @@ d.quotient --R Type: PositiveInteger --E 29 ---S 30 of 42 +--S 30 of 43 d.remainder --R --R @@ -73394,7 +76312,7 @@ d.remainder --R Type: PositiveInteger --E 30 ---S 31 of 42 +--S 31 of 43 factor 102400 --R --R @@ -73403,7 +76321,7 @@ factor 102400 --R Type: Factored(Integer) --E 31 ---S 32 of 42 +--S 32 of 43 prime? 7 --R --R @@ -73411,7 +76329,7 @@ prime? 7 --R Type: Boolean --E 32 ---S 33 of 42 +--S 33 of 43 prime? 8 --R --R @@ -73419,7 +76337,7 @@ prime? 8 --R Type: Boolean --E 33 ---S 34 of 42 +--S 34 of 43 nextPrime 100 --R --R @@ -73427,7 +76345,7 @@ nextPrime 100 --R Type: PositiveInteger --E 34 ---S 35 of 42 +--S 35 of 43 prevPrime 100 --R --R @@ -73435,7 +76353,7 @@ prevPrime 100 --R Type: PositiveInteger --E 35 ---S 36 of 42 +--S 36 of 43 primes(100,175) --R --R @@ -73443,7 +76361,7 @@ primes(100,175) --R Type: List(Integer) --E 36 ---S 37 of 42 +--S 37 of 43 factor(2 :: Complex Integer) --R --R @@ -73452,7 +76370,7 @@ factor(2 :: Complex Integer) --R Type: Factored(Complex(Integer)) --E 37 ---S 38 of 42 +--S 38 of 43 [fibonacci(k) for k in 0..] --R --R @@ -73460,7 +76378,7 @@ factor(2 :: Complex Integer) --R Type: Stream(Integer) --E 38 ---S 39 of 42 +--S 39 of 43 [legendre(i,11) for i in 0..10] --R --R @@ -73468,7 +76386,7 @@ factor(2 :: Complex Integer) --R Type: List(Integer) --E 39 ---S 40 of 42 +--S 40 of 43 [jacobi(i,15) for i in 0..9] --R --R @@ -73476,7 +76394,7 @@ factor(2 :: Complex Integer) --R Type: List(Integer) --E 40 ---S 41 of 42 +--S 41 of 43 [eulerPhi i for i in 1..] --R --R @@ -73484,13 +76402,91 @@ factor(2 :: Complex Integer) --R Type: Stream(Integer) --E 41 ---S 42 of 42 +--S 42 of 43 [moebiusMu i for i in 1..] --R --R --R (42) [1,- 1,- 1,0,- 1,1,- 1,0,0,1,...] --R Type: Stream(Integer) --E 42 + +--S 43 of 43 +)show Integer +--R +--R Integer is a domain constructor +--R Abbreviation for Integer is INT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for INT +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ? Boolean +--R ?<=? : (%,%) -> Boolean ?=? : (%,%) -> Boolean +--R ?>? : (%,%) -> Boolean ?>=? : (%,%) -> Boolean +--R D : % -> % D : (%,NonNegativeInteger) -> % +--R OMwrite : (%,Boolean) -> String OMwrite : % -> String +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R abs : % -> % addmod : (%,%,%) -> % +--R associates? : (%,%) -> Boolean base : () -> % +--R binomial : (%,%) -> % bit? : (%,%) -> Boolean +--R coerce : Integer -> % coerce : % -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R convert : % -> String convert : % -> DoubleFloat +--R convert : % -> Float convert : % -> Pattern(Integer) +--R convert : % -> InputForm convert : % -> Integer +--R copy : % -> % dec : % -> % +--R differentiate : % -> % even? : % -> Boolean +--R factor : % -> Factored(%) factorial : % -> % +--R gcd : List(%) -> % gcd : (%,%) -> % +--R hash : % -> % hash : % -> SingleInteger +--R inc : % -> % init : () -> % +--R invmod : (%,%) -> % latex : % -> String +--R lcm : List(%) -> % lcm : (%,%) -> % +--R length : % -> % mask : % -> % +--R max : (%,%) -> % min : (%,%) -> % +--R mulmod : (%,%,%) -> % negative? : % -> Boolean +--R nextItem : % -> Union(%,"failed") odd? : % -> Boolean +--R one? : % -> Boolean permutation : (%,%) -> % +--R positive? : % -> Boolean positiveRemainder : (%,%) -> % +--R powmod : (%,%,%) -> % prime? : % -> Boolean +--R ?quo? : (%,%) -> % random : % -> % +--R random : () -> % rational : % -> Fraction(Integer) +--R rational? : % -> Boolean recip : % -> Union(%,"failed") +--R ?rem? : (%,%) -> % retract : % -> Integer +--R sample : () -> % shift : (%,%) -> % +--R sign : % -> Integer sizeLess? : (%,%) -> Boolean +--R squareFree : % -> Factored(%) squareFreePart : % -> % +--R submod : (%,%,%) -> % symmetricRemainder : (%,%) -> % +--R unit? : % -> Boolean unitCanonical : % -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R OMwrite : (OpenMathDevice,%,Boolean) -> Void +--R OMwrite : (OpenMathDevice,%) -> Void +--R characteristic : () -> NonNegativeInteger +--R differentiate : (%,NonNegativeInteger) -> % +--R divide : (%,%) -> Record(quotient: %,remainder: %) +--R euclideanSize : % -> NonNegativeInteger +--R expressIdealMember : (List(%),%) -> Union(List(%),"failed") +--R exquo : (%,%) -> Union(%,"failed") +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") +--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) +--R lcmCoef : (%,%) -> Record(llcmres: %,coeff1: %,coeff2: %) +--R multiEuclidean : (List(%),%) -> Union(List(%),"failed") +--R patternMatch : (%,Pattern(Integer),PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) +--R principalIdeal : List(%) -> Record(coef: List(%),generator: %) +--R rationalIfCan : % -> Union(Fraction(Integer),"failed") +--R reducedSystem : Matrix(%) -> Matrix(Integer) +--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(Integer),vec: Vector(Integer)) +--R retractIfCan : % -> Union(Integer,"failed") +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) +--R +--E 43 + )spool )lisp (bye) \end{chunk} @@ -74189,6 +77185,7 @@ Integer: Join(IntegerNumberSystem, ConvertibleTo String, OpenMath) with --S 1 of 1 )show IntegerMod +--R --R IntegerMod(p: PositiveInteger) is a domain constructor --R Abbreviation for IntegerMod is ZMOD --R This constructor is not exposed in this frame. @@ -74196,24 +77193,22 @@ Integer: Join(IntegerNumberSystem, ConvertibleTo String, OpenMath) with --R --R------------------------------- Operations -------------------------------- --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ?=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % coerce : Integer -> % ---R coerce : % -> OutputForm convert : % -> Integer ---R enumerate : () -> List(%) hash : % -> SingleInteger ---R index : PositiveInteger -> % init : () -> % ---R latex : % -> String lookup : % -> PositiveInteger +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R convert : % -> Integer enumerate : () -> List(%) +--R hash : % -> SingleInteger index : PositiveInteger -> % +--R init : () -> % latex : % -> String +--R lookup : % -> PositiveInteger nextItem : % -> Union(%,"failed") --R one? : % -> Boolean random : () -> % --R recip : % -> Union(%,"failed") sample : () -> % --R size : () -> NonNegativeInteger zero? : % -> Boolean --R ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R ?^? : (%,NonNegativeInteger) -> % --R characteristic : () -> NonNegativeInteger ---R nextItem : % -> Union(%,"failed") --R subtractIfCan : (%,%) -> Union(%,"failed") --R --E 1 @@ -74537,17 +77532,16 @@ IntegrationFunctionsTable(): E == I where --R --R------------------------------- Operations -------------------------------- --R ?*? : (%,Fraction(Integer)) -> % ?*? : (Fraction(Integer),%) -> % ---R ?*? : (Integer,%) -> % ?*? : (PositiveInteger,%) -> % ---R ?+? : (%,%) -> % ?-? : (%,%) -> % ---R -? : % -> % ?=? : (%,%) -> Boolean ---R 0 : () -> % coerce : F -> % ---R coerce : % -> OutputForm differentiate : (%,(F -> F)) -> F ---R elem? : % -> Boolean hash : % -> SingleInteger ---R integral : (F,F) -> % latex : % -> String ---R ratpart : % -> F retract : % -> F ---R sample : () -> % zero? : % -> Boolean ---R ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % +--R ?*? : (Integer,%) -> % ?*? : (NonNegativeInteger,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?+? : (%,%) -> % +--R ?-? : (%,%) -> % -? : % -> % +--R ?=? : (%,%) -> Boolean 0 : () -> % +--R coerce : F -> % coerce : % -> OutputForm +--R differentiate : (%,(F -> F)) -> F elem? : % -> Boolean +--R hash : % -> SingleInteger integral : (F,F) -> % +--R latex : % -> String ratpart : % -> F +--R retract : % -> F sample : () -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean --R differentiate : (%,Symbol) -> F if F has PDRING(SYMBOL) --R integral : (F,Symbol) -> % if F has RETRACT(SYMBOL) --R logpart : % -> List(Record(scalar: Fraction(Integer),coeff: SparseUnivariatePolynomial(F),logand: SparseUnivariatePolynomial(F))) @@ -74911,13 +77905,15 @@ contains?(t3,0.3) --R --R------------------------------- Operations -------------------------------- --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,%) -> % ---R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % ---R ?-? : (%,%) -> % -? : % -> % ---R ? Boolean ?<=? : (%,%) -> Boolean ---R ?=? : (%,%) -> Boolean ?>? : (%,%) -> Boolean ---R ?>=? : (%,%) -> Boolean 1 : () -> % ---R 0 : () -> % ?^? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,Fraction(Integer)) -> % ?**? : (%,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ? Boolean +--R ?<=? : (%,%) -> Boolean ?=? : (%,%) -> Boolean +--R ?>? : (%,%) -> Boolean ?>=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % --R acos : % -> % acosh : % -> % --R acot : % -> % acoth : % -> % --R acsc : % -> % acsch : % -> % @@ -74948,10 +77944,6 @@ contains?(t3,0.3) --R tanh : % -> % unit? : % -> Boolean --R unitCanonical : % -> % width : % -> R --R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,Fraction(Integer)) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R ?^? : (%,NonNegativeInteger) -> % --R characteristic : () -> NonNegativeInteger --R exquo : (%,%) -> Union(%,"failed") --R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) @@ -75552,7 +78544,8 @@ Interval(R:Join(FloatingPointSystem,TranscendentalFunctionCategory)): IntervalCa )set message test on )set message auto off )clear all ---S 1 of 19 + +--S 1 of 20 x :: Expression Integer --R --R @@ -75560,7 +78553,7 @@ x :: Expression Integer --R Type: Expression(Integer) --E 1 ---S 2 of 19 +--S 2 of 20 kernel x --R --R @@ -75568,7 +78561,7 @@ kernel x --R Type: Kernel(Expression(Integer)) --E 2 ---S 3 of 19 +--S 3 of 20 sin(x) + cos(x) --R --R @@ -75576,7 +78569,7 @@ sin(x) + cos(x) --R Type: Expression(Integer) --E 3 ---S 4 of 19 +--S 4 of 20 kernels % --R --R @@ -75584,7 +78577,7 @@ kernels % --R Type: List(Kernel(Expression(Integer))) --E 4 ---S 5 of 19 +--S 5 of 20 sin(x)**2 + sin(x) + cos(x) --R --R @@ -75593,7 +78586,7 @@ sin(x)**2 + sin(x) + cos(x) --R Type: Expression(Integer) --E 5 ---S 6 of 19 +--S 6 of 20 kernels % --R --R @@ -75601,7 +78594,7 @@ kernels % --R Type: List(Kernel(Expression(Integer))) --E 6 ---S 7 of 19 +--S 7 of 20 kernels(1 :: Expression Integer) --R --R @@ -75609,7 +78602,7 @@ kernels(1 :: Expression Integer) --R Type: List(Kernel(Expression(Integer))) --E 7 ---S 8 of 19 +--S 8 of 20 mainKernel(cos(x) + tan(x)) --R --R @@ -75617,7 +78610,7 @@ mainKernel(cos(x) + tan(x)) --R Type: Union(Kernel(Expression(Integer)),...) --E 8 ---S 9 of 19 +--S 9 of 20 height kernel x --R --R @@ -75625,7 +78618,7 @@ height kernel x --R Type: PositiveInteger --E 9 ---S 10 of 19 +--S 10 of 20 height mainKernel(sin x) --R --R @@ -75633,7 +78626,7 @@ height mainKernel(sin x) --R Type: PositiveInteger --E 10 ---S 11 of 19 +--S 11 of 20 height mainKernel(sin cos x) --R --R @@ -75641,7 +78634,7 @@ height mainKernel(sin cos x) --R Type: PositiveInteger --E 11 ---S 12 of 19 +--S 12 of 20 height mainKernel(sin cos (tan x + sin x)) --R --R @@ -75649,7 +78642,7 @@ height mainKernel(sin cos (tan x + sin x)) --R Type: PositiveInteger --E 12 ---S 13 of 19 +--S 13 of 20 operator mainKernel(sin cos (tan x + sin x)) --R --R @@ -75657,7 +78650,7 @@ operator mainKernel(sin cos (tan x + sin x)) --R Type: BasicOperator --E 13 ---S 14 of 19 +--S 14 of 20 name mainKernel(sin cos (tan x + sin x)) --R --R @@ -75665,7 +78658,7 @@ name mainKernel(sin cos (tan x + sin x)) --R Type: Symbol --E 14 ---S 15 of 19 +--S 15 of 20 f := operator 'f --R --R @@ -75673,7 +78666,7 @@ f := operator 'f --R Type: BasicOperator --E 15 ---S 16 of 19 +--S 16 of 20 e := f(x, y, 10) --R --R @@ -75681,7 +78674,7 @@ e := f(x, y, 10) --R Type: Expression(Integer) --E 16 ---S 17 of 19 +--S 17 of 20 is?(e, f) --R --R @@ -75689,7 +78682,7 @@ is?(e, f) --R Type: Boolean --E 17 ---S 18 of 19 +--S 18 of 20 is?(e, 'f) --R --R @@ -75697,13 +78690,42 @@ is?(e, 'f) --R Type: Boolean --E 18 ---S 19 of 19 +--S 19 of 20 argument mainKernel e --R --R --R (19) [x,y,10] --R Type: List(Expression(Integer)) --E 19 + +--S 20 of 20 +)show Kernel +--R +--R Kernel(S: OrderedSet) is a domain constructor +--R Abbreviation for Kernel is KERNEL +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for KERNEL +--R +--R------------------------------- Operations -------------------------------- +--R ? Boolean ?<=? : (%,%) -> Boolean +--R ?=? : (%,%) -> Boolean ?>? : (%,%) -> Boolean +--R ?>=? : (%,%) -> Boolean argument : % -> List(S) +--R coerce : % -> OutputForm hash : % -> SingleInteger +--R height : % -> NonNegativeInteger is? : (%,Symbol) -> Boolean +--R is? : (%,BasicOperator) -> Boolean kernel : Symbol -> % +--R latex : % -> String max : (%,%) -> % +--R min : (%,%) -> % name : % -> Symbol +--R operator : % -> BasicOperator position : % -> NonNegativeInteger +--R ?~=? : (%,%) -> Boolean +--R convert : % -> InputForm if S has KONVERT(INFORM) +--R convert : % -> Pattern(Float) if S has KONVERT(PATTERN(FLOAT)) +--R convert : % -> Pattern(Integer) if S has KONVERT(PATTERN(INT)) +--R kernel : (BasicOperator,List(S),NonNegativeInteger) -> % +--R setPosition : (%,NonNegativeInteger) -> Void +--R symbolIfCan : % -> Union(Symbol,"failed") +--R +--E 20 + )spool )lisp (bye) \end{chunk} @@ -76043,7 +79065,7 @@ Kernel(S:OrderedSet): Exports == Implementation where )set message auto off )clear all ---S 1 of 20 +--S 1 of 21 ey: KeyedAccessFile(Integer) := open("editor.year", "output") --R --R @@ -76051,7 +79073,7 @@ ey: KeyedAccessFile(Integer) := open("editor.year", "output") --R Type: KeyedAccessFile(Integer) --E 1 ---S 2 of 20 +--S 2 of 21 ey."Char":= 1986 --R --R @@ -76059,7 +79081,7 @@ ey."Char":= 1986 --R Type: PositiveInteger --E 2 ---S 3 of 20 +--S 3 of 21 ey."Caviness" := 1985 --R --R @@ -76067,7 +79089,7 @@ ey."Caviness" := 1985 --R Type: PositiveInteger --E 3 ---S 4 of 20 +--S 4 of 21 ey."Fitch" := 1984 --R --R @@ -76075,7 +79097,7 @@ ey."Fitch" := 1984 --R Type: PositiveInteger --E 4 ---S 5 of 20 +--S 5 of 21 ey."Char" --R --R @@ -76083,7 +79105,7 @@ ey."Char" --R Type: PositiveInteger --E 5 ---S 6 of 20 +--S 6 of 21 ey("Char") --R --R @@ -76091,7 +79113,7 @@ ey("Char") --R Type: PositiveInteger --E 6 ---S 7 of 20 +--S 7 of 21 ey "Char" --R --R @@ -76099,7 +79121,7 @@ ey "Char" --R Type: PositiveInteger --E 7 ---S 8 of 20 +--S 8 of 21 search("Char", ey) --R --R @@ -76107,7 +79129,7 @@ search("Char", ey) --R Type: Union(Integer,...) --E 8 ---S 9 of 20 +--S 9 of 21 search("Smith", ey) --R --R @@ -76115,7 +79137,7 @@ search("Smith", ey) --R Type: Union("failed",...) --E 9 ---S 10 of 20 +--S 10 of 21 remove!("Char", ey) --R --R @@ -76123,7 +79145,7 @@ remove!("Char", ey) --R Type: Union(Integer,...) --E 10 ---S 11 of 20 +--S 11 of 21 keys ey --R --R @@ -76131,7 +79153,7 @@ keys ey --R Type: List(String) --E 11 ---S 12 of 20 +--S 12 of 21 #ey --R --R @@ -76139,7 +79161,7 @@ keys ey --R Type: PositiveInteger --E 12 ---S 13 of 20 +--S 13 of 21 KE := Record(key: String, entry: Integer) --R --R @@ -76147,7 +79169,7 @@ KE := Record(key: String, entry: Integer) --R Type: Domain --E 13 ---S 14 of 20 +--S 14 of 21 reopen!(ey, "output") --R --R @@ -76155,7 +79177,7 @@ reopen!(ey, "output") --R Type: KeyedAccessFile(Integer) --E 14 ---S 15 of 20 +--S 15 of 21 write!(ey, ["van Hulzen", 1983]$KE) --R --R @@ -76163,7 +79185,7 @@ write!(ey, ["van Hulzen", 1983]$KE) --R Type: Record(key: String,entry: Integer) --E 15 ---S 16 of 20 +--S 16 of 21 write!(ey, ["Calmet", 1982]$KE) --R --R @@ -76171,7 +79193,7 @@ write!(ey, ["Calmet", 1982]$KE) --R Type: Record(key: String,entry: Integer) --E 16 ---S 17 of 20 +--S 17 of 21 write!(ey, ["Wang", 1981]$KE) --R --R @@ -76179,7 +79201,7 @@ write!(ey, ["Wang", 1981]$KE) --R Type: Record(key: String,entry: Integer) --E 17 ---S 18 of 20 +--S 18 of 21 close! ey --R --R @@ -76187,7 +79209,7 @@ close! ey --R Type: KeyedAccessFile(Integer) --E 18 ---S 19 of 20 +--S 19 of 21 keys ey --R --R @@ -76195,7 +79217,7 @@ keys ey --R Type: List(String) --E 19 ---S 20 of 20 +--S 20 of 21 members ey --R --R @@ -76203,6 +79225,93 @@ members ey --R Type: List(Integer) --E 20 +--S 21 of 21 +)show KeyedAccessFile +--R +--R KeyedAccessFile(Entry: SetCategory) is a domain constructor +--R Abbreviation for KeyedAccessFile is KAFILE +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for KAFILE +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean close! : % -> % +--R coerce : % -> OutputForm copy : % -> % +--R dictionary : () -> % ?.? : (%,String) -> Entry +--R elt : (%,String,Entry) -> Entry empty : () -> % +--R empty? : % -> Boolean entries : % -> List(Entry) +--R eq? : (%,%) -> Boolean flush : % -> Void +--R hash : % -> SingleInteger index? : (String,%) -> Boolean +--R indices : % -> List(String) iomode : % -> String +--R key? : (String,%) -> Boolean keys : % -> List(String) +--R latex : % -> String map : ((Entry -> Entry),%) -> % +--R name : % -> FileName open : (FileName,String) -> % +--R open : FileName -> % pack! : % -> % +--R qelt : (%,String) -> Entry reopen! : (%,String) -> % +--R sample : () -> % setelt : (%,String,Entry) -> Entry +--R table : () -> % ?~=? : (%,%) -> Boolean +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R any? : ((Record(key: String,entry: Entry) -> Boolean),%) -> Boolean if $ has finiteAggregate +--R any? : ((Entry -> Boolean),%) -> Boolean if $ has finiteAggregate +--R bag : List(Record(key: String,entry: Entry)) -> % +--R construct : List(Record(key: String,entry: Entry)) -> % +--R convert : % -> InputForm if Record(key: String,entry: Entry) has KONVERT(INFORM) +--R count : ((Record(key: String,entry: Entry) -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R count : (Record(key: String,entry: Entry),%) -> NonNegativeInteger if $ has finiteAggregate and Record(key: String,entry: Entry) has SETCAT +--R count : (Entry,%) -> NonNegativeInteger if $ has finiteAggregate and Entry has SETCAT +--R count : ((Entry -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R dictionary : List(Record(key: String,entry: Entry)) -> % +--R entry? : (Entry,%) -> Boolean if $ has finiteAggregate and Entry has SETCAT +--R eval : (%,List(Equation(Record(key: String,entry: Entry)))) -> % if Record(key: String,entry: Entry) has EVALAB(Record(key: String,entry: Entry)) and Record(key: String,entry: Entry) has SETCAT +--R eval : (%,Equation(Record(key: String,entry: Entry))) -> % if Record(key: String,entry: Entry) has EVALAB(Record(key: String,entry: Entry)) and Record(key: String,entry: Entry) has SETCAT +--R eval : (%,Record(key: String,entry: Entry),Record(key: String,entry: Entry)) -> % if Record(key: String,entry: Entry) has EVALAB(Record(key: String,entry: Entry)) and Record(key: String,entry: Entry) has SETCAT +--R eval : (%,List(Record(key: String,entry: Entry)),List(Record(key: String,entry: Entry))) -> % if Record(key: String,entry: Entry) has EVALAB(Record(key: String,entry: Entry)) and Record(key: String,entry: Entry) has SETCAT +--R eval : (%,List(Entry),List(Entry)) -> % if Entry has EVALAB(Entry) and Entry has SETCAT +--R eval : (%,Entry,Entry) -> % if Entry has EVALAB(Entry) and Entry has SETCAT +--R eval : (%,Equation(Entry)) -> % if Entry has EVALAB(Entry) and Entry has SETCAT +--R eval : (%,List(Equation(Entry))) -> % if Entry has EVALAB(Entry) and Entry has SETCAT +--R every? : ((Record(key: String,entry: Entry) -> Boolean),%) -> Boolean if $ has finiteAggregate +--R every? : ((Entry -> Boolean),%) -> Boolean if $ has finiteAggregate +--R extract! : % -> Record(key: String,entry: Entry) +--R fill! : (%,Entry) -> % if $ has shallowlyMutable +--R find : ((Record(key: String,entry: Entry) -> Boolean),%) -> Union(Record(key: String,entry: Entry),"failed") +--R first : % -> Entry if String has ORDSET +--R insert! : (Record(key: String,entry: Entry),%) -> % +--R inspect : % -> Record(key: String,entry: Entry) +--R less? : (%,NonNegativeInteger) -> Boolean +--R map : ((Record(key: String,entry: Entry) -> Record(key: String,entry: Entry)),%) -> % +--R map : (((Entry,Entry) -> Entry),%,%) -> % +--R map! : ((Record(key: String,entry: Entry) -> Record(key: String,entry: Entry)),%) -> % if $ has shallowlyMutable +--R map! : ((Entry -> Entry),%) -> % if $ has shallowlyMutable +--R maxIndex : % -> String if String has ORDSET +--R member? : (Record(key: String,entry: Entry),%) -> Boolean if $ has finiteAggregate and Record(key: String,entry: Entry) has SETCAT +--R member? : (Entry,%) -> Boolean if $ has finiteAggregate and Entry has SETCAT +--R members : % -> List(Record(key: String,entry: Entry)) if $ has finiteAggregate +--R members : % -> List(Entry) if $ has finiteAggregate +--R minIndex : % -> String if String has ORDSET +--R more? : (%,NonNegativeInteger) -> Boolean +--R parts : % -> List(Record(key: String,entry: Entry)) if $ has finiteAggregate +--R parts : % -> List(Entry) if $ has finiteAggregate +--R qsetelt! : (%,String,Entry) -> Entry if $ has shallowlyMutable +--R read! : % -> Record(key: String,entry: Entry) +--R reduce : (((Record(key: String,entry: Entry),Record(key: String,entry: Entry)) -> Record(key: String,entry: Entry)),%,Record(key: String,entry: Entry),Record(key: String,entry: Entry)) -> Record(key: String,entry: Entry) if $ has finiteAggregate and Record(key: String,entry: Entry) has SETCAT +--R reduce : (((Record(key: String,entry: Entry),Record(key: String,entry: Entry)) -> Record(key: String,entry: Entry)),%,Record(key: String,entry: Entry)) -> Record(key: String,entry: Entry) if $ has finiteAggregate +--R reduce : (((Record(key: String,entry: Entry),Record(key: String,entry: Entry)) -> Record(key: String,entry: Entry)),%) -> Record(key: String,entry: Entry) if $ has finiteAggregate +--R remove : (Record(key: String,entry: Entry),%) -> % if $ has finiteAggregate and Record(key: String,entry: Entry) has SETCAT +--R remove : ((Record(key: String,entry: Entry) -> Boolean),%) -> % if $ has finiteAggregate +--R remove! : (Record(key: String,entry: Entry),%) -> % if $ has finiteAggregate +--R remove! : ((Record(key: String,entry: Entry) -> Boolean),%) -> % if $ has finiteAggregate +--R remove! : (String,%) -> Union(Entry,"failed") +--R removeDuplicates : % -> % if $ has finiteAggregate and Record(key: String,entry: Entry) has SETCAT +--R search : (String,%) -> Union(Entry,"failed") +--R select : ((Record(key: String,entry: Entry) -> Boolean),%) -> % if $ has finiteAggregate +--R select! : ((Record(key: String,entry: Entry) -> Boolean),%) -> % if $ has finiteAggregate +--R size? : (%,NonNegativeInteger) -> Boolean +--R swap! : (%,String,String) -> Void if $ has shallowlyMutable +--R table : List(Record(key: String,entry: Entry)) -> % +--R write! : (%,Record(key: String,entry: Entry)) -> Record(key: String,entry: Entry) +--R +--E 21 + )system rm -r editor.year )spool @@ -76542,34 +79651,35 @@ KeyedAccessFile(Entry): KAFcategory == KAFcapsule where --R --R------------------------------- Operations -------------------------------- --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ?=? : (%,%) -> Boolean --R D : % -> % if UP has DIFRING D : (%,(UP -> UP)) -> % --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % associates? : (%,%) -> Boolean ---R coefficient : (%,Integer) -> R coerce : UP -> % ---R coerce : R -> % coerce : % -> % ---R coerce : Integer -> % coerce : % -> OutputForm ---R convert : % -> Fraction(UP) degree : % -> Integer ---R hash : % -> SingleInteger latex : % -> String ---R leadingCoefficient : % -> R monomial : (R,Integer) -> % ---R monomial? : % -> Boolean one? : % -> Boolean ---R order : % -> Integer recip : % -> Union(%,"failed") ---R reductum : % -> % retract : % -> UP ---R retract : % -> R sample : () -> % ---R trailingCoefficient : % -> R unit? : % -> Boolean ---R unitCanonical : % -> % zero? : % -> Boolean ---R ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R associates? : (%,%) -> Boolean coefficient : (%,Integer) -> R +--R coerce : UP -> % coerce : R -> % +--R coerce : % -> % coerce : Integer -> % +--R coerce : % -> OutputForm convert : % -> Fraction(UP) +--R degree : % -> Integer gcd : (%,%) -> % if R has FIELD +--R gcd : List(%) -> % if R has FIELD hash : % -> SingleInteger +--R latex : % -> String lcm : (%,%) -> % if R has FIELD +--R lcm : List(%) -> % if R has FIELD leadingCoefficient : % -> R +--R monomial : (R,Integer) -> % monomial? : % -> Boolean +--R one? : % -> Boolean order : % -> Integer +--R ?quo? : (%,%) -> % if R has FIELD recip : % -> Union(%,"failed") +--R reductum : % -> % ?rem? : (%,%) -> % if R has FIELD +--R retract : % -> UP retract : % -> R +--R sample : () -> % trailingCoefficient : % -> R +--R unit? : % -> Boolean unitCanonical : % -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean --R D : (%,NonNegativeInteger) -> % if UP has DIFRING --R D : (%,Symbol) -> % if UP has PDRING(SYMBOL) --R D : (%,List(Symbol)) -> % if UP has PDRING(SYMBOL) --R D : (%,Symbol,NonNegativeInteger) -> % if UP has PDRING(SYMBOL) --R D : (%,List(Symbol),List(NonNegativeInteger)) -> % if UP has PDRING(SYMBOL) --R D : (%,(UP -> UP),NonNegativeInteger) -> % ---R ?^? : (%,NonNegativeInteger) -> % --R characteristic : () -> NonNegativeInteger --R charthRoot : % -> Union(%,"failed") if R has CHARNZ --R coerce : Fraction(Integer) -> % if R has RETRACT(FRAC(INT)) @@ -76587,16 +79697,10 @@ KeyedAccessFile(Entry): KAFcategory == KAFcapsule where --R exquo : (%,%) -> Union(%,"failed") --R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) if R has FIELD --R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") if R has FIELD ---R gcd : (%,%) -> % if R has FIELD ---R gcd : List(%) -> % if R has FIELD --R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) if R has FIELD ---R lcm : (%,%) -> % if R has FIELD ---R lcm : List(%) -> % if R has FIELD --R lcmCoef : (%,%) -> Record(llcmres: %,coeff1: %,coeff2: %) if R has FIELD --R multiEuclidean : (List(%),%) -> Union(List(%),"failed") if R has FIELD --R principalIdeal : List(%) -> Record(coef: List(%),generator: %) if R has FIELD ---R ?quo? : (%,%) -> % if R has FIELD ---R ?rem? : (%,%) -> % if R has FIELD --R retract : % -> Fraction(Integer) if R has RETRACT(FRAC(INT)) --R retract : % -> Integer if R has RETRACT(INT) --R retractIfCan : % -> Union(UP,"failed") @@ -76877,7 +79981,7 @@ LaurentPolynomial(R, UP): Exports == Implementation where )set message auto off )clear all ---S 1 of 7 +--S 1 of 8 stuff := library "Neat.stuff" --R --R @@ -76885,7 +79989,7 @@ stuff := library "Neat.stuff" --R Type: Library --E 1 ---S 2 of 7 +--S 2 of 8 stuff.int := 32**2 --R --R @@ -76893,7 +79997,7 @@ stuff.int := 32**2 --R Type: PositiveInteger --E 2 ---S 3 of 7 +--S 3 of 8 stuff."poly" := x**2 + 1 --R --R @@ -76902,7 +80006,7 @@ stuff."poly" := x**2 + 1 --R Type: Polynomial(Integer) --E 3 ---S 4 of 7 +--S 4 of 8 stuff.str := "Hello" --R --R @@ -76910,7 +80014,7 @@ stuff.str := "Hello" --R Type: String --E 4 ---S 5 of 7 +--S 5 of 8 keys stuff --R --R @@ -76918,7 +80022,7 @@ keys stuff --R Type: List(String) --E 5 ---S 6 of 7 +--S 6 of 8 stuff.poly --R --R @@ -76927,7 +80031,7 @@ stuff.poly --R Type: Polynomial(Integer) --E 6 ---S 7 of 7 +--S 7 of 8 stuff("poly") --R --R @@ -76936,6 +80040,92 @@ stuff("poly") --R Type: Polynomial(Integer) --E 7 +--S 8 of 8 +)show Library +--R +--R Library is a domain constructor +--R Abbreviation for Library is LIB +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for LIB +--R +--R------------------------------- Operations -------------------------------- +--R close! : % -> % copy : % -> % +--R dictionary : () -> % ?.? : (%,Symbol) -> Any +--R elt : (%,String,Any) -> Any ?.? : (%,String) -> Any +--R empty : () -> % empty? : % -> Boolean +--R entries : % -> List(Any) eq? : (%,%) -> Boolean +--R index? : (String,%) -> Boolean indices : % -> List(String) +--R key? : (String,%) -> Boolean keys : % -> List(String) +--R library : FileName -> % map : ((Any -> Any),%) -> % +--R pack! : % -> % qelt : (%,String) -> Any +--R sample : () -> % setelt : (%,Symbol,Any) -> Any +--R setelt : (%,String,Any) -> Any table : () -> % +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R ?=? : (%,%) -> Boolean if Any has SETCAT or Record(key: String,entry: Any) has SETCAT +--R any? : ((Any -> Boolean),%) -> Boolean if $ has finiteAggregate +--R any? : ((Record(key: String,entry: Any) -> Boolean),%) -> Boolean if $ has finiteAggregate +--R bag : List(Record(key: String,entry: Any)) -> % +--R coerce : % -> OutputForm if Any has SETCAT or Record(key: String,entry: Any) has SETCAT +--R construct : List(Record(key: String,entry: Any)) -> % +--R convert : % -> InputForm if Record(key: String,entry: Any) has KONVERT(INFORM) +--R count : ((Any -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R count : (Any,%) -> NonNegativeInteger if $ has finiteAggregate and Any has SETCAT +--R count : (Record(key: String,entry: Any),%) -> NonNegativeInteger if $ has finiteAggregate and Record(key: String,entry: Any) has SETCAT +--R count : ((Record(key: String,entry: Any) -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R dictionary : List(Record(key: String,entry: Any)) -> % +--R entry? : (Any,%) -> Boolean if $ has finiteAggregate and Any has SETCAT +--R eval : (%,List(Equation(Any))) -> % if Any has EVALAB(ANY) and Any has SETCAT +--R eval : (%,Equation(Any)) -> % if Any has EVALAB(ANY) and Any has SETCAT +--R eval : (%,Any,Any) -> % if Any has EVALAB(ANY) and Any has SETCAT +--R eval : (%,List(Any),List(Any)) -> % if Any has EVALAB(ANY) and Any has SETCAT +--R eval : (%,List(Record(key: String,entry: Any)),List(Record(key: String,entry: Any))) -> % if Record(key: String,entry: Any) has EVALAB(Record(key: String,entry: Any)) and Record(key: String,entry: Any) has SETCAT +--R eval : (%,Record(key: String,entry: Any),Record(key: String,entry: Any)) -> % if Record(key: String,entry: Any) has EVALAB(Record(key: String,entry: Any)) and Record(key: String,entry: Any) has SETCAT +--R eval : (%,Equation(Record(key: String,entry: Any))) -> % if Record(key: String,entry: Any) has EVALAB(Record(key: String,entry: Any)) and Record(key: String,entry: Any) has SETCAT +--R eval : (%,List(Equation(Record(key: String,entry: Any)))) -> % if Record(key: String,entry: Any) has EVALAB(Record(key: String,entry: Any)) and Record(key: String,entry: Any) has SETCAT +--R every? : ((Any -> Boolean),%) -> Boolean if $ has finiteAggregate +--R every? : ((Record(key: String,entry: Any) -> Boolean),%) -> Boolean if $ has finiteAggregate +--R extract! : % -> Record(key: String,entry: Any) +--R fill! : (%,Any) -> % if $ has shallowlyMutable +--R find : ((Record(key: String,entry: Any) -> Boolean),%) -> Union(Record(key: String,entry: Any),"failed") +--R first : % -> Any if String has ORDSET +--R hash : % -> SingleInteger if Any has SETCAT or Record(key: String,entry: Any) has SETCAT +--R insert! : (Record(key: String,entry: Any),%) -> % +--R inspect : % -> Record(key: String,entry: Any) +--R latex : % -> String if Any has SETCAT or Record(key: String,entry: Any) has SETCAT +--R less? : (%,NonNegativeInteger) -> Boolean +--R map : (((Any,Any) -> Any),%,%) -> % +--R map : ((Record(key: String,entry: Any) -> Record(key: String,entry: Any)),%) -> % +--R map! : ((Any -> Any),%) -> % if $ has shallowlyMutable +--R map! : ((Record(key: String,entry: Any) -> Record(key: String,entry: Any)),%) -> % if $ has shallowlyMutable +--R maxIndex : % -> String if String has ORDSET +--R member? : (Any,%) -> Boolean if $ has finiteAggregate and Any has SETCAT +--R member? : (Record(key: String,entry: Any),%) -> Boolean if $ has finiteAggregate and Record(key: String,entry: Any) has SETCAT +--R members : % -> List(Any) if $ has finiteAggregate +--R members : % -> List(Record(key: String,entry: Any)) if $ has finiteAggregate +--R minIndex : % -> String if String has ORDSET +--R more? : (%,NonNegativeInteger) -> Boolean +--R parts : % -> List(Any) if $ has finiteAggregate +--R parts : % -> List(Record(key: String,entry: Any)) if $ has finiteAggregate +--R qsetelt! : (%,String,Any) -> Any if $ has shallowlyMutable +--R reduce : (((Record(key: String,entry: Any),Record(key: String,entry: Any)) -> Record(key: String,entry: Any)),%) -> Record(key: String,entry: Any) if $ has finiteAggregate +--R reduce : (((Record(key: String,entry: Any),Record(key: String,entry: Any)) -> Record(key: String,entry: Any)),%,Record(key: String,entry: Any)) -> Record(key: String,entry: Any) if $ has finiteAggregate +--R reduce : (((Record(key: String,entry: Any),Record(key: String,entry: Any)) -> Record(key: String,entry: Any)),%,Record(key: String,entry: Any),Record(key: String,entry: Any)) -> Record(key: String,entry: Any) if $ has finiteAggregate and Record(key: String,entry: Any) has SETCAT +--R remove : ((Record(key: String,entry: Any) -> Boolean),%) -> % if $ has finiteAggregate +--R remove : (Record(key: String,entry: Any),%) -> % if $ has finiteAggregate and Record(key: String,entry: Any) has SETCAT +--R remove! : (String,%) -> Union(Any,"failed") +--R remove! : ((Record(key: String,entry: Any) -> Boolean),%) -> % if $ has finiteAggregate +--R remove! : (Record(key: String,entry: Any),%) -> % if $ has finiteAggregate +--R removeDuplicates : % -> % if $ has finiteAggregate and Record(key: String,entry: Any) has SETCAT +--R search : (String,%) -> Union(Any,"failed") +--R select : ((Record(key: String,entry: Any) -> Boolean),%) -> % if $ has finiteAggregate +--R select! : ((Record(key: String,entry: Any) -> Boolean),%) -> % if $ has finiteAggregate +--R size? : (%,NonNegativeInteger) -> Boolean +--R swap! : (%,String,String) -> Void if $ has shallowlyMutable +--R table : List(Record(key: String,entry: Any)) -> % +--R ?~=? : (%,%) -> Boolean if Any has SETCAT or Record(key: String,entry: Any) has SETCAT +--R +--E 8 + )system rm -rf Neat.stuff )spool )lisp (bye) @@ -77107,7 +80297,8 @@ Library(): TableAggregate(String, Any) with )set message test on )set message auto off )clear all ---S 1 of 13 + +--S 1 of 14 a: Symbol := 'a --R --R @@ -77115,7 +80306,7 @@ a: Symbol := 'a --R Type: Symbol --E 1 ---S 2 of 13 +--S 2 of 14 b: Symbol := 'b --R --R @@ -77123,7 +80314,7 @@ b: Symbol := 'b --R Type: Symbol --E 2 ---S 3 of 13 +--S 3 of 14 coef := Fraction(Integer) --R --R @@ -77131,7 +80322,7 @@ coef := Fraction(Integer) --R Type: Domain --E 3 ---S 4 of 13 +--S 4 of 14 group := LieExponentials(Symbol, coef, 3) --R --R @@ -77139,7 +80330,7 @@ group := LieExponentials(Symbol, coef, 3) --R Type: Domain --E 4 ---S 5 of 13 +--S 5 of 14 lpoly := LiePolynomial(Symbol, coef) --R --R @@ -77147,7 +80338,7 @@ lpoly := LiePolynomial(Symbol, coef) --R Type: Domain --E 5 ---S 6 of 13 +--S 6 of 14 poly := XPBWPolynomial(Symbol, coef) --R --R @@ -77155,7 +80346,7 @@ poly := XPBWPolynomial(Symbol, coef) --R Type: Domain --E 6 ---S 7 of 13 +--S 7 of 14 ea := exp(a::lpoly)$group --R --R @@ -77164,7 +80355,7 @@ ea := exp(a::lpoly)$group --R Type: LieExponentials(Symbol,Fraction(Integer),3) --E 7 ---S 8 of 13 +--S 8 of 14 eb := exp(b::lpoly)$group --R --R @@ -77173,7 +80364,7 @@ eb := exp(b::lpoly)$group --R Type: LieExponentials(Symbol,Fraction(Integer),3) --E 8 ---S 9 of 13 +--S 9 of 14 g: group := ea*eb --R --R @@ -77184,7 +80375,7 @@ g: group := ea*eb --R Type: LieExponentials(Symbol,Fraction(Integer),3) --E 9 ---S 10 of 13 +--S 10 of 14 g :: poly --R --R @@ -77203,7 +80394,7 @@ g :: poly --R Type: XPBWPolynomial(Symbol,Fraction(Integer)) --E 10 ---S 11 of 13 +--S 11 of 14 log(g)$group --R --R @@ -77213,7 +80404,7 @@ log(g)$group --R Type: LiePolynomial(Symbol,Fraction(Integer)) --E 11 ---S 12 of 13 +--S 12 of 14 g1: group := inv(g) --R --R @@ -77222,13 +80413,44 @@ g1: group := inv(g) --R Type: LieExponentials(Symbol,Fraction(Integer),3) --E 12 ---S 13 of 13 +--S 13 of 14 g*g1 --R --R --R (13) 1 --R Type: LieExponentials(Symbol,Fraction(Integer),3) --E 13 + +--S 14 of 14 +)show LieExponentials +--R +--R LieExponentials(VarSet: OrderedSet,R: Join(CommutativeRing,Module(Fraction(Integer))),Order: PositiveInteger) is a domain constructor +--R Abbreviation for LieExponentials is LEXP +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for LEXP +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,%) -> % ?**? : (%,Integer) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % +--R ?/? : (%,%) -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % ?^? : (%,Integer) -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R coerce : % -> OutputForm commutator : (%,%) -> % +--R conjugate : (%,%) -> % exp : LiePolynomial(VarSet,R) -> % +--R hash : % -> SingleInteger inv : % -> % +--R latex : % -> String log : % -> LiePolynomial(VarSet,R) +--R mirror : % -> % one? : % -> Boolean +--R recip : % -> Union(%,"failed") sample : () -> % +--R varList : % -> List(VarSet) ?~=? : (%,%) -> Boolean +--R LyndonBasis : List(VarSet) -> List(LiePolynomial(VarSet,R)) +--R LyndonCoordinates : % -> List(Record(k: LyndonWord(VarSet),c: R)) +--R coerce : % -> XPBWPolynomial(VarSet,R) +--R coerce : % -> XDistributedPolynomial(VarSet,R) +--R identification : (%,%) -> List(Equation(R)) +--R listOfTerms : % -> List(Record(k: PoincareBirkhoffWittLyndonBasis(VarSet),c: R)) +--R +--E 14 + )spool )lisp (bye) \end{chunk} @@ -77501,7 +80723,8 @@ LieExponentials(VarSet, R, Order): XDPcat == XDPdef where )set message test on )set message auto off )clear all ---S 1 of 28 + +--S 1 of 29 RN := Fraction Integer --R --R @@ -77509,7 +80732,7 @@ RN := Fraction Integer --R Type: Domain --E 1 ---S 2 of 28 +--S 2 of 29 Lpoly := LiePolynomial(Symbol,RN) --R --R @@ -77517,7 +80740,7 @@ Lpoly := LiePolynomial(Symbol,RN) --R Type: Domain --E 2 ---S 3 of 28 +--S 3 of 29 Dpoly := XDPOLY(Symbol,RN) --R --R @@ -77525,7 +80748,7 @@ Dpoly := XDPOLY(Symbol,RN) --R Type: Domain --E 3 ---S 4 of 28 +--S 4 of 29 Lword := LyndonWord Symbol --R --R @@ -77533,7 +80756,7 @@ Lword := LyndonWord Symbol --R Type: Domain --E 4 ---S 5 of 28 +--S 5 of 29 a:Symbol := 'a --R --R @@ -77541,7 +80764,7 @@ a:Symbol := 'a --R Type: Symbol --E 5 ---S 6 of 28 +--S 6 of 29 b:Symbol := 'b --R --R @@ -77549,7 +80772,7 @@ b:Symbol := 'b --R Type: Symbol --E 6 ---S 7 of 28 +--S 7 of 29 c:Symbol := 'c --R --R @@ -77557,7 +80780,7 @@ c:Symbol := 'c --R Type: Symbol --E 7 ---S 8 of 28 +--S 8 of 29 aa: Lpoly := a --R --R @@ -77565,7 +80788,7 @@ aa: Lpoly := a --R Type: LiePolynomial(Symbol,Fraction(Integer)) --E 8 ---S 9 of 28 +--S 9 of 29 bb: Lpoly := b --R --R @@ -77573,7 +80796,7 @@ bb: Lpoly := b --R Type: LiePolynomial(Symbol,Fraction(Integer)) --E 9 ---S 10 of 28 +--S 10 of 29 cc: Lpoly := c --R --R @@ -77581,7 +80804,7 @@ cc: Lpoly := c --R Type: LiePolynomial(Symbol,Fraction(Integer)) --E 10 ---S 11 of 28 +--S 11 of 29 p : Lpoly := [aa,bb] --R --R @@ -77589,7 +80812,7 @@ p : Lpoly := [aa,bb] --R Type: LiePolynomial(Symbol,Fraction(Integer)) --E 11 ---S 12 of 28 +--S 12 of 29 q : Lpoly := [p,bb] --R --R @@ -77598,7 +80821,7 @@ q : Lpoly := [p,bb] --R Type: LiePolynomial(Symbol,Fraction(Integer)) --E 12 ---S 13 of 28 +--S 13 of 29 liste : List Lword := LyndonWordsList([a,b], 4) --R --R @@ -77607,7 +80830,7 @@ liste : List Lword := LyndonWordsList([a,b], 4) --R Type: List(LyndonWord(Symbol)) --E 13 ---S 14 of 28 +--S 14 of 29 r: Lpoly := p + q + 3*LiePoly(liste.4)$Lpoly --R --R @@ -77616,7 +80839,7 @@ r: Lpoly := p + q + 3*LiePoly(liste.4)$Lpoly --R Type: LiePolynomial(Symbol,Fraction(Integer)) --E 14 ---S 15 of 28 +--S 15 of 29 s:Lpoly := [p,r] --R --R @@ -77625,7 +80848,7 @@ s:Lpoly := [p,r] --R Type: LiePolynomial(Symbol,Fraction(Integer)) --E 15 ---S 16 of 28 +--S 16 of 29 t:Lpoly := s + 2*LiePoly(liste.3) - 5*LiePoly(liste.5) --R --R @@ -77634,7 +80857,7 @@ t:Lpoly := s + 2*LiePoly(liste.3) - 5*LiePoly(liste.5) --R Type: LiePolynomial(Symbol,Fraction(Integer)) --E 16 ---S 17 of 28 +--S 17 of 29 degree t --R --R @@ -77642,7 +80865,7 @@ degree t --R Type: PositiveInteger --E 17 ---S 18 of 28 +--S 18 of 29 mirror t --R --R @@ -77651,7 +80874,7 @@ mirror t --R Type: LiePolynomial(Symbol,Fraction(Integer)) --E 18 ---S 19 of 28 +--S 19 of 29 Jacobi(p: Lpoly, q: Lpoly, r: Lpoly): Lpoly == _ [ [p,q]$Lpoly, r] + [ [q,r]$Lpoly, p] + [ [r,p]$Lpoly, q] --R @@ -77662,7 +80885,7 @@ Jacobi(p: Lpoly, q: Lpoly, r: Lpoly): Lpoly == _ --R Type: Void --E 19 ---S 20 of 28 +--S 20 of 29 test: Lpoly := Jacobi(a,b,b) --R --R Compiling function Jacobi with type (LiePolynomial(Symbol,Fraction( @@ -77674,7 +80897,7 @@ test: Lpoly := Jacobi(a,b,b) --R Type: LiePolynomial(Symbol,Fraction(Integer)) --E 20 ---S 21 of 28 +--S 21 of 29 test: Lpoly := Jacobi(p,q,r) --R --R @@ -77682,7 +80905,7 @@ test: Lpoly := Jacobi(p,q,r) --R Type: LiePolynomial(Symbol,Fraction(Integer)) --E 21 ---S 22 of 28 +--S 22 of 29 test: Lpoly := Jacobi(r,s,t) --R --R @@ -77690,7 +80913,7 @@ test: Lpoly := Jacobi(r,s,t) --R Type: LiePolynomial(Symbol,Fraction(Integer)) --E 22 ---S 23 of 28 +--S 23 of 29 eval(p, a, p)$Lpoly --R --R @@ -77699,7 +80922,7 @@ eval(p, a, p)$Lpoly --R Type: LiePolynomial(Symbol,Fraction(Integer)) --E 23 ---S 24 of 28 +--S 24 of 29 eval(p, [a,b], [2*bb, 3*aa])$Lpoly --R --R @@ -77707,7 +80930,7 @@ eval(p, [a,b], [2*bb, 3*aa])$Lpoly --R Type: LiePolynomial(Symbol,Fraction(Integer)) --E 24 ---S 25 of 28 +--S 25 of 29 r: Lpoly := [p,c] --R --R @@ -77715,7 +80938,7 @@ r: Lpoly := [p,c] --R Type: LiePolynomial(Symbol,Fraction(Integer)) --E 25 ---S 26 of 28 +--S 26 of 29 r1: Lpoly := eval(r, [a,b,c], [bb, cc, aa])$Lpoly --R --R @@ -77723,7 +80946,7 @@ r1: Lpoly := eval(r, [a,b,c], [bb, cc, aa])$Lpoly --R Type: LiePolynomial(Symbol,Fraction(Integer)) --E 26 ---S 27 of 28 +--S 27 of 29 r2: Lpoly := eval(r, [a,b,c], [cc, aa, bb])$Lpoly --R --R @@ -77731,13 +80954,61 @@ r2: Lpoly := eval(r, [a,b,c], [cc, aa, bb])$Lpoly --R Type: LiePolynomial(Symbol,Fraction(Integer)) --E 27 ---S 28 of 28 +--S 28 of 29 r + r1 + r2 --R --R --R (28) 0 --R Type: LiePolynomial(Symbol,Fraction(Integer)) --E 28 + +--S 29 of 29 +)show LiePolynomial +--R +--R LiePolynomial(VarSet: OrderedSet,R: CommutativeRing) is a domain constructor +--R Abbreviation for LiePolynomial is LPOLY +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for LPOLY +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (R,LyndonWord(VarSet)) -> % ?*? : (%,R) -> % +--R ?*? : (R,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?/? : (%,R) -> % if R has FIELD +--R ?=? : (%,%) -> Boolean LiePoly : LyndonWord(VarSet) -> % +--R 0 : () -> % coefficients : % -> List(R) +--R coerce : LyndonWord(VarSet) -> % coerce : VarSet -> % +--R coerce : % -> OutputForm construct : (%,%) -> % +--R degree : % -> NonNegativeInteger eval : (%,VarSet,%) -> % +--R hash : % -> SingleInteger latex : % -> String +--R leadingCoefficient : % -> R map : ((R -> R),%) -> % +--R mirror : % -> % monom : (LyndonWord(VarSet),R) -> % +--R monomial? : % -> Boolean monomials : % -> List(%) +--R reductum : % -> % retract : % -> LyndonWord(VarSet) +--R sample : () -> % varList : % -> List(VarSet) +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R LiePolyIfCan : XDistributedPolynomial(VarSet,R) -> Union(%,"failed") +--R coef : (XRecursivePolynomial(VarSet,R),%) -> R +--R coefficient : (%,LyndonWord(VarSet)) -> R +--R coerce : % -> XRecursivePolynomial(VarSet,R) +--R coerce : % -> XDistributedPolynomial(VarSet,R) +--R construct : (%,LyndonWord(VarSet)) -> % +--R construct : (LyndonWord(VarSet),%) -> % +--R construct : (LyndonWord(VarSet),LyndonWord(VarSet)) -> % +--R eval : (%,List(VarSet),List(%)) -> % +--R leadingMonomial : % -> LyndonWord(VarSet) +--R leadingTerm : % -> Record(k: LyndonWord(VarSet),c: R) +--R listOfTerms : % -> List(Record(k: LyndonWord(VarSet),c: R)) +--R lquo : (XRecursivePolynomial(VarSet,R),%) -> XRecursivePolynomial(VarSet,R) +--R numberOfMonomials : % -> NonNegativeInteger +--R retractIfCan : % -> Union(LyndonWord(VarSet),"failed") +--R rquo : (XRecursivePolynomial(VarSet,R),%) -> XRecursivePolynomial(VarSet,R) +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R trunc : (%,NonNegativeInteger) -> % +--R +--E 29 + )spool )lisp (bye) @@ -78158,11 +81429,13 @@ LiePolynomial(VarSet:OrderedSet, R:CommutativeRing) : Public == Private where --R------------------------------- Operations -------------------------------- --R ?*? : (R,%) -> % ?*? : (%,R) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % ---R -? : % -> % ?=? : (%,%) -> Boolean ---R D : % -> % if R has DIFRING D : (%,(R -> R)) -> % ---R 1 : () -> % 0 : () -> % +--R -? : % -> % ?/? : (%,R) -> % if R has FIELD +--R ?=? : (%,%) -> Boolean D : % -> % if R has DIFRING +--R D : (%,(R -> R)) -> % 1 : () -> % +--R 0 : () -> % ?^? : (%,NonNegativeInteger) -> % --R ?^? : (%,PositiveInteger) -> % alternative? : () -> Boolean --R antiAssociative? : () -> Boolean antiCommutative? : () -> Boolean --R antiCommutator : (%,%) -> % antisymmetric? : % -> Boolean @@ -78173,8 +81446,9 @@ LiePolynomial(VarSet:OrderedSet, R:CommutativeRing) : Public == Private where --R commutative? : () -> Boolean commutator : (%,%) -> % --R convert : % -> Vector(R) convert : Vector(R) -> % --R coordinates : % -> Vector(R) copy : % -> % ---R diagonal? : % -> Boolean diagonalMatrix : List(R) -> % ---R diagonalProduct : % -> R ?.? : (%,Integer) -> R +--R diagonal : % -> DirectProduct(n,R) diagonal? : % -> Boolean +--R diagonalMatrix : List(R) -> % diagonalProduct : % -> R +--R differentiate : (%,(R -> R)) -> % ?.? : (%,Integer) -> R --R elt : (%,Integer,Integer) -> R elt : (%,Integer,Integer,R) -> R --R empty : () -> % empty? : % -> Boolean --R eq? : (%,%) -> Boolean flexible? : () -> Boolean @@ -78193,27 +81467,23 @@ LiePolynomial(VarSet:OrderedSet, R:CommutativeRing) : Public == Private where --R powerAssociative? : () -> Boolean qelt : (%,Integer,Integer) -> R --R rank : () -> PositiveInteger recip : % -> Union(%,"failed") --R represents : Vector(R) -> % retract : % -> R ---R rightAlternative? : () -> Boolean rightDiscriminant : () -> R ---R rightNorm : % -> R rightTrace : % -> R ---R rightTraceMatrix : () -> Matrix(R) sample : () -> % ---R scalarMatrix : R -> % someBasis : () -> Vector(%) ---R square? : % -> Boolean symmetric? : % -> Boolean ---R trace : % -> R zero? : % -> Boolean ---R ?~=? : (%,%) -> Boolean +--R rightAlternative? : () -> Boolean rightDiscriminant : Vector(%) -> R +--R rightDiscriminant : () -> R rightNorm : % -> R +--R rightTrace : % -> R rightTraceMatrix : () -> Matrix(R) +--R sample : () -> % scalarMatrix : R -> % +--R someBasis : () -> Vector(%) square? : % -> Boolean +--R symmetric? : % -> Boolean trace : % -> R +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R ?*? : (DirectProduct(n,R),%) -> DirectProduct(n,R) --R ?*? : (%,DirectProduct(n,R)) -> DirectProduct(n,R) ---R ?*? : (NonNegativeInteger,%) -> % --R ?**? : (%,Integer) -> % if R has FIELD ---R ?**? : (%,NonNegativeInteger) -> % ---R ?/? : (%,R) -> % if R has FIELD --R D : (%,NonNegativeInteger) -> % if R has DIFRING --R D : (%,Symbol) -> % if R has PDRING(SYMBOL) --R D : (%,List(Symbol)) -> % if R has PDRING(SYMBOL) --R D : (%,Symbol,NonNegativeInteger) -> % if R has PDRING(SYMBOL) --R D : (%,List(Symbol),List(NonNegativeInteger)) -> % if R has PDRING(SYMBOL) --R D : (%,(R -> R),NonNegativeInteger) -> % ---R ?^? : (%,NonNegativeInteger) -> % --R any? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate --R associatorDependence : () -> List(Vector(R)) if R has INTDOM --R characteristic : () -> NonNegativeInteger @@ -78227,7 +81497,6 @@ LiePolynomial(VarSet:OrderedSet, R:CommutativeRing) : Public == Private where --R count : (R,%) -> NonNegativeInteger if $ has finiteAggregate and R has SETCAT --R count : ((R -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate --R determinant : % -> R if R has commutative(*) ---R diagonal : % -> DirectProduct(n,R) --R differentiate : % -> % if R has DIFRING --R differentiate : (%,NonNegativeInteger) -> % if R has DIFRING --R differentiate : (%,Symbol) -> % if R has PDRING(SYMBOL) @@ -78235,7 +81504,6 @@ LiePolynomial(VarSet:OrderedSet, R:CommutativeRing) : Public == Private where --R differentiate : (%,Symbol,NonNegativeInteger) -> % if R has PDRING(SYMBOL) --R differentiate : (%,List(Symbol),List(NonNegativeInteger)) -> % if R has PDRING(SYMBOL) --R differentiate : (%,(R -> R),NonNegativeInteger) -> % ---R differentiate : (%,(R -> R)) -> % --R eval : (%,List(R),List(R)) -> % if R has EVALAB(R) and R has SETCAT --R eval : (%,R,R) -> % if R has EVALAB(R) and R has SETCAT --R eval : (%,Equation(R)) -> % if R has EVALAB(R) and R has SETCAT @@ -78276,7 +81544,6 @@ LiePolynomial(VarSet:OrderedSet, R:CommutativeRing) : Public == Private where --R retractIfCan : % -> Union(Fraction(Integer),"failed") if R has RETRACT(FRAC(INT)) --R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT(INT) --R rightCharacteristicPolynomial : % -> SparseUnivariatePolynomial(R) ---R rightDiscriminant : Vector(%) -> R --R rightMinimalPolynomial : % -> SparseUnivariatePolynomial(R) if R has INTDOM --R rightPower : (%,PositiveInteger) -> % --R rightRankPolynomial : () -> SparseUnivariatePolynomial(Polynomial(R)) if R has FIELD @@ -78550,13 +81817,14 @@ LieSquareMatrix(n,R): Exports == Implementation where )set message test on )set message auto off )clear all ---S 1 of 16 + +--S 1 of 17 Dx: LODO(EXPR INT, f +-> D(f, x)) --R --R Type: Void --E 1 ---S 2 of 16 +--S 2 of 17 Dx := D() --R --R @@ -78564,7 +81832,7 @@ Dx := D() --IType: LinearOrdinaryDifferentialOperator(Expression(Integer),... --E 2 ---S 3 of 16 +--S 3 of 17 Dop:= Dx^3 + G/x^2*Dx + H/x^3 - 1 --R --R @@ -78576,55 +81844,55 @@ Dop:= Dx^3 + G/x^2*Dx + H/x^3 - 1 --IType: LinearOrdinaryDifferentialOperator(Expression(Integer),... --E 3 ---S 4 of 16 +--S 4 of 17 n == 3 --R --R Type: Void --E 4 ---S 5 of 16 +--S 5 of 17 phi == reduce(+,[subscript(s,[i])*exp(x)/x^i for i in 0..n]) --R --R Type: Void --E 5 ---S 6 of 16 +--S 6 of 17 phi1 == Dop(phi) / exp x --R --R Type: Void --E 6 ---S 7 of 16 +--S 7 of 17 phi2 == phi1 *x**(n+3) --R --R Type: Void --E 7 ---S 8 of 16 +--S 8 of 17 phi3 == retract(phi2)@(POLY INT) --R --R Type: Void --E 8 ---S 9 of 16 +--S 9 of 17 pans == phi3 ::UP(x,POLY INT) --R --R Type: Void --E 9 ---S 10 of 16 +--S 10 of 17 pans1 == [coefficient(pans, (n+3-i) :: NNI) for i in 2..n+1] --R --R Type: Void --E 10 ---S 11 of 16 +--S 11 of 17 leq == solve(pans1,[subscript(s,[i]) for i in 1..n]) --R --R Type: Void --E 11 ---S 12 of 16 +--S 12 of 17 leq --R --R Compiling body of rule n to compute value of type PositiveInteger @@ -78653,7 +81921,7 @@ leq --R Type: List(List(Equation(Fraction(Polynomial(Integer))))) --E 12 ---S 13 of 16 +--S 13 of 17 n==4 --R --R Compiled code for n has been cleared. @@ -78668,7 +81936,7 @@ n==4 --R Type: Void --E 13 ---S 14 of 16 +--S 14 of 17 leq --R --R Compiling body of rule n to compute value of type PositiveInteger @@ -78715,7 +81983,7 @@ leq --R Type: List(List(Equation(Fraction(Polynomial(Integer))))) --E 14 ---S 15 of 16 +--S 15 of 17 n==7 --R --R Compiled code for n has been cleared. @@ -78730,7 +81998,7 @@ n==7 --R Type: Void --E 15 ---S 16 of 16 +--S 16 of 17 leq --R --R Compiling body of rule n to compute value of type PositiveInteger @@ -78830,6 +82098,70 @@ leq --R ] --R Type: List(List(Equation(Fraction(Polynomial(Integer))))) --E 16 + +--S 17 of 17 +)show LinearOrdinaryDifferentialOperator +--R +--R LinearOrdinaryDifferentialOperator(A: Ring,diff: (A -> A)) is a domain constructor +--R Abbreviation for LinearOrdinaryDifferentialOperator is LODO +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for LODO +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (A,%) -> % ?*? : (%,A) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R D : () -> % 1 : () -> % +--R 0 : () -> % ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,PositiveInteger) -> % adjoint : % -> % +--R apply : (%,A,A) -> A coefficients : % -> List(A) +--R coerce : A -> % coerce : Integer -> % +--R coerce : % -> OutputForm content : % -> A if A has GCDDOM +--R degree : % -> NonNegativeInteger ?.? : (%,A) -> A +--R hash : % -> SingleInteger latex : % -> String +--R leadingCoefficient : % -> A one? : % -> Boolean +--R recip : % -> Union(%,"failed") reductum : % -> % +--R retract : % -> A sample : () -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R characteristic : () -> NonNegativeInteger +--R coefficient : (%,NonNegativeInteger) -> A +--R coerce : Fraction(Integer) -> % if A has RETRACT(FRAC(INT)) +--R directSum : (%,%) -> % if A has FIELD +--R exquo : (%,A) -> Union(%,"failed") if A has INTDOM +--R leftDivide : (%,%) -> Record(quotient: %,remainder: %) if A has FIELD +--R leftExactQuotient : (%,%) -> Union(%,"failed") if A has FIELD +--R leftExtendedGcd : (%,%) -> Record(coef1: %,coef2: %,generator: %) if A has FIELD +--R leftGcd : (%,%) -> % if A has FIELD +--R leftLcm : (%,%) -> % if A has FIELD +--R leftQuotient : (%,%) -> % if A has FIELD +--R leftRemainder : (%,%) -> % if A has FIELD +--R minimumDegree : % -> NonNegativeInteger +--R monicLeftDivide : (%,%) -> Record(quotient: %,remainder: %) if A has INTDOM +--R monicRightDivide : (%,%) -> Record(quotient: %,remainder: %) if A has INTDOM +--R monomial : (A,NonNegativeInteger) -> % +--R primitivePart : % -> % if A has GCDDOM +--R retract : % -> Fraction(Integer) if A has RETRACT(FRAC(INT)) +--R retract : % -> Integer if A has RETRACT(INT) +--R retractIfCan : % -> Union(A,"failed") +--R retractIfCan : % -> Union(Fraction(Integer),"failed") if A has RETRACT(FRAC(INT)) +--R retractIfCan : % -> Union(Integer,"failed") if A has RETRACT(INT) +--R rightDivide : (%,%) -> Record(quotient: %,remainder: %) if A has FIELD +--R rightExactQuotient : (%,%) -> Union(%,"failed") if A has FIELD +--R rightExtendedGcd : (%,%) -> Record(coef1: %,coef2: %,generator: %) if A has FIELD +--R rightGcd : (%,%) -> % if A has FIELD +--R rightLcm : (%,%) -> % if A has FIELD +--R rightQuotient : (%,%) -> % if A has FIELD +--R rightRemainder : (%,%) -> % if A has FIELD +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R symmetricPower : (%,NonNegativeInteger) -> % if A has FIELD +--R symmetricProduct : (%,%) -> % if A has FIELD +--R symmetricSquare : % -> % if A has FIELD +--R +--E 17 + )spool \end{chunk} @@ -79142,7 +82474,8 @@ LinearOrdinaryDifferentialOperator(A:Ring, diff: A -> A): )set message test on )set message auto off )clear all ---S 1 of 20 + +--S 1 of 21 RFZ := Fraction UnivariatePolynomial('x, Integer) --R --R @@ -79150,7 +82483,7 @@ RFZ := Fraction UnivariatePolynomial('x, Integer) --R Type: Domain --E 1 ---S 2 of 20 +--S 2 of 21 x : RFZ := 'x --R --R @@ -79158,7 +82491,7 @@ x : RFZ := 'x --R Type: Fraction(UnivariatePolynomial(x,Integer)) --E 2 ---S 3 of 20 +--S 3 of 21 Dx : LODO1 RFZ := D() --R --R @@ -79166,7 +82499,7 @@ Dx : LODO1 RFZ := D() --RType: LinearOrdinaryDifferentialOperator1(Fraction(UnivariatePolynomial(x,Integer))) --E 3 ---S 4 of 20 +--S 4 of 21 b : LODO1 RFZ := 3*x**2*Dx**2 + 2*Dx + 1/x --R --R @@ -79176,7 +82509,7 @@ b : LODO1 RFZ := 3*x**2*Dx**2 + 2*Dx + 1/x --RType: LinearOrdinaryDifferentialOperator1(Fraction(UnivariatePolynomial(x,Integer))) --E 4 ---S 5 of 20 +--S 5 of 21 a : LODO1 RFZ := b*(5*x*Dx + 7) --R --R @@ -79186,7 +82519,7 @@ a : LODO1 RFZ := b*(5*x*Dx + 7) --RType: LinearOrdinaryDifferentialOperator1(Fraction(UnivariatePolynomial(x,Integer))) --E 5 ---S 6 of 20 +--S 6 of 21 p := x**2 + 1/x**2 --R --R @@ -79198,7 +82531,7 @@ p := x**2 + 1/x**2 --R Type: Fraction(UnivariatePolynomial(x,Integer)) --E 6 ---S 7 of 20 +--S 7 of 21 (a*b - b*a) p --R --R @@ -79210,7 +82543,7 @@ p := x**2 + 1/x**2 --R Type: Fraction(UnivariatePolynomial(x,Integer)) --E 7 ---S 8 of 20 +--S 8 of 21 ld := leftDivide(a,b) --R --R @@ -79218,7 +82551,7 @@ ld := leftDivide(a,b) --IType: Record(quotient: LinearOrdinaryDifferentialOperator1(Fraction(... --E 8 ---S 9 of 20 +--S 9 of 21 a = b * ld.quotient + ld.remainder --R --R @@ -79228,7 +82561,7 @@ a = b * ld.quotient + ld.remainder --RType: Equation(LinearOrdinaryDifferentialOperator1(Fraction(UnivariatePolynomial(x,Integer)))) --E 9 ---S 10 of 20 +--S 10 of 21 rd := rightDivide(a,b) --R --R @@ -79238,7 +82571,7 @@ rd := rightDivide(a,b) --IType: Record(quotient: LinearOrdinaryDifferentialOperator1(... --E 10 ---S 11 of 20 +--S 11 of 21 a = rd.quotient * b + rd.remainder --R --R @@ -79248,7 +82581,7 @@ a = rd.quotient * b + rd.remainder --RType: Equation(LinearOrdinaryDifferentialOperator1(Fraction(UnivariatePolynomial(x,Integer)))) --E 11 ---S 12 of 20 +--S 12 of 21 rightQuotient(a,b) --R --R @@ -79256,7 +82589,7 @@ rightQuotient(a,b) --RType: LinearOrdinaryDifferentialOperator1(Fraction(UnivariatePolynomial(x,Integer))) --E 12 ---S 13 of 20 +--S 13 of 21 rightRemainder(a,b) --R --R @@ -79266,7 +82599,7 @@ rightRemainder(a,b) --RType: LinearOrdinaryDifferentialOperator1(Fraction(UnivariatePolynomial(x,Integer))) --E 13 ---S 14 of 20 +--S 14 of 21 leftExactQuotient(a,b) --R --R @@ -79274,7 +82607,7 @@ leftExactQuotient(a,b) --RType: Union(LinearOrdinaryDifferentialOperator1(Fraction(UnivariatePolynomial(x,Integer))),...) --E 14 ---S 15 of 20 +--S 15 of 21 e := leftGcd(a,b) --R --R @@ -79284,7 +82617,7 @@ e := leftGcd(a,b) --RType: LinearOrdinaryDifferentialOperator1(Fraction(UnivariatePolynomial(x,Integer))) --E 15 ---S 16 of 20 +--S 16 of 21 leftRemainder(a, e) --R --R @@ -79292,7 +82625,7 @@ leftRemainder(a, e) --RType: LinearOrdinaryDifferentialOperator1(Fraction(UnivariatePolynomial(x,Integer))) --E 16 ---S 17 of 20 +--S 17 of 21 rightRemainder(a, e) --R --R @@ -79302,7 +82635,7 @@ rightRemainder(a, e) --RType: LinearOrdinaryDifferentialOperator1(Fraction(UnivariatePolynomial(x,Integer))) --E 17 ---S 18 of 20 +--S 18 of 21 f := rightLcm(a,b) --R --R @@ -79312,7 +82645,7 @@ f := rightLcm(a,b) --RType: LinearOrdinaryDifferentialOperator1(Fraction(UnivariatePolynomial(x,Integer))) --E 18 ---S 19 of 20 +--S 19 of 21 rightRemainder(f, b) --R --R @@ -79322,13 +82655,77 @@ rightRemainder(f, b) --RType: LinearOrdinaryDifferentialOperator1(Fraction(UnivariatePolynomial(x,Integer))) --E 19 ---S 20 of 20 +--S 20 of 21 leftRemainder(f, b) --R --R --R (20) 0 --RType: LinearOrdinaryDifferentialOperator1(Fraction(UnivariatePolynomial(x,Integer))) --E 20 + +--S 21 of 21 +)show LinearOrdinaryDifferentialOperator1 +--R +--R LinearOrdinaryDifferentialOperator1(A: DifferentialRing) is a domain constructor +--R Abbreviation for LinearOrdinaryDifferentialOperator1 is LODO1 +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for LODO1 +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (A,%) -> % ?*? : (%,A) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R D : () -> % 1 : () -> % +--R 0 : () -> % ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,PositiveInteger) -> % adjoint : % -> % +--R apply : (%,A,A) -> A coefficients : % -> List(A) +--R coerce : A -> % coerce : Integer -> % +--R coerce : % -> OutputForm content : % -> A if A has GCDDOM +--R degree : % -> NonNegativeInteger ?.? : (%,A) -> A +--R hash : % -> SingleInteger latex : % -> String +--R leadingCoefficient : % -> A one? : % -> Boolean +--R recip : % -> Union(%,"failed") reductum : % -> % +--R retract : % -> A sample : () -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R characteristic : () -> NonNegativeInteger +--R coefficient : (%,NonNegativeInteger) -> A +--R coerce : Fraction(Integer) -> % if A has RETRACT(FRAC(INT)) +--R directSum : (%,%) -> % if A has FIELD +--R exquo : (%,A) -> Union(%,"failed") if A has INTDOM +--R leftDivide : (%,%) -> Record(quotient: %,remainder: %) if A has FIELD +--R leftExactQuotient : (%,%) -> Union(%,"failed") if A has FIELD +--R leftExtendedGcd : (%,%) -> Record(coef1: %,coef2: %,generator: %) if A has FIELD +--R leftGcd : (%,%) -> % if A has FIELD +--R leftLcm : (%,%) -> % if A has FIELD +--R leftQuotient : (%,%) -> % if A has FIELD +--R leftRemainder : (%,%) -> % if A has FIELD +--R minimumDegree : % -> NonNegativeInteger +--R monicLeftDivide : (%,%) -> Record(quotient: %,remainder: %) if A has INTDOM +--R monicRightDivide : (%,%) -> Record(quotient: %,remainder: %) if A has INTDOM +--R monomial : (A,NonNegativeInteger) -> % +--R primitivePart : % -> % if A has GCDDOM +--R retract : % -> Fraction(Integer) if A has RETRACT(FRAC(INT)) +--R retract : % -> Integer if A has RETRACT(INT) +--R retractIfCan : % -> Union(A,"failed") +--R retractIfCan : % -> Union(Fraction(Integer),"failed") if A has RETRACT(FRAC(INT)) +--R retractIfCan : % -> Union(Integer,"failed") if A has RETRACT(INT) +--R rightDivide : (%,%) -> Record(quotient: %,remainder: %) if A has FIELD +--R rightExactQuotient : (%,%) -> Union(%,"failed") if A has FIELD +--R rightExtendedGcd : (%,%) -> Record(coef1: %,coef2: %,generator: %) if A has FIELD +--R rightGcd : (%,%) -> % if A has FIELD +--R rightLcm : (%,%) -> % if A has FIELD +--R rightQuotient : (%,%) -> % if A has FIELD +--R rightRemainder : (%,%) -> % if A has FIELD +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R symmetricPower : (%,NonNegativeInteger) -> % if A has FIELD +--R symmetricProduct : (%,%) -> % if A has FIELD +--R symmetricSquare : % -> % if A has FIELD +--R +--E 21 + )spool )lisp (bye) \end{chunk} @@ -79623,7 +83020,8 @@ LinearOrdinaryDifferentialOperator1(A:DifferentialRing) == )set message test on )set message auto off )clear all ---S 1 of 26 + +--S 1 of 27 Q := Fraction Integer --R --R @@ -79631,7 +83029,7 @@ Q := Fraction Integer --R Type: Domain --E 1 ---S 2 of 26 +--S 2 of 27 PQ := UnivariatePolynomial('x, Q) --R --R @@ -79639,7 +83037,7 @@ PQ := UnivariatePolynomial('x, Q) --R Type: Domain --E 2 ---S 3 of 26 +--S 3 of 27 x: PQ := 'x --R --R @@ -79647,7 +83045,7 @@ x: PQ := 'x --R Type: UnivariatePolynomial(x,Fraction(Integer)) --E 3 ---S 4 of 26 +--S 4 of 27 Dx: LODO2(Q, PQ) := D() --R --R @@ -79655,7 +83053,7 @@ Dx: LODO2(Q, PQ) := D() --RType: LinearOrdinaryDifferentialOperator2(Fraction(Integer),UnivariatePolynomial(x,Fraction(Integer))) --E 4 ---S 5 of 26 +--S 5 of 27 a := Dx + 1 --R --R @@ -79663,7 +83061,7 @@ a := Dx + 1 --RType: LinearOrdinaryDifferentialOperator2(Fraction(Integer),UnivariatePolynomial(x,Fraction(Integer))) --E 5 ---S 6 of 26 +--S 6 of 27 b := a + 1/2*Dx**2 - 1/2 --R --R @@ -79673,7 +83071,7 @@ b := a + 1/2*Dx**2 - 1/2 --RType: LinearOrdinaryDifferentialOperator2(Fraction(Integer),UnivariatePolynomial(x,Fraction(Integer))) --E 6 ---S 7 of 26 +--S 7 of 27 p := 4*x**2 + 2/3 --R --R @@ -79683,7 +83081,7 @@ p := 4*x**2 + 2/3 --R Type: UnivariatePolynomial(x,Fraction(Integer)) --E 7 ---S 8 of 26 +--S 8 of 27 a p --R --R @@ -79693,7 +83091,7 @@ a p --R Type: UnivariatePolynomial(x,Fraction(Integer)) --E 8 ---S 9 of 26 +--S 9 of 27 (a * b) p = a b p --R --R @@ -79703,7 +83101,7 @@ a p --R Type: Equation(UnivariatePolynomial(x,Fraction(Integer))) --E 9 ---S 10 of 26 +--S 10 of 27 c := (1/9)*b*(a + b)^2 --R --R @@ -79713,7 +83111,7 @@ c := (1/9)*b*(a + b)^2 --RType: LinearOrdinaryDifferentialOperator2(Fraction(Integer),UnivariatePolynomial(x,Fraction(Integer))) --E 10 ---S 11 of 26 +--S 11 of 27 (a**2 - 3/4*b + c) (p + 1) --R --R @@ -79723,7 +83121,7 @@ c := (1/9)*b*(a + b)^2 --R Type: UnivariatePolynomial(x,Fraction(Integer)) --E 11 )clear all ---S 12 of 26 +--S 12 of 27 PZ := UnivariatePolynomial(x,Integer) --R --R @@ -79731,7 +83129,7 @@ PZ := UnivariatePolynomial(x,Integer) --R Type: Domain --E 12 ---S 13 of 26 +--S 13 of 27 x:PZ := 'x --R --R @@ -79739,7 +83137,7 @@ x:PZ := 'x --R Type: UnivariatePolynomial(x,Integer) --E 13 ---S 14 of 26 +--S 14 of 27 Mat := SquareMatrix(3,PZ) --R --R @@ -79747,7 +83145,7 @@ Mat := SquareMatrix(3,PZ) --R Type: Domain --E 14 ---S 15 of 26 +--S 15 of 27 Vect := DPMM(3, PZ, Mat, PZ) --R --R @@ -79757,7 +83155,7 @@ Vect := DPMM(3, PZ, Mat, PZ) --R Type: Domain --E 15 ---S 16 of 26 +--S 16 of 27 Modo := LODO2(Mat, Vect) --R --R @@ -79768,7 +83166,7 @@ Modo := LODO2(Mat, Vect) --R Type: Domain --E 16 ---S 17 of 26 +--S 17 of 27 m:Mat := matrix [ [x^2,1,0],[1,x^4,0],[0,0,4*x^2] ] --R --R @@ -79783,7 +83181,7 @@ m:Mat := matrix [ [x^2,1,0],[1,x^4,0],[0,0,4*x^2] ] --R Type: SquareMatrix(3,UnivariatePolynomial(x,Integer)) --E 17 ---S 18 of 26 +--S 18 of 27 p:Vect := directProduct [3*x^2+1,2*x,7*x^3+2*x] --R --R @@ -79792,7 +83190,7 @@ p:Vect := directProduct [3*x^2+1,2*x,7*x^3+2*x] --IType: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),... --E 18 ---S 19 of 26 +--S 19 of 27 q: Vect := m * p --R --R @@ -79801,7 +83199,7 @@ q: Vect := m * p --IType: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),... --E 19 ---S 20 of 26 +--S 20 of 27 Dx : Modo := D() --R --R @@ -79809,7 +83207,7 @@ Dx : Modo := D() --IType: LinearOrdinaryDifferentialOperator2(SquareMatrix(... --E 20 ---S 21 of 26 +--S 21 of 27 a : Modo := Dx + m --R --R @@ -79824,7 +83222,7 @@ a : Modo := Dx + m --IType: LinearOrdinaryDifferentialOperator2(SquareMatrix(... --E 21 ---S 22 of 26 +--S 22 of 27 b : Modo := m*Dx + 1 --R --R @@ -79839,7 +83237,7 @@ b : Modo := m*Dx + 1 --IType: LinearOrdinaryDifferentialOperator2(SquareMatrix(... --E 22 ---S 23 of 26 +--S 23 of 27 c := a*b --R --R @@ -79855,7 +83253,7 @@ c := a*b --IType: LinearOrdinaryDifferentialOperator2(SquareMatrix(3,... --E 23 ---S 24 of 26 +--S 24 of 27 a p --R --R @@ -79864,7 +83262,7 @@ a p --IType: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),... --E 24 ---S 25 of 26 +--S 25 of 27 b p --R --R @@ -79873,7 +83271,7 @@ b p --IType: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),... --E 25 ---S 26 of 26 +--S 26 of 27 (a + b + c) (p + q) --R --R @@ -79886,6 +83284,73 @@ b p --R 2240x + 224x + 1280x + 3508x + 492x + 751x + 98x + 18x + 4] --IType: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),... --E 26 + +--S 27 of 27 +)show LinearOrdinaryDifferentialOperator2 +--R +--R LinearOrdinaryDifferentialOperator2(A: DifferentialRing,M)where +--R M: LeftModule(A)with +--R differentiate : % -> % is a domain constructor +--R Abbreviation for LinearOrdinaryDifferentialOperator2 is LODO2 +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for LODO2 +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (A,%) -> % ?*? : (%,A) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R D : () -> % 1 : () -> % +--R 0 : () -> % ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,PositiveInteger) -> % adjoint : % -> % +--R apply : (%,A,A) -> A coefficients : % -> List(A) +--R coerce : A -> % coerce : Integer -> % +--R coerce : % -> OutputForm content : % -> A if A has GCDDOM +--R degree : % -> NonNegativeInteger ?.? : (%,M) -> M +--R ?.? : (%,A) -> A hash : % -> SingleInteger +--R latex : % -> String leadingCoefficient : % -> A +--R one? : % -> Boolean recip : % -> Union(%,"failed") +--R reductum : % -> % retract : % -> A +--R sample : () -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R characteristic : () -> NonNegativeInteger +--R coefficient : (%,NonNegativeInteger) -> A +--R coerce : Fraction(Integer) -> % if A has RETRACT(FRAC(INT)) +--R directSum : (%,%) -> % if A has FIELD +--R exquo : (%,A) -> Union(%,"failed") if A has INTDOM +--R leftDivide : (%,%) -> Record(quotient: %,remainder: %) if A has FIELD +--R leftExactQuotient : (%,%) -> Union(%,"failed") if A has FIELD +--R leftExtendedGcd : (%,%) -> Record(coef1: %,coef2: %,generator: %) if A has FIELD +--R leftGcd : (%,%) -> % if A has FIELD +--R leftLcm : (%,%) -> % if A has FIELD +--R leftQuotient : (%,%) -> % if A has FIELD +--R leftRemainder : (%,%) -> % if A has FIELD +--R minimumDegree : % -> NonNegativeInteger +--R monicLeftDivide : (%,%) -> Record(quotient: %,remainder: %) if A has INTDOM +--R monicRightDivide : (%,%) -> Record(quotient: %,remainder: %) if A has INTDOM +--R monomial : (A,NonNegativeInteger) -> % +--R primitivePart : % -> % if A has GCDDOM +--R retract : % -> Fraction(Integer) if A has RETRACT(FRAC(INT)) +--R retract : % -> Integer if A has RETRACT(INT) +--R retractIfCan : % -> Union(A,"failed") +--R retractIfCan : % -> Union(Fraction(Integer),"failed") if A has RETRACT(FRAC(INT)) +--R retractIfCan : % -> Union(Integer,"failed") if A has RETRACT(INT) +--R rightDivide : (%,%) -> Record(quotient: %,remainder: %) if A has FIELD +--R rightExactQuotient : (%,%) -> Union(%,"failed") if A has FIELD +--R rightExtendedGcd : (%,%) -> Record(coef1: %,coef2: %,generator: %) if A has FIELD +--R rightGcd : (%,%) -> % if A has FIELD +--R rightLcm : (%,%) -> % if A has FIELD +--R rightQuotient : (%,%) -> % if A has FIELD +--R rightRemainder : (%,%) -> % if A has FIELD +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R symmetricPower : (%,NonNegativeInteger) -> % if A has FIELD +--R symmetricProduct : (%,%) -> % if A has FIELD +--R symmetricSquare : % -> % if A has FIELD +--R +--E 27 + )spool )lisp (bye) \end{chunk} @@ -80243,7 +83708,8 @@ LinearOrdinaryDifferentialOperator2(A, M): Exports == Implementation where )set message test on )set message auto off )clear all ---S 1 of 34 + +--S 1 of 35 [2, 4, 5, 6] --R --R @@ -80251,7 +83717,7 @@ LinearOrdinaryDifferentialOperator2(A, M): Exports == Implementation where --R Type: List(PositiveInteger) --E 1 ---S 2 of 34 +--S 2 of 35 [1] --R --R @@ -80259,7 +83725,7 @@ LinearOrdinaryDifferentialOperator2(A, M): Exports == Implementation where --R Type: List(PositiveInteger) --E 2 ---S 3 of 34 +--S 3 of 35 list(1) --R --R @@ -80267,7 +83733,7 @@ list(1) --R Type: List(PositiveInteger) --E 3 ---S 4 of 34 +--S 4 of 35 append([1,2,3],[5,6,7]) --R --R @@ -80275,7 +83741,7 @@ append([1,2,3],[5,6,7]) --R Type: List(PositiveInteger) --E 4 ---S 5 of 34 +--S 5 of 35 cons(10,[9,8,7]) --R --R @@ -80283,7 +83749,7 @@ cons(10,[9,8,7]) --R Type: List(PositiveInteger) --E 5 ---S 6 of 34 +--S 6 of 35 empty? [x+1] --R --R @@ -80291,7 +83757,7 @@ empty? [x+1] --R Type: Boolean --E 6 ---S 7 of 34 +--S 7 of 35 ([] = nil)@Boolean --R --R @@ -80299,7 +83765,7 @@ empty? [x+1] --R Type: Boolean --E 7 ---S 8 of 34 +--S 8 of 35 k := [4,3,7,3,8,5,9,2] --R --R @@ -80307,7 +83773,7 @@ k := [4,3,7,3,8,5,9,2] --R Type: List(PositiveInteger) --E 8 ---S 9 of 34 +--S 9 of 35 first k --R --R @@ -80315,7 +83781,7 @@ first k --R Type: PositiveInteger --E 9 ---S 10 of 34 +--S 10 of 35 k.first --R --R @@ -80323,7 +83789,7 @@ k.first --R Type: PositiveInteger --E 10 ---S 11 of 34 +--S 11 of 35 k.1 --R --R @@ -80331,7 +83797,7 @@ k.1 --R Type: PositiveInteger --E 11 ---S 12 of 34 +--S 12 of 35 k(1) --R --R @@ -80339,7 +83805,7 @@ k(1) --R Type: PositiveInteger --E 12 ---S 13 of 34 +--S 13 of 35 n := #k --R --R @@ -80347,7 +83813,7 @@ n := #k --R Type: PositiveInteger --E 13 ---S 14 of 34 +--S 14 of 35 last k --R --R @@ -80355,7 +83821,7 @@ last k --R Type: PositiveInteger --E 14 ---S 15 of 34 +--S 15 of 35 k.last --R --R @@ -80363,7 +83829,7 @@ k.last --R Type: PositiveInteger --E 15 ---S 16 of 34 +--S 16 of 35 k.(#k) --R --R @@ -80371,7 +83837,7 @@ k.(#k) --R Type: PositiveInteger --E 16 ---S 17 of 34 +--S 17 of 35 k := [4,3,7,3,8,5,9,2] --R --R @@ -80379,7 +83845,7 @@ k := [4,3,7,3,8,5,9,2] --R Type: List(PositiveInteger) --E 17 ---S 18 of 34 +--S 18 of 35 k.1 := 999 --R --R @@ -80387,7 +83853,7 @@ k.1 := 999 --R Type: PositiveInteger --E 18 ---S 19 of 34 +--S 19 of 35 k --R --R @@ -80395,7 +83861,7 @@ k --R Type: List(PositiveInteger) --E 19 ---S 20 of 34 +--S 20 of 35 k := [1,2] --R --R @@ -80403,7 +83869,7 @@ k := [1,2] --R Type: List(PositiveInteger) --E 20 ---S 21 of 34 +--S 21 of 35 m := cons(0,k) --R --R @@ -80411,7 +83877,7 @@ m := cons(0,k) --R Type: List(Integer) --E 21 ---S 22 of 34 +--S 22 of 35 m.2 := 99 --R --R @@ -80419,7 +83885,7 @@ m.2 := 99 --R Type: PositiveInteger --E 22 ---S 23 of 34 +--S 23 of 35 m --R --R @@ -80427,7 +83893,7 @@ m --R Type: List(Integer) --E 23 ---S 24 of 34 +--S 24 of 35 k --R --R @@ -80435,7 +83901,7 @@ k --R Type: List(PositiveInteger) --E 24 ---S 25 of 34 +--S 25 of 35 k := [1,2,3] --R --R @@ -80443,7 +83909,7 @@ k := [1,2,3] --R Type: List(PositiveInteger) --E 25 ---S 26 of 34 +--S 26 of 35 rest k --R --R @@ -80451,7 +83917,7 @@ rest k --R Type: List(PositiveInteger) --E 26 ---S 27 of 34 +--S 27 of 35 removeDuplicates [4,3,4,3,5,3,4] --R --R @@ -80459,7 +83925,7 @@ removeDuplicates [4,3,4,3,5,3,4] --R Type: List(PositiveInteger) --E 27 ---S 28 of 34 +--S 28 of 35 reverse [1,2,3,4,5,6] --R --R @@ -80467,7 +83933,7 @@ reverse [1,2,3,4,5,6] --R Type: List(PositiveInteger) --E 28 ---S 29 of 34 +--S 29 of 35 member?(1/2,[3/4,5/6,1/2]) --R --R @@ -80475,7 +83941,7 @@ member?(1/2,[3/4,5/6,1/2]) --R Type: Boolean --E 29 ---S 30 of 34 +--S 30 of 35 member?(1/12,[3/4,5/6,1/2]) --R --R @@ -80483,7 +83949,7 @@ member?(1/12,[3/4,5/6,1/2]) --R Type: Boolean --E 30 ---S 31 of 34 +--S 31 of 35 reverse(rest(reverse(k))) --R --R @@ -80491,7 +83957,7 @@ reverse(rest(reverse(k))) --R Type: List(PositiveInteger) --E 31 ---S 32 of 34 +--S 32 of 35 [1..3,10,20..23] --R --R @@ -80499,7 +83965,7 @@ reverse(rest(reverse(k))) --R Type: List(Segment(PositiveInteger)) --E 32 ---S 33 of 34 +--S 33 of 35 expand [1..3,10,20..23] --R --R @@ -80507,13 +83973,138 @@ expand [1..3,10,20..23] --R Type: List(Integer) --E 33 ---S 34 of 34 +--S 34 of 35 expand [1..] --R --R --R (34) [1,2,3,4,5,6,7,8,9,10,...] --R Type: Stream(Integer) --E 34 + +--S 35 of 35 +)show List +--R +--R List(S: Type) is a domain constructor +--R Abbreviation for List is LIST +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for LIST +--R +--R------------------------------- Operations -------------------------------- +--R OMwrite : % -> String if S has OM append : (%,%) -> % +--R children : % -> List(%) concat : (%,S) -> % +--R concat : List(%) -> % concat : (S,%) -> % +--R concat : (%,%) -> % concat! : (%,S) -> % +--R concat! : (%,%) -> % cons : (S,%) -> % +--R construct : List(S) -> % copy : % -> % +--R cycleEntry : % -> % cycleTail : % -> % +--R cyclic? : % -> Boolean delete : (%,Integer) -> % +--R delete! : (%,Integer) -> % distance : (%,%) -> Integer +--R elt : (%,Integer,S) -> S ?.? : (%,Integer) -> S +--R ?.last : (%,last) -> S ?.rest : (%,rest) -> % +--R ?.first : (%,first) -> S ?.value : (%,value) -> S +--R empty : () -> % empty? : % -> Boolean +--R entries : % -> List(S) eq? : (%,%) -> Boolean +--R explicitlyFinite? : % -> Boolean first : % -> S +--R index? : (Integer,%) -> Boolean indices : % -> List(Integer) +--R insert : (S,%,Integer) -> % insert : (%,%,Integer) -> % +--R insert! : (S,%,Integer) -> % insert! : (%,%,Integer) -> % +--R last : (%,NonNegativeInteger) -> % last : % -> S +--R latex : % -> String if S has SETCAT leaf? : % -> Boolean +--R leaves : % -> List(S) list : S -> % +--R map : (((S,S) -> S),%,%) -> % map : ((S -> S),%) -> % +--R max : (%,%) -> % if S has ORDSET min : (%,%) -> % if S has ORDSET +--R new : (NonNegativeInteger,S) -> % nil : () -> % +--R nodes : % -> List(%) null : % -> Boolean +--R possiblyInfinite? : % -> Boolean qelt : (%,Integer) -> S +--R remove! : ((S -> Boolean),%) -> % rest : (%,NonNegativeInteger) -> % +--R rest : % -> % reverse : % -> % +--R sample : () -> % second : % -> S +--R select! : ((S -> Boolean),%) -> % sort : (((S,S) -> Boolean),%) -> % +--R sort : % -> % if S has ORDSET tail : % -> % +--R third : % -> S value : % -> S +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R ? Boolean if S has ORDSET +--R ?<=? : (%,%) -> Boolean if S has ORDSET +--R ?=? : (%,%) -> Boolean if S has SETCAT +--R ?>? : (%,%) -> Boolean if S has ORDSET +--R ?>=? : (%,%) -> Boolean if S has ORDSET +--R OMwrite : (OpenMathDevice,%,Boolean) -> Void if S has OM +--R OMwrite : (OpenMathDevice,%) -> Void if S has OM +--R OMwrite : (%,Boolean) -> String if S has OM +--R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R child? : (%,%) -> Boolean if S has SETCAT +--R coerce : % -> OutputForm if S has SETCAT +--R convert : % -> InputForm if S has KONVERT(INFORM) +--R copyInto! : (%,%,Integer) -> % if $ has shallowlyMutable +--R count : (S,%) -> NonNegativeInteger if $ has finiteAggregate and S has SETCAT +--R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R cycleLength : % -> NonNegativeInteger +--R cycleSplit! : % -> % if $ has shallowlyMutable +--R delete : (%,UniversalSegment(Integer)) -> % +--R delete! : (%,UniversalSegment(Integer)) -> % +--R ?.? : (%,UniversalSegment(Integer)) -> % +--R entry? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT +--R eval : (%,List(S),List(S)) -> % if S has EVALAB(S) and S has SETCAT +--R eval : (%,S,S) -> % if S has EVALAB(S) and S has SETCAT +--R eval : (%,Equation(S)) -> % if S has EVALAB(S) and S has SETCAT +--R eval : (%,List(Equation(S))) -> % if S has EVALAB(S) and S has SETCAT +--R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R fill! : (%,S) -> % if $ has shallowlyMutable +--R find : ((S -> Boolean),%) -> Union(S,"failed") +--R first : (%,NonNegativeInteger) -> % +--R hash : % -> SingleInteger if S has SETCAT +--R less? : (%,NonNegativeInteger) -> Boolean +--R map! : ((S -> S),%) -> % if $ has shallowlyMutable +--R maxIndex : % -> Integer if Integer has ORDSET +--R member? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT +--R members : % -> List(S) if $ has finiteAggregate +--R merge : (((S,S) -> Boolean),%,%) -> % +--R merge : (%,%) -> % if S has ORDSET +--R merge! : (((S,S) -> Boolean),%,%) -> % +--R merge! : (%,%) -> % if S has ORDSET +--R minIndex : % -> Integer if Integer has ORDSET +--R more? : (%,NonNegativeInteger) -> Boolean +--R node? : (%,%) -> Boolean if S has SETCAT +--R parts : % -> List(S) if $ has finiteAggregate +--R position : ((S -> Boolean),%) -> Integer +--R position : (S,%) -> Integer if S has SETCAT +--R position : (S,%,Integer) -> Integer if S has SETCAT +--R qsetelt! : (%,Integer,S) -> S if $ has shallowlyMutable +--R reduce : (((S,S) -> S),%,S,S) -> S if $ has finiteAggregate and S has SETCAT +--R reduce : (((S,S) -> S),%,S) -> S if $ has finiteAggregate +--R reduce : (((S,S) -> S),%) -> S if $ has finiteAggregate +--R remove : (S,%) -> % if $ has finiteAggregate and S has SETCAT +--R remove : ((S -> Boolean),%) -> % if $ has finiteAggregate +--R remove! : (S,%) -> % if S has SETCAT +--R removeDuplicates : % -> % if $ has finiteAggregate and S has SETCAT +--R removeDuplicates! : % -> % if S has SETCAT +--R reverse! : % -> % if $ has shallowlyMutable +--R select : ((S -> Boolean),%) -> % if $ has finiteAggregate +--R setDifference : (%,%) -> % if S has SETCAT +--R setIntersection : (%,%) -> % if S has SETCAT +--R setUnion : (%,%) -> % if S has SETCAT +--R setchildren! : (%,List(%)) -> % if $ has shallowlyMutable +--R setelt : (%,Integer,S) -> S if $ has shallowlyMutable +--R setelt : (%,UniversalSegment(Integer),S) -> S if $ has shallowlyMutable +--R setelt : (%,last,S) -> S if $ has shallowlyMutable +--R setelt : (%,rest,%) -> % if $ has shallowlyMutable +--R setelt : (%,first,S) -> S if $ has shallowlyMutable +--R setelt : (%,value,S) -> S if $ has shallowlyMutable +--R setfirst! : (%,S) -> S if $ has shallowlyMutable +--R setlast! : (%,S) -> S if $ has shallowlyMutable +--R setrest! : (%,%) -> % if $ has shallowlyMutable +--R setvalue! : (%,S) -> S if $ has shallowlyMutable +--R size? : (%,NonNegativeInteger) -> Boolean +--R sort! : (((S,S) -> Boolean),%) -> % if $ has shallowlyMutable +--R sort! : % -> % if $ has shallowlyMutable and S has ORDSET +--R sorted? : (((S,S) -> Boolean),%) -> Boolean +--R sorted? : % -> Boolean if S has ORDSET +--R split! : (%,Integer) -> % if $ has shallowlyMutable +--R swap! : (%,Integer,Integer) -> Void if $ has shallowlyMutable +--R ?~=? : (%,%) -> Boolean if S has SETCAT +--R +--E 35 + )spool )lisp (bye) \end{chunk} @@ -81325,8 +84916,9 @@ ListMonoidOps(S, E, un): Exports == Implementation where --R empty : () -> % empty? : % -> Boolean --R eq? : (%,%) -> Boolean extract! : % -> S --R insert! : (S,%) -> % inspect : % -> S ---R map : ((S -> S),%) -> % removeDuplicates! : % -> % ---R sample : () -> % substitute : (S,S,%) -> % +--R latex : % -> String if S has SETCAT map : ((S -> S),%) -> % +--R removeDuplicates! : % -> % sample : () -> % +--R substitute : (S,S,%) -> % --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R ?=? : (%,%) -> Boolean if S has SETCAT --R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate @@ -81343,7 +84935,6 @@ ListMonoidOps(S, E, un): Exports == Implementation where --R find : ((S -> Boolean),%) -> Union(S,"failed") --R hash : % -> SingleInteger if S has SETCAT --R insert! : (S,%,NonNegativeInteger) -> % ---R latex : % -> String if S has SETCAT --R less? : (%,NonNegativeInteger) -> Boolean --R map! : ((S -> S),%) -> % if $ has shallowlyMutable --R member? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT @@ -81599,29 +85190,26 @@ ListMultiDictionary(S:SetCategory): EE == II where --R------------------------------- Operations -------------------------------- --R ?*? : (R,%) -> % ?*? : (%,R) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ?/? : (A,S) -> % --R ?/? : (%,S) -> % ?=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % coerce : R -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R abs : % -> % if A has ORDRING coerce : R -> % --R coerce : Integer -> % coerce : % -> OutputForm --R denom : % -> S hash : % -> SingleInteger ---R latex : % -> String numer : % -> A +--R latex : % -> String max : (%,%) -> % if A has ORDRING +--R min : (%,%) -> % if A has ORDRING numer : % -> A --R one? : % -> Boolean recip : % -> Union(%,"failed") --R sample : () -> % zero? : % -> Boolean --R ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % --R ? Boolean if A has ORDRING --R ?<=? : (%,%) -> Boolean if A has ORDRING --R ?>? : (%,%) -> Boolean if A has ORDRING --R ?>=? : (%,%) -> Boolean if A has ORDRING ---R ?^? : (%,NonNegativeInteger) -> % ---R abs : % -> % if A has ORDRING --R characteristic : () -> NonNegativeInteger ---R max : (%,%) -> % if A has ORDRING ---R min : (%,%) -> % if A has ORDRING --R negative? : % -> Boolean if A has ORDRING --R positive? : % -> Boolean if A has ORDRING --R sign : % -> Integer if A has ORDRING @@ -81739,22 +85327,20 @@ LocalAlgebra(A: Algebra R, --R --R------------------------------- Operations -------------------------------- --R ?*? : (%,R) -> % ?*? : (R,%) -> % ---R ?*? : (Integer,%) -> % ?*? : (PositiveInteger,%) -> % ---R ?+? : (%,%) -> % ?-? : (%,%) -> % ---R -? : % -> % ?/? : (M,S) -> % ---R ?/? : (%,S) -> % ?=? : (%,%) -> Boolean ---R 0 : () -> % coerce : % -> OutputForm ---R denom : % -> S hash : % -> SingleInteger ---R latex : % -> String numer : % -> M ---R sample : () -> % zero? : % -> Boolean ---R ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % +--R ?*? : (Integer,%) -> % ?*? : (NonNegativeInteger,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?+? : (%,%) -> % +--R ?-? : (%,%) -> % -? : % -> % +--R ?/? : (M,S) -> % ?/? : (%,S) -> % +--R ?=? : (%,%) -> Boolean 0 : () -> % +--R coerce : % -> OutputForm denom : % -> S +--R hash : % -> SingleInteger latex : % -> String +--R max : (%,%) -> % if M has OAGROUP min : (%,%) -> % if M has OAGROUP +--R numer : % -> M sample : () -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean --R ? Boolean if M has OAGROUP --R ?<=? : (%,%) -> Boolean if M has OAGROUP --R ?>? : (%,%) -> Boolean if M has OAGROUP --R ?>=? : (%,%) -> Boolean if M has OAGROUP ---R max : (%,%) -> % if M has OAGROUP ---R min : (%,%) -> % if M has OAGROUP --R subtractIfCan : (%,%) -> Union(%,"failed") --R --E 1 @@ -81883,7 +85469,8 @@ Localize(M:Module R, )set message test on )set message auto off )clear all ---S 1 of 22 + +--S 1 of 23 a:Symbol :='a --R --R @@ -81891,7 +85478,7 @@ a:Symbol :='a --R Type: Symbol --E 1 ---S 2 of 22 +--S 2 of 23 b:Symbol :='b --R --R @@ -81899,7 +85486,7 @@ b:Symbol :='b --R Type: Symbol --E 2 ---S 3 of 22 +--S 3 of 23 c:Symbol :='c --R --R @@ -81907,7 +85494,7 @@ c:Symbol :='c --R Type: Symbol --E 3 ---S 4 of 22 +--S 4 of 23 lword:= LyndonWord(Symbol) --R --R @@ -81915,7 +85502,7 @@ lword:= LyndonWord(Symbol) --R Type: Domain --E 4 ---S 5 of 22 +--S 5 of 23 magma := Magma(Symbol) --R --R @@ -81923,7 +85510,7 @@ magma := Magma(Symbol) --R Type: Domain --E 5 ---S 6 of 22 +--S 6 of 23 word := OrderedFreeMonoid(Symbol) --R --R @@ -81931,7 +85518,7 @@ word := OrderedFreeMonoid(Symbol) --R Type: Domain --E 6 ---S 7 of 22 +--S 7 of 23 LyndonWordsList1([a,b,c],3)$lword --R --R @@ -81942,7 +85529,7 @@ LyndonWordsList1([a,b,c],3)$lword --R Type: OneDimensionalArray(List(LyndonWord(Symbol))) --E 7 ---S 8 of 22 +--S 8 of 23 LyndonWordsList([a,b,c],3)$lword --R --R @@ -81954,7 +85541,7 @@ LyndonWordsList([a,b,c],3)$lword --R Type: List(LyndonWord(Symbol)) --E 8 ---S 9 of 22 +--S 9 of 23 lw := LyndonWordsList([a,b],5)$lword --R --R @@ -81966,7 +85553,7 @@ lw := LyndonWordsList([a,b],5)$lword --R Type: List(LyndonWord(Symbol)) --E 9 ---S 10 of 22 +--S 10 of 23 w1 : word := lw.4 :: word --R --R @@ -81975,7 +85562,7 @@ w1 : word := lw.4 :: word --R Type: OrderedFreeMonoid(Symbol) --E 10 ---S 11 of 22 +--S 11 of 23 w2 : word := lw.5 :: word --R --R @@ -81984,7 +85571,7 @@ w2 : word := lw.5 :: word --R Type: OrderedFreeMonoid(Symbol) --E 11 ---S 12 of 22 +--S 12 of 23 factor(a::word)$lword --R --R @@ -81992,7 +85579,7 @@ factor(a::word)$lword --R Type: List(LyndonWord(Symbol)) --E 12 ---S 13 of 22 +--S 13 of 23 factor(w1*w2)$lword --R --R @@ -82001,7 +85588,7 @@ factor(w1*w2)$lword --R Type: List(LyndonWord(Symbol)) --E 13 ---S 14 of 22 +--S 14 of 23 factor(w2*w2)$lword --R --R @@ -82010,7 +85597,7 @@ factor(w2*w2)$lword --R Type: List(LyndonWord(Symbol)) --E 14 ---S 15 of 22 +--S 15 of 23 factor(w2*w1)$lword --R --R @@ -82019,7 +85606,7 @@ factor(w2*w1)$lword --R Type: List(LyndonWord(Symbol)) --E 15 ---S 16 of 22 +--S 16 of 23 lyndon?(w1)$lword --R --R @@ -82027,7 +85614,7 @@ lyndon?(w1)$lword --R Type: Boolean --E 16 ---S 17 of 22 +--S 17 of 23 lyndon?(w1*w2)$lword --R --R @@ -82035,7 +85622,7 @@ lyndon?(w1*w2)$lword --R Type: Boolean --E 17 ---S 18 of 22 +--S 18 of 23 lyndon?(w2*w1)$lword --R --R @@ -82043,7 +85630,7 @@ lyndon?(w2*w1)$lword --R Type: Boolean --E 18 ---S 19 of 22 +--S 19 of 23 lyndonIfCan(w1)$lword --R --R @@ -82052,7 +85639,7 @@ lyndonIfCan(w1)$lword --R Type: Union(LyndonWord(Symbol),...) --E 19 ---S 20 of 22 +--S 20 of 23 lyndonIfCan(w2*w1)$lword --R --R @@ -82060,7 +85647,7 @@ lyndonIfCan(w2*w1)$lword --R Type: Union("failed",...) --E 20 ---S 21 of 22 +--S 21 of 23 lyndon(w1)$lword --R --R @@ -82069,7 +85656,7 @@ lyndon(w1)$lword --R Type: LyndonWord(Symbol) --E 21 ---S 22 of 22 +--S 22 of 23 lyndon(w1*w2)$lword --R --R @@ -82077,6 +85664,37 @@ lyndon(w1*w2)$lword --R (22) [a b a b ] --R Type: LyndonWord(Symbol) --E 22 + +--S 23 of 23 +)show LyndonWord +--R +--R LyndonWord(VarSet: OrderedSet) is a domain constructor +--R Abbreviation for LyndonWord is LWORD +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for LWORD +--R +--R------------------------------- Operations -------------------------------- +--R ? Boolean ?<=? : (%,%) -> Boolean +--R ?=? : (%,%) -> Boolean ?>? : (%,%) -> Boolean +--R ?>=? : (%,%) -> Boolean coerce : % -> Magma(VarSet) +--R coerce : VarSet -> % coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R left : % -> % length : % -> PositiveInteger +--R lexico : (%,%) -> Boolean max : (%,%) -> % +--R min : (%,%) -> % retract : % -> VarSet +--R retractable? : % -> Boolean right : % -> % +--R varList : % -> List(VarSet) ?~=? : (%,%) -> Boolean +--R LyndonWordsList : (List(VarSet),PositiveInteger) -> List(%) +--R LyndonWordsList1 : (List(VarSet),PositiveInteger) -> OneDimensionalArray(List(%)) +--R coerce : % -> OrderedFreeMonoid(VarSet) +--R factor : OrderedFreeMonoid(VarSet) -> List(%) +--R lyndon : OrderedFreeMonoid(VarSet) -> % +--R lyndon? : OrderedFreeMonoid(VarSet) -> Boolean +--R lyndonIfCan : OrderedFreeMonoid(VarSet) -> Union(%,"failed") +--R retractIfCan : % -> Union(VarSet,"failed") +--R +--E 23 + )spool )lisp (bye) \end{chunk} @@ -82435,18 +86053,21 @@ LyndonWord(VarSet:OrderedSet):Public == Private where --R------------------------------- Operations -------------------------------- --R ?*? : (%,MachineFloat) -> % ?*? : (MachineFloat,%) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ? Boolean --R ?<=? : (%,%) -> Boolean ?=? : (%,%) -> Boolean --R ?>? : (%,%) -> Boolean ?>=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % associates? : (%,%) -> Boolean ---R basis : () -> Vector(%) coerce : % -> Complex(Float) +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R associates? : (%,%) -> Boolean basis : () -> Vector(%) +--R coerce : % -> Complex(Float) coerce : Complex(MachineFloat) -> % --R coerce : Complex(Integer) -> % coerce : Complex(Float) -> % --R coerce : MachineFloat -> % coerce : Integer -> % --R coerce : % -> % coerce : Integer -> % --R coerce : % -> OutputForm conjugate : % -> % +--R convert : % -> Vector(MachineFloat) convert : Vector(MachineFloat) -> % --R discriminant : () -> MachineFloat generator : () -> % --R hash : % -> SingleInteger imag : % -> MachineFloat --R imaginary : () -> % latex : % -> String @@ -82460,11 +86081,9 @@ LyndonWord(VarSet:OrderedSet):Public == Private where --R ?~=? : (%,%) -> Boolean --R ?*? : (%,Fraction(Integer)) -> % if MachineFloat has FIELD --R ?*? : (Fraction(Integer),%) -> % if MachineFloat has FIELD ---R ?*? : (NonNegativeInteger,%) -> % --R ?**? : (%,Integer) -> % if MachineFloat has FIELD --R ?**? : (%,Fraction(Integer)) -> % if MachineFloat has RADCAT and MachineFloat has TRANFUN --R ?**? : (%,%) -> % if MachineFloat has TRANFUN ---R ?**? : (%,NonNegativeInteger) -> % --R ?/? : (%,%) -> % if MachineFloat has FIELD --R D : % -> % if MachineFloat has DIFRING --R D : (%,NonNegativeInteger) -> % if MachineFloat has DIFRING @@ -82475,7 +86094,6 @@ LyndonWord(VarSet:OrderedSet):Public == Private where --R D : (%,(MachineFloat -> MachineFloat),NonNegativeInteger) -> % --R D : (%,(MachineFloat -> MachineFloat)) -> % --R ?^? : (%,Integer) -> % if MachineFloat has FIELD ---R ?^? : (%,NonNegativeInteger) -> % --R abs : % -> % if MachineFloat has RNS --R acos : % -> % if MachineFloat has TRANFUN --R acosh : % -> % if MachineFloat has TRANFUN @@ -82496,11 +86114,8 @@ LyndonWord(VarSet:OrderedSet):Public == Private where --R charthRoot : % -> % if MachineFloat has FFIELDC --R coerce : Fraction(Integer) -> % if MachineFloat has FIELD or MachineFloat has RETRACT(FRAC(INT)) --R coerce : Complex(MachineInteger) -> % ---R coerce : Complex(MachineFloat) -> % --R complex : (MachineFloat,MachineFloat) -> % --R conditionP : Matrix(%) -> Union(Vector(%),"failed") if $ has CHARNZ and MachineFloat has EUCDOM and MachineFloat has PFECAT or MachineFloat has FFIELDC ---R convert : % -> Vector(MachineFloat) ---R convert : Vector(MachineFloat) -> % --R convert : % -> SparseUnivariatePolynomial(MachineFloat) --R convert : SparseUnivariatePolynomial(MachineFloat) -> % --R convert : % -> Pattern(Integer) if MachineFloat has KONVERT(PATTERN(INT)) @@ -82853,14 +86468,16 @@ MachineComplex():Exports == Implementation where --R------------------------------- Operations -------------------------------- --R ?*? : (Fraction(Integer),%) -> % ?*? : (%,Fraction(Integer)) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % ---R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % ---R ?-? : (%,%) -> % -? : % -> % ---R ?/? : (%,%) -> % ? Boolean ---R ?<=? : (%,%) -> Boolean ?=? : (%,%) -> Boolean ---R ?>? : (%,%) -> Boolean ?>=? : (%,%) -> Boolean ---R 1 : () -> % 0 : () -> % ---R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,Fraction(Integer)) -> % ?**? : (%,Integer) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?/? : (%,%) -> % +--R ? Boolean ?<=? : (%,%) -> Boolean +--R ?=? : (%,%) -> Boolean ?>? : (%,%) -> Boolean +--R ?>=? : (%,%) -> Boolean 1 : () -> % +--R 0 : () -> % ?^? : (%,Integer) -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % --R abs : % -> % associates? : (%,%) -> Boolean --R base : () -> PositiveInteger bits : () -> PositiveInteger --R ceiling : % -> % coerce : MachineInteger -> % @@ -82877,8 +86494,9 @@ MachineComplex():Exports == Implementation where --R inv : % -> % latex : % -> String --R lcm : List(%) -> % lcm : (%,%) -> % --R mantissa : % -> Integer max : (%,%) -> % ---R maximumExponent : () -> Integer min : (%,%) -> % ---R minimumExponent : () -> Integer negative? : % -> Boolean +--R maximumExponent : () -> Integer maximumExponent : Integer -> Integer +--R min : (%,%) -> % minimumExponent : () -> Integer +--R minimumExponent : Integer -> Integer negative? : % -> Boolean --R norm : % -> % nthRoot : (%,Integer) -> % --R one? : % -> Boolean order : % -> Integer --R positive? : % -> Boolean precision : () -> PositiveInteger @@ -82892,10 +86510,6 @@ MachineComplex():Exports == Implementation where --R truncate : % -> % unit? : % -> Boolean --R unitCanonical : % -> % wholePart : % -> Integer --R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,Fraction(Integer)) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R ?^? : (%,NonNegativeInteger) -> % --R base : PositiveInteger -> PositiveInteger --R bits : PositiveInteger -> PositiveInteger if $ has arbitraryPrecision --R changeBase : (Integer,Integer,PositiveInteger) -> % @@ -82913,9 +86527,7 @@ MachineComplex():Exports == Implementation where --R increasePrecision : Integer -> PositiveInteger if $ has arbitraryPrecision --R lcmCoef : (%,%) -> Record(llcmres: %,coeff1: %,coeff2: %) --R max : () -> % if not(has($,arbitraryExponent)) and not(has($,arbitraryPrecision)) ---R maximumExponent : Integer -> Integer --R min : () -> % if not(has($,arbitraryExponent)) and not(has($,arbitraryPrecision)) ---R minimumExponent : Integer -> Integer --R multiEuclidean : (List(%),%) -> Union(List(%),"failed") --R patternMatch : (%,Pattern(Float),PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) --R precision : PositiveInteger -> PositiveInteger @@ -83354,33 +86966,35 @@ MachineFloat(): Exports == Implementation where --R --R------------------------------- Operations -------------------------------- --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ? Boolean --R ?<=? : (%,%) -> Boolean ?=? : (%,%) -> Boolean --R ?>? : (%,%) -> Boolean ?>=? : (%,%) -> Boolean --R D : (%,NonNegativeInteger) -> % D : % -> % --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % abs : % -> % ---R addmod : (%,%,%) -> % associates? : (%,%) -> Boolean ---R base : () -> % binomial : (%,%) -> % ---R bit? : (%,%) -> Boolean coerce : Integer -> % ---R coerce : % -> % coerce : Integer -> % ---R coerce : % -> OutputForm convert : % -> Integer ---R convert : % -> InputForm convert : % -> Pattern(Integer) ---R convert : % -> Float convert : % -> DoubleFloat ---R copy : % -> % dec : % -> % ---R differentiate : % -> % even? : % -> Boolean ---R factor : % -> Factored(%) factorial : % -> % ---R gcd : (%,%) -> % gcd : List(%) -> % ---R hash : % -> % hash : % -> SingleInteger ---R inc : % -> % init : () -> % ---R invmod : (%,%) -> % latex : % -> String ---R lcm : (%,%) -> % lcm : List(%) -> % ---R length : % -> % mask : % -> % ---R max : (%,%) -> % maxint : () -> PositiveInteger ---R min : (%,%) -> % mulmod : (%,%,%) -> % ---R negative? : % -> Boolean odd? : % -> Boolean +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R abs : % -> % addmod : (%,%,%) -> % +--R associates? : (%,%) -> Boolean base : () -> % +--R binomial : (%,%) -> % bit? : (%,%) -> Boolean +--R coerce : Integer -> % coerce : % -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R convert : % -> Integer convert : % -> InputForm +--R convert : % -> Pattern(Integer) convert : % -> Float +--R convert : % -> DoubleFloat copy : % -> % +--R dec : % -> % differentiate : % -> % +--R even? : % -> Boolean factor : % -> Factored(%) +--R factorial : % -> % gcd : (%,%) -> % +--R gcd : List(%) -> % hash : % -> % +--R hash : % -> SingleInteger inc : % -> % +--R init : () -> % invmod : (%,%) -> % +--R latex : % -> String lcm : (%,%) -> % +--R lcm : List(%) -> % length : % -> % +--R mask : % -> % max : (%,%) -> % +--R maxint : () -> PositiveInteger min : (%,%) -> % +--R mulmod : (%,%,%) -> % negative? : % -> Boolean +--R nextItem : % -> Union(%,"failed") odd? : % -> Boolean --R one? : % -> Boolean permutation : (%,%) -> % --R positive? : % -> Boolean positiveRemainder : (%,%) -> % --R powmod : (%,%,%) -> % prime? : % -> Boolean @@ -83394,9 +87008,6 @@ MachineFloat(): Exports == Implementation where --R submod : (%,%,%) -> % symmetricRemainder : (%,%) -> % --R unit? : % -> Boolean unitCanonical : % -> % --R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R ?^? : (%,NonNegativeInteger) -> % --R characteristic : () -> NonNegativeInteger --R coerce : Expression(Integer) -> Expression(%) --R differentiate : (%,NonNegativeInteger) -> % @@ -83410,7 +87021,6 @@ MachineFloat(): Exports == Implementation where --R lcmCoef : (%,%) -> Record(llcmres: %,coeff1: %,coeff2: %) --R maxint : PositiveInteger -> PositiveInteger --R multiEuclidean : (List(%),%) -> Union(List(%),"failed") ---R nextItem : % -> Union(%,"failed") --R patternMatch : (%,Pattern(Integer),PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) --R principalIdeal : List(%) -> Record(coef: List(%),generator: %) --R rationalIfCan : % -> Union(Fraction(Integer),"failed") @@ -83594,7 +87204,8 @@ MachineInteger(): Exports == Implementation where )set message test on )set message auto off )clear all ---S 1 of 22 + +--S 1 of 23 x:Symbol :='x --R --R @@ -83602,7 +87213,7 @@ x:Symbol :='x --R Type: Symbol --E 1 ---S 2 of 22 +--S 2 of 23 y:Symbol :='y --R --R @@ -83610,7 +87221,7 @@ y:Symbol :='y --R Type: Symbol --E 2 ---S 3 of 22 +--S 3 of 23 z:Symbol :='z --R --R @@ -83618,7 +87229,7 @@ z:Symbol :='z --R Type: Symbol --E 3 ---S 4 of 22 +--S 4 of 23 word := OrderedFreeMonoid(Symbol) --R --R @@ -83626,7 +87237,7 @@ word := OrderedFreeMonoid(Symbol) --R Type: Domain --E 4 ---S 5 of 22 +--S 5 of 23 tree := Magma(Symbol) --R --R @@ -83634,7 +87245,7 @@ tree := Magma(Symbol) --R Type: Domain --E 5 ---S 6 of 22 +--S 6 of 23 a:tree := x*x --R --R @@ -83642,7 +87253,7 @@ a:tree := x*x --R Type: Magma(Symbol) --E 6 ---S 7 of 22 +--S 7 of 23 b:tree := y*y --R --R @@ -83650,7 +87261,7 @@ b:tree := y*y --R Type: Magma(Symbol) --E 7 ---S 8 of 22 +--S 8 of 23 c:tree := a*b --R --R @@ -83658,7 +87269,7 @@ c:tree := a*b --R Type: Magma(Symbol) --E 8 ---S 9 of 22 +--S 9 of 23 left c --R --R @@ -83666,7 +87277,7 @@ left c --R Type: Magma(Symbol) --E 9 ---S 10 of 22 +--S 10 of 23 right c --R --R @@ -83674,7 +87285,7 @@ right c --R Type: Magma(Symbol) --E 10 ---S 11 of 22 +--S 11 of 23 length c --R --R @@ -83682,7 +87293,7 @@ length c --R Type: PositiveInteger --E 11 ---S 12 of 22 +--S 12 of 23 c::word --R --R @@ -83691,7 +87302,7 @@ c::word --R Type: OrderedFreeMonoid(Symbol) --E 12 ---S 13 of 22 +--S 13 of 23 a < b --R --R @@ -83699,7 +87310,7 @@ a < b --R Type: Boolean --E 13 ---S 14 of 22 +--S 14 of 23 a < c --R --R @@ -83707,7 +87318,7 @@ a < c --R Type: Boolean --E 14 ---S 15 of 22 +--S 15 of 23 b < c --R --R @@ -83715,7 +87326,7 @@ b < c --R Type: Boolean --E 15 ---S 16 of 22 +--S 16 of 23 first c --R --R @@ -83723,7 +87334,7 @@ first c --R Type: Symbol --E 16 ---S 17 of 22 +--S 17 of 23 rest c --R --R @@ -83731,7 +87342,7 @@ rest c --R Type: Magma(Symbol) --E 17 ---S 18 of 22 +--S 18 of 23 rest rest c --R --R @@ -83739,7 +87350,7 @@ rest rest c --R Type: Magma(Symbol) --E 18 ---S 19 of 22 +--S 19 of 23 ax:tree := a*x --R --R @@ -83747,7 +87358,7 @@ ax:tree := a*x --R Type: Magma(Symbol) --E 19 ---S 20 of 22 +--S 20 of 23 xa:tree := x*a --R --R @@ -83755,7 +87366,7 @@ xa:tree := x*a --R Type: Magma(Symbol) --E 20 ---S 21 of 22 +--S 21 of 23 xa < ax --R --R @@ -83763,13 +87374,40 @@ xa < ax --R Type: Boolean --E 21 ---S 22 of 22 +--S 22 of 23 lexico(xa,ax) --R --R --R (22) false --R Type: Boolean --E 22 + +--S 23 of 23 +)show Magma +--R +--R Magma(VarSet: OrderedSet) is a domain constructor +--R Abbreviation for Magma is MAGMA +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for MAGMA +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,%) -> % ? Boolean +--R ?<=? : (%,%) -> Boolean ?=? : (%,%) -> Boolean +--R ?>? : (%,%) -> Boolean ?>=? : (%,%) -> Boolean +--R coerce : VarSet -> % coerce : % -> OutputForm +--R first : % -> VarSet hash : % -> SingleInteger +--R latex : % -> String left : % -> % +--R length : % -> PositiveInteger lexico : (%,%) -> Boolean +--R max : (%,%) -> % min : (%,%) -> % +--R mirror : % -> % rest : % -> % +--R retract : % -> VarSet retractable? : % -> Boolean +--R right : % -> % varList : % -> List(VarSet) +--R ?~=? : (%,%) -> Boolean +--R coerce : % -> OrderedFreeMonoid(VarSet) +--R retractIfCan : % -> Union(VarSet,"failed") +--R +--E 23 + )spool )lisp (bye) \end{chunk} @@ -84088,8 +87726,7 @@ Magma(VarSet:OrderedSet):Public == Private where --R coerce : % -> S coerce : % -> OutputForm --R hash : % -> SingleInteger latex : % -> String --R max : (%,%) -> % min : (%,%) -> % ---R ?~=? : (%,%) -> Boolean ---R position : % -> NonNegativeInteger +--R position : % -> NonNegativeInteger ?~=? : (%,%) -> Boolean --R setPosition : (%,NonNegativeInteger) -> Void --R --E 1 @@ -84187,6 +87824,7 @@ MakeCachableSet(S:SetCategory): Exports == Implementation where --S 1 of 1 )show MathMLFormat +--R --R MathMLFormat is a domain constructor --R Abbreviation for MathMLFormat is MMLFORM --R This constructor is exposed in this frame. @@ -85703,6 +89341,7 @@ have to be switched by swapping names. --S 5 of 5 )show MathMLFormat +--R --R MathMLFormat is a domain constructor --R Abbreviation for MathMLFormat is MMLFORM --R This constructor is exposed in this frame. @@ -85845,7 +89484,8 @@ o )show MathMLFormat )set message test on )set message auto off )clear all ---S 1 of 38 + +--S 1 of 39 m : Matrix(Integer) := new(3,3,0) --R --R @@ -85857,7 +89497,7 @@ m : Matrix(Integer) := new(3,3,0) --R Type: Matrix(Integer) --E 1 ---S 2 of 38 +--S 2 of 39 setelt(m,2,3,5) --R --R @@ -85865,7 +89505,7 @@ setelt(m,2,3,5) --R Type: PositiveInteger --E 2 ---S 3 of 38 +--S 3 of 39 m(1,2) := 10 --R --R @@ -85873,7 +89513,7 @@ m(1,2) := 10 --R Type: PositiveInteger --E 3 ---S 4 of 38 +--S 4 of 39 m --R --R @@ -85885,7 +89525,7 @@ m --R Type: Matrix(Integer) --E 4 ---S 5 of 38 +--S 5 of 39 matrix [ [1,2,3,4],[0,9,8,7] ] --R --R @@ -85895,7 +89535,7 @@ matrix [ [1,2,3,4],[0,9,8,7] ] --R Type: Matrix(Integer) --E 5 ---S 6 of 38 +--S 6 of 39 dm := diagonalMatrix [1,x**2,x**3,x**4,x**5] --R --R @@ -85915,7 +89555,7 @@ dm := diagonalMatrix [1,x**2,x**3,x**4,x**5] --R Type: Matrix(Polynomial(Integer)) --E 6 ---S 7 of 38 +--S 7 of 39 setRow!(dm,5,vector [1,1,1,1,1]) --R --R @@ -85934,7 +89574,7 @@ setRow!(dm,5,vector [1,1,1,1,1]) --R Type: Matrix(Polynomial(Integer)) --E 7 ---S 8 of 38 +--S 8 of 39 setColumn!(dm,2,vector [y,y,y,y,y]) --R --R @@ -85952,7 +89592,7 @@ setColumn!(dm,2,vector [y,y,y,y,y]) --R Type: Matrix(Polynomial(Integer)) --E 8 ---S 9 of 38 +--S 9 of 39 cdm := copy(dm) --R --R @@ -85970,7 +89610,7 @@ cdm := copy(dm) --R Type: Matrix(Polynomial(Integer)) --E 9 ---S 10 of 38 +--S 10 of 39 setelt(dm,4,1,1-x**7) --R --R @@ -85979,7 +89619,7 @@ setelt(dm,4,1,1-x**7) --R Type: Polynomial(Integer) --E 10 ---S 11 of 38 +--S 11 of 39 [dm,cdm] --R --R @@ -85997,7 +89637,7 @@ setelt(dm,4,1,1-x**7) --R Type: List(Matrix(Polynomial(Integer))) --E 11 ---S 12 of 38 +--S 12 of 39 subMatrix(dm,2,3,2,4) --R --R @@ -86008,7 +89648,7 @@ subMatrix(dm,2,3,2,4) --R Type: Matrix(Polynomial(Integer)) --E 12 ---S 13 of 38 +--S 13 of 39 d := diagonalMatrix [1.2,-1.3,1.4,-1.5] --R --R @@ -86022,7 +89662,7 @@ d := diagonalMatrix [1.2,-1.3,1.4,-1.5] --R Type: Matrix(Float) --E 13 ---S 14 of 38 +--S 14 of 39 e := matrix [ [6.7,9.11],[-31.33,67.19] ] --R --R @@ -86032,7 +89672,7 @@ e := matrix [ [6.7,9.11],[-31.33,67.19] ] --R Type: Matrix(Float) --E 14 ---S 15 of 38 +--S 15 of 39 setsubMatrix!(d,1,2,e) --R --R @@ -86046,7 +89686,7 @@ setsubMatrix!(d,1,2,e) --R Type: Matrix(Float) --E 15 ---S 16 of 38 +--S 16 of 39 d --R --R @@ -86060,7 +89700,7 @@ d --R Type: Matrix(Float) --E 16 ---S 17 of 38 +--S 17 of 39 a := matrix [ [1/2,1/3,1/4],[1/5,1/6,1/7] ] --R --R @@ -86074,7 +89714,7 @@ a := matrix [ [1/2,1/3,1/4],[1/5,1/6,1/7] ] --R Type: Matrix(Fraction(Integer)) --E 17 ---S 18 of 38 +--S 18 of 39 b := matrix [ [3/5,3/7,3/11],[3/13,3/17,3/19] ] --R --R @@ -86088,7 +89728,7 @@ b := matrix [ [3/5,3/7,3/11],[3/13,3/17,3/19] ] --R Type: Matrix(Fraction(Integer)) --E 18 ---S 19 of 38 +--S 19 of 39 horizConcat(a,b) --R --R @@ -86102,7 +89742,7 @@ horizConcat(a,b) --R Type: Matrix(Fraction(Integer)) --E 19 ---S 20 of 38 +--S 20 of 39 vab := vertConcat(a,b) --R --R @@ -86124,7 +89764,7 @@ vab := vertConcat(a,b) --R Type: Matrix(Fraction(Integer)) --E 20 ---S 21 of 38 +--S 21 of 39 transpose vab --R --R @@ -86142,7 +89782,7 @@ transpose vab --R Type: Matrix(Fraction(Integer)) --E 21 ---S 22 of 38 +--S 22 of 39 m := matrix [ [1,2],[3,4] ] --R --R @@ -86152,7 +89792,7 @@ m := matrix [ [1,2],[3,4] ] --R Type: Matrix(Integer) --E 22 ---S 23 of 38 +--S 23 of 39 4 * m * (-5) --R --R @@ -86162,7 +89802,7 @@ m := matrix [ [1,2],[3,4] ] --R Type: Matrix(Integer) --E 23 ---S 24 of 38 +--S 24 of 39 n := matrix([ [1,0,-2],[-3,5,1] ]) --R --R @@ -86172,7 +89812,7 @@ n := matrix([ [1,0,-2],[-3,5,1] ]) --R Type: Matrix(Integer) --E 24 ---S 25 of 38 +--S 25 of 39 m * n --R --R @@ -86182,7 +89822,7 @@ m * n --R Type: Matrix(Integer) --E 25 ---S 26 of 38 +--S 26 of 39 vec := column(n,3) --R --R @@ -86190,7 +89830,7 @@ vec := column(n,3) --R Type: Vector(Integer) --E 26 ---S 27 of 38 +--S 27 of 39 vec * m --R --R @@ -86198,7 +89838,7 @@ vec * m --R Type: Vector(Integer) --E 27 ---S 28 of 38 +--S 28 of 39 m * vec --R --R @@ -86206,7 +89846,7 @@ m * vec --R Type: Vector(Integer) --E 28 ---S 29 of 38 +--S 29 of 39 hilb := matrix([ [1/(i + j) for i in 1..3] for j in 1..3]) --R --R @@ -86224,7 +89864,7 @@ hilb := matrix([ [1/(i + j) for i in 1..3] for j in 1..3]) --R Type: Matrix(Fraction(Integer)) --E 29 ---S 30 of 38 +--S 30 of 39 inverse(hilb) --R --R @@ -86236,7 +89876,7 @@ inverse(hilb) --R Type: Union(Matrix(Fraction(Integer)),...) --E 30 ---S 31 of 38 +--S 31 of 39 mm := matrix([ [1,2,3,4], [5,6,7,8], [9,10,11,12], [13,14,15,16] ]) --R --R @@ -86250,7 +89890,7 @@ mm := matrix([ [1,2,3,4], [5,6,7,8], [9,10,11,12], [13,14,15,16] ]) --R Type: Matrix(Integer) --E 31 ---S 32 of 38 +--S 32 of 39 inverse(mm) --R --R @@ -86258,7 +89898,7 @@ inverse(mm) --R Type: Union("failed",...) --E 32 ---S 33 of 38 +--S 33 of 39 determinant(mm) --R --R @@ -86266,7 +89906,7 @@ determinant(mm) --R Type: NonNegativeInteger --E 33 ---S 34 of 38 +--S 34 of 39 trace(mm) --R --R @@ -86274,7 +89914,7 @@ trace(mm) --R Type: PositiveInteger --E 34 ---S 35 of 38 +--S 35 of 39 rank(mm) --R --R @@ -86282,7 +89922,7 @@ rank(mm) --R Type: PositiveInteger --E 35 ---S 36 of 38 +--S 36 of 39 nullity(mm) --R --R @@ -86290,7 +89930,7 @@ nullity(mm) --R Type: PositiveInteger --E 36 ---S 37 of 38 +--S 37 of 39 nullSpace(mm) --R --R @@ -86298,7 +89938,7 @@ nullSpace(mm) --R Type: List(Vector(Integer)) --E 37 ---S 38 of 38 +--S 38 of 39 rowEchelon(mm) --R --R @@ -86311,6 +89951,87 @@ rowEchelon(mm) --R +0 0 0 0 + --R Type: Matrix(Integer) --E 38 + +--S 39 of 39 +)show Matrix +--R +--R Matrix(R: Ring) is a domain constructor +--R Abbreviation for Matrix is MATRIX +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for MATRIX +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (Vector(R),%) -> Vector(R) ?*? : (%,Vector(R)) -> Vector(R) +--R ?*? : (Integer,%) -> % ?*? : (%,R) -> % +--R ?*? : (R,%) -> % ?*? : (%,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?+? : (%,%) -> % +--R -? : % -> % ?-? : (%,%) -> % +--R ?/? : (%,R) -> % if R has FIELD antisymmetric? : % -> Boolean +--R coerce : Vector(R) -> % column : (%,Integer) -> Vector(R) +--R copy : % -> % diagonal? : % -> Boolean +--R diagonalMatrix : Vector(R) -> % diagonalMatrix : List(%) -> % +--R diagonalMatrix : List(R) -> % elt : (%,Integer,Integer,R) -> R +--R elt : (%,Integer,Integer) -> R empty : () -> % +--R empty? : % -> Boolean eq? : (%,%) -> Boolean +--R fill! : (%,R) -> % horizConcat : (%,%) -> % +--R latex : % -> String if R has SETCAT listOfLists : % -> List(List(R)) +--R map : (((R,R) -> R),%,%,R) -> % map : (((R,R) -> R),%,%) -> % +--R map : ((R -> R),%) -> % map! : ((R -> R),%) -> % +--R matrix : List(List(R)) -> % maxColIndex : % -> Integer +--R maxRowIndex : % -> Integer minColIndex : % -> Integer +--R minRowIndex : % -> Integer ncols : % -> NonNegativeInteger +--R nrows : % -> NonNegativeInteger parts : % -> List(R) +--R pfaffian : % -> R if R has COMRING qelt : (%,Integer,Integer) -> R +--R row : (%,Integer) -> Vector(R) sample : () -> % +--R setelt : (%,Integer,Integer,R) -> R square? : % -> Boolean +--R squareTop : % -> % symmetric? : % -> Boolean +--R transpose : % -> % transpose : Vector(R) -> % +--R vertConcat : (%,%) -> % +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R ?**? : (%,Integer) -> % if R has FIELD +--R ?=? : (%,%) -> Boolean if R has SETCAT +--R any? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate +--R coerce : % -> OutputForm if R has SETCAT +--R columnSpace : % -> List(Vector(R)) if R has EUCDOM +--R convert : % -> InputForm if R has KONVERT(INFORM) +--R count : (R,%) -> NonNegativeInteger if $ has finiteAggregate and R has SETCAT +--R count : ((R -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R determinant : % -> R if R has commutative(*) +--R elt : (%,List(Integer),List(Integer)) -> % +--R eval : (%,List(R),List(R)) -> % if R has EVALAB(R) and R has SETCAT +--R eval : (%,R,R) -> % if R has EVALAB(R) and R has SETCAT +--R eval : (%,Equation(R)) -> % if R has EVALAB(R) and R has SETCAT +--R eval : (%,List(Equation(R))) -> % if R has EVALAB(R) and R has SETCAT +--R every? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate +--R exquo : (%,R) -> Union(%,"failed") if R has INTDOM +--R hash : % -> SingleInteger if R has SETCAT +--R inverse : % -> Union(%,"failed") if R has FIELD +--R less? : (%,NonNegativeInteger) -> Boolean +--R matrix : (NonNegativeInteger,NonNegativeInteger,((Integer,Integer) -> R)) -> % +--R member? : (R,%) -> Boolean if $ has finiteAggregate and R has SETCAT +--R members : % -> List(R) if $ has finiteAggregate +--R minordet : % -> R if R has commutative(*) +--R more? : (%,NonNegativeInteger) -> Boolean +--R new : (NonNegativeInteger,NonNegativeInteger,R) -> % +--R nullSpace : % -> List(Vector(R)) if R has INTDOM +--R nullity : % -> NonNegativeInteger if R has INTDOM +--R qsetelt! : (%,Integer,Integer,R) -> R +--R rank : % -> NonNegativeInteger if R has INTDOM +--R rowEchelon : % -> % if R has EUCDOM +--R scalarMatrix : (NonNegativeInteger,R) -> % +--R setColumn! : (%,Integer,Vector(R)) -> % +--R setRow! : (%,Integer,Vector(R)) -> % +--R setelt : (%,List(Integer),List(Integer),%) -> % +--R setsubMatrix! : (%,Integer,Integer,%) -> % +--R size? : (%,NonNegativeInteger) -> Boolean +--R subMatrix : (%,Integer,Integer,Integer,Integer) -> % +--R swapColumns! : (%,Integer,Integer) -> % +--R swapRows! : (%,Integer,Integer) -> % +--R zero : (NonNegativeInteger,NonNegativeInteger) -> % +--R ?~=? : (%,%) -> Boolean if R has SETCAT +--R +--E 39 + )spool )lisp (bye) \end{chunk} @@ -87030,36 +90751,44 @@ Matrix(R): Exports == Implementation where --R------------------------------- Operations -------------------------------- --R ?*? : (%,R) -> % ?*? : (R,%) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % ---R -? : % -> % ?=? : (%,%) -> Boolean ---R An : % -> Vector(R) D : (%,(R -> R)) -> % ---R D : % -> % D : (%,NonNegativeInteger) -> % +--R -? : % -> % ?/? : (%,R) -> % if R has FIELD +--R ?=? : (%,%) -> Boolean An : % -> Vector(R) +--R D : (%,(R -> R)) -> % D : % -> % +--R D : (%,NonNegativeInteger) -> % D : (%,SingletonAsOrderedSet) -> % --R 1 : () -> % UnVectorise : Vector(R) -> % --R Vectorise : % -> Vector(R) 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % coefficients : % -> List(R) ---R coerce : Rep -> % coerce : R -> % ---R coerce : Integer -> % coerce : % -> OutputForm ---R degree : % -> NonNegativeInteger differentiate : % -> % ---R ?.? : (%,%) -> % ?.? : (%,R) -> R +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R coefficients : % -> List(R) coerce : % -> % if R has INTDOM +--R coerce : Rep -> % coerce : SingletonAsOrderedSet -> % +--R coerce : R -> % coerce : Integer -> % +--R coerce : % -> OutputForm content : % -> R if R has GCDDOM +--R degree : % -> NonNegativeInteger differentiate : (%,(R -> R)) -> % +--R differentiate : % -> % ?.? : (%,%) -> % +--R ?.? : (%,R) -> R eval : (%,List(%),List(%)) -> % --R eval : (%,%,%) -> % eval : (%,Equation(%)) -> % ---R ground : % -> R ground? : % -> Boolean ---R hash : % -> SingleInteger init : () -> % if R has STEP ---R latex : % -> String leadingCoefficient : % -> R ---R leadingMonomial : % -> % lift : % -> Rep ---R map : ((R -> R),%) -> % modulus : () -> Rep ---R monomial? : % -> Boolean monomials : % -> List(%) ---R one? : % -> Boolean pow : () -> PrimitiveArray(%) ---R pseudoRemainder : (%,%) -> % recip : % -> Union(%,"failed") +--R eval : (%,List(Equation(%))) -> % gcd : (%,%) -> % if R has GCDDOM +--R gcd : List(%) -> % if R has GCDDOM ground : % -> R +--R ground? : % -> Boolean hash : % -> SingleInteger +--R init : () -> % if R has STEP latex : % -> String +--R lcm : (%,%) -> % if R has GCDDOM lcm : List(%) -> % if R has GCDDOM +--R leadingCoefficient : % -> R leadingMonomial : % -> % +--R lift : % -> Rep map : ((R -> R),%) -> % +--R max : (%,%) -> % if R has ORDSET min : (%,%) -> % if R has ORDSET +--R modulus : () -> Rep monomial? : % -> Boolean +--R monomials : % -> List(%) one? : % -> Boolean +--R pow : () -> PrimitiveArray(%) primitiveMonomials : % -> List(%) +--R pseudoRemainder : (%,%) -> % ?quo? : (%,%) -> % if R has FIELD +--R random : () -> % if R has FINITE recip : % -> Union(%,"failed") --R reduce : Rep -> % reductum : % -> % ---R retract : % -> R sample : () -> % ---R setPoly : Rep -> Rep unvectorise : Vector(R) -> % ---R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?rem? : (%,%) -> % if R has FIELD retract : % -> R +--R sample : () -> % setPoly : Rep -> Rep +--R unvectorise : Vector(R) -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean --R ?*? : (Fraction(Integer),%) -> % if R has ALGEBRA(FRAC(INT)) --R ?*? : (%,Fraction(Integer)) -> % if R has ALGEBRA(FRAC(INT)) ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R ?/? : (%,R) -> % if R has FIELD --R ? Boolean if R has ORDSET --R ?<=? : (%,%) -> Boolean if R has ORDSET --R ?>? : (%,%) -> Boolean if R has ORDSET @@ -87072,8 +90801,6 @@ Matrix(R): Exports == Implementation where --R D : (%,List(SingletonAsOrderedSet),List(NonNegativeInteger)) -> % --R D : (%,SingletonAsOrderedSet,NonNegativeInteger) -> % --R D : (%,List(SingletonAsOrderedSet)) -> % ---R D : (%,SingletonAsOrderedSet) -> % ---R ?^? : (%,NonNegativeInteger) -> % --R associates? : (%,%) -> Boolean if R has INTDOM --R binomThmExpt : (%,%,NonNegativeInteger) -> % if R has COMRING --R characteristic : () -> NonNegativeInteger @@ -87081,22 +90808,18 @@ Matrix(R): Exports == Implementation where --R coefficient : (%,List(SingletonAsOrderedSet),List(NonNegativeInteger)) -> % --R coefficient : (%,SingletonAsOrderedSet,NonNegativeInteger) -> % --R coefficient : (%,NonNegativeInteger) -> R ---R coerce : % -> % if R has INTDOM --R coerce : Fraction(Integer) -> % if R has ALGEBRA(FRAC(INT)) or R has RETRACT(FRAC(INT)) ---R coerce : SingletonAsOrderedSet -> % --R composite : (Fraction(%),%) -> Union(Fraction(%),"failed") if R has INTDOM --R composite : (%,%) -> Union(%,"failed") if R has INTDOM --R computePowers : () -> PrimitiveArray(%) --R conditionP : Matrix(%) -> Union(Vector(%),"failed") if $ has CHARNZ and R has PFECAT --R content : (%,SingletonAsOrderedSet) -> % if R has GCDDOM ---R content : % -> R if R has GCDDOM --R convert : % -> InputForm if SingletonAsOrderedSet has KONVERT(INFORM) and R has KONVERT(INFORM) --R convert : % -> Pattern(Integer) if SingletonAsOrderedSet has KONVERT(PATTERN(INT)) and R has KONVERT(PATTERN(INT)) --R convert : % -> Pattern(Float) if SingletonAsOrderedSet has KONVERT(PATTERN(FLOAT)) and R has KONVERT(PATTERN(FLOAT)) --R degree : (%,List(SingletonAsOrderedSet)) -> List(NonNegativeInteger) --R degree : (%,SingletonAsOrderedSet) -> NonNegativeInteger --R differentiate : (%,(R -> R),%) -> % ---R differentiate : (%,(R -> R)) -> % --R differentiate : (%,(R -> R),NonNegativeInteger) -> % --R differentiate : (%,List(Symbol),List(NonNegativeInteger)) -> % if R has PDRING(SYMBOL) --R differentiate : (%,Symbol,NonNegativeInteger) -> % if R has PDRING(SYMBOL) @@ -87120,8 +90843,6 @@ Matrix(R): Exports == Implementation where --R eval : (%,SingletonAsOrderedSet,%) -> % --R eval : (%,List(SingletonAsOrderedSet),List(R)) -> % --R eval : (%,SingletonAsOrderedSet,R) -> % ---R eval : (%,List(%),List(%)) -> % ---R eval : (%,List(Equation(%))) -> % --R expressIdealMember : (List(%),%) -> Union(List(%),"failed") if R has FIELD --R exquo : (%,%) -> Union(%,"failed") if R has INTDOM --R exquo : (%,R) -> Union(%,"failed") if R has INTDOM @@ -87131,8 +90852,6 @@ Matrix(R): Exports == Implementation where --R factorPolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has PFECAT --R factorSquareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has PFECAT --R frobenius : % -> % if R has FFIELDC ---R gcd : (%,%) -> % if R has GCDDOM ---R gcd : List(%) -> % if R has GCDDOM --R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) if R has GCDDOM --R index : PositiveInteger -> % if R has FINITE --R integrate : % -> % if R has ALGEBRA(FRAC(INT)) @@ -87140,15 +90859,11 @@ Matrix(R): Exports == Implementation where --R isPlus : % -> Union(List(%),"failed") --R isTimes : % -> Union(List(%),"failed") --R karatsubaDivide : (%,NonNegativeInteger) -> Record(quotient: %,remainder: %) ---R lcm : (%,%) -> % if R has GCDDOM ---R lcm : List(%) -> % if R has GCDDOM --R lcmCoef : (%,%) -> Record(llcmres: %,coeff1: %,coeff2: %) if R has GCDDOM --R lookup : % -> PositiveInteger if R has FINITE --R mainVariable : % -> Union(SingletonAsOrderedSet,"failed") --R makeSUP : % -> SparseUnivariatePolynomial(R) --R mapExponents : ((NonNegativeInteger -> NonNegativeInteger),%) -> % ---R max : (%,%) -> % if R has ORDSET ---R min : (%,%) -> % if R has ORDSET --R minimumDegree : (%,List(SingletonAsOrderedSet)) -> List(NonNegativeInteger) --R minimumDegree : (%,SingletonAsOrderedSet) -> NonNegativeInteger --R minimumDegree : % -> NonNegativeInteger @@ -87168,19 +90883,15 @@ Matrix(R): Exports == Implementation where --R patternMatch : (%,Pattern(Float),PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if SingletonAsOrderedSet has PATMAB(FLOAT) and R has PATMAB(FLOAT) --R pomopo! : (%,R,NonNegativeInteger,%) -> % --R prime? : % -> Boolean if R has PFECAT ---R primitiveMonomials : % -> List(%) --R primitivePart : (%,SingletonAsOrderedSet) -> % if R has GCDDOM --R primitivePart : % -> % if R has GCDDOM --R principalIdeal : List(%) -> Record(coef: List(%),generator: %) if R has FIELD --R pseudoDivide : (%,%) -> Record(coef: R,quotient: %,remainder: %) if R has INTDOM --R pseudoQuotient : (%,%) -> % if R has INTDOM ---R ?quo? : (%,%) -> % if R has FIELD ---R random : () -> % if R has FINITE --R reducedSystem : Matrix(%) -> Matrix(R) --R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(R),vec: Vector(R)) --R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(Integer),vec: Vector(Integer)) if R has LINEXP(INT) --R reducedSystem : Matrix(%) -> Matrix(Integer) if R has LINEXP(INT) ---R ?rem? : (%,%) -> % if R has FIELD --R resultant : (%,%) -> R if R has COMRING --R resultant : (%,%,SingletonAsOrderedSet) -> % if R has COMRING --R retract : % -> SingletonAsOrderedSet @@ -87560,30 +91271,28 @@ ModMonic(R,Rep): C == T --R------------------------------- Operations -------------------------------- --R ?*? : (Fraction(Integer),%) -> % ?*? : (%,Fraction(Integer)) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,Integer) -> % ?**? : (%,NonNegativeInteger) -> % --R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % --R ?-? : (%,%) -> % -? : % -> % --R ?/? : (%,%) -> % ?=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % ---R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> % ---R associates? : (%,%) -> Boolean coerce : % -> R ---R coerce : Fraction(Integer) -> % coerce : % -> % ---R coerce : Integer -> % coerce : % -> OutputForm ---R factor : % -> Factored(%) gcd : List(%) -> % ---R gcd : (%,%) -> % hash : % -> SingleInteger ---R inv : % -> % latex : % -> String ---R lcm : List(%) -> % lcm : (%,%) -> % ---R modulus : % -> Mod one? : % -> Boolean ---R prime? : % -> Boolean ?quo? : (%,%) -> % ---R recip : % -> Union(%,"failed") reduce : (R,Mod) -> % ---R ?rem? : (%,%) -> % sample : () -> % ---R sizeLess? : (%,%) -> Boolean squareFree : % -> Factored(%) ---R squareFreePart : % -> % unit? : % -> Boolean ---R unitCanonical : % -> % zero? : % -> Boolean ---R ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,Integer) -> % ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,PositiveInteger) -> % associates? : (%,%) -> Boolean +--R coerce : % -> R coerce : Fraction(Integer) -> % +--R coerce : % -> % coerce : Integer -> % +--R coerce : % -> OutputForm factor : % -> Factored(%) +--R gcd : List(%) -> % gcd : (%,%) -> % +--R hash : % -> SingleInteger inv : % -> % +--R latex : % -> String lcm : List(%) -> % +--R lcm : (%,%) -> % modulus : % -> Mod +--R one? : % -> Boolean prime? : % -> Boolean +--R ?quo? : (%,%) -> % recip : % -> Union(%,"failed") +--R reduce : (R,Mod) -> % ?rem? : (%,%) -> % +--R sample : () -> % sizeLess? : (%,%) -> Boolean +--R squareFree : % -> Factored(%) squareFreePart : % -> % +--R unit? : % -> Boolean unitCanonical : % -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean --R characteristic : () -> NonNegativeInteger --R divide : (%,%) -> Record(quotient: %,remainder: %) --R euclideanSize : % -> NonNegativeInteger @@ -87723,6 +91432,7 @@ ModularField(R,Mod,reduction:(R,Mod) -> R, --S 1 of 1 )show ModularRing +--R --R ModularRing(R: CommutativeRing,Mod: AbelianMonoid,reduction: ((R,Mod) -> R),merge: ((Mod,Mod) -> Union(Mod,"failed")),exactQuo: ((R,R,Mod) -> Union(R,"failed"))) is a domain constructor --R Abbreviation for ModularRing is MODRING --R This constructor is not exposed in this frame. @@ -87730,20 +91440,19 @@ ModularField(R,Mod,reduction:(R,Mod) -> R, --R --R------------------------------- Operations -------------------------------- --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ?=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % coerce : % -> R ---R coerce : Integer -> % coerce : % -> OutputForm ---R hash : % -> SingleInteger inv : % -> % ---R latex : % -> String modulus : % -> Mod ---R one? : % -> Boolean recip : % -> Union(%,"failed") ---R reduce : (R,Mod) -> % sample : () -> % ---R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R coerce : % -> R coerce : Integer -> % +--R coerce : % -> OutputForm hash : % -> SingleInteger +--R inv : % -> % latex : % -> String +--R modulus : % -> Mod one? : % -> Boolean +--R recip : % -> Union(%,"failed") reduce : (R,Mod) -> % +--R sample : () -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean --R characteristic : () -> NonNegativeInteger --R exQuo : (%,%) -> Union(%,"failed") --R subtractIfCan : (%,%) -> Union(%,"failed") @@ -87904,6 +91613,7 @@ ModularRing(R,Mod,reduction:(R,Mod) -> R, --S 1 of 1 )show ModuleMonomial +--R --R ModuleMonomial(IS: OrderedSet,E: SetCategory,ff: ((Record(index: IS,exponent: E),Record(index: IS,exponent: E)) -> Boolean)) is a domain constructor --R Abbreviation for ModuleMonomial is MODMONOM --R This constructor is not exposed in this frame. @@ -88019,31 +91729,27 @@ ModuleMonomial(IS: OrderedSet, --R Issue )edit bookvol10.3.pamphlet to see algebra source code for MODOP --R --R------------------------------- Operations -------------------------------- +--R ?*? : (%,R) -> % if R has COMRING ?*? : (R,%) -> % if R has COMRING --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % ---R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % ---R ?-? : (%,%) -> % -? : % -> % ---R ?=? : (%,%) -> Boolean 1 : () -> % ---R 0 : () -> % ?^? : (%,PositiveInteger) -> % ---R coerce : BasicOperator -> % coerce : R -> % ---R coerce : Integer -> % coerce : % -> OutputForm +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,Integer) -> % ?**? : (BasicOperator,Integer) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R adjoint : % -> % if R has COMRING coerce : BasicOperator -> % +--R coerce : R -> % coerce : Integer -> % +--R coerce : % -> OutputForm conjug : R -> R if R has COMRING --R ?.? : (%,M) -> M evaluate : (%,(M -> M)) -> % --R hash : % -> SingleInteger latex : % -> String --R one? : % -> Boolean opeval : (BasicOperator,M) -> M --R recip : % -> Union(%,"failed") retract : % -> BasicOperator --R retract : % -> R sample : () -> % --R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (%,R) -> % if R has COMRING ---R ?*? : (R,%) -> % if R has COMRING ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (BasicOperator,Integer) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R ?^? : (%,NonNegativeInteger) -> % --R adjoint : (%,%) -> % if R has COMRING ---R adjoint : % -> % if R has COMRING --R characteristic : () -> NonNegativeInteger --R charthRoot : % -> Union(%,"failed") if R has CHARNZ ---R conjug : R -> R if R has COMRING --R evaluateInverse : (%,(M -> M)) -> % --R makeop : (R,FreeGroup(BasicOperator)) -> % --R retractIfCan : % -> Union(BasicOperator,"failed") @@ -88362,9 +92068,10 @@ ModuleOperator(R: Ring, M:LeftModule(R)): Exports == Implementation where --R --R------------------------------- Operations -------------------------------- --R ?*? : (%,%) -> % ?**? : (%,Integer) -> % ---R ?**? : (%,PositiveInteger) -> % ?/? : (%,%) -> % ---R ?=? : (%,%) -> Boolean 1 : () -> % ---R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % +--R ?/? : (%,%) -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % ?^? : (%,Integer) -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % --R coerce : % -> OutputForm commutator : (%,%) -> % --R conjugate : (%,%) -> % eval : (%,F) -> F --R hash : % -> SingleInteger inv : % -> % @@ -88374,8 +92081,6 @@ ModuleOperator(R: Ring, M:LeftModule(R)): Exports == Implementation where --R sample : () -> % scale : (%,F) -> % --R scale : F -> % shift : (%,F) -> % --R shift : F -> % ?~=? : (%,%) -> Boolean ---R ?**? : (%,NonNegativeInteger) -> % ---R ?^? : (%,NonNegativeInteger) -> % --R eval : (%,OnePointCompletion(F)) -> OnePointCompletion(F) --R --E 1 @@ -88542,32 +92247,31 @@ MoebiusTransform(F): Exports == Implementation where --S 1 of 1 )show MonoidRing +--R --R MonoidRing(R: Ring,M: Monoid) is a domain constructor --R Abbreviation for MonoidRing is MRING --R This constructor is not exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for MRING --R --R------------------------------- Operations -------------------------------- +--R ?*? : (%,R) -> % if R has COMRING ?*? : (R,%) -> % if R has COMRING --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ?=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % coefficient : (%,M) -> R ---R coefficients : % -> List(R) coerce : R -> % ---R coerce : M -> % coerce : Integer -> % ---R coerce : % -> OutputForm hash : % -> SingleInteger ---R latex : % -> String map : ((R -> R),%) -> % ---R monomial : (R,M) -> % monomial? : % -> Boolean ---R monomials : % -> List(%) one? : % -> Boolean ---R recip : % -> Union(%,"failed") retract : % -> R +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R coefficient : (%,M) -> R coefficients : % -> List(R) +--R coerce : R -> % coerce : M -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R map : ((R -> R),%) -> % monomial : (R,M) -> % +--R monomial? : % -> Boolean monomials : % -> List(%) +--R one? : % -> Boolean recip : % -> Union(%,"failed") +--R reductum : % -> % if M has ORDSET retract : % -> R --R retract : % -> M sample : () -> % --R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (%,R) -> % if R has COMRING ---R ?*? : (R,%) -> % if R has COMRING ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R ?^? : (%,NonNegativeInteger) -> % --R characteristic : () -> NonNegativeInteger --R charthRoot : % -> Union(%,"failed") if R has CHARNZ --R coerce : List(Record(coef: R,monom: M)) -> % @@ -88578,7 +92282,6 @@ MoebiusTransform(F): Exports == Implementation where --R lookup : % -> PositiveInteger if M has FINITE and R has FINITE --R numberOfMonomials : % -> NonNegativeInteger --R random : () -> % if M has FINITE and R has FINITE ---R reductum : % -> % if M has ORDSET --R retractIfCan : % -> Union(R,"failed") --R retractIfCan : % -> Union(M,"failed") --R size : () -> NonNegativeInteger if M has FINITE and R has FINITE @@ -88987,7 +92690,8 @@ MonoidRing(R: Ring, M: Monoid): MRcategory == MRdefinition where )set message test on )set message auto off )clear all ---S 1 of 14 + +--S 1 of 15 s := multiset [1,2,3,4,5,4,3,2,3,4,5,6,7,4,10] --R --R @@ -88995,7 +92699,7 @@ s := multiset [1,2,3,4,5,4,3,2,3,4,5,6,7,4,10] --R Type: Multiset(PositiveInteger) --E 1 ---S 2 of 14 +--S 2 of 15 insert!(3,s) --R --R @@ -89003,7 +92707,7 @@ insert!(3,s) --R Type: Multiset(PositiveInteger) --E 2 ---S 3 of 14 +--S 3 of 15 remove!(3,s,1) --R --R @@ -89011,7 +92715,7 @@ remove!(3,s,1) --R Type: Multiset(PositiveInteger) --E 3 ---S 4 of 14 +--S 4 of 15 s --R --R @@ -89019,7 +92723,7 @@ s --R Type: Multiset(PositiveInteger) --E 4 ---S 5 of 14 +--S 5 of 15 remove!(5,s) --R --R @@ -89027,7 +92731,7 @@ remove!(5,s) --R Type: Multiset(PositiveInteger) --E 5 ---S 6 of 14 +--S 6 of 15 s --R --R @@ -89035,7 +92739,7 @@ s --R Type: Multiset(PositiveInteger) --E 6 ---S 7 of 14 +--S 7 of 15 count(5,s) --R --R @@ -89043,7 +92747,7 @@ count(5,s) --R Type: NonNegativeInteger --E 7 ---S 8 of 14 +--S 8 of 15 t := multiset [2,2,2,-9] --R --R @@ -89051,7 +92755,7 @@ t := multiset [2,2,2,-9] --R Type: Multiset(Integer) --E 8 ---S 9 of 14 +--S 9 of 15 U := union(s,t) --R --R @@ -89059,7 +92763,7 @@ U := union(s,t) --R Type: Multiset(Integer) --E 9 ---S 10 of 14 +--S 10 of 15 I := intersect(s,t) --R --R @@ -89067,7 +92771,7 @@ I := intersect(s,t) --R Type: Multiset(Integer) --E 10 ---S 11 of 14 +--S 11 of 15 difference(s,t) --R --R @@ -89075,7 +92779,7 @@ difference(s,t) --R Type: Multiset(Integer) --E 11 ---S 12 of 14 +--S 12 of 15 S := symmetricDifference(s,t) --R --R @@ -89083,7 +92787,7 @@ S := symmetricDifference(s,t) --R Type: Multiset(Integer) --E 12 ---S 13 of 14 +--S 13 of 15 (U = union(S,I))@Boolean --R --R @@ -89091,13 +92795,76 @@ S := symmetricDifference(s,t) --R Type: Boolean --E 13 ---S 14 of 14 +--S 14 of 15 t1 := multiset [1,2,2,3]; [t1 < t, t1 < s, t < s, t1 <= s] --R --R --R (14) [false,true,false,true] --R Type: List(Boolean) --E 14 + +--S 15 of 15 +)show Multiset +--R +--R Multiset(S: SetCategory) is a domain constructor +--R Abbreviation for Multiset is MSET +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for MSET +--R +--R------------------------------- Operations -------------------------------- +--R ? Boolean ?=? : (%,%) -> Boolean +--R bag : List(S) -> % brace : () -> % +--R brace : List(S) -> % coerce : % -> OutputForm +--R construct : List(S) -> % copy : % -> % +--R dictionary : List(S) -> % dictionary : () -> % +--R difference : (%,%) -> % difference : (%,S) -> % +--R empty : () -> % empty? : % -> Boolean +--R eq? : (%,%) -> Boolean extract! : % -> S +--R hash : % -> SingleInteger insert! : (S,%) -> % +--R inspect : % -> S intersect : (%,%) -> % +--R latex : % -> String map : ((S -> S),%) -> % +--R members : % -> List(S) multiset : List(S) -> % +--R multiset : S -> % multiset : () -> % +--R remove : (S,%,Integer) -> % remove! : (S,%,Integer) -> % +--R removeDuplicates! : % -> % sample : () -> % +--R set : () -> % set : List(S) -> % +--R subset? : (%,%) -> Boolean symmetricDifference : (%,%) -> % +--R union : (%,%) -> % union : (%,S) -> % +--R union : (S,%) -> % ?~=? : (%,%) -> Boolean +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R convert : % -> InputForm if S has KONVERT(INFORM) +--R count : (S,%) -> NonNegativeInteger if $ has finiteAggregate and S has SETCAT +--R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R duplicates : % -> List(Record(entry: S,count: NonNegativeInteger)) +--R eval : (%,List(S),List(S)) -> % if S has EVALAB(S) and S has SETCAT +--R eval : (%,S,S) -> % if S has EVALAB(S) and S has SETCAT +--R eval : (%,Equation(S)) -> % if S has EVALAB(S) and S has SETCAT +--R eval : (%,List(Equation(S))) -> % if S has EVALAB(S) and S has SETCAT +--R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R find : ((S -> Boolean),%) -> Union(S,"failed") +--R insert! : (S,%,NonNegativeInteger) -> % +--R less? : (%,NonNegativeInteger) -> Boolean +--R map! : ((S -> S),%) -> % if $ has shallowlyMutable +--R member? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT +--R more? : (%,NonNegativeInteger) -> Boolean +--R parts : % -> List(S) if $ has finiteAggregate +--R reduce : (((S,S) -> S),%) -> S if $ has finiteAggregate +--R reduce : (((S,S) -> S),%,S) -> S if $ has finiteAggregate +--R reduce : (((S,S) -> S),%,S,S) -> S if $ has finiteAggregate and S has SETCAT +--R remove : ((S -> Boolean),%,Integer) -> % +--R remove : ((S -> Boolean),%) -> % if $ has finiteAggregate +--R remove : (S,%) -> % if $ has finiteAggregate and S has SETCAT +--R remove! : ((S -> Boolean),%,Integer) -> % +--R remove! : ((S -> Boolean),%) -> % if $ has finiteAggregate +--R remove! : (S,%) -> % if $ has finiteAggregate +--R removeDuplicates : % -> % if $ has finiteAggregate and S has SETCAT +--R select : ((S -> Boolean),%) -> % if $ has finiteAggregate +--R select! : ((S -> Boolean),%) -> % if $ has finiteAggregate +--R size? : (%,NonNegativeInteger) -> Boolean +--R +--E 15 + )spool )lisp (bye) \end{chunk} @@ -89544,7 +93311,8 @@ Multiset(S: SetCategory): MultisetAggregate S with )set message test on )set message auto off )clear all ---S 1 of 9 + +--S 1 of 10 m : MPOLY([x,y],INT) := (x^2 - x*y^3 +3*y)^2 --R --R @@ -89553,7 +93321,7 @@ m : MPOLY([x,y],INT) := (x^2 - x*y^3 +3*y)^2 --R Type: MultivariatePolynomial([x,y],Integer) --E 1 ---S 2 of 9 +--S 2 of 10 m :: MPOLY([y,x],INT) --R --R @@ -89562,13 +93330,13 @@ m :: MPOLY([y,x],INT) --R Type: MultivariatePolynomial([y,x],Integer) --E 2 ---S 3 of 9 +--S 3 of 10 p : MPOLY([x,y],POLY INT) --R --R Type: Void --E 3 ---S 4 of 9 +--S 4 of 10 p :: POLY INT --R --R @@ -89576,7 +93344,7 @@ p :: POLY INT --R Type: Polynomial(Integer) --E 4 ---S 5 of 9 +--S 5 of 10 % :: MPOLY([a,b],POLY INT) --R --R @@ -89584,13 +93352,13 @@ p :: POLY INT --R Type: MultivariatePolynomial([a,b],Polynomial(Integer)) --E 5 ---S 6 of 9 +--S 6 of 10 q : UP(x, FRAC MPOLY([y,z],INT)) --R --R Type: Void --E 6 ---S 7 of 9 +--S 7 of 10 q := (x^2 - x*(z+1)/y +2)^2 --R --R @@ -89602,7 +93370,7 @@ q := (x^2 - x*(z+1)/y +2)^2 --RType: UnivariatePolynomial(x,Fraction(MultivariatePolynomial([y,z],Integer))) --E 7 ---S 8 of 9 +--S 8 of 10 q :: UP(z, FRAC MPOLY([x,y],INT)) --R --R @@ -89615,7 +93383,7 @@ q :: UP(z, FRAC MPOLY([x,y],INT)) --RType: UnivariatePolynomial(z,Fraction(MultivariatePolynomial([x,y],Integer))) --E 8 ---S 9 of 9 +--S 9 of 10 q :: MPOLY([x,z], FRAC UP(y,INT)) --R --R @@ -89626,6 +93394,133 @@ q :: MPOLY([x,z], FRAC UP(y,INT)) --R y y y --RType: MultivariatePolynomial([x,z],Fraction(UnivariatePolynomial(y,Integer))) --E 9 + +--S 10 of 10 +)show MultivariatePolynomial +--R +--R MultivariatePolynomial(vl: List(Symbol),R: Ring) is a domain constructor +--R Abbreviation for MultivariatePolynomial is MPOLY +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for MPOLY +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,R) -> % ?*? : (R,%) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?/? : (%,R) -> % if R has FIELD +--R ?=? : (%,%) -> Boolean 1 : () -> % +--R 0 : () -> % ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,PositiveInteger) -> % coefficients : % -> List(R) +--R coerce : % -> % if R has INTDOM coerce : R -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R content : % -> R if R has GCDDOM eval : (%,List(%),List(%)) -> % +--R eval : (%,%,%) -> % eval : (%,Equation(%)) -> % +--R eval : (%,List(Equation(%))) -> % gcd : (%,%) -> % if R has GCDDOM +--R gcd : List(%) -> % if R has GCDDOM ground : % -> R +--R ground? : % -> Boolean hash : % -> SingleInteger +--R latex : % -> String lcm : (%,%) -> % if R has GCDDOM +--R lcm : List(%) -> % if R has GCDDOM leadingCoefficient : % -> R +--R leadingMonomial : % -> % map : ((R -> R),%) -> % +--R max : (%,%) -> % if R has ORDSET min : (%,%) -> % if R has ORDSET +--R monomial? : % -> Boolean monomials : % -> List(%) +--R one? : % -> Boolean primitiveMonomials : % -> List(%) +--R recip : % -> Union(%,"failed") reductum : % -> % +--R retract : % -> R sample : () -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (Fraction(Integer),%) -> % if R has ALGEBRA(FRAC(INT)) +--R ?*? : (%,Fraction(Integer)) -> % if R has ALGEBRA(FRAC(INT)) +--R ? Boolean if R has ORDSET +--R ?<=? : (%,%) -> Boolean if R has ORDSET +--R ?>? : (%,%) -> Boolean if R has ORDSET +--R ?>=? : (%,%) -> Boolean if R has ORDSET +--R D : (%,List(OrderedVariableList(vl)),List(NonNegativeInteger)) -> % +--R D : (%,OrderedVariableList(vl),NonNegativeInteger) -> % +--R D : (%,List(OrderedVariableList(vl))) -> % +--R D : (%,OrderedVariableList(vl)) -> % +--R associates? : (%,%) -> Boolean if R has INTDOM +--R binomThmExpt : (%,%,NonNegativeInteger) -> % if R has COMRING +--R characteristic : () -> NonNegativeInteger +--R charthRoot : % -> Union(%,"failed") if $ has CHARNZ and R has PFECAT or R has CHARNZ +--R coefficient : (%,List(OrderedVariableList(vl)),List(NonNegativeInteger)) -> % +--R coefficient : (%,OrderedVariableList(vl),NonNegativeInteger) -> % +--R coefficient : (%,IndexedExponents(OrderedVariableList(vl))) -> R +--R coerce : Fraction(Integer) -> % if R has ALGEBRA(FRAC(INT)) or R has RETRACT(FRAC(INT)) +--R coerce : OrderedVariableList(vl) -> % +--R conditionP : Matrix(%) -> Union(Vector(%),"failed") if $ has CHARNZ and R has PFECAT +--R content : (%,OrderedVariableList(vl)) -> % if R has GCDDOM +--R convert : % -> InputForm if OrderedVariableList(vl) has KONVERT(INFORM) and R has KONVERT(INFORM) +--R convert : % -> Pattern(Integer) if OrderedVariableList(vl) has KONVERT(PATTERN(INT)) and R has KONVERT(PATTERN(INT)) +--R convert : % -> Pattern(Float) if OrderedVariableList(vl) has KONVERT(PATTERN(FLOAT)) and R has KONVERT(PATTERN(FLOAT)) +--R degree : (%,List(OrderedVariableList(vl))) -> List(NonNegativeInteger) +--R degree : (%,OrderedVariableList(vl)) -> NonNegativeInteger +--R degree : % -> IndexedExponents(OrderedVariableList(vl)) +--R differentiate : (%,List(OrderedVariableList(vl)),List(NonNegativeInteger)) -> % +--R differentiate : (%,OrderedVariableList(vl),NonNegativeInteger) -> % +--R differentiate : (%,List(OrderedVariableList(vl))) -> % +--R differentiate : (%,OrderedVariableList(vl)) -> % +--R discriminant : (%,OrderedVariableList(vl)) -> % if R has COMRING +--R eval : (%,List(OrderedVariableList(vl)),List(%)) -> % +--R eval : (%,OrderedVariableList(vl),%) -> % +--R eval : (%,List(OrderedVariableList(vl)),List(R)) -> % +--R eval : (%,OrderedVariableList(vl),R) -> % +--R exquo : (%,%) -> Union(%,"failed") if R has INTDOM +--R exquo : (%,R) -> Union(%,"failed") if R has INTDOM +--R factor : % -> Factored(%) if R has PFECAT +--R factorPolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has PFECAT +--R factorSquareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has PFECAT +--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) if R has GCDDOM +--R isExpt : % -> Union(Record(var: OrderedVariableList(vl),exponent: NonNegativeInteger),"failed") +--R isPlus : % -> Union(List(%),"failed") +--R isTimes : % -> Union(List(%),"failed") +--R lcmCoef : (%,%) -> Record(llcmres: %,coeff1: %,coeff2: %) if R has GCDDOM +--R mainVariable : % -> Union(OrderedVariableList(vl),"failed") +--R mapExponents : ((IndexedExponents(OrderedVariableList(vl)) -> IndexedExponents(OrderedVariableList(vl))),%) -> % +--R minimumDegree : (%,List(OrderedVariableList(vl))) -> List(NonNegativeInteger) +--R minimumDegree : (%,OrderedVariableList(vl)) -> NonNegativeInteger +--R minimumDegree : % -> IndexedExponents(OrderedVariableList(vl)) +--R monicDivide : (%,%,OrderedVariableList(vl)) -> Record(quotient: %,remainder: %) +--R monomial : (%,List(OrderedVariableList(vl)),List(NonNegativeInteger)) -> % +--R monomial : (%,OrderedVariableList(vl),NonNegativeInteger) -> % +--R monomial : (R,IndexedExponents(OrderedVariableList(vl))) -> % +--R multivariate : (SparseUnivariatePolynomial(%),OrderedVariableList(vl)) -> % +--R multivariate : (SparseUnivariatePolynomial(R),OrderedVariableList(vl)) -> % +--R numberOfMonomials : % -> NonNegativeInteger +--R patternMatch : (%,Pattern(Integer),PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if OrderedVariableList(vl) has PATMAB(INT) and R has PATMAB(INT) +--R patternMatch : (%,Pattern(Float),PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if OrderedVariableList(vl) has PATMAB(FLOAT) and R has PATMAB(FLOAT) +--R pomopo! : (%,R,IndexedExponents(OrderedVariableList(vl)),%) -> % +--R prime? : % -> Boolean if R has PFECAT +--R primitivePart : (%,OrderedVariableList(vl)) -> % if R has GCDDOM +--R primitivePart : % -> % if R has GCDDOM +--R reducedSystem : Matrix(%) -> Matrix(R) +--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(R),vec: Vector(R)) +--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(Integer),vec: Vector(Integer)) if R has LINEXP(INT) +--R reducedSystem : Matrix(%) -> Matrix(Integer) if R has LINEXP(INT) +--R resultant : (%,%,OrderedVariableList(vl)) -> % if R has COMRING +--R retract : % -> OrderedVariableList(vl) +--R retract : % -> Integer if R has RETRACT(INT) +--R retract : % -> Fraction(Integer) if R has RETRACT(FRAC(INT)) +--R retractIfCan : % -> Union(OrderedVariableList(vl),"failed") +--R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT(INT) +--R retractIfCan : % -> Union(Fraction(Integer),"failed") if R has RETRACT(FRAC(INT)) +--R retractIfCan : % -> Union(R,"failed") +--R solveLinearPolynomialEquation : (List(SparseUnivariatePolynomial(%)),SparseUnivariatePolynomial(%)) -> Union(List(SparseUnivariatePolynomial(%)),"failed") if R has PFECAT +--R squareFree : % -> Factored(%) if R has GCDDOM +--R squareFreePart : % -> % if R has GCDDOM +--R squareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has PFECAT +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R totalDegree : (%,List(OrderedVariableList(vl))) -> NonNegativeInteger +--R totalDegree : % -> NonNegativeInteger +--R unit? : % -> Boolean if R has INTDOM +--R unitCanonical : % -> % if R has INTDOM +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) if R has INTDOM +--R univariate : % -> SparseUnivariatePolynomial(R) +--R univariate : (%,OrderedVariableList(vl)) -> SparseUnivariatePolynomial(%) +--R variables : % -> List(OrderedVariableList(vl)) +--R +--E 10 + )spool )lisp (bye) \end{chunk} @@ -89871,33 +93766,42 @@ MultivariatePolynomial(vl:List Symbol, R:Ring) --R Issue )edit bookvol10.3.pamphlet to see algebra source code for MYEXPR --R --R------------------------------- Operations -------------------------------- ---R ?*? : (PositiveInteger,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (%,%) -> % ?**? : (%,%) -> % ---R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?*? : (NonNegativeInteger,%) -> % +--R ?*? : (Integer,%) -> % ?*? : (%,%) -> % +--R ?*? : (%,R) -> % if R has COMRING ?*? : (R,%) -> % if R has COMRING +--R ?**? : (%,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?+? : (%,%) -> % --R -? : % -> % ?-? : (%,%) -> % --R ?/? : (%,%) -> % ? Boolean --R ?<=? : (%,%) -> Boolean ?=? : (%,%) -> Boolean --R ?>? : (%,%) -> Boolean ?>=? : (%,%) -> Boolean --R D : (%,Symbol) -> % D : (%,List(Symbol)) -> % --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % applyQuote : (Symbol,%,%) -> % ---R applyQuote : (Symbol,%) -> % associates? : (%,%) -> Boolean ---R belong? : BasicOperator -> Boolean binomial : (%,%) -> % ---R box : List(%) -> % box : % -> % ---R coerce : Integer -> % coerce : % -> % ---R coerce : R -> % coerce : Symbol -> % ---R coerce : Kernel(%) -> % coerce : % -> OutputForm ---R denominator : % -> % differentiate : (%,Symbol) -> % ---R distribute : (%,%) -> % distribute : % -> % ---R elt : (BasicOperator,%,%) -> % elt : (BasicOperator,%) -> % ---R eval : (%,%,%) -> % eval : (%,Equation(%)) -> % +--R ?^? : (%,PositiveInteger) -> % ?^? : (%,NonNegativeInteger) -> % +--R applyQuote : (Symbol,List(%)) -> % applyQuote : (Symbol,%,%,%) -> % +--R applyQuote : (Symbol,%,%) -> % applyQuote : (Symbol,%) -> % +--R associates? : (%,%) -> Boolean belong? : BasicOperator -> Boolean +--R binomial : (%,%) -> % box : List(%) -> % +--R box : % -> % coerce : Integer -> % +--R coerce : % -> % coerce : R -> % +--R coerce : Symbol -> % coerce : Kernel(%) -> % +--R coerce : % -> OutputForm denominator : % -> % +--R differentiate : (%,Symbol) -> % distribute : (%,%) -> % +--R distribute : % -> % elt : (BasicOperator,List(%)) -> % +--R elt : (BasicOperator,%,%,%) -> % elt : (BasicOperator,%,%) -> % +--R elt : (BasicOperator,%) -> % eval : (%,Symbol,(% -> %)) -> % +--R eval : (%,List(%),List(%)) -> % eval : (%,%,%) -> % +--R eval : (%,Equation(%)) -> % eval : (%,List(Equation(%))) -> % --R eval : (%,Kernel(%),%) -> % factorial : % -> % --R factorials : % -> % factorials : (%,Symbol) -> % --R freeOf? : (%,Symbol) -> Boolean freeOf? : (%,%) -> Boolean +--R gcd : (%,%) -> % if R has INTDOM gcd : List(%) -> % if R has INTDOM --R ground : % -> R ground? : % -> Boolean --R hash : % -> SingleInteger height : % -> NonNegativeInteger ---R is? : (%,Symbol) -> Boolean kernel : (BasicOperator,%) -> % ---R kernels : % -> List(Kernel(%)) latex : % -> String +--R is? : (%,Symbol) -> Boolean is? : (%,BasicOperator) -> Boolean +--R kernel : (BasicOperator,%) -> % kernels : % -> List(Kernel(%)) +--R latex : % -> String lcm : (%,%) -> % if R has INTDOM +--R lcm : List(%) -> % if R has INTDOM map : ((% -> %),Kernel(%)) -> % --R max : (%,%) -> % min : (%,%) -> % --R numerator : % -> % one? : % -> Boolean --R paren : List(%) -> % paren : % -> % @@ -89909,21 +93813,14 @@ MultivariatePolynomial(vl:List Symbol, R:Ring) --R tower : % -> List(Kernel(%)) unit? : % -> Boolean --R unitCanonical : % -> % variables : % -> List(Symbol) --R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?*? : (%,R) -> % if R has COMRING ---R ?*? : (R,%) -> % if R has COMRING --R ?*? : (%,Fraction(Integer)) -> % if R has INTDOM --R ?*? : (Fraction(Integer),%) -> % if R has INTDOM --R ?**? : (%,Integer) -> % if R has GROUP or R has INTDOM ---R ?**? : (%,NonNegativeInteger) -> % --R ?/? : (SparseMultivariatePolynomial(R,Kernel(%)),SparseMultivariatePolynomial(R,Kernel(%))) -> % if R has INTDOM --R D : (%,Symbol,NonNegativeInteger) -> % --R D : (%,List(Symbol),List(NonNegativeInteger)) -> % --R ?^? : (%,Integer) -> % if R has GROUP or R has INTDOM ---R ?^? : (%,NonNegativeInteger) -> % ---R applyQuote : (Symbol,List(%)) -> % --R applyQuote : (Symbol,%,%,%,%) -> % ---R applyQuote : (Symbol,%,%,%) -> % --R characteristic : () -> NonNegativeInteger --R charthRoot : % -> Union(%,"failed") if R has CHARNZ --R coerce : Fraction(Integer) -> % if R has INTDOM or R has RETRACT(FRAC(INT)) @@ -89947,9 +93844,7 @@ MultivariatePolynomial(vl:List Symbol, R:Ring) --R differentiate : (%,Symbol,NonNegativeInteger) -> % --R differentiate : (%,List(Symbol),List(NonNegativeInteger)) -> % --R divide : (%,%) -> Record(quotient: %,remainder: %) if R has INTDOM ---R elt : (BasicOperator,List(%)) -> % --R elt : (BasicOperator,%,%,%,%) -> % ---R elt : (BasicOperator,%,%,%) -> % --R euclideanSize : % -> NonNegativeInteger if R has INTDOM --R eval : (%,Symbol,NonNegativeInteger,(% -> %)) -> % if R has RING --R eval : (%,Symbol,NonNegativeInteger,(List(%) -> %)) -> % if R has RING @@ -89964,12 +93859,9 @@ MultivariatePolynomial(vl:List Symbol, R:Ring) --R eval : (%,BasicOperator,(List(%) -> %)) -> % --R eval : (%,List(BasicOperator),List((List(%) -> %))) -> % --R eval : (%,List(BasicOperator),List((% -> %))) -> % ---R eval : (%,Symbol,(% -> %)) -> % --R eval : (%,Symbol,(List(%) -> %)) -> % --R eval : (%,List(Symbol),List((List(%) -> %))) -> % --R eval : (%,List(Symbol),List((% -> %))) -> % ---R eval : (%,List(%),List(%)) -> % ---R eval : (%,List(Equation(%))) -> % --R eval : (%,List(Kernel(%)),List(%)) -> % --R even? : % -> Boolean if $ has RETRACT(INT) --R expressIdealMember : (List(%),%) -> Union(List(%),"failed") if R has INTDOM @@ -89977,11 +93869,8 @@ MultivariatePolynomial(vl:List Symbol, R:Ring) --R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) if R has INTDOM --R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") if R has INTDOM --R factor : % -> Factored(%) if R has INTDOM ---R gcd : (%,%) -> % if R has INTDOM ---R gcd : List(%) -> % if R has INTDOM --R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) if R has INTDOM --R inv : % -> % if R has GROUP or R has INTDOM ---R is? : (%,BasicOperator) -> Boolean --R isExpt : (%,Symbol) -> Union(Record(var: Kernel(%),exponent: Integer),"failed") if R has RING --R isExpt : (%,BasicOperator) -> Union(Record(var: Kernel(%),exponent: Integer),"failed") if R has RING --R isExpt : % -> Union(Record(var: Kernel(%),exponent: Integer),"failed") if R has SGROUP @@ -89990,11 +93879,8 @@ MultivariatePolynomial(vl:List Symbol, R:Ring) --R isPower : % -> Union(Record(val: %,exponent: Integer),"failed") if R has RING --R isTimes : % -> Union(List(%),"failed") if R has SGROUP --R kernel : (BasicOperator,List(%)) -> % ---R lcm : (%,%) -> % if R has INTDOM ---R lcm : List(%) -> % if R has INTDOM --R lcmCoef : (%,%) -> Record(llcmres: %,coeff1: %,coeff2: %) if R has INTDOM --R mainKernel : % -> Union(Kernel(%),"failed") ---R map : ((% -> %),Kernel(%)) -> % --R minPoly : Kernel(%) -> SparseUnivariatePolynomial(%) if $ has RING --R multiEuclidean : (List(%),%) -> Union(List(%),"failed") if R has INTDOM --R numer : % -> SparseMultivariatePolynomial(R,Kernel(%)) if R has RING @@ -90244,34 +94130,41 @@ MyExpression(q: Symbol, R): Exports == Implementation where --R------------------------------- Operations -------------------------------- --R ?*? : (%,R) -> % ?*? : (R,%) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % ---R -? : % -> % ?=? : (%,%) -> Boolean ---R D : (%,(R -> R)) -> % D : % -> % ---R D : (%,NonNegativeInteger) -> % 1 : () -> % ---R 0 : () -> % ?^? : (%,PositiveInteger) -> % ---R coefficients : % -> List(R) coerce : Symbol -> % +--R -? : % -> % ?/? : (%,R) -> % if R has FIELD +--R ?=? : (%,%) -> Boolean D : (%,(R -> R)) -> % +--R D : % -> % D : (%,NonNegativeInteger) -> % +--R D : (%,SingletonAsOrderedSet) -> % 1 : () -> % +--R 0 : () -> % ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,PositiveInteger) -> % coefficients : % -> List(R) +--R coerce : % -> % if R has INTDOM coerce : Symbol -> % --R coerce : Polynomial(R) -> % coerce : Variable(x) -> % ---R coerce : R -> % coerce : Integer -> % ---R coerce : % -> OutputForm degree : % -> NonNegativeInteger ---R differentiate : % -> % ?.? : (%,%) -> % ---R ?.? : (%,R) -> R eval : (%,%,%) -> % ---R eval : (%,Equation(%)) -> % ground : % -> R ---R ground? : % -> Boolean hash : % -> SingleInteger ---R init : () -> % if R has STEP latex : % -> String ---R leadingCoefficient : % -> R leadingMonomial : % -> % ---R map : ((R -> R),%) -> % monomial? : % -> Boolean ---R monomials : % -> List(%) one? : % -> Boolean ---R pseudoRemainder : (%,%) -> % recip : % -> Union(%,"failed") ---R reductum : % -> % retract : % -> Symbol +--R coerce : SingletonAsOrderedSet -> % coerce : R -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R content : % -> R if R has GCDDOM degree : % -> NonNegativeInteger +--R differentiate : (%,(R -> R)) -> % differentiate : % -> % +--R ?.? : (%,%) -> % ?.? : (%,R) -> R +--R eval : (%,List(%),List(%)) -> % eval : (%,%,%) -> % +--R eval : (%,Equation(%)) -> % eval : (%,List(Equation(%))) -> % +--R gcd : (%,%) -> % if R has GCDDOM gcd : List(%) -> % if R has GCDDOM +--R ground : % -> R ground? : % -> Boolean +--R hash : % -> SingleInteger init : () -> % if R has STEP +--R latex : % -> String lcm : (%,%) -> % if R has GCDDOM +--R lcm : List(%) -> % if R has GCDDOM leadingCoefficient : % -> R +--R leadingMonomial : % -> % map : ((R -> R),%) -> % +--R max : (%,%) -> % if R has ORDSET min : (%,%) -> % if R has ORDSET +--R monomial? : % -> Boolean monomials : % -> List(%) +--R one? : % -> Boolean primitiveMonomials : % -> List(%) +--R pseudoRemainder : (%,%) -> % ?quo? : (%,%) -> % if R has FIELD +--R recip : % -> Union(%,"failed") reductum : % -> % +--R ?rem? : (%,%) -> % if R has FIELD retract : % -> Symbol --R retract : % -> R sample : () -> % --R unvectorise : Vector(R) -> % zero? : % -> Boolean --R ?~=? : (%,%) -> Boolean --R ?*? : (Fraction(Integer),%) -> % if R has ALGEBRA(FRAC(INT)) --R ?*? : (%,Fraction(Integer)) -> % if R has ALGEBRA(FRAC(INT)) ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R ?/? : (%,R) -> % if R has FIELD --R ? Boolean if R has ORDSET --R ?<=? : (%,%) -> Boolean if R has ORDSET --R ?>? : (%,%) -> Boolean if R has ORDSET @@ -90284,8 +94177,6 @@ MyExpression(q: Symbol, R): Exports == Implementation where --R D : (%,List(SingletonAsOrderedSet),List(NonNegativeInteger)) -> % --R D : (%,SingletonAsOrderedSet,NonNegativeInteger) -> % --R D : (%,List(SingletonAsOrderedSet)) -> % ---R D : (%,SingletonAsOrderedSet) -> % ---R ?^? : (%,NonNegativeInteger) -> % --R associates? : (%,%) -> Boolean if R has INTDOM --R binomThmExpt : (%,%,NonNegativeInteger) -> % if R has COMRING --R characteristic : () -> NonNegativeInteger @@ -90293,21 +94184,17 @@ MyExpression(q: Symbol, R): Exports == Implementation where --R coefficient : (%,List(SingletonAsOrderedSet),List(NonNegativeInteger)) -> % --R coefficient : (%,SingletonAsOrderedSet,NonNegativeInteger) -> % --R coefficient : (%,NonNegativeInteger) -> R ---R coerce : % -> % if R has INTDOM --R coerce : Fraction(Integer) -> % if R has ALGEBRA(FRAC(INT)) or R has RETRACT(FRAC(INT)) ---R coerce : SingletonAsOrderedSet -> % --R composite : (Fraction(%),%) -> Union(Fraction(%),"failed") if R has INTDOM --R composite : (%,%) -> Union(%,"failed") if R has INTDOM --R conditionP : Matrix(%) -> Union(Vector(%),"failed") if $ has CHARNZ and R has PFECAT --R content : (%,SingletonAsOrderedSet) -> % if R has GCDDOM ---R content : % -> R if R has GCDDOM --R convert : % -> InputForm if SingletonAsOrderedSet has KONVERT(INFORM) and R has KONVERT(INFORM) --R convert : % -> Pattern(Integer) if SingletonAsOrderedSet has KONVERT(PATTERN(INT)) and R has KONVERT(PATTERN(INT)) --R convert : % -> Pattern(Float) if SingletonAsOrderedSet has KONVERT(PATTERN(FLOAT)) and R has KONVERT(PATTERN(FLOAT)) --R degree : (%,List(SingletonAsOrderedSet)) -> List(NonNegativeInteger) --R degree : (%,SingletonAsOrderedSet) -> NonNegativeInteger --R differentiate : (%,(R -> R),%) -> % ---R differentiate : (%,(R -> R)) -> % --R differentiate : (%,(R -> R),NonNegativeInteger) -> % --R differentiate : (%,List(Symbol),List(NonNegativeInteger)) -> % if R has PDRING(SYMBOL) --R differentiate : (%,Symbol,NonNegativeInteger) -> % if R has PDRING(SYMBOL) @@ -90330,8 +94217,6 @@ MyExpression(q: Symbol, R): Exports == Implementation where --R eval : (%,SingletonAsOrderedSet,%) -> % --R eval : (%,List(SingletonAsOrderedSet),List(R)) -> % --R eval : (%,SingletonAsOrderedSet,R) -> % ---R eval : (%,List(%),List(%)) -> % ---R eval : (%,List(Equation(%))) -> % --R expressIdealMember : (List(%),%) -> Union(List(%),"failed") if R has FIELD --R exquo : (%,%) -> Union(%,"failed") if R has INTDOM --R exquo : (%,R) -> Union(%,"failed") if R has INTDOM @@ -90341,22 +94226,16 @@ MyExpression(q: Symbol, R): Exports == Implementation where --R factorPolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has PFECAT --R factorSquareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has PFECAT --R fmecg : (%,NonNegativeInteger,R,%) -> % ---R gcd : (%,%) -> % if R has GCDDOM ---R gcd : List(%) -> % if R has GCDDOM --R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) if R has GCDDOM --R integrate : % -> % if R has ALGEBRA(FRAC(INT)) --R isExpt : % -> Union(Record(var: SingletonAsOrderedSet,exponent: NonNegativeInteger),"failed") --R isPlus : % -> Union(List(%),"failed") --R isTimes : % -> Union(List(%),"failed") --R karatsubaDivide : (%,NonNegativeInteger) -> Record(quotient: %,remainder: %) ---R lcm : (%,%) -> % if R has GCDDOM ---R lcm : List(%) -> % if R has GCDDOM --R lcmCoef : (%,%) -> Record(llcmres: %,coeff1: %,coeff2: %) if R has GCDDOM --R mainVariable : % -> Union(SingletonAsOrderedSet,"failed") --R makeSUP : % -> SparseUnivariatePolynomial(R) --R mapExponents : ((NonNegativeInteger -> NonNegativeInteger),%) -> % ---R max : (%,%) -> % if R has ORDSET ---R min : (%,%) -> % if R has ORDSET --R minimumDegree : (%,List(SingletonAsOrderedSet)) -> List(NonNegativeInteger) --R minimumDegree : (%,SingletonAsOrderedSet) -> NonNegativeInteger --R minimumDegree : % -> NonNegativeInteger @@ -90376,18 +94255,15 @@ MyExpression(q: Symbol, R): Exports == Implementation where --R patternMatch : (%,Pattern(Float),PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if SingletonAsOrderedSet has PATMAB(FLOAT) and R has PATMAB(FLOAT) --R pomopo! : (%,R,NonNegativeInteger,%) -> % --R prime? : % -> Boolean if R has PFECAT ---R primitiveMonomials : % -> List(%) --R primitivePart : (%,SingletonAsOrderedSet) -> % if R has GCDDOM --R primitivePart : % -> % if R has GCDDOM --R principalIdeal : List(%) -> Record(coef: List(%),generator: %) if R has FIELD --R pseudoDivide : (%,%) -> Record(coef: R,quotient: %,remainder: %) if R has INTDOM --R pseudoQuotient : (%,%) -> % if R has INTDOM ---R ?quo? : (%,%) -> % if R has FIELD --R reducedSystem : Matrix(%) -> Matrix(R) --R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(R),vec: Vector(R)) --R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(Integer),vec: Vector(Integer)) if R has LINEXP(INT) --R reducedSystem : Matrix(%) -> Matrix(Integer) if R has LINEXP(INT) ---R ?rem? : (%,%) -> % if R has FIELD --R resultant : (%,%) -> R if R has COMRING --R resultant : (%,%,SingletonAsOrderedSet) -> % if R has COMRING --R retract : % -> SingletonAsOrderedSet @@ -90625,32 +94501,36 @@ MyUnivariatePolynomial(x:Symbol, R:Ring): --R ?*? : (%,K) -> % ?*? : (K,%) -> % --R ?*? : (Fraction(Integer),%) -> % ?*? : (%,Fraction(Integer)) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,Integer) -> % ?**? : (%,NonNegativeInteger) -> % --R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % --R ?-? : (%,%) -> % -? : % -> % ---R ?/? : (%,%) -> % ?=? : (%,%) -> Boolean ---R 1 : () -> % 0 : () -> % ---R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> % +--R ?/? : (%,K) -> % if K has FIELD ?/? : (%,%) -> % +--R ?=? : (%,%) -> Boolean 1 : () -> % +--R 0 : () -> % ?^? : (%,Integer) -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % --R associates? : (%,%) -> Boolean center : % -> K --R children : % -> List(%) coefOfFirstNonZeroTerm : % -> K ---R coefficient : (%,Integer) -> K coerce : Fraction(Integer) -> % ---R coerce : % -> % coerce : Integer -> % ---R coerce : % -> OutputForm complete : % -> % ---R concat : (%,%) -> % concat : List(%) -> % ---R copy : % -> % cycleEntry : % -> % ---R cycleTail : % -> % cyclic? : % -> Boolean ---R degree : % -> Integer delay : (() -> %) -> % ---R delete : (%,Integer) -> % distance : (%,%) -> Integer ---R ?.rest : (%,rest) -> % ?.? : (%,Integer) -> K ---R empty : () -> % empty? : % -> Boolean ---R eq? : (%,%) -> Boolean explicitEntries? : % -> Boolean ---R explicitlyEmpty? : % -> Boolean explicitlyFinite? : % -> Boolean ---R extend : (%,Integer) -> % factor : % -> Factored(%) ---R filterUpTo : (%,Integer) -> % findCoef : (%,Integer) -> K +--R coefficient : (%,Integer) -> K coerce : K -> % if K has COMRING +--R coerce : Fraction(Integer) -> % coerce : % -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R complete : % -> % concat : (%,%) -> % +--R concat : List(%) -> % copy : % -> % +--R cycleEntry : % -> % cycleTail : % -> % +--R cyclic? : % -> Boolean degree : % -> Integer +--R delay : (() -> %) -> % delete : (%,Integer) -> % +--R distance : (%,%) -> Integer ?.rest : (%,rest) -> % +--R ?.? : (%,Integer) -> K empty : () -> % +--R empty? : % -> Boolean eq? : (%,%) -> Boolean +--R explicitEntries? : % -> Boolean explicitlyEmpty? : % -> Boolean +--R explicitlyFinite? : % -> Boolean extend : (%,Integer) -> % +--R factor : % -> Factored(%) filterUpTo : (%,Integer) -> % +--R findCoef : (%,Integer) -> K frst : % -> Record(k: Integer,c: K) --R gcd : List(%) -> % gcd : (%,%) -> % --R hash : % -> SingleInteger index? : (Integer,%) -> Boolean --R indices : % -> List(Integer) insert : (%,%,Integer) -> % ---R inv : % -> % latex : % -> String +--R inv : % -> % last : % -> Record(k: Integer,c: K) +--R last : (%,NonNegativeInteger) -> % latex : % -> String --R lazy? : % -> Boolean lazyEvaluate : % -> % --R lcm : List(%) -> % lcm : (%,%) -> % --R leadingCoefficient : % -> K leadingMonomial : % -> % @@ -90665,25 +94545,22 @@ MyUnivariatePolynomial(x:Symbol, R:Ring): --R recip : % -> Union(%,"failed") reductum : % -> % --R ?rem? : (%,%) -> % removeFirstZeroes : % -> % --R removeZeroes : % -> % removeZeroes : (Integer,%) -> % ---R rest : % -> % rst : % -> % ---R sample : () -> % sbt : (%,%) -> % ---R series : (Integer,K,%) -> % shift : (%,Integer) -> % ---R sizeLess? : (%,%) -> Boolean squareFree : % -> Factored(%) ---R squareFreePart : % -> % tail : % -> % ---R truncate : (%,Integer) -> % unit? : % -> Boolean ---R unitCanonical : % -> % variable : % -> Symbol ---R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R rest : % -> % rest : (%,NonNegativeInteger) -> % +--R rst : % -> % sample : () -> % +--R sbt : (%,%) -> % series : (Integer,K,%) -> % +--R shift : (%,Integer) -> % sizeLess? : (%,%) -> Boolean +--R squareFree : % -> Factored(%) squareFreePart : % -> % +--R tail : % -> % truncate : (%,Integer) -> % +--R unit? : % -> Boolean unitCanonical : % -> % +--R variable : % -> Symbol zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean --R #? : % -> NonNegativeInteger if $ has finiteAggregate ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R ?/? : (%,K) -> % if K has FIELD --R D : (%,List(Symbol),List(NonNegativeInteger)) -> % if K has *: (Integer,K) -> K and K has PDRING(SYMBOL) --R D : (%,Symbol,NonNegativeInteger) -> % if K has *: (Integer,K) -> K and K has PDRING(SYMBOL) --R D : (%,List(Symbol)) -> % if K has *: (Integer,K) -> K and K has PDRING(SYMBOL) --R D : (%,Symbol) -> % if K has *: (Integer,K) -> K and K has PDRING(SYMBOL) --R D : (%,NonNegativeInteger) -> % if K has *: (Integer,K) -> K --R D : % -> % if K has *: (Integer,K) -> K ---R ?^? : (%,NonNegativeInteger) -> % --R any? : ((Record(k: Integer,c: K) -> Boolean),%) -> Boolean if $ has finiteAggregate --R approximate : (%,Integer) -> K if K has **: (K,Integer) -> K and K has coerce: Symbol -> K --R characteristic : () -> NonNegativeInteger @@ -90691,7 +94568,6 @@ MyUnivariatePolynomial(x:Symbol, R:Ring): --R child? : (%,%) -> Boolean if Record(k: Integer,c: K) has SETCAT --R coerce : % -> Stream(Record(k: Integer,c: K)) --R coerce : Stream(Record(k: Integer,c: K)) -> % ---R coerce : K -> % if K has COMRING --R concat : (Record(k: Integer,c: K),%) -> % --R concat : (%,Record(k: Integer,c: K)) -> % --R concat! : (%,%) -> % if $ has shallowlyMutable @@ -90735,11 +94611,8 @@ MyUnivariatePolynomial(x:Symbol, R:Ring): --R findTerm : (%,Integer) -> Record(k: Integer,c: K) --R first : % -> Record(k: Integer,c: K) --R first : (%,NonNegativeInteger) -> % ---R frst : % -> Record(k: Integer,c: K) --R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) --R insert : (Record(k: Integer,c: K),%,Integer) -> % ---R last : % -> Record(k: Integer,c: K) ---R last : (%,NonNegativeInteger) -> % --R lcmCoef : (%,%) -> Record(llcmres: %,coeff1: %,coeff2: %) --R leaves : % -> List(Record(k: Integer,c: K)) --R less? : (%,NonNegativeInteger) -> Boolean @@ -90770,7 +94643,6 @@ MyUnivariatePolynomial(x:Symbol, R:Ring): --R remove : (Record(k: Integer,c: K),%) -> % if $ has finiteAggregate and Record(k: Integer,c: K) has SETCAT --R remove : ((Record(k: Integer,c: K) -> Boolean),%) -> % --R removeDuplicates : % -> % if $ has finiteAggregate and Record(k: Integer,c: K) has SETCAT ---R rest : (%,NonNegativeInteger) -> % --R second : % -> Record(k: Integer,c: K) --R select : ((Record(k: Integer,c: K) -> Boolean),%) -> % --R setchildren! : (%,List(%)) -> % if $ has shallowlyMutable @@ -91242,46 +95114,52 @@ by means of triangular sets. --R------------------------------- Operations -------------------------------- --R ?*? : (%,R) -> % ?*? : (R,%) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % ---R -? : % -> % ?=? : (%,%) -> Boolean ---R D : (%,List(VarSet)) -> % D : (%,VarSet) -> % ---R 1 : () -> % 0 : () -> % +--R -? : % -> % ?/? : (%,R) -> % if R has FIELD +--R ?=? : (%,%) -> Boolean D : (%,List(VarSet)) -> % +--R D : (%,VarSet) -> % 1 : () -> % +--R 0 : () -> % ?^? : (%,NonNegativeInteger) -> % --R ?^? : (%,PositiveInteger) -> % coefficients : % -> List(R) ---R coerce : VarSet -> % coerce : R -> % ---R coerce : Integer -> % coerce : % -> OutputForm +--R coerce : % -> % if R has INTDOM coerce : VarSet -> % +--R coerce : R -> % coerce : Integer -> % +--R coerce : % -> OutputForm content : % -> R if R has GCDDOM --R deepestInitial : % -> % deepestTail : % -> % --R differentiate : (%,VarSet) -> % eval : (%,VarSet,%) -> % ---R eval : (%,VarSet,R) -> % eval : (%,%,%) -> % ---R eval : (%,Equation(%)) -> % ground : % -> R ---R ground? : % -> Boolean hash : % -> SingleInteger ---R head : % -> % headReduce : (%,%) -> % ---R headReduced? : (%,%) -> Boolean infRittWu? : (%,%) -> Boolean ---R init : % -> % initiallyReduce : (%,%) -> % ---R iteratedInitials : % -> List(%) latex : % -> String ---R lazyPquo : (%,%,VarSet) -> % lazyPquo : (%,%) -> % ---R lazyPrem : (%,%,VarSet) -> % lazyPrem : (%,%) -> % ---R leadingCoefficient : % -> R leadingMonomial : % -> % ---R leastMonomial : % -> % mainCoefficients : % -> List(%) ---R mainMonomial : % -> % mainMonomials : % -> List(%) ---R map : ((R -> R),%) -> % mdeg : % -> NonNegativeInteger ---R monic? : % -> Boolean monicModulo : (%,%) -> % ---R monomial? : % -> Boolean monomials : % -> List(%) ---R mvar : % -> VarSet normalized? : (%,%) -> Boolean ---R one? : % -> Boolean pquo : (%,%,VarSet) -> % ---R pquo : (%,%) -> % prem : (%,%,VarSet) -> % ---R prem : (%,%) -> % quasiMonic? : % -> Boolean ---R recip : % -> Union(%,"failed") reduced? : (%,%) -> Boolean ---R reductum : (%,VarSet) -> % reductum : % -> % ---R retract : % -> VarSet retract : % -> R ---R sample : () -> % supRittWu? : (%,%) -> Boolean ---R tail : % -> % variables : % -> List(VarSet) ---R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R eval : (%,VarSet,R) -> % eval : (%,List(%),List(%)) -> % +--R eval : (%,%,%) -> % eval : (%,Equation(%)) -> % +--R eval : (%,List(Equation(%))) -> % gcd : (%,%) -> % if R has GCDDOM +--R gcd : List(%) -> % if R has GCDDOM gcd : (R,%) -> R if R has GCDDOM +--R ground : % -> R ground? : % -> Boolean +--R hash : % -> SingleInteger head : % -> % +--R headReduce : (%,%) -> % headReduced? : (%,%) -> Boolean +--R infRittWu? : (%,%) -> Boolean init : % -> % +--R initiallyReduce : (%,%) -> % iteratedInitials : % -> List(%) +--R latex : % -> String lazyPquo : (%,%,VarSet) -> % +--R lazyPquo : (%,%) -> % lazyPrem : (%,%,VarSet) -> % +--R lazyPrem : (%,%) -> % lcm : (%,%) -> % if R has GCDDOM +--R lcm : List(%) -> % if R has GCDDOM leadingCoefficient : % -> R +--R leadingMonomial : % -> % leastMonomial : % -> % +--R mainCoefficients : % -> List(%) mainMonomial : % -> % +--R mainMonomials : % -> List(%) map : ((R -> R),%) -> % +--R max : (%,%) -> % if R has ORDSET mdeg : % -> NonNegativeInteger +--R min : (%,%) -> % if R has ORDSET monic? : % -> Boolean +--R monicModulo : (%,%) -> % monomial? : % -> Boolean +--R monomials : % -> List(%) mvar : % -> VarSet +--R normalized? : (%,%) -> Boolean one? : % -> Boolean +--R pquo : (%,%,VarSet) -> % pquo : (%,%) -> % +--R prem : (%,%,VarSet) -> % prem : (%,%) -> % +--R primitiveMonomials : % -> List(%) quasiMonic? : % -> Boolean +--R recip : % -> Union(%,"failed") reduced? : (%,List(%)) -> Boolean +--R reduced? : (%,%) -> Boolean reductum : (%,VarSet) -> % +--R reductum : % -> % retract : % -> VarSet +--R retract : % -> R sample : () -> % +--R supRittWu? : (%,%) -> Boolean tail : % -> % +--R variables : % -> List(VarSet) zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean --R ?*? : (Fraction(Integer),%) -> % if R has ALGEBRA(FRAC(INT)) --R ?*? : (%,Fraction(Integer)) -> % if R has ALGEBRA(FRAC(INT)) ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R ?/? : (%,R) -> % if R has FIELD --R ? Boolean if R has ORDSET --R ?<=? : (%,%) -> Boolean if R has ORDSET --R ?>? : (%,%) -> Boolean if R has ORDSET @@ -91291,7 +95169,6 @@ by means of triangular sets. --R LazardQuotient : (%,%,NonNegativeInteger) -> % if R has INTDOM --R LazardQuotient2 : (%,%,%,NonNegativeInteger) -> % if R has INTDOM --R RittWuCompare : (%,%) -> Union(Boolean,"failed") ---R ?^? : (%,NonNegativeInteger) -> % --R associates? : (%,%) -> Boolean if R has INTDOM --R binomThmExpt : (%,%,NonNegativeInteger) -> % if R has COMRING --R characteristic : () -> NonNegativeInteger @@ -91299,14 +95176,12 @@ by means of triangular sets. --R coefficient : (%,List(VarSet),List(NonNegativeInteger)) -> % --R coefficient : (%,VarSet,NonNegativeInteger) -> % --R coefficient : (%,IndexedExponents(VarSet)) -> R ---R coerce : % -> % if R has INTDOM --R coerce : Fraction(Integer) -> % if R has ALGEBRA(FRAC(INT)) or R has RETRACT(FRAC(INT)) --R coerce : SparseMultivariatePolynomial(R,VarSet) -> % --R coerce : % -> SparseMultivariatePolynomial(R,VarSet) --R coerce : % -> Polynomial(R) if VarSet has KONVERT(SYMBOL) --R conditionP : Matrix(%) -> Union(Vector(%),"failed") if $ has CHARNZ and R has PFECAT --R content : (%,VarSet) -> % if R has GCDDOM ---R content : % -> R if R has GCDDOM --R convert : % -> Polynomial(R) if VarSet has KONVERT(SYMBOL) --R convert : % -> String if R has RETRACT(INT) and VarSet has KONVERT(SYMBOL) --R convert : Polynomial(R) -> % if VarSet has KONVERT(SYMBOL) @@ -91324,8 +95199,6 @@ by means of triangular sets. --R discriminant : (%,VarSet) -> % if R has COMRING --R eval : (%,List(VarSet),List(%)) -> % --R eval : (%,List(VarSet),List(R)) -> % ---R eval : (%,List(%),List(%)) -> % ---R eval : (%,List(Equation(%))) -> % --R exactQuotient : (%,%) -> % if R has INTDOM --R exactQuotient : (%,R) -> % if R has INTDOM --R exactQuotient! : (%,%) -> % if R has INTDOM @@ -91336,9 +95209,6 @@ by means of triangular sets. --R factor : % -> Factored(%) if R has PFECAT --R factorPolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has PFECAT --R factorSquareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has PFECAT ---R gcd : (%,%) -> % if R has GCDDOM ---R gcd : List(%) -> % if R has GCDDOM ---R gcd : (R,%) -> R if R has GCDDOM --R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) if R has GCDDOM --R halfExtendedSubResultantGcd1 : (%,%) -> Record(gcd: %,coef1: %) if R has INTDOM --R halfExtendedSubResultantGcd2 : (%,%) -> Record(gcd: %,coef2: %) if R has INTDOM @@ -91354,8 +95224,6 @@ by means of triangular sets. --R lazyPseudoDivide : (%,%,VarSet) -> Record(coef: %,gap: NonNegativeInteger,quotient: %,remainder: %) --R lazyPseudoDivide : (%,%) -> Record(coef: %,gap: NonNegativeInteger,quotient: %,remainder: %) --R lazyResidueClass : (%,%) -> Record(polnum: %,polden: %,power: NonNegativeInteger) ---R lcm : (%,%) -> % if R has GCDDOM ---R lcm : List(%) -> % if R has GCDDOM --R lcmCoef : (%,%) -> Record(llcmres: %,coeff1: %,coeff2: %) if R has GCDDOM --R leadingCoefficient : (%,VarSet) -> % --R mainContent : % -> % if R has GCDDOM @@ -91363,8 +95231,6 @@ by means of triangular sets. --R mainSquareFreePart : % -> % if R has GCDDOM --R mainVariable : % -> Union(VarSet,"failed") --R mapExponents : ((IndexedExponents(VarSet) -> IndexedExponents(VarSet)),%) -> % ---R max : (%,%) -> % if R has ORDSET ---R min : (%,%) -> % if R has ORDSET --R minimumDegree : (%,List(VarSet)) -> List(NonNegativeInteger) --R minimumDegree : (%,VarSet) -> NonNegativeInteger --R minimumDegree : % -> IndexedExponents(VarSet) @@ -91383,12 +95249,10 @@ by means of triangular sets. --R primPartElseUnitCanonical : % -> % if R has INTDOM --R primPartElseUnitCanonical! : % -> % if R has INTDOM --R prime? : % -> Boolean if R has PFECAT ---R primitiveMonomials : % -> List(%) --R primitivePart : (%,VarSet) -> % if R has GCDDOM --R primitivePart : % -> % if R has GCDDOM --R primitivePart! : % -> % if R has GCDDOM --R pseudoDivide : (%,%) -> Record(quotient: %,remainder: %) ---R reduced? : (%,List(%)) -> Boolean --R reducedSystem : Matrix(%) -> Matrix(R) --R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(R),vec: Vector(R)) --R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(Integer),vec: Vector(Integer)) if R has LINEXP(INT) @@ -92014,33 +95878,40 @@ constructur {\bf SparseUnivariatePolynomial}. --R------------------------------- Operations -------------------------------- --R ?*? : (%,R) -> % ?*? : (R,%) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % ---R -? : % -> % ?=? : (%,%) -> Boolean ---R D : (%,(R -> R)) -> % D : % -> % ---R D : (%,NonNegativeInteger) -> % 1 : () -> % ---R 0 : () -> % ?^? : (%,PositiveInteger) -> % ---R coefficients : % -> List(R) coerce : R -> % ---R coerce : Integer -> % coerce : % -> OutputForm ---R degree : % -> NonNegativeInteger differentiate : % -> % ---R ?.? : (%,%) -> % ?.? : (%,R) -> R +--R -? : % -> % ?/? : (%,R) -> % if R has FIELD +--R ?=? : (%,%) -> Boolean D : (%,(R -> R)) -> % +--R D : % -> % D : (%,NonNegativeInteger) -> % +--R D : (%,SingletonAsOrderedSet) -> % 1 : () -> % +--R 0 : () -> % ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,PositiveInteger) -> % coefficients : % -> List(R) +--R coerce : % -> % if R has INTDOM coerce : SingletonAsOrderedSet -> % +--R coerce : R -> % coerce : Integer -> % +--R coerce : % -> OutputForm content : % -> R if R has GCDDOM +--R degree : % -> NonNegativeInteger differentiate : (%,(R -> R)) -> % +--R differentiate : % -> % ?.? : (%,%) -> % +--R ?.? : (%,R) -> R eval : (%,List(%),List(%)) -> % --R eval : (%,%,%) -> % eval : (%,Equation(%)) -> % ---R ground : % -> R ground? : % -> Boolean ---R hash : % -> SingleInteger init : () -> % if R has STEP ---R latex : % -> String lazyPseudoQuotient : (%,%) -> % +--R eval : (%,List(Equation(%))) -> % gcd : (%,%) -> % if R has GCDDOM +--R gcd : List(%) -> % if R has GCDDOM ground : % -> R +--R ground? : % -> Boolean hash : % -> SingleInteger +--R init : () -> % if R has STEP latex : % -> String +--R lazyPseudoQuotient : (%,%) -> % lazyPseudoRemainder : (%,%) -> % +--R lcm : (%,%) -> % if R has GCDDOM lcm : List(%) -> % if R has GCDDOM --R leadingCoefficient : % -> R leadingMonomial : % -> % ---R map : ((R -> R),%) -> % monicModulo : (%,%) -> % +--R map : ((R -> R),%) -> % max : (%,%) -> % if R has ORDSET +--R min : (%,%) -> % if R has ORDSET monicModulo : (%,%) -> % --R monomial? : % -> Boolean monomials : % -> List(%) ---R one? : % -> Boolean pseudoRemainder : (%,%) -> % +--R one? : % -> Boolean primitiveMonomials : % -> List(%) +--R pseudoRemainder : (%,%) -> % ?quo? : (%,%) -> % if R has FIELD --R recip : % -> Union(%,"failed") reductum : % -> % ---R retract : % -> R sample : () -> % ---R unvectorise : Vector(R) -> % zero? : % -> Boolean ---R ?~=? : (%,%) -> Boolean +--R ?rem? : (%,%) -> % if R has FIELD retract : % -> R +--R sample : () -> % unvectorise : Vector(R) -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean --R ?*? : (Fraction(Integer),%) -> % if R has ALGEBRA(FRAC(INT)) --R ?*? : (%,Fraction(Integer)) -> % if R has ALGEBRA(FRAC(INT)) ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R ?/? : (%,R) -> % if R has FIELD --R ? Boolean if R has ORDSET --R ?<=? : (%,%) -> Boolean if R has ORDSET --R ?>? : (%,%) -> Boolean if R has ORDSET @@ -92053,8 +95924,6 @@ constructur {\bf SparseUnivariatePolynomial}. --R D : (%,List(SingletonAsOrderedSet),List(NonNegativeInteger)) -> % --R D : (%,SingletonAsOrderedSet,NonNegativeInteger) -> % --R D : (%,List(SingletonAsOrderedSet)) -> % ---R D : (%,SingletonAsOrderedSet) -> % ---R ?^? : (%,NonNegativeInteger) -> % --R associates? : (%,%) -> Boolean if R has INTDOM --R binomThmExpt : (%,%,NonNegativeInteger) -> % if R has COMRING --R characteristic : () -> NonNegativeInteger @@ -92062,23 +95931,19 @@ constructur {\bf SparseUnivariatePolynomial}. --R coefficient : (%,List(SingletonAsOrderedSet),List(NonNegativeInteger)) -> % --R coefficient : (%,SingletonAsOrderedSet,NonNegativeInteger) -> % --R coefficient : (%,NonNegativeInteger) -> R ---R coerce : % -> % if R has INTDOM --R coerce : Fraction(Integer) -> % if R has ALGEBRA(FRAC(INT)) or R has RETRACT(FRAC(INT)) --R coerce : SparseUnivariatePolynomial(R) -> % --R coerce : % -> SparseUnivariatePolynomial(R) ---R coerce : SingletonAsOrderedSet -> % --R composite : (Fraction(%),%) -> Union(Fraction(%),"failed") if R has INTDOM --R composite : (%,%) -> Union(%,"failed") if R has INTDOM --R conditionP : Matrix(%) -> Union(Vector(%),"failed") if $ has CHARNZ and R has PFECAT --R content : (%,SingletonAsOrderedSet) -> % if R has GCDDOM ---R content : % -> R if R has GCDDOM --R convert : % -> InputForm if SingletonAsOrderedSet has KONVERT(INFORM) and R has KONVERT(INFORM) --R convert : % -> Pattern(Integer) if SingletonAsOrderedSet has KONVERT(PATTERN(INT)) and R has KONVERT(PATTERN(INT)) --R convert : % -> Pattern(Float) if SingletonAsOrderedSet has KONVERT(PATTERN(FLOAT)) and R has KONVERT(PATTERN(FLOAT)) --R degree : (%,List(SingletonAsOrderedSet)) -> List(NonNegativeInteger) --R degree : (%,SingletonAsOrderedSet) -> NonNegativeInteger --R differentiate : (%,(R -> R),%) -> % ---R differentiate : (%,(R -> R)) -> % --R differentiate : (%,(R -> R),NonNegativeInteger) -> % --R differentiate : (%,List(Symbol),List(NonNegativeInteger)) -> % if R has PDRING(SYMBOL) --R differentiate : (%,Symbol,NonNegativeInteger) -> % if R has PDRING(SYMBOL) @@ -92101,8 +95966,6 @@ constructur {\bf SparseUnivariatePolynomial}. --R eval : (%,SingletonAsOrderedSet,%) -> % --R eval : (%,List(SingletonAsOrderedSet),List(R)) -> % --R eval : (%,SingletonAsOrderedSet,R) -> % ---R eval : (%,List(%),List(%)) -> % ---R eval : (%,List(Equation(%))) -> % --R expressIdealMember : (List(%),%) -> Union(List(%),"failed") if R has FIELD --R exquo : (%,%) -> Union(%,"failed") if R has INTDOM --R exquo : (%,R) -> Union(%,"failed") if R has INTDOM @@ -92114,8 +95977,6 @@ constructur {\bf SparseUnivariatePolynomial}. --R factorPolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has PFECAT --R factorSquareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has PFECAT --R fmecg : (%,NonNegativeInteger,R,%) -> % ---R gcd : (%,%) -> % if R has GCDDOM ---R gcd : List(%) -> % if R has GCDDOM --R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) if R has GCDDOM --R halfExtendedResultant1 : (%,%) -> Record(resultant: R,coef1: %) if R has INTDOM --R halfExtendedResultant2 : (%,%) -> Record(resultant: R,coef2: %) if R has INTDOM @@ -92128,16 +95989,11 @@ constructur {\bf SparseUnivariatePolynomial}. --R karatsubaDivide : (%,NonNegativeInteger) -> Record(quotient: %,remainder: %) --R lastSubResultant : (%,%) -> % if R has INTDOM --R lazyPseudoDivide : (%,%) -> Record(coef: R,gap: NonNegativeInteger,quotient: %,remainder: %) ---R lazyPseudoRemainder : (%,%) -> % --R lazyResidueClass : (%,%) -> Record(polnum: %,polden: R,power: NonNegativeInteger) ---R lcm : (%,%) -> % if R has GCDDOM ---R lcm : List(%) -> % if R has GCDDOM --R lcmCoef : (%,%) -> Record(llcmres: %,coeff1: %,coeff2: %) if R has GCDDOM --R mainVariable : % -> Union(SingletonAsOrderedSet,"failed") --R makeSUP : % -> SparseUnivariatePolynomial(R) --R mapExponents : ((NonNegativeInteger -> NonNegativeInteger),%) -> % ---R max : (%,%) -> % if R has ORDSET ---R min : (%,%) -> % if R has ORDSET --R minimumDegree : (%,List(SingletonAsOrderedSet)) -> List(NonNegativeInteger) --R minimumDegree : (%,SingletonAsOrderedSet) -> NonNegativeInteger --R minimumDegree : % -> NonNegativeInteger @@ -92157,18 +96013,15 @@ constructur {\bf SparseUnivariatePolynomial}. --R patternMatch : (%,Pattern(Float),PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if SingletonAsOrderedSet has PATMAB(FLOAT) and R has PATMAB(FLOAT) --R pomopo! : (%,R,NonNegativeInteger,%) -> % --R prime? : % -> Boolean if R has PFECAT ---R primitiveMonomials : % -> List(%) --R primitivePart : (%,SingletonAsOrderedSet) -> % if R has GCDDOM --R primitivePart : % -> % if R has GCDDOM --R principalIdeal : List(%) -> Record(coef: List(%),generator: %) if R has FIELD --R pseudoDivide : (%,%) -> Record(coef: R,quotient: %,remainder: %) if R has INTDOM --R pseudoQuotient : (%,%) -> % if R has INTDOM ---R ?quo? : (%,%) -> % if R has FIELD --R reducedSystem : Matrix(%) -> Matrix(R) --R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(R),vec: Vector(R)) --R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(Integer),vec: Vector(Integer)) if R has LINEXP(INT) --R reducedSystem : Matrix(%) -> Matrix(Integer) if R has LINEXP(INT) ---R ?rem? : (%,%) -> % if R has FIELD --R resultant : (%,%) -> R if R has COMRING --R resultant : (%,%,SingletonAsOrderedSet) -> % if R has COMRING --R retract : % -> SparseUnivariatePolynomial(R) @@ -92627,7 +96480,7 @@ NewSparseUnivariatePolynomial(R): Exports == Implementation where )set message test on )set message auto off )clear all ---S 1 of 3 +--S 1 of 4 [ ] --R --R @@ -92635,7 +96488,7 @@ NewSparseUnivariatePolynomial(R): Exports == Implementation where --R Type: List(None) --E 1 ---S 2 of 3 +--S 2 of 4 [ ] :: List Float --R --R @@ -92643,13 +96496,29 @@ NewSparseUnivariatePolynomial(R): Exports == Implementation where --R Type: List(Float) --E 2 ---S 3 of 3 +--S 3 of 4 [ ]$List(NonNegativeInteger) --R --R --R (3) [] --R Type: List(NonNegativeInteger) --E 3 + +--S 4 of 4 +)show None +--R +--R None is a domain constructor +--R Abbreviation for None is NONE +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for NONE +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R ?~=? : (%,%) -> Boolean +--R +--E 4 + )spool )lisp (bye) \end{chunk} @@ -92734,29 +96603,29 @@ None():SetCategory == add --S 1 of 1 )show NonNegativeInteger +--R --R NonNegativeInteger is a domain constructor --R Abbreviation for NonNegativeInteger is NNI --R This constructor is exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for NNI --R --R------------------------------- Operations -------------------------------- ---R ?*? : (%,%) -> % ?*? : (PositiveInteger,%) -> % ---R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % +--R ?*? : (%,%) -> % ?*? : (NonNegativeInteger,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?+? : (%,%) -> % --R ? Boolean ?<=? : (%,%) -> Boolean --R ?=? : (%,%) -> Boolean ?>? : (%,%) -> Boolean --R ?>=? : (%,%) -> Boolean 1 : () -> % --R 0 : () -> % ?^? : (%,PositiveInteger) -> % ---R coerce : % -> OutputForm gcd : (%,%) -> % ---R hash : % -> SingleInteger latex : % -> String ---R max : (%,%) -> % min : (%,%) -> % ---R one? : % -> Boolean ?quo? : (%,%) -> % ---R random : % -> % recip : % -> Union(%,"failed") ---R ?rem? : (%,%) -> % sample : () -> % ---R shift : (%,Integer) -> % sup : (%,%) -> % ---R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % coerce : % -> OutputForm +--R gcd : (%,%) -> % hash : % -> SingleInteger +--R latex : % -> String max : (%,%) -> % +--R min : (%,%) -> % one? : % -> Boolean +--R ?quo? : (%,%) -> % random : % -> % +--R recip : % -> Union(%,"failed") ?rem? : (%,%) -> % +--R sample : () -> % shift : (%,Integer) -> % +--R sup : (%,%) -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean --R divide : (%,%) -> Record(quotient: %,remainder: %) --R exquo : (%,%) -> Union(%,"failed") --R subtractIfCan : (%,%) -> Union(%,"failed") @@ -92945,16 +96814,15 @@ sample()$NOTTING(PF(1783)) --R --R------------------------------- Operations -------------------------------- --R ?*? : (%,%) -> % ?**? : (%,Integer) -> % ---R ?**? : (%,PositiveInteger) -> % ?/? : (%,%) -> % ---R ?=? : (%,%) -> Boolean 1 : () -> % ---R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % +--R ?/? : (%,%) -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % ?^? : (%,Integer) -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % --R coerce : % -> OutputForm commutator : (%,%) -> % --R conjugate : (%,%) -> % hash : % -> SingleInteger --R inv : % -> % latex : % -> String --R one? : % -> Boolean recip : % -> Union(%,"failed") --R sample : () -> % ?~=? : (%,%) -> Boolean ---R ?**? : (%,NonNegativeInteger) -> % ---R ?^? : (%,NonNegativeInteger) -> % --R retract : UnivariateFormalPowerSeries(F) -> % --R --E 8 @@ -93665,7 +97533,7 @@ associative, since $I*(J*K) \ne (I*J)*K$. )set message test on )set message auto off )clear all ---S 1 of 15 +--S 1 of 16 oci1 := octon(1,2,3,4,5,6,7,8) --R --R @@ -93673,7 +97541,7 @@ oci1 := octon(1,2,3,4,5,6,7,8) --R Type: Octonion(Integer) --E 1 ---S 2 of 15 +--S 2 of 16 oci2 := octon(7,2,3,-4,5,6,-7,0) --R --R @@ -93681,7 +97549,7 @@ oci2 := octon(7,2,3,-4,5,6,-7,0) --R Type: Octonion(Integer) --E 2 ---S 3 of 15 +--S 3 of 16 oci3 := octon(quatern(-7,-12,3,-10), quatern(5,6,9,0)) --R --R @@ -93689,7 +97557,7 @@ oci3 := octon(quatern(-7,-12,3,-10), quatern(5,6,9,0)) --R Type: Octonion(Integer) --E 3 ---S 4 of 15 +--S 4 of 16 (oci1 * oci2) * oci3 - oci1 * (oci2 * oci3) --R --R @@ -93697,7 +97565,7 @@ oci3 := octon(quatern(-7,-12,3,-10), quatern(5,6,9,0)) --R Type: Octonion(Integer) --E 4 ---S 5 of 15 +--S 5 of 16 [real oci1, imagi oci1, imagj oci1, imagk oci1, _ imagE oci1, imagI oci1, imagJ oci1, imagK oci1] --R @@ -93706,7 +97574,7 @@ oci3 := octon(quatern(-7,-12,3,-10), quatern(5,6,9,0)) --R Type: List(PositiveInteger) --E 5 ---S 6 of 15 +--S 6 of 16 q : Quaternion Polynomial Integer := quatern(q1, qi, qj, qk) --R --R @@ -93714,7 +97582,7 @@ q : Quaternion Polynomial Integer := quatern(q1, qi, qj, qk) --R Type: Quaternion(Polynomial(Integer)) --E 6 ---S 7 of 15 +--S 7 of 16 E : Octonion Polynomial Integer:= octon(0,0,0,0,1,0,0,0) --R --R @@ -93722,7 +97590,7 @@ E : Octonion Polynomial Integer:= octon(0,0,0,0,1,0,0,0) --R Type: Octonion(Polynomial(Integer)) --E 7 ---S 8 of 15 +--S 8 of 16 q * E --R --R @@ -93730,7 +97598,7 @@ q * E --R Type: Octonion(Polynomial(Integer)) --E 8 ---S 9 of 15 +--S 9 of 16 E * q --R --R @@ -93738,7 +97606,7 @@ E * q --R Type: Octonion(Polynomial(Integer)) --E 9 ---S 10 of 15 +--S 10 of 16 q * 1$(Octonion Polynomial Integer) --R --R @@ -93746,7 +97614,7 @@ q * 1$(Octonion Polynomial Integer) --R Type: Octonion(Polynomial(Integer)) --E 10 ---S 11 of 15 +--S 11 of 16 1$(Octonion Polynomial Integer) * q --R --R @@ -93754,7 +97622,7 @@ q * 1$(Octonion Polynomial Integer) --R Type: Octonion(Polynomial(Integer)) --E 11 ---S 12 of 15 +--S 12 of 16 o : Octonion Polynomial Integer := octon(o1, oi, oj, ok, oE, oI, oJ, oK) --R --R @@ -93762,7 +97630,7 @@ o : Octonion Polynomial Integer := octon(o1, oi, oj, ok, oE, oI, oJ, oK) --R Type: Octonion(Polynomial(Integer)) --E 12 ---S 13 of 15 +--S 13 of 16 norm o --R --R @@ -93771,7 +97639,7 @@ norm o --R Type: Polynomial(Integer) --E 13 ---S 14 of 15 +--S 14 of 16 p : Octonion Polynomial Integer := octon(p1, pi, pj, pk, pE, pI, pJ, pK) --R --R @@ -93779,13 +97647,79 @@ p : Octonion Polynomial Integer := octon(p1, pi, pj, pk, pE, pI, pJ, pK) --R Type: Octonion(Polynomial(Integer)) --E 14 ---S 15 of 15 +--S 15 of 16 norm(o*p)-norm(p)*norm(o) --R --R --R (15) 0 --R Type: Polynomial(Integer) --E 15 + +--S 16 of 16 +)show Octonion +--R +--R Octonion(R: CommutativeRing) is a domain constructor +--R Abbreviation for Octonion is OCT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for OCT +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (R,%) -> % ?*? : (%,R) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R abs : % -> R if R has RNS coerce : Quaternion(R) -> % +--R coerce : R -> % coerce : Integer -> % +--R coerce : % -> OutputForm conjugate : % -> % +--R hash : % -> SingleInteger imagE : % -> R +--R imagI : % -> R imagJ : % -> R +--R imagK : % -> R imagi : % -> R +--R imagj : % -> R imagk : % -> R +--R inv : % -> % if R has FIELD latex : % -> String +--R map : ((R -> R),%) -> % max : (%,%) -> % if R has ORDSET +--R min : (%,%) -> % if R has ORDSET norm : % -> R +--R octon : (R,R,R,R,R,R,R,R) -> % one? : % -> Boolean +--R random : () -> % if R has FINITE real : % -> R +--R recip : % -> Union(%,"failed") retract : % -> Quaternion(R) +--R retract : % -> R sample : () -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ? Boolean if R has ORDSET +--R ?<=? : (%,%) -> Boolean if R has ORDSET +--R ?>? : (%,%) -> Boolean if R has ORDSET +--R ?>=? : (%,%) -> Boolean if R has ORDSET +--R characteristic : () -> NonNegativeInteger +--R charthRoot : % -> Union(%,"failed") if R has CHARNZ +--R coerce : Fraction(Integer) -> % if Quaternion(R) has RETRACT(FRAC(INT)) or R has RETRACT(FRAC(INT)) +--R convert : % -> InputForm if R has KONVERT(INFORM) +--R ?.? : (%,R) -> % if R has ELTAB(R,R) +--R enumerate : () -> List(%) if R has FINITE +--R eval : (%,Symbol,R) -> % if R has IEVALAB(SYMBOL,R) +--R eval : (%,List(Symbol),List(R)) -> % if R has IEVALAB(SYMBOL,R) +--R eval : (%,List(Equation(R))) -> % if R has EVALAB(R) +--R eval : (%,Equation(R)) -> % if R has EVALAB(R) +--R eval : (%,R,R) -> % if R has EVALAB(R) +--R eval : (%,List(R),List(R)) -> % if R has EVALAB(R) +--R index : PositiveInteger -> % if R has FINITE +--R lookup : % -> PositiveInteger if R has FINITE +--R octon : (Quaternion(R),Quaternion(R)) -> % +--R rational : % -> Fraction(Integer) if R has INS +--R rational? : % -> Boolean if R has INS +--R rationalIfCan : % -> Union(Fraction(Integer),"failed") if R has INS +--R retract : % -> Fraction(Integer) if Quaternion(R) has RETRACT(FRAC(INT)) or R has RETRACT(FRAC(INT)) +--R retract : % -> Integer if Quaternion(R) has RETRACT(INT) or R has RETRACT(INT) +--R retractIfCan : % -> Union(Fraction(Integer),"failed") if Quaternion(R) has RETRACT(FRAC(INT)) or R has RETRACT(FRAC(INT)) +--R retractIfCan : % -> Union(Integer,"failed") if Quaternion(R) has RETRACT(INT) or R has RETRACT(INT) +--R retractIfCan : % -> Union(Quaternion(R),"failed") +--R retractIfCan : % -> Union(R,"failed") +--R size : () -> NonNegativeInteger if R has FINITE +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R +--E 16 + )spool )lisp (bye) \end{chunk} @@ -94171,7 +98105,8 @@ ODEIntensityFunctionsTable(): E == I where )set message test on )set message auto off )clear all ---S 1 of 9 + +--S 1 of 10 oneDimensionalArray [i**2 for i in 1..10] --R --R @@ -94179,7 +98114,7 @@ oneDimensionalArray [i**2 for i in 1..10] --R Type: OneDimensionalArray(PositiveInteger) --E 1 ---S 2 of 9 +--S 2 of 10 a : ARRAY1 INT := new(10,0) --R --R @@ -94187,7 +98122,7 @@ a : ARRAY1 INT := new(10,0) --R Type: OneDimensionalArray(Integer) --E 2 ---S 3 of 9 +--S 3 of 10 for i in 1..10 repeat a.i := i; a --R --R @@ -94195,7 +98130,7 @@ for i in 1..10 repeat a.i := i; a --R Type: OneDimensionalArray(Integer) --E 3 ---S 4 of 9 +--S 4 of 10 map!(i +-> i ** 2,a); a --R --R @@ -94203,7 +98138,7 @@ map!(i +-> i ** 2,a); a --R Type: OneDimensionalArray(Integer) --E 4 ---S 5 of 9 +--S 5 of 10 reverse! a --R --R @@ -94211,7 +98146,7 @@ reverse! a --R Type: OneDimensionalArray(Integer) --E 5 ---S 6 of 9 +--S 6 of 10 swap!(a,4,5); a --R --R @@ -94219,7 +98154,7 @@ swap!(a,4,5); a --R Type: OneDimensionalArray(Integer) --E 6 ---S 7 of 9 +--S 7 of 10 sort! a --R --R @@ -94227,7 +98162,7 @@ sort! a --R Type: OneDimensionalArray(Integer) --E 7 ---S 8 of 9 +--S 8 of 10 b := a(6..10) --R --R @@ -94235,13 +98170,97 @@ b := a(6..10) --R Type: OneDimensionalArray(Integer) --E 8 ---S 9 of 9 +--S 9 of 10 copyInto!(a,b,1) --R --R --R (9) [36,49,64,81,100,36,49,64,81,100] --R Type: OneDimensionalArray(Integer) --E 9 + +--S 10 of 10 +)show OneDimensionalArray +--R +--R OneDimensionalArray(S: Type) is a domain constructor +--R Abbreviation for OneDimensionalArray is ARRAY1 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for ARRAY1 +--R +--R------------------------------- Operations -------------------------------- +--R concat : List(%) -> % concat : (%,%) -> % +--R concat : (S,%) -> % concat : (%,S) -> % +--R construct : List(S) -> % copy : % -> % +--R delete : (%,Integer) -> % ?.? : (%,Integer) -> S +--R elt : (%,Integer,S) -> S empty : () -> % +--R empty? : % -> Boolean entries : % -> List(S) +--R eq? : (%,%) -> Boolean index? : (Integer,%) -> Boolean +--R indices : % -> List(Integer) insert : (%,%,Integer) -> % +--R insert : (S,%,Integer) -> % latex : % -> String if S has SETCAT +--R map : (((S,S) -> S),%,%) -> % map : ((S -> S),%) -> % +--R max : (%,%) -> % if S has ORDSET min : (%,%) -> % if S has ORDSET +--R new : (NonNegativeInteger,S) -> % oneDimensionalArray : List(S) -> % +--R qelt : (%,Integer) -> S reverse : % -> % +--R sample : () -> % sort : % -> % if S has ORDSET +--R sort : (((S,S) -> Boolean),%) -> % +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R ? Boolean if S has ORDSET +--R ?<=? : (%,%) -> Boolean if S has ORDSET +--R ?=? : (%,%) -> Boolean if S has SETCAT +--R ?>? : (%,%) -> Boolean if S has ORDSET +--R ?>=? : (%,%) -> Boolean if S has ORDSET +--R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R coerce : % -> OutputForm if S has SETCAT +--R convert : % -> InputForm if S has KONVERT(INFORM) +--R copyInto! : (%,%,Integer) -> % if $ has shallowlyMutable +--R count : (S,%) -> NonNegativeInteger if $ has finiteAggregate and S has SETCAT +--R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R delete : (%,UniversalSegment(Integer)) -> % +--R ?.? : (%,UniversalSegment(Integer)) -> % +--R entry? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT +--R eval : (%,List(S),List(S)) -> % if S has EVALAB(S) and S has SETCAT +--R eval : (%,S,S) -> % if S has EVALAB(S) and S has SETCAT +--R eval : (%,Equation(S)) -> % if S has EVALAB(S) and S has SETCAT +--R eval : (%,List(Equation(S))) -> % if S has EVALAB(S) and S has SETCAT +--R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R fill! : (%,S) -> % if $ has shallowlyMutable +--R find : ((S -> Boolean),%) -> Union(S,"failed") +--R first : % -> S if Integer has ORDSET +--R hash : % -> SingleInteger if S has SETCAT +--R less? : (%,NonNegativeInteger) -> Boolean +--R map! : ((S -> S),%) -> % if $ has shallowlyMutable +--R maxIndex : % -> Integer if Integer has ORDSET +--R member? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT +--R members : % -> List(S) if $ has finiteAggregate +--R merge : (%,%) -> % if S has ORDSET +--R merge : (((S,S) -> Boolean),%,%) -> % +--R minIndex : % -> Integer if Integer has ORDSET +--R more? : (%,NonNegativeInteger) -> Boolean +--R oneDimensionalArray : (NonNegativeInteger,S) -> % +--R parts : % -> List(S) if $ has finiteAggregate +--R position : (S,%,Integer) -> Integer if S has SETCAT +--R position : (S,%) -> Integer if S has SETCAT +--R position : ((S -> Boolean),%) -> Integer +--R qsetelt! : (%,Integer,S) -> S if $ has shallowlyMutable +--R reduce : (((S,S) -> S),%) -> S if $ has finiteAggregate +--R reduce : (((S,S) -> S),%,S) -> S if $ has finiteAggregate +--R reduce : (((S,S) -> S),%,S,S) -> S if $ has finiteAggregate and S has SETCAT +--R remove : ((S -> Boolean),%) -> % if $ has finiteAggregate +--R remove : (S,%) -> % if $ has finiteAggregate and S has SETCAT +--R removeDuplicates : % -> % if $ has finiteAggregate and S has SETCAT +--R reverse! : % -> % if $ has shallowlyMutable +--R select : ((S -> Boolean),%) -> % if $ has finiteAggregate +--R setelt : (%,UniversalSegment(Integer),S) -> S if $ has shallowlyMutable +--R setelt : (%,Integer,S) -> S if $ has shallowlyMutable +--R size? : (%,NonNegativeInteger) -> Boolean +--R sort! : % -> % if $ has shallowlyMutable and S has ORDSET +--R sort! : (((S,S) -> Boolean),%) -> % if $ has shallowlyMutable +--R sorted? : % -> Boolean if S has ORDSET +--R sorted? : (((S,S) -> Boolean),%) -> Boolean +--R swap! : (%,Integer,Integer) -> Void if $ has shallowlyMutable +--R ?~=? : (%,%) -> Boolean if S has SETCAT +--R +--E 10 + )spool )lisp (bye) \end{chunk} @@ -94451,33 +98470,30 @@ OneDimensionalArray(S:Type): Exports == Implementation where --R Issue )edit bookvol10.3.pamphlet to see algebra source code for ONECOMP --R --R------------------------------- Operations -------------------------------- ---R -? : % -> % if R has ABELGRP ?=? : (%,%) -> Boolean ---R 1 : () -> % if R has ORDRING 0 : () -> % if R has ABELGRP +--R ?*? : (%,%) -> % if R has ORDRING ?+? : (%,%) -> % if R has ABELGRP +--R -? : % -> % if R has ABELGRP ?-? : (%,%) -> % if R has ABELGRP +--R ?=? : (%,%) -> Boolean 1 : () -> % if R has ORDRING +--R 0 : () -> % if R has ABELGRP abs : % -> % if R has ORDRING --R coerce : R -> % coerce : % -> OutputForm --R finite? : % -> Boolean hash : % -> SingleInteger --R infinite? : % -> Boolean infinity : () -> % ---R latex : % -> String retract : % -> R ---R ?~=? : (%,%) -> Boolean +--R latex : % -> String max : (%,%) -> % if R has ORDRING +--R min : (%,%) -> % if R has ORDRING retract : % -> R +--R sample : () -> % if R has ABELGRP ?~=? : (%,%) -> Boolean --R ?*? : (PositiveInteger,%) -> % if R has ABELGRP --R ?*? : (NonNegativeInteger,%) -> % if R has ABELGRP --R ?*? : (Integer,%) -> % if R has ABELGRP ---R ?*? : (%,%) -> % if R has ORDRING --R ?**? : (%,NonNegativeInteger) -> % if R has ORDRING --R ?**? : (%,PositiveInteger) -> % if R has ORDRING ---R ?+? : (%,%) -> % if R has ABELGRP ---R ?-? : (%,%) -> % if R has ABELGRP --R ? Boolean if R has ORDRING --R ?<=? : (%,%) -> Boolean if R has ORDRING --R ?>? : (%,%) -> Boolean if R has ORDRING --R ?>=? : (%,%) -> Boolean if R has ORDRING --R ?^? : (%,NonNegativeInteger) -> % if R has ORDRING --R ?^? : (%,PositiveInteger) -> % if R has ORDRING ---R abs : % -> % if R has ORDRING --R characteristic : () -> NonNegativeInteger if R has ORDRING --R coerce : Integer -> % if R has ORDRING or R has RETRACT(INT) --R coerce : Fraction(Integer) -> % if R has RETRACT(FRAC(INT)) ---R max : (%,%) -> % if R has ORDRING ---R min : (%,%) -> % if R has ORDRING --R negative? : % -> Boolean if R has ORDRING --R one? : % -> Boolean if R has ORDRING --R positive? : % -> Boolean if R has ORDRING @@ -94490,7 +98506,6 @@ OneDimensionalArray(S:Type): Exports == Implementation where --R retractIfCan : % -> Union(R,"failed") --R retractIfCan : % -> Union(Fraction(Integer),"failed") if R has RETRACT(FRAC(INT)) --R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT(INT) ---R sample : () -> % if R has ABELGRP --R sign : % -> Integer if R has ORDRING --R subtractIfCan : (%,%) -> Union(%,"failed") if R has ABELGRP --R zero? : % -> Boolean if R has ABELGRP @@ -94683,6 +98698,7 @@ OnePointCompletion(R:SetCategory): Exports == Implementation where --S 1 of 1 )show OpenMathConnection +--R --R OpenMathConnection is a domain constructor --R Abbreviation for OpenMathConnection is OMCONN --R This constructor is exposed in this frame. @@ -94778,6 +98794,7 @@ OpenMathConnection(): with --S 1 of 1 )show OpenMathDevice +--R --R OpenMathDevice is a domain constructor --R Abbreviation for OpenMathDevice is OMDEV --R This constructor is exposed in this frame. @@ -94800,15 +98817,14 @@ OpenMathConnection(): with --R OMputEndAtp : % -> Void OMputEndAttr : % -> Void --R OMputEndBVar : % -> Void OMputEndBind : % -> Void --R OMputEndError : % -> Void OMputEndObject : % -> Void ---R OMputError : % -> Void OMputObject : % -> Void ---R OMputString : (%,String) -> Void +--R OMputError : % -> Void OMputInteger : (%,Integer) -> Void +--R OMputObject : % -> Void OMputString : (%,String) -> Void +--R OMputVariable : (%,Symbol) -> Void --R OMgetSymbol : % -> Record(cd: String,name: String) --R OMopenFile : (String,String,OpenMathEncoding) -> % --R OMopenString : (String,OpenMathEncoding) -> % --R OMputFloat : (%,DoubleFloat) -> Void ---R OMputInteger : (%,Integer) -> Void --R OMputSymbol : (%,String,String) -> Void ---R OMputVariable : (%,Symbol) -> Void --R OMsetEncoding : (%,OpenMathEncoding) -> Void --R --E 1 @@ -95061,6 +99077,7 @@ OpenMathDevice(): with --S 1 of 1 )show OpenMathEncoding +--R --R OpenMathEncoding is a domain constructor --R Abbreviation for OpenMathEncoding is OMENC --R This constructor is exposed in this frame. @@ -95175,9 +99192,9 @@ OpenMathEncoding(): SetCategory with --R --R------------------------------- Operations -------------------------------- --R ?=? : (%,%) -> Boolean coerce : % -> OutputForm ---R errorInfo : % -> List(Symbol) hash : % -> SingleInteger ---R latex : % -> String ?~=? : (%,%) -> Boolean ---R errorKind : % -> OpenMathErrorKind +--R errorInfo : % -> List(Symbol) errorKind : % -> OpenMathErrorKind +--R hash : % -> SingleInteger latex : % -> String +--R ?~=? : (%,%) -> Boolean --R omError : (OpenMathErrorKind,List(Symbol)) -> % --R --E 1 @@ -95272,6 +99289,7 @@ OpenMathError() : SetCategory with --S 1 of 1 )show OpenMathErrorKind +--R --R OpenMathErrorKind is a domain constructor --R Abbreviation for OpenMathErrorKind is OMERRK --R This constructor is exposed in this frame. @@ -95379,37 +99397,76 @@ OpenMathErrorKind() : SetCategory with )set message test on )set message auto off )clear all ---S 1 of 21 + +--S 1 of 22 +)show Operator +--R +--R Operator(R: Ring) is a domain constructor +--R Abbreviation for Operator is OP +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for OP +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,R) -> % if R has COMRING ?*? : (R,%) -> % if R has COMRING +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,Integer) -> % ?**? : (BasicOperator,Integer) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R adjoint : % -> % if R has COMRING coerce : BasicOperator -> % +--R coerce : R -> % coerce : Integer -> % +--R coerce : % -> OutputForm conjug : R -> R if R has COMRING +--R ?.? : (%,R) -> R evaluate : (%,(R -> R)) -> % +--R hash : % -> SingleInteger latex : % -> String +--R one? : % -> Boolean opeval : (BasicOperator,R) -> R +--R recip : % -> Union(%,"failed") retract : % -> BasicOperator +--R retract : % -> R sample : () -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R adjoint : (%,%) -> % if R has COMRING +--R characteristic : () -> NonNegativeInteger +--R charthRoot : % -> Union(%,"failed") if R has CHARNZ +--R evaluateInverse : (%,(R -> R)) -> % +--R makeop : (R,FreeGroup(BasicOperator)) -> % +--R retractIfCan : % -> Union(BasicOperator,"failed") +--R retractIfCan : % -> Union(R,"failed") +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R +--E 1 + +--S 2 of 22 R := SQMATRIX(2, INT) --R --R --R (1) SquareMatrix(2,Integer) --R Type: Domain ---E 1 +--E 2 ---S 2 of 21 +--S 3 of 22 t := operator("tilde") :: OP(R) --R --R --R (2) tilde --R Type: Operator(SquareMatrix(2,Integer)) ---E 2 +--E 3 ---S 3 of 21 +--S 4 of 22 )set expose add constructor Operator --R --I Operator is now explicitly exposed in frame frame0 ---E 3 +--E 4 ---S 4 of 21 +--S 5 of 22 evaluate(t, m +-> transpose m) --R --R --R (3) tilde --R Type: Operator(SquareMatrix(2,Integer)) ---E 4 +--E 5 ---S 5 of 21 +--S 6 of 22 s : R := matrix [ [0, 1], [1, 0] ] --R --R @@ -95417,9 +99474,9 @@ s : R := matrix [ [0, 1], [1, 0] ] --R (4) | | --R +1 0+ --R Type: SquareMatrix(2,Integer) ---E 5 +--E 6 ---S 6 of 21 +--S 7 of 22 rho := t * s --R --R @@ -95427,9 +99484,9 @@ rho := t * s --R (5) tilde| | --R +1 0+ --R Type: Operator(SquareMatrix(2,Integer)) ---E 6 +--E 7 ---S 7 of 21 +--S 8 of 22 z := rho**4 - 1 --R --R @@ -95437,9 +99494,9 @@ z := rho**4 - 1 --R (6) - 1 + tilde| |tilde| |tilde| |tilde| | --R +1 0+ +1 0+ +1 0+ +1 0+ --R Type: Operator(SquareMatrix(2,Integer)) ---E 7 +--E 8 ---S 8 of 21 +--S 9 of 22 m:R := matrix [ [1, 2], [3, 4] ] --R --R @@ -95447,9 +99504,9 @@ m:R := matrix [ [1, 2], [3, 4] ] --R (7) | | --R +3 4+ --R Type: SquareMatrix(2,Integer) ---E 8 +--E 9 ---S 9 of 21 +--S 10 of 22 z m --R --R @@ -95457,9 +99514,9 @@ z m --R (8) | | --R +0 0+ --R Type: SquareMatrix(2,Integer) ---E 9 +--E 10 ---S 10 of 21 +--S 11 of 22 rho m --R --R @@ -95467,9 +99524,9 @@ rho m --R (9) | | --R +4 2+ --R Type: SquareMatrix(2,Integer) ---E 10 +--E 11 ---S 11 of 21 +--S 12 of 22 rho rho m --R --R @@ -95477,9 +99534,9 @@ rho rho m --R (10) | | --R +2 1+ --R Type: SquareMatrix(2,Integer) ---E 11 +--E 12 ---S 12 of 21 +--S 13 of 22 (rho^3) m --R --R @@ -95487,9 +99544,9 @@ rho rho m --R (11) | | --R +1 3+ --R Type: SquareMatrix(2,Integer) ---E 12 +--E 13 ---S 13 of 21 +--S 14 of 22 b := t * s - s * t --R --R @@ -95497,9 +99554,9 @@ b := t * s - s * t --R (12) - | |tilde + tilde| | --R +1 0+ +1 0+ --R Type: Operator(SquareMatrix(2,Integer)) ---E 13 +--E 14 ---S 14 of 21 +--S 15 of 22 b m --R --R @@ -95507,40 +99564,40 @@ b m --R (13) | | --R +3 - 1+ --R Type: SquareMatrix(2,Integer) ---E 14 +--E 15 ---S 15 of 21 +--S 16 of 22 L n == n = 0 => 1 n = 1 => x (2*n-1)/n * x * L(n-1) - (n-1)/n * L(n-2) --R --R Type: Void ---E 15 +--E 16 ---S 16 of 21 +--S 17 of 22 dx := operator("D") :: OP(POLY FRAC INT) --R --R --R (15) D --R Type: Operator(Polynomial(Fraction(Integer))) ---E 16 +--E 17 ---S 17 of 21 +--S 18 of 22 evaluate(dx, p +-> D(p, 'x)) --R --R --R (16) D --R Type: Operator(Polynomial(Fraction(Integer))) ---E 17 +--E 18 ---S 18 of 21 +--S 19 of 22 E n == (1 - x**2) * dx**2 - 2 * x * dx + n*(n+1) --R --R Type: Void ---E 18 +--E 19 ---S 19 of 21 +--S 20 of 22 L 15 --R --R Compiling function L with type Integer -> Polynomial(Fraction( @@ -95556,9 +99613,9 @@ L 15 --R - ------- x + ------ x - ---- x --R 2048 2048 2048 --R Type: Polynomial(Fraction(Integer)) ---E 19 +--E 20 ---S 20 of 21 +--S 21 of 22 E 15 --R --R Compiling function E with type PositiveInteger -> Operator( @@ -95567,15 +99624,16 @@ E 15 --R 2 2 --R (19) 240 - 2x D - (x - 1)D --R Type: Operator(Polynomial(Fraction(Integer))) ---E 20 +--E 21 ---S 21 of 21 +--S 22 of 22 (E 15)(L 15) --R --R --R (20) 0 --R Type: Polynomial(Fraction(Integer)) ---E 21 +--E 22 + )spool )lisp (bye) \end{chunk} @@ -95835,11 +99893,13 @@ Operator(R: Ring) == ModuleOperator(R,R) --R------------------------------- Operations -------------------------------- --R ?*? : (R,%) -> % ?*? : (%,R) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ?=? : (%,%) -> Boolean --R D : % -> % if P has DIFRING 1 : () -> % ---R 0 : () -> % ?^? : (%,PositiveInteger) -> % +--R 0 : () -> % ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,PositiveInteger) -> % coerce : R -> % if R has COMRING --R coerce : Integer -> % coerce : % -> OutputForm --R degree : % -> NonNegativeInteger hash : % -> SingleInteger --R latex : % -> String leadingCoefficient : % -> R @@ -95847,13 +99907,9 @@ Operator(R: Ring) == ModuleOperator(R,R) --R po : % -> P recip : % -> Union(%,"failed") --R reductum : % -> % sample : () -> % --R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % --R D : (%,NonNegativeInteger) -> % if P has DIFRING ---R ?^? : (%,NonNegativeInteger) -> % --R characteristic : () -> NonNegativeInteger --R coefficient : (%,NonNegativeInteger) -> R ---R coerce : R -> % if R has COMRING --R differentiate : % -> % if P has DIFRING --R differentiate : (%,NonNegativeInteger) -> % if P has DIFRING --R minimumDegree : % -> NonNegativeInteger @@ -95975,34 +100031,31 @@ OppositeMonogenicLinearOperator(P, R): OPRcat == OPRdef where --R Issue )edit bookvol10.3.pamphlet to see algebra source code for ORDCOMP --R --R------------------------------- Operations -------------------------------- ---R -? : % -> % if R has ABELGRP ?=? : (%,%) -> Boolean ---R 1 : () -> % if R has ORDRING 0 : () -> % if R has ABELGRP +--R ?*? : (%,%) -> % if R has ORDRING ?+? : (%,%) -> % if R has ABELGRP +--R -? : % -> % if R has ABELGRP ?-? : (%,%) -> % if R has ABELGRP +--R ?=? : (%,%) -> Boolean 1 : () -> % if R has ORDRING +--R 0 : () -> % if R has ABELGRP abs : % -> % if R has ORDRING --R coerce : R -> % coerce : % -> OutputForm --R finite? : % -> Boolean hash : % -> SingleInteger --R infinite? : % -> Boolean latex : % -> String +--R max : (%,%) -> % if R has ORDRING min : (%,%) -> % if R has ORDRING --R minusInfinity : () -> % plusInfinity : () -> % ---R retract : % -> R whatInfinity : % -> SingleInteger ---R ?~=? : (%,%) -> Boolean +--R retract : % -> R sample : () -> % if R has ABELGRP +--R whatInfinity : % -> SingleInteger ?~=? : (%,%) -> Boolean --R ?*? : (PositiveInteger,%) -> % if R has ABELGRP --R ?*? : (NonNegativeInteger,%) -> % if R has ABELGRP --R ?*? : (Integer,%) -> % if R has ABELGRP ---R ?*? : (%,%) -> % if R has ORDRING --R ?**? : (%,NonNegativeInteger) -> % if R has ORDRING --R ?**? : (%,PositiveInteger) -> % if R has ORDRING ---R ?+? : (%,%) -> % if R has ABELGRP ---R ?-? : (%,%) -> % if R has ABELGRP --R ? Boolean if R has ORDRING --R ?<=? : (%,%) -> Boolean if R has ORDRING --R ?>? : (%,%) -> Boolean if R has ORDRING --R ?>=? : (%,%) -> Boolean if R has ORDRING --R ?^? : (%,NonNegativeInteger) -> % if R has ORDRING --R ?^? : (%,PositiveInteger) -> % if R has ORDRING ---R abs : % -> % if R has ORDRING --R characteristic : () -> NonNegativeInteger if R has ORDRING --R coerce : Integer -> % if R has ORDRING or R has RETRACT(INT) --R coerce : Fraction(Integer) -> % if R has RETRACT(FRAC(INT)) ---R max : (%,%) -> % if R has ORDRING ---R min : (%,%) -> % if R has ORDRING --R negative? : % -> Boolean if R has ORDRING --R one? : % -> Boolean if R has ORDRING --R positive? : % -> Boolean if R has ORDRING @@ -96015,7 +100068,6 @@ OppositeMonogenicLinearOperator(P, R): OPRcat == OPRdef where --R retractIfCan : % -> Union(R,"failed") --R retractIfCan : % -> Union(Fraction(Integer),"failed") if R has RETRACT(FRAC(INT)) --R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT(INT) ---R sample : () -> % if R has ABELGRP --R sign : % -> Integer if R has ORDRING --R subtractIfCan : (%,%) -> Union(%,"failed") if R has ABELGRP --R zero? : % -> Boolean if R has ABELGRP @@ -96236,33 +100288,35 @@ OrderedCompletion(R:SetCategory): Exports == Implementation where --S 1 of 1 )show OrderedDirectProduct +--R --R OrderedDirectProduct(dim: NonNegativeInteger,S: OrderedAbelianMonoidSup,f: ((Vector(S),Vector(S)) -> Boolean)) is a domain constructor --R Abbreviation for OrderedDirectProduct is ODP --R This constructor is not exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for ODP --R --R------------------------------- Operations -------------------------------- ---R -? : % -> % if S has RING 1 : () -> % if S has MONOID ---R 0 : () -> % if S has CABMON coerce : % -> Vector(S) +--R ?*? : (S,%) -> % if S has MONOID ?*? : (%,S) -> % if S has MONOID +--R ?*? : (%,%) -> % if S has MONOID ?+? : (%,%) -> % if S has ABELSG +--R -? : % -> % if S has RING ?-? : (%,%) -> % if S has RING +--R ?/? : (%,S) -> % if S has FIELD 1 : () -> % if S has MONOID +--R 0 : () -> % if S has CABMON abs : % -> % if S has ORDRING +--R coerce : S -> % if S has SETCAT coerce : % -> Vector(S) --R copy : % -> % directProduct : Vector(S) -> % ---R ?.? : (%,Integer) -> S elt : (%,Integer,S) -> S ---R empty : () -> % empty? : % -> Boolean ---R entries : % -> List(S) eq? : (%,%) -> Boolean ---R index? : (Integer,%) -> Boolean indices : % -> List(Integer) ---R map : ((S -> S),%) -> % qelt : (%,Integer) -> S ---R sample : () -> % +--R dot : (%,%) -> S if S has RING ?.? : (%,Integer) -> S +--R elt : (%,Integer,S) -> S empty : () -> % +--R empty? : % -> Boolean entries : % -> List(S) +--R eq? : (%,%) -> Boolean index? : (Integer,%) -> Boolean +--R indices : % -> List(Integer) latex : % -> String if S has SETCAT +--R map : ((S -> S),%) -> % one? : % -> Boolean if S has MONOID +--R qelt : (%,Integer) -> S random : () -> % if S has FINITE +--R retract : % -> S if S has SETCAT sample : () -> % +--R sup : (%,%) -> % if S has OAMONS --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R ?*? : (PositiveInteger,%) -> % if S has ABELSG --R ?*? : (NonNegativeInteger,%) -> % if S has CABMON ---R ?*? : (S,%) -> % if S has MONOID ---R ?*? : (%,S) -> % if S has MONOID ---R ?*? : (%,%) -> % if S has MONOID --R ?*? : (Integer,%) -> % if S has RING --R ?**? : (%,PositiveInteger) -> % if S has MONOID --R ?**? : (%,NonNegativeInteger) -> % if S has MONOID ---R ?+? : (%,%) -> % if S has ABELSG ---R ?-? : (%,%) -> % if S has RING ---R ?/? : (%,S) -> % if S has FIELD --R ? Boolean if S has OAMONS or S has ORDRING --R ?<=? : (%,%) -> Boolean if S has OAMONS or S has ORDRING --R ?=? : (%,%) -> Boolean if S has SETCAT @@ -96278,10 +100332,8 @@ OrderedCompletion(R:SetCategory): Exports == Implementation where --R D : % -> % if S has DIFRING and S has RING --R ?^? : (%,PositiveInteger) -> % if S has MONOID --R ?^? : (%,NonNegativeInteger) -> % if S has MONOID ---R abs : % -> % if S has ORDRING --R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate --R characteristic : () -> NonNegativeInteger if S has RING ---R coerce : S -> % if S has SETCAT --R coerce : Fraction(Integer) -> % if S has RETRACT(FRAC(INT)) and S has SETCAT --R coerce : Integer -> % if S has RETRACT(INT) and S has SETCAT or S has RING --R coerce : % -> OutputForm if S has SETCAT @@ -96296,7 +100348,6 @@ OrderedCompletion(R:SetCategory): Exports == Implementation where --R differentiate : (%,NonNegativeInteger) -> % if S has DIFRING and S has RING --R differentiate : % -> % if S has DIFRING and S has RING --R dimension : () -> CardinalNumber if S has FIELD ---R dot : (%,%) -> S if S has RING --R entry? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT --R enumerate : () -> List(%) if S has FINITE --R eval : (%,List(S),List(S)) -> % if S has EVALAB(S) and S has SETCAT @@ -96308,7 +100359,6 @@ OrderedCompletion(R:SetCategory): Exports == Implementation where --R first : % -> S if Integer has ORDSET --R hash : % -> SingleInteger if S has SETCAT --R index : PositiveInteger -> % if S has FINITE ---R latex : % -> String if S has SETCAT --R less? : (%,NonNegativeInteger) -> Boolean --R lookup : % -> PositiveInteger if S has FINITE --R map! : ((S -> S),%) -> % if $ has shallowlyMutable @@ -96320,17 +100370,14 @@ OrderedCompletion(R:SetCategory): Exports == Implementation where --R minIndex : % -> Integer if Integer has ORDSET --R more? : (%,NonNegativeInteger) -> Boolean --R negative? : % -> Boolean if S has ORDRING ---R one? : % -> Boolean if S has MONOID --R parts : % -> List(S) if $ has finiteAggregate --R positive? : % -> Boolean if S has ORDRING --R qsetelt! : (%,Integer,S) -> S if $ has shallowlyMutable ---R random : () -> % if S has FINITE --R recip : % -> Union(%,"failed") if S has MONOID --R reducedSystem : Matrix(%) -> Matrix(S) if S has RING --R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(S),vec: Vector(S)) if S has RING --R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(Integer),vec: Vector(Integer)) if S has LINEXP(INT) and S has RING --R reducedSystem : Matrix(%) -> Matrix(Integer) if S has LINEXP(INT) and S has RING ---R retract : % -> S if S has SETCAT --R retract : % -> Fraction(Integer) if S has RETRACT(FRAC(INT)) and S has SETCAT --R retract : % -> Integer if S has RETRACT(INT) and S has SETCAT --R retractIfCan : % -> Union(S,"failed") if S has SETCAT @@ -96341,7 +100388,6 @@ OrderedCompletion(R:SetCategory): Exports == Implementation where --R size : () -> NonNegativeInteger if S has FINITE --R size? : (%,NonNegativeInteger) -> Boolean --R subtractIfCan : (%,%) -> Union(%,"failed") if S has CABMON ---R sup : (%,%) -> % if S has OAMONS --R swap! : (%,Integer,Integer) -> Void if $ has shallowlyMutable --R unitVector : PositiveInteger -> % if S has RING --R zero? : % -> Boolean if S has CABMON @@ -96502,7 +100548,7 @@ OrderedDirectProduct(dim:NonNegativeInteger, )set message auto off )clear all ---S 1 of 24 +--S 1 of 25 m1:=(x*y*y*z)$OFMONOID(Symbol) --R --R @@ -96511,7 +100557,7 @@ m1:=(x*y*y*z)$OFMONOID(Symbol) --R Type: OrderedFreeMonoid(Symbol) --E 1 ---S 2 of 24 +--S 2 of 25 m2:=(x*y)$OFMONOID(Symbol) --R --R @@ -96519,7 +100565,7 @@ m2:=(x*y)$OFMONOID(Symbol) --R Type: OrderedFreeMonoid(Symbol) --E 2 ---S 3 of 24 +--S 3 of 25 lquo(m1,m2) --R --R @@ -96527,7 +100573,7 @@ lquo(m1,m2) --R Type: Union(OrderedFreeMonoid(Symbol),...) --E 3 ---S 4 of 24 +--S 4 of 25 m3:=(y*y)$OFMONOID(Symbol) --R --R @@ -96536,7 +100582,7 @@ m3:=(y*y)$OFMONOID(Symbol) --R Type: OrderedFreeMonoid(Symbol) --E 4 ---S 5 of 24 +--S 5 of 25 divide(m1,m2) --R --R @@ -96544,7 +100590,7 @@ divide(m1,m2) --IType: Union(Record(lm: Union(OrderedFreeMonoid(Symbol),"failed"),... --E 5 ---S 6 of 24 +--S 6 of 25 divide(m1,m3) --R --R @@ -96552,7 +100598,7 @@ divide(m1,m3) --IType: Union(Record(lm: Union(OrderedFreeMonoid(Symbol),"failed"),... --E 6 ---S 7 of 24 +--S 7 of 25 m4:=(y^3)$OFMONOID(Symbol) --R --R @@ -96561,7 +100607,7 @@ m4:=(y^3)$OFMONOID(Symbol) --R Type: OrderedFreeMonoid(Symbol) --E 7 ---S 8 of 24 +--S 8 of 25 divide(m1,m4) --R --R @@ -96586,7 +100632,7 @@ divide(m1,m4) -- Generic elements of k (OVAR is OrderedVariableList) ---S 9 of 24 +--S 9 of 25 C ==> OVAR [a,b] --R --R Type: Void @@ -96596,7 +100642,7 @@ C ==> OVAR [a,b] -- Q = Fraction Integer -- SMP = SparseMultivariatePolynomials ---S 10 of 24 +--S 10 of 25 K ==> SMP(FRAC INT,C) --R --R Type: Void @@ -96604,7 +100650,7 @@ K ==> SMP(FRAC INT,C) -- Non-commutative variables ---S 11 of 24 +--S 11 of 25 V ==> OVAR [x,y] --R --R Type: Void @@ -96613,7 +100659,7 @@ V ==> OVAR [x,y] -- Non-commuative algebra k=k[x,y] -- XDPOLY XDistributedPolynomial ---S 12 of 24 +--S 12 of 25 H ==> XDPOLY(V,K) --R --R Type: Void @@ -96621,7 +100667,7 @@ H ==> XDPOLY(V,K) -- Free Monoid ---S 13 of 24 +--S 13 of 25 M ==> OFMONOID V --R --R Type: Void @@ -96630,7 +100676,7 @@ M ==> OFMONOID V -- Substitution rules are applied to words from the monoid over the -- variables and retun polynomials ---S 14 of 24 +--S 14 of 25 subs(w:M):H == -- x*y*x = y*x*y n1:=lquo(w,(x::V*y::V*x::V)$M)$M @@ -96653,7 +100699,7 @@ subs(w:M):H == --E 14 -- Apply rules to a term. Keep coefficients ---S 15 of 24 +--S 15 of 25 newterm(x:Record(k:M,c:K)):H == x.c*subs(x,k) --R --R Function declaration newterm : Record(k: OrderedFreeMonoid( @@ -96667,7 +100713,7 @@ newterm(x:Record(k:M,c:K)):H == x.c*subs(x,k) -- Reconstruct the polynomial term by term ---S 16 of 24 +--S 16 of 25 newpoly(t:H):H == reduce(+,map(newterm,listOfTerms(t))) --R --R Function declaration newpoly : XDistributedPolynomial( @@ -96681,7 +100727,7 @@ newpoly(t:H):H == reduce(+,map(newterm,listOfTerms(t))) -- Example calcuations ---S 17 of 24 +--S 17 of 25 p1:(x::V+y::V)$H^2 --R --R @@ -96689,7 +100735,7 @@ p1:(x::V+y::V)$H^2 --R Category, domain or package constructor ^ is not available. --E 17 ---S 18 of 24 +--S 18 of 25 newpoly(p1) --R --R Compiling function newpoly with type XDistributedPolynomial( @@ -96728,7 +100774,7 @@ newpoly(p1) --R $ to specify which version of the function you need. --E 18 ---S 19 of 24 +--S 19 of 25 p2:=(x::V+y::V)$H^3 --R --R @@ -96737,7 +100783,7 @@ p2:=(x::V+y::V)$H^3 --IType: XDistributedPolynomial(OrderedVariableList([x,y]),... --E 19 ---S 20 of 24 +--S 20 of 25 pNew:=newpoly(p2) --R --R There are no library operations named subs @@ -96772,7 +100818,7 @@ pNew:=newpoly(p2) --E 20 -- But the rules should be applied more than once ---S 21 of 24 +--S 21 of 25 while pNew ~= p2 repeat p2 := pNew pNew := newpoly(p2) @@ -96808,7 +100854,7 @@ while pNew ~= p2 repeat --R $ to specify which version of the function you need. --E 21 ---S 22 of 24 +--S 22 of 25 pNew --R --R @@ -96816,7 +100862,7 @@ pNew --R Type: Variable(pNew) --E 22 ---S 23 of 24 +--S 23 of 25 reduce(p:H):H == p2 := newpoly(p) p3 := newpoly(p2) @@ -96835,7 +100881,7 @@ reduce(p:H):H == --R Type: Void --E 23 ---S 24 of 24 +--S 24 of 25 reduce(p2) --R --R Compiling function newpoly with type XDistributedPolynomial( @@ -96879,6 +100925,43 @@ reduce(p2) --R $ to specify which version of the function you need. --E 24 +--S 25 of 25 +)show OrderedFreeMonoid +--R +--R OrderedFreeMonoid(S: OrderedSet) is a domain constructor +--R Abbreviation for OrderedFreeMonoid is OFMONOID +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for OFMONOID +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,S) -> % ?*? : (S,%) -> % +--R ?*? : (%,%) -> % ?**? : (S,NonNegativeInteger) -> % +--R ?**? : (%,PositiveInteger) -> % ?**? : (%,NonNegativeInteger) -> % +--R ? Boolean ?<=? : (%,%) -> Boolean +--R ?=? : (%,%) -> Boolean ?>? : (%,%) -> Boolean +--R ?>=? : (%,%) -> Boolean 1 : () -> % +--R ?^? : (%,PositiveInteger) -> % ?^? : (%,NonNegativeInteger) -> % +--R coerce : S -> % coerce : % -> OutputForm +--R first : % -> S hash : % -> SingleInteger +--R hclf : (%,%) -> % hcrf : (%,%) -> % +--R latex : % -> String length : % -> NonNegativeInteger +--R lexico : (%,%) -> Boolean lquo : (%,S) -> Union(%,"failed") +--R lquo : (%,%) -> Union(%,"failed") max : (%,%) -> % +--R min : (%,%) -> % mirror : % -> % +--R nthFactor : (%,Integer) -> S one? : % -> Boolean +--R recip : % -> Union(%,"failed") rest : % -> % +--R retract : % -> S rquo : (%,S) -> Union(%,"failed") +--R rquo : (%,%) -> Union(%,"failed") sample : () -> % +--R size : % -> NonNegativeInteger varList : % -> List(S) +--R ?~=? : (%,%) -> Boolean +--R divide : (%,%) -> Union(Record(lm: Union(%,"failed"),rm: Union(%,"failed")),"failed") +--R factors : % -> List(Record(gen: S,exp: NonNegativeInteger)) +--R nthExpon : (%,Integer) -> NonNegativeInteger +--R overlap : (%,%) -> Record(lm: %,mm: %,rm: %) +--R retractIfCan : % -> Union(S,"failed") +--R +--E 25 + )spool )lisp (bye) \end{chunk} @@ -97299,7 +101382,8 @@ OrderedFreeMonoid(S: OrderedSet): OFMcategory == OFMdefinition where )set message test on )set message auto off )clear all ---S 1 of 5 + +--S 1 of 6 ls:List Symbol:=['x,'a,'z] --R --R @@ -97307,7 +101391,7 @@ ls:List Symbol:=['x,'a,'z] --R Type: List(Symbol) --E 1 ---S 2 of 5 +--S 2 of 6 Z:=OVAR ls --R --R @@ -97315,7 +101399,7 @@ Z:=OVAR ls --R Type: Domain --E 2 ---S 3 of 5 +--S 3 of 6 size()$Z --R --R @@ -97323,7 +101407,7 @@ size()$Z --R Type: NonNegativeInteger --E 3 ---S 4 of 5 +--S 4 of 6 lv:=[index(i::PI)$Z for i in 1..size()$Z] --R --I Compiling function G1408 with type Integer -> Boolean @@ -97333,13 +101417,37 @@ lv:=[index(i::PI)$Z for i in 1..size()$Z] --R Type: List(OrderedVariableList([x,a,z])) --E 4 ---S 5 of 5 +--S 5 of 6 sorted?(>,lv) --R --R --R (5) true --R Type: Boolean --E 5 + +--S 6 of 6 +)show OrderedVariableList +--R +--R OrderedVariableList(VariableList: List(Symbol)) is a domain constructor +--R Abbreviation for OrderedVariableList is OVAR +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for OVAR +--R +--R------------------------------- Operations -------------------------------- +--R ? Boolean ?<=? : (%,%) -> Boolean +--R ?=? : (%,%) -> Boolean ?>? : (%,%) -> Boolean +--R ?>=? : (%,%) -> Boolean coerce : % -> OutputForm +--R convert : % -> Pattern(Integer) convert : % -> Pattern(Float) +--R convert : % -> InputForm convert : % -> Symbol +--R enumerate : () -> List(%) hash : % -> SingleInteger +--R index : PositiveInteger -> % latex : % -> String +--R lookup : % -> PositiveInteger max : (%,%) -> % +--R min : (%,%) -> % random : () -> % +--R size : () -> NonNegativeInteger ?~=? : (%,%) -> Boolean +--R variable : Symbol -> Union(%,"failed") +--R +--E 6 + )spool )lisp (bye) \end{chunk} @@ -97459,7 +101567,8 @@ OrderedVariableList(VariableList:List Symbol): )set message test on )set message auto off )clear all ---S 1 of 36 + +--S 1 of 37 dpol:= ODPOL(FRAC INT) --R --R @@ -97467,7 +101576,7 @@ dpol:= ODPOL(FRAC INT) --R Type: Domain --E 1 ---S 2 of 36 +--S 2 of 37 w := makeVariable('w)$dpol --R --R @@ -97475,7 +101584,7 @@ w := makeVariable('w)$dpol --RType: (NonNegativeInteger -> OrderlyDifferentialPolynomial(Fraction(Integer))) --E 2 ---S 3 of 36 +--S 3 of 37 z := makeVariable('z)$dpol --R --R @@ -97483,7 +101592,7 @@ z := makeVariable('z)$dpol --RType: (NonNegativeInteger -> OrderlyDifferentialPolynomial(Fraction(Integer))) --E 3 ---S 4 of 36 +--S 4 of 37 w.5 --R --R @@ -97492,7 +101601,7 @@ w.5 --R Type: OrderlyDifferentialPolynomial(Fraction(Integer)) --E 4 ---S 5 of 36 +--S 5 of 37 w 0 --R --R @@ -97500,7 +101609,7 @@ w 0 --R Type: OrderlyDifferentialPolynomial(Fraction(Integer)) --E 5 ---S 6 of 36 +--S 6 of 37 [z.i for i in 1..5] --R --R @@ -97509,7 +101618,7 @@ w 0 --R Type: List(OrderlyDifferentialPolynomial(Fraction(Integer))) --E 6 ---S 7 of 36 +--S 7 of 37 f:= w.4 - w.1 * w.1 * z.3 --R --R @@ -97519,7 +101628,7 @@ f:= w.4 - w.1 * w.1 * z.3 --R Type: OrderlyDifferentialPolynomial(Fraction(Integer)) --E 7 ---S 8 of 36 +--S 8 of 37 g:=(z.1)**3 * (z.2)**2 - w.2 --R --R @@ -97529,7 +101638,7 @@ g:=(z.1)**3 * (z.2)**2 - w.2 --R Type: OrderlyDifferentialPolynomial(Fraction(Integer)) --E 8 ---S 9 of 36 +--S 9 of 37 D(f) --R --R @@ -97539,7 +101648,7 @@ D(f) --R Type: OrderlyDifferentialPolynomial(Fraction(Integer)) --E 9 ---S 10 of 36 +--S 10 of 37 D(f,4) --R --R @@ -97554,7 +101663,7 @@ D(f,4) --R Type: OrderlyDifferentialPolynomial(Fraction(Integer)) --E 10 ---S 11 of 36 +--S 11 of 37 df:=makeVariable(f)$dpol --R --R @@ -97562,7 +101671,7 @@ df:=makeVariable(f)$dpol --RType: (NonNegativeInteger -> OrderlyDifferentialPolynomial(Fraction(Integer))) --E 11 ---S 12 of 36 +--S 12 of 37 df.4 --R --R @@ -97577,7 +101686,7 @@ df.4 --R Type: OrderlyDifferentialPolynomial(Fraction(Integer)) --E 12 ---S 13 of 36 +--S 13 of 37 order(g) --R --R @@ -97585,7 +101694,7 @@ order(g) --R Type: PositiveInteger --E 13 ---S 14 of 36 +--S 14 of 37 order(g, 'w) --R --R @@ -97593,7 +101702,7 @@ order(g, 'w) --R Type: PositiveInteger --E 14 ---S 15 of 36 +--S 15 of 37 differentialVariables(g) --R --R @@ -97601,7 +101710,7 @@ differentialVariables(g) --R Type: List(Symbol) --E 15 ---S 16 of 36 +--S 16 of 37 degree(g) --R --R @@ -97611,7 +101720,7 @@ degree(g) --R Type: IndexedExponents(OrderlyDifferentialVariable(Symbol)) --E 16 ---S 17 of 36 +--S 17 of 37 degree(g, 'w) --R --R @@ -97619,7 +101728,7 @@ degree(g, 'w) --R Type: PositiveInteger --E 17 ---S 18 of 36 +--S 18 of 37 weights(g) --R --R @@ -97627,7 +101736,7 @@ weights(g) --R Type: List(NonNegativeInteger) --E 18 ---S 19 of 36 +--S 19 of 37 weights(g,'w) --R --R @@ -97635,7 +101744,7 @@ weights(g,'w) --R Type: List(NonNegativeInteger) --E 19 ---S 20 of 36 +--S 20 of 37 weight(g) --R --R @@ -97643,7 +101752,7 @@ weight(g) --R Type: PositiveInteger --E 20 ---S 21 of 36 +--S 21 of 37 isobaric?(g) --R --R @@ -97651,7 +101760,7 @@ isobaric?(g) --R Type: Boolean --E 21 ---S 22 of 36 +--S 22 of 37 eval(g,['w::Symbol],[f]) --R --R @@ -97661,7 +101770,7 @@ eval(g,['w::Symbol],[f]) --R Type: OrderlyDifferentialPolynomial(Fraction(Integer)) --E 22 ---S 23 of 36 +--S 23 of 37 eval(g,variables(w.0),[f]) --R --R @@ -97671,7 +101780,7 @@ eval(g,variables(w.0),[f]) --R Type: OrderlyDifferentialPolynomial(Fraction(Integer)) --E 23 ---S 24 of 36 +--S 24 of 37 monomials(g) --R --R @@ -97681,7 +101790,7 @@ monomials(g) --R Type: List(OrderlyDifferentialPolynomial(Fraction(Integer))) --E 24 ---S 25 of 36 +--S 25 of 37 variables(g) --R --R @@ -97690,7 +101799,7 @@ variables(g) --R Type: List(OrderlyDifferentialVariable(Symbol)) --E 25 ---S 26 of 36 +--S 26 of 37 gcd(f,g) --R --R @@ -97698,7 +101807,7 @@ gcd(f,g) --R Type: OrderlyDifferentialPolynomial(Fraction(Integer)) --E 26 ---S 27 of 36 +--S 27 of 37 groebner([f,g]) --R --R @@ -97708,7 +101817,7 @@ groebner([f,g]) --R Type: List(OrderlyDifferentialPolynomial(Fraction(Integer))) --E 27 ---S 28 of 36 +--S 28 of 37 lg:=leader(g) --R --R @@ -97717,7 +101826,7 @@ lg:=leader(g) --R Type: OrderlyDifferentialVariable(Symbol) --E 28 ---S 29 of 36 +--S 29 of 37 sg:=separant(g) --R --R @@ -97727,7 +101836,7 @@ sg:=separant(g) --R Type: OrderlyDifferentialPolynomial(Fraction(Integer)) --E 29 ---S 30 of 36 +--S 30 of 37 ig:=initial(g) --R --R @@ -97737,7 +101846,7 @@ ig:=initial(g) --R Type: OrderlyDifferentialPolynomial(Fraction(Integer)) --E 30 ---S 31 of 36 +--S 31 of 37 g1 := D g --R --R @@ -97747,7 +101856,7 @@ g1 := D g --R Type: OrderlyDifferentialPolynomial(Fraction(Integer)) --E 31 ---S 32 of 36 +--S 32 of 37 lg1:= leader g1 --R --R @@ -97756,7 +101865,7 @@ lg1:= leader g1 --R Type: OrderlyDifferentialVariable(Symbol) --E 32 ---S 33 of 36 +--S 33 of 37 pdf:=D(f, lg1) --R --R @@ -97766,7 +101875,7 @@ pdf:=D(f, lg1) --R Type: OrderlyDifferentialPolynomial(Fraction(Integer)) --E 33 ---S 34 of 36 +--S 34 of 37 prf:=sg * f- pdf * g1 --R --R @@ -97776,7 +101885,7 @@ prf:=sg * f- pdf * g1 --R Type: OrderlyDifferentialPolynomial(Fraction(Integer)) --E 34 ---S 35 of 36 +--S 35 of 37 lcf:=leadingCoefficient univariate(prf, lg) --R --R @@ -97786,7 +101895,7 @@ lcf:=leadingCoefficient univariate(prf, lg) --R Type: OrderlyDifferentialPolynomial(Fraction(Integer)) --E 35 ---S 36 of 36 +--S 36 of 37 ig * prf - lcf * g * lg --R --R @@ -97795,6 +101904,168 @@ ig * prf - lcf * g * lg --R 1 2 4 1 1 3 1 1 2 2 --R Type: OrderlyDifferentialPolynomial(Fraction(Integer)) --E 36 + +--S 37 of 37 +)show OrderlyDifferentialPolynomial +--R +--R OrderlyDifferentialPolynomial(R: Ring) is a domain constructor +--R Abbreviation for OrderlyDifferentialPolynomial is ODPOL +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for ODPOL +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,R) -> % ?*? : (R,%) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?/? : (%,R) -> % if R has FIELD +--R ?=? : (%,%) -> Boolean D : (%,(R -> R)) -> % +--R D : % -> % if R has DIFRING 1 : () -> % +--R 0 : () -> % ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,PositiveInteger) -> % coefficients : % -> List(R) +--R coerce : % -> % if R has INTDOM coerce : Symbol -> % +--R coerce : R -> % coerce : Integer -> % +--R coerce : % -> OutputForm content : % -> R if R has GCDDOM +--R differentiate : (%,(R -> R)) -> % eval : (%,List(%),List(%)) -> % +--R eval : (%,%,%) -> % eval : (%,Equation(%)) -> % +--R eval : (%,List(Equation(%))) -> % gcd : (%,%) -> % if R has GCDDOM +--R gcd : List(%) -> % if R has GCDDOM ground : % -> R +--R ground? : % -> Boolean hash : % -> SingleInteger +--R initial : % -> % isobaric? : % -> Boolean +--R latex : % -> String lcm : (%,%) -> % if R has GCDDOM +--R lcm : List(%) -> % if R has GCDDOM leadingCoefficient : % -> R +--R leadingMonomial : % -> % map : ((R -> R),%) -> % +--R max : (%,%) -> % if R has ORDSET min : (%,%) -> % if R has ORDSET +--R monomial? : % -> Boolean monomials : % -> List(%) +--R one? : % -> Boolean order : % -> NonNegativeInteger +--R primitiveMonomials : % -> List(%) recip : % -> Union(%,"failed") +--R reductum : % -> % retract : % -> Symbol +--R retract : % -> R sample : () -> % +--R separant : % -> % weight : % -> NonNegativeInteger +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (Fraction(Integer),%) -> % if R has ALGEBRA(FRAC(INT)) +--R ?*? : (%,Fraction(Integer)) -> % if R has ALGEBRA(FRAC(INT)) +--R ? Boolean if R has ORDSET +--R ?<=? : (%,%) -> Boolean if R has ORDSET +--R ?>? : (%,%) -> Boolean if R has ORDSET +--R ?>=? : (%,%) -> Boolean if R has ORDSET +--R D : (%,(R -> R),NonNegativeInteger) -> % +--R D : (%,List(Symbol),List(NonNegativeInteger)) -> % if R has PDRING(SYMBOL) +--R D : (%,Symbol,NonNegativeInteger) -> % if R has PDRING(SYMBOL) +--R D : (%,List(Symbol)) -> % if R has PDRING(SYMBOL) +--R D : (%,Symbol) -> % if R has PDRING(SYMBOL) +--R D : (%,NonNegativeInteger) -> % if R has DIFRING +--R D : (%,List(OrderlyDifferentialVariable(Symbol)),List(NonNegativeInteger)) -> % +--R D : (%,OrderlyDifferentialVariable(Symbol),NonNegativeInteger) -> % +--R D : (%,List(OrderlyDifferentialVariable(Symbol))) -> % +--R D : (%,OrderlyDifferentialVariable(Symbol)) -> % +--R associates? : (%,%) -> Boolean if R has INTDOM +--R binomThmExpt : (%,%,NonNegativeInteger) -> % if R has COMRING +--R characteristic : () -> NonNegativeInteger +--R charthRoot : % -> Union(%,"failed") if $ has CHARNZ and R has PFECAT or R has CHARNZ +--R coefficient : (%,List(OrderlyDifferentialVariable(Symbol)),List(NonNegativeInteger)) -> % +--R coefficient : (%,OrderlyDifferentialVariable(Symbol),NonNegativeInteger) -> % +--R coefficient : (%,IndexedExponents(OrderlyDifferentialVariable(Symbol))) -> R +--R coerce : Fraction(Integer) -> % if R has ALGEBRA(FRAC(INT)) or R has RETRACT(FRAC(INT)) +--R coerce : SparseMultivariatePolynomial(R,Symbol) -> % +--R coerce : OrderlyDifferentialVariable(Symbol) -> % +--R conditionP : Matrix(%) -> Union(Vector(%),"failed") if $ has CHARNZ and R has PFECAT +--R content : (%,OrderlyDifferentialVariable(Symbol)) -> % if R has GCDDOM +--R convert : % -> InputForm if OrderlyDifferentialVariable(Symbol) has KONVERT(INFORM) and R has KONVERT(INFORM) +--R convert : % -> Pattern(Integer) if OrderlyDifferentialVariable(Symbol) has KONVERT(PATTERN(INT)) and R has KONVERT(PATTERN(INT)) +--R convert : % -> Pattern(Float) if OrderlyDifferentialVariable(Symbol) has KONVERT(PATTERN(FLOAT)) and R has KONVERT(PATTERN(FLOAT)) +--R degree : (%,Symbol) -> NonNegativeInteger +--R degree : (%,List(OrderlyDifferentialVariable(Symbol))) -> List(NonNegativeInteger) +--R degree : (%,OrderlyDifferentialVariable(Symbol)) -> NonNegativeInteger +--R degree : % -> IndexedExponents(OrderlyDifferentialVariable(Symbol)) +--R differentialVariables : % -> List(Symbol) +--R differentiate : (%,(R -> R),NonNegativeInteger) -> % +--R differentiate : (%,List(Symbol),List(NonNegativeInteger)) -> % if R has PDRING(SYMBOL) +--R differentiate : (%,Symbol,NonNegativeInteger) -> % if R has PDRING(SYMBOL) +--R differentiate : (%,List(Symbol)) -> % if R has PDRING(SYMBOL) +--R differentiate : (%,Symbol) -> % if R has PDRING(SYMBOL) +--R differentiate : (%,NonNegativeInteger) -> % if R has DIFRING +--R differentiate : % -> % if R has DIFRING +--R differentiate : (%,List(OrderlyDifferentialVariable(Symbol)),List(NonNegativeInteger)) -> % +--R differentiate : (%,OrderlyDifferentialVariable(Symbol),NonNegativeInteger) -> % +--R differentiate : (%,List(OrderlyDifferentialVariable(Symbol))) -> % +--R differentiate : (%,OrderlyDifferentialVariable(Symbol)) -> % +--R discriminant : (%,OrderlyDifferentialVariable(Symbol)) -> % if R has COMRING +--R eval : (%,List(Symbol),List(R)) -> % if R has DIFRING +--R eval : (%,Symbol,R) -> % if R has DIFRING +--R eval : (%,List(Symbol),List(%)) -> % if R has DIFRING +--R eval : (%,Symbol,%) -> % if R has DIFRING +--R eval : (%,List(OrderlyDifferentialVariable(Symbol)),List(%)) -> % +--R eval : (%,OrderlyDifferentialVariable(Symbol),%) -> % +--R eval : (%,List(OrderlyDifferentialVariable(Symbol)),List(R)) -> % +--R eval : (%,OrderlyDifferentialVariable(Symbol),R) -> % +--R exquo : (%,%) -> Union(%,"failed") if R has INTDOM +--R exquo : (%,R) -> Union(%,"failed") if R has INTDOM +--R factor : % -> Factored(%) if R has PFECAT +--R factorPolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has PFECAT +--R factorSquareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has PFECAT +--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) if R has GCDDOM +--R isExpt : % -> Union(Record(var: OrderlyDifferentialVariable(Symbol),exponent: NonNegativeInteger),"failed") +--R isPlus : % -> Union(List(%),"failed") +--R isTimes : % -> Union(List(%),"failed") +--R lcmCoef : (%,%) -> Record(llcmres: %,coeff1: %,coeff2: %) if R has GCDDOM +--R leader : % -> OrderlyDifferentialVariable(Symbol) +--R mainVariable : % -> Union(OrderlyDifferentialVariable(Symbol),"failed") +--R makeVariable : % -> (NonNegativeInteger -> %) if R has DIFRING +--R makeVariable : Symbol -> (NonNegativeInteger -> %) +--R mapExponents : ((IndexedExponents(OrderlyDifferentialVariable(Symbol)) -> IndexedExponents(OrderlyDifferentialVariable(Symbol))),%) -> % +--R minimumDegree : (%,List(OrderlyDifferentialVariable(Symbol))) -> List(NonNegativeInteger) +--R minimumDegree : (%,OrderlyDifferentialVariable(Symbol)) -> NonNegativeInteger +--R minimumDegree : % -> IndexedExponents(OrderlyDifferentialVariable(Symbol)) +--R monicDivide : (%,%,OrderlyDifferentialVariable(Symbol)) -> Record(quotient: %,remainder: %) +--R monomial : (%,List(OrderlyDifferentialVariable(Symbol)),List(NonNegativeInteger)) -> % +--R monomial : (%,OrderlyDifferentialVariable(Symbol),NonNegativeInteger) -> % +--R monomial : (R,IndexedExponents(OrderlyDifferentialVariable(Symbol))) -> % +--R multivariate : (SparseUnivariatePolynomial(%),OrderlyDifferentialVariable(Symbol)) -> % +--R multivariate : (SparseUnivariatePolynomial(R),OrderlyDifferentialVariable(Symbol)) -> % +--R numberOfMonomials : % -> NonNegativeInteger +--R order : (%,Symbol) -> NonNegativeInteger +--R patternMatch : (%,Pattern(Integer),PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if OrderlyDifferentialVariable(Symbol) has PATMAB(INT) and R has PATMAB(INT) +--R patternMatch : (%,Pattern(Float),PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if OrderlyDifferentialVariable(Symbol) has PATMAB(FLOAT) and R has PATMAB(FLOAT) +--R pomopo! : (%,R,IndexedExponents(OrderlyDifferentialVariable(Symbol)),%) -> % +--R prime? : % -> Boolean if R has PFECAT +--R primitivePart : (%,OrderlyDifferentialVariable(Symbol)) -> % if R has GCDDOM +--R primitivePart : % -> % if R has GCDDOM +--R reducedSystem : Matrix(%) -> Matrix(R) +--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(R),vec: Vector(R)) +--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(Integer),vec: Vector(Integer)) if R has LINEXP(INT) +--R reducedSystem : Matrix(%) -> Matrix(Integer) if R has LINEXP(INT) +--R resultant : (%,%,OrderlyDifferentialVariable(Symbol)) -> % if R has COMRING +--R retract : % -> SparseMultivariatePolynomial(R,Symbol) +--R retract : % -> OrderlyDifferentialVariable(Symbol) +--R retract : % -> Integer if R has RETRACT(INT) +--R retract : % -> Fraction(Integer) if R has RETRACT(FRAC(INT)) +--R retractIfCan : % -> Union(SparseMultivariatePolynomial(R,Symbol),"failed") +--R retractIfCan : % -> Union(Symbol,"failed") +--R retractIfCan : % -> Union(OrderlyDifferentialVariable(Symbol),"failed") +--R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT(INT) +--R retractIfCan : % -> Union(Fraction(Integer),"failed") if R has RETRACT(FRAC(INT)) +--R retractIfCan : % -> Union(R,"failed") +--R solveLinearPolynomialEquation : (List(SparseUnivariatePolynomial(%)),SparseUnivariatePolynomial(%)) -> Union(List(SparseUnivariatePolynomial(%)),"failed") if R has PFECAT +--R squareFree : % -> Factored(%) if R has GCDDOM +--R squareFreePart : % -> % if R has GCDDOM +--R squareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has PFECAT +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R totalDegree : (%,List(OrderlyDifferentialVariable(Symbol))) -> NonNegativeInteger +--R totalDegree : % -> NonNegativeInteger +--R unit? : % -> Boolean if R has INTDOM +--R unitCanonical : % -> % if R has INTDOM +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) if R has INTDOM +--R univariate : % -> SparseUnivariatePolynomial(R) +--R univariate : (%,OrderlyDifferentialVariable(Symbol)) -> SparseUnivariatePolynomial(%) +--R variables : % -> List(OrderlyDifferentialVariable(Symbol)) +--R weight : (%,Symbol) -> NonNegativeInteger +--R weights : (%,Symbol) -> List(NonNegativeInteger) +--R weights : % -> List(NonNegativeInteger) +--R +--E 37 + )spool )lisp (bye) \end{chunk} @@ -98388,30 +102659,31 @@ OrderlyDifferentialVariable(S:OrderedSet):DifferentialVariableCategory(S) --R --R------------------------------- Operations -------------------------------- --R ?*? : (%,%) -> % ?*? : (%,%) -> % ---R ?*? : (Integer,%) -> % ?*? : (PositiveInteger,%) -> % ---R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % +--R ?*? : (Integer,%) -> % ?*? : (NonNegativeInteger,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?+? : (%,%) -> % --R ?-? : (%,%) -> % -? : % -> % ---R ?=? : (%,%) -> Boolean D : % -> % ---R D : (%,NonNegativeInteger) -> % 1 : () -> % ---R 0 : () -> % ?^? : (%,PositiveInteger) -> % ---R coerce : % -> R coerce : R -> % ---R coerce : Integer -> % coerce : % -> OutputForm ---R differentiate : % -> % hash : % -> SingleInteger ---R inv : % -> % if R has FIELD latex : % -> String ---R one? : % -> Boolean recip : % -> Union(%,"failed") ---R sample : () -> % zero? : % -> Boolean +--R ?/? : (%,%) -> % if R has FIELD ?=? : (%,%) -> Boolean +--R D : % -> % D : (%,NonNegativeInteger) -> % +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % ?^? : (%,NonNegativeInteger) -> % +--R coerce : % -> % if R has FIELD coerce : % -> R +--R coerce : R -> % coerce : Integer -> % +--R coerce : % -> OutputForm differentiate : % -> % +--R gcd : (%,%) -> % if R has FIELD gcd : List(%) -> % if R has FIELD +--R hash : % -> SingleInteger inv : % -> % if R has FIELD +--R latex : % -> String lcm : (%,%) -> % if R has FIELD +--R lcm : List(%) -> % if R has FIELD one? : % -> Boolean +--R ?quo? : (%,%) -> % if R has FIELD recip : % -> Union(%,"failed") +--R ?rem? : (%,%) -> % if R has FIELD sample : () -> % +--R unit? : % -> Boolean if R has FIELD zero? : % -> Boolean --R ?~=? : (%,%) -> Boolean --R ?*? : (%,Fraction(Integer)) -> % if R has FIELD --R ?*? : (Fraction(Integer),%) -> % if R has FIELD ---R ?*? : (NonNegativeInteger,%) -> % --R ?**? : (%,Integer) -> % if R has FIELD ---R ?**? : (%,NonNegativeInteger) -> % ---R ?/? : (%,%) -> % if R has FIELD --R ?^? : (%,Integer) -> % if R has FIELD ---R ?^? : (%,NonNegativeInteger) -> % --R associates? : (%,%) -> Boolean if R has FIELD --R characteristic : () -> NonNegativeInteger ---R coerce : % -> % if R has FIELD --R coerce : Fraction(Integer) -> % if R has FIELD --R differentiate : (%,NonNegativeInteger) -> % --R divide : (%,%) -> Record(quotient: %,remainder: %) if R has FIELD @@ -98421,22 +102693,15 @@ OrderlyDifferentialVariable(S:OrderedSet):DifferentialVariableCategory(S) --R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) if R has FIELD --R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") if R has FIELD --R factor : % -> Factored(%) if R has FIELD ---R gcd : (%,%) -> % if R has FIELD ---R gcd : List(%) -> % if R has FIELD --R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) if R has FIELD ---R lcm : (%,%) -> % if R has FIELD ---R lcm : List(%) -> % if R has FIELD --R lcmCoef : (%,%) -> Record(llcmres: %,coeff1: %,coeff2: %) if R has FIELD --R multiEuclidean : (List(%),%) -> Union(List(%),"failed") if R has FIELD --R prime? : % -> Boolean if R has FIELD --R principalIdeal : List(%) -> Record(coef: List(%),generator: %) if R has FIELD ---R ?quo? : (%,%) -> % if R has FIELD ---R ?rem? : (%,%) -> % if R has FIELD --R sizeLess? : (%,%) -> Boolean if R has FIELD --R squareFree : % -> Factored(%) if R has FIELD --R squareFreePart : % -> % if R has FIELD --R subtractIfCan : (%,%) -> Union(%,"failed") ---R unit? : % -> Boolean if R has FIELD --R unitCanonical : % -> % if R has FIELD --R unitNormal : % -> Record(unit: %,canonical: %,associate: %) if R has FIELD --R @@ -98571,26 +102836,23 @@ OrdinaryDifferentialRing(Kernels,R,var): DRcategory == DRcapsule where --R Issue )edit bookvol10.3.pamphlet to see algebra source code for OWP --R --R------------------------------- Operations -------------------------------- +--R ?*? : (%,R) -> % if R has COMRING ?*? : (R,%) -> % if R has COMRING --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ?=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % coerce : Polynomial(R) -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R coerce : R -> % if R has COMRING coerce : Polynomial(R) -> % --R coerce : % -> Polynomial(R) coerce : Integer -> % --R coerce : % -> OutputForm hash : % -> SingleInteger --R latex : % -> String one? : % -> Boolean --R recip : % -> Union(%,"failed") sample : () -> % --R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (%,R) -> % if R has COMRING ---R ?*? : (R,%) -> % if R has COMRING ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % --R ?/? : (%,%) -> Union(%,"failed") if R has FIELD ---R ?^? : (%,NonNegativeInteger) -> % --R changeWeightLevel : NonNegativeInteger -> Void --R characteristic : () -> NonNegativeInteger ---R coerce : R -> % if R has COMRING --R subtractIfCan : (%,%) -> Union(%,"failed") --R --E 1 @@ -98694,6 +102956,7 @@ OrdinaryWeightedPolynomials(R:Ring, --S 1 of 1 )show OrdSetInts +--R --R OrdSetInts is a domain constructor --R Abbreviation for OrdSetInts is OSI --R This constructor is exposed in this frame. @@ -98825,45 +103088,44 @@ OrdSetInts: Export == Implement where --R bracket : List(%) -> % bracket : % -> % --R center : % -> % center : (%,Integer) -> % --R coerce : % -> OutputForm commaSeparate : List(%) -> % ---R ?div? : (%,%) -> % dot : % -> % ---R ?.? : (%,List(%)) -> % empty : () -> % ---R exquo : (%,%) -> % hash : % -> SingleInteger ---R hconcat : List(%) -> % hconcat : (%,%) -> % ---R height : () -> Integer height : % -> Integer ---R hspace : Integer -> % infix : (%,%,%) -> % ---R infix : (%,List(%)) -> % infix? : % -> Boolean ---R int : (%,%,%) -> % int : (%,%) -> % ---R int : % -> % label : (%,%) -> % ---R latex : % -> String left : % -> % ---R left : (%,Integer) -> % matrix : List(List(%)) -> % ---R message : String -> % messagePrint : String -> Void ---R not? : % -> % ?or? : (%,%) -> % ---R outputForm : DoubleFloat -> % outputForm : String -> % ---R outputForm : Symbol -> % outputForm : Integer -> % ---R over : (%,%) -> % overbar : % -> % ---R overlabel : (%,%) -> % paren : List(%) -> % ---R paren : % -> % pile : List(%) -> % ---R postfix : (%,%) -> % prefix : (%,List(%)) -> % ---R presub : (%,%) -> % presuper : (%,%) -> % ---R prime : % -> % print : % -> Void ---R prod : (%,%,%) -> % prod : (%,%) -> % ---R prod : % -> % ?quo? : (%,%) -> % ---R quote : % -> % rarrow : (%,%) -> % ---R ?rem? : (%,%) -> % right : % -> % ---R right : (%,Integer) -> % root : (%,%) -> % ---R root : % -> % rspace : (Integer,Integer) -> % ---R scripts : (%,List(%)) -> % semicolonSeparate : List(%) -> % ---R slash : (%,%) -> % string : % -> % ---R sub : (%,%) -> % subHeight : % -> Integer ---R sum : (%,%,%) -> % sum : (%,%) -> % ---R sum : % -> % super : (%,%) -> % ---R superHeight : % -> Integer supersub : (%,List(%)) -> % ---R vconcat : List(%) -> % vconcat : (%,%) -> % ---R vspace : Integer -> % width : () -> Integer ---R width : % -> Integer zag : (%,%) -> % ---R ?~=? : (%,%) -> Boolean +--R ?div? : (%,%) -> % dot : (%,NonNegativeInteger) -> % +--R dot : % -> % ?.? : (%,List(%)) -> % +--R empty : () -> % exquo : (%,%) -> % +--R hash : % -> SingleInteger hconcat : List(%) -> % +--R hconcat : (%,%) -> % height : () -> Integer +--R height : % -> Integer hspace : Integer -> % +--R infix : (%,%,%) -> % infix : (%,List(%)) -> % +--R infix? : % -> Boolean int : (%,%,%) -> % +--R int : (%,%) -> % int : % -> % +--R label : (%,%) -> % latex : % -> String +--R left : % -> % left : (%,Integer) -> % +--R matrix : List(List(%)) -> % message : String -> % +--R messagePrint : String -> Void not? : % -> % +--R ?or? : (%,%) -> % outputForm : DoubleFloat -> % +--R outputForm : String -> % outputForm : Symbol -> % +--R outputForm : Integer -> % over : (%,%) -> % +--R overbar : % -> % overlabel : (%,%) -> % +--R paren : List(%) -> % paren : % -> % +--R pile : List(%) -> % postfix : (%,%) -> % +--R prefix : (%,List(%)) -> % presub : (%,%) -> % +--R presuper : (%,%) -> % prime : % -> % +--R print : % -> Void prod : (%,%,%) -> % +--R prod : (%,%) -> % prod : % -> % +--R ?quo? : (%,%) -> % quote : % -> % +--R rarrow : (%,%) -> % ?rem? : (%,%) -> % +--R right : % -> % right : (%,Integer) -> % +--R root : (%,%) -> % root : % -> % +--R rspace : (Integer,Integer) -> % scripts : (%,List(%)) -> % +--R semicolonSeparate : List(%) -> % slash : (%,%) -> % +--R string : % -> % sub : (%,%) -> % +--R subHeight : % -> Integer sum : (%,%,%) -> % +--R sum : (%,%) -> % sum : % -> % +--R super : (%,%) -> % superHeight : % -> Integer +--R supersub : (%,List(%)) -> % vconcat : List(%) -> % +--R vconcat : (%,%) -> % vspace : Integer -> % +--R width : () -> Integer width : % -> Integer +--R zag : (%,%) -> % ?~=? : (%,%) -> Boolean --R differentiate : (%,NonNegativeInteger) -> % ---R dot : (%,NonNegativeInteger) -> % --R prime : (%,NonNegativeInteger) -> % --R --E 1 @@ -99456,28 +103718,26 @@ OutputForm(): SetCategory with --R --R------------------------------- Operations -------------------------------- --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ?=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % associates? : (%,%) -> Boolean ---R coerce : % -> % coerce : Integer -> % ---R coerce : % -> OutputForm complete : % -> % ---R digits : % -> Stream(Integer) extend : (%,Integer) -> % ---R gcd : List(%) -> % gcd : (%,%) -> % ---R hash : % -> SingleInteger latex : % -> String ---R lcm : List(%) -> % lcm : (%,%) -> % ---R moduloP : % -> Integer modulus : () -> Integer ---R one? : % -> Boolean order : % -> NonNegativeInteger ---R ?quo? : (%,%) -> % quotientByP : % -> % ---R recip : % -> Union(%,"failed") ?rem? : (%,%) -> % ---R sample : () -> % sizeLess? : (%,%) -> Boolean ---R sqrt : (%,Integer) -> % unit? : % -> Boolean ---R unitCanonical : % -> % zero? : % -> Boolean ---R ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R associates? : (%,%) -> Boolean coerce : % -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R complete : % -> % digits : % -> Stream(Integer) +--R extend : (%,Integer) -> % gcd : List(%) -> % +--R gcd : (%,%) -> % hash : % -> SingleInteger +--R latex : % -> String lcm : List(%) -> % +--R lcm : (%,%) -> % moduloP : % -> Integer +--R modulus : () -> Integer one? : % -> Boolean +--R order : % -> NonNegativeInteger ?quo? : (%,%) -> % +--R quotientByP : % -> % recip : % -> Union(%,"failed") +--R ?rem? : (%,%) -> % sample : () -> % +--R sizeLess? : (%,%) -> Boolean sqrt : (%,Integer) -> % +--R unit? : % -> Boolean unitCanonical : % -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean --R approximate : (%,Integer) -> Integer --R characteristic : () -> NonNegativeInteger --R divide : (%,%) -> Record(quotient: %,remainder: %) @@ -99614,31 +103874,31 @@ PAdicInteger(p:Integer) == InnerPAdicInteger(p,true$Boolean) --R ?*? : (%,PAdicInteger(p)) -> % ?*? : (PAdicInteger(p),%) -> % --R ?*? : (Fraction(Integer),%) -> % ?*? : (%,Fraction(Integer)) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,Integer) -> % ?**? : (%,NonNegativeInteger) -> % --R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % --R ?-? : (%,%) -> % -? : % -> % --R ?/? : (%,%) -> % ?=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % ---R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> % ---R associates? : (%,%) -> Boolean coerce : PAdicInteger(p) -> % ---R coerce : Fraction(Integer) -> % coerce : % -> % ---R coerce : Integer -> % coerce : % -> OutputForm ---R denom : % -> PAdicInteger(p) denominator : % -> % ---R factor : % -> Factored(%) gcd : List(%) -> % ---R gcd : (%,%) -> % hash : % -> SingleInteger ---R inv : % -> % latex : % -> String ---R lcm : List(%) -> % lcm : (%,%) -> % ---R numer : % -> PAdicInteger(p) numerator : % -> % ---R one? : % -> Boolean prime? : % -> Boolean ---R ?quo? : (%,%) -> % recip : % -> Union(%,"failed") ---R ?rem? : (%,%) -> % removeZeroes : (Integer,%) -> % ---R removeZeroes : % -> % retract : % -> PAdicInteger(p) ---R sample : () -> % sizeLess? : (%,%) -> Boolean ---R squareFree : % -> Factored(%) squareFreePart : % -> % ---R unit? : % -> Boolean unitCanonical : % -> % ---R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % +--R ?^? : (%,Integer) -> % ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,PositiveInteger) -> % associates? : (%,%) -> Boolean +--R coerce : PAdicInteger(p) -> % coerce : Fraction(Integer) -> % +--R coerce : % -> % coerce : Integer -> % +--R coerce : % -> OutputForm denom : % -> PAdicInteger(p) +--R denominator : % -> % factor : % -> Factored(%) +--R gcd : List(%) -> % gcd : (%,%) -> % +--R hash : % -> SingleInteger inv : % -> % +--R latex : % -> String lcm : List(%) -> % +--R lcm : (%,%) -> % numer : % -> PAdicInteger(p) +--R numerator : % -> % one? : % -> Boolean +--R prime? : % -> Boolean ?quo? : (%,%) -> % +--R recip : % -> Union(%,"failed") ?rem? : (%,%) -> % +--R removeZeroes : (Integer,%) -> % removeZeroes : % -> % +--R retract : % -> PAdicInteger(p) sample : () -> % +--R sizeLess? : (%,%) -> Boolean squareFree : % -> Factored(%) +--R squareFreePart : % -> % unit? : % -> Boolean +--R unitCanonical : % -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean --R ?/? : (PAdicInteger(p),PAdicInteger(p)) -> % --R ? Boolean if PAdicInteger(p) has ORDSET --R ?<=? : (%,%) -> Boolean if PAdicInteger(p) has ORDSET @@ -99652,7 +103912,6 @@ PAdicInteger(p:Integer) == InnerPAdicInteger(p,true$Boolean) --R D : (%,Symbol) -> % if PAdicInteger(p) has PDRING(SYMBOL) --R D : (%,NonNegativeInteger) -> % if PAdicInteger(p) has DIFRING --R D : % -> % if PAdicInteger(p) has DIFRING ---R ?^? : (%,NonNegativeInteger) -> % --R abs : % -> % if PAdicInteger(p) has OINTDOM --R approximate : (%,Integer) -> Fraction(Integer) --R ceiling : % -> PAdicInteger(p) if PAdicInteger(p) has INS @@ -99878,24 +104137,28 @@ PAdicRational(p:Integer) == PAdicRationalConstructor(p,PAdicInteger p) --R ?*? : (%,PADIC) -> % ?*? : (PADIC,%) -> % --R ?*? : (Fraction(Integer),%) -> % ?*? : (%,Fraction(Integer)) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,Integer) -> % ?**? : (%,NonNegativeInteger) -> % --R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % --R ?-? : (%,%) -> % -? : % -> % --R ?/? : (PADIC,PADIC) -> % ?/? : (%,%) -> % --R ?=? : (%,%) -> Boolean D : (%,(PADIC -> PADIC)) -> % ---R 1 : () -> % 0 : () -> % ---R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> % ---R associates? : (%,%) -> Boolean coerce : PADIC -> % ---R coerce : Fraction(Integer) -> % coerce : % -> % ---R coerce : Integer -> % coerce : % -> OutputForm ---R denom : % -> PADIC denominator : % -> % ---R factor : % -> Factored(%) gcd : List(%) -> % +--R D : % -> % if PADIC has DIFRING 1 : () -> % +--R 0 : () -> % ?^? : (%,Integer) -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R abs : % -> % if PADIC has OINTDOM associates? : (%,%) -> Boolean +--R coerce : PADIC -> % coerce : Fraction(Integer) -> % +--R coerce : % -> % coerce : Integer -> % +--R coerce : % -> OutputForm denom : % -> PADIC +--R denominator : % -> % factor : % -> Factored(%) +--R floor : % -> PADIC if PADIC has INS gcd : List(%) -> % --R gcd : (%,%) -> % hash : % -> SingleInteger ---R inv : % -> % latex : % -> String ---R lcm : List(%) -> % lcm : (%,%) -> % ---R map : ((PADIC -> PADIC),%) -> % numer : % -> PADIC ---R numerator : % -> % one? : % -> Boolean ---R prime? : % -> Boolean ?quo? : (%,%) -> % +--R init : () -> % if PADIC has STEP inv : % -> % +--R latex : % -> String lcm : List(%) -> % +--R lcm : (%,%) -> % map : ((PADIC -> PADIC),%) -> % +--R numer : % -> PADIC numerator : % -> % +--R one? : % -> Boolean prime? : % -> Boolean +--R ?quo? : (%,%) -> % random : () -> % if PADIC has INS --R recip : % -> Union(%,"failed") ?rem? : (%,%) -> % --R removeZeroes : (Integer,%) -> % removeZeroes : % -> % --R retract : % -> PADIC sample : () -> % @@ -99903,8 +104166,6 @@ PAdicRational(p:Integer) == PAdicRationalConstructor(p,PAdicInteger p) --R squareFreePart : % -> % unit? : % -> Boolean --R unitCanonical : % -> % zero? : % -> Boolean --R ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % --R ? Boolean if PADIC has ORDSET --R ?<=? : (%,%) -> Boolean if PADIC has ORDSET --R ?>? : (%,%) -> Boolean if PADIC has ORDSET @@ -99915,9 +104176,6 @@ PAdicRational(p:Integer) == PAdicRationalConstructor(p,PAdicInteger p) --R D : (%,List(Symbol)) -> % if PADIC has PDRING(SYMBOL) --R D : (%,Symbol) -> % if PADIC has PDRING(SYMBOL) --R D : (%,NonNegativeInteger) -> % if PADIC has DIFRING ---R D : % -> % if PADIC has DIFRING ---R ?^? : (%,NonNegativeInteger) -> % ---R abs : % -> % if PADIC has OINTDOM --R approximate : (%,Integer) -> Fraction(Integer) --R ceiling : % -> PADIC if PADIC has INS --R characteristic : () -> NonNegativeInteger @@ -99953,10 +104211,8 @@ PAdicRational(p:Integer) == PAdicRationalConstructor(p,PAdicInteger p) --R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) --R factorPolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if PADIC has PFECAT --R factorSquareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if PADIC has PFECAT ---R floor : % -> PADIC if PADIC has INS --R fractionPart : % -> % if PADIC has EUCDOM --R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) ---R init : () -> % if PADIC has STEP --R lcmCoef : (%,%) -> Record(llcmres: %,coeff1: %,coeff2: %) --R max : (%,%) -> % if PADIC has ORDSET --R min : (%,%) -> % if PADIC has ORDSET @@ -99967,7 +104223,6 @@ PAdicRational(p:Integer) == PAdicRationalConstructor(p,PAdicInteger p) --R patternMatch : (%,Pattern(Integer),PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if PADIC has PATMAB(INT) --R positive? : % -> Boolean if PADIC has OINTDOM --R principalIdeal : List(%) -> Record(coef: List(%),generator: %) ---R random : () -> % if PADIC has INS --R reducedSystem : Matrix(%) -> Matrix(PADIC) --R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(PADIC),vec: Vector(PADIC)) --R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(Integer),vec: Vector(Integer)) if PADIC has LINEXP(INT) @@ -100294,6 +104549,7 @@ PAdicRationalConstructor(p,PADIC): Exports == Implementation where --S 1 of 1 )show Palette +--R --R Palette is a domain constructor --R Abbreviation for Palette is PALETTE --R This constructor is exposed in this frame. @@ -100696,7 +104952,7 @@ ParametricSurface(ComponentFunction): Exports == Implementation where )set message auto off )clear all ---S 1 of 22 +--S 1 of 23 partialFraction(1,factorial 10) --R --R @@ -100707,7 +104963,7 @@ partialFraction(1,factorial 10) --R Type: PartialFraction(Integer) --E 1 ---S 2 of 22 +--S 2 of 23 f := padicFraction(%) --R --R @@ -100718,7 +104974,7 @@ f := padicFraction(%) --R Type: PartialFraction(Integer) --E 2 ---S 3 of 22 +--S 3 of 23 compactFraction(f) --R --R @@ -100729,7 +104985,7 @@ compactFraction(f) --R Type: PartialFraction(Integer) --E 3 ---S 4 of 22 +--S 4 of 23 numberOfFractionalTerms(f) --R --R @@ -100737,7 +104993,7 @@ numberOfFractionalTerms(f) --R Type: PositiveInteger --E 4 ---S 5 of 22 +--S 5 of 23 nthFractionalTerm(f,3) --R --R @@ -100748,7 +105004,7 @@ nthFractionalTerm(f,3) --R Type: PartialFraction(Integer) --E 5 ---S 6 of 22 +--S 6 of 23 partialFraction(1,- 13 + 14 * %i) --R --R @@ -100758,7 +105014,7 @@ partialFraction(1,- 13 + 14 * %i) --R Type: PartialFraction(Complex(Integer)) --E 6 ---S 7 of 22 +--S 7 of 23 % :: Fraction Complex Integer --R --R @@ -100768,7 +105024,7 @@ partialFraction(1,- 13 + 14 * %i) --R Type: Fraction(Complex(Integer)) --E 7 ---S 8 of 22 +--S 8 of 23 u : FR UP(x, FRAC INT) := reduce(*,[primeFactor(x+i,i) for i in 1..4]) --R --R @@ -100777,7 +105033,7 @@ u : FR UP(x, FRAC INT) := reduce(*,[primeFactor(x+i,i) for i in 1..4]) --R Type: Factored(UnivariatePolynomial(x,Fraction(Integer))) --E 8 ---S 9 of 22 +--S 9 of 23 partialFraction(1,u) --R --R @@ -100791,7 +105047,7 @@ partialFraction(1,u) --R Type: PartialFraction(UnivariatePolynomial(x,Fraction(Integer))) --E 9 ---S 10 of 22 +--S 10 of 23 padicFraction % --R --R @@ -100812,7 +105068,7 @@ padicFraction % --R Type: PartialFraction(UnivariatePolynomial(x,Fraction(Integer))) --E 10 ---S 11 of 22 +--S 11 of 23 fraction:=Fraction(Polynomial(Integer)) --R --R @@ -100820,7 +105076,7 @@ fraction:=Fraction(Polynomial(Integer)) --R Type: Domain --E 11 ---S 12 of 22 +--S 12 of 23 up:=UnivariatePolynomial(y,fraction) --R --R @@ -100828,7 +105084,7 @@ up:=UnivariatePolynomial(y,fraction) --R Type: Domain --E 12 ---S 13 of 22 +--S 13 of 23 pfup:=PartialFraction(up) --R --R @@ -100837,7 +105093,7 @@ pfup:=PartialFraction(up) --R Type: Domain --E 13 ---S 14 of 22 +--S 14 of 23 a:=x+1/(y+1) --R --R @@ -100847,7 +105103,7 @@ a:=x+1/(y+1) --R Type: Fraction(Polynomial(Integer)) --E 14 ---S 15 of 22 +--S 15 of 23 b:=partialFraction(a,y)$PartialFractionPackage(Integer) --R --R @@ -100857,7 +105113,7 @@ b:=partialFraction(a,y)$PartialFractionPackage(Integer) --R Type: PartialFraction(UnivariatePolynomial(y,Fraction(Polynomial(Integer)))) --E 15 ---S 16 of 22 +--S 16 of 23 c:=b::pfup --R --R @@ -100867,7 +105123,7 @@ c:=b::pfup --R Type: PartialFraction(UnivariatePolynomial(y,Fraction(Polynomial(Integer)))) --E 16 ---S 17 of 22 +--S 17 of 23 cw:=(wholePart c)::Expression(Integer) --R --R @@ -100875,7 +105131,7 @@ cw:=(wholePart c)::Expression(Integer) --R Type: Expression(Integer) --E 17 ---S 18 of 22 +--S 18 of 23 m:=numberOfFractionalTerms(c) --R --R @@ -100883,7 +105139,7 @@ m:=numberOfFractionalTerms(c) --R Type: PositiveInteger --E 18 ---S 19 of 22 +--S 19 of 23 crList:=[nthFractionalTerm(c,i) for i in 1..m] --R --R @@ -100893,7 +105149,7 @@ crList:=[nthFractionalTerm(c,i) for i in 1..m] --RType: List(PartialFraction(UnivariatePolynomial(y,Fraction(Polynomial(Integer))))) --E 19 ---S 20 of 22 +--S 20 of 23 cc:=reduce(+,crList) --R --R @@ -100903,7 +105159,7 @@ cc:=reduce(+,crList) --R Type: PartialFraction(UnivariatePolynomial(y,Fraction(Polynomial(Integer)))) --E 20 ---S 21 of 22 +--S 21 of 23 ccx:=cc::(Fraction(up))::(Expression(Integer)) --R --R @@ -100913,7 +105169,7 @@ ccx:=cc::(Fraction(up))::(Expression(Integer)) --R Type: Expression(Integer) --E 21 ---S 22 of 22 +--S 22 of 23 sin(cw)*cos(ccx)+sin(ccx)*cos(cw) --R --R @@ -100923,6 +105179,63 @@ sin(cw)*cos(ccx)+sin(ccx)*cos(cw) --R Type: Expression(Integer) --E 22 +--S 23 of 23 +)show PartialFraction +--R +--R PartialFraction(R: EuclideanDomain) is a domain constructor +--R Abbreviation for PartialFraction is PFR +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for PFR +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,R) -> % ?*? : (R,%) -> % +--R ?*? : (Fraction(Integer),%) -> % ?*? : (%,Fraction(Integer)) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,Integer) -> % ?**? : (%,NonNegativeInteger) -> % +--R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % +--R ?-? : (%,%) -> % -? : % -> % +--R ?/? : (%,%) -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,Integer) -> % ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,PositiveInteger) -> % associates? : (%,%) -> Boolean +--R coerce : Fraction(Factored(R)) -> % coerce : % -> Fraction(R) +--R coerce : R -> % coerce : Fraction(Integer) -> % +--R coerce : % -> % coerce : Integer -> % +--R coerce : % -> OutputForm compactFraction : % -> % +--R factor : % -> Factored(%) firstDenom : % -> Factored(R) +--R firstNumer : % -> R gcd : List(%) -> % +--R gcd : (%,%) -> % hash : % -> SingleInteger +--R inv : % -> % latex : % -> String +--R lcm : List(%) -> % lcm : (%,%) -> % +--R one? : % -> Boolean padicFraction : % -> % +--R prime? : % -> Boolean ?quo? : (%,%) -> % +--R recip : % -> Union(%,"failed") ?rem? : (%,%) -> % +--R sample : () -> % sizeLess? : (%,%) -> Boolean +--R squareFree : % -> Factored(%) squareFreePart : % -> % +--R unit? : % -> Boolean unitCanonical : % -> % +--R wholePart : % -> R zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R characteristic : () -> NonNegativeInteger +--R divide : (%,%) -> Record(quotient: %,remainder: %) +--R euclideanSize : % -> NonNegativeInteger +--R expressIdealMember : (List(%),%) -> Union(List(%),"failed") +--R exquo : (%,%) -> Union(%,"failed") +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) +--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) +--R lcmCoef : (%,%) -> Record(llcmres: %,coeff1: %,coeff2: %) +--R multiEuclidean : (List(%),%) -> Union(List(%),"failed") +--R nthFractionalTerm : (%,Integer) -> % +--R numberOfFractionalTerms : % -> Integer +--R padicallyExpand : (R,R) -> SparseUnivariatePolynomial(R) +--R partialFraction : (R,Factored(R)) -> % +--R principalIdeal : List(%) -> Record(coef: List(%),generator: %) +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) +--R +--E 23 + )spool )lisp (bye) \end{chunk} @@ -101513,18 +105826,17 @@ PartialFraction(R: EuclideanDomain): Cat == Capsule where --R Issue )edit bookvol10.3.pamphlet to see algebra source code for PRTITION --R --R------------------------------- Operations -------------------------------- ---R ?*? : (PositiveInteger,%) -> % ?+? : (%,%) -> % ---R ? Boolean ?<=? : (%,%) -> Boolean ---R ?=? : (%,%) -> Boolean ?>? : (%,%) -> Boolean ---R ?>=? : (%,%) -> Boolean 0 : () -> % ---R coerce : % -> List(Integer) coerce : % -> OutputForm ---R conjugate : % -> % convert : % -> List(Integer) ---R hash : % -> SingleInteger latex : % -> String ---R max : (%,%) -> % min : (%,%) -> % ---R partition : List(Integer) -> % pdct : % -> Integer ---R sample : () -> % zero? : % -> Boolean ---R ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?+? : (%,%) -> % ? Boolean +--R ?<=? : (%,%) -> Boolean ?=? : (%,%) -> Boolean +--R ?>? : (%,%) -> Boolean ?>=? : (%,%) -> Boolean +--R 0 : () -> % coerce : % -> List(Integer) +--R coerce : % -> OutputForm conjugate : % -> % +--R convert : % -> List(Integer) hash : % -> SingleInteger +--R latex : % -> String max : (%,%) -> % +--R min : (%,%) -> % partition : List(Integer) -> % +--R pdct : % -> Integer sample : () -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean --R powers : List(Integer) -> List(List(Integer)) --R subtractIfCan : (%,%) -> Union(%,"failed") --R @@ -101734,23 +106046,23 @@ Partition: Exports == Implementation where --R --R------------------------------- Operations -------------------------------- --R ?*? : (%,%) -> % ?**? : (%,%) -> % ---R ?+? : (%,%) -> % ?/? : (%,%) -> % ---R ?=? : (%,%) -> Boolean 1 : () -> % ---R 0 : () -> % addBadValue : (%,Any) -> % ---R coerce : Symbol -> % coerce : R -> % ---R coerce : % -> OutputForm constant? : % -> Boolean ---R convert : List(%) -> % copy : % -> % ---R depth : % -> NonNegativeInteger generic? : % -> Boolean +--R ?**? : (%,NonNegativeInteger) -> % ?+? : (%,%) -> % +--R ?/? : (%,%) -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R addBadValue : (%,Any) -> % coerce : Symbol -> % +--R coerce : R -> % coerce : % -> OutputForm +--R constant? : % -> Boolean convert : List(%) -> % +--R copy : % -> % depth : % -> NonNegativeInteger +--R elt : (BasicOperator,List(%)) -> % generic? : % -> Boolean --R getBadValues : % -> List(Any) hasPredicate? : % -> Boolean --R hasTopPredicate? : % -> Boolean hash : % -> SingleInteger --R inR? : % -> Boolean latex : % -> String --R multiple? : % -> Boolean optional? : % -> Boolean --R predicates : % -> List(Any) quoted? : % -> Boolean --R resetBadValues : % -> % retract : % -> Symbol ---R retract : % -> R symbol? : % -> Boolean ---R variables : % -> List(%) ?~=? : (%,%) -> Boolean ---R ?**? : (%,NonNegativeInteger) -> % ---R elt : (BasicOperator,List(%)) -> % +--R retract : % -> R setPredicates : (%,List(Any)) -> % +--R symbol? : % -> Boolean variables : % -> List(%) +--R ?~=? : (%,%) -> Boolean --R isExpt : % -> Union(Record(val: %,exponent: NonNegativeInteger),"failed") --R isList : % -> Union(List(%),"failed") --R isOp : % -> Union(Record(op: BasicOperator,arg: List(%)),"failed") @@ -101763,7 +106075,6 @@ Partition: Exports == Implementation where --R patternVariable : (Symbol,Boolean,Boolean,Boolean) -> % --R retractIfCan : % -> Union(Symbol,"failed") --R retractIfCan : % -> Union(R,"failed") ---R setPredicates : (%,List(Any)) -> % --R setTopPredicate : (%,List(Symbol),Any) -> % --R topPredicate : % -> Record(var: List(Symbol),pred: Any) --R withPredicates : (%,List(Any)) -> % @@ -102547,12 +106858,12 @@ PatternMatchResult(R:SetCategory, S:SetCategory): SetCategory with --R distance : (%,%) -> Integer ?.right : (%,right) -> % --R ?.left : (%,left) -> % ?.value : (%,value) -> S --R empty : () -> % empty? : % -> Boolean ---R eq? : (%,%) -> Boolean leaf? : % -> Boolean ---R leaves : % -> List(S) left : % -> % ---R map : ((S -> S),%) -> % nodes : % -> List(%) ---R ptree : (%,%) -> % ptree : S -> % ---R right : % -> % sample : () -> % ---R value : % -> S +--R eq? : (%,%) -> Boolean latex : % -> String if S has SETCAT +--R leaf? : % -> Boolean leaves : % -> List(S) +--R left : % -> % map : ((S -> S),%) -> % +--R nodes : % -> List(%) ptree : (%,%) -> % +--R ptree : S -> % right : % -> % +--R sample : () -> % value : % -> S --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R ?=? : (%,%) -> Boolean if S has SETCAT --R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate @@ -102566,7 +106877,6 @@ PatternMatchResult(R:SetCategory, S:SetCategory): SetCategory with --R eval : (%,List(Equation(S))) -> % if S has EVALAB(S) and S has SETCAT --R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate --R hash : % -> SingleInteger if S has SETCAT ---R latex : % -> String if S has SETCAT --R less? : (%,NonNegativeInteger) -> Boolean --R map! : ((S -> S),%) -> % if $ has shallowlyMutable --R member? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT @@ -102725,7 +107035,8 @@ PendantTree(S: SetCategory): T == C where )set message test on )set message auto off )clear all ---S 1 of 8 + +--S 1 of 9 p := coercePreimagesImages([[1,2,3],[1,2,3]]) --R --R @@ -102733,7 +107044,7 @@ p := coercePreimagesImages([[1,2,3],[1,2,3]]) --R Type: Permutation(PositiveInteger) --E 1 ---S 2 of 8 +--S 2 of 9 movedPoints p -- should return {} --R --R @@ -102741,7 +107052,7 @@ movedPoints p -- should return {} --R Type: Set(PositiveInteger) --E 2 ---S 3 of 8 +--S 3 of 9 even? p -- should return true --R --R @@ -102749,7 +107060,7 @@ even? p -- should return true --R Type: Boolean --E 3 ---S 4 of 8 +--S 4 of 9 p := coercePreimagesImages([[0,1,2,3],[3,0,2,1]])$PERM ZMOD 4 --R --R @@ -102757,7 +107068,7 @@ p := coercePreimagesImages([[0,1,2,3],[3,0,2,1]])$PERM ZMOD 4 --R Type: Permutation(IntegerMod(4)) --E 4 ---S 5 of 8 +--S 5 of 9 fixedPoints p -- should return {2} --R --R @@ -102765,7 +107076,7 @@ fixedPoints p -- should return {2} --R Type: Set(IntegerMod(4)) --E 5 ---S 6 of 8 +--S 6 of 9 q := coercePreimagesImages([[0,1,2,3],[1,0]])$PERM ZMOD 4 --R --R @@ -102773,7 +107084,7 @@ q := coercePreimagesImages([[0,1,2,3],[1,0]])$PERM ZMOD 4 --R Type: Permutation(IntegerMod(4)) --E 6 ---S 7 of 8 +--S 7 of 9 fixedPoints(p*q) -- should return {2,0} --R --R @@ -102781,13 +107092,55 @@ fixedPoints(p*q) -- should return {2,0} --R Type: Set(IntegerMod(4)) --E 7 ---S 8 of 8 +--S 8 of 9 even?(p*q) -- should return false --R --R --R (8) false --R Type: Boolean --E 8 + +--S 9 of 9 +)show Permutation +--R +--R Permutation(S: SetCategory) is a domain constructor +--R Abbreviation for Permutation is PERM +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for PERM +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,%) -> % ?**? : (%,Integer) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % +--R ?/? : (%,%) -> % ? Boolean +--R ?=? : (%,%) -> Boolean 1 : () -> % +--R ?^? : (%,Integer) -> % ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,PositiveInteger) -> % coerce : List(S) -> % +--R coerce : List(List(S)) -> % coerce : % -> OutputForm +--R coerceImages : List(S) -> % commutator : (%,%) -> % +--R conjugate : (%,%) -> % cycle : List(S) -> % +--R cyclePartition : % -> Partition cycles : List(List(S)) -> % +--R degree : % -> NonNegativeInteger ?.? : (%,S) -> S +--R eval : (%,S) -> S even? : % -> Boolean +--R hash : % -> SingleInteger inv : % -> % +--R latex : % -> String movedPoints : % -> Set(S) +--R odd? : % -> Boolean one? : % -> Boolean +--R orbit : (%,S) -> Set(S) order : % -> NonNegativeInteger +--R recip : % -> Union(%,"failed") sample : () -> % +--R sign : % -> Integer sort : List(%) -> List(%) +--R ?~=? : (%,%) -> Boolean +--R ?<=? : (%,%) -> Boolean if S has FINITE or S has ORDSET +--R ?>? : (%,%) -> Boolean if S has FINITE or S has ORDSET +--R ?>=? : (%,%) -> Boolean if S has FINITE or S has ORDSET +--R coerceListOfPairs : List(List(S)) -> % +--R coercePreimagesImages : List(List(S)) -> % +--R fixedPoints : % -> Set(S) if S has FINITE +--R listRepresentation : % -> Record(preimage: List(S),image: List(S)) +--R max : (%,%) -> % if S has FINITE or S has ORDSET +--R min : (%,%) -> % if S has FINITE or S has ORDSET +--R numberOfCycles : % -> NonNegativeInteger +--R +--E 9 + )spool )lisp (bye) \end{chunk} @@ -103394,7 +107747,7 @@ member? ( y , g2 ) --E 12 --S 13 of 13 -)sh PERMGRP +)show PermutationGroup --R --R PermutationGroup(S: SetCategory) is a domain constructor --R Abbreviation for PermutationGroup is PERMGRP @@ -103404,20 +107757,18 @@ member? ( y , g2 ) --R------------------------------- Operations -------------------------------- --R ? Boolean ?<=? : (%,%) -> Boolean --R ?=? : (%,%) -> Boolean base : % -> List(S) +--R coerce : List(Permutation(S)) -> % coerce : % -> List(Permutation(S)) --R coerce : % -> OutputForm degree : % -> NonNegativeInteger --R hash : % -> SingleInteger latex : % -> String ---R movedPoints : % -> Set(S) orbit : (%,Set(S)) -> Set(Set(S)) ---R orbit : (%,S) -> Set(S) orbits : % -> Set(Set(S)) ---R order : % -> NonNegativeInteger random : % -> Permutation(S) ---R ?~=? : (%,%) -> Boolean ---R coerce : List(Permutation(S)) -> % ---R coerce : % -> List(Permutation(S)) +--R movedPoints : % -> Set(S) orbit : (%,List(S)) -> Set(List(S)) +--R orbit : (%,Set(S)) -> Set(Set(S)) orbit : (%,S) -> Set(S) +--R orbits : % -> Set(Set(S)) order : % -> NonNegativeInteger +--R random : % -> Permutation(S) ?~=? : (%,%) -> Boolean --R ?.? : (%,NonNegativeInteger) -> Permutation(S) --R generators : % -> List(Permutation(S)) --R initializeGroupForWordProblem : (%,Integer,Integer) -> Void --R initializeGroupForWordProblem : % -> Void --R member? : (Permutation(S),%) -> Boolean ---R orbit : (%,List(S)) -> Set(List(S)) --R permutationGroup : List(Permutation(S)) -> % --R random : (%,Integer) -> Permutation(S) --R strongGenerators : % -> List(Permutation(S)) @@ -105341,32 +109692,31 @@ non-interactive environment (library), HACKPI would not exist. --R------------------------------- Operations -------------------------------- --R ?*? : (Fraction(Integer),%) -> % ?*? : (%,Fraction(Integer)) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,Integer) -> % ?**? : (%,NonNegativeInteger) -> % --R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % --R ?-? : (%,%) -> % -? : % -> % --R ?/? : (%,%) -> % ?=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % ---R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> % ---R associates? : (%,%) -> Boolean coerce : % -> Float ---R coerce : % -> DoubleFloat coerce : Fraction(Integer) -> % ---R coerce : % -> % coerce : Integer -> % ---R coerce : % -> OutputForm convert : % -> InputForm ---R convert : % -> DoubleFloat convert : % -> Float ---R factor : % -> Factored(%) gcd : List(%) -> % ---R gcd : (%,%) -> % hash : % -> SingleInteger ---R inv : % -> % latex : % -> String ---R lcm : List(%) -> % lcm : (%,%) -> % ---R one? : % -> Boolean pi : () -> % ---R prime? : % -> Boolean ?quo? : (%,%) -> % ---R recip : % -> Union(%,"failed") ?rem? : (%,%) -> % ---R retract : % -> Fraction(Integer) retract : % -> Integer ---R sample : () -> % sizeLess? : (%,%) -> Boolean ---R squareFree : % -> Factored(%) squareFreePart : % -> % ---R unit? : % -> Boolean unitCanonical : % -> % ---R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,Integer) -> % ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,PositiveInteger) -> % associates? : (%,%) -> Boolean +--R coerce : % -> Float coerce : % -> DoubleFloat +--R coerce : Fraction(Integer) -> % coerce : % -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R convert : % -> InputForm convert : % -> DoubleFloat +--R convert : % -> Float factor : % -> Factored(%) +--R gcd : List(%) -> % gcd : (%,%) -> % +--R hash : % -> SingleInteger inv : % -> % +--R latex : % -> String lcm : List(%) -> % +--R lcm : (%,%) -> % one? : % -> Boolean +--R pi : () -> % prime? : % -> Boolean +--R ?quo? : (%,%) -> % recip : % -> Union(%,"failed") +--R ?rem? : (%,%) -> % retract : % -> Fraction(Integer) +--R retract : % -> Integer sample : () -> % +--R sizeLess? : (%,%) -> Boolean squareFree : % -> Factored(%) +--R squareFreePart : % -> % unit? : % -> Boolean +--R unitCanonical : % -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean --R characteristic : () -> NonNegativeInteger --R convert : % -> Fraction(SparseUnivariatePolynomial(Integer)) --R divide : (%,%) -> Record(quotient: %,remainder: %) @@ -106083,7 +110433,7 @@ listBranches(refined) --E 4 --S 5 of 5 -)show ACPLOT +)show PlaneAlgebraicCurvePlot --R --R PlaneAlgebraicCurvePlot is a domain constructor --R Abbreviation for PlaneAlgebraicCurvePlot is ACPLOT @@ -106092,10 +110442,9 @@ listBranches(refined) --R --R------------------------------- Operations -------------------------------- --R coerce : % -> OutputForm refine : (%,DoubleFloat) -> % +--R xRange : % -> Segment(DoubleFloat) yRange : % -> Segment(DoubleFloat) --R listBranches : % -> List(List(Point(DoubleFloat))) --R makeSketch : (Polynomial(Integer),Symbol,Symbol,Segment(Fraction(Integer)),Segment(Fraction(Integer))) -> % ---R xRange : % -> Segment(DoubleFloat) ---R yRange : % -> Segment(DoubleFloat) --R --E 5 @@ -107811,14 +112160,15 @@ Plcs(K:Field,PCS:LocalPowerSeriesCategory(K)):Exports == Implementation where )set message test on )set message auto off )clear all ---S 1 of 2 + +--S 1 of 3 fp:=(t:DFLOAT):DFLOAT +-> sin(t) --R --R (1) theMap(Closure) --R Type: (DoubleFloat -> DoubleFloat) --E 1 ---S 2 of 2 +--S 2 of 3 plot(fp,-1.0..1.0)$PLOT --R --R @@ -107874,6 +112224,43 @@ plot(fp,-1.0..1.0)$PLOT --R [1.,0.8414709848078965] --R Type: Plot --E 2 + +--S 3 of 3 +)show Plot +--R +--R Plot is a domain constructor +--R Abbreviation for Plot is PLOT +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for PLOT +--R +--R------------------------------- Operations -------------------------------- +--R adaptive? : () -> Boolean coerce : % -> OutputForm +--R debug : Boolean -> Boolean maxPoints : () -> Integer +--R minPoints : () -> Integer numFunEvals : () -> Integer +--R parametric? : % -> Boolean refine : % -> % +--R screenResolution : () -> Integer setAdaptive : Boolean -> Boolean +--R setMaxPoints : Integer -> Integer setMinPoints : Integer -> Integer +--R tRange : % -> Segment(DoubleFloat) xRange : % -> Segment(DoubleFloat) +--R yRange : % -> Segment(DoubleFloat) +--R listBranches : % -> List(List(Point(DoubleFloat))) +--R plot : (%,Segment(DoubleFloat)) -> % +--R plot : ((DoubleFloat -> DoubleFloat),(DoubleFloat -> DoubleFloat),Segment(DoubleFloat),Segment(DoubleFloat),Segment(DoubleFloat)) -> % +--R plot : ((DoubleFloat -> DoubleFloat),(DoubleFloat -> DoubleFloat),Segment(DoubleFloat)) -> % +--R plot : (List((DoubleFloat -> DoubleFloat)),Segment(DoubleFloat),Segment(DoubleFloat)) -> % +--R plot : (List((DoubleFloat -> DoubleFloat)),Segment(DoubleFloat)) -> % +--R plot : ((DoubleFloat -> DoubleFloat),Segment(DoubleFloat),Segment(DoubleFloat)) -> % +--R plot : ((DoubleFloat -> DoubleFloat),Segment(DoubleFloat)) -> % +--R plotPolar : (DoubleFloat -> DoubleFloat) -> % +--R plotPolar : ((DoubleFloat -> DoubleFloat),Segment(DoubleFloat)) -> % +--R pointPlot : ((DoubleFloat -> Point(DoubleFloat)),Segment(DoubleFloat),Segment(DoubleFloat),Segment(DoubleFloat)) -> % +--R pointPlot : ((DoubleFloat -> Point(DoubleFloat)),Segment(DoubleFloat)) -> % +--R refine : (%,Segment(DoubleFloat)) -> % +--R setScreenResolution : Integer -> Integer +--R zoom : (%,Segment(DoubleFloat),Segment(DoubleFloat)) -> % +--R zoom : (%,Segment(DoubleFloat)) -> % +--R +--E 3 + )spool )lisp (bye) \end{chunk} @@ -108518,7 +112905,10 @@ Plot(): Exports == Implementation where --R debug3D : Boolean -> Boolean maxPoints3D : () -> Integer --R minPoints3D : () -> Integer numFunEvals3D : () -> Integer --R refine : % -> % screenResolution3D : () -> Integer ---R setAdaptive3D : Boolean -> Boolean +--R setAdaptive3D : Boolean -> Boolean setMaxPoints3D : Integer -> Integer +--R setMinPoints3D : Integer -> Integer tRange : % -> Segment(DoubleFloat) +--R xRange : % -> Segment(DoubleFloat) yRange : % -> Segment(DoubleFloat) +--R zRange : % -> Segment(DoubleFloat) --R listBranches : % -> List(List(Point(DoubleFloat))) --R plot : (%,Segment(DoubleFloat)) -> % --R plot : ((DoubleFloat -> DoubleFloat),(DoubleFloat -> DoubleFloat),(DoubleFloat -> DoubleFloat),(DoubleFloat -> DoubleFloat),Segment(DoubleFloat),Segment(DoubleFloat),Segment(DoubleFloat),Segment(DoubleFloat)) -> % @@ -108526,14 +112916,8 @@ Plot(): Exports == Implementation where --R pointPlot : ((DoubleFloat -> Point(DoubleFloat)),Segment(DoubleFloat),Segment(DoubleFloat),Segment(DoubleFloat),Segment(DoubleFloat)) -> % --R pointPlot : ((DoubleFloat -> Point(DoubleFloat)),Segment(DoubleFloat)) -> % --R refine : (%,Segment(DoubleFloat)) -> % ---R setMaxPoints3D : Integer -> Integer ---R setMinPoints3D : Integer -> Integer --R setScreenResolution3D : Integer -> Integer ---R tRange : % -> Segment(DoubleFloat) --R tValues : % -> List(List(DoubleFloat)) ---R xRange : % -> Segment(DoubleFloat) ---R yRange : % -> Segment(DoubleFloat) ---R zRange : % -> Segment(DoubleFloat) --R zoom : (%,Segment(DoubleFloat),Segment(DoubleFloat),Segment(DoubleFloat)) -> % --R --E 1 @@ -109281,27 +113665,28 @@ PoincareBirkhoffWittLyndonBasis(VarSet: OrderedSet): Public == Private where --R Issue )edit bookvol10.3.pamphlet to see algebra source code for POINT --R --R------------------------------- Operations -------------------------------- +--R ?*? : (%,R) -> % if R has MONOID ?*? : (R,%) -> % if R has MONOID +--R ?+? : (%,%) -> % if R has ABELSG ?-? : (%,%) -> % if R has ABELGRP --R -? : % -> % if R has ABELGRP concat : List(%) -> % --R concat : (%,%) -> % concat : (R,%) -> % --R concat : (%,R) -> % construct : List(R) -> % --R convert : List(R) -> % copy : % -> % --R cross : (%,%) -> % delete : (%,Integer) -> % ---R dimension : % -> PositiveInteger ?.? : (%,Integer) -> R ---R elt : (%,Integer,R) -> R empty : () -> % ---R empty? : % -> Boolean entries : % -> List(R) ---R eq? : (%,%) -> Boolean extend : (%,List(R)) -> % ---R index? : (Integer,%) -> Boolean indices : % -> List(Integer) ---R insert : (%,%,Integer) -> % insert : (R,%,Integer) -> % +--R dimension : % -> PositiveInteger dot : (%,%) -> R if R has RING +--R ?.? : (%,Integer) -> R elt : (%,Integer,R) -> R +--R empty : () -> % empty? : % -> Boolean +--R entries : % -> List(R) eq? : (%,%) -> Boolean +--R extend : (%,List(R)) -> % index? : (Integer,%) -> Boolean +--R indices : % -> List(Integer) insert : (%,%,Integer) -> % +--R insert : (R,%,Integer) -> % latex : % -> String if R has SETCAT --R map : (((R,R) -> R),%,%) -> % map : ((R -> R),%) -> % +--R max : (%,%) -> % if R has ORDSET min : (%,%) -> % if R has ORDSET --R new : (NonNegativeInteger,R) -> % point : List(R) -> % --R qelt : (%,Integer) -> R reverse : % -> % ---R sample : () -> % +--R sample : () -> % sort : % -> % if R has ORDSET +--R sort : (((R,R) -> Boolean),%) -> % --R #? : % -> NonNegativeInteger if $ has finiteAggregate ---R ?*? : (%,R) -> % if R has MONOID ---R ?*? : (R,%) -> % if R has MONOID --R ?*? : (Integer,%) -> % if R has ABELGRP ---R ?+? : (%,%) -> % if R has ABELSG ---R ?-? : (%,%) -> % if R has ABELGRP --R ? Boolean if R has ORDSET --R ?<=? : (%,%) -> Boolean if R has ORDSET --R ?=? : (%,%) -> Boolean if R has SETCAT @@ -109314,7 +113699,6 @@ PoincareBirkhoffWittLyndonBasis(VarSet: OrderedSet): Public == Private where --R count : (R,%) -> NonNegativeInteger if $ has finiteAggregate and R has SETCAT --R count : ((R -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate --R delete : (%,UniversalSegment(Integer)) -> % ---R dot : (%,%) -> R if R has RING --R ?.? : (%,UniversalSegment(Integer)) -> % --R entry? : (R,%) -> Boolean if $ has finiteAggregate and R has SETCAT --R eval : (%,List(R),List(R)) -> % if R has EVALAB(R) and R has SETCAT @@ -109326,18 +113710,15 @@ PoincareBirkhoffWittLyndonBasis(VarSet: OrderedSet): Public == Private where --R find : ((R -> Boolean),%) -> Union(R,"failed") --R first : % -> R if Integer has ORDSET --R hash : % -> SingleInteger if R has SETCAT ---R latex : % -> String if R has SETCAT --R length : % -> R if R has RADCAT and R has RING --R less? : (%,NonNegativeInteger) -> Boolean --R magnitude : % -> R if R has RADCAT and R has RING --R map! : ((R -> R),%) -> % if $ has shallowlyMutable ---R max : (%,%) -> % if R has ORDSET --R maxIndex : % -> Integer if Integer has ORDSET --R member? : (R,%) -> Boolean if $ has finiteAggregate and R has SETCAT --R members : % -> List(R) if $ has finiteAggregate --R merge : (%,%) -> % if R has ORDSET --R merge : (((R,R) -> Boolean),%,%) -> % ---R min : (%,%) -> % if R has ORDSET --R minIndex : % -> Integer if Integer has ORDSET --R more? : (%,NonNegativeInteger) -> Boolean --R outerProduct : (%,%) -> Matrix(R) if R has RING @@ -109357,8 +113738,6 @@ PoincareBirkhoffWittLyndonBasis(VarSet: OrderedSet): Public == Private where --R setelt : (%,UniversalSegment(Integer),R) -> R if $ has shallowlyMutable --R setelt : (%,Integer,R) -> R if $ has shallowlyMutable --R size? : (%,NonNegativeInteger) -> Boolean ---R sort : % -> % if R has ORDSET ---R sort : (((R,R) -> Boolean),%) -> % --R sort! : % -> % if $ has shallowlyMutable and R has ORDSET --R sort! : (((R,R) -> Boolean),%) -> % if $ has shallowlyMutable --R sorted? : % -> Boolean if R has ORDSET @@ -109522,7 +113901,8 @@ Point(R:Ring) : Exports == Implementation where )spool Polynomial.output )set message test on )set message auto off ---S 1 of 46 + +--S 1 of 47 x + 1 --R --R @@ -109530,7 +113910,7 @@ x + 1 --R Type: Polynomial(Integer) --E 1 ---S 2 of 46 +--S 2 of 47 z - 2.3 --R --R @@ -109538,7 +113918,7 @@ z - 2.3 --R Type: Polynomial(Float) --E 2 ---S 3 of 46 +--S 3 of 47 y**2 - z + 3/4 --R --R @@ -109548,7 +113928,7 @@ y**2 - z + 3/4 --R Type: Polynomial(Fraction(Integer)) --E 3 ---S 4 of 46 +--S 4 of 47 y **2 + x*y + y --R --R @@ -109557,7 +113937,7 @@ y **2 + x*y + y --R Type: Polynomial(Integer) --E 4 ---S 5 of 46 +--S 5 of 47 % :: DMP([y,x],INT) --R --R @@ -109566,7 +113946,7 @@ y **2 + x*y + y --R Type: DistributedMultivariatePolynomial([y,x],Integer) --E 5 ---S 6 of 46 +--S 6 of 47 p := (y-1)**2 * x * z --R --R @@ -109575,7 +113955,7 @@ p := (y-1)**2 * x * z --R Type: Polynomial(Integer) --E 6 ---S 7 of 46 +--S 7 of 47 q := (y-1) * x * (z+5) --R --R @@ -109583,7 +113963,7 @@ q := (y-1) * x * (z+5) --R Type: Polynomial(Integer) --E 7 ---S 8 of 46 +--S 8 of 47 factor(q) --R --R @@ -109591,7 +113971,7 @@ factor(q) --R Type: Factored(Polynomial(Integer)) --E 8 ---S 9 of 46 +--S 9 of 47 p - q**2 --R --R @@ -109604,7 +113984,7 @@ p - q**2 --R Type: Polynomial(Integer) --E 9 ---S 10 of 46 +--S 10 of 47 gcd(p,q) --R --R @@ -109612,7 +113992,7 @@ gcd(p,q) --R Type: Polynomial(Integer) --E 10 ---S 11 of 46 +--S 11 of 47 factor % --R --R @@ -109620,7 +114000,7 @@ factor % --R Type: Factored(Polynomial(Integer)) --E 11 ---S 12 of 46 +--S 12 of 47 lcm(p,q) --R --R @@ -109629,7 +114009,7 @@ lcm(p,q) --R Type: Polynomial(Integer) --E 12 ---S 13 of 46 +--S 13 of 47 content p --R --R @@ -109637,7 +114017,7 @@ content p --R Type: PositiveInteger --E 13 ---S 14 of 46 +--S 14 of 47 resultant(p,q,z) --R --R @@ -109646,7 +114026,7 @@ resultant(p,q,z) --R Type: Polynomial(Integer) --E 14 ---S 15 of 46 +--S 15 of 47 resultant(p,q,x) --R --R @@ -109654,7 +114034,7 @@ resultant(p,q,x) --R Type: Polynomial(Integer) --E 15 ---S 16 of 46 +--S 16 of 47 mainVariable p --R --R @@ -109662,7 +114042,7 @@ mainVariable p --R Type: Union(Symbol,...) --E 16 ---S 17 of 46 +--S 17 of 47 mainVariable(1 :: POLY INT) --R --R @@ -109670,7 +114050,7 @@ mainVariable(1 :: POLY INT) --R Type: Union("failed",...) --E 17 ---S 18 of 46 +--S 18 of 47 ground? p --R --R @@ -109678,7 +114058,7 @@ ground? p --R Type: Boolean --E 18 ---S 19 of 46 +--S 19 of 47 ground?(1 :: POLY INT) --R --R @@ -109686,7 +114066,7 @@ ground?(1 :: POLY INT) --R Type: Boolean --E 19 ---S 20 of 46 +--S 20 of 47 variables p --R --R @@ -109694,7 +114074,7 @@ variables p --R Type: List(Symbol) --E 20 ---S 21 of 46 +--S 21 of 47 degree(p,x) --R --R @@ -109702,7 +114082,7 @@ degree(p,x) --R Type: PositiveInteger --E 21 ---S 22 of 46 +--S 22 of 47 degree(p,y) --R --R @@ -109710,7 +114090,7 @@ degree(p,y) --R Type: PositiveInteger --E 22 ---S 23 of 46 +--S 23 of 47 degree(p,z) --R --R @@ -109718,7 +114098,7 @@ degree(p,z) --R Type: PositiveInteger --E 23 ---S 24 of 46 +--S 24 of 47 degree(p,[x,y,z]) --R --R @@ -109726,7 +114106,7 @@ degree(p,[x,y,z]) --R Type: List(NonNegativeInteger) --E 24 ---S 25 of 46 +--S 25 of 47 minimumDegree(p,z) --R --R @@ -109734,7 +114114,7 @@ minimumDegree(p,z) --R Type: PositiveInteger --E 25 ---S 26 of 46 +--S 26 of 47 totalDegree p --R --R @@ -109742,7 +114122,7 @@ totalDegree p --R Type: PositiveInteger --E 26 ---S 27 of 46 +--S 27 of 47 leadingMonomial p --R --R @@ -109751,7 +114131,7 @@ leadingMonomial p --R Type: Polynomial(Integer) --E 27 ---S 28 of 46 +--S 28 of 47 reductum p --R --R @@ -109759,7 +114139,7 @@ reductum p --R Type: Polynomial(Integer) --E 28 ---S 29 of 46 +--S 29 of 47 p - leadingMonomial p - reductum p --R --R @@ -109767,7 +114147,7 @@ p - leadingMonomial p - reductum p --R Type: Polynomial(Integer) --E 29 ---S 30 of 46 +--S 30 of 47 leadingCoefficient p --R --R @@ -109775,7 +114155,7 @@ leadingCoefficient p --R Type: PositiveInteger --E 30 ---S 31 of 46 +--S 31 of 47 p --R --R @@ -109784,7 +114164,7 @@ p --R Type: Polynomial(Integer) --E 31 ---S 32 of 46 +--S 32 of 47 eval(p,x,w) --R --R @@ -109793,7 +114173,7 @@ eval(p,x,w) --R Type: Polynomial(Integer) --E 32 ---S 33 of 46 +--S 33 of 47 eval(p,x,1) --R --R @@ -109802,7 +114182,7 @@ eval(p,x,1) --R Type: Polynomial(Integer) --E 33 ---S 34 of 46 +--S 34 of 47 eval(p,x,y^2 - 1) --R --R @@ -109811,7 +114191,7 @@ eval(p,x,y^2 - 1) --R Type: Polynomial(Integer) --E 34 ---S 35 of 46 +--S 35 of 47 D(p,x) --R --R @@ -109820,7 +114200,7 @@ D(p,x) --R Type: Polynomial(Integer) --E 35 ---S 36 of 46 +--S 36 of 47 D(p,y) --R --R @@ -109828,7 +114208,7 @@ D(p,y) --R Type: Polynomial(Integer) --E 36 ---S 37 of 46 +--S 37 of 47 D(p,z) --R --R @@ -109837,7 +114217,7 @@ D(p,z) --R Type: Polynomial(Integer) --E 37 ---S 38 of 46 +--S 38 of 47 integrate(p,y) --R --R @@ -109847,7 +114227,7 @@ integrate(p,y) --R Type: Polynomial(Fraction(Integer)) --E 38 ---S 39 of 46 +--S 39 of 47 qr := monicDivide(p,x+1,x) --R --R @@ -109856,7 +114236,7 @@ qr := monicDivide(p,x+1,x) --R Type: Record(quotient: Polynomial(Integer),remainder: Polynomial(Integer)) --E 39 ---S 40 of 46 +--S 40 of 47 qr.remainder --R --R @@ -109865,7 +114245,7 @@ qr.remainder --R Type: Polynomial(Integer) --E 40 ---S 41 of 46 +--S 41 of 47 p - ((x+1) * qr.quotient + qr.remainder) --R --R @@ -109873,7 +114253,7 @@ p - ((x+1) * qr.quotient + qr.remainder) --R Type: Polynomial(Integer) --E 41 ---S 42 of 46 +--S 42 of 47 p/q --R --R @@ -109883,7 +114263,7 @@ p/q --R Type: Fraction(Polynomial(Integer)) --E 42 ---S 43 of 46 +--S 43 of 47 (2/3) * x**2 - y + 4/5 --R --R @@ -109893,7 +114273,7 @@ p/q --R Type: Polynomial(Fraction(Integer)) --E 43 ---S 44 of 46 +--S 44 of 47 % :: FRAC POLY INT --R --R @@ -109904,7 +114284,7 @@ p/q --R Type: Fraction(Polynomial(Integer)) --E 44 ---S 45 of 46 +--S 45 of 47 % :: POLY FRAC INT --R --R @@ -109914,7 +114294,7 @@ p/q --R Type: Polynomial(Fraction(Integer)) --E 45 ---S 46 of 46 +--S 46 of 47 map(numeric,%) --R --R @@ -109922,6 +114302,130 @@ map(numeric,%) --R (46) - 1.0 y + 0.6666666666 6666666667 x + 0.8 --R Type: Polynomial(Float) --E 46 + +--S 47 of 47 +)show Polynomial +--R +--R Polynomial(R: Ring) is a domain constructor +--R Abbreviation for Polynomial is POLY +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for POLY +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,R) -> % ?*? : (R,%) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?/? : (%,R) -> % if R has FIELD +--R ?=? : (%,%) -> Boolean D : (%,List(Symbol)) -> % +--R D : (%,Symbol) -> % 1 : () -> % +--R 0 : () -> % ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,PositiveInteger) -> % coefficients : % -> List(R) +--R coerce : % -> % if R has INTDOM coerce : Symbol -> % +--R coerce : R -> % coerce : Integer -> % +--R coerce : % -> OutputForm content : % -> R if R has GCDDOM +--R differentiate : (%,Symbol) -> % eval : (%,Symbol,%) -> % +--R eval : (%,Symbol,R) -> % eval : (%,List(%),List(%)) -> % +--R eval : (%,%,%) -> % eval : (%,Equation(%)) -> % +--R eval : (%,List(Equation(%))) -> % gcd : (%,%) -> % if R has GCDDOM +--R gcd : List(%) -> % if R has GCDDOM ground : % -> R +--R ground? : % -> Boolean hash : % -> SingleInteger +--R latex : % -> String lcm : (%,%) -> % if R has GCDDOM +--R lcm : List(%) -> % if R has GCDDOM leadingCoefficient : % -> R +--R leadingMonomial : % -> % map : ((R -> R),%) -> % +--R max : (%,%) -> % if R has ORDSET min : (%,%) -> % if R has ORDSET +--R monomial? : % -> Boolean monomials : % -> List(%) +--R one? : % -> Boolean primitiveMonomials : % -> List(%) +--R recip : % -> Union(%,"failed") reductum : % -> % +--R retract : % -> Symbol retract : % -> R +--R sample : () -> % variables : % -> List(Symbol) +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (Fraction(Integer),%) -> % if R has ALGEBRA(FRAC(INT)) +--R ?*? : (%,Fraction(Integer)) -> % if R has ALGEBRA(FRAC(INT)) +--R ? Boolean if R has ORDSET +--R ?<=? : (%,%) -> Boolean if R has ORDSET +--R ?>? : (%,%) -> Boolean if R has ORDSET +--R ?>=? : (%,%) -> Boolean if R has ORDSET +--R D : (%,List(Symbol),List(NonNegativeInteger)) -> % +--R D : (%,Symbol,NonNegativeInteger) -> % +--R associates? : (%,%) -> Boolean if R has INTDOM +--R binomThmExpt : (%,%,NonNegativeInteger) -> % if R has COMRING +--R characteristic : () -> NonNegativeInteger +--R charthRoot : % -> Union(%,"failed") if $ has CHARNZ and R has PFECAT or R has CHARNZ +--R coefficient : (%,List(Symbol),List(NonNegativeInteger)) -> % +--R coefficient : (%,Symbol,NonNegativeInteger) -> % +--R coefficient : (%,IndexedExponents(Symbol)) -> R +--R coerce : Fraction(Integer) -> % if R has ALGEBRA(FRAC(INT)) or R has RETRACT(FRAC(INT)) +--R conditionP : Matrix(%) -> Union(Vector(%),"failed") if $ has CHARNZ and R has PFECAT +--R content : (%,Symbol) -> % if R has GCDDOM +--R convert : % -> InputForm if Symbol has KONVERT(INFORM) and R has KONVERT(INFORM) +--R convert : % -> Pattern(Integer) if Symbol has KONVERT(PATTERN(INT)) and R has KONVERT(PATTERN(INT)) +--R convert : % -> Pattern(Float) if Symbol has KONVERT(PATTERN(FLOAT)) and R has KONVERT(PATTERN(FLOAT)) +--R degree : (%,List(Symbol)) -> List(NonNegativeInteger) +--R degree : (%,Symbol) -> NonNegativeInteger +--R degree : % -> IndexedExponents(Symbol) +--R differentiate : (%,List(Symbol),List(NonNegativeInteger)) -> % +--R differentiate : (%,Symbol,NonNegativeInteger) -> % +--R differentiate : (%,List(Symbol)) -> % +--R discriminant : (%,Symbol) -> % if R has COMRING +--R eval : (%,List(Symbol),List(%)) -> % +--R eval : (%,List(Symbol),List(R)) -> % +--R exquo : (%,%) -> Union(%,"failed") if R has INTDOM +--R exquo : (%,R) -> Union(%,"failed") if R has INTDOM +--R factor : % -> Factored(%) if R has PFECAT +--R factorPolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has PFECAT +--R factorSquareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has PFECAT +--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) if R has GCDDOM +--R integrate : (%,Symbol) -> % if R has ALGEBRA(FRAC(INT)) +--R isExpt : % -> Union(Record(var: Symbol,exponent: NonNegativeInteger),"failed") +--R isPlus : % -> Union(List(%),"failed") +--R isTimes : % -> Union(List(%),"failed") +--R lcmCoef : (%,%) -> Record(llcmres: %,coeff1: %,coeff2: %) if R has GCDDOM +--R mainVariable : % -> Union(Symbol,"failed") +--R mapExponents : ((IndexedExponents(Symbol) -> IndexedExponents(Symbol)),%) -> % +--R minimumDegree : (%,List(Symbol)) -> List(NonNegativeInteger) +--R minimumDegree : (%,Symbol) -> NonNegativeInteger +--R minimumDegree : % -> IndexedExponents(Symbol) +--R monicDivide : (%,%,Symbol) -> Record(quotient: %,remainder: %) +--R monomial : (%,List(Symbol),List(NonNegativeInteger)) -> % +--R monomial : (%,Symbol,NonNegativeInteger) -> % +--R monomial : (R,IndexedExponents(Symbol)) -> % +--R multivariate : (SparseUnivariatePolynomial(%),Symbol) -> % +--R multivariate : (SparseUnivariatePolynomial(R),Symbol) -> % +--R numberOfMonomials : % -> NonNegativeInteger +--R patternMatch : (%,Pattern(Integer),PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if Symbol has PATMAB(INT) and R has PATMAB(INT) +--R patternMatch : (%,Pattern(Float),PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if Symbol has PATMAB(FLOAT) and R has PATMAB(FLOAT) +--R pomopo! : (%,R,IndexedExponents(Symbol),%) -> % +--R prime? : % -> Boolean if R has PFECAT +--R primitivePart : (%,Symbol) -> % if R has GCDDOM +--R primitivePart : % -> % if R has GCDDOM +--R reducedSystem : Matrix(%) -> Matrix(R) +--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(R),vec: Vector(R)) +--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(Integer),vec: Vector(Integer)) if R has LINEXP(INT) +--R reducedSystem : Matrix(%) -> Matrix(Integer) if R has LINEXP(INT) +--R resultant : (%,%,Symbol) -> % if R has COMRING +--R retract : % -> Integer if R has RETRACT(INT) +--R retract : % -> Fraction(Integer) if R has RETRACT(FRAC(INT)) +--R retractIfCan : % -> Union(Symbol,"failed") +--R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT(INT) +--R retractIfCan : % -> Union(Fraction(Integer),"failed") if R has RETRACT(FRAC(INT)) +--R retractIfCan : % -> Union(R,"failed") +--R solveLinearPolynomialEquation : (List(SparseUnivariatePolynomial(%)),SparseUnivariatePolynomial(%)) -> Union(List(SparseUnivariatePolynomial(%)),"failed") if R has PFECAT +--R squareFree : % -> Factored(%) if R has GCDDOM +--R squareFreePart : % -> % if R has GCDDOM +--R squareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has PFECAT +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R totalDegree : (%,List(Symbol)) -> NonNegativeInteger +--R totalDegree : % -> NonNegativeInteger +--R unit? : % -> Boolean if R has INTDOM +--R unitCanonical : % -> % if R has INTDOM +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) if R has INTDOM +--R univariate : % -> SparseUnivariatePolynomial(R) +--R univariate : (%,Symbol) -> SparseUnivariatePolynomial(%) +--R +--E 47 + )spool )lisp (bye) \end{chunk} @@ -110461,20 +114965,20 @@ Polynomial(R:Ring): --R Issue )edit bookvol10.3.pamphlet to see algebra source code for IDEAL --R --R------------------------------- Operations -------------------------------- ---R ?*? : (%,%) -> % ?+? : (%,%) -> % ---R ?=? : (%,%) -> Boolean coerce : List(DPoly) -> % ---R coerce : % -> OutputForm dimension : % -> Integer ---R element? : (DPoly,%) -> Boolean generators : % -> List(DPoly) ---R groebner : % -> % groebner? : % -> Boolean ---R groebnerIdeal : List(DPoly) -> % hash : % -> SingleInteger ---R ideal : List(DPoly) -> % in? : (%,%) -> Boolean ---R inRadical? : (DPoly,%) -> Boolean intersect : List(%) -> % ---R intersect : (%,%) -> % latex : % -> String ---R leadingIdeal : % -> % one? : % -> Boolean ---R quotient : (%,DPoly) -> % quotient : (%,%) -> % ---R saturate : (%,DPoly) -> % zero? : % -> Boolean ---R zeroDim? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?**? : (%,NonNegativeInteger) -> % +--R ?*? : (%,%) -> % ?**? : (%,NonNegativeInteger) -> % +--R ?+? : (%,%) -> % ?=? : (%,%) -> Boolean +--R coerce : List(DPoly) -> % coerce : % -> OutputForm +--R dimension : % -> Integer element? : (DPoly,%) -> Boolean +--R generators : % -> List(DPoly) groebner : % -> % +--R groebner? : % -> Boolean groebnerIdeal : List(DPoly) -> % +--R hash : % -> SingleInteger ideal : List(DPoly) -> % +--R in? : (%,%) -> Boolean inRadical? : (DPoly,%) -> Boolean +--R intersect : List(%) -> % intersect : (%,%) -> % +--R latex : % -> String leadingIdeal : % -> % +--R one? : % -> Boolean quotient : (%,DPoly) -> % +--R quotient : (%,%) -> % saturate : (%,DPoly) -> % +--R zero? : % -> Boolean zeroDim? : % -> Boolean +--R ?~=? : (%,%) -> Boolean --R backOldPos : Record(mval: Matrix(F),invmval: Matrix(F),genIdeal: %) -> % --R dimension : (%,List(VarSet)) -> Integer --R generalPosition : (%,List(VarSet)) -> Record(mval: Matrix(F),invmval: Matrix(F),genIdeal: %) @@ -110990,13 +115494,16 @@ PolynomialIdeals(F,Expon,VarSet,DPoly) : C == T --R------------------------------- Operations -------------------------------- --R ?*? : (R,%) -> % ?*? : (%,R) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % ---R -? : % -> % ?=? : (%,%) -> Boolean ---R 1 : () -> % 0 : () -> % +--R -? : % -> % ?/? : (%,R) -> % if R has FIELD +--R ?=? : (%,%) -> Boolean 1 : () -> % +--R 0 : () -> % ?^? : (%,NonNegativeInteger) -> % --R ?^? : (%,PositiveInteger) -> % coefficient : (%,E) -> R --R coefficients : % -> List(R) coerce : R -> % ---R coerce : Integer -> % coerce : % -> OutputForm +--R coerce : % -> % if R has INTDOM coerce : Integer -> % +--R coerce : % -> OutputForm content : % -> R if R has GCDDOM --R degree : % -> E ground : % -> R --R ground? : % -> Boolean hash : % -> SingleInteger --R latex : % -> String leadingCoefficient : % -> R @@ -111009,17 +115516,11 @@ PolynomialIdeals(F,Expon,VarSet,DPoly) : C == T --R zero? : % -> Boolean ?~=? : (%,%) -> Boolean --R ?*? : (%,Fraction(Integer)) -> % if R has ALGEBRA(FRAC(INT)) --R ?*? : (Fraction(Integer),%) -> % if R has ALGEBRA(FRAC(INT)) ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R ?/? : (%,R) -> % if R has FIELD ---R ?^? : (%,NonNegativeInteger) -> % --R associates? : (%,%) -> Boolean if R has INTDOM --R binomThmExpt : (%,%,NonNegativeInteger) -> % if R has COMRING --R characteristic : () -> NonNegativeInteger --R charthRoot : % -> Union(%,"failed") if R has CHARNZ --R coerce : Fraction(Integer) -> % if R has ALGEBRA(FRAC(INT)) or R has RETRACT(FRAC(INT)) ---R coerce : % -> % if R has INTDOM ---R content : % -> R if R has GCDDOM --R exquo : (%,R) -> Union(%,"failed") if R has INTDOM --R exquo : (%,%) -> Union(%,"failed") if R has INTDOM --R fmecg : (%,E,R,%) -> % if E has CABMON and R has INTDOM @@ -111435,6 +115936,7 @@ PolynomialRing(R:Ring,E:OrderedAbelianMonoid): T == C --S 1 of 1 )show PositiveInteger +--R --R PositiveInteger is a domain constructor --R Abbreviation for PositiveInteger is PI --R This constructor is exposed in this frame. @@ -111442,18 +115944,17 @@ PolynomialRing(R:Ring,E:OrderedAbelianMonoid): T == C --R --R------------------------------- Operations -------------------------------- --R ?*? : (%,%) -> % ?*? : (PositiveInteger,%) -> % ---R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % ---R ? Boolean ?<=? : (%,%) -> Boolean ---R ?=? : (%,%) -> Boolean ?>? : (%,%) -> Boolean ---R ?>=? : (%,%) -> Boolean 1 : () -> % ---R ?^? : (%,PositiveInteger) -> % coerce : % -> OutputForm +--R ?**? : (%,PositiveInteger) -> % ?**? : (%,NonNegativeInteger) -> % +--R ?+? : (%,%) -> % ? Boolean +--R ?<=? : (%,%) -> Boolean ?=? : (%,%) -> Boolean +--R ?>? : (%,%) -> Boolean ?>=? : (%,%) -> Boolean +--R 1 : () -> % ?^? : (%,PositiveInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % coerce : % -> OutputForm --R gcd : (%,%) -> % hash : % -> SingleInteger --R latex : % -> String max : (%,%) -> % --R min : (%,%) -> % one? : % -> Boolean --R recip : % -> Union(%,"failed") sample : () -> % --R ?~=? : (%,%) -> Boolean ---R ?**? : (%,NonNegativeInteger) -> % ---R ?^? : (%,NonNegativeInteger) -> % --R --E 1 @@ -111550,13 +116051,15 @@ PositiveInteger: Join(AbelianSemiGroup,OrderedSet,Monoid) with --R------------------------------- Operations -------------------------------- --R ?*? : (Fraction(Integer),%) -> % ?*? : (%,Fraction(Integer)) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,Integer) -> % ?**? : (%,NonNegativeInteger) -> % --R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % --R ?-? : (%,%) -> % -? : % -> % --R ?/? : (%,%) -> % ?=? : (%,%) -> Boolean --R D : % -> % D : (%,NonNegativeInteger) -> % ---R 1 : () -> % 0 : () -> % ---R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> % +--R Frobenius : % -> % if $ has FINITE 1 : () -> % +--R 0 : () -> % ?^? : (%,Integer) -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % --R algebraic? : % -> Boolean associates? : (%,%) -> Boolean --R basis : () -> Vector(%) charthRoot : % -> % --R coerce : Fraction(Integer) -> % coerce : % -> % @@ -111566,11 +116069,12 @@ PositiveInteger: Join(AbelianSemiGroup,OrderedSet,Monoid) with --R differentiate : % -> % dimension : () -> CardinalNumber --R enumerate : () -> List(%) factor : % -> Factored(%) --R gcd : List(%) -> % gcd : (%,%) -> % ---R hash : % -> SingleInteger inGroundField? : % -> Boolean ---R index : PositiveInteger -> % init : () -> % ---R inv : % -> % latex : % -> String ---R lcm : List(%) -> % lcm : (%,%) -> % ---R lookup : % -> PositiveInteger norm : % -> % +--R generator : () -> % if $ has FINITE hash : % -> SingleInteger +--R inGroundField? : % -> Boolean index : PositiveInteger -> % +--R init : () -> % inv : % -> % +--R latex : % -> String lcm : List(%) -> % +--R lcm : (%,%) -> % lookup : % -> PositiveInteger +--R nextItem : % -> Union(%,"failed") norm : % -> % --R one? : % -> Boolean order : % -> PositiveInteger --R prime? : % -> Boolean primeFrobenius : % -> % --R primitive? : % -> Boolean primitiveElement : () -> % @@ -111583,11 +116087,7 @@ PositiveInteger: Join(AbelianSemiGroup,OrderedSet,Monoid) with --R transcendent? : % -> Boolean unit? : % -> Boolean --R unitCanonical : % -> % zero? : % -> Boolean --R ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R Frobenius : % -> % if $ has FINITE --R Frobenius : (%,NonNegativeInteger) -> % if $ has FINITE ---R ?^? : (%,NonNegativeInteger) -> % --R basis : PositiveInteger -> Vector(%) --R characteristic : () -> NonNegativeInteger --R charthRoot : % -> Union(%,"failed") @@ -111609,7 +116109,6 @@ PositiveInteger: Join(AbelianSemiGroup,OrderedSet,Monoid) with --R extensionDegree : () -> PositiveInteger --R factorsOfCyclicGroupSize : () -> List(Record(factor: Integer,exponent: Integer)) --R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) ---R generator : () -> % if $ has FINITE --R lcmCoef : (%,%) -> Record(llcmres: %,coeff1: %,coeff2: %) --R linearAssociatedExp : (%,SparseUnivariatePolynomial(%)) -> % if $ has FINITE --R linearAssociatedLog : % -> SparseUnivariatePolynomial(%) if $ has FINITE @@ -111618,7 +116117,6 @@ PositiveInteger: Join(AbelianSemiGroup,OrderedSet,Monoid) with --R minimalPolynomial : % -> SparseUnivariatePolynomial(%) --R minimalPolynomial : (%,PositiveInteger) -> SparseUnivariatePolynomial(%) if $ has FINITE --R multiEuclidean : (List(%),%) -> Union(List(%),"failed") ---R nextItem : % -> Union(%,"failed") --R norm : (%,PositiveInteger) -> % if $ has FINITE --R normal? : % -> Boolean if $ has FINITE --R normalElement : () -> % if $ has FINITE @@ -111804,10 +116302,12 @@ PrimeField(p:PositiveInteger): Exp == Impl where --R empty? : % -> Boolean entries : % -> List(S) --R eq? : (%,%) -> Boolean index? : (Integer,%) -> Boolean --R indices : % -> List(Integer) insert : (%,%,Integer) -> % ---R insert : (S,%,Integer) -> % map : (((S,S) -> S),%,%) -> % ---R map : ((S -> S),%) -> % new : (NonNegativeInteger,S) -> % ---R qelt : (%,Integer) -> S reverse : % -> % ---R sample : () -> % +--R insert : (S,%,Integer) -> % latex : % -> String if S has SETCAT +--R map : (((S,S) -> S),%,%) -> % map : ((S -> S),%) -> % +--R max : (%,%) -> % if S has ORDSET min : (%,%) -> % if S has ORDSET +--R new : (NonNegativeInteger,S) -> % qelt : (%,Integer) -> S +--R reverse : % -> % sample : () -> % +--R sort : % -> % if S has ORDSET sort : (((S,S) -> Boolean),%) -> % --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R ? Boolean if S has ORDSET --R ?<=? : (%,%) -> Boolean if S has ORDSET @@ -111832,16 +116332,13 @@ PrimeField(p:PositiveInteger): Exp == Impl where --R find : ((S -> Boolean),%) -> Union(S,"failed") --R first : % -> S if Integer has ORDSET --R hash : % -> SingleInteger if S has SETCAT ---R latex : % -> String if S has SETCAT --R less? : (%,NonNegativeInteger) -> Boolean --R map! : ((S -> S),%) -> % if $ has shallowlyMutable ---R max : (%,%) -> % if S has ORDSET --R maxIndex : % -> Integer if Integer has ORDSET --R member? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT --R members : % -> List(S) if $ has finiteAggregate --R merge : (%,%) -> % if S has ORDSET --R merge : (((S,S) -> Boolean),%,%) -> % ---R min : (%,%) -> % if S has ORDSET --R minIndex : % -> Integer if Integer has ORDSET --R more? : (%,NonNegativeInteger) -> Boolean --R parts : % -> List(S) if $ has finiteAggregate @@ -111860,8 +116357,6 @@ PrimeField(p:PositiveInteger): Exp == Impl where --R setelt : (%,UniversalSegment(Integer),S) -> S if $ has shallowlyMutable --R setelt : (%,Integer,S) -> S if $ has shallowlyMutable --R size? : (%,NonNegativeInteger) -> Boolean ---R sort : % -> % if S has ORDSET ---R sort : (((S,S) -> Boolean),%) -> % --R sort! : % -> % if $ has shallowlyMutable and S has ORDSET --R sort! : (((S,S) -> Boolean),%) -> % if $ has shallowlyMutable --R sorted? : % -> Boolean if S has ORDSET @@ -112008,7 +116503,7 @@ PrimitiveArray(S:Type): OneDimensionalArrayAggregate S == add )set message auto off )clear all ---S 1 of 6 +--S 1 of 7 f:=(x:INT):INT +-> 3*x --R --R @@ -112016,7 +116511,7 @@ f:=(x:INT):INT +-> 3*x --R Type: (Integer -> Integer) --E 1 ---S 2 of 6 +--S 2 of 7 f(3) --R --R @@ -112024,7 +116519,7 @@ f(3) --R Type: PositiveInteger --E 2 ---S 3 of 6 +--S 3 of 7 g:=(x:INT):INT +-> x^3 --R --R @@ -112032,7 +116527,7 @@ g:=(x:INT):INT +-> x^3 --R Type: (Integer -> Integer) --E 3 ---S 4 of 6 +--S 4 of 7 g(3) --R --R @@ -112040,7 +116535,7 @@ g(3) --R Type: PositiveInteger --E 4 ---S 5 of 6 +--S 5 of 7 h(x:INT):Product(INT,INT) == makeprod(f x, g x) --R --R Function declaration h : Integer -> Product(Integer,Integer) has @@ -112048,7 +116543,7 @@ h(x:INT):Product(INT,INT) == makeprod(f x, g x) --R Type: Void --E 5 ---S 6 of 6 +--S 6 of 7 h(3) --R --R Compiling function h with type Integer -> Product(Integer,Integer) @@ -112057,6 +116552,58 @@ h(3) --R Type: Product(Integer,Integer) --E 6 +--S 7 of 7 +)show Product +--R +--R Product(A: SetCategory,B: SetCategory) is a domain constructor +--R Abbreviation for Product is PRODUCT +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for PRODUCT +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R makeprod : (A,B) -> % selectfirst : % -> A +--R selectsecond : % -> B ?~=? : (%,%) -> Boolean +--R ?*? : (%,%) -> % if A has GROUP and B has GROUP or A has MONOID and B has MONOID +--R ?*? : (PositiveInteger,%) -> % if A has ABELGRP and B has ABELGRP or A has ABELMON and B has ABELMON or A has CABMON and B has CABMON or A has OAMONS and B has OAMONS +--R ?*? : (NonNegativeInteger,%) -> % if A has ABELGRP and B has ABELGRP or A has ABELMON and B has ABELMON or A has CABMON and B has CABMON or A has OAMONS and B has OAMONS +--R ?*? : (Integer,%) -> % if A has ABELGRP and B has ABELGRP +--R ?**? : (%,PositiveInteger) -> % if A has GROUP and B has GROUP or A has MONOID and B has MONOID +--R ?**? : (%,NonNegativeInteger) -> % if A has GROUP and B has GROUP or A has MONOID and B has MONOID +--R ?**? : (%,Integer) -> % if A has GROUP and B has GROUP +--R ?+? : (%,%) -> % if A has ABELGRP and B has ABELGRP or A has ABELMON and B has ABELMON or A has CABMON and B has CABMON or A has OAMONS and B has OAMONS +--R -? : % -> % if A has ABELGRP and B has ABELGRP +--R ?-? : (%,%) -> % if A has ABELGRP and B has ABELGRP +--R ?/? : (%,%) -> % if A has GROUP and B has GROUP +--R ? Boolean if A has OAMONS and B has OAMONS or A has ORDSET and B has ORDSET +--R ?<=? : (%,%) -> Boolean if A has OAMONS and B has OAMONS or A has ORDSET and B has ORDSET +--R ?>? : (%,%) -> Boolean if A has OAMONS and B has OAMONS or A has ORDSET and B has ORDSET +--R ?>=? : (%,%) -> Boolean if A has OAMONS and B has OAMONS or A has ORDSET and B has ORDSET +--R 1 : () -> % if A has GROUP and B has GROUP or A has MONOID and B has MONOID +--R 0 : () -> % if A has ABELGRP and B has ABELGRP or A has ABELMON and B has ABELMON or A has CABMON and B has CABMON or A has OAMONS and B has OAMONS +--R ?^? : (%,PositiveInteger) -> % if A has GROUP and B has GROUP or A has MONOID and B has MONOID +--R ?^? : (%,NonNegativeInteger) -> % if A has GROUP and B has GROUP or A has MONOID and B has MONOID +--R ?^? : (%,Integer) -> % if A has GROUP and B has GROUP +--R commutator : (%,%) -> % if A has GROUP and B has GROUP +--R conjugate : (%,%) -> % if A has GROUP and B has GROUP +--R enumerate : () -> List(%) if A has FINITE and B has FINITE +--R index : PositiveInteger -> % if A has FINITE and B has FINITE +--R inv : % -> % if A has GROUP and B has GROUP +--R lookup : % -> PositiveInteger if A has FINITE and B has FINITE +--R max : (%,%) -> % if A has OAMONS and B has OAMONS or A has ORDSET and B has ORDSET +--R min : (%,%) -> % if A has OAMONS and B has OAMONS or A has ORDSET and B has ORDSET +--R one? : % -> Boolean if A has GROUP and B has GROUP or A has MONOID and B has MONOID +--R random : () -> % if A has FINITE and B has FINITE +--R recip : % -> Union(%,"failed") if A has GROUP and B has GROUP or A has MONOID and B has MONOID +--R sample : () -> % if A has ABELGRP and B has ABELGRP or A has ABELMON and B has ABELMON or A has CABMON and B has CABMON or A has GROUP and B has GROUP or A has MONOID and B has MONOID or A has OAMONS and B has OAMONS +--R size : () -> NonNegativeInteger if A has FINITE and B has FINITE +--R subtractIfCan : (%,%) -> Union(%,"failed") if A has ABELGRP and B has ABELGRP or A has CABMON and B has CABMON or A has OAMONS and B has OAMONS +--R sup : (%,%) -> % if A has OAMONS and B has OAMONS +--R zero? : % -> Boolean if A has ABELGRP and B has ABELGRP or A has ABELMON and B has ABELMON or A has CABMON and B has CABMON or A has OAMONS and B has OAMONS +--R +--E 7 + )spool )lisp (bye) \end{chunk} @@ -112677,6 +117224,91 @@ ProjectiveSpace(dim,K):Exports == Implementation where --S 1 of 1 )show PseudoAlgebraicClosureOfAlgExtOfRationalNumber +--R +--R PseudoAlgebraicClosureOfAlgExtOfRationalNumber(downLevel: PseudoAlgebraicClosureOfRationalNumber) is a domain constructor +--R Abbreviation for PseudoAlgebraicClosureOfAlgExtOfRationalNumber is PACEXT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for PACEXT +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,Fraction(Integer)) -> % ?*? : (Fraction(Integer),%) -> % +--R ?*? : (Fraction(Integer),%) -> % ?*? : (%,Fraction(Integer)) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,Integer) -> % ?**? : (%,NonNegativeInteger) -> % +--R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % +--R ?-? : (%,%) -> % -? : % -> % +--R ?/? : (%,Fraction(Integer)) -> % ?/? : (%,%) -> % +--R ?=? : (%,%) -> Boolean 1 : () -> % +--R 0 : () -> % ?^? : (%,Integer) -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R algebraic? : % -> Boolean associates? : (%,%) -> Boolean +--R coerce : Fraction(Integer) -> % coerce : Fraction(Integer) -> % +--R coerce : Integer -> % coerce : Fraction(Integer) -> % +--R coerce : % -> % coerce : Integer -> % +--R coerce : % -> OutputForm conjugate : % -> % +--R dimension : () -> CardinalNumber extDegree : % -> PositiveInteger +--R factor : % -> Factored(%) fullOutput : % -> OutputForm +--R gcd : List(%) -> % gcd : (%,%) -> % +--R ground? : % -> Boolean hash : % -> SingleInteger +--R inGroundField? : % -> Boolean inv : % -> % +--R latex : % -> String lcm : List(%) -> % +--R lcm : (%,%) -> % maxTower : List(%) -> % +--R one? : % -> Boolean previousTower : % -> % +--R prime? : % -> Boolean ?quo? : (%,%) -> % +--R recip : % -> Union(%,"failed") ?rem? : (%,%) -> % +--R retract : % -> Fraction(Integer) retract : % -> Fraction(Integer) +--R retract : % -> Integer sample : () -> % +--R setTower! : % -> Void sizeLess? : (%,%) -> Boolean +--R squareFree : % -> Factored(%) squareFreePart : % -> % +--R transcendent? : % -> Boolean unit? : % -> Boolean +--R unitCanonical : % -> % vectorise : (%,%) -> Vector(%) +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (%,PseudoAlgebraicClosureOfRationalNumber) -> % +--R ?*? : (PseudoAlgebraicClosureOfRationalNumber,%) -> % +--R ?/? : (%,PseudoAlgebraicClosureOfRationalNumber) -> % +--R Frobenius : % -> % if Fraction(Integer) has FINITE or PseudoAlgebraicClosureOfRationalNumber has FINITE +--R Frobenius : (%,NonNegativeInteger) -> % if Fraction(Integer) has FINITE or PseudoAlgebraicClosureOfRationalNumber has FINITE +--R characteristic : () -> NonNegativeInteger +--R charthRoot : % -> Union(%,"failed") if Fraction(Integer) has CHARNZ or Fraction(Integer) has FINITE or PseudoAlgebraicClosureOfRationalNumber has CHARNZ or PseudoAlgebraicClosureOfRationalNumber has FINITE +--R coerce : PseudoAlgebraicClosureOfRationalNumber -> % +--R coerce : PseudoAlgebraicClosureOfRationalNumber -> % +--R definingPolynomial : % -> SparseUnivariatePolynomial(%) +--R definingPolynomial : () -> SparseUnivariatePolynomial(%) +--R degree : % -> OnePointCompletion(PositiveInteger) +--R discreteLog : (%,%) -> Union(NonNegativeInteger,"failed") if Fraction(Integer) has CHARNZ or Fraction(Integer) has FINITE or PseudoAlgebraicClosureOfRationalNumber has CHARNZ or PseudoAlgebraicClosureOfRationalNumber has FINITE +--R distinguishedRootsOf : (SparseUnivariatePolynomial(%),%) -> List(%) +--R divide : (%,%) -> Record(quotient: %,remainder: %) +--R euclideanSize : % -> NonNegativeInteger +--R expressIdealMember : (List(%),%) -> Union(List(%),"failed") +--R exquo : (%,%) -> Union(%,"failed") +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) +--R extensionDegree : () -> OnePointCompletion(PositiveInteger) +--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) +--R lcmCoef : (%,%) -> Record(llcmres: %,coeff1: %,coeff2: %) +--R lift : (%,%) -> SparseUnivariatePolynomial(%) +--R lift : % -> SparseUnivariatePolynomial(%) +--R multiEuclidean : (List(%),%) -> Union(List(%),"failed") +--R newElement : (SparseUnivariatePolynomial(%),Symbol) -> % +--R newElement : (SparseUnivariatePolynomial(%),%,Symbol) -> % +--R order : % -> OnePointCompletion(PositiveInteger) if Fraction(Integer) has CHARNZ or Fraction(Integer) has FINITE or PseudoAlgebraicClosureOfRationalNumber has CHARNZ or PseudoAlgebraicClosureOfRationalNumber has FINITE +--R primeFrobenius : % -> % if Fraction(Integer) has CHARNZ or Fraction(Integer) has FINITE or PseudoAlgebraicClosureOfRationalNumber has CHARNZ or PseudoAlgebraicClosureOfRationalNumber has FINITE +--R primeFrobenius : (%,NonNegativeInteger) -> % if Fraction(Integer) has CHARNZ or Fraction(Integer) has FINITE or PseudoAlgebraicClosureOfRationalNumber has CHARNZ or PseudoAlgebraicClosureOfRationalNumber has FINITE +--R principalIdeal : List(%) -> Record(coef: List(%),generator: %) +--R reduce : SparseUnivariatePolynomial(%) -> % +--R retract : % -> PseudoAlgebraicClosureOfRationalNumber +--R retract : % -> PseudoAlgebraicClosureOfRationalNumber +--R retractIfCan : % -> Union(PseudoAlgebraicClosureOfRationalNumber,"failed") +--R retractIfCan : % -> Union(PseudoAlgebraicClosureOfRationalNumber,"failed") +--R retractIfCan : % -> Union(Fraction(Integer),"failed") +--R retractIfCan : % -> Union(Fraction(Integer),"failed") +--R retractIfCan : % -> Union(Integer,"failed") +--R retractToGrn : % -> PseudoAlgebraicClosureOfRationalNumber +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R transcendenceDegree : () -> NonNegativeInteger +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) +--R --E 1 )spool @@ -113049,13 +117681,15 @@ PseudoAlgebraicClosureOfAlgExtOfRationalNumber(downLevel:K):Exp == Impl where --R ?*? : (%,K) -> % ?*? : (K,%) -> % --R ?*? : (Fraction(Integer),%) -> % ?*? : (%,Fraction(Integer)) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,Integer) -> % ?**? : (%,NonNegativeInteger) -> % --R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % --R ?-? : (%,%) -> % -? : % -> % --R ?/? : (%,K) -> % ?/? : (%,%) -> % --R ?=? : (%,%) -> Boolean D : % -> % ---R D : (%,NonNegativeInteger) -> % 1 : () -> % ---R 0 : () -> % ?^? : (%,Integer) -> % +--R D : (%,NonNegativeInteger) -> % Frobenius : % -> % if K has FINITE +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,Integer) -> % ?^? : (%,NonNegativeInteger) -> % --R ?^? : (%,PositiveInteger) -> % algebraic? : % -> Boolean --R associates? : (%,%) -> Boolean charthRoot : % -> % --R coerce : K -> % coerce : Fraction(Integer) -> % @@ -113071,23 +117705,20 @@ PseudoAlgebraicClosureOfAlgExtOfRationalNumber(downLevel:K):Exp == Impl where --R inv : % -> % latex : % -> String --R lcm : List(%) -> % lcm : (%,%) -> % --R lookup : % -> PositiveInteger maxTower : List(%) -> % ---R one? : % -> Boolean order : % -> PositiveInteger ---R previousTower : % -> % prime? : % -> Boolean ---R primeFrobenius : % -> % primitive? : % -> Boolean ---R primitiveElement : () -> % ?quo? : (%,%) -> % ---R random : () -> % recip : % -> Union(%,"failed") ---R ?rem? : (%,%) -> % retract : % -> K ---R sample : () -> % setTower! : % -> Void ---R size : () -> NonNegativeInteger sizeLess? : (%,%) -> Boolean ---R squareFree : % -> Factored(%) squareFreePart : % -> % ---R transcendent? : % -> Boolean unit? : % -> Boolean ---R unitCanonical : % -> % vectorise : (%,%) -> Vector(%) ---R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R Frobenius : % -> % if K has FINITE +--R nextItem : % -> Union(%,"failed") one? : % -> Boolean +--R order : % -> PositiveInteger previousTower : % -> % +--R prime? : % -> Boolean primeFrobenius : % -> % +--R primitive? : % -> Boolean primitiveElement : () -> % +--R ?quo? : (%,%) -> % random : () -> % +--R recip : % -> Union(%,"failed") ?rem? : (%,%) -> % +--R retract : % -> K sample : () -> % +--R setTower! : % -> Void size : () -> NonNegativeInteger +--R sizeLess? : (%,%) -> Boolean squareFree : % -> Factored(%) +--R squareFreePart : % -> % transcendent? : % -> Boolean +--R unit? : % -> Boolean unitCanonical : % -> % +--R vectorise : (%,%) -> Vector(%) zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean --R Frobenius : (%,NonNegativeInteger) -> % if K has FINITE ---R ?^? : (%,NonNegativeInteger) -> % --R characteristic : () -> NonNegativeInteger --R charthRoot : % -> Union(%,"failed") --R conditionP : Matrix(%) -> Union(Vector(%),"failed") @@ -113113,7 +117744,6 @@ PseudoAlgebraicClosureOfAlgExtOfRationalNumber(downLevel:K):Exp == Impl where --R multiEuclidean : (List(%),%) -> Union(List(%),"failed") --R newElement : (SparseUnivariatePolynomial(%),%,Symbol) -> % --R newElement : (SparseUnivariatePolynomial(%),Symbol) -> % ---R nextItem : % -> Union(%,"failed") --R order : % -> OnePointCompletion(PositiveInteger) --R primeFrobenius : (%,NonNegativeInteger) -> % --R principalIdeal : List(%) -> Record(coef: List(%),generator: %) @@ -113609,40 +118239,38 @@ PseudoAlgebraicClosureOfFiniteField(K):Exports == Implementation where --R ?*? : (%,Fraction(Integer)) -> % ?*? : (Fraction(Integer),%) -> % --R ?*? : (Fraction(Integer),%) -> % ?*? : (%,Fraction(Integer)) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,Integer) -> % ?**? : (%,NonNegativeInteger) -> % --R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % --R ?-? : (%,%) -> % -? : % -> % --R ?/? : (%,Fraction(Integer)) -> % ?/? : (%,%) -> % --R ?=? : (%,%) -> Boolean 1 : () -> % --R 0 : () -> % ?^? : (%,Integer) -> % ---R ?^? : (%,PositiveInteger) -> % algebraic? : % -> Boolean ---R associates? : (%,%) -> Boolean coerce : Fraction(Integer) -> % ---R coerce : Fraction(Integer) -> % coerce : Integer -> % ---R coerce : Fraction(Integer) -> % coerce : % -> % ---R coerce : Integer -> % coerce : % -> OutputForm ---R conjugate : % -> % dimension : () -> CardinalNumber ---R extDegree : % -> PositiveInteger factor : % -> Factored(%) ---R fullOutput : % -> OutputForm gcd : List(%) -> % ---R gcd : (%,%) -> % ground? : % -> Boolean ---R hash : % -> SingleInteger inGroundField? : % -> Boolean ---R inv : % -> % latex : % -> String ---R lcm : List(%) -> % lcm : (%,%) -> % ---R maxTower : List(%) -> % one? : % -> Boolean ---R previousTower : % -> % prime? : % -> Boolean ---R ?quo? : (%,%) -> % recip : % -> Union(%,"failed") ---R ?rem? : (%,%) -> % retract : % -> Fraction(Integer) ---R retract : % -> Fraction(Integer) retract : % -> Integer ---R sample : () -> % setTower! : % -> Void ---R sizeLess? : (%,%) -> Boolean squareFree : % -> Factored(%) ---R squareFreePart : % -> % transcendent? : % -> Boolean ---R unit? : % -> Boolean unitCanonical : % -> % ---R vectorise : (%,%) -> Vector(%) zero? : % -> Boolean ---R ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R algebraic? : % -> Boolean associates? : (%,%) -> Boolean +--R coerce : Fraction(Integer) -> % coerce : Fraction(Integer) -> % +--R coerce : Integer -> % coerce : Fraction(Integer) -> % +--R coerce : % -> % coerce : Integer -> % +--R coerce : % -> OutputForm conjugate : % -> % +--R dimension : () -> CardinalNumber extDegree : % -> PositiveInteger +--R factor : % -> Factored(%) fullOutput : % -> OutputForm +--R gcd : List(%) -> % gcd : (%,%) -> % +--R ground? : % -> Boolean hash : % -> SingleInteger +--R inGroundField? : % -> Boolean inv : % -> % +--R latex : % -> String lcm : List(%) -> % +--R lcm : (%,%) -> % maxTower : List(%) -> % +--R one? : % -> Boolean previousTower : % -> % +--R prime? : % -> Boolean ?quo? : (%,%) -> % +--R recip : % -> Union(%,"failed") ?rem? : (%,%) -> % +--R retract : % -> Fraction(Integer) retract : % -> Fraction(Integer) +--R retract : % -> Integer sample : () -> % +--R setTower! : % -> Void sizeLess? : (%,%) -> Boolean +--R squareFree : % -> Factored(%) squareFreePart : % -> % +--R transcendent? : % -> Boolean unit? : % -> Boolean +--R unitCanonical : % -> % vectorise : (%,%) -> Vector(%) +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean --R Frobenius : % -> % if Fraction(Integer) has FINITE --R Frobenius : (%,NonNegativeInteger) -> % if Fraction(Integer) has FINITE ---R ?^? : (%,NonNegativeInteger) -> % --R characteristic : () -> NonNegativeInteger --R charthRoot : % -> Union(%,"failed") if Fraction(Integer) has CHARNZ or Fraction(Integer) has FINITE --R definingPolynomial : % -> SparseUnivariatePolynomial(%) @@ -114095,21 +118723,21 @@ PseudoAlgebraicClosureOfRationalNumber:Exports == Implementation where --S 1 of 1 )show QuadraticForm +--R --R QuadraticForm(n: PositiveInteger,K: Field) is a domain constructor --R Abbreviation for QuadraticForm is QFORM --R This constructor is exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for QFORM --R --R------------------------------- Operations -------------------------------- ---R ?*? : (Integer,%) -> % ?*? : (PositiveInteger,%) -> % ---R ?+? : (%,%) -> % ?-? : (%,%) -> % ---R -? : % -> % ?=? : (%,%) -> Boolean ---R 0 : () -> % coerce : % -> OutputForm ---R ?.? : (%,DirectProduct(n,K)) -> K hash : % -> SingleInteger ---R latex : % -> String matrix : % -> SquareMatrix(n,K) ---R sample : () -> % zero? : % -> Boolean ---R ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % +--R ?*? : (Integer,%) -> % ?*? : (NonNegativeInteger,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?+? : (%,%) -> % +--R ?-? : (%,%) -> % -? : % -> % +--R ?=? : (%,%) -> Boolean 0 : () -> % +--R coerce : % -> OutputForm ?.? : (%,DirectProduct(n,K)) -> K +--R hash : % -> SingleInteger latex : % -> String +--R matrix : % -> SquareMatrix(n,K) sample : () -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean --R quadraticForm : SquareMatrix(n,K) -> % --R subtractIfCan : (%,%) -> Union(%,"failed") --R @@ -114489,7 +119117,8 @@ QuasiAlgebraicSet(R, Var,Expon,Dpoly) : C == T )set message test on )set message auto off )clear all ---S 1 of 13 + +--S 1 of 14 q := quatern(2/11,-8,3/4,1) --R --R @@ -114499,7 +119128,7 @@ q := quatern(2/11,-8,3/4,1) --R Type: Quaternion(Fraction(Integer)) --E 1 ---S 2 of 13 +--S 2 of 14 [real q, imagI q, imagJ q, imagK q] --R --R @@ -114509,7 +119138,7 @@ q := quatern(2/11,-8,3/4,1) --R Type: List(Fraction(Integer)) --E 2 ---S 3 of 13 +--S 3 of 14 inv q --R --R @@ -114519,7 +119148,7 @@ inv q --R Type: Quaternion(Fraction(Integer)) --E 3 ---S 4 of 13 +--S 4 of 14 q^6 --R --R @@ -114529,7 +119158,7 @@ q^6 --R Type: Quaternion(Fraction(Integer)) --E 4 ---S 5 of 13 +--S 5 of 14 r := quatern(-2,3,23/9,-89); q + r --R --R @@ -114539,7 +119168,7 @@ r := quatern(-2,3,23/9,-89); q + r --R Type: Quaternion(Fraction(Integer)) --E 5 ---S 6 of 13 +--S 6 of 14 q * r - r * q --R --R @@ -114549,7 +119178,7 @@ q * r - r * q --R Type: Quaternion(Fraction(Integer)) --E 6 ---S 7 of 13 +--S 7 of 14 i:=quatern(0,1,0,0) --R --R @@ -114557,7 +119186,7 @@ i:=quatern(0,1,0,0) --R Type: Quaternion(Integer) --E 7 ---S 8 of 13 +--S 8 of 14 j:=quatern(0,0,1,0) --R --R @@ -114565,7 +119194,7 @@ j:=quatern(0,0,1,0) --R Type: Quaternion(Integer) --E 8 ---S 9 of 13 +--S 9 of 14 k:=quatern(0,0,0,1) --R --R @@ -114573,7 +119202,7 @@ k:=quatern(0,0,0,1) --R Type: Quaternion(Integer) --E 9 ---S 10 of 13 +--S 10 of 14 [i*i, j*j, k*k, i*j, j*k, k*i, q*i] --R --R @@ -114583,7 +119212,7 @@ k:=quatern(0,0,0,1) --R Type: List(Quaternion(Fraction(Integer))) --E 10 ---S 11 of 13 +--S 11 of 14 norm q --R --R @@ -114593,7 +119222,7 @@ norm q --R Type: Fraction(Integer) --E 11 ---S 12 of 13 +--S 12 of 14 conjugate q --R --R @@ -114603,7 +119232,7 @@ conjugate q --R Type: Quaternion(Fraction(Integer)) --E 12 ---S 13 of 13 +--S 13 of 14 q * % --R --R @@ -114612,6 +119241,87 @@ q * % --R 1936 --R Type: Quaternion(Fraction(Integer)) --E 13 + +--S 14 of 14 +)show Quaternion + Quaternion(R: CommutativeRing) is a domain constructor + Abbreviation for Quaternion is QUAT + This constructor is exposed in this frame. + Issue )edit bookvol10.3.pamphlet to see algebra source code for QUAT + +------------------------------- Operations -------------------------------- + ?*? : (R,%) -> % ?*? : (%,R) -> % + ?*? : (%,%) -> % ?*? : (Integer,%) -> % + ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % + ?+? : (%,%) -> % ?-? : (%,%) -> % + -? : % -> % ?=? : (%,%) -> Boolean + D : (%,(R -> R)) -> % D : % -> % if R has DIFRING + 1 : () -> % 0 : () -> % + ?^? : (%,PositiveInteger) -> % abs : % -> R if R has RNS + coerce : R -> % coerce : Integer -> % + coerce : % -> OutputForm conjugate : % -> % + hash : % -> SingleInteger imagI : % -> R + imagJ : % -> R imagK : % -> R + inv : % -> % if R has FIELD latex : % -> String + map : ((R -> R),%) -> % norm : % -> R + one? : % -> Boolean quatern : (R,R,R,R) -> % + real : % -> R recip : % -> Union(%,"failed") + retract : % -> R sample : () -> % + zero? : % -> Boolean ?~=? : (%,%) -> Boolean + ?*? : (Fraction(Integer),%) -> % if R has FIELD + ?*? : (%,Fraction(Integer)) -> % if R has FIELD + ?*? : (NonNegativeInteger,%) -> % + ?**? : (%,Integer) -> % if R has FIELD + ?**? : (%,NonNegativeInteger) -> % + ? Boolean if R has ORDSET + ?<=? : (%,%) -> Boolean if R has ORDSET + ?>? : (%,%) -> Boolean if R has ORDSET + ?>=? : (%,%) -> Boolean if R has ORDSET + D : (%,(R -> R),NonNegativeInteger) -> % + D : (%,List(Symbol),List(NonNegativeInteger)) -> % if R has PDRING(SYMBOL) + D : (%,Symbol,NonNegativeInteger) -> % if R has PDRING(SYMBOL) + D : (%,List(Symbol)) -> % if R has PDRING(SYMBOL) + D : (%,Symbol) -> % if R has PDRING(SYMBOL) + D : (%,NonNegativeInteger) -> % if R has DIFRING + ?^? : (%,Integer) -> % if R has FIELD + ?^? : (%,NonNegativeInteger) -> % + characteristic : () -> NonNegativeInteger + charthRoot : % -> Union(%,"failed") if R has CHARNZ + coerce : Fraction(Integer) -> % if R has FIELD or R has RETRACT(FRAC(INT)) + convert : % -> InputForm if R has KONVERT(INFORM) + differentiate : (%,(R -> R)) -> % + differentiate : (%,(R -> R),NonNegativeInteger) -> % + differentiate : (%,List(Symbol),List(NonNegativeInteger)) -> % if R has PDRING(SYMBOL) + differentiate : (%,Symbol,NonNegativeInteger) -> % if R has PDRING(SYMBOL) + differentiate : (%,List(Symbol)) -> % if R has PDRING(SYMBOL) + differentiate : (%,Symbol) -> % if R has PDRING(SYMBOL) + differentiate : (%,NonNegativeInteger) -> % if R has DIFRING + differentiate : % -> % if R has DIFRING + ?.? : (%,R) -> % if R has ELTAB(R,R) + eval : (%,Symbol,R) -> % if R has IEVALAB(SYMBOL,R) + eval : (%,List(Symbol),List(R)) -> % if R has IEVALAB(SYMBOL,R) + eval : (%,List(Equation(R))) -> % if R has EVALAB(R) + eval : (%,Equation(R)) -> % if R has EVALAB(R) + eval : (%,R,R) -> % if R has EVALAB(R) + eval : (%,List(R),List(R)) -> % if R has EVALAB(R) + max : (%,%) -> % if R has ORDSET + min : (%,%) -> % if R has ORDSET + rational : % -> Fraction(Integer) if R has INS + rational? : % -> Boolean if R has INS + rationalIfCan : % -> Union(Fraction(Integer),"failed") if R has INS + reducedSystem : Matrix(%) -> Matrix(R) + reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(R),vec: Vector(R)) + reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(Integer),vec: Vector(Integer)) if R has LINEXP(INT) + reducedSystem : Matrix(%) -> Matrix(Integer) if R has LINEXP(INT) + retract : % -> Fraction(Integer) if R has RETRACT(FRAC(INT)) + retract : % -> Integer if R has RETRACT(INT) + retractIfCan : % -> Union(R,"failed") + retractIfCan : % -> Union(Fraction(Integer),"failed") if R has RETRACT(FRAC(INT)) + retractIfCan : % -> Union(Integer,"failed") if R has RETRACT(INT) + subtractIfCan : (%,%) -> Union(%,"failed") + +--E 14 + )spool )lisp (bye) \end{chunk} @@ -114827,6 +119537,7 @@ Quaternion(R:CommutativeRing): QuaternionCategory(R) == add --S 1 of 1 )show QueryEquation +--R --R QueryEquation is a domain constructor --R Abbreviation for QueryEquation is QEQUAT --R This constructor is exposed in this frame. @@ -115282,9 +119993,9 @@ latex a --R enqueue! : (S,%) -> S eq? : (%,%) -> Boolean --R extract! : % -> S front : % -> S --R insert! : (S,%) -> % inspect : % -> S ---R length : % -> NonNegativeInteger map : ((S -> S),%) -> % ---R queue : List(S) -> % rotate! : % -> % ---R sample : () -> % +--R latex : % -> String if S has SETCAT length : % -> NonNegativeInteger +--R map : ((S -> S),%) -> % queue : List(S) -> % +--R rotate! : % -> % sample : () -> % --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R ?=? : (%,%) -> Boolean if S has SETCAT --R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate @@ -115297,7 +120008,6 @@ latex a --R eval : (%,List(Equation(S))) -> % if S has EVALAB(S) and S has SETCAT --R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate --R hash : % -> SingleInteger if S has SETCAT ---R latex : % -> String if S has SETCAT --R less? : (%,NonNegativeInteger) -> Boolean --R map! : ((S -> S),%) -> % if $ has shallowlyMutable --R member? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT @@ -115815,34 +120525,37 @@ Queue(S:SetCategory): QueueAggregate S with --R------------------------------- Operations -------------------------------- --R ?*? : (Fraction(UP),%) -> % ?*? : (%,Fraction(UP)) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ?=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % basis : () -> Vector(%) ---R branchPoint? : UP -> Boolean branchPoint? : F -> Boolean ---R coerce : Fraction(UP) -> % coerce : Integer -> % ---R coerce : % -> OutputForm convert : UPUP -> % ---R convert : % -> UPUP definingPolynomial : () -> UPUP ---R discriminant : () -> Fraction(UP) elt : (%,F,F) -> F +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R basis : () -> Vector(%) branchPoint? : UP -> Boolean +--R branchPoint? : F -> Boolean coerce : Fraction(UP) -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R convert : UPUP -> % convert : % -> UPUP +--R convert : Vector(Fraction(UP)) -> % convert : % -> Vector(Fraction(UP)) +--R definingPolynomial : () -> UPUP discriminant : () -> Fraction(UP) +--R elliptic : () -> Union(UP,"failed") elt : (%,F,F) -> F --R generator : () -> % genus : () -> NonNegativeInteger --R hash : % -> SingleInteger integral? : (%,UP) -> Boolean --R integral? : (%,F) -> Boolean integral? : % -> Boolean ---R integralBasis : () -> Vector(%) latex : % -> String ---R lift : % -> UPUP norm : % -> Fraction(UP) ---R one? : % -> Boolean primitivePart : % -> % ---R ramified? : UP -> Boolean ramified? : F -> Boolean +--R integralAtInfinity? : % -> Boolean integralBasis : () -> Vector(%) +--R latex : % -> String lift : % -> UPUP +--R norm : % -> Fraction(UP) one? : % -> Boolean +--R primitivePart : % -> % ramified? : UP -> Boolean +--R ramified? : F -> Boolean ramifiedAtInfinity? : () -> Boolean --R rank : () -> PositiveInteger rationalPoint? : (F,F) -> Boolean --R recip : % -> Union(%,"failed") reduce : UPUP -> % --R represents : (Vector(UP),UP) -> % retract : % -> Fraction(UP) --R sample : () -> % singular? : UP -> Boolean ---R singular? : F -> Boolean trace : % -> Fraction(UP) ---R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R singular? : F -> Boolean singularAtInfinity? : () -> Boolean +--R trace : % -> Fraction(UP) zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean --R ?*? : (%,Fraction(Integer)) -> % if Fraction(UP) has FIELD --R ?*? : (Fraction(Integer),%) -> % if Fraction(UP) has FIELD ---R ?*? : (NonNegativeInteger,%) -> % --R ?**? : (%,Integer) -> % if Fraction(UP) has FIELD ---R ?**? : (%,NonNegativeInteger) -> % --R ?/? : (%,%) -> % if Fraction(UP) has FIELD --R D : % -> % if Fraction(UP) has DIFRING and Fraction(UP) has FIELD or Fraction(UP) has FFIELDC --R D : (%,NonNegativeInteger) -> % if Fraction(UP) has DIFRING and Fraction(UP) has FIELD or Fraction(UP) has FFIELDC @@ -115853,7 +120566,6 @@ Queue(S:SetCategory): QueueAggregate S with --R D : (%,(Fraction(UP) -> Fraction(UP))) -> % if Fraction(UP) has FIELD --R D : (%,(Fraction(UP) -> Fraction(UP)),NonNegativeInteger) -> % if Fraction(UP) has FIELD --R ?^? : (%,Integer) -> % if Fraction(UP) has FIELD ---R ?^? : (%,NonNegativeInteger) -> % --R absolutelyIrreducible? : () -> Boolean --R algSplitSimple : (%,(UP -> UP)) -> Record(num: %,den: UP,derivden: UP,gd: UP) --R associates? : (%,%) -> Boolean if Fraction(UP) has FIELD @@ -115866,8 +120578,6 @@ Queue(S:SetCategory): QueueAggregate S with --R coerce : Fraction(Integer) -> % if Fraction(UP) has FIELD or Fraction(UP) has RETRACT(FRAC(INT)) --R complementaryBasis : Vector(%) -> Vector(%) --R conditionP : Matrix(%) -> Union(Vector(%),"failed") if Fraction(UP) has FFIELDC ---R convert : Vector(Fraction(UP)) -> % ---R convert : % -> Vector(Fraction(UP)) --R coordinates : Vector(%) -> Matrix(Fraction(UP)) --R coordinates : % -> Vector(Fraction(UP)) --R coordinates : (Vector(%),Vector(%)) -> Matrix(Fraction(UP)) @@ -115887,7 +120597,6 @@ Queue(S:SetCategory): QueueAggregate S with --R discreteLog : % -> NonNegativeInteger if Fraction(UP) has FFIELDC --R discriminant : Vector(%) -> Fraction(UP) --R divide : (%,%) -> Record(quotient: %,remainder: %) if Fraction(UP) has FIELD ---R elliptic : () -> Union(UP,"failed") --R enumerate : () -> List(%) if Fraction(UP) has FINITE --R euclideanSize : % -> NonNegativeInteger if Fraction(UP) has FIELD --R expressIdealMember : (List(%),%) -> Union(List(%),"failed") if Fraction(UP) has FIELD @@ -115902,7 +120611,6 @@ Queue(S:SetCategory): QueueAggregate S with --R hyperelliptic : () -> Union(UP,"failed") --R index : PositiveInteger -> % if Fraction(UP) has FINITE --R init : () -> % if Fraction(UP) has FFIELDC ---R integralAtInfinity? : % -> Boolean --R integralBasisAtInfinity : () -> Vector(%) --R integralCoordinates : % -> Record(num: Vector(UP),den: UP) --R integralDerivationMatrix : (UP -> UP) -> Record(num: Matrix(UP),den: UP) @@ -115931,7 +120639,6 @@ Queue(S:SetCategory): QueueAggregate S with --R primitiveElement : () -> % if Fraction(UP) has FFIELDC --R principalIdeal : List(%) -> Record(coef: List(%),generator: %) if Fraction(UP) has FIELD --R ?quo? : (%,%) -> % if Fraction(UP) has FIELD ---R ramifiedAtInfinity? : () -> Boolean --R random : () -> % if Fraction(UP) has FINITE --R rationalPoints : () -> List(List(F)) if F has FINITE --R reduce : Fraction(UPUP) -> Union(%,"failed") if Fraction(UP) has FIELD @@ -115951,7 +120658,6 @@ Queue(S:SetCategory): QueueAggregate S with --R retractIfCan : % -> Union(Fraction(UP),"failed") --R retractIfCan : % -> Union(Fraction(Integer),"failed") if Fraction(UP) has RETRACT(FRAC(INT)) --R retractIfCan : % -> Union(Integer,"failed") if Fraction(UP) has RETRACT(INT) ---R singularAtInfinity? : () -> Boolean --R size : () -> NonNegativeInteger if Fraction(UP) has FINITE --R sizeLess? : (%,%) -> Boolean if Fraction(UP) has FIELD --R squareFree : % -> Factored(%) if Fraction(UP) has FIELD @@ -116320,7 +121026,8 @@ RadicalFunctionField(F, UP, UPUP, radicnd, n): Exports == Impl where )set message test on )set message auto off )clear all ---S 1 of 17 + +--S 1 of 18 111::RadixExpansion(5) --R --R @@ -116328,7 +121035,7 @@ RadicalFunctionField(F, UP, UPUP, radicnd, n): Exports == Impl where --R Type: RadixExpansion(5) --E 1 ---S 2 of 17 +--S 2 of 18 (5/24)::RadixExpansion(2) --R --R @@ -116337,7 +121044,7 @@ RadicalFunctionField(F, UP, UPUP, radicnd, n): Exports == Impl where --R Type: RadixExpansion(2) --E 2 ---S 3 of 17 +--S 3 of 18 (5/24)::RadixExpansion(3) --R --R @@ -116346,7 +121053,7 @@ RadicalFunctionField(F, UP, UPUP, radicnd, n): Exports == Impl where --R Type: RadixExpansion(3) --E 3 ---S 4 of 17 +--S 4 of 18 (5/24)::RadixExpansion(8) --R --R @@ -116355,7 +121062,7 @@ RadicalFunctionField(F, UP, UPUP, radicnd, n): Exports == Impl where --R Type: RadixExpansion(8) --E 4 ---S 5 of 17 +--S 5 of 18 (5/24)::RadixExpansion(10) --R --R @@ -116364,7 +121071,7 @@ RadicalFunctionField(F, UP, UPUP, radicnd, n): Exports == Impl where --R Type: RadixExpansion(10) --E 5 ---S 6 of 17 +--S 6 of 18 (5/24)::RadixExpansion(12) --R --R @@ -116372,7 +121079,7 @@ RadicalFunctionField(F, UP, UPUP, radicnd, n): Exports == Impl where --R Type: RadixExpansion(12) --E 6 ---S 7 of 17 +--S 7 of 18 (5/24)::RadixExpansion(16) --R --R @@ -116381,7 +121088,7 @@ RadicalFunctionField(F, UP, UPUP, radicnd, n): Exports == Impl where --R Type: RadixExpansion(16) --E 7 ---S 8 of 17 +--S 8 of 18 (5/24)::RadixExpansion(36) --R --R @@ -116389,7 +121096,7 @@ RadicalFunctionField(F, UP, UPUP, radicnd, n): Exports == Impl where --R Type: RadixExpansion(36) --E 8 ---S 9 of 17 +--S 9 of 18 (5/24)::RadixExpansion(38) --R --R @@ -116398,7 +121105,7 @@ RadicalFunctionField(F, UP, UPUP, radicnd, n): Exports == Impl where --R Type: RadixExpansion(38) --E 9 ---S 10 of 17 +--S 10 of 18 a := (76543/210)::RadixExpansion(8) --R --R @@ -116407,7 +121114,7 @@ a := (76543/210)::RadixExpansion(8) --R Type: RadixExpansion(8) --E 10 ---S 11 of 17 +--S 11 of 18 w := wholeRagits a --R --R @@ -116415,7 +121122,7 @@ w := wholeRagits a --R Type: List(Integer) --E 11 ---S 12 of 17 +--S 12 of 18 f0 := prefixRagits a --R --R @@ -116423,7 +121130,7 @@ f0 := prefixRagits a --R Type: List(Integer) --E 12 ---S 13 of 17 +--S 13 of 18 f1 := cycleRagits a --R --R @@ -116431,7 +121138,7 @@ f1 := cycleRagits a --R Type: List(Integer) --E 13 ---S 14 of 17 +--S 14 of 18 u:RadixExpansion(8):=wholeRadix(w)+fractRadix(f0,f1) --R --R @@ -116440,7 +121147,7 @@ u:RadixExpansion(8):=wholeRadix(w)+fractRadix(f0,f1) --R Type: RadixExpansion(8) --E 14 ---S 15 of 17 +--S 15 of 18 v: RadixExpansion(12) := fractRadix([1,2,3,11], [0]) --R --R @@ -116449,7 +121156,7 @@ v: RadixExpansion(12) := fractRadix([1,2,3,11], [0]) --R Type: RadixExpansion(12) --E 15 ---S 16 of 17 +--S 16 of 18 fractRagits(u) --R --R @@ -116458,7 +121165,7 @@ fractRagits(u) --R Type: Stream(Integer) --E 16 ---S 17 of 17 +--S 17 of 18 a :: Fraction(Integer) --R --R @@ -116467,6 +121174,128 @@ a :: Fraction(Integer) --R 210 --R Type: Fraction(Integer) --E 17 + +--S 18 of 18 +)show RadixExpansion +--R +--R RadixExpansion(bb: Integer) is a domain constructor +--R Abbreviation for RadixExpansion is RADIX +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for RADIX +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,Integer) -> % ?*? : (Integer,%) -> % +--R ?*? : (Fraction(Integer),%) -> % ?*? : (%,Fraction(Integer)) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,Integer) -> % ?**? : (%,NonNegativeInteger) -> % +--R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % +--R ?-? : (%,%) -> % -? : % -> % +--R ?/? : (Integer,Integer) -> % ?/? : (%,%) -> % +--R ?=? : (%,%) -> Boolean D : (%,(Integer -> Integer)) -> % +--R D : % -> % if Integer has DIFRING 1 : () -> % +--R 0 : () -> % ?^? : (%,Integer) -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R associates? : (%,%) -> Boolean coerce : % -> Fraction(Integer) +--R coerce : Integer -> % coerce : Fraction(Integer) -> % +--R coerce : % -> % coerce : Integer -> % +--R coerce : % -> OutputForm cycleRagits : % -> List(Integer) +--R denom : % -> Integer denominator : % -> % +--R factor : % -> Factored(%) fractRagits : % -> Stream(Integer) +--R gcd : List(%) -> % gcd : (%,%) -> % +--R hash : % -> SingleInteger init : () -> % if Integer has STEP +--R inv : % -> % latex : % -> String +--R lcm : List(%) -> % lcm : (%,%) -> % +--R numer : % -> Integer numerator : % -> % +--R one? : % -> Boolean prefixRagits : % -> List(Integer) +--R prime? : % -> Boolean ?quo? : (%,%) -> % +--R random : () -> % if Integer has INS recip : % -> Union(%,"failed") +--R ?rem? : (%,%) -> % retract : % -> Integer +--R sample : () -> % sizeLess? : (%,%) -> Boolean +--R squareFree : % -> Factored(%) squareFreePart : % -> % +--R unit? : % -> Boolean unitCanonical : % -> % +--R wholeRadix : List(Integer) -> % wholeRagits : % -> List(Integer) +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ? Boolean if Integer has ORDSET +--R ?<=? : (%,%) -> Boolean if Integer has ORDSET +--R ?>? : (%,%) -> Boolean if Integer has ORDSET +--R ?>=? : (%,%) -> Boolean if Integer has ORDSET +--R D : (%,(Integer -> Integer),NonNegativeInteger) -> % +--R D : (%,List(Symbol),List(NonNegativeInteger)) -> % if Integer has PDRING(SYMBOL) +--R D : (%,Symbol,NonNegativeInteger) -> % if Integer has PDRING(SYMBOL) +--R D : (%,List(Symbol)) -> % if Integer has PDRING(SYMBOL) +--R D : (%,Symbol) -> % if Integer has PDRING(SYMBOL) +--R D : (%,NonNegativeInteger) -> % if Integer has DIFRING +--R abs : % -> % if Integer has OINTDOM +--R ceiling : % -> Integer if Integer has INS +--R characteristic : () -> NonNegativeInteger +--R charthRoot : % -> Union(%,"failed") if $ has CHARNZ and Integer has PFECAT or Integer has CHARNZ +--R coerce : Symbol -> % if Integer has RETRACT(SYMBOL) +--R conditionP : Matrix(%) -> Union(Vector(%),"failed") if $ has CHARNZ and Integer has PFECAT +--R convert : % -> DoubleFloat if Integer has REAL +--R convert : % -> Float if Integer has REAL +--R convert : % -> InputForm if Integer has KONVERT(INFORM) +--R convert : % -> Pattern(Float) if Integer has KONVERT(PATTERN(FLOAT)) +--R convert : % -> Pattern(Integer) if Integer has KONVERT(PATTERN(INT)) +--R differentiate : (%,(Integer -> Integer)) -> % +--R differentiate : (%,(Integer -> Integer),NonNegativeInteger) -> % +--R differentiate : (%,List(Symbol),List(NonNegativeInteger)) -> % if Integer has PDRING(SYMBOL) +--R differentiate : (%,Symbol,NonNegativeInteger) -> % if Integer has PDRING(SYMBOL) +--R differentiate : (%,List(Symbol)) -> % if Integer has PDRING(SYMBOL) +--R differentiate : (%,Symbol) -> % if Integer has PDRING(SYMBOL) +--R differentiate : (%,NonNegativeInteger) -> % if Integer has DIFRING +--R differentiate : % -> % if Integer has DIFRING +--R divide : (%,%) -> Record(quotient: %,remainder: %) +--R ?.? : (%,Integer) -> % if Integer has ELTAB(INT,INT) +--R euclideanSize : % -> NonNegativeInteger +--R eval : (%,Symbol,Integer) -> % if Integer has IEVALAB(SYMBOL,INT) +--R eval : (%,List(Symbol),List(Integer)) -> % if Integer has IEVALAB(SYMBOL,INT) +--R eval : (%,List(Equation(Integer))) -> % if Integer has EVALAB(INT) +--R eval : (%,Equation(Integer)) -> % if Integer has EVALAB(INT) +--R eval : (%,Integer,Integer) -> % if Integer has EVALAB(INT) +--R eval : (%,List(Integer),List(Integer)) -> % if Integer has EVALAB(INT) +--R expressIdealMember : (List(%),%) -> Union(List(%),"failed") +--R exquo : (%,%) -> Union(%,"failed") +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) +--R factorPolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if Integer has PFECAT +--R factorSquareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if Integer has PFECAT +--R floor : % -> Integer if Integer has INS +--R fractRadix : (List(Integer),List(Integer)) -> % +--R fractionPart : % -> Fraction(Integer) +--R fractionPart : % -> % if Integer has EUCDOM +--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) +--R lcmCoef : (%,%) -> Record(llcmres: %,coeff1: %,coeff2: %) +--R map : ((Integer -> Integer),%) -> % +--R max : (%,%) -> % if Integer has ORDSET +--R min : (%,%) -> % if Integer has ORDSET +--R multiEuclidean : (List(%),%) -> Union(List(%),"failed") +--R negative? : % -> Boolean if Integer has OINTDOM +--R nextItem : % -> Union(%,"failed") if Integer has STEP +--R patternMatch : (%,Pattern(Float),PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if Integer has PATMAB(FLOAT) +--R patternMatch : (%,Pattern(Integer),PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if Integer has PATMAB(INT) +--R positive? : % -> Boolean if Integer has OINTDOM +--R principalIdeal : List(%) -> Record(coef: List(%),generator: %) +--R reducedSystem : Matrix(%) -> Matrix(Integer) +--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(Integer),vec: Vector(Integer)) +--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(Integer),vec: Vector(Integer)) if Integer has LINEXP(INT) +--R reducedSystem : Matrix(%) -> Matrix(Integer) if Integer has LINEXP(INT) +--R retract : % -> Integer if Integer has RETRACT(INT) +--R retract : % -> Fraction(Integer) if Integer has RETRACT(INT) +--R retract : % -> Symbol if Integer has RETRACT(SYMBOL) +--R retractIfCan : % -> Union(Integer,"failed") if Integer has RETRACT(INT) +--R retractIfCan : % -> Union(Fraction(Integer),"failed") if Integer has RETRACT(INT) +--R retractIfCan : % -> Union(Symbol,"failed") if Integer has RETRACT(SYMBOL) +--R retractIfCan : % -> Union(Integer,"failed") +--R sign : % -> Integer if Integer has OINTDOM +--R solveLinearPolynomialEquation : (List(SparseUnivariatePolynomial(%)),SparseUnivariatePolynomial(%)) -> Union(List(SparseUnivariatePolynomial(%)),"failed") if Integer has PFECAT +--R squareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if Integer has PFECAT +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) +--R wholePart : % -> Integer if Integer has EUCDOM +--R +--E 18 + )spool )lisp (bye) \end{chunk} @@ -116983,7 +121812,8 @@ depending on several "real roots". )set message test on )set message auto off )clear all ---S 1 of 67 + +--S 1 of 68 Ran := RECLOS(FRAC INT) --R --R @@ -116991,7 +121821,7 @@ Ran := RECLOS(FRAC INT) --R Type: Domain --E 1 ---S 2 of 67 +--S 2 of 68 fourSquares(a:Ran,b:Ran,c:Ran,d:Ran):Ran==sqrt(a)+sqrt(b)-sqrt(c)-sqrt(d) --R --R Function declaration fourSquares : (RealClosure(Fraction(Integer)), @@ -117001,7 +121831,7 @@ fourSquares(a:Ran,b:Ran,c:Ran,d:Ran):Ran==sqrt(a)+sqrt(b)-sqrt(c)-sqrt(d) --R Type: Void --E 2 ---S 3 of 67 +--S 3 of 68 squareDiff1 := fourSquares(73,548,60,586) --R --R Compiling function fourSquares with type (RealClosure(Fraction( @@ -117014,7 +121844,7 @@ squareDiff1 := fourSquares(73,548,60,586) --R Type: RealClosure(Fraction(Integer)) --E 3 ---S 4 of 67 +--S 4 of 68 recip(squareDiff1) --R --R @@ -117027,7 +121857,7 @@ recip(squareDiff1) --R Type: Union(RealClosure(Fraction(Integer)),...) --E 4 ---S 5 of 67 +--S 5 of 68 sign(squareDiff1) --R --R @@ -117035,7 +121865,7 @@ sign(squareDiff1) --R Type: PositiveInteger --E 5 ---S 6 of 67 +--S 6 of 68 squareDiff2 := fourSquares(165,778,86,990) --R --R @@ -117044,7 +121874,7 @@ squareDiff2 := fourSquares(165,778,86,990) --R Type: RealClosure(Fraction(Integer)) --E 6 ---S 7 of 67 +--S 7 of 68 recip(squareDiff2) --R --R @@ -117060,7 +121890,7 @@ recip(squareDiff2) --R Type: Union(RealClosure(Fraction(Integer)),...) --E 7 ---S 8 of 67 +--S 8 of 68 sign(squareDiff2) --R --R @@ -117068,7 +121898,7 @@ sign(squareDiff2) --R Type: PositiveInteger --E 8 ---S 9 of 67 +--S 9 of 68 squareDiff3 := fourSquares(217,708,226,692) --R --R @@ -117077,7 +121907,7 @@ squareDiff3 := fourSquares(217,708,226,692) --R Type: RealClosure(Fraction(Integer)) --E 9 ---S 10 of 67 +--S 10 of 68 recip(squareDiff3) --R --R @@ -117090,7 +121920,7 @@ recip(squareDiff3) --R Type: Union(RealClosure(Fraction(Integer)),...) --E 10 ---S 11 of 67 +--S 11 of 68 sign(squareDiff3) --R --R @@ -117098,7 +121928,7 @@ sign(squareDiff3) --R Type: Integer --E 11 ---S 12 of 67 +--S 12 of 68 squareDiff4 := fourSquares(155,836,162,820) --R --R @@ -117107,7 +121937,7 @@ squareDiff4 := fourSquares(155,836,162,820) --R Type: RealClosure(Fraction(Integer)) --E 12 ---S 13 of 67 +--S 13 of 68 recip(squareDiff4) --R --R @@ -117120,7 +121950,7 @@ recip(squareDiff4) --R Type: Union(RealClosure(Fraction(Integer)),...) --E 13 ---S 14 of 67 +--S 14 of 68 sign(squareDiff4) --R --R @@ -117128,7 +121958,7 @@ sign(squareDiff4) --R Type: Integer --E 14 ---S 15 of 67 +--S 15 of 68 squareDiff5 := fourSquares(591,772,552,818) --R --R @@ -117137,7 +121967,7 @@ squareDiff5 := fourSquares(591,772,552,818) --R Type: RealClosure(Fraction(Integer)) --E 15 ---S 16 of 67 +--S 16 of 68 recip(squareDiff5) --R --R @@ -117150,7 +121980,7 @@ recip(squareDiff5) --R Type: Union(RealClosure(Fraction(Integer)),...) --E 16 ---S 17 of 67 +--S 17 of 68 sign(squareDiff5) --R --R @@ -117158,7 +121988,7 @@ sign(squareDiff5) --R Type: PositiveInteger --E 17 ---S 18 of 67 +--S 18 of 68 squareDiff6 := fourSquares(434,1053,412,1088) --R --R @@ -117167,7 +121997,7 @@ squareDiff6 := fourSquares(434,1053,412,1088) --R Type: RealClosure(Fraction(Integer)) --E 18 ---S 19 of 67 +--S 19 of 68 recip(squareDiff6) --R --R @@ -117183,7 +122013,7 @@ recip(squareDiff6) --R Type: Union(RealClosure(Fraction(Integer)),...) --E 19 ---S 20 of 67 +--S 20 of 68 sign(squareDiff6) --R --R @@ -117191,7 +122021,7 @@ sign(squareDiff6) --R Type: PositiveInteger --E 20 ---S 21 of 67 +--S 21 of 68 squareDiff7 := fourSquares(514,1049,446,1152) --R --R @@ -117200,7 +122030,7 @@ squareDiff7 := fourSquares(514,1049,446,1152) --R Type: RealClosure(Fraction(Integer)) --E 21 ---S 22 of 67 +--S 22 of 68 recip(squareDiff7) --R --R @@ -117216,7 +122046,7 @@ recip(squareDiff7) --R Type: Union(RealClosure(Fraction(Integer)),...) --E 22 ---S 23 of 67 +--S 23 of 68 sign(squareDiff7) --R --R @@ -117224,7 +122054,7 @@ sign(squareDiff7) --R Type: PositiveInteger --E 23 ---S 24 of 67 +--S 24 of 68 squareDiff8 := fourSquares(190,1751,208,1698) --R --R @@ -117233,7 +122063,7 @@ squareDiff8 := fourSquares(190,1751,208,1698) --R Type: RealClosure(Fraction(Integer)) --E 24 ---S 25 of 67 +--S 25 of 68 recip(squareDiff8) --R --R @@ -117254,7 +122084,7 @@ recip(squareDiff8) --R Type: Union(RealClosure(Fraction(Integer)),...) --E 25 ---S 26 of 67 +--S 26 of 68 sign(squareDiff8) --R --R @@ -117262,7 +122092,7 @@ sign(squareDiff8) --R Type: Integer --E 26 ---S 27 of 67 +--S 27 of 68 relativeApprox(squareDiff8,10**(-3))::Float --R --R @@ -117270,7 +122100,7 @@ relativeApprox(squareDiff8,10**(-3))::Float --R Type: Float --E 27 ---S 28 of 67 +--S 28 of 68 l := allRootsOf((x**2-2)**2-2)$Ran --R --R @@ -117278,7 +122108,7 @@ l := allRootsOf((x**2-2)**2-2)$Ran --R Type: List(RealClosure(Fraction(Integer))) --E 28 ---S 29 of 67 +--S 29 of 68 removeDuplicates map(mainDefiningPolynomial,l) --R --R @@ -117287,7 +122117,7 @@ removeDuplicates map(mainDefiningPolynomial,l) --RType: List(Union(SparseUnivariatePolynomial(RealClosure(Fraction(Integer))),"failed")) --E 29 ---S 30 of 67 +--S 30 of 68 map(mainCharacterization,l) --R --R @@ -117295,7 +122125,7 @@ map(mainCharacterization,l) --IType: List(Union(RightOpenIntervalRootCharacterization(... --E 30 ---S 31 of 67 +--S 31 of 68 [reduce(+,l),reduce(*,l)-2] --R --R @@ -117303,7 +122133,7 @@ map(mainCharacterization,l) --R Type: List(RealClosure(Fraction(Integer))) --E 31 ---S 32 of 67 +--S 32 of 68 (s2, s5, s10) := (sqrt(2)$Ran, sqrt(5)$Ran, sqrt(10)$Ran) --R --R @@ -117312,7 +122142,7 @@ map(mainCharacterization,l) --R Type: RealClosure(Fraction(Integer)) --E 32 ---S 33 of 67 +--S 33 of 68 eq1:=sqrt(s10+3)*sqrt(s5+2) - sqrt(s10-3)*sqrt(s5-2) = sqrt(10*s2+10) --R --R @@ -117322,7 +122152,7 @@ eq1:=sqrt(s10+3)*sqrt(s5+2) - sqrt(s10-3)*sqrt(s5-2) = sqrt(10*s2+10) --R Type: Equation(RealClosure(Fraction(Integer))) --E 33 ---S 34 of 67 +--S 34 of 68 eq1::Boolean --R --R @@ -117330,7 +122160,7 @@ eq1::Boolean --R Type: Boolean --E 34 ---S 35 of 67 +--S 35 of 68 eq2:=sqrt(s5+2)*sqrt(s2+1) - sqrt(s5-2)*sqrt(s2-1) = sqrt(2*s10+2) --R --R @@ -117340,7 +122170,7 @@ eq2:=sqrt(s5+2)*sqrt(s2+1) - sqrt(s5-2)*sqrt(s2-1) = sqrt(2*s10+2) --R Type: Equation(RealClosure(Fraction(Integer))) --E 35 ---S 36 of 67 +--S 36 of 68 eq2::Boolean --R --R @@ -117348,7 +122178,7 @@ eq2::Boolean --R Type: Boolean --E 36 ---S 37 of 67 +--S 37 of 68 s3 := sqrt(3)$Ran --R --R @@ -117357,7 +122187,7 @@ s3 := sqrt(3)$Ran --R Type: RealClosure(Fraction(Integer)) --E 37 ---S 38 of 67 +--S 38 of 68 s7:= sqrt(7)$Ran --R --R @@ -117366,7 +122196,7 @@ s7:= sqrt(7)$Ran --R Type: RealClosure(Fraction(Integer)) --E 38 ---S 39 of 67 +--S 39 of 68 e1 := sqrt(2*s7-3*s3,3) --R --R @@ -117376,7 +122206,7 @@ e1 := sqrt(2*s7-3*s3,3) --R Type: RealClosure(Fraction(Integer)) --E 39 ---S 40 of 67 +--S 40 of 68 e2 := sqrt(2*s7+3*s3,3) --R --R @@ -117386,7 +122216,7 @@ e2 := sqrt(2*s7+3*s3,3) --R Type: RealClosure(Fraction(Integer)) --E 40 ---S 41 of 67 +--S 41 of 68 e2-e1-s3 --R --R @@ -117394,7 +122224,7 @@ e2-e1-s3 --R Type: RealClosure(Fraction(Integer)) --E 41 ---S 42 of 67 +--S 42 of 68 pol : UP(x,Ran) := x**4+(7/3)*x**2+30*x-(100/3) --R --R @@ -117404,7 +122234,7 @@ pol : UP(x,Ran) := x**4+(7/3)*x**2+30*x-(100/3) --R Type: UnivariatePolynomial(x,RealClosure(Fraction(Integer))) --E 42 ---S 43 of 67 +--S 43 of 68 r1 := sqrt(7633)$Ran --R --R @@ -117413,7 +122243,7 @@ r1 := sqrt(7633)$Ran --R Type: RealClosure(Fraction(Integer)) --E 43 ---S 44 of 67 +--S 44 of 68 alpha := sqrt(5*r1-436,3)/3 --R --R @@ -117424,7 +122254,7 @@ alpha := sqrt(5*r1-436,3)/3 --R Type: RealClosure(Fraction(Integer)) --E 44 ---S 45 of 67 +--S 45 of 68 beta := -sqrt(5*r1+436,3)/3 --R --R @@ -117435,7 +122265,7 @@ beta := -sqrt(5*r1+436,3)/3 --R Type: RealClosure(Fraction(Integer)) --E 45 ---S 46 of 67 +--S 46 of 68 pol.(alpha+beta-1/3) --R --R @@ -117443,7 +122273,7 @@ pol.(alpha+beta-1/3) --R Type: RealClosure(Fraction(Integer)) --E 46 ---S 47 of 67 +--S 47 of 68 qol : UP(x,Ran) := x**5+10*x**3+20*x+22 --R --R @@ -117452,7 +122282,7 @@ qol : UP(x,Ran) := x**5+10*x**3+20*x+22 --R Type: UnivariatePolynomial(x,RealClosure(Fraction(Integer))) --E 47 ---S 48 of 67 +--S 48 of 68 r2 := sqrt(153)$Ran --R --R @@ -117461,7 +122291,7 @@ r2 := sqrt(153)$Ran --R Type: RealClosure(Fraction(Integer)) --E 48 ---S 49 of 67 +--S 49 of 68 alpha2 := sqrt(r2-11,5) --R --R @@ -117471,7 +122301,7 @@ alpha2 := sqrt(r2-11,5) --R Type: RealClosure(Fraction(Integer)) --E 49 ---S 50 of 67 +--S 50 of 68 beta2 := -sqrt(r2+11,5) --R --R @@ -117481,7 +122311,7 @@ beta2 := -sqrt(r2+11,5) --R Type: RealClosure(Fraction(Integer)) --E 50 ---S 51 of 67 +--S 51 of 68 qol(alpha2+beta2) --R --R @@ -117489,7 +122319,7 @@ qol(alpha2+beta2) --R Type: RealClosure(Fraction(Integer)) --E 51 ---S 52 of 67 +--S 52 of 68 dst1:=sqrt(9+4*s2)=1+2*s2 --R --R @@ -117499,7 +122329,7 @@ dst1:=sqrt(9+4*s2)=1+2*s2 --R Type: Equation(RealClosure(Fraction(Integer))) --E 52 ---S 53 of 67 +--S 53 of 68 dst1::Boolean --R --R @@ -117507,7 +122337,7 @@ dst1::Boolean --R Type: Boolean --E 53 ---S 54 of 67 +--S 54 of 68 s6:Ran:=sqrt 6 --R --R @@ -117516,7 +122346,7 @@ s6:Ran:=sqrt 6 --R Type: RealClosure(Fraction(Integer)) --E 54 ---S 55 of 67 +--S 55 of 68 dst2:=sqrt(5+2*s6)+sqrt(5-2*s6) = 2*s3 --R --R @@ -117526,7 +122356,7 @@ dst2:=sqrt(5+2*s6)+sqrt(5-2*s6) = 2*s3 --R Type: Equation(RealClosure(Fraction(Integer))) --E 55 ---S 56 of 67 +--S 56 of 68 dst2::Boolean --R --R @@ -117534,7 +122364,7 @@ dst2::Boolean --R Type: Boolean --E 56 ---S 57 of 67 +--S 57 of 68 s29:Ran:=sqrt 29 --R --R @@ -117543,7 +122373,7 @@ s29:Ran:=sqrt 29 --R Type: RealClosure(Fraction(Integer)) --E 57 ---S 58 of 67 +--S 58 of 68 dst4:=sqrt(16-2*s29+2*sqrt(55-10*s29)) = sqrt(22+2*s5)-sqrt(11+2*s29)+s5 --R --R @@ -117555,7 +122385,7 @@ dst4:=sqrt(16-2*s29+2*sqrt(55-10*s29)) = sqrt(22+2*s5)-sqrt(11+2*s29)+s5 --R Type: Equation(RealClosure(Fraction(Integer))) --E 58 ---S 59 of 67 +--S 59 of 68 dst4::Boolean --R --R @@ -117563,7 +122393,7 @@ dst4::Boolean --R Type: Boolean --E 59 ---S 60 of 67 +--S 60 of 68 dst6:=sqrt((112+70*s2)+(46+34*s2)*s5) = (5+4*s2)+(3+s2)*s5 --R --R @@ -117573,7 +122403,7 @@ dst6:=sqrt((112+70*s2)+(46+34*s2)*s5) = (5+4*s2)+(3+s2)*s5 --R Type: Equation(RealClosure(Fraction(Integer))) --E 60 ---S 61 of 67 +--S 61 of 68 dst6::Boolean --R --R @@ -117581,7 +122411,7 @@ dst6::Boolean --R Type: Boolean --E 61 ---S 62 of 67 +--S 62 of 68 f3:Ran:=sqrt(3,5) --R --R @@ -117590,7 +122420,7 @@ f3:Ran:=sqrt(3,5) --R Type: RealClosure(Fraction(Integer)) --E 62 ---S 63 of 67 +--S 63 of 68 f25:Ran:=sqrt(1/25,5) --R --R @@ -117601,7 +122431,7 @@ f25:Ran:=sqrt(1/25,5) --R Type: RealClosure(Fraction(Integer)) --E 63 ---S 64 of 67 +--S 64 of 68 f32:Ran:=sqrt(32/5,5) --R --R @@ -117612,7 +122442,7 @@ f32:Ran:=sqrt(32/5,5) --R Type: RealClosure(Fraction(Integer)) --E 64 ---S 65 of 67 +--S 65 of 68 f27:Ran:=sqrt(27/5,5) --R --R @@ -117623,7 +122453,7 @@ f27:Ran:=sqrt(27/5,5) --R Type: RealClosure(Fraction(Integer)) --E 65 ---S 66 of 67 +--S 66 of 68 dst5:=sqrt((f32-f27,3)) = f25*(1+f3-f3**2) --R --R @@ -117635,13 +122465,98 @@ dst5:=sqrt((f32-f27,3)) = f25*(1+f3-f3**2) --R Type: Equation(RealClosure(Fraction(Integer))) --E 66 ---S 67 of 67 +--S 67 of 68 dst5::Boolean --R --R --R (67) true --R Type: Boolean --E 67 + +--S 68 of 68 +)show RealClosure +--R +--R RealClosure(TheField: Join(OrderedRing,Field,RealConstant)) is a domain constructor +--R Abbreviation for RealClosure is RECLOS +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for RECLOS +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,TheField) -> % ?*? : (TheField,%) -> % +--R ?*? : (%,Fraction(Integer)) -> % ?*? : (Fraction(Integer),%) -> % +--R ?*? : (%,Integer) -> % ?*? : (Integer,%) -> % +--R ?*? : (%,Fraction(Integer)) -> % ?*? : (Fraction(Integer),%) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,Fraction(Integer)) -> % ?**? : (%,Integer) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?/? : (%,%) -> % +--R ? Boolean ?<=? : (%,%) -> Boolean +--R ?=? : (%,%) -> Boolean ?>? : (%,%) -> Boolean +--R ?>=? : (%,%) -> Boolean 1 : () -> % +--R 0 : () -> % ?^? : (%,Integer) -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R abs : % -> % associates? : (%,%) -> Boolean +--R coerce : TheField -> % coerce : Fraction(Integer) -> % +--R coerce : Integer -> % coerce : Fraction(Integer) -> % +--R coerce : % -> % coerce : Fraction(Integer) -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R factor : % -> Factored(%) gcd : (%,%) -> % +--R gcd : List(%) -> % hash : % -> SingleInteger +--R inv : % -> % latex : % -> String +--R lcm : (%,%) -> % lcm : List(%) -> % +--R max : (%,%) -> % min : (%,%) -> % +--R negative? : % -> Boolean nthRoot : (%,Integer) -> % +--R one? : % -> Boolean positive? : % -> Boolean +--R prime? : % -> Boolean ?quo? : (%,%) -> % +--R recip : % -> Union(%,"failed") ?rem? : (%,%) -> % +--R rename : (%,OutputForm) -> % rename! : (%,OutputForm) -> % +--R retract : % -> TheField retract : % -> Fraction(Integer) +--R sample : () -> % sign : % -> Integer +--R sizeLess? : (%,%) -> Boolean sqrt : Integer -> % +--R sqrt : Fraction(Integer) -> % sqrt : (%,NonNegativeInteger) -> % +--R sqrt : % -> % squareFree : % -> Factored(%) +--R squareFreePart : % -> % unit? : % -> Boolean +--R unitCanonical : % -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R algebraicOf : (RightOpenIntervalRootCharacterization(%,SparseUnivariatePolynomial(%)),OutputForm) -> % +--R allRootsOf : Polynomial(Integer) -> List(%) +--R allRootsOf : Polynomial(Fraction(Integer)) -> List(%) +--R allRootsOf : Polynomial(%) -> List(%) +--R allRootsOf : SparseUnivariatePolynomial(Integer) -> List(%) +--R allRootsOf : SparseUnivariatePolynomial(Fraction(Integer)) -> List(%) +--R allRootsOf : SparseUnivariatePolynomial(%) -> List(%) +--R approximate : (%,%) -> Fraction(Integer) +--R characteristic : () -> NonNegativeInteger +--R divide : (%,%) -> Record(quotient: %,remainder: %) +--R euclideanSize : % -> NonNegativeInteger +--R expressIdealMember : (List(%),%) -> Union(List(%),"failed") +--R exquo : (%,%) -> Union(%,"failed") +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") +--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) +--R lcmCoef : (%,%) -> Record(llcmres: %,coeff1: %,coeff2: %) +--R mainCharacterization : % -> Union(RightOpenIntervalRootCharacterization(%,SparseUnivariatePolynomial(%)),"failed") +--R mainDefiningPolynomial : % -> Union(SparseUnivariatePolynomial(%),"failed") +--R mainForm : % -> Union(OutputForm,"failed") +--R mainValue : % -> Union(SparseUnivariatePolynomial(%),"failed") +--R multiEuclidean : (List(%),%) -> Union(List(%),"failed") +--R principalIdeal : List(%) -> Record(coef: List(%),generator: %) +--R relativeApprox : (%,%) -> Fraction(Integer) +--R retract : % -> Integer if Fraction(Integer) has RETRACT(INT) or TheField has RETRACT(INT) +--R retract : % -> Fraction(Integer) if Fraction(Integer) has RETRACT(FRAC(INT)) +--R retractIfCan : % -> Union(Integer,"failed") if Fraction(Integer) has RETRACT(INT) or TheField has RETRACT(INT) +--R retractIfCan : % -> Union(TheField,"failed") +--R retractIfCan : % -> Union(Fraction(Integer),"failed") +--R retractIfCan : % -> Union(Fraction(Integer),"failed") if Fraction(Integer) has RETRACT(FRAC(INT)) +--R rootOf : (SparseUnivariatePolynomial(%),PositiveInteger) -> Union(%,"failed") +--R rootOf : (SparseUnivariatePolynomial(%),PositiveInteger,OutputForm) -> Union(%,"failed") +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) +--R +--E 68 + )spool )lisp (bye) \end{chunk} @@ -118564,9 +123479,10 @@ RealClosure(TheField): PUB == PRIV where --R --R------------------------------- Operations -------------------------------- --R ?*? : (%,R) -> % ?*? : (R,%) -> % ---R ?*? : (Integer,%) -> % ?*? : (PositiveInteger,%) -> % ---R ?+? : (%,%) -> % ?-? : (%,%) -> % ---R -? : % -> % ?=? : (%,%) -> Boolean +--R ?*? : (Integer,%) -> % ?*? : (NonNegativeInteger,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?+? : (%,%) -> % +--R ?-? : (%,%) -> % -? : % -> % +--R ?/? : (%,R) -> % if R has FIELD ?=? : (%,%) -> Boolean --R 0 : () -> % antisymmetric? : % -> Boolean --R coerce : % -> Matrix(R) coerce : % -> OutputForm --R copy : % -> % diagonal? : % -> Boolean @@ -118579,12 +123495,10 @@ RealClosure(TheField): PUB == PRIV where --R maxRowIndex : % -> Integer minColIndex : % -> Integer --R minRowIndex : % -> Integer ncols : % -> NonNegativeInteger --R nrows : % -> NonNegativeInteger qelt : (%,Integer,Integer) -> R ---R sample : () -> % square? : % -> Boolean ---R symmetric? : % -> Boolean zero? : % -> Boolean ---R ?~=? : (%,%) -> Boolean +--R rectangularMatrix : Matrix(R) -> % sample : () -> % +--R square? : % -> Boolean symmetric? : % -> Boolean +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean --R #? : % -> NonNegativeInteger if $ has finiteAggregate ---R ?*? : (NonNegativeInteger,%) -> % ---R ?/? : (%,R) -> % if R has FIELD --R any? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate --R column : (%,Integer) -> DirectProduct(m,R) --R convert : % -> InputForm if R has KONVERT(INFORM) @@ -118606,7 +123520,6 @@ RealClosure(TheField): PUB == PRIV where --R nullity : % -> NonNegativeInteger if R has INTDOM --R parts : % -> List(R) if $ has finiteAggregate --R rank : % -> NonNegativeInteger if R has INTDOM ---R rectangularMatrix : Matrix(R) -> % --R row : (%,Integer) -> DirectProduct(n,R) --R rowEchelon : % -> % if R has EUCDOM --R size? : (%,NonNegativeInteger) -> Boolean @@ -118806,11 +123719,11 @@ RectangularMatrix(m,n,R): Exports == Implementation where --R --R------------------------------- Operations -------------------------------- --R ?=? : (%,%) -> Boolean deref : % -> S ---R elt : % -> S ref : S -> % ---R setelt : (%,S) -> S setref : (%,S) -> S +--R elt : % -> S latex : % -> String if S has SETCAT +--R ref : S -> % setelt : (%,S) -> S +--R setref : (%,S) -> S --R coerce : % -> OutputForm if S has SETCAT --R hash : % -> SingleInteger if S has SETCAT ---R latex : % -> String if S has SETCAT --R ?~=? : (%,%) -> Boolean if S has SETCAT --R --E 1 @@ -118925,10 +123838,11 @@ Reference(S:Type): Type with --R empty? : % -> Boolean eq? : (%,%) -> Boolean --R hash : % -> SingleInteger headReduced? : % -> Boolean --R infRittWu? : (%,%) -> Boolean initiallyReduced? : % -> Boolean ---R latex : % -> String normalized? : % -> Boolean ---R purelyAlgebraic? : % -> Boolean rest : % -> Union(%,"failed") ---R sample : () -> % stronglyReduced? : % -> Boolean ---R trivialIdeal? : % -> Boolean ?~=? : (%,%) -> Boolean +--R latex : % -> String mvar : % -> OrderedVariableList(ls) +--R normalized? : % -> Boolean purelyAlgebraic? : % -> Boolean +--R rest : % -> Union(%,"failed") sample : () -> % +--R stronglyReduced? : % -> Boolean trivialIdeal? : % -> Boolean +--R ?~=? : (%,%) -> Boolean --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R algebraic? : (OrderedVariableList(ls),%) -> Boolean --R algebraicCoefficients? : (NewSparseMultivariatePolynomial(R,OrderedVariableList(ls)),%) -> Boolean @@ -118990,7 +123904,6 @@ Reference(S:Type): Type with --R member? : (NewSparseMultivariatePolynomial(R,OrderedVariableList(ls)),%) -> Boolean if $ has finiteAggregate and NewSparseMultivariatePolynomial(R,OrderedVariableList(ls)) has SETCAT --R members : % -> List(NewSparseMultivariatePolynomial(R,OrderedVariableList(ls))) if $ has finiteAggregate --R more? : (%,NonNegativeInteger) -> Boolean ---R mvar : % -> OrderedVariableList(ls) --R normalized? : (NewSparseMultivariatePolynomial(R,OrderedVariableList(ls)),%) -> Boolean --R parts : % -> List(NewSparseMultivariatePolynomial(R,OrderedVariableList(ls))) if $ has finiteAggregate --R purelyAlgebraic? : (NewSparseMultivariatePolynomial(R,OrderedVariableList(ls)),%) -> Boolean @@ -119205,7 +124118,8 @@ in order to produce decompositions by means of Lazard triangular sets. )set message test on )set message auto off )clear all ---S 1 of 34 + +--S 1 of 35 R := Integer --R --R @@ -119213,7 +124127,7 @@ R := Integer --R Type: Domain --E 1 ---S 2 of 34 +--S 2 of 35 ls : List Symbol := [x,y,z,t] --R --R @@ -119221,7 +124135,7 @@ ls : List Symbol := [x,y,z,t] --R Type: List(Symbol) --E 2 ---S 3 of 34 +--S 3 of 35 V := OVAR(ls) --R --R @@ -119229,7 +124143,7 @@ V := OVAR(ls) --R Type: Domain --E 3 ---S 4 of 34 +--S 4 of 35 E := IndexedExponents V --R --R @@ -119237,7 +124151,7 @@ E := IndexedExponents V --R Type: Domain --E 4 ---S 5 of 34 +--S 5 of 35 P := NSMP(R, V) --R --R @@ -119246,7 +124160,7 @@ P := NSMP(R, V) --R Type: Domain --E 5 ---S 6 of 34 +--S 6 of 35 x: P := 'x --R --R @@ -119254,7 +124168,7 @@ x: P := 'x --RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList([x,y,z,t])) --E 6 ---S 7 of 34 +--S 7 of 35 y: P := 'y --R --R @@ -119262,7 +124176,7 @@ y: P := 'y --RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList([x,y,z,t])) --E 7 ---S 8 of 34 +--S 8 of 35 z: P := 'z --R --R @@ -119270,7 +124184,7 @@ z: P := 'z --RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList([x,y,z,t])) --E 8 ---S 9 of 34 +--S 9 of 35 t: P := 't --R --R @@ -119278,7 +124192,7 @@ t: P := 't --RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList([x,y,z,t])) --E 9 ---S 10 of 34 +--S 10 of 35 T := REGSET(R,E,V,P) --R --R @@ -119289,7 +124203,7 @@ T := REGSET(R,E,V,P) --R Type: Domain --E 10 ---S 11 of 34 +--S 11 of 35 p1 := x ** 31 - x ** 6 - x - y --R --R @@ -119298,7 +124212,7 @@ p1 := x ** 31 - x ** 6 - x - y --RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList([x,y,z,t])) --E 11 ---S 12 of 34 +--S 12 of 35 p2 := x ** 8 - z --R --R @@ -119307,7 +124221,7 @@ p2 := x ** 8 - z --RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList([x,y,z,t])) --E 12 ---S 13 of 34 +--S 13 of 35 p3 := x ** 10 - t --R --R @@ -119316,7 +124230,7 @@ p3 := x ** 10 - t --RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList([x,y,z,t])) --E 13 ---S 14 of 34 +--S 14 of 35 lp := [p1, p2, p3] --R --R @@ -119325,7 +124239,7 @@ lp := [p1, p2, p3] --RType: List(NewSparseMultivariatePolynomial(Integer,OrderedVariableList([x,y,z,t]))) --E 14 ---S 15 of 34 +--S 15 of 35 zeroSetSplit(lp)$T --R --R @@ -119334,7 +124248,7 @@ zeroSetSplit(lp)$T --IType: List(RegularTriangularSet(Integer,IndexedExponents(... --E 15 ---S 16 of 34 +--S 16 of 35 lts := zeroSetSplit(lp,false)$T --R --R @@ -119346,7 +124260,7 @@ lts := zeroSetSplit(lp,false)$T --IType: List(RegularTriangularSet(Integer,IndexedExponents(... --E 16 ---S 17 of 34 +--S 17 of 35 [coHeight(ts) for ts in lts] --R --R @@ -119354,7 +124268,7 @@ lts := zeroSetSplit(lp,false)$T --R Type: List(NonNegativeInteger) --E 17 ---S 18 of 34 +--S 18 of 35 f1 := y**2*z+2*x*y*t-2*x-z --R --R @@ -119363,7 +124277,7 @@ f1 := y**2*z+2*x*y*t-2*x-z --RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList([x,y,z,t])) --E 18 ---S 19 of 34 +--S 19 of 35 f2:=-x**3*z+ 4*x*y**2*z+4*x**2*y*t+2*y**3*t+4*x**2-10*y**2+4*x*z-10*y*t+2 --R --R @@ -119372,7 +124286,7 @@ f2:=-x**3*z+ 4*x*y**2*z+4*x**2*y*t+2*y**3*t+4*x**2-10*y**2+4*x*z-10*y*t+2 --RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList([x,y,z,t])) --E 19 ---S 20 of 34 +--S 20 of 35 f3 := 2*y*z*t+x*t**2-x-2*z --R --R @@ -119381,7 +124295,7 @@ f3 := 2*y*z*t+x*t**2-x-2*z --RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList([x,y,z,t])) --E 20 ---S 21 of 34 +--S 21 of 35 f4:=-x*z**3+4*y*z**2*t+4*x*z*t**2+2*y*t**3+4*x*z+4*z**2-10*y*t- 10*t**2+2 --R --R @@ -119390,7 +124304,7 @@ f4:=-x*z**3+4*y*z**2*t+4*x*z*t**2+2*y*t**3+4*x*z+4*z**2-10*y*t- 10*t**2+2 --RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList([x,y,z,t])) --E 21 ---S 22 of 34 +--S 22 of 35 lf := [f1, f2, f3, f4] --R --R @@ -119406,7 +124320,7 @@ lf := [f1, f2, f3, f4] --RType: List(NewSparseMultivariatePolynomial(Integer,OrderedVariableList([x,y,z,t]))) --E 22 ---S 23 of 34 +--S 23 of 35 zeroSetSplit(lf)$T --R --R @@ -119422,7 +124336,7 @@ zeroSetSplit(lf)$T --IType: List(RegularTriangularSet(Integer,IndexedExponents(... --E 23 ---S 24 of 34 +--S 24 of 35 lts2 := zeroSetSplit(lf,false)$T --R --R @@ -119436,7 +124350,7 @@ lts2 := zeroSetSplit(lf,false)$T --IType: List(RegularTriangularSet(Integer,IndexedExponents(... --E 24 ---S 25 of 34 +--S 25 of 35 [coHeight(ts) for ts in lts2] --R --R @@ -119444,7 +124358,7 @@ lts2 := zeroSetSplit(lf,false)$T --R Type: List(NonNegativeInteger) --E 25 ---S 26 of 34 +--S 26 of 35 degrees := [degree(ts) for ts in lts2] --R --R @@ -119452,7 +124366,7 @@ degrees := [degree(ts) for ts in lts2] --R Type: List(NonNegativeInteger) --E 26 ---S 27 of 34 +--S 27 of 35 reduce(+,degrees) --R --R @@ -119460,7 +124374,7 @@ reduce(+,degrees) --R Type: PositiveInteger --E 27 ---S 28 of 34 +--S 28 of 35 u : R := 2 --R --R @@ -119468,7 +124382,7 @@ u : R := 2 --R Type: Integer --E 28 ---S 29 of 34 +--S 29 of 35 q1 := 2*(u-1)**2+ 2*(x-z*x+z**2)+ y**2*(x-1)**2- 2*u*x+ 2*y*t*(1-x)*(x-z)+_ 2*u*z*t*(t-y)+ u**2*t**2*(1-2*z)+ 2*u*t**2*(z-x)+ 2*u*t*y*(z-1)+_ 2*u*z*x*(y+1)+ (u**2-2*u)*z**2*t**2+ 2*u**2*z**2+ 4*u*(1-u)*z+_ @@ -119484,7 +124398,7 @@ q1 := 2*(u-1)**2+ 2*(x-z*x+z**2)+ y**2*(x-1)**2- 2*u*x+ 2*y*t*(1-x)*(x-z)+_ --RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList([x,y,z,t])) --E 29 ---S 30 of 34 +--S 30 of 35 q2 := t*(2*z+1)*(x-z)+ y*(z+2)*(1-x)+ u*(u-2)*t+ u*(1-2*u)*z*t+_ u*y*(x+u-z*x-1)+ u*(u+1)*z**2*t --R @@ -119494,7 +124408,7 @@ q2 := t*(2*z+1)*(x-z)+ y*(z+2)*(1-x)+ u*(u-2)*t+ u*(1-2*u)*z*t+_ --RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList([x,y,z,t])) --E 30 ---S 31 of 34 +--S 31 of 35 q3 := -u**2*(z-1)**2+ 2*z*(z-x)-2*(x-1) --R --R @@ -119503,7 +124417,7 @@ q3 := -u**2*(z-1)**2+ 2*z*(z-x)-2*(x-1) --RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList([x,y,z,t])) --E 31 ---S 32 of 34 +--S 32 of 35 q4 := u**2+4*(z-x**2)+3*y**2*(x-1)**2- 3*t**2*(z-x)**2+_ 3*u**2*t**2*(z-1)**2+u**2*z*(z-2)+6*u*t*y*(z+x+z*x-1) --R @@ -119517,7 +124431,7 @@ q4 := u**2+4*(z-x**2)+3*y**2*(x-1)**2- 3*t**2*(z-x)**2+_ --RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList([x,y,z,t])) --E 32 ---S 33 of 34 +--S 33 of 35 lq := [q1, q2, q3, q4] --R --R @@ -119544,7 +124458,7 @@ lq := [q1, q2, q3, q4] --RType: List(NewSparseMultivariatePolynomial(Integer,OrderedVariableList([x,y,z,t]))) --E 33 ---S 34 of 34 +--S 34 of 35 zeroSetSplit(lq,true,true)$T --R --I[1 <4,0> -> |4|; {0}]W[2 <5,0>,<3,1> -> |8|; ... @@ -119737,6 +124651,114 @@ zeroSetSplit(lq,true,true)$T --R ] --IType: List(RegularTriangularSet(Integer,IndexedExponents(... --E 34 + +--S 35 of 35 +)show RegularTriangularSet +--R +--R RegularTriangularSet(R: GcdDomain,E: OrderedAbelianMonoidSup,V: OrderedSet,P: RecursivePolynomialCategory(R,E,V)) is a domain constructor +--R Abbreviation for RegularTriangularSet is REGSET +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for REGSET +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean algebraic? : (V,%) -> Boolean +--R algebraicVariables : % -> List(V) augment : (List(P),%) -> List(%) +--R augment : (P,List(%)) -> List(%) augment : (P,%) -> List(%) +--R coerce : % -> List(P) coerce : % -> OutputForm +--R collect : (%,V) -> % collectQuasiMonic : % -> % +--R collectUnder : (%,V) -> % collectUpper : (%,V) -> % +--R construct : List(P) -> % copy : % -> % +--R degree : % -> NonNegativeInteger empty : () -> % +--R empty? : % -> Boolean eq? : (%,%) -> Boolean +--R extend : (List(P),%) -> List(%) extend : (P,List(%)) -> List(%) +--R extend : (P,%) -> List(%) extend : (%,P) -> % +--R first : % -> Union(P,"failed") hash : % -> SingleInteger +--R headReduce : (P,%) -> P headReduced? : % -> Boolean +--R headReduced? : (P,%) -> Boolean infRittWu? : (%,%) -> Boolean +--R initiallyReduce : (P,%) -> P initiallyReduced? : % -> Boolean +--R initials : % -> List(P) internalAugment : (List(P),%) -> % +--R internalAugment : (P,%) -> % intersect : (P,List(%)) -> List(%) +--R intersect : (List(P),%) -> List(%) intersect : (P,%) -> List(%) +--R invertible? : (P,%) -> Boolean invertibleSet : (P,%) -> List(%) +--R last : % -> Union(P,"failed") latex : % -> String +--R mainVariable? : (V,%) -> Boolean mainVariables : % -> List(V) +--R map : ((P -> P),%) -> % mvar : % -> V +--R normalized? : % -> Boolean normalized? : (P,%) -> Boolean +--R purelyAlgebraic? : % -> Boolean purelyAlgebraic? : (P,%) -> Boolean +--R reduceByQuasiMonic : (P,%) -> P removeZero : (P,%) -> P +--R rest : % -> Union(%,"failed") retract : List(P) -> % +--R sample : () -> % select : (%,V) -> Union(P,"failed") +--R stronglyReduce : (P,%) -> P stronglyReduced? : % -> Boolean +--R stronglyReduced? : (P,%) -> Boolean trivialIdeal? : % -> Boolean +--R variables : % -> List(V) zeroSetSplit : List(P) -> List(%) +--R ?~=? : (%,%) -> Boolean +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R algebraicCoefficients? : (P,%) -> Boolean +--R any? : ((P -> Boolean),%) -> Boolean if $ has finiteAggregate +--R augment : (List(P),List(%)) -> List(%) +--R autoReduced? : (%,((P,List(P)) -> Boolean)) -> Boolean +--R basicSet : (List(P),(P -> Boolean),((P,P) -> Boolean)) -> Union(Record(bas: %,top: List(P)),"failed") +--R basicSet : (List(P),((P,P) -> Boolean)) -> Union(Record(bas: %,top: List(P)),"failed") +--R coHeight : % -> NonNegativeInteger if V has FINITE +--R convert : % -> InputForm if P has KONVERT(INFORM) +--R count : ((P -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R count : (P,%) -> NonNegativeInteger if $ has finiteAggregate and P has SETCAT +--R eval : (%,List(Equation(P))) -> % if P has EVALAB(P) and P has SETCAT +--R eval : (%,Equation(P)) -> % if P has EVALAB(P) and P has SETCAT +--R eval : (%,P,P) -> % if P has EVALAB(P) and P has SETCAT +--R eval : (%,List(P),List(P)) -> % if P has EVALAB(P) and P has SETCAT +--R every? : ((P -> Boolean),%) -> Boolean if $ has finiteAggregate +--R extend : (List(P),List(%)) -> List(%) +--R extendIfCan : (%,P) -> Union(%,"failed") +--R find : ((P -> Boolean),%) -> Union(P,"failed") +--R headRemainder : (P,%) -> Record(num: P,den: R) if R has INTDOM +--R initiallyReduced? : (P,%) -> Boolean +--R internalAugment : (P,%,Boolean,Boolean,Boolean,Boolean,Boolean) -> List(%) +--R internalZeroSetSplit : (List(P),Boolean,Boolean,Boolean) -> List(%) +--R intersect : (List(P),List(%)) -> List(%) +--R invertible? : (P,%) -> List(Record(val: Boolean,tower: %)) +--R invertibleElseSplit? : (P,%) -> Union(Boolean,List(%)) +--R lastSubResultant : (P,P,%) -> List(Record(val: P,tower: %)) +--R lastSubResultantElseSplit : (P,P,%) -> Union(P,List(%)) +--R less? : (%,NonNegativeInteger) -> Boolean +--R map! : ((P -> P),%) -> % if $ has shallowlyMutable +--R member? : (P,%) -> Boolean if $ has finiteAggregate and P has SETCAT +--R members : % -> List(P) if $ has finiteAggregate +--R more? : (%,NonNegativeInteger) -> Boolean +--R parts : % -> List(P) if $ has finiteAggregate +--R preprocess : (List(P),Boolean,Boolean) -> Record(val: List(P),towers: List(%)) +--R purelyAlgebraicLeadingMonomial? : (P,%) -> Boolean +--R purelyTranscendental? : (P,%) -> Boolean +--R quasiComponent : % -> Record(close: List(P),open: List(P)) +--R reduce : (P,%,((P,P) -> P),((P,P) -> Boolean)) -> P +--R reduce : (((P,P) -> P),%) -> P if $ has finiteAggregate +--R reduce : (((P,P) -> P),%,P) -> P if $ has finiteAggregate +--R reduce : (((P,P) -> P),%,P,P) -> P if $ has finiteAggregate and P has SETCAT +--R reduced? : (P,%,((P,P) -> Boolean)) -> Boolean +--R remainder : (P,%) -> Record(rnum: R,polnum: P,den: R) if R has INTDOM +--R remove : ((P -> Boolean),%) -> % if $ has finiteAggregate +--R remove : (P,%) -> % if $ has finiteAggregate and P has SETCAT +--R removeDuplicates : % -> % if $ has finiteAggregate and P has SETCAT +--R retractIfCan : List(P) -> Union(%,"failed") +--R rewriteIdealWithHeadRemainder : (List(P),%) -> List(P) if R has INTDOM +--R rewriteIdealWithRemainder : (List(P),%) -> List(P) if R has INTDOM +--R rewriteSetWithReduction : (List(P),%,((P,P) -> P),((P,P) -> Boolean)) -> List(P) +--R roughBase? : % -> Boolean if R has INTDOM +--R roughEqualIdeals? : (%,%) -> Boolean if R has INTDOM +--R roughSubIdeal? : (%,%) -> Boolean if R has INTDOM +--R roughUnitIdeal? : % -> Boolean if R has INTDOM +--R select : ((P -> Boolean),%) -> % if $ has finiteAggregate +--R size? : (%,NonNegativeInteger) -> Boolean +--R sort : (%,V) -> Record(under: %,floor: %,upper: %) +--R squareFreePart : (P,%) -> List(Record(val: P,tower: %)) +--R triangular? : % -> Boolean if R has INTDOM +--R zeroSetSplit : (List(P),Boolean,Boolean,Boolean,Boolean) -> List(%) +--R zeroSetSplit : (List(P),Boolean,Boolean) -> List(%) +--R zeroSetSplit : (List(P),Boolean) -> List(%) +--R zeroSetSplitIntoTriangularSystems : List(P) -> List(Record(close: %,open: List(P))) +--R +--E 35 + )spool )lisp (bye) \end{chunk} @@ -121078,20 +126100,19 @@ RegularTriangularSet(R,E,V,P) : Exports == Implementation where --R------------------------------- Operations -------------------------------- --R ?*? : (%,F) -> % ?*? : (F,%) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ?=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % coerce : FPol -> % ---R coerce : F -> % coerce : Integer -> % ---R coerce : % -> OutputForm hash : % -> SingleInteger ---R latex : % -> String lift : % -> FPol ---R one? : % -> Boolean recip : % -> Union(%,"failed") ---R reduce : FPol -> % sample : () -> % ---R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R coerce : FPol -> % coerce : F -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R lift : % -> FPol one? : % -> Boolean +--R recip : % -> Union(%,"failed") reduce : FPol -> % +--R sample : () -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean --R characteristic : () -> NonNegativeInteger --R subtractIfCan : (%,%) -> Union(%,"failed") --R @@ -121224,7 +126245,7 @@ ResidueRing(F,Expon,VarSet,FPol,LFPol) : Dom == Body --R key? : (Symbol,%) -> Boolean keys : % -> List(Symbol) --R map : ((Any -> Any),%) -> % qelt : (%,Symbol) -> Any --R sample : () -> % setelt : (%,Symbol,Any) -> Any ---R table : () -> % +--R showArrayValues : Boolean -> Boolean table : () -> % --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R ?=? : (%,%) -> Boolean if Any has SETCAT or Record(key: Symbol,entry: Any) has SETCAT --R any? : ((Any -> Boolean),%) -> Boolean if $ has finiteAggregate @@ -121284,7 +126305,6 @@ ResidueRing(F,Expon,VarSet,FPol,LFPol) : Dom == Body --R search : (Symbol,%) -> Union(Any,"failed") --R select : ((Record(key: Symbol,entry: Any) -> Boolean),%) -> % if $ has finiteAggregate --R select! : ((Record(key: Symbol,entry: Any) -> Boolean),%) -> % if $ has finiteAggregate ---R showArrayValues : Boolean -> Boolean --R showScalarValues : Boolean -> Boolean --R size? : (%,NonNegativeInteger) -> Boolean --R swap! : (%,Symbol,Symbol) -> Void if $ has shallowlyMutable @@ -121475,10 +126495,10 @@ Result():Exports==Implementation where --R coerce : % -> OutputForm elt : (%,F,PositiveInteger) -> F --R ?.? : (%,F) -> F hash : % -> SingleInteger --R latex : % -> String lhs : % -> F ---R pattern : % -> Pattern(Base) retract : % -> Equation(F) ---R rhs : % -> F rule : (F,F,List(Symbol)) -> % ---R rule : (F,F) -> % ?~=? : (%,%) -> Boolean ---R quotedOperators : % -> List(Symbol) +--R pattern : % -> Pattern(Base) quotedOperators : % -> List(Symbol) +--R retract : % -> Equation(F) rhs : % -> F +--R rule : (F,F,List(Symbol)) -> % rule : (F,F) -> % +--R ?~=? : (%,%) -> Boolean --R retractIfCan : % -> Union(Equation(F),"failed") --R suchThat : (%,List(Symbol),(List(F) -> Boolean)) -> % --R @@ -121760,14 +126780,13 @@ depending on several "real roots". --R --R------------------------------- Operations -------------------------------- --R ?=? : (%,%) -> Boolean allRootsOf : ThePolDom -> List(%) ---R coerce : % -> OutputForm hash : % -> SingleInteger ---R latex : % -> String left : % -> TheField ---R middle : % -> TheField refine : % -> % ---R right : % -> TheField sign : (ThePolDom,%) -> Integer ---R size : % -> TheField zero? : (ThePolDom,%) -> Boolean ---R ?~=? : (%,%) -> Boolean +--R coerce : % -> OutputForm definingPolynomial : % -> ThePolDom +--R hash : % -> SingleInteger latex : % -> String +--R left : % -> TheField middle : % -> TheField +--R refine : % -> % right : % -> TheField +--R sign : (ThePolDom,%) -> Integer size : % -> TheField +--R zero? : (ThePolDom,%) -> Boolean ?~=? : (%,%) -> Boolean --R approximate : (ThePolDom,%,TheField) -> TheField ---R definingPolynomial : % -> ThePolDom --R mightHaveRoots : (ThePolDom,%) -> Boolean --R negative? : (ThePolDom,%) -> Boolean --R positive? : (ThePolDom,%) -> Boolean @@ -122295,7 +127314,8 @@ RightOpenIntervalRootCharacterization(TheField,ThePolDom) : PUB == PRIV where )set message test on )set message auto off )clear all ---S 1 of 15 + +--S 1 of 16 f := operator 'f --R --R @@ -122303,7 +127323,7 @@ f := operator 'f --R Type: BasicOperator --E 1 ---S 2 of 15 +--S 2 of 16 D(f x,x,7) --R --R @@ -122313,7 +127333,7 @@ D(f x,x,7) --R Type: Expression(Integer) --E 2 ---S 3 of 15 +--S 3 of 16 a := roman(1978 - 1965) --R --R @@ -122321,7 +127341,7 @@ a := roman(1978 - 1965) --R Type: RomanNumeral --E 3 ---S 4 of 15 +--S 4 of 16 x : UTS(ROMAN,'x,0) := x --R --R @@ -122329,7 +127349,7 @@ x : UTS(ROMAN,'x,0) := x --R Type: UnivariateTaylorSeries(RomanNumeral,x,0) --E 4 ---S 5 of 15 +--S 5 of 16 recip(1 - x - x**2) --R --R @@ -122342,13 +127362,13 @@ recip(1 - x - x**2) --R Type: Union(UnivariateTaylorSeries(RomanNumeral,x,0),...) --E 5 ---S 6 of 15 +--S 6 of 16 m : MATRIX FRAC ROMAN --R --R Type: Void --E 6 ---S 7 of 15 +--S 7 of 16 m := matrix [ [1/(i + j) for i in 1..3] for j in 1..3] --R --R @@ -122366,7 +127386,7 @@ m := matrix [ [1/(i + j) for i in 1..3] for j in 1..3] --R Type: Matrix(Fraction(RomanNumeral)) --E 7 ---S 8 of 15 +--S 8 of 16 inverse m --R --R @@ -122378,7 +127398,7 @@ inverse m --R Type: Union(Matrix(Fraction(RomanNumeral)),...) --E 8 ---S 9 of 15 +--S 9 of 16 y := factorial 10 --R --R @@ -122386,7 +127406,7 @@ y := factorial 10 --R Type: PositiveInteger --E 9 ---S 10 of 15 +--S 10 of 16 roman y --R --R @@ -122396,7 +127416,7 @@ roman y --R Type: RomanNumeral --E 10 ---S 11 of 15 +--S 11 of 16 a := roman(78) --R --R @@ -122404,7 +127424,7 @@ a := roman(78) --R Type: RomanNumeral --E 11 ---S 12 of 15 +--S 12 of 16 b := roman(87) --R --R @@ -122412,7 +127432,7 @@ b := roman(87) --R Type: RomanNumeral --E 12 ---S 13 of 15 +--S 13 of 16 a + b --R --R @@ -122420,7 +127440,7 @@ a + b --R Type: RomanNumeral --E 13 ---S 14 of 15 +--S 14 of 16 a * b --R --R @@ -122428,13 +127448,89 @@ a * b --R Type: RomanNumeral --E 14 ---S 15 of 15 +--S 15 of 16 b rem a --R --R --R (15) IX --R Type: RomanNumeral --E 15 + +--S 16 of 16 +)show RomanNumeral +--R +--R RomanNumeral is a domain constructor +--R Abbreviation for RomanNumeral is ROMAN +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for ROMAN +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ? Boolean +--R ?<=? : (%,%) -> Boolean ?=? : (%,%) -> Boolean +--R ?>? : (%,%) -> Boolean ?>=? : (%,%) -> Boolean +--R D : % -> % D : (%,NonNegativeInteger) -> % +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R abs : % -> % addmod : (%,%,%) -> % +--R associates? : (%,%) -> Boolean base : () -> % +--R binomial : (%,%) -> % bit? : (%,%) -> Boolean +--R coerce : Integer -> % coerce : % -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R convert : Symbol -> % convert : % -> DoubleFloat +--R convert : % -> Float convert : % -> Pattern(Integer) +--R convert : % -> InputForm convert : % -> Integer +--R copy : % -> % dec : % -> % +--R differentiate : % -> % even? : % -> Boolean +--R factor : % -> Factored(%) factorial : % -> % +--R gcd : List(%) -> % gcd : (%,%) -> % +--R hash : % -> % hash : % -> SingleInteger +--R inc : % -> % init : () -> % +--R invmod : (%,%) -> % latex : % -> String +--R lcm : List(%) -> % lcm : (%,%) -> % +--R length : % -> % mask : % -> % +--R max : (%,%) -> % min : (%,%) -> % +--R mulmod : (%,%,%) -> % negative? : % -> Boolean +--R nextItem : % -> Union(%,"failed") odd? : % -> Boolean +--R one? : % -> Boolean permutation : (%,%) -> % +--R positive? : % -> Boolean positiveRemainder : (%,%) -> % +--R powmod : (%,%,%) -> % prime? : % -> Boolean +--R ?quo? : (%,%) -> % random : % -> % +--R random : () -> % rational : % -> Fraction(Integer) +--R rational? : % -> Boolean recip : % -> Union(%,"failed") +--R ?rem? : (%,%) -> % retract : % -> Integer +--R roman : Integer -> % roman : Symbol -> % +--R sample : () -> % shift : (%,%) -> % +--R sign : % -> Integer sizeLess? : (%,%) -> Boolean +--R squareFree : % -> Factored(%) squareFreePart : % -> % +--R submod : (%,%,%) -> % symmetricRemainder : (%,%) -> % +--R unit? : % -> Boolean unitCanonical : % -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R characteristic : () -> NonNegativeInteger +--R differentiate : (%,NonNegativeInteger) -> % +--R divide : (%,%) -> Record(quotient: %,remainder: %) +--R euclideanSize : % -> NonNegativeInteger +--R expressIdealMember : (List(%),%) -> Union(List(%),"failed") +--R exquo : (%,%) -> Union(%,"failed") +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") +--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) +--R lcmCoef : (%,%) -> Record(llcmres: %,coeff1: %,coeff2: %) +--R multiEuclidean : (List(%),%) -> Union(List(%),"failed") +--R patternMatch : (%,Pattern(Integer),PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) +--R principalIdeal : List(%) -> Record(coef: List(%),generator: %) +--R rationalIfCan : % -> Union(Fraction(Integer),"failed") +--R reducedSystem : Matrix(%) -> Matrix(Integer) +--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(Integer),vec: Vector(Integer)) +--R retractIfCan : % -> Union(Integer,"failed") +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) +--R +--E 16 + )spool )lisp (bye) \end{chunk} @@ -122738,9 +127834,10 @@ RomanNumeral(): IntegerNumberSystem with --R keys : % -> List(Symbol) map : ((Any -> Any),%) -> % --R qelt : (%,Symbol) -> Any routines : () -> % --R sample : () -> % selectFiniteRoutines : % -> % ---R selectNonFiniteRoutines : % -> % selectODEIVPRoutines : % -> % ---R selectPDERoutines : % -> % setelt : (%,Symbol,Any) -> Any ---R showTheRoutinesTable : () -> % table : () -> % +--R selectIntegrationRoutines : % -> % selectNonFiniteRoutines : % -> % +--R selectODEIVPRoutines : % -> % selectPDERoutines : % -> % +--R setelt : (%,Symbol,Any) -> Any showTheRoutinesTable : () -> % +--R table : () -> % --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R ?=? : (%,%) -> Boolean if Any has SETCAT or Record(key: Symbol,entry: Any) has SETCAT --R any? : ((Any -> Boolean),%) -> Boolean if $ has finiteAggregate @@ -122804,7 +127901,6 @@ RomanNumeral(): IntegerNumberSystem with --R search : (Symbol,%) -> Union(Any,"failed") --R select : ((Record(key: Symbol,entry: Any) -> Boolean),%) -> % if $ has finiteAggregate --R select! : ((Record(key: Symbol,entry: Any) -> Boolean),%) -> % if $ has finiteAggregate ---R selectIntegrationRoutines : % -> % --R selectMultiDimensionalRoutines : % -> % --R selectOptimizationRoutines : % -> % --R selectSumOfSquaresRoutines : % -> % @@ -123501,12 +128597,12 @@ Ruleset(Base, R, F): Exports == Implementation where --R --R------------------------------- Operations -------------------------------- --R ?=? : (%,%) -> Boolean coerce : OutputForm -> % ---R coerce : % -> OutputForm display : % -> Void ---R display : (%,Integer) -> Void epilogue : % -> List(String) ---R formula : % -> List(String) hash : % -> SingleInteger ---R latex : % -> String new : () -> % ---R prologue : % -> List(String) ?~=? : (%,%) -> Boolean ---R convert : (OutputForm,Integer) -> % +--R coerce : % -> OutputForm convert : (OutputForm,Integer) -> % +--R display : % -> Void display : (%,Integer) -> Void +--R epilogue : % -> List(String) formula : % -> List(String) +--R hash : % -> SingleInteger latex : % -> String +--R new : () -> % prologue : % -> List(String) +--R ?~=? : (%,%) -> Boolean --R setEpilogue! : (%,List(String)) -> List(String) --R setFormula! : (%,List(String)) -> List(String) --R setPrologue! : (%,List(String)) -> List(String) @@ -123994,7 +129090,8 @@ ScriptFormulaFormat(): public == private where )set message test on )set message auto off )clear all ---S 1 of 10 + +--S 1 of 11 s := 3..10 --R --R @@ -124002,7 +129099,7 @@ s := 3..10 --R Type: Segment(PositiveInteger) --E 1 ---S 2 of 10 +--S 2 of 11 lo s --R --R @@ -124010,7 +129107,7 @@ lo s --R Type: PositiveInteger --E 2 ---S 3 of 10 +--S 3 of 11 hi s --R --R @@ -124018,7 +129115,7 @@ hi s --R Type: PositiveInteger --E 3 ---S 4 of 10 +--S 4 of 11 t := 10..3 by -2 --R --R @@ -124026,7 +129123,7 @@ t := 10..3 by -2 --R Type: Segment(PositiveInteger) --E 4 ---S 5 of 10 +--S 5 of 11 incr s --R --R @@ -124034,7 +129131,7 @@ incr s --R Type: PositiveInteger --E 5 ---S 6 of 10 +--S 6 of 11 incr t --R --R @@ -124042,7 +129139,7 @@ incr t --R Type: Integer --E 6 ---S 7 of 10 +--S 7 of 11 l := [1..3, 5, 9, 15..11 by -1] --R --R @@ -124050,7 +129147,7 @@ l := [1..3, 5, 9, 15..11 by -1] --R Type: List(Segment(PositiveInteger)) --E 7 ---S 8 of 10 +--S 8 of 11 expand s --R --R @@ -124058,7 +129155,7 @@ expand s --R Type: List(Integer) --E 8 ---S 9 of 10 +--S 9 of 11 expand t --R --R @@ -124066,13 +129163,38 @@ expand t --R Type: List(Integer) --E 9 ---S 10 of 10 +--S 10 of 11 expand l --R --R --R (10) [1,2,3,5,9,15,14,13,12,11] --R Type: List(Integer) --E 10 + +--S 11 of 11 +)show Segment +--R +--R Segment(S: Type) is a domain constructor +--R Abbreviation for Segment is SEG +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for SEG +--R +--R------------------------------- Operations -------------------------------- +--R BY : (%,Integer) -> % ?..? : (S,S) -> % +--R convert : S -> % hi : % -> S +--R high : % -> S incr : % -> Integer +--R latex : % -> String if S has SETCAT lo : % -> S +--R low : % -> S segment : (S,S) -> % +--R ?=? : (%,%) -> Boolean if S has SETCAT +--R coerce : % -> OutputForm if S has SETCAT +--R expand : List(%) -> List(S) if S has ORDRING +--R expand : % -> List(S) if S has ORDRING +--R hash : % -> SingleInteger if S has SETCAT +--R map : ((S -> S),%) -> List(S) if S has ORDRING +--R ?~=? : (%,%) -> Boolean if S has SETCAT +--R +--E 11 + )spool )lisp (bye) \end{chunk} @@ -124269,7 +129391,8 @@ Segment(S:Type): SegmentCategory(S) with )set message test on )set message auto off )clear all ---S 1 of 5 + +--S 1 of 6 x = a..b --R --R @@ -124277,7 +129400,7 @@ x = a..b --R Type: SegmentBinding Symbol --E 1 ---S 2 of 5 +--S 2 of 6 sum(i**2, i = 0..n) --R --R @@ -124288,7 +129411,7 @@ sum(i**2, i = 0..n) --R Type: Fraction Polynomial Integer --E 2 ---S 3 of 5 +--S 3 of 6 sb := y = 1/2..3/2 --R --R @@ -124298,7 +129421,7 @@ sb := y = 1/2..3/2 --R Type: SegmentBinding Fraction Integer --E 3 ---S 4 of 5 +--S 4 of 6 variable(sb) --R --R @@ -124306,7 +129429,7 @@ variable(sb) --R Type: Symbol --E 4 ---S 5 of 5 +--S 5 of 6 segment(sb) --R --R @@ -124315,6 +129438,26 @@ segment(sb) --R 2 2 --R Type: Segment Fraction Integer --E 5 + +--S 6 of 6 +)show SegmentBinding +--R +--R SegmentBinding(S: Type) is a domain constructor +--R Abbreviation for SegmentBinding is SEGBIND +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for SEGBIND +--R +--R------------------------------- Operations -------------------------------- +--R segment : % -> Segment(S) variable : % -> Symbol +--R ?=? : (%,%) -> Boolean if S has SETCAT +--R coerce : % -> OutputForm if S has SETCAT +--R equation : (Symbol,Segment(S)) -> % +--R hash : % -> SingleInteger if S has SETCAT +--R latex : % -> String if S has SETCAT +--R ?~=? : (%,%) -> Boolean if S has SETCAT +--R +--E 6 + )spool )lisp (bye) \end{chunk} @@ -124445,7 +129588,8 @@ SegmentBinding(S:Type): Type with )set message test on )set message auto off )clear all ---S 1 of 20 + +--S 1 of 21 s := set [x**2-1, y**2-1, z**2-1] --R --R @@ -124454,7 +129598,7 @@ s := set [x**2-1, y**2-1, z**2-1] --R Type: Set(Polynomial(Integer)) --E 1 ---S 2 of 20 +--S 2 of 21 t := set [x**i - i+1 for i in 2..10 | prime? i] --R --R @@ -124463,7 +129607,7 @@ t := set [x**i - i+1 for i in 2..10 | prime? i] --R Type: Set(Polynomial(Integer)) --E 2 ---S 3 of 20 +--S 3 of 21 i := intersect(s,t) --R --R @@ -124472,7 +129616,7 @@ i := intersect(s,t) --R Type: Set(Polynomial(Integer)) --E 3 ---S 4 of 20 +--S 4 of 21 u := union(s,t) --R --R @@ -124481,7 +129625,7 @@ u := union(s,t) --R Type: Set(Polynomial(Integer)) --E 4 ---S 5 of 20 +--S 5 of 21 difference(s,t) --R --R @@ -124490,7 +129634,7 @@ difference(s,t) --R Type: Set(Polynomial(Integer)) --E 5 ---S 6 of 20 +--S 6 of 21 symmetricDifference(s,t) --R --R @@ -124499,7 +129643,7 @@ symmetricDifference(s,t) --R Type: Set(Polynomial(Integer)) --E 6 ---S 7 of 20 +--S 7 of 21 member?(y, s) --R --R @@ -124507,7 +129651,7 @@ member?(y, s) --R Type: Boolean --E 7 ---S 8 of 20 +--S 8 of 21 member?((y+1)*(y-1), s) --R --R @@ -124515,7 +129659,7 @@ member?((y+1)*(y-1), s) --R Type: Boolean --E 8 ---S 9 of 20 +--S 9 of 21 subset?(i, s) --R --R @@ -124523,7 +129667,7 @@ subset?(i, s) --R Type: Boolean --E 9 ---S 10 of 20 +--S 10 of 21 subset?(u, s) --R --R @@ -124531,7 +129675,7 @@ subset?(u, s) --R Type: Boolean --E 10 ---S 11 of 20 +--S 11 of 21 gs := set [g for i in 1..11 | primitive?(g := i::PF 11)] --R --R @@ -124539,7 +129683,7 @@ gs := set [g for i in 1..11 | primitive?(g := i::PF 11)] --R Type: Set(PrimeField(11)) --E 11 ---S 12 of 20 +--S 12 of 21 complement gs --R --R @@ -124547,7 +129691,7 @@ complement gs --R Type: Set(PrimeField(11)) --E 12 ---S 13 of 20 +--S 13 of 21 a := set [i**2 for i in 1..5] --R --R @@ -124555,7 +129699,7 @@ a := set [i**2 for i in 1..5] --R Type: Set(PositiveInteger) --E 13 ---S 14 of 20 +--S 14 of 21 insert!(32, a) --R --R @@ -124563,7 +129707,7 @@ insert!(32, a) --R Type: Set(PositiveInteger) --E 14 ---S 15 of 20 +--S 15 of 21 remove!(25, a) --R --R @@ -124571,7 +129715,7 @@ remove!(25, a) --R Type: Set(PositiveInteger) --E 15 ---S 16 of 20 +--S 16 of 21 a --R --R @@ -124579,7 +129723,7 @@ a --R Type: Set(PositiveInteger) --E 16 ---S 17 of 20 +--S 17 of 21 b := b0 := set [i**2 for i in 1..5] --R --R @@ -124587,7 +129731,7 @@ b := b0 := set [i**2 for i in 1..5] --R Type: Set(PositiveInteger) --E 17 ---S 18 of 20 +--S 18 of 21 b := union(b, {32}) --R --R @@ -124595,7 +129739,7 @@ b := union(b, {32}) --R Type: Set(PositiveInteger) --E 18 ---S 19 of 20 +--S 19 of 21 b := difference(b, {25}) --R --R @@ -124603,13 +129747,78 @@ b := difference(b, {25}) --R Type: Set(PositiveInteger) --E 19 ---S 20 of 20 +--S 20 of 21 b0 --R --R --R (20) {1,4,9,16,25} --R Type: Set(PositiveInteger) --E 20 + +--S 21 of 21 +)show Set +--R +--R Set(S: SetCategory) is a domain constructor +--R Abbreviation for Set is SET +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for SET +--R +--R------------------------------- Operations -------------------------------- +--R ? Boolean ?=? : (%,%) -> Boolean +--R bag : List(S) -> % brace : () -> % +--R brace : List(S) -> % coerce : % -> OutputForm +--R construct : List(S) -> % copy : % -> % +--R dictionary : List(S) -> % dictionary : () -> % +--R difference : (%,%) -> % difference : (%,S) -> % +--R empty : () -> % empty? : % -> Boolean +--R eq? : (%,%) -> Boolean extract! : % -> S +--R hash : % -> SingleInteger insert! : (S,%) -> % +--R inspect : % -> S intersect : (%,%) -> % +--R latex : % -> String map : ((S -> S),%) -> % +--R max : % -> S if S has ORDSET min : % -> S if S has ORDSET +--R random : () -> % if S has FINITE sample : () -> % +--R set : () -> % set : List(S) -> % +--R subset? : (%,%) -> Boolean symmetricDifference : (%,%) -> % +--R union : (%,%) -> % union : (%,S) -> % +--R union : (S,%) -> % universe : () -> % if S has FINITE +--R ?~=? : (%,%) -> Boolean +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R cardinality : % -> NonNegativeInteger +--R complement : % -> % if S has FINITE +--R convert : % -> InputForm if S has KONVERT(INFORM) +--R count : (S,%) -> NonNegativeInteger if $ has finiteAggregate and S has SETCAT +--R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R enumerate : () -> List(%) if S has FINITE +--R eval : (%,List(S),List(S)) -> % if S has EVALAB(S) and S has SETCAT +--R eval : (%,S,S) -> % if S has EVALAB(S) and S has SETCAT +--R eval : (%,Equation(S)) -> % if S has EVALAB(S) and S has SETCAT +--R eval : (%,List(Equation(S))) -> % if S has EVALAB(S) and S has SETCAT +--R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R find : ((S -> Boolean),%) -> Union(S,"failed") +--R index : PositiveInteger -> % if S has FINITE +--R less? : (%,NonNegativeInteger) -> Boolean +--R lookup : % -> PositiveInteger if S has FINITE +--R map! : ((S -> S),%) -> % if $ has shallowlyMutable +--R member? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT +--R members : % -> List(S) if $ has finiteAggregate +--R more? : (%,NonNegativeInteger) -> Boolean +--R parts : % -> List(S) if $ has finiteAggregate +--R reduce : (((S,S) -> S),%) -> S if $ has finiteAggregate +--R reduce : (((S,S) -> S),%,S) -> S if $ has finiteAggregate +--R reduce : (((S,S) -> S),%,S,S) -> S if $ has finiteAggregate and S has SETCAT +--R remove : ((S -> Boolean),%) -> % if $ has finiteAggregate +--R remove : (S,%) -> % if $ has finiteAggregate and S has SETCAT +--R remove! : ((S -> Boolean),%) -> % if $ has finiteAggregate +--R remove! : (S,%) -> % if $ has finiteAggregate +--R removeDuplicates : % -> % if $ has finiteAggregate and S has SETCAT +--R select : ((S -> Boolean),%) -> % if $ has finiteAggregate +--R select! : ((S -> Boolean),%) -> % if $ has finiteAggregate +--R size : () -> NonNegativeInteger if S has FINITE +--R size? : (%,NonNegativeInteger) -> Boolean +--R +--E 21 + )spool )lisp (bye) \end{chunk} @@ -125000,6 +130209,7 @@ Set(S:SetCategory): FiniteSetAggregate S == add --S 1 of 1 )show SetOfMIntegersInOneToN +--R --R SetOfMIntegersInOneToN(m: PositiveInteger,n: PositiveInteger) is a domain constructor --R Abbreviation for SetOfMIntegersInOneToN is SETMN --R This constructor is not exposed in this frame. @@ -125235,31 +130445,36 @@ SetOfMIntegersInOneToN(m, n): Exports == Implementation where --R------------------------------- Operations -------------------------------- --R ?*? : (%,R) -> % ?*? : (R,%) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % ---R -? : % -> % ?=? : (%,%) -> Boolean ---R D : (%,(R -> R)) -> % D : % -> % if R has DIFRING ---R 1 : () -> % 0 : () -> % +--R -? : % -> % ?/? : (%,R) -> % if R has FIELD +--R ?=? : (%,%) -> Boolean D : (%,(R -> R)) -> % +--R D : % -> % if R has DIFRING 1 : () -> % +--R 0 : () -> % ?^? : (%,NonNegativeInteger) -> % --R ?^? : (%,PositiveInteger) -> % coefficients : % -> List(R) ---R coerce : Symbol -> % coerce : R -> % ---R coerce : Integer -> % coerce : % -> OutputForm +--R coerce : % -> % if R has INTDOM coerce : Symbol -> % +--R coerce : R -> % coerce : Integer -> % +--R coerce : % -> OutputForm content : % -> R if R has GCDDOM +--R differentiate : (%,(R -> R)) -> % eval : (%,List(%),List(%)) -> % --R eval : (%,%,%) -> % eval : (%,Equation(%)) -> % ---R ground : % -> R ground? : % -> Boolean ---R hash : % -> SingleInteger initial : % -> % ---R isobaric? : % -> Boolean latex : % -> String ---R leadingCoefficient : % -> R leadingMonomial : % -> % ---R map : ((R -> R),%) -> % monomial? : % -> Boolean ---R monomials : % -> List(%) one? : % -> Boolean ---R order : % -> NonNegativeInteger recip : % -> Union(%,"failed") +--R eval : (%,List(Equation(%))) -> % gcd : (%,%) -> % if R has GCDDOM +--R gcd : List(%) -> % if R has GCDDOM ground : % -> R +--R ground? : % -> Boolean hash : % -> SingleInteger +--R initial : % -> % isobaric? : % -> Boolean +--R latex : % -> String lcm : (%,%) -> % if R has GCDDOM +--R lcm : List(%) -> % if R has GCDDOM leadingCoefficient : % -> R +--R leadingMonomial : % -> % map : ((R -> R),%) -> % +--R max : (%,%) -> % if R has ORDSET min : (%,%) -> % if R has ORDSET +--R monomial? : % -> Boolean monomials : % -> List(%) +--R one? : % -> Boolean order : % -> NonNegativeInteger +--R primitiveMonomials : % -> List(%) recip : % -> Union(%,"failed") --R reductum : % -> % retract : % -> Symbol --R retract : % -> R sample : () -> % --R separant : % -> % weight : % -> NonNegativeInteger --R zero? : % -> Boolean ?~=? : (%,%) -> Boolean --R ?*? : (Fraction(Integer),%) -> % if R has ALGEBRA(FRAC(INT)) --R ?*? : (%,Fraction(Integer)) -> % if R has ALGEBRA(FRAC(INT)) ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R ?/? : (%,R) -> % if R has FIELD --R ? Boolean if R has ORDSET --R ?<=? : (%,%) -> Boolean if R has ORDSET --R ?>? : (%,%) -> Boolean if R has ORDSET @@ -125274,7 +130489,6 @@ SetOfMIntegersInOneToN(m, n): Exports == Implementation where --R D : (%,SequentialDifferentialVariable(Symbol),NonNegativeInteger) -> % --R D : (%,List(SequentialDifferentialVariable(Symbol))) -> % --R D : (%,SequentialDifferentialVariable(Symbol)) -> % ---R ?^? : (%,NonNegativeInteger) -> % --R associates? : (%,%) -> Boolean if R has INTDOM --R binomThmExpt : (%,%,NonNegativeInteger) -> % if R has COMRING --R characteristic : () -> NonNegativeInteger @@ -125282,13 +130496,11 @@ SetOfMIntegersInOneToN(m, n): Exports == Implementation where --R coefficient : (%,List(SequentialDifferentialVariable(Symbol)),List(NonNegativeInteger)) -> % --R coefficient : (%,SequentialDifferentialVariable(Symbol),NonNegativeInteger) -> % --R coefficient : (%,IndexedExponents(SequentialDifferentialVariable(Symbol))) -> R ---R coerce : % -> % if R has INTDOM --R coerce : Fraction(Integer) -> % if R has ALGEBRA(FRAC(INT)) or R has RETRACT(FRAC(INT)) --R coerce : SparseMultivariatePolynomial(R,Symbol) -> % --R coerce : SequentialDifferentialVariable(Symbol) -> % --R conditionP : Matrix(%) -> Union(Vector(%),"failed") if $ has CHARNZ and R has PFECAT --R content : (%,SequentialDifferentialVariable(Symbol)) -> % if R has GCDDOM ---R content : % -> R if R has GCDDOM --R convert : % -> InputForm if SequentialDifferentialVariable(Symbol) has KONVERT(INFORM) and R has KONVERT(INFORM) --R convert : % -> Pattern(Integer) if SequentialDifferentialVariable(Symbol) has KONVERT(PATTERN(INT)) and R has KONVERT(PATTERN(INT)) --R convert : % -> Pattern(Float) if SequentialDifferentialVariable(Symbol) has KONVERT(PATTERN(FLOAT)) and R has KONVERT(PATTERN(FLOAT)) @@ -125297,7 +130509,6 @@ SetOfMIntegersInOneToN(m, n): Exports == Implementation where --R degree : (%,SequentialDifferentialVariable(Symbol)) -> NonNegativeInteger --R degree : % -> IndexedExponents(SequentialDifferentialVariable(Symbol)) --R differentialVariables : % -> List(Symbol) ---R differentiate : (%,(R -> R)) -> % --R differentiate : (%,(R -> R),NonNegativeInteger) -> % --R differentiate : (%,List(Symbol),List(NonNegativeInteger)) -> % if R has PDRING(SYMBOL) --R differentiate : (%,Symbol,NonNegativeInteger) -> % if R has PDRING(SYMBOL) @@ -125318,29 +130529,21 @@ SetOfMIntegersInOneToN(m, n): Exports == Implementation where --R eval : (%,SequentialDifferentialVariable(Symbol),%) -> % --R eval : (%,List(SequentialDifferentialVariable(Symbol)),List(R)) -> % --R eval : (%,SequentialDifferentialVariable(Symbol),R) -> % ---R eval : (%,List(%),List(%)) -> % ---R eval : (%,List(Equation(%))) -> % --R exquo : (%,%) -> Union(%,"failed") if R has INTDOM --R exquo : (%,R) -> Union(%,"failed") if R has INTDOM --R factor : % -> Factored(%) if R has PFECAT --R factorPolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has PFECAT --R factorSquareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has PFECAT ---R gcd : (%,%) -> % if R has GCDDOM ---R gcd : List(%) -> % if R has GCDDOM --R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) if R has GCDDOM --R isExpt : % -> Union(Record(var: SequentialDifferentialVariable(Symbol),exponent: NonNegativeInteger),"failed") --R isPlus : % -> Union(List(%),"failed") --R isTimes : % -> Union(List(%),"failed") ---R lcm : (%,%) -> % if R has GCDDOM ---R lcm : List(%) -> % if R has GCDDOM --R lcmCoef : (%,%) -> Record(llcmres: %,coeff1: %,coeff2: %) if R has GCDDOM --R leader : % -> SequentialDifferentialVariable(Symbol) --R mainVariable : % -> Union(SequentialDifferentialVariable(Symbol),"failed") --R makeVariable : % -> (NonNegativeInteger -> %) if R has DIFRING --R makeVariable : Symbol -> (NonNegativeInteger -> %) --R mapExponents : ((IndexedExponents(SequentialDifferentialVariable(Symbol)) -> IndexedExponents(SequentialDifferentialVariable(Symbol))),%) -> % ---R max : (%,%) -> % if R has ORDSET ---R min : (%,%) -> % if R has ORDSET --R minimumDegree : (%,List(SequentialDifferentialVariable(Symbol))) -> List(NonNegativeInteger) --R minimumDegree : (%,SequentialDifferentialVariable(Symbol)) -> NonNegativeInteger --R minimumDegree : % -> IndexedExponents(SequentialDifferentialVariable(Symbol)) @@ -125356,7 +130559,6 @@ SetOfMIntegersInOneToN(m, n): Exports == Implementation where --R patternMatch : (%,Pattern(Float),PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if SequentialDifferentialVariable(Symbol) has PATMAB(FLOAT) and R has PATMAB(FLOAT) --R pomopo! : (%,R,IndexedExponents(SequentialDifferentialVariable(Symbol)),%) -> % --R prime? : % -> Boolean if R has PFECAT ---R primitiveMonomials : % -> List(%) --R primitivePart : (%,SequentialDifferentialVariable(Symbol)) -> % if R has GCDDOM --R primitivePart : % -> % if R has GCDDOM --R reducedSystem : Matrix(%) -> Matrix(R) @@ -125969,31 +131171,36 @@ SExpressionOf(Str, Sym, Int, Flt, Expr): Decl == Body where --R------------------------------- Operations -------------------------------- --R ?*? : (R,%) -> % ?*? : (%,R) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % ---R -? : % -> % ?=? : (%,%) -> Boolean ---R 1 : () -> % 0 : () -> % +--R -? : % -> % ?/? : (%,%) -> % if R has FIELD +--R ?=? : (%,%) -> Boolean 1 : () -> % +--R 0 : () -> % ?^? : (%,NonNegativeInteger) -> % --R ?^? : (%,PositiveInteger) -> % basis : () -> Vector(%) +--R characteristicPolynomial : % -> UP coerce : % -> % if R has FIELD --R coerce : R -> % coerce : Integer -> % --R coerce : % -> OutputForm convert : UP -> % --R convert : % -> UP convert : Vector(R) -> % --R convert : % -> Vector(R) coordinates : % -> Vector(R) --R definingPolynomial : () -> UP discriminant : () -> R ---R discriminant : Vector(%) -> R generator : () -> % ---R hash : % -> SingleInteger inv : % -> % if R has FIELD ---R latex : % -> String lift : % -> UP ---R norm : % -> R one? : % -> Boolean ---R rank : () -> PositiveInteger recip : % -> Union(%,"failed") ---R reduce : UP -> % represents : Vector(R) -> % +--R discriminant : Vector(%) -> R gcd : (%,%) -> % if R has FIELD +--R gcd : List(%) -> % if R has FIELD generator : () -> % +--R hash : % -> SingleInteger init : () -> % if R has FFIELDC +--R inv : % -> % if R has FIELD latex : % -> String +--R lcm : (%,%) -> % if R has FIELD lcm : List(%) -> % if R has FIELD +--R lift : % -> UP norm : % -> R +--R one? : % -> Boolean ?quo? : (%,%) -> % if R has FIELD +--R random : () -> % if R has FINITE rank : () -> PositiveInteger +--R recip : % -> Union(%,"failed") reduce : UP -> % +--R ?rem? : (%,%) -> % if R has FIELD represents : Vector(R) -> % --R retract : % -> R sample : () -> % --R trace : % -> R traceMatrix : () -> Matrix(R) ---R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R unit? : % -> Boolean if R has FIELD zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean --R ?*? : (%,Fraction(Integer)) -> % if R has FIELD --R ?*? : (Fraction(Integer),%) -> % if R has FIELD ---R ?*? : (NonNegativeInteger,%) -> % --R ?**? : (%,Integer) -> % if R has FIELD ---R ?**? : (%,NonNegativeInteger) -> % ---R ?/? : (%,%) -> % if R has FIELD --R D : (%,(R -> R)) -> % if R has FIELD --R D : (%,(R -> R),NonNegativeInteger) -> % if R has FIELD --R D : (%,List(Symbol),List(NonNegativeInteger)) -> % if R has FIELD and R has PDRING(SYMBOL) @@ -126003,14 +131210,11 @@ SExpressionOf(Str, Sym, Int, Flt, Expr): Decl == Body where --R D : (%,NonNegativeInteger) -> % if R has DIFRING and R has FIELD or R has FFIELDC --R D : % -> % if R has DIFRING and R has FIELD or R has FFIELDC --R ?^? : (%,Integer) -> % if R has FIELD ---R ?^? : (%,NonNegativeInteger) -> % --R associates? : (%,%) -> Boolean if R has FIELD --R characteristic : () -> NonNegativeInteger ---R characteristicPolynomial : % -> UP --R charthRoot : % -> Union(%,"failed") if R has CHARNZ --R charthRoot : % -> % if R has FFIELDC --R coerce : Fraction(Integer) -> % if R has FIELD or R has RETRACT(FRAC(INT)) ---R coerce : % -> % if R has FIELD --R conditionP : Matrix(%) -> Union(Vector(%),"failed") if R has FFIELDC --R coordinates : Vector(%) -> Matrix(R) --R coordinates : (Vector(%),Vector(%)) -> Matrix(R) @@ -126036,13 +131240,8 @@ SExpressionOf(Str, Sym, Int, Flt, Expr): Decl == Body where --R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") if R has FIELD --R factor : % -> Factored(%) if R has FIELD --R factorsOfCyclicGroupSize : () -> List(Record(factor: Integer,exponent: Integer)) if R has FFIELDC ---R gcd : (%,%) -> % if R has FIELD ---R gcd : List(%) -> % if R has FIELD --R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) if R has FIELD --R index : PositiveInteger -> % if R has FINITE ---R init : () -> % if R has FFIELDC ---R lcm : (%,%) -> % if R has FIELD ---R lcm : List(%) -> % if R has FIELD --R lcmCoef : (%,%) -> Record(llcmres: %,coeff1: %,coeff2: %) if R has FIELD --R lookup : % -> PositiveInteger if R has FINITE --R minimalPolynomial : % -> UP if R has FIELD @@ -126056,8 +131255,6 @@ SExpressionOf(Str, Sym, Int, Flt, Expr): Decl == Body where --R primitive? : % -> Boolean if R has FFIELDC --R primitiveElement : () -> % if R has FFIELDC --R principalIdeal : List(%) -> Record(coef: List(%),generator: %) if R has FIELD ---R ?quo? : (%,%) -> % if R has FIELD ---R random : () -> % if R has FINITE --R reduce : Fraction(UP) -> Union(%,"failed") if R has FIELD --R reducedSystem : Matrix(%) -> Matrix(R) --R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(R),vec: Vector(R)) @@ -126065,7 +131262,6 @@ SExpressionOf(Str, Sym, Int, Flt, Expr): Decl == Body where --R reducedSystem : Matrix(%) -> Matrix(Integer) if R has LINEXP(INT) --R regularRepresentation : % -> Matrix(R) --R regularRepresentation : (%,Vector(%)) -> Matrix(R) ---R ?rem? : (%,%) -> % if R has FIELD --R representationType : () -> Union("prime",polynomial,normal,cyclic) if R has FFIELDC --R represents : (Vector(R),Vector(%)) -> % --R retract : % -> Fraction(Integer) if R has RETRACT(FRAC(INT)) @@ -126080,7 +131276,6 @@ SExpressionOf(Str, Sym, Int, Flt, Expr): Decl == Body where --R subtractIfCan : (%,%) -> Union(%,"failed") --R tableForDiscreteLogarithm : Integer -> Table(PositiveInteger,NonNegativeInteger) if R has FFIELDC --R traceMatrix : Vector(%) -> Matrix(R) ---R unit? : % -> Boolean if R has FIELD --R unitCanonical : % -> % if R has FIELD --R unitNormal : % -> Record(unit: %,canonical: %,associate: %) if R has FIELD --R @@ -126399,6 +131594,21 @@ specification of an algebraic value. --S 1 of 1 )show SimpleCell +--R +--R SimpleCell(TheField: RealClosedField,ThePols: UnivariatePolynomialCategory(TheField)) is a domain constructor +--R Abbreviation for SimpleCell is SCELL +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for SCELL +--R +--R------------------------------- Operations -------------------------------- +--R coerce : % -> OutputForm hasDimension? : % -> Boolean +--R samplePoint : % -> TheField stablePol : % -> ThePols +--R variableOf : % -> Symbol +--R allSimpleCells : (List(ThePols),Symbol) -> List(%) +--R allSimpleCells : (ThePols,Symbol) -> List(%) +--R pointToCell : (TheField,Boolean,Symbol) -> % +--R separe : (List(TheField),TheField,TheField) -> List(TheField) +--R --E 1 )spool @@ -126687,7 +131897,8 @@ machine integers. )set message test on )set message auto off )clear all ---S 1 of 11 + +--S 1 of 12 min()$SingleInteger --R --R @@ -126695,7 +131906,7 @@ min()$SingleInteger --R Type: SingleInteger --E 1 ---S 2 of 11 +--S 2 of 12 max()$SingleInteger --R --R @@ -126703,7 +131914,7 @@ max()$SingleInteger --R Type: SingleInteger --E 2 ---S 3 of 11 +--S 3 of 12 a := 1234 :: SingleInteger --R --R @@ -126711,7 +131922,7 @@ a := 1234 :: SingleInteger --R Type: SingleInteger --E 3 ---S 4 of 11 +--S 4 of 12 b := 124$SingleInteger --R --R @@ -126719,7 +131930,7 @@ b := 124$SingleInteger --R Type: SingleInteger --E 4 ---S 5 of 11 +--S 5 of 12 gcd(a,b) --R --R @@ -126727,7 +131938,7 @@ gcd(a,b) --R Type: SingleInteger --E 5 ---S 6 of 11 +--S 6 of 12 lcm(a,b) --R --R @@ -126735,7 +131946,7 @@ lcm(a,b) --R Type: SingleInteger --E 6 ---S 7 of 11 +--S 7 of 12 mulmod(5,6,13)$SingleInteger --R --R @@ -126743,7 +131954,7 @@ mulmod(5,6,13)$SingleInteger --R Type: SingleInteger --E 7 ---S 8 of 11 +--S 8 of 12 positiveRemainder(37,13)$SingleInteger --R --R @@ -126751,7 +131962,7 @@ positiveRemainder(37,13)$SingleInteger --R Type: SingleInteger --E 8 ---S 9 of 11 +--S 9 of 12 And(3,4)$SingleInteger --R --R @@ -126759,7 +131970,7 @@ And(3,4)$SingleInteger --R Type: SingleInteger --E 9 ---S 10 of 11 +--S 10 of 12 shift(1,4)$SingleInteger --R --R @@ -126767,13 +131978,96 @@ shift(1,4)$SingleInteger --R Type: SingleInteger --E 10 ---S 11 of 11 +--S 11 of 12 shift(31,-1)$SingleInteger --R --R --R (11) 15 --R Type: SingleInteger --E 11 + +--S 12 of 12 +)show SingleInteger +--R +--R SingleInteger is a domain constructor +--R Abbreviation for SingleInteger is SINT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for SINT +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?/\? : (%,%) -> % +--R ? Boolean ?<=? : (%,%) -> Boolean +--R ?=? : (%,%) -> Boolean ?>? : (%,%) -> Boolean +--R ?>=? : (%,%) -> Boolean And : (%,%) -> % +--R D : % -> % D : (%,NonNegativeInteger) -> % +--R Not : % -> % OMwrite : (%,Boolean) -> String +--R OMwrite : % -> String 1 : () -> % +--R Or : (%,%) -> % 0 : () -> % +--R ?\/? : (%,%) -> % ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,PositiveInteger) -> % abs : % -> % +--R addmod : (%,%,%) -> % associates? : (%,%) -> Boolean +--R base : () -> % binomial : (%,%) -> % +--R bit? : (%,%) -> Boolean coerce : Integer -> % +--R coerce : % -> % coerce : Integer -> % +--R coerce : % -> OutputForm convert : % -> DoubleFloat +--R convert : % -> Float convert : % -> Pattern(Integer) +--R convert : % -> InputForm convert : % -> Integer +--R copy : % -> % dec : % -> % +--R differentiate : % -> % even? : % -> Boolean +--R factor : % -> Factored(%) factorial : % -> % +--R gcd : List(%) -> % gcd : (%,%) -> % +--R hash : % -> % hash : % -> SingleInteger +--R inc : % -> % init : () -> % +--R invmod : (%,%) -> % latex : % -> String +--R lcm : List(%) -> % lcm : (%,%) -> % +--R length : % -> % mask : % -> % +--R max : () -> % max : (%,%) -> % +--R min : () -> % min : (%,%) -> % +--R mulmod : (%,%,%) -> % negative? : % -> Boolean +--R nextItem : % -> Union(%,"failed") not? : % -> % +--R odd? : % -> Boolean one? : % -> Boolean +--R permutation : (%,%) -> % positive? : % -> Boolean +--R positiveRemainder : (%,%) -> % powmod : (%,%,%) -> % +--R prime? : % -> Boolean ?quo? : (%,%) -> % +--R random : % -> % random : () -> % +--R rational : % -> Fraction(Integer) rational? : % -> Boolean +--R recip : % -> Union(%,"failed") ?rem? : (%,%) -> % +--R retract : % -> Integer sample : () -> % +--R shift : (%,%) -> % sign : % -> Integer +--R sizeLess? : (%,%) -> Boolean squareFree : % -> Factored(%) +--R squareFreePart : % -> % submod : (%,%,%) -> % +--R symmetricRemainder : (%,%) -> % unit? : % -> Boolean +--R unitCanonical : % -> % xor : (%,%) -> % +--R zero? : % -> Boolean ~? : % -> % +--R ?~=? : (%,%) -> Boolean +--R OMwrite : (OpenMathDevice,%,Boolean) -> Void +--R OMwrite : (OpenMathDevice,%) -> Void +--R characteristic : () -> NonNegativeInteger +--R differentiate : (%,NonNegativeInteger) -> % +--R divide : (%,%) -> Record(quotient: %,remainder: %) +--R euclideanSize : % -> NonNegativeInteger +--R expressIdealMember : (List(%),%) -> Union(List(%),"failed") +--R exquo : (%,%) -> Union(%,"failed") +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") +--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) +--R lcmCoef : (%,%) -> Record(llcmres: %,coeff1: %,coeff2: %) +--R multiEuclidean : (List(%),%) -> Union(List(%),"failed") +--R patternMatch : (%,Pattern(Integer),PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) +--R principalIdeal : List(%) -> Record(coef: List(%),generator: %) +--R rationalIfCan : % -> Union(Fraction(Integer),"failed") +--R reducedSystem : Matrix(%) -> Matrix(Integer) +--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(Integer),vec: Vector(Integer)) +--R retractIfCan : % -> Union(Integer,"failed") +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) +--R +--E 12 + )spool )lisp (bye) \end{chunk} @@ -127179,6 +132473,7 @@ SingleInteger(): Join(IntegerNumberSystem,Logic,OpenMath) with --S 1 of 1 )show SingletonAsOrderedSet +--R --R SingletonAsOrderedSet is a domain constructor --R Abbreviation for SingletonAsOrderedSet is SAOS --R This constructor is not exposed in this frame. @@ -127281,18 +132576,17 @@ SingletonAsOrderedSet(): OrderedSet with --R coerce : % -> Matrix(D) coerce : % -> OutputForm --R copy : % -> % deleteRow! : (%,Integer) -> Void --R elimZeroCols! : % -> Void elt : (%,Integer,C) -> D ---R horizJoin : (%,%) -> % join : (%,%) -> % ---R ncols : % -> NonNegativeInteger new : (List(C),Integer) -> % ---R nrows : % -> NonNegativeInteger setelt! : (%,Integer,C,D) -> Void +--R extract : (%,Integer,Integer) -> % horizJoin : (%,%) -> % +--R join : (%,%) -> % ncols : % -> NonNegativeInteger +--R new : (List(C),Integer) -> % nrows : % -> NonNegativeInteger +--R purge! : (%,(C -> Boolean)) -> Void setelt! : (%,Integer,C,D) -> Void --R ?*? : (Matrix(Fraction(D)),%) -> % if D has INTDOM --R appendRow! : (%,Record(Indices: List(C),Entries: List(D))) -> Void --R consRow! : (%,Record(Indices: List(C),Entries: List(D))) -> Void ---R extract : (%,Integer,Integer) -> % --R horizSplit : (%,C) -> Record(Left: %,Right: %) --R pivot : (%,Integer) -> Record(Index: C,Entry: D) --R pivots : % -> Record(Indices: List(C),Entries: List(D)) --R primitiveRowEchelon : % -> Record(Ech: %,Lt: Matrix(Fraction(D)),Pivots: List(D),Rank: NonNegativeInteger) if D has GCDDOM ---R purge! : (%,(C -> Boolean)) -> Void --R row : (%,Integer) -> Record(Indices: List(C),Entries: List(D)) --R rowEchelon : % -> Record(Ech: %,Lt: Matrix(D),Pivots: List(D),Rank: NonNegativeInteger) --R setGcdMode : Symbol -> Symbol if D has GCDDOM @@ -128151,38 +133445,41 @@ SparseEchelonMatrix(C : OrderedSet, D : Ring) : Cat == Def where --R------------------------------- Operations -------------------------------- --R ?*? : (%,R) -> % ?*? : (R,%) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % ---R -? : % -> % ?=? : (%,%) -> Boolean ---R D : (%,List(VarSet)) -> % D : (%,VarSet) -> % ---R 1 : () -> % 0 : () -> % +--R -? : % -> % ?/? : (%,R) -> % if R has FIELD +--R ?=? : (%,%) -> Boolean D : (%,List(VarSet)) -> % +--R D : (%,VarSet) -> % 1 : () -> % +--R 0 : () -> % ?^? : (%,NonNegativeInteger) -> % --R ?^? : (%,PositiveInteger) -> % coefficients : % -> List(R) ---R coerce : VarSet -> % coerce : R -> % ---R coerce : Integer -> % coerce : % -> OutputForm +--R coerce : % -> % if R has INTDOM coerce : VarSet -> % +--R coerce : R -> % coerce : Integer -> % +--R coerce : % -> OutputForm content : % -> R if R has GCDDOM --R differentiate : (%,VarSet) -> % eval : (%,VarSet,%) -> % ---R eval : (%,VarSet,R) -> % eval : (%,%,%) -> % ---R eval : (%,Equation(%)) -> % ground : % -> R +--R eval : (%,VarSet,R) -> % eval : (%,List(%),List(%)) -> % +--R eval : (%,%,%) -> % eval : (%,Equation(%)) -> % +--R eval : (%,List(Equation(%))) -> % gcd : (%,%) -> % if R has GCDDOM +--R gcd : List(%) -> % if R has GCDDOM ground : % -> R --R ground? : % -> Boolean hash : % -> SingleInteger ---R latex : % -> String leadingCoefficient : % -> R +--R latex : % -> String lcm : (%,%) -> % if R has GCDDOM +--R lcm : List(%) -> % if R has GCDDOM leadingCoefficient : % -> R --R leadingMonomial : % -> % map : ((R -> R),%) -> % +--R max : (%,%) -> % if R has ORDSET min : (%,%) -> % if R has ORDSET --R monomial? : % -> Boolean monomials : % -> List(%) ---R one? : % -> Boolean recip : % -> Union(%,"failed") ---R reductum : % -> % retract : % -> VarSet ---R retract : % -> R sample : () -> % ---R variables : % -> List(VarSet) zero? : % -> Boolean ---R ?~=? : (%,%) -> Boolean +--R one? : % -> Boolean primitiveMonomials : % -> List(%) +--R recip : % -> Union(%,"failed") reductum : % -> % +--R retract : % -> VarSet retract : % -> R +--R sample : () -> % variables : % -> List(VarSet) +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean --R ?*? : (Fraction(Integer),%) -> % if R has ALGEBRA(FRAC(INT)) --R ?*? : (%,Fraction(Integer)) -> % if R has ALGEBRA(FRAC(INT)) ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R ?/? : (%,R) -> % if R has FIELD --R ? Boolean if R has ORDSET --R ?<=? : (%,%) -> Boolean if R has ORDSET --R ?>? : (%,%) -> Boolean if R has ORDSET --R ?>=? : (%,%) -> Boolean if R has ORDSET --R D : (%,List(VarSet),List(NonNegativeInteger)) -> % --R D : (%,VarSet,NonNegativeInteger) -> % ---R ?^? : (%,NonNegativeInteger) -> % --R associates? : (%,%) -> Boolean if R has INTDOM --R binomThmExpt : (%,%,NonNegativeInteger) -> % if R has COMRING --R characteristic : () -> NonNegativeInteger @@ -128191,10 +133488,8 @@ SparseEchelonMatrix(C : OrderedSet, D : Ring) : Cat == Def where --R coefficient : (%,VarSet,NonNegativeInteger) -> % --R coefficient : (%,IndexedExponents(VarSet)) -> R --R coerce : Fraction(Integer) -> % if R has ALGEBRA(FRAC(INT)) or R has RETRACT(FRAC(INT)) ---R coerce : % -> % if R has INTDOM --R conditionP : Matrix(%) -> Union(Vector(%),"failed") if $ has CHARNZ and R has PFECAT --R content : (%,VarSet) -> % if R has GCDDOM ---R content : % -> R if R has GCDDOM --R convert : % -> InputForm if R has KONVERT(INFORM) and VarSet has KONVERT(INFORM) --R convert : % -> Pattern(Integer) if R has KONVERT(PATTERN(INT)) and VarSet has KONVERT(PATTERN(INT)) --R convert : % -> Pattern(Float) if R has KONVERT(PATTERN(FLOAT)) and VarSet has KONVERT(PATTERN(FLOAT)) @@ -128207,26 +133502,18 @@ SparseEchelonMatrix(C : OrderedSet, D : Ring) : Cat == Def where --R discriminant : (%,VarSet) -> % if R has COMRING --R eval : (%,List(VarSet),List(%)) -> % --R eval : (%,List(VarSet),List(R)) -> % ---R eval : (%,List(%),List(%)) -> % ---R eval : (%,List(Equation(%))) -> % --R exquo : (%,%) -> Union(%,"failed") if R has INTDOM --R exquo : (%,R) -> Union(%,"failed") if R has INTDOM --R factor : % -> Factored(%) if R has PFECAT --R factorPolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has PFECAT --R factorSquareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has PFECAT ---R gcd : (%,%) -> % if R has GCDDOM ---R gcd : List(%) -> % if R has GCDDOM --R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) if R has GCDDOM --R isExpt : % -> Union(Record(var: VarSet,exponent: NonNegativeInteger),"failed") --R isPlus : % -> Union(List(%),"failed") --R isTimes : % -> Union(List(%),"failed") ---R lcm : (%,%) -> % if R has GCDDOM ---R lcm : List(%) -> % if R has GCDDOM --R lcmCoef : (%,%) -> Record(llcmres: %,coeff1: %,coeff2: %) if R has GCDDOM --R mainVariable : % -> Union(VarSet,"failed") --R mapExponents : ((IndexedExponents(VarSet) -> IndexedExponents(VarSet)),%) -> % ---R max : (%,%) -> % if R has ORDSET ---R min : (%,%) -> % if R has ORDSET --R minimumDegree : (%,List(VarSet)) -> List(NonNegativeInteger) --R minimumDegree : (%,VarSet) -> NonNegativeInteger --R minimumDegree : % -> IndexedExponents(VarSet) @@ -128241,7 +133528,6 @@ SparseEchelonMatrix(C : OrderedSet, D : Ring) : Cat == Def where --R patternMatch : (%,Pattern(Float),PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if R has PATMAB(FLOAT) and VarSet has PATMAB(FLOAT) --R pomopo! : (%,R,IndexedExponents(VarSet),%) -> % --R prime? : % -> Boolean if R has PFECAT ---R primitiveMonomials : % -> List(%) --R primitivePart : (%,VarSet) -> % if R has GCDDOM --R primitivePart : % -> % if R has GCDDOM --R reducedSystem : Matrix(%) -> Matrix(R) @@ -128953,7 +134239,7 @@ SparseMultivariatePolynomial(R: Ring,VarSet: OrderedSet): C == T where )set message auto off )clear all ---S 1 of 12 +--S 1 of 13 xts:=x::TaylorSeries Fraction Integer --R --R @@ -128961,7 +134247,7 @@ xts:=x::TaylorSeries Fraction Integer --R Type: TaylorSeries(Fraction(Integer)) --E 1 ---S 2 of 12 +--S 2 of 13 yts:=y::TaylorSeries Fraction Integer --R --R @@ -128969,7 +134255,7 @@ yts:=y::TaylorSeries Fraction Integer --R Type: TaylorSeries(Fraction(Integer)) --E 2 ---S 3 of 12 +--S 3 of 13 zts:=z::TaylorSeries Fraction Integer --R --R @@ -128977,7 +134263,7 @@ zts:=z::TaylorSeries Fraction Integer --R Type: TaylorSeries(Fraction(Integer)) --E 3 ---S 4 of 12 +--S 4 of 13 t1:=sin(xts) --R --R @@ -128987,7 +134273,7 @@ t1:=sin(xts) --R Type: TaylorSeries(Fraction(Integer)) --E 4 ---S 5 of 12 +--S 5 of 13 coefficient(t1,3) --R --R @@ -128997,7 +134283,7 @@ coefficient(t1,3) --R Type: Polynomial(Fraction(Integer)) --E 5 ---S 6 of 12 +--S 6 of 13 coefficient(t1,monomial(3,x)$IndexedExponents Symbol) --R --R @@ -129007,7 +134293,7 @@ coefficient(t1,monomial(3,x)$IndexedExponents Symbol) --R Type: Fraction(Integer) --E 6 ---S 7 of 12 +--S 7 of 13 t2:=sin(xts + yts) --R --R @@ -129042,7 +134328,7 @@ t2:=sin(xts + yts) --R Type: TaylorSeries(Fraction(Integer)) --E 7 ---S 8 of 12 +--S 8 of 13 coefficient(t2,3) --R --R @@ -129052,7 +134338,7 @@ coefficient(t2,3) --R Type: Polynomial(Fraction(Integer)) --E 8 ---S 9 of 12 +--S 9 of 13 coefficient(t2,monomial(3,x)$IndexedExponents Symbol) --R --R @@ -129062,7 +134348,7 @@ coefficient(t2,monomial(3,x)$IndexedExponents Symbol) --R Type: Fraction(Integer) --E 9 ---S 10 of 12 +--S 10 of 13 polynomial(t2,5) --R --R @@ -129077,14 +134363,136 @@ polynomial(t2,5) --R Type: Polynomial(Fraction(Integer)) --E 10 ---S 11 of 12 +--S 11 of 13 t3:=coefficients(t2) +--R +--R There are 4 exposed and 3 unexposed library operations named +--R coefficients having 1 argument(s) but none was determined to be +--R applicable. Use HyperDoc Browse, or issue +--R )display op coefficients +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R coefficients with argument type(s) +--R TaylorSeries(Fraction(Integer)) +--R Perhaps you should use @ to indicate the required return type, or +--R $ to specify which version of the function you need. --E 11 ---S 12 of 12 +--S 12 of 13 t4:=series(t3) +--R +--R +--R (11) t3 +--R Type: UnivariatePuiseuxSeries(Expression(Integer),t3,0) --E 12 +--S 13 of 13 +)show SparseMultivariateTaylorSeries +--R +--R SparseMultivariateTaylorSeries(Coef: Ring,Var: OrderedSet,SMP: PolynomialCategory(Coef,IndexedExponents(Var),Var)) is a domain constructor +--R Abbreviation for SparseMultivariateTaylorSeries is SMTS +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for SMTS +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (SMP,%) -> % ?*? : (%,Coef) -> % +--R ?*? : (Coef,%) -> % ?*? : (%,%) -> % +--R ?*? : (Integer,%) -> % ?*? : (NonNegativeInteger,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,NonNegativeInteger) -> % +--R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % +--R ?-? : (%,%) -> % -? : % -> % +--R ?=? : (%,%) -> Boolean D : (%,List(Var)) -> % +--R D : (%,Var) -> % 1 : () -> % +--R 0 : () -> % ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,PositiveInteger) -> % coefficients : % -> Stream(SMP) +--R coerce : SMP -> % coerce : Var -> % +--R coerce : % -> % if Coef has INTDOM coerce : Integer -> % +--R coerce : % -> OutputForm complete : % -> % +--R degree : % -> IndexedExponents(Var) differentiate : (%,List(Var)) -> % +--R differentiate : (%,Var) -> % eval : (%,List(%),List(%)) -> % +--R eval : (%,%,%) -> % eval : (%,Equation(%)) -> % +--R eval : (%,List(Equation(%))) -> % eval : (%,List(Var),List(%)) -> % +--R eval : (%,Var,%) -> % hash : % -> SingleInteger +--R latex : % -> String leadingCoefficient : % -> Coef +--R leadingMonomial : % -> % map : ((Coef -> Coef),%) -> % +--R monomial? : % -> Boolean one? : % -> Boolean +--R pole? : % -> Boolean recip : % -> Union(%,"failed") +--R reductum : % -> % sample : () -> % +--R series : Stream(SMP) -> % variables : % -> List(Var) +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (Fraction(Integer),%) -> % if Coef has ALGEBRA(FRAC(INT)) +--R ?*? : (%,Fraction(Integer)) -> % if Coef has ALGEBRA(FRAC(INT)) +--R ?**? : (%,Fraction(Integer)) -> % if Coef has ALGEBRA(FRAC(INT)) +--R ?**? : (%,%) -> % if Coef has ALGEBRA(FRAC(INT)) +--R ?/? : (%,Coef) -> % if Coef has FIELD +--R D : (%,List(Var),List(NonNegativeInteger)) -> % +--R D : (%,Var,NonNegativeInteger) -> % +--R acos : % -> % if Coef has ALGEBRA(FRAC(INT)) +--R acosh : % -> % if Coef has ALGEBRA(FRAC(INT)) +--R acot : % -> % if Coef has ALGEBRA(FRAC(INT)) +--R acoth : % -> % if Coef has ALGEBRA(FRAC(INT)) +--R acsc : % -> % if Coef has ALGEBRA(FRAC(INT)) +--R acsch : % -> % if Coef has ALGEBRA(FRAC(INT)) +--R asec : % -> % if Coef has ALGEBRA(FRAC(INT)) +--R asech : % -> % if Coef has ALGEBRA(FRAC(INT)) +--R asin : % -> % if Coef has ALGEBRA(FRAC(INT)) +--R asinh : % -> % if Coef has ALGEBRA(FRAC(INT)) +--R associates? : (%,%) -> Boolean if Coef has INTDOM +--R atan : % -> % if Coef has ALGEBRA(FRAC(INT)) +--R atanh : % -> % if Coef has ALGEBRA(FRAC(INT)) +--R characteristic : () -> NonNegativeInteger +--R charthRoot : % -> Union(%,"failed") if Coef has CHARNZ +--R coefficient : (%,NonNegativeInteger) -> SMP +--R coefficient : (%,List(Var),List(NonNegativeInteger)) -> % +--R coefficient : (%,Var,NonNegativeInteger) -> % +--R coefficient : (%,IndexedExponents(Var)) -> Coef +--R coerce : Fraction(Integer) -> % if Coef has ALGEBRA(FRAC(INT)) +--R coerce : Coef -> % if Coef has COMRING +--R cos : % -> % if Coef has ALGEBRA(FRAC(INT)) +--R cosh : % -> % if Coef has ALGEBRA(FRAC(INT)) +--R cot : % -> % if Coef has ALGEBRA(FRAC(INT)) +--R coth : % -> % if Coef has ALGEBRA(FRAC(INT)) +--R csc : % -> % if Coef has ALGEBRA(FRAC(INT)) +--R csch : % -> % if Coef has ALGEBRA(FRAC(INT)) +--R csubst : (List(Var),List(Stream(SMP))) -> (SMP -> Stream(SMP)) +--R differentiate : (%,List(Var),List(NonNegativeInteger)) -> % +--R differentiate : (%,Var,NonNegativeInteger) -> % +--R exp : % -> % if Coef has ALGEBRA(FRAC(INT)) +--R exquo : (%,%) -> Union(%,"failed") if Coef has INTDOM +--R extend : (%,NonNegativeInteger) -> % +--R fintegrate : ((() -> %),Var,Coef) -> % if Coef has ALGEBRA(FRAC(INT)) +--R integrate : (%,Var,Coef) -> % if Coef has ALGEBRA(FRAC(INT)) +--R integrate : (%,Var) -> % if Coef has ALGEBRA(FRAC(INT)) +--R log : % -> % if Coef has ALGEBRA(FRAC(INT)) +--R monomial : (%,List(Var),List(NonNegativeInteger)) -> % +--R monomial : (%,Var,NonNegativeInteger) -> % +--R monomial : (Coef,IndexedExponents(Var)) -> % +--R monomial : (%,Var,IndexedExponents(Var)) -> % +--R monomial : (%,List(Var),List(IndexedExponents(Var))) -> % +--R nthRoot : (%,Integer) -> % if Coef has ALGEBRA(FRAC(INT)) +--R order : (%,Var,NonNegativeInteger) -> NonNegativeInteger +--R order : (%,Var) -> NonNegativeInteger +--R pi : () -> % if Coef has ALGEBRA(FRAC(INT)) +--R polynomial : (%,NonNegativeInteger,NonNegativeInteger) -> Polynomial(Coef) +--R polynomial : (%,NonNegativeInteger) -> Polynomial(Coef) +--R sec : % -> % if Coef has ALGEBRA(FRAC(INT)) +--R sech : % -> % if Coef has ALGEBRA(FRAC(INT)) +--R sin : % -> % if Coef has ALGEBRA(FRAC(INT)) +--R sinh : % -> % if Coef has ALGEBRA(FRAC(INT)) +--R sqrt : % -> % if Coef has ALGEBRA(FRAC(INT)) +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R tan : % -> % if Coef has ALGEBRA(FRAC(INT)) +--R tanh : % -> % if Coef has ALGEBRA(FRAC(INT)) +--R unit? : % -> Boolean if Coef has INTDOM +--R unitCanonical : % -> % if Coef has INTDOM +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) if Coef has INTDOM +--R +--E 13 + )spool )lisp (bye) \end{chunk} @@ -129656,7 +135064,8 @@ SparseMultivariateTaylorSeries(Coef,Var,SMP):_ )set message test on )set message auto off )clear all ---S 1 of 7 + +--S 1 of 8 t: SparseTable(Integer, String, "Try again!") := table() --R --R @@ -129664,7 +135073,7 @@ t: SparseTable(Integer, String, "Try again!") := table() --R Type: SparseTable(Integer,String,Try again!) --E 1 ---S 2 of 7 +--S 2 of 8 t.3 := "Number three" --R --R @@ -129672,7 +135081,7 @@ t.3 := "Number three" --R Type: String --E 2 ---S 3 of 7 +--S 3 of 8 t.4 := "Number four" --R --R @@ -129680,7 +135089,7 @@ t.4 := "Number four" --R Type: String --E 3 ---S 4 of 7 +--S 4 of 8 t.3 --R --R @@ -129688,7 +135097,7 @@ t.3 --R Type: String --E 4 ---S 5 of 7 +--S 5 of 8 t.2 --R --R @@ -129696,7 +135105,7 @@ t.2 --R Type: String --E 5 ---S 6 of 7 +--S 6 of 8 keys t --R --R @@ -129704,13 +135113,97 @@ keys t --R Type: List(Integer) --E 6 ---S 7 of 7 +--S 7 of 8 entries t --R --R --R (7) ["Number four","Number three"] --R Type: List(String) --E 7 + +--S 8 of 8 +)show SparseTable +--R +--R SparseTable(Key: SetCategory,Ent: SetCategory,dent: Ent) is a domain constructor +--R Abbreviation for SparseTable is STBL +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for STBL +--R +--R------------------------------- Operations -------------------------------- +--R copy : % -> % dictionary : () -> % +--R elt : (%,Key,Ent) -> Ent ?.? : (%,Key) -> Ent +--R empty : () -> % empty? : % -> Boolean +--R entries : % -> List(Ent) eq? : (%,%) -> Boolean +--R first : % -> Ent if Key has ORDSET index? : (Key,%) -> Boolean +--R indices : % -> List(Key) key? : (Key,%) -> Boolean +--R keys : % -> List(Key) map : ((Ent -> Ent),%) -> % +--R qelt : (%,Key) -> Ent sample : () -> % +--R setelt : (%,Key,Ent) -> Ent table : () -> % +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R ?=? : (%,%) -> Boolean if Record(key: Key,entry: Ent) has SETCAT or Ent has SETCAT +--R any? : ((Ent -> Boolean),%) -> Boolean if $ has finiteAggregate +--R any? : ((Record(key: Key,entry: Ent) -> Boolean),%) -> Boolean if $ has finiteAggregate +--R bag : List(Record(key: Key,entry: Ent)) -> % +--R coerce : % -> OutputForm if Record(key: Key,entry: Ent) has SETCAT or Ent has SETCAT +--R construct : List(Record(key: Key,entry: Ent)) -> % +--R convert : % -> InputForm if Record(key: Key,entry: Ent) has KONVERT(INFORM) +--R count : ((Ent -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R count : (Ent,%) -> NonNegativeInteger if $ has finiteAggregate and Ent has SETCAT +--R count : (Record(key: Key,entry: Ent),%) -> NonNegativeInteger if $ has finiteAggregate and Record(key: Key,entry: Ent) has SETCAT +--R count : ((Record(key: Key,entry: Ent) -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R dictionary : List(Record(key: Key,entry: Ent)) -> % +--R entry? : (Ent,%) -> Boolean if $ has finiteAggregate and Ent has SETCAT +--R eval : (%,List(Equation(Ent))) -> % if Ent has EVALAB(Ent) and Ent has SETCAT +--R eval : (%,Equation(Ent)) -> % if Ent has EVALAB(Ent) and Ent has SETCAT +--R eval : (%,Ent,Ent) -> % if Ent has EVALAB(Ent) and Ent has SETCAT +--R eval : (%,List(Ent),List(Ent)) -> % if Ent has EVALAB(Ent) and Ent has SETCAT +--R eval : (%,List(Record(key: Key,entry: Ent)),List(Record(key: Key,entry: Ent))) -> % if Record(key: Key,entry: Ent) has EVALAB(Record(key: Key,entry: Ent)) and Record(key: Key,entry: Ent) has SETCAT +--R eval : (%,Record(key: Key,entry: Ent),Record(key: Key,entry: Ent)) -> % if Record(key: Key,entry: Ent) has EVALAB(Record(key: Key,entry: Ent)) and Record(key: Key,entry: Ent) has SETCAT +--R eval : (%,Equation(Record(key: Key,entry: Ent))) -> % if Record(key: Key,entry: Ent) has EVALAB(Record(key: Key,entry: Ent)) and Record(key: Key,entry: Ent) has SETCAT +--R eval : (%,List(Equation(Record(key: Key,entry: Ent)))) -> % if Record(key: Key,entry: Ent) has EVALAB(Record(key: Key,entry: Ent)) and Record(key: Key,entry: Ent) has SETCAT +--R every? : ((Ent -> Boolean),%) -> Boolean if $ has finiteAggregate +--R every? : ((Record(key: Key,entry: Ent) -> Boolean),%) -> Boolean if $ has finiteAggregate +--R extract! : % -> Record(key: Key,entry: Ent) +--R fill! : (%,Ent) -> % if $ has shallowlyMutable +--R find : ((Record(key: Key,entry: Ent) -> Boolean),%) -> Union(Record(key: Key,entry: Ent),"failed") +--R hash : % -> SingleInteger if Record(key: Key,entry: Ent) has SETCAT or Ent has SETCAT +--R insert! : (Record(key: Key,entry: Ent),%) -> % +--R inspect : % -> Record(key: Key,entry: Ent) +--R latex : % -> String if Record(key: Key,entry: Ent) has SETCAT or Ent has SETCAT +--R less? : (%,NonNegativeInteger) -> Boolean +--R map : (((Ent,Ent) -> Ent),%,%) -> % +--R map : ((Record(key: Key,entry: Ent) -> Record(key: Key,entry: Ent)),%) -> % +--R map! : ((Ent -> Ent),%) -> % if $ has shallowlyMutable +--R map! : ((Record(key: Key,entry: Ent) -> Record(key: Key,entry: Ent)),%) -> % if $ has shallowlyMutable +--R maxIndex : % -> Key if Key has ORDSET +--R member? : (Ent,%) -> Boolean if $ has finiteAggregate and Ent has SETCAT +--R member? : (Record(key: Key,entry: Ent),%) -> Boolean if $ has finiteAggregate and Record(key: Key,entry: Ent) has SETCAT +--R members : % -> List(Ent) if $ has finiteAggregate +--R members : % -> List(Record(key: Key,entry: Ent)) if $ has finiteAggregate +--R minIndex : % -> Key if Key has ORDSET +--R more? : (%,NonNegativeInteger) -> Boolean +--R parts : % -> List(Ent) if $ has finiteAggregate +--R parts : % -> List(Record(key: Key,entry: Ent)) if $ has finiteAggregate +--R qsetelt! : (%,Key,Ent) -> Ent if $ has shallowlyMutable +--R reduce : (((Record(key: Key,entry: Ent),Record(key: Key,entry: Ent)) -> Record(key: Key,entry: Ent)),%) -> Record(key: Key,entry: Ent) if $ has finiteAggregate +--R reduce : (((Record(key: Key,entry: Ent),Record(key: Key,entry: Ent)) -> Record(key: Key,entry: Ent)),%,Record(key: Key,entry: Ent)) -> Record(key: Key,entry: Ent) if $ has finiteAggregate +--R reduce : (((Record(key: Key,entry: Ent),Record(key: Key,entry: Ent)) -> Record(key: Key,entry: Ent)),%,Record(key: Key,entry: Ent),Record(key: Key,entry: Ent)) -> Record(key: Key,entry: Ent) if $ has finiteAggregate and Record(key: Key,entry: Ent) has SETCAT +--R remove : ((Record(key: Key,entry: Ent) -> Boolean),%) -> % if $ has finiteAggregate +--R remove : (Record(key: Key,entry: Ent),%) -> % if $ has finiteAggregate and Record(key: Key,entry: Ent) has SETCAT +--R remove! : (Key,%) -> Union(Ent,"failed") +--R remove! : ((Record(key: Key,entry: Ent) -> Boolean),%) -> % if $ has finiteAggregate +--R remove! : (Record(key: Key,entry: Ent),%) -> % if $ has finiteAggregate +--R removeDuplicates : % -> % if $ has finiteAggregate and Record(key: Key,entry: Ent) has SETCAT +--R search : (Key,%) -> Union(Ent,"failed") +--R select : ((Record(key: Key,entry: Ent) -> Boolean),%) -> % if $ has finiteAggregate +--R select! : ((Record(key: Key,entry: Ent) -> Boolean),%) -> % if $ has finiteAggregate +--R size? : (%,NonNegativeInteger) -> Boolean +--R swap! : (%,Key,Key) -> Void if $ has shallowlyMutable +--R table : List(Record(key: Key,entry: Ent)) -> % +--R ?~=? : (%,%) -> Boolean if Record(key: Key,entry: Ent) has SETCAT or Ent has SETCAT +--R +--E 8 + )spool )lisp (bye) \end{chunk} @@ -129881,16 +135374,18 @@ SparseTable(Key:SetCategory, Ent:SetCategory, dent:Ent) == --R------------------------------- Operations -------------------------------- --R ?*? : (Coef,%) -> % ?*? : (%,Coef) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ?=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % center : % -> Coef ---R coefficient : (%,Integer) -> Coef coerce : Variable(var) -> % ---R coerce : Integer -> % coerce : % -> OutputForm ---R complete : % -> % degree : % -> Integer ---R ?.? : (%,Integer) -> Coef extend : (%,Integer) -> % ---R hash : % -> SingleInteger latex : % -> String +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R center : % -> Coef coefficient : (%,Integer) -> Coef +--R coerce : Variable(var) -> % coerce : Integer -> % +--R coerce : % -> OutputForm complete : % -> % +--R degree : % -> Integer ?.? : (%,Integer) -> Coef +--R extend : (%,Integer) -> % hash : % -> SingleInteger +--R inv : % -> % if Coef has FIELD latex : % -> String --R leadingCoefficient : % -> Coef leadingMonomial : % -> % --R map : ((Coef -> Coef),%) -> % monomial : (Coef,Integer) -> % --R monomial? : % -> Boolean one? : % -> Boolean @@ -129904,11 +135399,9 @@ SparseTable(Key:SetCategory, Ent:SetCategory, dent:Ent) == --R ?*? : (Fraction(Integer),%) -> % if Coef has ALGEBRA(FRAC(INT)) --R ?*? : (SparseUnivariateTaylorSeries(Coef,var,cen),%) -> % if Coef has FIELD --R ?*? : (%,SparseUnivariateTaylorSeries(Coef,var,cen)) -> % if Coef has FIELD ---R ?*? : (NonNegativeInteger,%) -> % --R ?**? : (%,Fraction(Integer)) -> % if Coef has ALGEBRA(FRAC(INT)) --R ?**? : (%,%) -> % if Coef has ALGEBRA(FRAC(INT)) --R ?**? : (%,Integer) -> % if Coef has FIELD ---R ?**? : (%,NonNegativeInteger) -> % --R ?/? : (SparseUnivariateTaylorSeries(Coef,var,cen),SparseUnivariateTaylorSeries(Coef,var,cen)) -> % if Coef has FIELD --R ?/? : (%,%) -> % if Coef has FIELD --R ?/? : (%,Coef) -> % if Coef has FIELD @@ -129925,7 +135418,6 @@ SparseTable(Key:SetCategory, Ent:SetCategory, dent:Ent) == --R D : (%,(SparseUnivariateTaylorSeries(Coef,var,cen) -> SparseUnivariateTaylorSeries(Coef,var,cen)),NonNegativeInteger) -> % if Coef has FIELD --R D : (%,(SparseUnivariateTaylorSeries(Coef,var,cen) -> SparseUnivariateTaylorSeries(Coef,var,cen))) -> % if Coef has FIELD --R ?^? : (%,Integer) -> % if Coef has FIELD ---R ?^? : (%,NonNegativeInteger) -> % --R abs : % -> % if SparseUnivariateTaylorSeries(Coef,var,cen) has OINTDOM and Coef has FIELD --R acos : % -> % if Coef has ALGEBRA(FRAC(INT)) --R acosh : % -> % if Coef has ALGEBRA(FRAC(INT)) @@ -130000,7 +135492,6 @@ SparseTable(Key:SetCategory, Ent:SetCategory, dent:Ent) == --R integrate : (%,Variable(var)) -> % if Coef has ALGEBRA(FRAC(INT)) --R integrate : (%,Symbol) -> % if Coef has integrate: (Coef,Symbol) -> Coef and Coef has variables: Coef -> List(Symbol) and Coef has ALGEBRA(FRAC(INT)) or Coef has ACFS(INT) and Coef has ALGEBRA(FRAC(INT)) and Coef has PRIMCAT and Coef has TRANFUN --R integrate : % -> % if Coef has ALGEBRA(FRAC(INT)) ---R inv : % -> % if Coef has FIELD --R laurent : (Integer,SparseUnivariateTaylorSeries(Coef,var,cen)) -> % --R lcm : (%,%) -> % if Coef has FIELD --R lcm : List(%) -> % if Coef has FIELD @@ -130450,32 +135941,39 @@ SparseUnivariateLaurentSeries(Coef,var,cen): Exports == Implementation where --R------------------------------- Operations -------------------------------- --R ?*? : (%,R) -> % ?*? : (R,%) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % ---R -? : % -> % ?=? : (%,%) -> Boolean ---R D : (%,(R -> R)) -> % D : % -> % ---R D : (%,NonNegativeInteger) -> % 1 : () -> % ---R 0 : () -> % ?^? : (%,PositiveInteger) -> % ---R coefficients : % -> List(R) coerce : R -> % ---R coerce : Integer -> % coerce : % -> OutputForm ---R degree : % -> NonNegativeInteger differentiate : % -> % ---R ?.? : (%,%) -> % ?.? : (%,R) -> R +--R -? : % -> % ?/? : (%,R) -> % if R has FIELD +--R ?=? : (%,%) -> Boolean D : (%,(R -> R)) -> % +--R D : % -> % D : (%,NonNegativeInteger) -> % +--R D : (%,SingletonAsOrderedSet) -> % 1 : () -> % +--R 0 : () -> % ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,PositiveInteger) -> % coefficients : % -> List(R) +--R coerce : % -> % if R has INTDOM coerce : SingletonAsOrderedSet -> % +--R coerce : R -> % coerce : Integer -> % +--R coerce : % -> OutputForm content : % -> R if R has GCDDOM +--R degree : % -> NonNegativeInteger differentiate : (%,(R -> R)) -> % +--R differentiate : % -> % ?.? : (%,%) -> % +--R ?.? : (%,R) -> R eval : (%,List(%),List(%)) -> % --R eval : (%,%,%) -> % eval : (%,Equation(%)) -> % ---R ground : % -> R ground? : % -> Boolean ---R hash : % -> SingleInteger init : () -> % if R has STEP ---R latex : % -> String leadingCoefficient : % -> R ---R leadingMonomial : % -> % map : ((R -> R),%) -> % ---R monomial? : % -> Boolean monomials : % -> List(%) ---R one? : % -> Boolean pseudoRemainder : (%,%) -> % ---R recip : % -> Union(%,"failed") reductum : % -> % +--R eval : (%,List(Equation(%))) -> % gcd : (%,%) -> % if R has GCDDOM +--R gcd : List(%) -> % if R has GCDDOM ground : % -> R +--R ground? : % -> Boolean hash : % -> SingleInteger +--R init : () -> % if R has STEP latex : % -> String +--R lcm : (%,%) -> % if R has GCDDOM lcm : List(%) -> % if R has GCDDOM +--R leadingCoefficient : % -> R leadingMonomial : % -> % +--R map : ((R -> R),%) -> % max : (%,%) -> % if R has ORDSET +--R min : (%,%) -> % if R has ORDSET monomial? : % -> Boolean +--R monomials : % -> List(%) one? : % -> Boolean +--R primitiveMonomials : % -> List(%) pseudoRemainder : (%,%) -> % +--R ?quo? : (%,%) -> % if R has FIELD recip : % -> Union(%,"failed") +--R reductum : % -> % ?rem? : (%,%) -> % if R has FIELD --R retract : % -> R sample : () -> % --R unvectorise : Vector(R) -> % zero? : % -> Boolean --R ?~=? : (%,%) -> Boolean --R ?*? : (Fraction(Integer),%) -> % if R has ALGEBRA(FRAC(INT)) --R ?*? : (%,Fraction(Integer)) -> % if R has ALGEBRA(FRAC(INT)) ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R ?/? : (%,R) -> % if R has FIELD --R ? Boolean if R has ORDSET --R ?<=? : (%,%) -> Boolean if R has ORDSET --R ?>? : (%,%) -> Boolean if R has ORDSET @@ -130488,8 +135986,6 @@ SparseUnivariateLaurentSeries(Coef,var,cen): Exports == Implementation where --R D : (%,List(SingletonAsOrderedSet),List(NonNegativeInteger)) -> % --R D : (%,SingletonAsOrderedSet,NonNegativeInteger) -> % --R D : (%,List(SingletonAsOrderedSet)) -> % ---R D : (%,SingletonAsOrderedSet) -> % ---R ?^? : (%,NonNegativeInteger) -> % --R associates? : (%,%) -> Boolean if R has INTDOM --R binomThmExpt : (%,%,NonNegativeInteger) -> % if R has COMRING --R characteristic : () -> NonNegativeInteger @@ -130497,21 +135993,17 @@ SparseUnivariateLaurentSeries(Coef,var,cen): Exports == Implementation where --R coefficient : (%,List(SingletonAsOrderedSet),List(NonNegativeInteger)) -> % --R coefficient : (%,SingletonAsOrderedSet,NonNegativeInteger) -> % --R coefficient : (%,NonNegativeInteger) -> R ---R coerce : % -> % if R has INTDOM --R coerce : Fraction(Integer) -> % if R has ALGEBRA(FRAC(INT)) or R has RETRACT(FRAC(INT)) ---R coerce : SingletonAsOrderedSet -> % --R composite : (Fraction(%),%) -> Union(Fraction(%),"failed") if R has INTDOM --R composite : (%,%) -> Union(%,"failed") if R has INTDOM --R conditionP : Matrix(%) -> Union(Vector(%),"failed") if $ has CHARNZ and R has PFECAT --R content : (%,SingletonAsOrderedSet) -> % if R has GCDDOM ---R content : % -> R if R has GCDDOM --R convert : % -> InputForm if SingletonAsOrderedSet has KONVERT(INFORM) and R has KONVERT(INFORM) --R convert : % -> Pattern(Integer) if SingletonAsOrderedSet has KONVERT(PATTERN(INT)) and R has KONVERT(PATTERN(INT)) --R convert : % -> Pattern(Float) if SingletonAsOrderedSet has KONVERT(PATTERN(FLOAT)) and R has KONVERT(PATTERN(FLOAT)) --R degree : (%,List(SingletonAsOrderedSet)) -> List(NonNegativeInteger) --R degree : (%,SingletonAsOrderedSet) -> NonNegativeInteger --R differentiate : (%,(R -> R),%) -> % ---R differentiate : (%,(R -> R)) -> % --R differentiate : (%,(R -> R),NonNegativeInteger) -> % --R differentiate : (%,List(Symbol),List(NonNegativeInteger)) -> % if R has PDRING(SYMBOL) --R differentiate : (%,Symbol,NonNegativeInteger) -> % if R has PDRING(SYMBOL) @@ -130534,8 +136026,6 @@ SparseUnivariateLaurentSeries(Coef,var,cen): Exports == Implementation where --R eval : (%,SingletonAsOrderedSet,%) -> % --R eval : (%,List(SingletonAsOrderedSet),List(R)) -> % --R eval : (%,SingletonAsOrderedSet,R) -> % ---R eval : (%,List(%),List(%)) -> % ---R eval : (%,List(Equation(%))) -> % --R expressIdealMember : (List(%),%) -> Union(List(%),"failed") if R has FIELD --R exquo : (%,%) -> Union(%,"failed") if R has INTDOM --R exquo : (%,R) -> Union(%,"failed") if R has INTDOM @@ -130545,22 +136035,16 @@ SparseUnivariateLaurentSeries(Coef,var,cen): Exports == Implementation where --R factorPolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has PFECAT --R factorSquareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has PFECAT --R fmecg : (%,NonNegativeInteger,R,%) -> % ---R gcd : (%,%) -> % if R has GCDDOM ---R gcd : List(%) -> % if R has GCDDOM --R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) if R has GCDDOM --R integrate : % -> % if R has ALGEBRA(FRAC(INT)) --R isExpt : % -> Union(Record(var: SingletonAsOrderedSet,exponent: NonNegativeInteger),"failed") --R isPlus : % -> Union(List(%),"failed") --R isTimes : % -> Union(List(%),"failed") --R karatsubaDivide : (%,NonNegativeInteger) -> Record(quotient: %,remainder: %) ---R lcm : (%,%) -> % if R has GCDDOM ---R lcm : List(%) -> % if R has GCDDOM --R lcmCoef : (%,%) -> Record(llcmres: %,coeff1: %,coeff2: %) if R has GCDDOM --R mainVariable : % -> Union(SingletonAsOrderedSet,"failed") --R makeSUP : % -> SparseUnivariatePolynomial(R) --R mapExponents : ((NonNegativeInteger -> NonNegativeInteger),%) -> % ---R max : (%,%) -> % if R has ORDSET ---R min : (%,%) -> % if R has ORDSET --R minimumDegree : (%,List(SingletonAsOrderedSet)) -> List(NonNegativeInteger) --R minimumDegree : (%,SingletonAsOrderedSet) -> NonNegativeInteger --R minimumDegree : % -> NonNegativeInteger @@ -130581,18 +136065,15 @@ SparseUnivariateLaurentSeries(Coef,var,cen): Exports == Implementation where --R patternMatch : (%,Pattern(Float),PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if SingletonAsOrderedSet has PATMAB(FLOAT) and R has PATMAB(FLOAT) --R pomopo! : (%,R,NonNegativeInteger,%) -> % --R prime? : % -> Boolean if R has PFECAT ---R primitiveMonomials : % -> List(%) --R primitivePart : (%,SingletonAsOrderedSet) -> % if R has GCDDOM --R primitivePart : % -> % if R has GCDDOM --R principalIdeal : List(%) -> Record(coef: List(%),generator: %) if R has FIELD --R pseudoDivide : (%,%) -> Record(coef: R,quotient: %,remainder: %) if R has INTDOM --R pseudoQuotient : (%,%) -> % if R has INTDOM ---R ?quo? : (%,%) -> % if R has FIELD --R reducedSystem : Matrix(%) -> Matrix(R) --R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(R),vec: Vector(R)) --R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(Integer),vec: Vector(Integer)) if R has LINEXP(INT) --R reducedSystem : Matrix(%) -> Matrix(Integer) if R has LINEXP(INT) ---R ?rem? : (%,%) -> % if R has FIELD --R resultant : (%,%) -> R if R has COMRING --R resultant : (%,%,SingletonAsOrderedSet) -> % if R has COMRING --R retract : % -> SingletonAsOrderedSet @@ -131161,33 +136642,53 @@ unfortunately. --R------------------------------- Operations -------------------------------- --R ?*? : (%,R) -> % ?*? : (R,%) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % ---R -? : % -> % ?=? : (%,%) -> Boolean ---R D : (%,(R -> R)) -> % D : % -> % ---R D : (%,NonNegativeInteger) -> % 1 : () -> % ---R 0 : () -> % ?^? : (%,PositiveInteger) -> % ---R coefficients : % -> List(R) coerce : R -> % ---R coerce : Integer -> % coerce : % -> OutputForm ---R degree : % -> NonNegativeInteger differentiate : % -> % ---R ?.? : (%,%) -> % ?.? : (%,R) -> R +--R -? : % -> % ?/? : (%,R) -> % if R has FIELD +--R ?=? : (%,%) -> Boolean D : (%,(R -> R)) -> % +--R D : % -> % D : (%,NonNegativeInteger) -> % +--R D : (%,SingletonAsOrderedSet) -> % 1 : () -> % +--R 0 : () -> % ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,PositiveInteger) -> % acos : % -> % if R has TRANFUN +--R acosh : % -> % if R has TRANFUN acot : % -> % if R has TRANFUN +--R acoth : % -> % if R has TRANFUN acsc : % -> % if R has TRANFUN +--R acsch : % -> % if R has TRANFUN asec : % -> % if R has TRANFUN +--R asech : % -> % if R has TRANFUN asin : % -> % if R has TRANFUN +--R asinh : % -> % if R has TRANFUN atan : % -> % if R has TRANFUN +--R atanh : % -> % if R has TRANFUN coefficients : % -> List(R) +--R coerce : % -> % if R has INTDOM coerce : SingletonAsOrderedSet -> % +--R coerce : R -> % coerce : Integer -> % +--R coerce : % -> OutputForm content : % -> R if R has GCDDOM +--R cos : % -> % if R has TRANFUN cosh : % -> % if R has TRANFUN +--R cot : % -> % if R has TRANFUN coth : % -> % if R has TRANFUN +--R csc : % -> % if R has TRANFUN csch : % -> % if R has TRANFUN +--R degree : % -> NonNegativeInteger differentiate : (%,(R -> R)) -> % +--R differentiate : % -> % ?.? : (%,%) -> % +--R ?.? : (%,R) -> R eval : (%,List(%),List(%)) -> % --R eval : (%,%,%) -> % eval : (%,Equation(%)) -> % +--R eval : (%,List(Equation(%))) -> % exp : % -> % if R has TRANFUN +--R gcd : (%,%) -> % if R has GCDDOM gcd : List(%) -> % if R has GCDDOM --R ground : % -> R ground? : % -> Boolean --R hash : % -> SingleInteger init : () -> % if R has STEP ---R latex : % -> String leadingCoefficient : % -> R ---R leadingMonomial : % -> % map : ((R -> R),%) -> % ---R monomial? : % -> Boolean monomials : % -> List(%) ---R one? : % -> Boolean pi : () -> % if R has TRANFUN ---R pseudoRemainder : (%,%) -> % recip : % -> Union(%,"failed") ---R reductum : % -> % retract : % -> R ---R sample : () -> % unvectorise : Vector(R) -> % +--R latex : % -> String lcm : (%,%) -> % if R has GCDDOM +--R lcm : List(%) -> % if R has GCDDOM leadingCoefficient : % -> R +--R leadingMonomial : % -> % log : % -> % if R has TRANFUN +--R map : ((R -> R),%) -> % max : (%,%) -> % if R has ORDSET +--R min : (%,%) -> % if R has ORDSET monomial? : % -> Boolean +--R monomials : % -> List(%) one? : % -> Boolean +--R pi : () -> % if R has TRANFUN primitiveMonomials : % -> List(%) +--R pseudoRemainder : (%,%) -> % ?quo? : (%,%) -> % if R has FIELD +--R recip : % -> Union(%,"failed") reductum : % -> % +--R ?rem? : (%,%) -> % if R has FIELD retract : % -> R +--R sample : () -> % sec : % -> % if R has TRANFUN +--R sech : % -> % if R has TRANFUN sin : % -> % if R has TRANFUN +--R sinh : % -> % if R has TRANFUN tan : % -> % if R has TRANFUN +--R tanh : % -> % if R has TRANFUN unvectorise : Vector(R) -> % --R zero? : % -> Boolean ?~=? : (%,%) -> Boolean --R ?*? : (Fraction(Integer),%) -> % if R has ALGEBRA(FRAC(INT)) --R ?*? : (%,Fraction(Integer)) -> % if R has ALGEBRA(FRAC(INT)) ---R ?*? : (NonNegativeInteger,%) -> % --R ?**? : (%,%) -> % if R has TRANFUN ---R ?**? : (%,NonNegativeInteger) -> % ---R ?/? : (%,R) -> % if R has FIELD --R ? Boolean if R has ORDSET --R ?<=? : (%,%) -> Boolean if R has ORDSET --R ?>? : (%,%) -> Boolean if R has ORDSET @@ -131200,48 +136701,24 @@ unfortunately. --R D : (%,List(SingletonAsOrderedSet),List(NonNegativeInteger)) -> % --R D : (%,SingletonAsOrderedSet,NonNegativeInteger) -> % --R D : (%,List(SingletonAsOrderedSet)) -> % ---R D : (%,SingletonAsOrderedSet) -> % ---R ?^? : (%,NonNegativeInteger) -> % ---R acos : % -> % if R has TRANFUN ---R acosh : % -> % if R has TRANFUN ---R acot : % -> % if R has TRANFUN ---R acoth : % -> % if R has TRANFUN ---R acsc : % -> % if R has TRANFUN ---R acsch : % -> % if R has TRANFUN ---R asec : % -> % if R has TRANFUN ---R asech : % -> % if R has TRANFUN ---R asin : % -> % if R has TRANFUN ---R asinh : % -> % if R has TRANFUN --R associates? : (%,%) -> Boolean if R has INTDOM ---R atan : % -> % if R has TRANFUN ---R atanh : % -> % if R has TRANFUN --R binomThmExpt : (%,%,NonNegativeInteger) -> % if R has COMRING --R characteristic : () -> NonNegativeInteger --R charthRoot : % -> Union(%,"failed") if $ has CHARNZ and R has PFECAT or R has CHARNZ --R coefficient : (%,List(SingletonAsOrderedSet),List(NonNegativeInteger)) -> % --R coefficient : (%,SingletonAsOrderedSet,NonNegativeInteger) -> % --R coefficient : (%,NonNegativeInteger) -> R ---R coerce : % -> % if R has INTDOM --R coerce : Fraction(Integer) -> % if R has ALGEBRA(FRAC(INT)) or R has RETRACT(FRAC(INT)) ---R coerce : SingletonAsOrderedSet -> % --R composite : (Fraction(%),%) -> Union(Fraction(%),"failed") if R has INTDOM --R composite : (%,%) -> Union(%,"failed") if R has INTDOM --R conditionP : Matrix(%) -> Union(Vector(%),"failed") if $ has CHARNZ and R has PFECAT --R content : (%,SingletonAsOrderedSet) -> % if R has GCDDOM ---R content : % -> R if R has GCDDOM --R convert : % -> InputForm if SingletonAsOrderedSet has KONVERT(INFORM) and R has KONVERT(INFORM) --R convert : % -> Pattern(Integer) if SingletonAsOrderedSet has KONVERT(PATTERN(INT)) and R has KONVERT(PATTERN(INT)) --R convert : % -> Pattern(Float) if SingletonAsOrderedSet has KONVERT(PATTERN(FLOAT)) and R has KONVERT(PATTERN(FLOAT)) ---R cos : % -> % if R has TRANFUN ---R cosh : % -> % if R has TRANFUN ---R cot : % -> % if R has TRANFUN ---R coth : % -> % if R has TRANFUN ---R csc : % -> % if R has TRANFUN ---R csch : % -> % if R has TRANFUN --R degree : (%,List(SingletonAsOrderedSet)) -> List(NonNegativeInteger) --R degree : (%,SingletonAsOrderedSet) -> NonNegativeInteger --R differentiate : (%,(R -> R),%) -> % ---R differentiate : (%,(R -> R)) -> % --R differentiate : (%,(R -> R),NonNegativeInteger) -> % --R differentiate : (%,List(Symbol),List(NonNegativeInteger)) -> % if R has PDRING(SYMBOL) --R differentiate : (%,Symbol,NonNegativeInteger) -> % if R has PDRING(SYMBOL) @@ -131264,9 +136741,6 @@ unfortunately. --R eval : (%,SingletonAsOrderedSet,%) -> % --R eval : (%,List(SingletonAsOrderedSet),List(R)) -> % --R eval : (%,SingletonAsOrderedSet,R) -> % ---R eval : (%,List(%),List(%)) -> % ---R eval : (%,List(Equation(%))) -> % ---R exp : % -> % if R has TRANFUN --R expressIdealMember : (List(%),%) -> Union(List(%),"failed") if R has FIELD --R exquo : (%,%) -> Union(%,"failed") if R has INTDOM --R exquo : (%,R) -> Union(%,"failed") if R has INTDOM @@ -131275,23 +136749,16 @@ unfortunately. --R factor : % -> Factored(%) if R has PFECAT --R factorPolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has PFECAT --R factorSquareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has PFECAT ---R gcd : (%,%) -> % if R has GCDDOM ---R gcd : List(%) -> % if R has GCDDOM --R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) if R has GCDDOM --R integrate : % -> % if R has ALGEBRA(FRAC(INT)) --R isExpt : % -> Union(Record(var: SingletonAsOrderedSet,exponent: NonNegativeInteger),"failed") --R isPlus : % -> Union(List(%),"failed") --R isTimes : % -> Union(List(%),"failed") --R karatsubaDivide : (%,NonNegativeInteger) -> Record(quotient: %,remainder: %) ---R lcm : (%,%) -> % if R has GCDDOM ---R lcm : List(%) -> % if R has GCDDOM --R lcmCoef : (%,%) -> Record(llcmres: %,coeff1: %,coeff2: %) if R has GCDDOM ---R log : % -> % if R has TRANFUN --R mainVariable : % -> Union(SingletonAsOrderedSet,"failed") --R makeSUP : % -> SparseUnivariatePolynomial(R) --R mapExponents : ((NonNegativeInteger -> NonNegativeInteger),%) -> % ---R max : (%,%) -> % if R has ORDSET ---R min : (%,%) -> % if R has ORDSET --R minimumDegree : (%,List(SingletonAsOrderedSet)) -> List(NonNegativeInteger) --R minimumDegree : (%,SingletonAsOrderedSet) -> NonNegativeInteger --R minimumDegree : % -> NonNegativeInteger @@ -131311,18 +136778,15 @@ unfortunately. --R patternMatch : (%,Pattern(Float),PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if SingletonAsOrderedSet has PATMAB(FLOAT) and R has PATMAB(FLOAT) --R pomopo! : (%,R,NonNegativeInteger,%) -> % --R prime? : % -> Boolean if R has PFECAT ---R primitiveMonomials : % -> List(%) --R primitivePart : (%,SingletonAsOrderedSet) -> % if R has GCDDOM --R primitivePart : % -> % if R has GCDDOM --R principalIdeal : List(%) -> Record(coef: List(%),generator: %) if R has FIELD --R pseudoDivide : (%,%) -> Record(coef: R,quotient: %,remainder: %) if R has INTDOM --R pseudoQuotient : (%,%) -> % if R has INTDOM ---R ?quo? : (%,%) -> % if R has FIELD --R reducedSystem : Matrix(%) -> Matrix(R) --R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(R),vec: Vector(R)) --R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(Integer),vec: Vector(Integer)) if R has LINEXP(INT) --R reducedSystem : Matrix(%) -> Matrix(Integer) if R has LINEXP(INT) ---R ?rem? : (%,%) -> % if R has FIELD --R resultant : (%,%) -> R if R has COMRING --R resultant : (%,%,SingletonAsOrderedSet) -> % if R has COMRING --R retract : % -> SingletonAsOrderedSet @@ -131332,13 +136796,9 @@ unfortunately. --R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT(INT) --R retractIfCan : % -> Union(Fraction(Integer),"failed") if R has RETRACT(FRAC(INT)) --R retractIfCan : % -> Union(R,"failed") ---R sec : % -> % if R has TRANFUN ---R sech : % -> % if R has TRANFUN --R separate : (%,%) -> Record(primePart: %,commonPart: %) if R has GCDDOM --R shiftLeft : (%,NonNegativeInteger) -> % --R shiftRight : (%,NonNegativeInteger) -> % ---R sin : % -> % if R has TRANFUN ---R sinh : % -> % if R has TRANFUN --R sizeLess? : (%,%) -> Boolean if R has FIELD --R solveLinearPolynomialEquation : (List(SparseUnivariatePolynomial(%)),SparseUnivariatePolynomial(%)) -> Union(List(SparseUnivariatePolynomial(%)),"failed") if R has PFECAT --R squareFree : % -> Factored(%) if R has GCDDOM @@ -131346,8 +136806,6 @@ unfortunately. --R squareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has PFECAT --R subResultantGcd : (%,%) -> % if R has INTDOM --R subtractIfCan : (%,%) -> Union(%,"failed") ---R tan : % -> % if R has TRANFUN ---R tanh : % -> % if R has TRANFUN --R totalDegree : (%,List(SingletonAsOrderedSet)) -> NonNegativeInteger --R totalDegree : % -> NonNegativeInteger --R unit? : % -> Boolean if R has INTDOM @@ -131593,14 +137051,17 @@ SparseUnivariatePolynomialExpressions(R: Ring): Exports == Implementation where --R------------------------------- Operations -------------------------------- --R ?*? : (Coef,%) -> % ?*? : (%,Coef) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ?=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % center : % -> Coef +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R center : % -> Coef coerce : % -> % if Coef has INTDOM --R coerce : Variable(var) -> % coerce : Integer -> % --R coerce : % -> OutputForm complete : % -> % ---R degree : % -> Fraction(Integer) hash : % -> SingleInteger +--R degree : % -> Fraction(Integer) ?.? : (%,Fraction(Integer)) -> Coef +--R hash : % -> SingleInteger inv : % -> % if Coef has FIELD --R latex : % -> String leadingCoefficient : % -> Coef --R leadingMonomial : % -> % map : ((Coef -> Coef),%) -> % --R monomial? : % -> Boolean one? : % -> Boolean @@ -131610,11 +137071,9 @@ SparseUnivariatePolynomialExpressions(R: Ring): Exports == Implementation where --R zero? : % -> Boolean ?~=? : (%,%) -> Boolean --R ?*? : (%,Fraction(Integer)) -> % if Coef has ALGEBRA(FRAC(INT)) --R ?*? : (Fraction(Integer),%) -> % if Coef has ALGEBRA(FRAC(INT)) ---R ?*? : (NonNegativeInteger,%) -> % --R ?**? : (%,Fraction(Integer)) -> % if Coef has ALGEBRA(FRAC(INT)) --R ?**? : (%,%) -> % if Coef has ALGEBRA(FRAC(INT)) --R ?**? : (%,Integer) -> % if Coef has FIELD ---R ?**? : (%,NonNegativeInteger) -> % --R ?/? : (%,%) -> % if Coef has FIELD --R ?/? : (%,Coef) -> % if Coef has FIELD --R D : % -> % if Coef has *: (Fraction(Integer),Coef) -> Coef @@ -131624,7 +137083,6 @@ SparseUnivariatePolynomialExpressions(R: Ring): Exports == Implementation where --R D : (%,Symbol,NonNegativeInteger) -> % if Coef has *: (Fraction(Integer),Coef) -> Coef and Coef has PDRING(SYMBOL) --R D : (%,List(Symbol),List(NonNegativeInteger)) -> % if Coef has *: (Fraction(Integer),Coef) -> Coef and Coef has PDRING(SYMBOL) --R ?^? : (%,Integer) -> % if Coef has FIELD ---R ?^? : (%,NonNegativeInteger) -> % --R acos : % -> % if Coef has ALGEBRA(FRAC(INT)) --R acosh : % -> % if Coef has ALGEBRA(FRAC(INT)) --R acot : % -> % if Coef has ALGEBRA(FRAC(INT)) @@ -131642,7 +137100,6 @@ SparseUnivariatePolynomialExpressions(R: Ring): Exports == Implementation where --R characteristic : () -> NonNegativeInteger --R charthRoot : % -> Union(%,"failed") if Coef has CHARNZ --R coefficient : (%,Fraction(Integer)) -> Coef ---R coerce : % -> % if Coef has INTDOM --R coerce : Fraction(Integer) -> % if Coef has ALGEBRA(FRAC(INT)) --R coerce : SparseUnivariateTaylorSeries(Coef,var,cen) -> % --R coerce : SparseUnivariateLaurentSeries(Coef,var,cen) -> % @@ -131662,7 +137119,6 @@ SparseUnivariatePolynomialExpressions(R: Ring): Exports == Implementation where --R differentiate : (%,List(Symbol),List(NonNegativeInteger)) -> % if Coef has *: (Fraction(Integer),Coef) -> Coef and Coef has PDRING(SYMBOL) --R divide : (%,%) -> Record(quotient: %,remainder: %) if Coef has FIELD --R ?.? : (%,%) -> % if Fraction(Integer) has SGROUP ---R ?.? : (%,Fraction(Integer)) -> Coef --R euclideanSize : % -> NonNegativeInteger if Coef has FIELD --R eval : (%,Coef) -> Stream(Coef) if Coef has **: (Coef,Fraction(Integer)) -> Coef --R exp : % -> % if Coef has ALGEBRA(FRAC(INT)) @@ -131678,7 +137134,6 @@ SparseUnivariatePolynomialExpressions(R: Ring): Exports == Implementation where --R integrate : (%,Variable(var)) -> % if Coef has ALGEBRA(FRAC(INT)) --R integrate : (%,Symbol) -> % if Coef has integrate: (Coef,Symbol) -> Coef and Coef has variables: Coef -> List(Symbol) and Coef has ALGEBRA(FRAC(INT)) or Coef has ACFS(INT) and Coef has ALGEBRA(FRAC(INT)) and Coef has PRIMCAT and Coef has TRANFUN --R integrate : % -> % if Coef has ALGEBRA(FRAC(INT)) ---R inv : % -> % if Coef has FIELD --R laurent : % -> SparseUnivariateLaurentSeries(Coef,var,cen) --R laurentIfCan : % -> Union(SparseUnivariateLaurentSeries(Coef,var,cen),"failed") --R laurentRep : % -> SparseUnivariateLaurentSeries(Coef,var,cen) @@ -131967,26 +137422,24 @@ SparseUnivariatePuiseuxSeries(Coef,var,cen): Exports == Implementation where --R------------------------------- Operations -------------------------------- --R ?*? : (R,%) -> % ?*? : (%,R) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ?=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % apply : (%,R,R) -> R ---R coefficients : % -> List(R) coerce : R -> % ---R coerce : Integer -> % coerce : % -> OutputForm +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R apply : (%,R,R) -> R coefficients : % -> List(R) +--R coerce : R -> % coerce : Integer -> % +--R coerce : % -> OutputForm content : % -> R if R has GCDDOM --R degree : % -> NonNegativeInteger hash : % -> SingleInteger --R latex : % -> String leadingCoefficient : % -> R --R one? : % -> Boolean recip : % -> Union(%,"failed") --R reductum : % -> % retract : % -> R --R sample : () -> % zero? : % -> Boolean --R ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R ?^? : (%,NonNegativeInteger) -> % --R characteristic : () -> NonNegativeInteger --R coefficient : (%,NonNegativeInteger) -> R --R coerce : Fraction(Integer) -> % if R has RETRACT(FRAC(INT)) ---R content : % -> R if R has GCDDOM --R exquo : (%,R) -> Union(%,"failed") if R has INTDOM --R leftDivide : (%,%) -> Record(quotient: %,remainder: %) if R has FIELD --R leftExactQuotient : (%,%) -> Union(%,"failed") if R has FIELD @@ -132152,12 +137605,14 @@ SparseUnivariateSkewPolynomial(R:Ring, sigma:Automorphism R, delta: R -> R): --R------------------------------- Operations -------------------------------- --R ?*? : (Coef,%) -> % ?*? : (%,Coef) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ?=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % center : % -> Coef ---R coefficients : % -> Stream(Coef) coerce : Variable(var) -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R center : % -> Coef coefficients : % -> Stream(Coef) +--R coerce : Variable(var) -> % coerce : % -> % if Coef has INTDOM --R coerce : Integer -> % coerce : % -> OutputForm --R complete : % -> % degree : % -> NonNegativeInteger --R hash : % -> SingleInteger latex : % -> String @@ -132171,11 +137626,9 @@ SparseUnivariateSkewPolynomial(R:Ring, sigma:Automorphism R, delta: R -> R): --R ?~=? : (%,%) -> Boolean --R ?*? : (%,Fraction(Integer)) -> % if Coef has ALGEBRA(FRAC(INT)) --R ?*? : (Fraction(Integer),%) -> % if Coef has ALGEBRA(FRAC(INT)) ---R ?*? : (NonNegativeInteger,%) -> % --R ?**? : (%,Fraction(Integer)) -> % if Coef has ALGEBRA(FRAC(INT)) --R ?**? : (%,%) -> % if Coef has ALGEBRA(FRAC(INT)) --R ?**? : (%,Coef) -> % if Coef has FIELD ---R ?**? : (%,NonNegativeInteger) -> % --R ?/? : (%,Coef) -> % if Coef has FIELD --R D : % -> % if Coef has *: (NonNegativeInteger,Coef) -> Coef --R D : (%,NonNegativeInteger) -> % if Coef has *: (NonNegativeInteger,Coef) -> Coef @@ -132183,7 +137636,6 @@ SparseUnivariateSkewPolynomial(R:Ring, sigma:Automorphism R, delta: R -> R): --R D : (%,List(Symbol)) -> % if Coef has *: (NonNegativeInteger,Coef) -> Coef and Coef has PDRING(SYMBOL) --R D : (%,Symbol,NonNegativeInteger) -> % if Coef has *: (NonNegativeInteger,Coef) -> Coef and Coef has PDRING(SYMBOL) --R D : (%,List(Symbol),List(NonNegativeInteger)) -> % if Coef has *: (NonNegativeInteger,Coef) -> Coef and Coef has PDRING(SYMBOL) ---R ?^? : (%,NonNegativeInteger) -> % --R acos : % -> % if Coef has ALGEBRA(FRAC(INT)) --R acosh : % -> % if Coef has ALGEBRA(FRAC(INT)) --R acot : % -> % if Coef has ALGEBRA(FRAC(INT)) @@ -132203,7 +137655,6 @@ SparseUnivariateSkewPolynomial(R:Ring, sigma:Automorphism R, delta: R -> R): --R coefficient : (%,NonNegativeInteger) -> Coef --R coerce : UnivariatePolynomial(var,Coef) -> % --R coerce : Coef -> % if Coef has COMRING ---R coerce : % -> % if Coef has INTDOM --R coerce : Fraction(Integer) -> % if Coef has ALGEBRA(FRAC(INT)) --R cos : % -> % if Coef has ALGEBRA(FRAC(INT)) --R cosh : % -> % if Coef has ALGEBRA(FRAC(INT)) @@ -132769,33 +138220,35 @@ SparseUnivariateTaylorSeries(Coef,var,cen): Exports == Implementation where --S 1 of 1 )show SplitHomogeneousDirectProduct +--R --R SplitHomogeneousDirectProduct(dimtot: NonNegativeInteger,dim1: NonNegativeInteger,S: OrderedAbelianMonoidSup) is a domain constructor --R Abbreviation for SplitHomogeneousDirectProduct is SHDP --R This constructor is not exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for SHDP --R --R------------------------------- Operations -------------------------------- ---R -? : % -> % if S has RING 1 : () -> % if S has MONOID ---R 0 : () -> % if S has CABMON coerce : % -> Vector(S) +--R ?*? : (S,%) -> % if S has MONOID ?*? : (%,S) -> % if S has MONOID +--R ?*? : (%,%) -> % if S has MONOID ?+? : (%,%) -> % if S has ABELSG +--R -? : % -> % if S has RING ?-? : (%,%) -> % if S has RING +--R ?/? : (%,S) -> % if S has FIELD 1 : () -> % if S has MONOID +--R 0 : () -> % if S has CABMON abs : % -> % if S has ORDRING +--R coerce : S -> % if S has SETCAT coerce : % -> Vector(S) --R copy : % -> % directProduct : Vector(S) -> % ---R ?.? : (%,Integer) -> S elt : (%,Integer,S) -> S ---R empty : () -> % empty? : % -> Boolean ---R entries : % -> List(S) eq? : (%,%) -> Boolean ---R index? : (Integer,%) -> Boolean indices : % -> List(Integer) ---R map : ((S -> S),%) -> % qelt : (%,Integer) -> S ---R sample : () -> % +--R dot : (%,%) -> S if S has RING ?.? : (%,Integer) -> S +--R elt : (%,Integer,S) -> S empty : () -> % +--R empty? : % -> Boolean entries : % -> List(S) +--R eq? : (%,%) -> Boolean index? : (Integer,%) -> Boolean +--R indices : % -> List(Integer) latex : % -> String if S has SETCAT +--R map : ((S -> S),%) -> % one? : % -> Boolean if S has MONOID +--R qelt : (%,Integer) -> S random : () -> % if S has FINITE +--R retract : % -> S if S has SETCAT sample : () -> % +--R sup : (%,%) -> % if S has OAMONS --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R ?*? : (PositiveInteger,%) -> % if S has ABELSG --R ?*? : (NonNegativeInteger,%) -> % if S has CABMON ---R ?*? : (S,%) -> % if S has MONOID ---R ?*? : (%,S) -> % if S has MONOID ---R ?*? : (%,%) -> % if S has MONOID --R ?*? : (Integer,%) -> % if S has RING --R ?**? : (%,PositiveInteger) -> % if S has MONOID --R ?**? : (%,NonNegativeInteger) -> % if S has MONOID ---R ?+? : (%,%) -> % if S has ABELSG ---R ?-? : (%,%) -> % if S has RING ---R ?/? : (%,S) -> % if S has FIELD --R ? Boolean if S has OAMONS or S has ORDRING --R ?<=? : (%,%) -> Boolean if S has OAMONS or S has ORDRING --R ?=? : (%,%) -> Boolean if S has SETCAT @@ -132811,10 +138264,8 @@ SparseUnivariateTaylorSeries(Coef,var,cen): Exports == Implementation where --R D : % -> % if S has DIFRING and S has RING --R ?^? : (%,PositiveInteger) -> % if S has MONOID --R ?^? : (%,NonNegativeInteger) -> % if S has MONOID ---R abs : % -> % if S has ORDRING --R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate --R characteristic : () -> NonNegativeInteger if S has RING ---R coerce : S -> % if S has SETCAT --R coerce : Fraction(Integer) -> % if S has RETRACT(FRAC(INT)) and S has SETCAT --R coerce : Integer -> % if S has RETRACT(INT) and S has SETCAT or S has RING --R coerce : % -> OutputForm if S has SETCAT @@ -132829,7 +138280,6 @@ SparseUnivariateTaylorSeries(Coef,var,cen): Exports == Implementation where --R differentiate : (%,NonNegativeInteger) -> % if S has DIFRING and S has RING --R differentiate : % -> % if S has DIFRING and S has RING --R dimension : () -> CardinalNumber if S has FIELD ---R dot : (%,%) -> S if S has RING --R entry? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT --R enumerate : () -> List(%) if S has FINITE --R eval : (%,List(S),List(S)) -> % if S has EVALAB(S) and S has SETCAT @@ -132841,7 +138291,6 @@ SparseUnivariateTaylorSeries(Coef,var,cen): Exports == Implementation where --R first : % -> S if Integer has ORDSET --R hash : % -> SingleInteger if S has SETCAT --R index : PositiveInteger -> % if S has FINITE ---R latex : % -> String if S has SETCAT --R less? : (%,NonNegativeInteger) -> Boolean --R lookup : % -> PositiveInteger if S has FINITE --R map! : ((S -> S),%) -> % if $ has shallowlyMutable @@ -132853,17 +138302,14 @@ SparseUnivariateTaylorSeries(Coef,var,cen): Exports == Implementation where --R minIndex : % -> Integer if Integer has ORDSET --R more? : (%,NonNegativeInteger) -> Boolean --R negative? : % -> Boolean if S has ORDRING ---R one? : % -> Boolean if S has MONOID --R parts : % -> List(S) if $ has finiteAggregate --R positive? : % -> Boolean if S has ORDRING --R qsetelt! : (%,Integer,S) -> S if $ has shallowlyMutable ---R random : () -> % if S has FINITE --R recip : % -> Union(%,"failed") if S has MONOID --R reducedSystem : Matrix(%) -> Matrix(S) if S has RING --R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(S),vec: Vector(S)) if S has RING --R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(Integer),vec: Vector(Integer)) if S has LINEXP(INT) and S has RING --R reducedSystem : Matrix(%) -> Matrix(Integer) if S has LINEXP(INT) and S has RING ---R retract : % -> S if S has SETCAT --R retract : % -> Fraction(Integer) if S has RETRACT(FRAC(INT)) and S has SETCAT --R retract : % -> Integer if S has RETRACT(INT) and S has SETCAT --R retractIfCan : % -> Union(S,"failed") if S has SETCAT @@ -132874,7 +138320,6 @@ SparseUnivariateTaylorSeries(Coef,var,cen): Exports == Implementation where --R size : () -> NonNegativeInteger if S has FINITE --R size? : (%,NonNegativeInteger) -> Boolean --R subtractIfCan : (%,%) -> Union(%,"failed") if S has CABMON ---R sup : (%,%) -> % if S has OAMONS --R swap! : (%,Integer,Integer) -> Void if $ has shallowlyMutable --R unitVector : PositiveInteger -> % if S has RING --R zero? : % -> Boolean if S has CABMON @@ -133056,15 +138501,14 @@ SplitHomogeneousDirectProduct(dimtot,dim1,S) : T == C where --R --R------------------------------- Operations -------------------------------- --R ?=? : (%,%) -> Boolean coerce : % -> OutputForm ---R condition : % -> C construct : (V,C) -> % ---R construct : (V,C,Boolean) -> % copy : % -> % ---R empty : () -> % empty? : % -> Boolean ---R hash : % -> SingleInteger latex : % -> String ---R setCondition! : (%,C) -> % setEmpty! : % -> % ---R setStatus! : (%,Boolean) -> % setValue! : (%,V) -> % ---R status : % -> Boolean value : % -> V ---R ?~=? : (%,%) -> Boolean ---R construct : (V,List(C)) -> List(%) +--R condition : % -> C construct : (V,List(C)) -> List(%) +--R construct : (V,C) -> % construct : (V,C,Boolean) -> % +--R copy : % -> % empty : () -> % +--R empty? : % -> Boolean hash : % -> SingleInteger +--R latex : % -> String setCondition! : (%,C) -> % +--R setEmpty! : % -> % setStatus! : (%,Boolean) -> % +--R setValue! : (%,V) -> % status : % -> Boolean +--R value : % -> V ?~=? : (%,%) -> Boolean --R construct : List(Record(val: V,tower: C)) -> List(%) --R construct : Record(val: V,tower: C) -> % --R infLex? : (%,%,((V,V) -> Boolean),((C,C) -> Boolean)) -> Boolean @@ -133298,19 +138742,18 @@ SplittingNode(V,C) : Exports == Implementation where --R------------------------------- Operations -------------------------------- --R children : % -> List(%) conditions : % -> List(C) --R construct : (V,C,V,List(C)) -> % construct : (V,C,List(%)) -> % ---R copy : % -> % cyclic? : % -> Boolean ---R distance : (%,%) -> Integer empty : () -> % ---R empty? : % -> Boolean eq? : (%,%) -> Boolean ---R leaf? : % -> Boolean nodes : % -> List(%) ---R sample : () -> % updateStatus! : % -> % ---R value : % -> SplittingNode(V,C) +--R construct : SplittingNode(V,C) -> % copy : % -> % +--R cyclic? : % -> Boolean distance : (%,%) -> Integer +--R empty : () -> % empty? : % -> Boolean +--R eq? : (%,%) -> Boolean leaf? : % -> Boolean +--R nodes : % -> List(%) sample : () -> % +--R updateStatus! : % -> % value : % -> SplittingNode(V,C) --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R ?=? : (%,%) -> Boolean if SplittingNode(V,C) has SETCAT --R any? : ((SplittingNode(V,C) -> Boolean),%) -> Boolean if $ has finiteAggregate --R child? : (%,%) -> Boolean if SplittingNode(V,C) has SETCAT --R coerce : % -> OutputForm if SplittingNode(V,C) has SETCAT --R construct : (V,C,List(SplittingNode(V,C))) -> % ---R construct : SplittingNode(V,C) -> % --R count : (SplittingNode(V,C),%) -> NonNegativeInteger if $ has finiteAggregate and SplittingNode(V,C) has SETCAT --R count : ((SplittingNode(V,C) -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate --R ?.value : (%,value) -> SplittingNode(V,C) @@ -133747,7 +139190,8 @@ SplittingTree(V,C) : Exports == Implementation where )set message test on )set message auto off )clear all ---S 1 of 23 + +--S 1 of 24 R := Integer --R --R @@ -133755,7 +139199,7 @@ R := Integer --R Type: Domain --E 1 ---S 2 of 23 +--S 2 of 24 ls : List Symbol := [x,y,z,t] --R --R @@ -133763,7 +139207,7 @@ ls : List Symbol := [x,y,z,t] --R Type: List(Symbol) --E 2 ---S 3 of 23 +--S 3 of 24 V := OVAR(ls) --R --R @@ -133771,7 +139215,7 @@ V := OVAR(ls) --R Type: Domain --E 3 ---S 4 of 23 +--S 4 of 24 E := IndexedExponents V --R --R @@ -133779,7 +139223,7 @@ E := IndexedExponents V --R Type: Domain --E 4 ---S 5 of 23 +--S 5 of 24 P := NSMP(R, V) --R --R @@ -133788,7 +139232,7 @@ P := NSMP(R, V) --R Type: Domain --E 5 ---S 6 of 23 +--S 6 of 24 x: P := 'x --R --R @@ -133796,7 +139240,7 @@ x: P := 'x --RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList([x,y,z,t])) --E 6 ---S 7 of 23 +--S 7 of 24 y: P := 'y --R --R @@ -133804,7 +139248,7 @@ y: P := 'y --RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList([x,y,z,t])) --E 7 ---S 8 of 23 +--S 8 of 24 z: P := 'z --R --R @@ -133812,7 +139256,7 @@ z: P := 'z --RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList([x,y,z,t])) --E 8 ---S 9 of 23 +--S 9 of 24 t: P := 't --R --R @@ -133820,7 +139264,7 @@ t: P := 't --RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList([x,y,z,t])) --E 9 ---S 10 of 23 +--S 10 of 24 ST := SREGSET(R,E,V,P) --R --R @@ -133831,7 +139275,7 @@ ST := SREGSET(R,E,V,P) --R Type: Domain --E 10 ---S 11 of 23 +--S 11 of 24 p1 := x ** 31 - x ** 6 - x - y --R --R @@ -133840,7 +139284,7 @@ p1 := x ** 31 - x ** 6 - x - y --RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList([x,y,z,t])) --E 11 ---S 12 of 23 +--S 12 of 24 p2 := x ** 8 - z --R --R @@ -133849,7 +139293,7 @@ p2 := x ** 8 - z --RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList([x,y,z,t])) --E 12 ---S 13 of 23 +--S 13 of 24 p3 := x ** 10 - t --R --R @@ -133858,7 +139302,7 @@ p3 := x ** 10 - t --RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList([x,y,z,t])) --E 13 ---S 14 of 23 +--S 14 of 24 lp := [p1, p2, p3] --R --R @@ -133867,7 +139311,7 @@ lp := [p1, p2, p3] --IType: List(NewSparseMultivariatePolynomial(Integer,... --E 14 ---S 15 of 23 +--S 15 of 24 zeroSetSplit(lp)$ST --R --R @@ -133876,7 +139320,7 @@ zeroSetSplit(lp)$ST --IType: List(SquareFreeRegularTriangularSet(Integer,... --E 15 ---S 16 of 23 +--S 16 of 24 zeroSetSplit(lp,false)$ST --R --R @@ -133888,7 +139332,7 @@ zeroSetSplit(lp,false)$ST --IType: List(SquareFreeRegularTriangularSet(Integer,... --E 16 ---S 17 of 23 +--S 17 of 24 T := REGSET(R,E,V,P) --R --R @@ -133899,7 +139343,7 @@ T := REGSET(R,E,V,P) --R Type: Domain --E 17 ---S 18 of 23 +--S 18 of 24 lts := zeroSetSplit(lp,false)$T --R --R @@ -133911,7 +139355,7 @@ lts := zeroSetSplit(lp,false)$T --IType: List(RegularTriangularSet(Integer,IndexedExponents(... --E 18 ---S 19 of 23 +--S 19 of 24 ts := lts.2 --R --R @@ -133920,7 +139364,7 @@ ts := lts.2 --IType: RegularTriangularSet(Integer,IndexedExponents(... --E 19 ---S 20 of 23 +--S 20 of 24 pol := select(ts,'y)$T --R --R @@ -133929,7 +139373,7 @@ pol := select(ts,'y)$T --IType: Union(NewSparseMultivariatePolynomial(Integer,... --E 20 ---S 21 of 23 +--S 21 of 24 tower := collectUnder(ts,'y)$T --R --R @@ -133938,7 +139382,7 @@ tower := collectUnder(ts,'y)$T --IType: RegularTriangularSet(Integer,IndexedExponents(... --E 21 ---S 22 of 23 +--S 22 of 24 pack := RegularTriangularSetGcdPackage(R,E,V,P,T) --R --R @@ -133951,7 +139395,7 @@ pack := RegularTriangularSetGcdPackage(R,E,V,P,T) --R Type: Domain --E 22 ---S 23 of 23 +--S 23 of 24 toseSquareFreePart(pol,tower)$pack --R --R @@ -133959,6 +139403,114 @@ toseSquareFreePart(pol,tower)$pack --R (23) [[val= t y + z ,tower= {t - 1,z - t}]] --IType: List(Record(val: NewSparseMultivariatePolynomial(... --E 23 + +--S 24 of 24 +)show SquareFreeRegularTriangularSet +--R +--R SquareFreeRegularTriangularSet(R: GcdDomain,E: OrderedAbelianMonoidSup,V: OrderedSet,P: RecursivePolynomialCategory(R,E,V)) is a domain constructor +--R Abbreviation for SquareFreeRegularTriangularSet is SREGSET +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for SREGSET +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean algebraic? : (V,%) -> Boolean +--R algebraicVariables : % -> List(V) augment : (List(P),%) -> List(%) +--R augment : (P,List(%)) -> List(%) augment : (P,%) -> List(%) +--R coerce : % -> List(P) coerce : % -> OutputForm +--R collect : (%,V) -> % collectQuasiMonic : % -> % +--R collectUnder : (%,V) -> % collectUpper : (%,V) -> % +--R construct : List(P) -> % copy : % -> % +--R degree : % -> NonNegativeInteger empty : () -> % +--R empty? : % -> Boolean eq? : (%,%) -> Boolean +--R extend : (List(P),%) -> List(%) extend : (P,List(%)) -> List(%) +--R extend : (P,%) -> List(%) extend : (%,P) -> % +--R first : % -> Union(P,"failed") hash : % -> SingleInteger +--R headReduce : (P,%) -> P headReduced? : % -> Boolean +--R headReduced? : (P,%) -> Boolean infRittWu? : (%,%) -> Boolean +--R initiallyReduce : (P,%) -> P initiallyReduced? : % -> Boolean +--R initials : % -> List(P) internalAugment : (List(P),%) -> % +--R internalAugment : (P,%) -> % intersect : (P,List(%)) -> List(%) +--R intersect : (List(P),%) -> List(%) intersect : (P,%) -> List(%) +--R invertible? : (P,%) -> Boolean invertibleSet : (P,%) -> List(%) +--R last : % -> Union(P,"failed") latex : % -> String +--R mainVariable? : (V,%) -> Boolean mainVariables : % -> List(V) +--R map : ((P -> P),%) -> % mvar : % -> V +--R normalized? : % -> Boolean normalized? : (P,%) -> Boolean +--R purelyAlgebraic? : % -> Boolean purelyAlgebraic? : (P,%) -> Boolean +--R reduceByQuasiMonic : (P,%) -> P removeZero : (P,%) -> P +--R rest : % -> Union(%,"failed") retract : List(P) -> % +--R sample : () -> % select : (%,V) -> Union(P,"failed") +--R stronglyReduce : (P,%) -> P stronglyReduced? : % -> Boolean +--R stronglyReduced? : (P,%) -> Boolean trivialIdeal? : % -> Boolean +--R variables : % -> List(V) zeroSetSplit : List(P) -> List(%) +--R ?~=? : (%,%) -> Boolean +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R algebraicCoefficients? : (P,%) -> Boolean +--R any? : ((P -> Boolean),%) -> Boolean if $ has finiteAggregate +--R augment : (List(P),List(%)) -> List(%) +--R autoReduced? : (%,((P,List(P)) -> Boolean)) -> Boolean +--R basicSet : (List(P),(P -> Boolean),((P,P) -> Boolean)) -> Union(Record(bas: %,top: List(P)),"failed") +--R basicSet : (List(P),((P,P) -> Boolean)) -> Union(Record(bas: %,top: List(P)),"failed") +--R coHeight : % -> NonNegativeInteger if V has FINITE +--R convert : % -> InputForm if P has KONVERT(INFORM) +--R count : ((P -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R count : (P,%) -> NonNegativeInteger if $ has finiteAggregate and P has SETCAT +--R eval : (%,List(Equation(P))) -> % if P has EVALAB(P) and P has SETCAT +--R eval : (%,Equation(P)) -> % if P has EVALAB(P) and P has SETCAT +--R eval : (%,P,P) -> % if P has EVALAB(P) and P has SETCAT +--R eval : (%,List(P),List(P)) -> % if P has EVALAB(P) and P has SETCAT +--R every? : ((P -> Boolean),%) -> Boolean if $ has finiteAggregate +--R extend : (List(P),List(%)) -> List(%) +--R extendIfCan : (%,P) -> Union(%,"failed") +--R find : ((P -> Boolean),%) -> Union(P,"failed") +--R headRemainder : (P,%) -> Record(num: P,den: R) if R has INTDOM +--R initiallyReduced? : (P,%) -> Boolean +--R internalAugment : (P,%,Boolean,Boolean,Boolean,Boolean,Boolean) -> List(%) +--R internalZeroSetSplit : (List(P),Boolean,Boolean,Boolean) -> List(%) +--R intersect : (List(P),List(%)) -> List(%) +--R invertible? : (P,%) -> List(Record(val: Boolean,tower: %)) +--R invertibleElseSplit? : (P,%) -> Union(Boolean,List(%)) +--R lastSubResultant : (P,P,%) -> List(Record(val: P,tower: %)) +--R lastSubResultantElseSplit : (P,P,%) -> Union(P,List(%)) +--R less? : (%,NonNegativeInteger) -> Boolean +--R map! : ((P -> P),%) -> % if $ has shallowlyMutable +--R member? : (P,%) -> Boolean if $ has finiteAggregate and P has SETCAT +--R members : % -> List(P) if $ has finiteAggregate +--R more? : (%,NonNegativeInteger) -> Boolean +--R parts : % -> List(P) if $ has finiteAggregate +--R preprocess : (List(P),Boolean,Boolean) -> Record(val: List(P),towers: List(%)) +--R purelyAlgebraicLeadingMonomial? : (P,%) -> Boolean +--R purelyTranscendental? : (P,%) -> Boolean +--R quasiComponent : % -> Record(close: List(P),open: List(P)) +--R reduce : (P,%,((P,P) -> P),((P,P) -> Boolean)) -> P +--R reduce : (((P,P) -> P),%) -> P if $ has finiteAggregate +--R reduce : (((P,P) -> P),%,P) -> P if $ has finiteAggregate +--R reduce : (((P,P) -> P),%,P,P) -> P if $ has finiteAggregate and P has SETCAT +--R reduced? : (P,%,((P,P) -> Boolean)) -> Boolean +--R remainder : (P,%) -> Record(rnum: R,polnum: P,den: R) if R has INTDOM +--R remove : ((P -> Boolean),%) -> % if $ has finiteAggregate +--R remove : (P,%) -> % if $ has finiteAggregate and P has SETCAT +--R removeDuplicates : % -> % if $ has finiteAggregate and P has SETCAT +--R retractIfCan : List(P) -> Union(%,"failed") +--R rewriteIdealWithHeadRemainder : (List(P),%) -> List(P) if R has INTDOM +--R rewriteIdealWithRemainder : (List(P),%) -> List(P) if R has INTDOM +--R rewriteSetWithReduction : (List(P),%,((P,P) -> P),((P,P) -> Boolean)) -> List(P) +--R roughBase? : % -> Boolean if R has INTDOM +--R roughEqualIdeals? : (%,%) -> Boolean if R has INTDOM +--R roughSubIdeal? : (%,%) -> Boolean if R has INTDOM +--R roughUnitIdeal? : % -> Boolean if R has INTDOM +--R select : ((P -> Boolean),%) -> % if $ has finiteAggregate +--R size? : (%,NonNegativeInteger) -> Boolean +--R sort : (%,V) -> Record(under: %,floor: %,upper: %) +--R squareFreePart : (P,%) -> List(Record(val: P,tower: %)) +--R triangular? : % -> Boolean if R has INTDOM +--R zeroSetSplit : (List(P),Boolean,Boolean,Boolean,Boolean) -> List(%) +--R zeroSetSplit : (List(P),Boolean,Boolean) -> List(%) +--R zeroSetSplit : (List(P),Boolean) -> List(%) +--R zeroSetSplitIntoTriangularSystems : List(P) -> List(Record(close: %,open: List(P))) +--R +--E 24 + )spool )lisp (bye) \end{chunk} @@ -134721,13 +140273,112 @@ SquareFreeRegularTriangularSet(R,E,V,P) : Exports == Implementation where )set message test on )set message auto off )clear all ---S 1 of 6 + +--S 1 of 7 +)show SquareMatrix +--R +--R SquareMatrix(ndim: NonNegativeInteger,R: Ring) is a domain constructor +--R Abbreviation for SquareMatrix is SQMATRIX +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for SQMATRIX +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (R,%) -> % ?*? : (%,R) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?/? : (%,R) -> % if R has FIELD +--R ?=? : (%,%) -> Boolean D : % -> % if R has DIFRING +--R D : (%,(R -> R)) -> % 1 : () -> % +--R 0 : () -> % ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,PositiveInteger) -> % antisymmetric? : % -> Boolean +--R coerce : % -> Matrix(R) coerce : R -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R copy : % -> % diagonal? : % -> Boolean +--R diagonalMatrix : List(R) -> % diagonalProduct : % -> R +--R differentiate : (%,(R -> R)) -> % elt : (%,Integer,Integer) -> R +--R elt : (%,Integer,Integer,R) -> R empty : () -> % +--R empty? : % -> Boolean eq? : (%,%) -> Boolean +--R hash : % -> SingleInteger latex : % -> String +--R listOfLists : % -> List(List(R)) map : ((R -> R),%) -> % +--R map : (((R,R) -> R),%,%) -> % matrix : List(List(R)) -> % +--R maxColIndex : % -> Integer maxRowIndex : % -> Integer +--R minColIndex : % -> Integer minRowIndex : % -> Integer +--R ncols : % -> NonNegativeInteger nrows : % -> NonNegativeInteger +--R one? : % -> Boolean qelt : (%,Integer,Integer) -> R +--R recip : % -> Union(%,"failed") retract : % -> R +--R sample : () -> % scalarMatrix : R -> % +--R square? : % -> Boolean squareMatrix : Matrix(R) -> % +--R symmetric? : % -> Boolean trace : % -> R +--R transpose : % -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R ?*? : (DirectProduct(ndim,R),%) -> DirectProduct(ndim,R) +--R ?*? : (%,DirectProduct(ndim,R)) -> DirectProduct(ndim,R) +--R ?**? : (%,Integer) -> % if R has FIELD +--R D : (%,NonNegativeInteger) -> % if R has DIFRING +--R D : (%,Symbol) -> % if R has PDRING(SYMBOL) +--R D : (%,List(Symbol)) -> % if R has PDRING(SYMBOL) +--R D : (%,Symbol,NonNegativeInteger) -> % if R has PDRING(SYMBOL) +--R D : (%,List(Symbol),List(NonNegativeInteger)) -> % if R has PDRING(SYMBOL) +--R D : (%,(R -> R),NonNegativeInteger) -> % +--R any? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate +--R characteristic : () -> NonNegativeInteger +--R coerce : Fraction(Integer) -> % if R has RETRACT(FRAC(INT)) +--R column : (%,Integer) -> DirectProduct(ndim,R) +--R convert : % -> InputForm if R has KONVERT(INFORM) +--R count : (R,%) -> NonNegativeInteger if $ has finiteAggregate and R has SETCAT +--R count : ((R -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R determinant : % -> R if R has commutative(*) +--R diagonal : % -> DirectProduct(ndim,R) +--R differentiate : % -> % if R has DIFRING +--R differentiate : (%,NonNegativeInteger) -> % if R has DIFRING +--R differentiate : (%,Symbol) -> % if R has PDRING(SYMBOL) +--R differentiate : (%,List(Symbol)) -> % if R has PDRING(SYMBOL) +--R differentiate : (%,Symbol,NonNegativeInteger) -> % if R has PDRING(SYMBOL) +--R differentiate : (%,List(Symbol),List(NonNegativeInteger)) -> % if R has PDRING(SYMBOL) +--R differentiate : (%,(R -> R),NonNegativeInteger) -> % +--R eval : (%,List(R),List(R)) -> % if R has EVALAB(R) and R has SETCAT +--R eval : (%,R,R) -> % if R has EVALAB(R) and R has SETCAT +--R eval : (%,Equation(R)) -> % if R has EVALAB(R) and R has SETCAT +--R eval : (%,List(Equation(R))) -> % if R has EVALAB(R) and R has SETCAT +--R every? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate +--R exquo : (%,R) -> Union(%,"failed") if R has INTDOM +--R inverse : % -> Union(%,"failed") if R has FIELD +--R less? : (%,NonNegativeInteger) -> Boolean +--R map! : ((R -> R),%) -> % if $ has shallowlyMutable +--R member? : (R,%) -> Boolean if $ has finiteAggregate and R has SETCAT +--R members : % -> List(R) if $ has finiteAggregate +--R minordet : % -> R if R has commutative(*) +--R more? : (%,NonNegativeInteger) -> Boolean +--R nullSpace : % -> List(DirectProduct(ndim,R)) if R has INTDOM +--R nullity : % -> NonNegativeInteger if R has INTDOM +--R parts : % -> List(R) if $ has finiteAggregate +--R rank : % -> NonNegativeInteger if R has INTDOM +--R reducedSystem : Matrix(%) -> Matrix(R) +--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(R),vec: Vector(R)) +--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(Integer),vec: Vector(Integer)) if R has LINEXP(INT) +--R reducedSystem : Matrix(%) -> Matrix(Integer) if R has LINEXP(INT) +--R retract : % -> Fraction(Integer) if R has RETRACT(FRAC(INT)) +--R retract : % -> Integer if R has RETRACT(INT) +--R retractIfCan : % -> Union(R,"failed") +--R retractIfCan : % -> Union(Fraction(Integer),"failed") if R has RETRACT(FRAC(INT)) +--R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT(INT) +--R row : (%,Integer) -> DirectProduct(ndim,R) +--R rowEchelon : % -> % if R has EUCDOM +--R size? : (%,NonNegativeInteger) -> Boolean +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R +--E 7 + +--S 2 of 7 )set expose add constructor SquareMatrix --R --I SquareMatrix is now explicitly exposed in frame frame0 ---E 1 +--E 2 ---S 2 of 6 +--S 3 of 7 m := squareMatrix [ [1,-%i],[%i,4] ] --R --R @@ -134735,9 +140386,9 @@ m := squareMatrix [ [1,-%i],[%i,4] ] --R (1) | | --R +%i 4 + --R Type: SquareMatrix(2,Complex(Integer)) ---E 2 +--E 3 ---S 3 of 6 +--S 4 of 7 m*m - m --R --R @@ -134745,9 +140396,9 @@ m*m - m --R (2) | | --R +4%i 13 + --R Type: SquareMatrix(2,Complex(Integer)) ---E 3 +--E 4 ---S 4 of 6 +--S 5 of 7 mm := squareMatrix [ [m, 1], [1-m, m**2] ] --R --R @@ -134759,9 +140410,9 @@ mm := squareMatrix [ [m, 1], [1-m, m**2] ] --R || | | || --R ++- %i - 3+ +5%i 17 ++ --R Type: SquareMatrix(2,SquareMatrix(2,Complex(Integer))) ---E 4 +--E 5 ---S 5 of 6 +--S 6 of 7 p := (x + m)**2 --R --R @@ -134769,9 +140420,9 @@ p := (x + m)**2 --R (4) x + | |x + | | --R +2%i 8 + +5%i 17 + --R Type: Polynomial(SquareMatrix(2,Complex(Integer))) ---E 5 +--E 6 ---S 6 of 6 +--S 7 of 7 p::SquareMatrix(2, ?) --R --R @@ -134781,7 +140432,8 @@ p::SquareMatrix(2, ?) --R | 2 | --R +2%i x + 5%i x + 8x + 17 + --R Type: SquareMatrix(2,Polynomial(Complex(Integer))) ---E 6 +--E 7 + )spool )lisp (bye) \end{chunk} @@ -135409,10 +141061,10 @@ latex a --R depth : % -> NonNegativeInteger empty : () -> % --R empty? : % -> Boolean eq? : (%,%) -> Boolean --R extract! : % -> S insert! : (S,%) -> % ---R inspect : % -> S map : ((S -> S),%) -> % ---R pop! : % -> S push! : (S,%) -> S ---R sample : () -> % stack : List(S) -> % ---R top : % -> S +--R inspect : % -> S latex : % -> String if S has SETCAT +--R map : ((S -> S),%) -> % pop! : % -> S +--R push! : (S,%) -> S sample : () -> % +--R stack : List(S) -> % top : % -> S --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R ?=? : (%,%) -> Boolean if S has SETCAT --R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate @@ -135425,7 +141077,6 @@ latex a --R eval : (%,List(Equation(S))) -> % if S has EVALAB(S) and S has SETCAT --R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate --R hash : % -> SingleInteger if S has SETCAT ---R latex : % -> String if S has SETCAT --R less? : (%,NonNegativeInteger) -> Boolean --R map! : ((S -> S),%) -> % if $ has shallowlyMutable --R member? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT @@ -135436,6 +141087,7 @@ latex a --R ?~=? : (%,%) -> Boolean if S has SETCAT --R --E 44 + )spool )lisp (bye) @@ -135910,7 +141562,7 @@ Stack(S:SetCategory): StackAggregate S with )set message auto off )clear all ---S 1 of 12 +--S 1 of 13 dt := introduce!(t,dt) --R --R @@ -135918,7 +141570,7 @@ dt := introduce!(t,dt) --R Type: Union(BasicStochasticDifferential,...) --E 1 ---S 2 of 12 +--S 2 of 13 dX := introduce!(X,dX) --R --R @@ -135926,7 +141578,7 @@ dX := introduce!(X,dX) --R Type: Union(BasicStochasticDifferential,...) --E 2 ---S 3 of 12 +--S 3 of 13 dY := introduce!(Y,dY) --R --R @@ -135934,7 +141586,7 @@ dY := introduce!(Y,dY) --R Type: Union(BasicStochasticDifferential,...) --E 3 ---S 4 of 12 +--S 4 of 13 copyBSD() --R --R @@ -135942,7 +141594,7 @@ copyBSD() --R Type: List(BasicStochasticDifferential) --E 4 ---S 5 of 12 +--S 5 of 13 copyIto() --R --R @@ -135950,7 +141602,7 @@ copyIto() --R Type: Table(Symbol,BasicStochasticDifferential) --E 5 ---S 6 of 12 +--S 6 of 13 copyQuadVar() -- display of multiplication table --R --R @@ -135958,7 +141610,7 @@ copyQuadVar() -- display of multiplication table --R Type: Table(StochasticDifferential(Integer),StochasticDifferential(Integer)) --E 6 ---S 7 of 12 +--S 7 of 13 statusIto() --R --R @@ -135976,7 +141628,7 @@ statusIto() --R Type: OutputForm --E 7 ---S 8 of 12 +--S 8 of 13 copyDrift() -- display of drift list --R --R @@ -135984,7 +141636,7 @@ copyDrift() -- display of drift list --R Type: Table(StochasticDifferential(Integer),StochasticDifferential(Integer)) --E 8 ---S 9 of 12 +--S 9 of 13 nbsd := #copyBSD() --R --R @@ -135992,7 +141644,7 @@ nbsd := #copyBSD() --R Type: PositiveInteger --E 9 ---S 10 of 12 +--S 10 of 13 ItoMultArray:ARRAY2(SD INT) :=new(nbsd,nbsd,0$SD(INT)) --R --R @@ -136004,7 +141656,7 @@ ItoMultArray:ARRAY2(SD INT) :=new(nbsd,nbsd,0$SD(INT)) --R Type: TwoDimensionalArray(StochasticDifferential(Integer)) --E 10 ---S 11 of 12 +--S 11 of 13 ItoMultArray --R --R @@ -136016,7 +141668,7 @@ ItoMultArray --R Type: TwoDimensionalArray(StochasticDifferential(Integer)) --E 11 ---S 12 of 12 +--S 12 of 13 statusIto() --R --R @@ -136033,6 +141685,44 @@ statusIto() --R + dt : ? ? ? + --R Type: OutputForm --E 12 + +--S 13 of 13 +)show StochasticDifferential +--R +--R StochasticDifferential(R: Join(OrderedSet,IntegralDomain)) is a domain constructor +--R Abbreviation for StochasticDifferential is SD +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for SD +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (Expression(R),%) -> % ?*? : (%,Expression(R)) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % +--R ?-? : (%,%) -> % -? : % -> % +--R ?/? : (%,Expression(R)) -> % ?=? : (%,%) -> Boolean +--R 0 : () -> % ?^? : (%,PositiveInteger) -> % +--R coerce : % -> OutputForm copyDrift : () -> Table(%,%) +--R copyQuadVar : () -> Table(%,%) drift : % -> % +--R hash : % -> SingleInteger latex : % -> String +--R sample : () -> % statusIto : () -> OutputForm +--R uncorrelated? : (%,%) -> Boolean zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R alterDrift! : (BasicStochasticDifferential,%) -> Union(%,"failed") +--R alterQuadVar! : (BasicStochasticDifferential,BasicStochasticDifferential,%) -> Union(%,"failed") +--R coefficient : (%,BasicStochasticDifferential) -> Expression(R) +--R coerce : BasicStochasticDifferential -> % +--R equation : (R,%) -> Union(Equation(%),"failed") +--R equation : (%,R) -> Union(Equation(%),"failed") +--R freeOf? : (%,BasicStochasticDifferential) -> Boolean +--R listSD : % -> List(BasicStochasticDifferential) +--R retract : % -> BasicStochasticDifferential +--R retractIfCan : % -> Union(BasicStochasticDifferential,"failed") +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R uncorrelated? : List(List(%)) -> Boolean +--R uncorrelated? : (List(%),List(%)) -> Boolean +--R +--E 13 )spool )lisp (bye) @@ -136397,7 +142087,8 @@ StochasticDifferential(R:Join(OrderedSet, IntegralDomain)): )set message test on )set message auto off )clear all ---S 1 of 12 + +--S 1 of 13 ints := [i for i in 0..] --R --R @@ -136405,19 +142096,19 @@ ints := [i for i in 0..] --R Type: Stream(NonNegativeInteger) --E 1 ---S 2 of 12 +--S 2 of 13 f : List INT -> List INT --R --R Type: Void --E 2 ---S 3 of 12 +--S 3 of 13 f x == [x.1 + x.2, x.1] --R --R Type: Void --E 3 ---S 4 of 12 +--S 4 of 13 fibs := [i.2 for i in [generate(f,[1,1])]] --R --R Compiling function f with type List(Integer) -> List(Integer) @@ -136426,7 +142117,7 @@ fibs := [i.2 for i in [generate(f,[1,1])]] --R Type: Stream(Integer) --E 4 ---S 5 of 12 +--S 5 of 13 [i for i in ints | odd? i] --R --R @@ -136434,7 +142125,7 @@ fibs := [i.2 for i in [generate(f,[1,1])]] --R Type: Stream(NonNegativeInteger) --E 5 ---S 6 of 12 +--S 6 of 13 odds := [2*i+1 for i in ints] --R --R @@ -136442,7 +142133,7 @@ odds := [2*i+1 for i in ints] --R Type: Stream(NonNegativeInteger) --E 6 ---S 7 of 12 +--S 7 of 13 scan(0,+,odds) --R --R @@ -136450,7 +142141,7 @@ scan(0,+,odds) --R Type: Stream(NonNegativeInteger) --E 7 ---S 8 of 12 +--S 8 of 13 [i*j for i in ints for j in odds] --R --R @@ -136458,7 +142149,7 @@ scan(0,+,odds) --R Type: Stream(NonNegativeInteger) --E 8 ---S 9 of 12 +--S 9 of 13 map(*,ints,odds) --R --R @@ -136466,7 +142157,7 @@ map(*,ints,odds) --R Type: Stream(NonNegativeInteger) --E 9 ---S 10 of 12 +--S 10 of 13 first ints --R --R @@ -136474,7 +142165,7 @@ first ints --R Type: NonNegativeInteger --E 10 ---S 11 of 12 +--S 11 of 13 rest ints --R --R @@ -136482,13 +142173,120 @@ rest ints --R Type: Stream(NonNegativeInteger) --E 11 ---S 12 of 12 +--S 12 of 13 fibs 20 --R --R --R (12) 6765 --R Type: PositiveInteger --E 12 + +--S 13 of 13 +)show Stream +--R +--R Stream(S: Type) is a domain constructor +--R Abbreviation for Stream is STREAM +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for STREAM +--R +--R------------------------------- Operations -------------------------------- +--R children : % -> List(%) coerce : List(S) -> % +--R complete : % -> % concat : (%,S) -> % +--R concat : List(%) -> % concat : (S,%) -> % +--R concat : (%,%) -> % cons : (S,%) -> % +--R construct : List(S) -> % copy : % -> % +--R cycleEntry : % -> % cycleTail : % -> % +--R cyclic? : % -> Boolean delay : (() -> %) -> % +--R delete : (%,Integer) -> % distance : (%,%) -> Integer +--R elt : (%,Integer,S) -> S ?.? : (%,Integer) -> S +--R ?.last : (%,last) -> S ?.rest : (%,rest) -> % +--R ?.first : (%,first) -> S ?.value : (%,value) -> S +--R empty : () -> % empty? : % -> Boolean +--R entries : % -> List(S) eq? : (%,%) -> Boolean +--R explicitEntries? : % -> Boolean explicitlyEmpty? : % -> Boolean +--R explicitlyFinite? : % -> Boolean extend : (%,Integer) -> % +--R first : % -> S frst : % -> S +--R generate : ((S -> S),S) -> % generate : (() -> S) -> % +--R index? : (Integer,%) -> Boolean indices : % -> List(Integer) +--R insert : (S,%,Integer) -> % insert : (%,%,Integer) -> % +--R last : (%,NonNegativeInteger) -> % last : % -> S +--R latex : % -> String if S has SETCAT lazy? : % -> Boolean +--R lazyEvaluate : % -> % leaf? : % -> Boolean +--R leaves : % -> List(S) map : (((S,S) -> S),%,%) -> % +--R map : ((S -> S),%) -> % new : (NonNegativeInteger,S) -> % +--R nodes : % -> List(%) possiblyInfinite? : % -> Boolean +--R qelt : (%,Integer) -> S remove : ((S -> Boolean),%) -> % +--R repeating : List(S) -> % rest : (%,NonNegativeInteger) -> % +--R rest : % -> % rst : % -> % +--R sample : () -> % second : % -> S +--R select : ((S -> Boolean),%) -> % setrest! : (%,Integer,%) -> % +--R tail : % -> % third : % -> S +--R value : % -> S +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R ?=? : (%,%) -> Boolean if S has SETCAT +--R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R child? : (%,%) -> Boolean if S has SETCAT +--R coerce : % -> OutputForm if S has SETCAT +--R concat! : (%,S) -> % if $ has shallowlyMutable +--R concat! : (%,%) -> % if $ has shallowlyMutable +--R convert : % -> InputForm if S has KONVERT(INFORM) +--R count : (S,%) -> NonNegativeInteger if $ has finiteAggregate and S has SETCAT +--R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R cycleLength : % -> NonNegativeInteger +--R cycleSplit! : % -> % if $ has shallowlyMutable +--R delete : (%,UniversalSegment(Integer)) -> % +--R ?.? : (%,UniversalSegment(Integer)) -> % +--R entry? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT +--R eval : (%,List(S),List(S)) -> % if S has EVALAB(S) and S has SETCAT +--R eval : (%,S,S) -> % if S has EVALAB(S) and S has SETCAT +--R eval : (%,Equation(S)) -> % if S has EVALAB(S) and S has SETCAT +--R eval : (%,List(Equation(S))) -> % if S has EVALAB(S) and S has SETCAT +--R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R fill! : (%,S) -> % if $ has shallowlyMutable +--R filterUntil : ((S -> Boolean),%) -> % +--R filterWhile : ((S -> Boolean),%) -> % +--R find : ((S -> Boolean),%) -> Union(S,"failed") +--R findCycle : (NonNegativeInteger,%) -> Record(cycle?: Boolean,prefix: NonNegativeInteger,period: NonNegativeInteger) +--R first : (%,NonNegativeInteger) -> % +--R hash : % -> SingleInteger if S has SETCAT +--R less? : (%,NonNegativeInteger) -> Boolean +--R map! : ((S -> S),%) -> % if $ has shallowlyMutable +--R maxIndex : % -> Integer if Integer has ORDSET +--R member? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT +--R members : % -> List(S) if $ has finiteAggregate +--R minIndex : % -> Integer if Integer has ORDSET +--R more? : (%,NonNegativeInteger) -> Boolean +--R node? : (%,%) -> Boolean if S has SETCAT +--R numberOfComputedEntries : % -> NonNegativeInteger +--R output : (Integer,%) -> Void if S has SETCAT +--R parts : % -> List(S) if $ has finiteAggregate +--R qsetelt! : (%,Integer,S) -> S if $ has shallowlyMutable +--R reduce : (((S,S) -> S),%,S,S) -> S if $ has finiteAggregate and S has SETCAT +--R reduce : (((S,S) -> S),%,S) -> S if $ has finiteAggregate +--R reduce : (((S,S) -> S),%) -> S if $ has finiteAggregate +--R remove : (S,%) -> % if $ has finiteAggregate and S has SETCAT +--R removeDuplicates : % -> % if $ has finiteAggregate and S has SETCAT +--R repeating? : (List(S),%) -> Boolean if S has SETCAT +--R setchildren! : (%,List(%)) -> % if $ has shallowlyMutable +--R setelt : (%,Integer,S) -> S if $ has shallowlyMutable +--R setelt : (%,UniversalSegment(Integer),S) -> S if $ has shallowlyMutable +--R setelt : (%,last,S) -> S if $ has shallowlyMutable +--R setelt : (%,rest,%) -> % if $ has shallowlyMutable +--R setelt : (%,first,S) -> S if $ has shallowlyMutable +--R setelt : (%,value,S) -> S if $ has shallowlyMutable +--R setfirst! : (%,S) -> S if $ has shallowlyMutable +--R setlast! : (%,S) -> S if $ has shallowlyMutable +--R setrest! : (%,%) -> % if $ has shallowlyMutable +--R setvalue! : (%,S) -> S if $ has shallowlyMutable +--R showAll? : () -> Boolean if S has SETCAT +--R showAllElements : % -> OutputForm if S has SETCAT +--R size? : (%,NonNegativeInteger) -> Boolean +--R split! : (%,Integer) -> % if $ has shallowlyMutable +--R swap! : (%,Integer,Integer) -> Void if $ has shallowlyMutable +--R ?~=? : (%,%) -> Boolean if S has SETCAT +--R +--E 13 + )spool )lisp (bye) \end{chunk} @@ -137343,7 +143141,8 @@ Stream(S): Exports == Implementation where )set message test on )set message auto off )clear all ---S 1 of 35 + +--S 1 of 36 hello := "Hello, I'm AXIOM!" --R --R @@ -137351,7 +143150,7 @@ hello := "Hello, I'm AXIOM!" --R Type: String --E 1 ---S 2 of 35 +--S 2 of 36 said := "Jane said, \_"Look!\_"" --R --R @@ -137359,7 +143158,7 @@ said := "Jane said, \_"Look!\_"" --R Type: String --E 2 ---S 3 of 35 +--S 3 of 36 saw := "She saw exactly one underscore: \_\_." --R --R @@ -137367,7 +143166,7 @@ saw := "She saw exactly one underscore: \_\_." --R Type: String --E 3 ---S 4 of 35 +--S 4 of 36 gasp: String := new(32, char "x") --R --R @@ -137375,7 +143174,7 @@ gasp: String := new(32, char "x") --R Type: String --E 4 ---S 5 of 35 +--S 5 of 36 #gasp --R --R @@ -137383,7 +143182,7 @@ gasp: String := new(32, char "x") --R Type: PositiveInteger --E 5 ---S 6 of 35 +--S 6 of 36 hello.2 --R --R @@ -137391,7 +143190,7 @@ hello.2 --R Type: Character --E 6 ---S 7 of 35 +--S 7 of 36 hello 2 --R --R @@ -137399,7 +143198,7 @@ hello 2 --R Type: Character --E 7 ---S 8 of 35 +--S 8 of 36 hello(2) --R --R @@ -137407,7 +143206,7 @@ hello(2) --R Type: Character --E 8 ---S 9 of 35 +--S 9 of 36 hullo := copy hello --R --R @@ -137415,7 +143214,7 @@ hullo := copy hello --R Type: String --E 9 ---S 10 of 35 +--S 10 of 36 hullo.2 := char "u"; [hello, hullo] --R --R @@ -137423,7 +143222,7 @@ hullo.2 := char "u"; [hello, hullo] --R Type: List(String) --E 10 ---S 11 of 35 +--S 11 of 36 saidsaw := concat ["alpha","---","omega"] --R --R @@ -137431,7 +143230,7 @@ saidsaw := concat ["alpha","---","omega"] --R Type: String --E 11 ---S 12 of 35 +--S 12 of 36 concat("hello ","goodbye") --R --R @@ -137439,7 +143238,7 @@ concat("hello ","goodbye") --R Type: String --E 12 ---S 13 of 35 +--S 13 of 36 "This " "is " "several " "strings " "concatenated." --R --R @@ -137447,7 +143246,7 @@ concat("hello ","goodbye") --R Type: String --E 13 ---S 14 of 35 +--S 14 of 36 hello(1..5) --R --R @@ -137455,7 +143254,7 @@ hello(1..5) --R Type: String --E 14 ---S 15 of 35 +--S 15 of 36 hello(8..) --R --R @@ -137463,7 +143262,7 @@ hello(8..) --R Type: String --E 15 ---S 16 of 35 +--S 16 of 36 split(hello, char " ") --R --R @@ -137471,13 +143270,13 @@ split(hello, char " ") --R Type: List(String) --E 16 ---S 17 of 35 +--S 17 of 36 other := complement alphanumeric(); --R --R Type: CharacterClass --E 17 ---S 18 of 35 +--S 18 of 36 split(saidsaw, other) --R --R @@ -137485,7 +143284,7 @@ split(saidsaw, other) --R Type: List(String) --E 18 ---S 19 of 35 +--S 19 of 36 trim("## ++ relax ++ ##", char "#") --R --R @@ -137493,7 +143292,7 @@ trim("## ++ relax ++ ##", char "#") --R Type: String --E 19 ---S 20 of 35 +--S 20 of 36 trim("## ++ relax ++ ##", other) --R --R @@ -137501,7 +143300,7 @@ trim("## ++ relax ++ ##", other) --R Type: String --E 20 ---S 21 of 35 +--S 21 of 36 leftTrim("## ++ relax ++ ##", other) --R --R @@ -137509,7 +143308,7 @@ leftTrim("## ++ relax ++ ##", other) --R Type: String --E 21 ---S 22 of 35 +--S 22 of 36 rightTrim("## ++ relax ++ ##", other) --R --R @@ -137517,7 +143316,7 @@ rightTrim("## ++ relax ++ ##", other) --R Type: String --E 22 ---S 23 of 35 +--S 23 of 36 upperCase hello --R --R @@ -137525,7 +143324,7 @@ upperCase hello --R Type: String --E 23 ---S 24 of 35 +--S 24 of 36 lowerCase hello --R --R @@ -137533,7 +143332,7 @@ lowerCase hello --R Type: String --E 24 ---S 25 of 35 +--S 25 of 36 prefix?("He", "Hello") --R --R @@ -137541,7 +143340,7 @@ prefix?("He", "Hello") --R Type: Boolean --E 25 ---S 26 of 35 +--S 26 of 36 prefix?("Her", "Hello") --R --R @@ -137549,7 +143348,7 @@ prefix?("Her", "Hello") --R Type: Boolean --E 26 ---S 27 of 35 +--S 27 of 36 suffix?("", "Hello") --R --R @@ -137557,7 +143356,7 @@ suffix?("", "Hello") --R Type: Boolean --E 27 ---S 28 of 35 +--S 28 of 36 suffix?("LO", "Hello") --R --R @@ -137565,7 +143364,7 @@ suffix?("LO", "Hello") --R Type: Boolean --E 28 ---S 29 of 35 +--S 29 of 36 substring?("ll", "Hello", 3) --R --R @@ -137573,7 +143372,7 @@ substring?("ll", "Hello", 3) --R Type: Boolean --E 29 ---S 30 of 35 +--S 30 of 36 substring?("ll", "Hello", 4) --R --R @@ -137581,7 +143380,7 @@ substring?("ll", "Hello", 4) --R Type: Boolean --E 30 ---S 31 of 35 +--S 31 of 36 n := position("nd", "underground", 1) --R --R @@ -137589,7 +143388,7 @@ n := position("nd", "underground", 1) --R Type: PositiveInteger --E 31 ---S 32 of 35 +--S 32 of 36 n := position("nd", "underground", n+1) --R --R @@ -137597,7 +143396,7 @@ n := position("nd", "underground", n+1) --R Type: PositiveInteger --E 32 ---S 33 of 35 +--S 33 of 36 n := position("nd", "underground", n+1) --R --R @@ -137605,7 +143404,7 @@ n := position("nd", "underground", n+1) --R Type: NonNegativeInteger --E 33 ---S 34 of 35 +--S 34 of 36 position(char "d", "underground", 1) --R --R @@ -137613,13 +143412,116 @@ position(char "d", "underground", 1) --R Type: PositiveInteger --E 34 ---S 35 of 35 +--S 35 of 36 position(hexDigit(), "underground", 1) --R --R --R (35) 3 --R Type: PositiveInteger --E 35 + +--S 36 of 36 +)show String +--R +--R String is a domain constructor +--R Abbreviation for String is STRING +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for STRING +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean OMwrite : (%,Boolean) -> String +--R OMwrite : % -> String coerce : % -> OutputForm +--R coerce : Character -> % concat : List(%) -> % +--R concat : (%,%) -> % concat : (Character,%) -> % +--R concat : (%,Character) -> % construct : List(Character) -> % +--R copy : % -> % delete : (%,Integer) -> % +--R ?.? : (%,%) -> % ?.? : (%,Integer) -> Character +--R empty : () -> % empty? : % -> Boolean +--R entries : % -> List(Character) eq? : (%,%) -> Boolean +--R hash : % -> SingleInteger index? : (Integer,%) -> Boolean +--R indices : % -> List(Integer) insert : (%,%,Integer) -> % +--R latex : % -> String leftTrim : (%,CharacterClass) -> % +--R leftTrim : (%,Character) -> % lowerCase : % -> % +--R lowerCase! : % -> % prefix? : (%,%) -> Boolean +--R qelt : (%,Integer) -> Character reverse : % -> % +--R rightTrim : (%,Character) -> % sample : () -> % +--R split : (%,Character) -> List(%) string : Integer -> % +--R suffix? : (%,%) -> Boolean trim : (%,CharacterClass) -> % +--R trim : (%,Character) -> % upperCase : % -> % +--R upperCase! : % -> % ?~=? : (%,%) -> Boolean +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R ? Boolean if Character has ORDSET +--R ?<=? : (%,%) -> Boolean if Character has ORDSET +--R ?>? : (%,%) -> Boolean if Character has ORDSET +--R ?>=? : (%,%) -> Boolean if Character has ORDSET +--R OMwrite : (OpenMathDevice,%,Boolean) -> Void +--R OMwrite : (OpenMathDevice,%) -> Void +--R any? : ((Character -> Boolean),%) -> Boolean if $ has finiteAggregate +--R convert : % -> InputForm if Character has KONVERT(INFORM) +--R copyInto! : (%,%,Integer) -> % if $ has shallowlyMutable +--R count : (Character,%) -> NonNegativeInteger if $ has finiteAggregate and Character has SETCAT +--R count : ((Character -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R delete : (%,UniversalSegment(Integer)) -> % +--R ?.? : (%,UniversalSegment(Integer)) -> % +--R elt : (%,Integer,Character) -> Character +--R entry? : (Character,%) -> Boolean if $ has finiteAggregate and Character has SETCAT +--R eval : (%,List(Character),List(Character)) -> % if Character has EVALAB(CHAR) and Character has SETCAT +--R eval : (%,Character,Character) -> % if Character has EVALAB(CHAR) and Character has SETCAT +--R eval : (%,Equation(Character)) -> % if Character has EVALAB(CHAR) and Character has SETCAT +--R eval : (%,List(Equation(Character))) -> % if Character has EVALAB(CHAR) and Character has SETCAT +--R every? : ((Character -> Boolean),%) -> Boolean if $ has finiteAggregate +--R fill! : (%,Character) -> % if $ has shallowlyMutable +--R find : ((Character -> Boolean),%) -> Union(Character,"failed") +--R first : % -> Character if Integer has ORDSET +--R insert : (Character,%,Integer) -> % +--R less? : (%,NonNegativeInteger) -> Boolean +--R map : (((Character,Character) -> Character),%,%) -> % +--R map : ((Character -> Character),%) -> % +--R map! : ((Character -> Character),%) -> % if $ has shallowlyMutable +--R match : (%,%,Character) -> NonNegativeInteger +--R match? : (%,%,Character) -> Boolean +--R max : (%,%) -> % if Character has ORDSET +--R maxIndex : % -> Integer if Integer has ORDSET +--R member? : (Character,%) -> Boolean if $ has finiteAggregate and Character has SETCAT +--R members : % -> List(Character) if $ has finiteAggregate +--R merge : (%,%) -> % if Character has ORDSET +--R merge : (((Character,Character) -> Boolean),%,%) -> % +--R min : (%,%) -> % if Character has ORDSET +--R minIndex : % -> Integer if Integer has ORDSET +--R more? : (%,NonNegativeInteger) -> Boolean +--R new : (NonNegativeInteger,Character) -> % +--R parts : % -> List(Character) if $ has finiteAggregate +--R position : (CharacterClass,%,Integer) -> Integer +--R position : (%,%,Integer) -> Integer +--R position : (Character,%,Integer) -> Integer if Character has SETCAT +--R position : (Character,%) -> Integer if Character has SETCAT +--R position : ((Character -> Boolean),%) -> Integer +--R qsetelt! : (%,Integer,Character) -> Character if $ has shallowlyMutable +--R reduce : (((Character,Character) -> Character),%) -> Character if $ has finiteAggregate +--R reduce : (((Character,Character) -> Character),%,Character) -> Character if $ has finiteAggregate +--R reduce : (((Character,Character) -> Character),%,Character,Character) -> Character if $ has finiteAggregate and Character has SETCAT +--R remove : ((Character -> Boolean),%) -> % if $ has finiteAggregate +--R remove : (Character,%) -> % if $ has finiteAggregate and Character has SETCAT +--R removeDuplicates : % -> % if $ has finiteAggregate and Character has SETCAT +--R replace : (%,UniversalSegment(Integer),%) -> % +--R reverse! : % -> % if $ has shallowlyMutable +--R rightTrim : (%,CharacterClass) -> % +--R select : ((Character -> Boolean),%) -> % if $ has finiteAggregate +--R setelt : (%,UniversalSegment(Integer),Character) -> Character if $ has shallowlyMutable +--R setelt : (%,Integer,Character) -> Character if $ has shallowlyMutable +--R size? : (%,NonNegativeInteger) -> Boolean +--R sort : % -> % if Character has ORDSET +--R sort : (((Character,Character) -> Boolean),%) -> % +--R sort! : % -> % if $ has shallowlyMutable and Character has ORDSET +--R sort! : (((Character,Character) -> Boolean),%) -> % if $ has shallowlyMutable +--R sorted? : % -> Boolean if Character has ORDSET +--R sorted? : (((Character,Character) -> Boolean),%) -> Boolean +--R split : (%,CharacterClass) -> List(%) +--R substring? : (%,%,Integer) -> Boolean +--R swap! : (%,Integer,Integer) -> Void if $ has shallowlyMutable +--R +--E 36 + )spool )lisp (bye) \end{chunk} @@ -137990,7 +143892,7 @@ String(): StringCategory == IndexedString(1) add )set message test on )set message auto off )clear all ---S 1 of 3 +--S 1 of 4 t: StringTable(Integer) := table() --R --R @@ -137998,7 +143900,7 @@ t: StringTable(Integer) := table() --R Type: StringTable(Integer) --E 1 ---S 2 of 3 +--S 2 of 4 for s in split("My name is Ian Watt.",char " ") repeat t.s := #s @@ -138006,7 +143908,7 @@ for s in split("My name is Ian Watt.",char " ") --R Type: Void --E 2 ---S 3 of 3 +--S 3 of 4 for key in keys t repeat output [key, t.key] --R --R ["Watt.",5] @@ -138016,6 +143918,91 @@ for key in keys t repeat output [key, t.key] --R ["My",2] --R Type: Void --E 3 + +--S 4 of 4 +)show StringTable +--R +--R StringTable(Entry: SetCategory) is a domain constructor +--R Abbreviation for StringTable is STRTBL +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for STRTBL +--R +--R------------------------------- Operations -------------------------------- +--R copy : % -> % dictionary : () -> % +--R elt : (%,String,Entry) -> Entry ?.? : (%,String) -> Entry +--R empty : () -> % empty? : % -> Boolean +--R entries : % -> List(Entry) eq? : (%,%) -> Boolean +--R index? : (String,%) -> Boolean indices : % -> List(String) +--R key? : (String,%) -> Boolean keys : % -> List(String) +--R map : ((Entry -> Entry),%) -> % qelt : (%,String) -> Entry +--R sample : () -> % setelt : (%,String,Entry) -> Entry +--R table : () -> % +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R ?=? : (%,%) -> Boolean if Record(key: String,entry: Entry) has SETCAT or Entry has SETCAT +--R any? : ((Entry -> Boolean),%) -> Boolean if $ has finiteAggregate +--R any? : ((Record(key: String,entry: Entry) -> Boolean),%) -> Boolean if $ has finiteAggregate +--R bag : List(Record(key: String,entry: Entry)) -> % +--R coerce : % -> OutputForm if Record(key: String,entry: Entry) has SETCAT or Entry has SETCAT +--R construct : List(Record(key: String,entry: Entry)) -> % +--R convert : % -> InputForm if Record(key: String,entry: Entry) has KONVERT(INFORM) +--R count : ((Entry -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R count : (Entry,%) -> NonNegativeInteger if $ has finiteAggregate and Entry has SETCAT +--R count : (Record(key: String,entry: Entry),%) -> NonNegativeInteger if $ has finiteAggregate and Record(key: String,entry: Entry) has SETCAT +--R count : ((Record(key: String,entry: Entry) -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R dictionary : List(Record(key: String,entry: Entry)) -> % +--R entry? : (Entry,%) -> Boolean if $ has finiteAggregate and Entry has SETCAT +--R eval : (%,List(Equation(Entry))) -> % if Entry has EVALAB(Entry) and Entry has SETCAT +--R eval : (%,Equation(Entry)) -> % if Entry has EVALAB(Entry) and Entry has SETCAT +--R eval : (%,Entry,Entry) -> % if Entry has EVALAB(Entry) and Entry has SETCAT +--R eval : (%,List(Entry),List(Entry)) -> % if Entry has EVALAB(Entry) and Entry has SETCAT +--R eval : (%,List(Record(key: String,entry: Entry)),List(Record(key: String,entry: Entry))) -> % if Record(key: String,entry: Entry) has EVALAB(Record(key: String,entry: Entry)) and Record(key: String,entry: Entry) has SETCAT +--R eval : (%,Record(key: String,entry: Entry),Record(key: String,entry: Entry)) -> % if Record(key: String,entry: Entry) has EVALAB(Record(key: String,entry: Entry)) and Record(key: String,entry: Entry) has SETCAT +--R eval : (%,Equation(Record(key: String,entry: Entry))) -> % if Record(key: String,entry: Entry) has EVALAB(Record(key: String,entry: Entry)) and Record(key: String,entry: Entry) has SETCAT +--R eval : (%,List(Equation(Record(key: String,entry: Entry)))) -> % if Record(key: String,entry: Entry) has EVALAB(Record(key: String,entry: Entry)) and Record(key: String,entry: Entry) has SETCAT +--R every? : ((Entry -> Boolean),%) -> Boolean if $ has finiteAggregate +--R every? : ((Record(key: String,entry: Entry) -> Boolean),%) -> Boolean if $ has finiteAggregate +--R extract! : % -> Record(key: String,entry: Entry) +--R fill! : (%,Entry) -> % if $ has shallowlyMutable +--R find : ((Record(key: String,entry: Entry) -> Boolean),%) -> Union(Record(key: String,entry: Entry),"failed") +--R first : % -> Entry if String has ORDSET +--R hash : % -> SingleInteger if Record(key: String,entry: Entry) has SETCAT or Entry has SETCAT +--R insert! : (Record(key: String,entry: Entry),%) -> % +--R inspect : % -> Record(key: String,entry: Entry) +--R latex : % -> String if Record(key: String,entry: Entry) has SETCAT or Entry has SETCAT +--R less? : (%,NonNegativeInteger) -> Boolean +--R map : (((Entry,Entry) -> Entry),%,%) -> % +--R map : ((Record(key: String,entry: Entry) -> Record(key: String,entry: Entry)),%) -> % +--R map! : ((Entry -> Entry),%) -> % if $ has shallowlyMutable +--R map! : ((Record(key: String,entry: Entry) -> Record(key: String,entry: Entry)),%) -> % if $ has shallowlyMutable +--R maxIndex : % -> String if String has ORDSET +--R member? : (Entry,%) -> Boolean if $ has finiteAggregate and Entry has SETCAT +--R member? : (Record(key: String,entry: Entry),%) -> Boolean if $ has finiteAggregate and Record(key: String,entry: Entry) has SETCAT +--R members : % -> List(Entry) if $ has finiteAggregate +--R members : % -> List(Record(key: String,entry: Entry)) if $ has finiteAggregate +--R minIndex : % -> String if String has ORDSET +--R more? : (%,NonNegativeInteger) -> Boolean +--R parts : % -> List(Entry) if $ has finiteAggregate +--R parts : % -> List(Record(key: String,entry: Entry)) if $ has finiteAggregate +--R qsetelt! : (%,String,Entry) -> Entry if $ has shallowlyMutable +--R reduce : (((Record(key: String,entry: Entry),Record(key: String,entry: Entry)) -> Record(key: String,entry: Entry)),%) -> Record(key: String,entry: Entry) if $ has finiteAggregate +--R reduce : (((Record(key: String,entry: Entry),Record(key: String,entry: Entry)) -> Record(key: String,entry: Entry)),%,Record(key: String,entry: Entry)) -> Record(key: String,entry: Entry) if $ has finiteAggregate +--R reduce : (((Record(key: String,entry: Entry),Record(key: String,entry: Entry)) -> Record(key: String,entry: Entry)),%,Record(key: String,entry: Entry),Record(key: String,entry: Entry)) -> Record(key: String,entry: Entry) if $ has finiteAggregate and Record(key: String,entry: Entry) has SETCAT +--R remove : ((Record(key: String,entry: Entry) -> Boolean),%) -> % if $ has finiteAggregate +--R remove : (Record(key: String,entry: Entry),%) -> % if $ has finiteAggregate and Record(key: String,entry: Entry) has SETCAT +--R remove! : (String,%) -> Union(Entry,"failed") +--R remove! : ((Record(key: String,entry: Entry) -> Boolean),%) -> % if $ has finiteAggregate +--R remove! : (Record(key: String,entry: Entry),%) -> % if $ has finiteAggregate +--R removeDuplicates : % -> % if $ has finiteAggregate and Record(key: String,entry: Entry) has SETCAT +--R search : (String,%) -> Union(Entry,"failed") +--R select : ((Record(key: String,entry: Entry) -> Boolean),%) -> % if $ has finiteAggregate +--R select! : ((Record(key: String,entry: Entry) -> Boolean),%) -> % if $ has finiteAggregate +--R size? : (%,NonNegativeInteger) -> Boolean +--R swap! : (%,String,String) -> Void if $ has shallowlyMutable +--R table : List(Record(key: String,entry: Entry)) -> % +--R ?~=? : (%,%) -> Boolean if Record(key: String,entry: Entry) has SETCAT or Entry has SETCAT +--R +--E 4 + )spool )lisp (bye) \end{chunk} @@ -138736,6 +144723,7 @@ SubSpace(n:PI,R:Ring) : Exports == Implementation where --S 1 of 1 )show SubSpaceComponentProperty +--R --R SubSpaceComponentProperty is a domain constructor --R Abbreviation for SubSpaceComponentProperty is COMPPROP --R This constructor is not exposed in this frame. @@ -138855,6 +144843,7 @@ SubSpaceComponentProperty() : Exports == Implementation where --S 1 of 1 )show SuchThat +--R --R SuchThat(S1: SetCategory,S2: SetCategory) is a domain constructor --R Abbreviation for SuchThat is SUCH --R This constructor is not exposed in this frame. @@ -139110,7 +145099,8 @@ Switch():public == private where )set message test on )set message auto off )clear all ---S 1 of 24 + +--S 1 of 25 X: Symbol := 'x --R --R @@ -139118,7 +145108,7 @@ X: Symbol := 'x --R Type: Symbol --E 1 ---S 2 of 24 +--S 2 of 25 XX: Symbol := x --R --R @@ -139126,7 +145116,7 @@ XX: Symbol := x --R Type: Symbol --E 2 ---S 3 of 24 +--S 3 of 25 A := 'a --R --R @@ -139134,7 +145124,7 @@ A := 'a --R Type: Variable(a) --E 3 ---S 4 of 24 +--S 4 of 25 B := b --R --R @@ -139142,7 +145132,7 @@ B := b --R Type: Variable(b) --E 4 ---S 5 of 24 +--S 5 of 25 x**2 + 1 --R --R @@ -139151,7 +145141,7 @@ x**2 + 1 --R Type: Polynomial(Integer) --E 5 ---S 6 of 24 +--S 6 of 25 "Hello"::Symbol --R --R @@ -139159,7 +145149,7 @@ x**2 + 1 --R Type: Symbol --E 6 ---S 7 of 24 +--S 7 of 25 new()$Symbol --R --R @@ -139167,7 +145157,7 @@ new()$Symbol --R Type: Symbol --E 7 ---S 8 of 24 +--S 8 of 25 new()$Symbol --R --R @@ -139175,7 +145165,7 @@ new()$Symbol --R Type: Symbol --E 8 ---S 9 of 24 +--S 9 of 25 new("xyz")$Symbol --R --R @@ -139183,7 +145173,7 @@ new("xyz")$Symbol --R Type: Symbol --E 9 ---S 10 of 24 +--S 10 of 25 X[i,j] --R --R @@ -139192,7 +145182,7 @@ X[i,j] --R Type: Symbol --E 10 ---S 11 of 24 +--S 11 of 25 U := subscript(u, [1,2,1,2]) --R --R @@ -139201,7 +145191,7 @@ U := subscript(u, [1,2,1,2]) --R Type: Symbol --E 11 ---S 12 of 24 +--S 12 of 25 V := superscript(v, [n]) --R --R @@ -139210,7 +145200,7 @@ V := superscript(v, [n]) --R Type: Symbol --E 12 ---S 13 of 24 +--S 13 of 25 P := argscript(p, [t]) --R --R @@ -139218,7 +145208,7 @@ P := argscript(p, [t]) --R Type: Symbol --E 13 ---S 14 of 24 +--S 14 of 25 scripted? U --R --R @@ -139226,7 +145216,7 @@ scripted? U --R Type: Boolean --E 14 ---S 15 of 24 +--S 15 of 25 scripted? X --R --R @@ -139234,7 +145224,7 @@ scripted? X --R Type: Boolean --E 15 ---S 16 of 24 +--S 16 of 25 string X --R --R @@ -139242,7 +145232,7 @@ string X --R Type: String --E 16 ---S 17 of 24 +--S 17 of 25 name U --R --R @@ -139250,7 +145240,7 @@ name U --R Type: Symbol --E 17 ---S 18 of 24 +--S 18 of 25 scripts U --R --R @@ -139258,7 +145248,7 @@ scripts U --IType: Record(sub: List(OutputForm),sup: List(OutputForm),... --E 18 ---S 19 of 24 +--S 19 of 25 name X --R --R @@ -139266,7 +145256,7 @@ name X --R Type: Symbol --E 19 ---S 20 of 24 +--S 20 of 25 scripts X --R --R @@ -139274,7 +145264,7 @@ scripts X --IType: Record(sub: List(OutputForm),sup: List(OutputForm),... --E 20 ---S 21 of 24 +--S 21 of 25 M := script(Mammoth, [ [i,j],[k,l],[0,1],[2],[u,v,w] ]) --R --R @@ -139284,7 +145274,7 @@ M := script(Mammoth, [ [i,j],[k,l],[0,1],[2],[u,v,w] ]) --R Type: Symbol --E 21 ---S 22 of 24 +--S 22 of 25 scripts M --R --R @@ -139292,7 +145282,7 @@ scripts M --IType: Record(sub: List(OutputForm),sup: List(OutputForm),... --E 22 ---S 23 of 24 +--S 23 of 25 N := script(Nut, [ [i,j],[k,l],[0,1] ]) --R --R @@ -139302,13 +145292,50 @@ N := script(Nut, [ [i,j],[k,l],[0,1] ]) --R Type: Symbol --E 23 ---S 24 of 24 +--S 24 of 25 scripts N --R --R --R (24) [sub= [i,j],sup= [k,l],presup= [0,1],presub= [],args= []] --IType: Record(sub: List(OutputForm),sup: List(OutputForm),... --E 24 + +--S 25 of 25 +)show Symbol +--R +--R Symbol is a domain constructor +--R Abbreviation for Symbol is SYMBOL +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for SYMBOL +--R +--R------------------------------- Operations -------------------------------- +--R ? Boolean ?<=? : (%,%) -> Boolean +--R ?=? : (%,%) -> Boolean ?>? : (%,%) -> Boolean +--R ?>=? : (%,%) -> Boolean OMwrite : (%,Boolean) -> String +--R OMwrite : % -> String coerce : String -> % +--R coerce : % -> OutputForm convert : % -> Pattern(Float) +--R convert : % -> Pattern(Integer) convert : % -> Symbol +--R convert : % -> InputForm ?.? : (%,List(OutputForm)) -> % +--R hash : % -> SingleInteger latex : % -> String +--R list : % -> List(%) max : (%,%) -> % +--R min : (%,%) -> % name : % -> % +--R new : % -> % new : () -> % +--R resetNew : () -> Void sample : () -> % +--R scripted? : % -> Boolean string : % -> String +--R ?~=? : (%,%) -> Boolean +--R OMwrite : (OpenMathDevice,%,Boolean) -> Void +--R OMwrite : (OpenMathDevice,%) -> Void +--R argscript : (%,List(OutputForm)) -> % +--R patternMatch : (%,Pattern(Float),PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) +--R patternMatch : (%,Pattern(Integer),PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) +--R script : (%,Record(sub: List(OutputForm),sup: List(OutputForm),presup: List(OutputForm),presub: List(OutputForm),args: List(OutputForm))) -> % +--R script : (%,List(List(OutputForm))) -> % +--R scripts : % -> Record(sub: List(OutputForm),sup: List(OutputForm),presup: List(OutputForm),presub: List(OutputForm),args: List(OutputForm)) +--R subscript : (%,List(OutputForm)) -> % +--R superscript : (%,List(OutputForm)) -> % +--R +--E 25 + )spool )lisp (bye) \end{chunk} @@ -140108,41 +146135,38 @@ SymbolTable() : exports == implementation where --R------------------------------- Operations -------------------------------- --R ?*? : (R,%) -> % ?*? : (%,R) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % ---R -? : % -> % ?=? : (%,%) -> Boolean ---R 1 : () -> % 0 : () -> % +--R -? : % -> % ?/? : (%,R) -> % if R has FIELD +--R ?=? : (%,%) -> Boolean 1 : () -> % +--R 0 : () -> % ?^? : (%,NonNegativeInteger) -> % --R ?^? : (%,PositiveInteger) -> % coefficient : (%,Partition) -> R --R coefficients : % -> List(R) coerce : R -> % ---R coerce : Integer -> % coerce : % -> OutputForm +--R coerce : % -> % if R has INTDOM coerce : Integer -> % +--R coerce : % -> OutputForm content : % -> R if R has GCDDOM --R degree : % -> Partition ground : % -> R --R ground? : % -> Boolean hash : % -> SingleInteger --R latex : % -> String leadingCoefficient : % -> R --R leadingMonomial : % -> % map : ((R -> R),%) -> % --R minimumDegree : % -> Partition monomial : (R,Partition) -> % --R monomial? : % -> Boolean one? : % -> Boolean ---R recip : % -> Union(%,"failed") reductum : % -> % ---R retract : % -> R sample : () -> % ---R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R pomopo! : (%,R,Partition,%) -> % recip : % -> Union(%,"failed") +--R reductum : % -> % retract : % -> R +--R sample : () -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean --R ?*? : (%,Fraction(Integer)) -> % if R has ALGEBRA(FRAC(INT)) --R ?*? : (Fraction(Integer),%) -> % if R has ALGEBRA(FRAC(INT)) ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R ?/? : (%,R) -> % if R has FIELD ---R ?^? : (%,NonNegativeInteger) -> % --R associates? : (%,%) -> Boolean if R has INTDOM --R binomThmExpt : (%,%,NonNegativeInteger) -> % if R has COMRING --R characteristic : () -> NonNegativeInteger --R charthRoot : % -> Union(%,"failed") if R has CHARNZ --R coerce : Fraction(Integer) -> % if R has ALGEBRA(FRAC(INT)) or R has RETRACT(FRAC(INT)) ---R coerce : % -> % if R has INTDOM ---R content : % -> R if R has GCDDOM --R exquo : (%,R) -> Union(%,"failed") if R has INTDOM --R exquo : (%,%) -> Union(%,"failed") if R has INTDOM --R fmecg : (%,Partition,R,%) -> % if Partition has CABMON and R has INTDOM --R mapExponents : ((Partition -> Partition),%) -> % --R numberOfMonomials : % -> NonNegativeInteger ---R pomopo! : (%,R,Partition,%) -> % --R primitivePart : % -> % if R has GCDDOM --R retract : % -> Fraction(Integer) if R has RETRACT(FRAC(INT)) --R retract : % -> Integer if R has RETRACT(INT) @@ -140282,7 +146306,8 @@ SymmetricPolynomial(R:Ring) == PolynomialRing(R,Partition) add )set message test on )set message auto off )clear all ---S 1 of 18 + +--S 1 of 19 t: Table(Polynomial Integer, String) := table() --R --R @@ -140290,7 +146315,7 @@ t: Table(Polynomial Integer, String) := table() --R Type: Table(Polynomial(Integer),String) --E 1 ---S 2 of 18 +--S 2 of 19 setelt(t, x**2 - 1, "Easy to factor") --R --R @@ -140298,7 +146323,7 @@ setelt(t, x**2 - 1, "Easy to factor") --R Type: String --E 2 ---S 3 of 18 +--S 3 of 19 t(x**3 + 1) := "Harder to factor" --R --R @@ -140306,7 +146331,7 @@ t(x**3 + 1) := "Harder to factor" --R Type: String --E 3 ---S 4 of 18 +--S 4 of 19 t(x) := "The easiest to factor" --R --R @@ -140314,7 +146339,7 @@ t(x) := "The easiest to factor" --R Type: String --E 4 ---S 5 of 18 +--S 5 of 19 elt(t, x) --R --R @@ -140322,7 +146347,7 @@ elt(t, x) --R Type: String --E 5 ---S 6 of 18 +--S 6 of 19 t.x --R --R @@ -140330,7 +146355,7 @@ t.x --R Type: String --E 6 ---S 7 of 18 +--S 7 of 19 t x --R --R @@ -140338,7 +146363,7 @@ t x --R Type: String --E 7 ---S 8 of 18 +--S 8 of 19 t.(x**2 - 1) --R --R @@ -140346,7 +146371,7 @@ t.(x**2 - 1) --R Type: String --E 8 ---S 9 of 18 +--S 9 of 19 t (x**3 + 1) --R --R @@ -140354,7 +146379,7 @@ t (x**3 + 1) --R Type: String --E 9 ---S 10 of 18 +--S 10 of 19 keys t --R --R @@ -140363,7 +146388,7 @@ keys t --R Type: List(Polynomial(Integer)) --E 10 ---S 11 of 18 +--S 11 of 19 search(x, t) --R --R @@ -140371,7 +146396,7 @@ search(x, t) --R Type: Union(String,...) --E 11 ---S 12 of 18 +--S 12 of 19 search(x**2, t) --R --R @@ -140379,7 +146404,7 @@ search(x**2, t) --R Type: Union("failed",...) --E 12 ---S 13 of 18 +--S 13 of 19 search(x**2, t) case "failed" --R --R @@ -140387,7 +146412,7 @@ search(x**2, t) case "failed" --R Type: Boolean --E 13 ---S 14 of 18 +--S 14 of 19 remove!(x**2-1, t) --R --R @@ -140395,7 +146420,7 @@ remove!(x**2-1, t) --R Type: Union(String,...) --E 14 ---S 15 of 18 +--S 15 of 19 remove!(x-1, t) --R --R @@ -140403,7 +146428,7 @@ remove!(x-1, t) --R Type: Union("failed",...) --E 15 ---S 16 of 18 +--S 16 of 19 #t --R --R @@ -140411,7 +146436,7 @@ remove!(x-1, t) --R Type: PositiveInteger --E 16 ---S 17 of 18 +--S 17 of 19 members t --R --R @@ -140419,13 +146444,98 @@ members t --R Type: List(String) --E 17 ---S 18 of 18 +--S 18 of 19 count(s: String +-> prefix?("Hard", s), t) --R --R --R (18) 1 --R Type: PositiveInteger --E 18 + +--S 19 of 19 +)show Table +--R +--R Table(Key: SetCategory,Entry: SetCategory) is a domain constructor +--R Abbreviation for Table is TABLE +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for TABLE +--R +--R------------------------------- Operations -------------------------------- +--R copy : % -> % dictionary : () -> % +--R elt : (%,Key,Entry) -> Entry ?.? : (%,Key) -> Entry +--R empty : () -> % empty? : % -> Boolean +--R entries : % -> List(Entry) eq? : (%,%) -> Boolean +--R index? : (Key,%) -> Boolean indices : % -> List(Key) +--R key? : (Key,%) -> Boolean keys : % -> List(Key) +--R map : ((Entry -> Entry),%) -> % qelt : (%,Key) -> Entry +--R sample : () -> % setelt : (%,Key,Entry) -> Entry +--R table : () -> % +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R ?=? : (%,%) -> Boolean if Record(key: Key,entry: Entry) has SETCAT or Entry has SETCAT +--R any? : ((Entry -> Boolean),%) -> Boolean if $ has finiteAggregate +--R any? : ((Record(key: Key,entry: Entry) -> Boolean),%) -> Boolean if $ has finiteAggregate +--R bag : List(Record(key: Key,entry: Entry)) -> % +--R coerce : % -> OutputForm if Record(key: Key,entry: Entry) has SETCAT or Entry has SETCAT +--R construct : List(Record(key: Key,entry: Entry)) -> % +--R convert : % -> InputForm if Record(key: Key,entry: Entry) has KONVERT(INFORM) +--R count : ((Entry -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R count : (Entry,%) -> NonNegativeInteger if $ has finiteAggregate and Entry has SETCAT +--R count : (Record(key: Key,entry: Entry),%) -> NonNegativeInteger if $ has finiteAggregate and Record(key: Key,entry: Entry) has SETCAT +--R count : ((Record(key: Key,entry: Entry) -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R dictionary : List(Record(key: Key,entry: Entry)) -> % +--R entry? : (Entry,%) -> Boolean if $ has finiteAggregate and Entry has SETCAT +--R eval : (%,List(Equation(Entry))) -> % if Entry has EVALAB(Entry) and Entry has SETCAT +--R eval : (%,Equation(Entry)) -> % if Entry has EVALAB(Entry) and Entry has SETCAT +--R eval : (%,Entry,Entry) -> % if Entry has EVALAB(Entry) and Entry has SETCAT +--R eval : (%,List(Entry),List(Entry)) -> % if Entry has EVALAB(Entry) and Entry has SETCAT +--R eval : (%,List(Record(key: Key,entry: Entry)),List(Record(key: Key,entry: Entry))) -> % if Record(key: Key,entry: Entry) has EVALAB(Record(key: Key,entry: Entry)) and Record(key: Key,entry: Entry) has SETCAT +--R eval : (%,Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> % if Record(key: Key,entry: Entry) has EVALAB(Record(key: Key,entry: Entry)) and Record(key: Key,entry: Entry) has SETCAT +--R eval : (%,Equation(Record(key: Key,entry: Entry))) -> % if Record(key: Key,entry: Entry) has EVALAB(Record(key: Key,entry: Entry)) and Record(key: Key,entry: Entry) has SETCAT +--R eval : (%,List(Equation(Record(key: Key,entry: Entry)))) -> % if Record(key: Key,entry: Entry) has EVALAB(Record(key: Key,entry: Entry)) and Record(key: Key,entry: Entry) has SETCAT +--R every? : ((Entry -> Boolean),%) -> Boolean if $ has finiteAggregate +--R every? : ((Record(key: Key,entry: Entry) -> Boolean),%) -> Boolean if $ has finiteAggregate +--R extract! : % -> Record(key: Key,entry: Entry) +--R fill! : (%,Entry) -> % if $ has shallowlyMutable +--R find : ((Record(key: Key,entry: Entry) -> Boolean),%) -> Union(Record(key: Key,entry: Entry),"failed") +--R first : % -> Entry if Key has ORDSET +--R hash : % -> SingleInteger if Record(key: Key,entry: Entry) has SETCAT or Entry has SETCAT +--R insert! : (Record(key: Key,entry: Entry),%) -> % +--R inspect : % -> Record(key: Key,entry: Entry) +--R latex : % -> String if Record(key: Key,entry: Entry) has SETCAT or Entry has SETCAT +--R less? : (%,NonNegativeInteger) -> Boolean +--R map : (((Entry,Entry) -> Entry),%,%) -> % +--R map : ((Record(key: Key,entry: Entry) -> Record(key: Key,entry: Entry)),%) -> % +--R map! : ((Entry -> Entry),%) -> % if $ has shallowlyMutable +--R map! : ((Record(key: Key,entry: Entry) -> Record(key: Key,entry: Entry)),%) -> % if $ has shallowlyMutable +--R maxIndex : % -> Key if Key has ORDSET +--R member? : (Entry,%) -> Boolean if $ has finiteAggregate and Entry has SETCAT +--R member? : (Record(key: Key,entry: Entry),%) -> Boolean if $ has finiteAggregate and Record(key: Key,entry: Entry) has SETCAT +--R members : % -> List(Entry) if $ has finiteAggregate +--R members : % -> List(Record(key: Key,entry: Entry)) if $ has finiteAggregate +--R minIndex : % -> Key if Key has ORDSET +--R more? : (%,NonNegativeInteger) -> Boolean +--R parts : % -> List(Entry) if $ has finiteAggregate +--R parts : % -> List(Record(key: Key,entry: Entry)) if $ has finiteAggregate +--R qsetelt! : (%,Key,Entry) -> Entry if $ has shallowlyMutable +--R reduce : (((Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry)),%) -> Record(key: Key,entry: Entry) if $ has finiteAggregate +--R reduce : (((Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry)),%,Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry) if $ has finiteAggregate +--R reduce : (((Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry)),%,Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry) if $ has finiteAggregate and Record(key: Key,entry: Entry) has SETCAT +--R remove : ((Record(key: Key,entry: Entry) -> Boolean),%) -> % if $ has finiteAggregate +--R remove : (Record(key: Key,entry: Entry),%) -> % if $ has finiteAggregate and Record(key: Key,entry: Entry) has SETCAT +--R remove! : (Key,%) -> Union(Entry,"failed") +--R remove! : ((Record(key: Key,entry: Entry) -> Boolean),%) -> % if $ has finiteAggregate +--R remove! : (Record(key: Key,entry: Entry),%) -> % if $ has finiteAggregate +--R removeDuplicates : % -> % if $ has finiteAggregate and Record(key: Key,entry: Entry) has SETCAT +--R search : (Key,%) -> Union(Entry,"failed") +--R select : ((Record(key: Key,entry: Entry) -> Boolean),%) -> % if $ has finiteAggregate +--R select! : ((Record(key: Key,entry: Entry) -> Boolean),%) -> % if $ has finiteAggregate +--R size? : (%,NonNegativeInteger) -> Boolean +--R swap! : (%,Key,Key) -> Void if $ has shallowlyMutable +--R table : List(Record(key: Key,entry: Entry)) -> % +--R ?~=? : (%,%) -> Boolean if Record(key: Key,entry: Entry) has SETCAT or Entry has SETCAT +--R +--E 19 + )spool )lisp (bye) \end{chunk} @@ -140798,16 +146908,19 @@ Tableau(S:SetCategory):Exports == Implementation where --R------------------------------- Operations -------------------------------- --R ?*? : (%,Coef) -> % ?*? : (Coef,%) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ?=? : (%,%) -> Boolean --R D : (%,List(Symbol)) -> % D : (%,Symbol) -> % --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % coerce : Polynomial(Coef) -> % ---R coerce : Symbol -> % coerce : Integer -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R coerce : Polynomial(Coef) -> % coerce : Symbol -> % +--R coerce : % -> % if Coef has INTDOM coerce : Integer -> % --R coerce : % -> OutputForm complete : % -> % ---R differentiate : (%,Symbol) -> % eval : (%,%,%) -> % ---R eval : (%,Equation(%)) -> % eval : (%,Symbol,%) -> % +--R differentiate : (%,Symbol) -> % eval : (%,List(%),List(%)) -> % +--R eval : (%,%,%) -> % eval : (%,Equation(%)) -> % +--R eval : (%,List(Equation(%))) -> % eval : (%,Symbol,%) -> % --R hash : % -> SingleInteger latex : % -> String --R leadingCoefficient : % -> Coef leadingMonomial : % -> % --R map : ((Coef -> Coef),%) -> % monomial? : % -> Boolean @@ -140817,14 +146930,11 @@ Tableau(S:SetCategory):Exports == Implementation where --R zero? : % -> Boolean ?~=? : (%,%) -> Boolean --R ?*? : (Fraction(Integer),%) -> % if Coef has ALGEBRA(FRAC(INT)) --R ?*? : (%,Fraction(Integer)) -> % if Coef has ALGEBRA(FRAC(INT)) ---R ?*? : (NonNegativeInteger,%) -> % --R ?**? : (%,Fraction(Integer)) -> % if Coef has ALGEBRA(FRAC(INT)) --R ?**? : (%,%) -> % if Coef has ALGEBRA(FRAC(INT)) ---R ?**? : (%,NonNegativeInteger) -> % --R ?/? : (%,Coef) -> % if Coef has FIELD --R D : (%,List(Symbol),List(NonNegativeInteger)) -> % --R D : (%,Symbol,NonNegativeInteger) -> % ---R ?^? : (%,NonNegativeInteger) -> % --R acos : % -> % if Coef has ALGEBRA(FRAC(INT)) --R acosh : % -> % if Coef has ALGEBRA(FRAC(INT)) --R acot : % -> % if Coef has ALGEBRA(FRAC(INT)) @@ -140845,7 +146955,6 @@ Tableau(S:SetCategory):Exports == Implementation where --R coefficient : (%,Symbol,NonNegativeInteger) -> % --R coefficient : (%,IndexedExponents(Symbol)) -> Coef --R coerce : Fraction(Integer) -> % if Coef has ALGEBRA(FRAC(INT)) ---R coerce : % -> % if Coef has INTDOM --R coerce : Coef -> % if Coef has COMRING --R cos : % -> % if Coef has ALGEBRA(FRAC(INT)) --R cosh : % -> % if Coef has ALGEBRA(FRAC(INT)) @@ -140857,8 +146966,6 @@ Tableau(S:SetCategory):Exports == Implementation where --R differentiate : (%,List(Symbol),List(NonNegativeInteger)) -> % --R differentiate : (%,Symbol,NonNegativeInteger) -> % --R differentiate : (%,List(Symbol)) -> % ---R eval : (%,List(%),List(%)) -> % ---R eval : (%,List(Equation(%))) -> % --R eval : (%,List(Symbol),List(%)) -> % --R exp : % -> % if Coef has ALGEBRA(FRAC(INT)) --R exquo : (%,%) -> Union(%,"failed") if Coef has INTDOM @@ -141185,13 +147292,13 @@ in addition we need to add a line defining [[PI2]] in [[formatPlex]]: --R --R------------------------------- Operations -------------------------------- --R ?=? : (%,%) -> Boolean coerce : OutputForm -> % ---R coerce : % -> OutputForm display : % -> Void ---R display : (%,Integer) -> Void epilogue : % -> List(String) ---R hash : % -> SingleInteger latex : % -> String ---R new : () -> % prologue : % -> List(String) ---R tex : % -> List(String) ?~=? : (%,%) -> Boolean +--R coerce : % -> OutputForm convert : (OutputForm,Integer) -> % +--R display : % -> Void display : (%,Integer) -> Void +--R epilogue : % -> List(String) hash : % -> SingleInteger +--R latex : % -> String new : () -> % +--R prologue : % -> List(String) tex : % -> List(String) +--R ?~=? : (%,%) -> Boolean --R convert : (OutputForm,Integer,OutputForm) -> % ---R convert : (OutputForm,Integer) -> % --R setEpilogue! : (%,List(String)) -> List(String) --R setPrologue! : (%,List(String)) -> List(String) --R setTex! : (%,List(String)) -> List(String) @@ -141862,7 +147969,8 @@ TexFormat(): public == private where )set message test on )set message auto off )clear all ---S 1 of 10 + +--S 1 of 11 f1: TextFile := open("/etc/group", "input") --R --R @@ -141870,7 +147978,7 @@ f1: TextFile := open("/etc/group", "input") --R Type: TextFile --E 1 ---S 2 of 10 +--S 2 of 11 f2: TextFile := open("MOTD", "output") --R --R @@ -141878,7 +147986,7 @@ f2: TextFile := open("MOTD", "output") --R Type: TextFile --E 2 ---S 3 of 10 +--S 3 of 11 l := readLine! f1 --R --R @@ -141886,7 +147994,7 @@ l := readLine! f1 --R Type: String --E 3 ---S 4 of 10 +--S 4 of 11 writeLine!(f2, upperCase l) --R --R @@ -141894,7 +148002,7 @@ writeLine!(f2, upperCase l) --R Type: String --E 4 ---S 5 of 10 +--S 5 of 11 while not endOfFile? f1 repeat s := readLine! f1 writeLine!(f2, upperCase s) @@ -141902,7 +148010,7 @@ while not endOfFile? f1 repeat --R Type: Void --E 5 ---S 6 of 10 +--S 6 of 11 close! f1 --R --R @@ -141910,7 +148018,7 @@ close! f1 --R Type: TextFile --E 6 ---S 7 of 10 +--S 7 of 11 write!(f2, "-The-") --R --R @@ -141918,7 +148026,7 @@ write!(f2, "-The-") --R Type: String --E 7 ---S 8 of 10 +--S 8 of 11 write!(f2, "-End-") --R --R @@ -141926,7 +148034,7 @@ write!(f2, "-End-") --R Type: String --E 8 ---S 9 of 10 +--S 9 of 11 writeLine! f2 --R --R @@ -141934,13 +148042,37 @@ writeLine! f2 --R Type: String --E 9 ---S 10 of 10 +--S 10 of 11 close! f2 --R --R --R (10) "MOTD" --R Type: TextFile --E 10 + +--S 11 of 11 +)show TextFile +--R +--R TextFile is a domain constructor +--R Abbreviation for TextFile is TEXTFILE +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for TEXTFILE +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean close! : % -> % +--R coerce : % -> OutputForm endOfFile? : % -> Boolean +--R flush : % -> Void hash : % -> SingleInteger +--R iomode : % -> String latex : % -> String +--R name : % -> FileName open : (FileName,String) -> % +--R open : FileName -> % read! : % -> String +--R readLine! : % -> String reopen! : (%,String) -> % +--R write! : (%,String) -> String writeLine! : % -> String +--R writeLine! : (%,String) -> String ?~=? : (%,%) -> Boolean +--R readIfCan! : % -> Union(String,"failed") +--R readLineIfCan! : % -> Union(String,"failed") +--R +--E 11 + )system rm -f MOTD )spool )lisp (bye) @@ -142158,17 +148290,16 @@ TextFile: Cat == Def where --R Issue )edit bookvol10.3.pamphlet to see algebra source code for SYMS --R --R------------------------------- Operations -------------------------------- +--R argumentList! : List(Symbol) -> Void clearTheSymbolTable : Symbol -> Void --R clearTheSymbolTable : () -> Void coerce : % -> OutputForm --R currentSubProgram : () -> Symbol empty : () -> % --R endSubProgram : () -> Symbol newSubProgram : Symbol -> Void --R printHeader : () -> Void printHeader : Symbol -> Void --R printHeader : (Symbol,%) -> Void printTypes : Symbol -> Void --R showTheSymbolTable : () -> % ---R argumentList! : List(Symbol) -> Void --R argumentList! : (Symbol,List(Symbol)) -> Void --R argumentList! : (Symbol,List(Symbol),%) -> Void --R argumentListOf : (Symbol,%) -> List(Symbol) ---R clearTheSymbolTable : Symbol -> Void --R declare! : (Symbol,FortranType,Symbol) -> FortranType --R declare! : (Symbol,FortranType) -> FortranType --R declare! : (List(Symbol),FortranType,Symbol,%) -> FortranType @@ -142447,7 +148578,8 @@ TheSymbolTable() : Exports == Implementation where --R------------------------------- Operations -------------------------------- --R copy : % -> % empty : () -> % --R empty? : % -> Boolean eq? : (%,%) -> Boolean ---R map : ((R -> R),%) -> % sample : () -> % +--R latex : % -> String if R has SETCAT map : ((R -> R),%) -> % +--R plus : (%,%) -> % if R has RING sample : () -> % --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R ?=? : (%,%) -> Boolean if R has SETCAT --R any? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate @@ -142465,7 +148597,6 @@ TheSymbolTable() : Exports == Implementation where --R every? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate --R hash : % -> SingleInteger if R has SETCAT --R identityMatrix : NonNegativeInteger -> % if R has RING ---R latex : % -> String if R has SETCAT --R less? : (%,NonNegativeInteger) -> Boolean --R map! : ((R -> R),%) -> % if $ has shallowlyMutable --R matrixConcat3D : (Symbol,%,%) -> % @@ -142474,7 +148605,6 @@ TheSymbolTable() : Exports == Implementation where --R members : % -> List(R) if $ has finiteAggregate --R more? : (%,NonNegativeInteger) -> Boolean --R parts : % -> List(R) if $ has finiteAggregate ---R plus : (%,%) -> % if R has RING --R setelt! : (%,NonNegativeInteger,NonNegativeInteger,NonNegativeInteger,R) -> R --R size? : (%,NonNegativeInteger) -> Boolean --R zeroMatrix : (NonNegativeInteger,NonNegativeInteger,NonNegativeInteger) -> % if R has RING @@ -142814,23 +148944,25 @@ ThreeDimensionalMatrix(R) : Exports == Implementation where --R------------------------------- Operations -------------------------------- --R ?=? : (%,%) -> Boolean axes : (%,String) -> Void --R clipSurface : (%,String) -> Void close : % -> Void ---R coerce : % -> OutputForm controlPanel : (%,String) -> Void ---R diagonals : (%,String) -> Void drawStyle : (%,String) -> Void ---R eyeDistance : (%,Float) -> Void hash : % -> SingleInteger ---R hitherPlane : (%,Float) -> Void intensity : (%,Float) -> Void ---R key : % -> Integer latex : % -> String ---R makeViewport3D : % -> % options : % -> List(DrawOption) +--R coerce : % -> OutputForm colorDef : (%,Color,Color) -> Void +--R controlPanel : (%,String) -> Void diagonals : (%,String) -> Void +--R drawStyle : (%,String) -> Void eyeDistance : (%,Float) -> Void +--R hash : % -> SingleInteger hitherPlane : (%,Float) -> Void +--R intensity : (%,Float) -> Void key : % -> Integer +--R latex : % -> String makeViewport3D : % -> % +--R options : % -> List(DrawOption) outlineRender : (%,String) -> Void --R perspective : (%,String) -> Void reset : % -> Void ---R rotate : (%,Float,Float) -> Void showRegion : (%,String) -> Void ---R title : (%,String) -> Void viewDeltaXDefault : Float -> Float +--R rotate : (%,Float,Float) -> Void showClipRegion : (%,String) -> Void +--R showRegion : (%,String) -> Void title : (%,String) -> Void +--R translate : (%,Float,Float) -> Void viewDeltaXDefault : Float -> Float --R viewDeltaXDefault : () -> Float viewDeltaYDefault : Float -> Float --R viewDeltaYDefault : () -> Float viewPhiDefault : Float -> Float --R viewPhiDefault : () -> Float viewThetaDefault : Float -> Float --R viewThetaDefault : () -> Float viewZoomDefault : Float -> Float ---R viewZoomDefault : () -> Float viewport3D : () -> % +--R viewZoomDefault : () -> Float viewpoint : (%,Float,Float) -> Void +--R viewport3D : () -> % write : (%,String,String) -> String --R write : (%,String) -> String zoom : (%,Float) -> Void --R ?~=? : (%,%) -> Boolean ---R colorDef : (%,Color,Color) -> Void --R dimensions : (%,NonNegativeInteger,NonNegativeInteger,PositiveInteger,PositiveInteger) -> Void --R lighting : (%,Float,Float,Float) -> Void --R makeViewport3D : (ThreeSpace(DoubleFloat),List(DrawOption)) -> % @@ -142838,21 +148970,16 @@ ThreeDimensionalMatrix(R) : Exports == Implementation where --R modifyPointData : (%,NonNegativeInteger,Point(DoubleFloat)) -> Void --R move : (%,NonNegativeInteger,NonNegativeInteger) -> Void --R options : (%,List(DrawOption)) -> % ---R outlineRender : (%,String) -> Void --R resize : (%,PositiveInteger,PositiveInteger) -> Void --R rotate : (%,Integer,Integer) -> Void ---R showClipRegion : (%,String) -> Void --R subspace : (%,ThreeSpace(DoubleFloat)) -> % --R subspace : % -> ThreeSpace(DoubleFloat) ---R translate : (%,Float,Float) -> Void --R viewpoint : (%,Float,Float,Float) -> Void ---R viewpoint : (%,Float,Float) -> Void --R viewpoint : (%,Integer,Integer,Float,Float,Float) -> Void --R viewpoint : (%,Record(theta: DoubleFloat,phi: DoubleFloat,scale: DoubleFloat,scaleX: DoubleFloat,scaleY: DoubleFloat,scaleZ: DoubleFloat,deltaX: DoubleFloat,deltaY: DoubleFloat)) -> Void --R viewpoint : % -> Record(theta: DoubleFloat,phi: DoubleFloat,scale: DoubleFloat,scaleX: DoubleFloat,scaleY: DoubleFloat,scaleZ: DoubleFloat,deltaX: DoubleFloat,deltaY: DoubleFloat) --R viewpoint : (%,Float,Float,Float,Float,Float) -> Void --R write : (%,String,List(String)) -> String ---R write : (%,String,String) -> String --R zoom : (%,Float,Float,Float) -> Void --R --E 1 @@ -143905,8 +150032,9 @@ ThreeDimensionalViewport(): Exports == Implementation where --R point : Point(R) -> % point : (%,List(R)) -> % --R point : (%,Point(R)) -> % point? : % -> Boolean --R polygon : % -> List(Point(R)) polygon : List(Point(R)) -> % ---R polygon : (%,List(List(R))) -> % polygon? : % -> Boolean ---R subspace : % -> SubSpace(3,R) ?~=? : (%,%) -> Boolean +--R polygon : (%,List(List(R))) -> % polygon : (%,List(Point(R))) -> % +--R polygon? : % -> Boolean subspace : % -> SubSpace(3,R) +--R ?~=? : (%,%) -> Boolean --R closedCurve : (%,List(List(R))) -> % --R closedCurve : (%,List(Point(R))) -> % --R enterPointData : (%,List(Point(R))) -> NonNegativeInteger @@ -143924,7 +150052,6 @@ ThreeDimensionalViewport(): Exports == Implementation where --R numberOfComposites : % -> NonNegativeInteger --R objects : % -> Record(points: NonNegativeInteger,curves: NonNegativeInteger,polygons: NonNegativeInteger,constructs: NonNegativeInteger) --R point : (%,NonNegativeInteger) -> % ---R polygon : (%,List(Point(R))) -> % --R --E 1 @@ -144354,11 +150481,11 @@ ThreeSpace(R:Ring):Exports == Implementation where --R cyclicParents : % -> List(%) distance : (%,%) -> Integer --R ?.value : (%,value) -> S empty : () -> % --R empty? : % -> Boolean eq? : (%,%) -> Boolean ---R leaf? : % -> Boolean leaves : % -> List(S) ---R map : ((S -> S),%) -> % nodes : % -> List(%) ---R sample : () -> % tree : S -> % ---R tree : List(S) -> % tree : (S,List(%)) -> % ---R value : % -> S +--R latex : % -> String if S has SETCAT leaf? : % -> Boolean +--R leaves : % -> List(S) map : ((S -> S),%) -> % +--R nodes : % -> List(%) sample : () -> % +--R tree : S -> % tree : List(S) -> % +--R tree : (S,List(%)) -> % value : % -> S --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R ?=? : (%,%) -> Boolean if S has SETCAT --R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate @@ -144372,7 +150499,6 @@ ThreeSpace(R:Ring):Exports == Implementation where --R eval : (%,List(Equation(S))) -> % if S has EVALAB(S) and S has SETCAT --R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate --R hash : % -> SingleInteger if S has SETCAT ---R latex : % -> String if S has SETCAT --R less? : (%,NonNegativeInteger) -> Boolean --R map! : ((S -> S),%) -> % if $ has shallowlyMutable --R member? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT @@ -144814,9 +150940,8 @@ Tree(S: SetCategory): T==C where --R --R------------------------------- Operations -------------------------------- --R closed? : % -> Boolean getCurve : % -> Curve ---R open? : % -> Boolean +--R open? : % -> Boolean setClosed : (%,Boolean) -> Boolean --R listLoops : % -> List(List(Point(DoubleFloat))) ---R setClosed : (%,Boolean) -> Boolean --R tube : (Curve,List(List(Point(DoubleFloat))),Boolean) -> % --R --E 1 @@ -144932,11 +151057,10 @@ TubePlot(Curve): Exports == Implementation where --R --R------------------------------- Operations -------------------------------- --R coerce : PrimitiveArray(S) -> % coerce : % -> PrimitiveArray(S) ---R length : % -> NonNegativeInteger +--R latex : % -> String if S has SETCAT length : % -> NonNegativeInteger --R ?=? : (%,%) -> Boolean if S has SETCAT --R coerce : % -> OutputForm if S has SETCAT --R hash : % -> SingleInteger if S has SETCAT ---R latex : % -> String if S has SETCAT --R select : (%,NonNegativeInteger) -> S --R ?~=? : (%,%) -> Boolean if S has SETCAT --R @@ -145044,7 +151168,8 @@ Tuple(S:Type): CoercibleTo(PrimitiveArray S) with )set message test on )set message auto off )clear all ---S 1 of 20 + +--S 1 of 21 arr : ARRAY2 INT := new(5,4,0) --R --R @@ -145060,7 +151185,7 @@ arr : ARRAY2 INT := new(5,4,0) --R Type: TwoDimensionalArray(Integer) --E 1 ---S 2 of 20 +--S 2 of 21 setelt(arr,1,1,17) --R --R @@ -145068,7 +151193,7 @@ setelt(arr,1,1,17) --R Type: PositiveInteger --E 2 ---S 3 of 20 +--S 3 of 21 arr --R --R @@ -145084,7 +151209,7 @@ arr --R Type: TwoDimensionalArray(Integer) --E 3 ---S 4 of 20 +--S 4 of 21 elt(arr,1,1) --R --R @@ -145092,7 +151217,7 @@ elt(arr,1,1) --R Type: PositiveInteger --E 4 ---S 5 of 20 +--S 5 of 21 arr(3,2) := 15 --R --R @@ -145100,7 +151225,7 @@ arr(3,2) := 15 --R Type: PositiveInteger --E 5 ---S 6 of 20 +--S 6 of 21 arr(3,2) --R --R @@ -145108,7 +151233,7 @@ arr(3,2) --R Type: PositiveInteger --E 6 ---S 7 of 20 +--S 7 of 21 row(arr,1) --R --R @@ -145116,7 +151241,7 @@ row(arr,1) --R Type: OneDimensionalArray(Integer) --E 7 ---S 8 of 20 +--S 8 of 21 column(arr,1) --R --R @@ -145124,7 +151249,7 @@ column(arr,1) --R Type: OneDimensionalArray(Integer) --E 8 ---S 9 of 20 +--S 9 of 21 nrows(arr) --R --R @@ -145132,7 +151257,7 @@ nrows(arr) --R Type: PositiveInteger --E 9 ---S 10 of 20 +--S 10 of 21 ncols(arr) --R --R @@ -145140,7 +151265,7 @@ ncols(arr) --R Type: PositiveInteger --E 10 ---S 11 of 20 +--S 11 of 21 map(-,arr) --R --R @@ -145156,7 +151281,7 @@ map(-,arr) --R Type: TwoDimensionalArray(Integer) --E 11 ---S 12 of 20 +--S 12 of 21 map((x +-> x + x),arr) --R --R @@ -145172,7 +151297,7 @@ map((x +-> x + x),arr) --R Type: TwoDimensionalArray(Integer) --E 12 ---S 13 of 20 +--S 13 of 21 arrc := copy(arr) --R --R @@ -145188,7 +151313,7 @@ arrc := copy(arr) --R Type: TwoDimensionalArray(Integer) --E 13 ---S 14 of 20 +--S 14 of 21 map!(-,arrc) --R --R @@ -145204,7 +151329,7 @@ map!(-,arrc) --R Type: TwoDimensionalArray(Integer) --E 14 ---S 15 of 20 +--S 15 of 21 arrc --R --R @@ -145220,7 +151345,7 @@ arrc --R Type: TwoDimensionalArray(Integer) --E 15 ---S 16 of 20 +--S 16 of 21 arr --R --R @@ -145236,7 +151361,7 @@ arr --R Type: TwoDimensionalArray(Integer) --E 16 ---S 17 of 20 +--S 17 of 21 member?(17,arr) --R --R @@ -145244,7 +151369,7 @@ member?(17,arr) --R Type: Boolean --E 17 ---S 18 of 20 +--S 18 of 21 member?(10317,arr) --R --R @@ -145252,7 +151377,7 @@ member?(10317,arr) --R Type: Boolean --E 18 ---S 19 of 20 +--S 19 of 21 count(17,arr) --R --R @@ -145260,13 +151385,61 @@ count(17,arr) --R Type: PositiveInteger --E 19 ---S 20 of 20 +--S 20 of 21 count(0,arr) --R --R --R (20) 18 --R Type: PositiveInteger --E 20 + +--S 21 of 21 +)show TwoDimensionalArray + TwoDimensionalArray(R: Type) is a domain constructor + Abbreviation for TwoDimensionalArray is ARRAY2 + This constructor is not exposed in this frame. + Issue )edit bookvol10.3.pamphlet to see algebra source code for ARRAY2 + +------------------------------- Operations -------------------------------- + copy : % -> % elt : (%,Integer,Integer,R) -> R + elt : (%,Integer,Integer) -> R empty : () -> % + empty? : % -> Boolean eq? : (%,%) -> Boolean + fill! : (%,R) -> % map : (((R,R) -> R),%,%,R) -> % + map : (((R,R) -> R),%,%) -> % map : ((R -> R),%) -> % + map! : ((R -> R),%) -> % maxColIndex : % -> Integer + maxRowIndex : % -> Integer minColIndex : % -> Integer + minRowIndex : % -> Integer ncols : % -> NonNegativeInteger + nrows : % -> NonNegativeInteger parts : % -> List(R) + qelt : (%,Integer,Integer) -> R sample : () -> % + #? : % -> NonNegativeInteger if $ has finiteAggregate + ?=? : (%,%) -> Boolean if R has SETCAT + any? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate + coerce : % -> OutputForm if R has SETCAT + column : (%,Integer) -> OneDimensionalArray(R) + count : (R,%) -> NonNegativeInteger if $ has finiteAggregate and R has SETCAT + count : ((R -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate + eval : (%,List(R),List(R)) -> % if R has EVALAB(R) and R has SETCAT + eval : (%,R,R) -> % if R has EVALAB(R) and R has SETCAT + eval : (%,Equation(R)) -> % if R has EVALAB(R) and R has SETCAT + eval : (%,List(Equation(R))) -> % if R has EVALAB(R) and R has SETCAT + every? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate + hash : % -> SingleInteger if R has SETCAT + latex : % -> String if R has SETCAT + less? : (%,NonNegativeInteger) -> Boolean + member? : (R,%) -> Boolean if $ has finiteAggregate and R has SETCAT + members : % -> List(R) if $ has finiteAggregate + more? : (%,NonNegativeInteger) -> Boolean + new : (NonNegativeInteger,NonNegativeInteger,R) -> % + qsetelt! : (%,Integer,Integer,R) -> R + row : (%,Integer) -> OneDimensionalArray(R) + setColumn! : (%,Integer,OneDimensionalArray(R)) -> % + setRow! : (%,Integer,OneDimensionalArray(R)) -> % + setelt : (%,Integer,Integer,R) -> R + size? : (%,NonNegativeInteger) -> Boolean + ?~=? : (%,%) -> Boolean if R has SETCAT + +--E 21 + )spool )lisp (bye) \end{chunk} @@ -145571,6 +151744,45 @@ TwoDimensionalArray(R):Exports == Implementation where --S 1 of 1 )show TwoDimensionalViewport +--R +--R TwoDimensionalViewport is a domain constructor +--R Abbreviation for TwoDimensionalViewport is VIEW2D +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for VIEW2D +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean close : % -> Void +--R coerce : % -> OutputForm controlPanel : (%,String) -> Void +--R hash : % -> SingleInteger key : % -> Integer +--R latex : % -> String makeViewport2D : % -> % +--R options : % -> List(DrawOption) reset : % -> Void +--R title : (%,String) -> Void viewport2D : () -> % +--R write : (%,String) -> String ?~=? : (%,%) -> Boolean +--R axes : (%,PositiveInteger,Palette) -> Void +--R axes : (%,PositiveInteger,String) -> Void +--R connect : (%,PositiveInteger,String) -> Void +--R dimensions : (%,NonNegativeInteger,NonNegativeInteger,PositiveInteger,PositiveInteger) -> Void +--R getGraph : (%,PositiveInteger) -> GraphImage +--R getPickedPoints : % -> List(Point(DoubleFloat)) +--R graphState : (%,PositiveInteger,DoubleFloat,DoubleFloat,DoubleFloat,DoubleFloat,Integer,Integer,Integer,Integer,Palette,Integer,Palette,Integer) -> Void +--R graphStates : % -> Vector(Record(scaleX: DoubleFloat,scaleY: DoubleFloat,deltaX: DoubleFloat,deltaY: DoubleFloat,points: Integer,connect: Integer,spline: Integer,axes: Integer,axesColor: Palette,units: Integer,unitsColor: Palette,showing: Integer)) +--R graphs : % -> Vector(Union(GraphImage,undefined)) +--R makeViewport2D : (GraphImage,List(DrawOption)) -> % +--R move : (%,NonNegativeInteger,NonNegativeInteger) -> Void +--R options : (%,List(DrawOption)) -> % +--R points : (%,PositiveInteger,String) -> Void +--R putGraph : (%,GraphImage,PositiveInteger) -> Void +--R region : (%,PositiveInteger,String) -> Void +--R resize : (%,PositiveInteger,PositiveInteger) -> Void +--R scale : (%,PositiveInteger,Float,Float) -> Void +--R show : (%,PositiveInteger,String) -> Void +--R translate : (%,PositiveInteger,Float,Float) -> Void +--R units : (%,PositiveInteger,Palette) -> Void +--R units : (%,PositiveInteger,String) -> Void +--R update : (%,GraphImage,PositiveInteger) -> Void +--R write : (%,String,List(String)) -> String +--R write : (%,String,String) -> String +--R --E 1 )spool @@ -146539,12 +152751,14 @@ TwoDimensionalViewport ():Exports == Implementation where --R------------------------------- Operations -------------------------------- --R ?*? : (Coef,%) -> % ?*? : (%,Coef) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ?=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % center : % -> Coef ---R coefficients : % -> Stream(Coef) coerce : Variable(QUOTE(x)) -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R center : % -> Coef coefficients : % -> Stream(Coef) +--R coerce : Variable(QUOTE(x)) -> % coerce : % -> % if Coef has INTDOM --R coerce : Integer -> % coerce : % -> OutputForm --R complete : % -> % degree : % -> NonNegativeInteger --R evenlambert : % -> % hash : % -> SingleInteger @@ -146560,11 +152774,9 @@ TwoDimensionalViewport ():Exports == Implementation where --R zero? : % -> Boolean ?~=? : (%,%) -> Boolean --R ?*? : (%,Fraction(Integer)) -> % if Coef has ALGEBRA(FRAC(INT)) --R ?*? : (Fraction(Integer),%) -> % if Coef has ALGEBRA(FRAC(INT)) ---R ?*? : (NonNegativeInteger,%) -> % --R ?**? : (%,Fraction(Integer)) -> % if Coef has ALGEBRA(FRAC(INT)) --R ?**? : (%,%) -> % if Coef has ALGEBRA(FRAC(INT)) --R ?**? : (%,Coef) -> % if Coef has FIELD ---R ?**? : (%,NonNegativeInteger) -> % --R ?/? : (%,Coef) -> % if Coef has FIELD --R D : % -> % if Coef has *: (NonNegativeInteger,Coef) -> Coef --R D : (%,NonNegativeInteger) -> % if Coef has *: (NonNegativeInteger,Coef) -> Coef @@ -146572,7 +152784,6 @@ TwoDimensionalViewport ():Exports == Implementation where --R D : (%,List(Symbol)) -> % if Coef has *: (NonNegativeInteger,Coef) -> Coef and Coef has PDRING(SYMBOL) --R D : (%,Symbol,NonNegativeInteger) -> % if Coef has *: (NonNegativeInteger,Coef) -> Coef and Coef has PDRING(SYMBOL) --R D : (%,List(Symbol),List(NonNegativeInteger)) -> % if Coef has *: (NonNegativeInteger,Coef) -> Coef and Coef has PDRING(SYMBOL) ---R ?^? : (%,NonNegativeInteger) -> % --R acos : % -> % if Coef has ALGEBRA(FRAC(INT)) --R acosh : % -> % if Coef has ALGEBRA(FRAC(INT)) --R acot : % -> % if Coef has ALGEBRA(FRAC(INT)) @@ -146592,7 +152803,6 @@ TwoDimensionalViewport ():Exports == Implementation where --R coefficient : (%,NonNegativeInteger) -> Coef --R coerce : UnivariatePolynomial(QUOTE(x),Coef) -> % --R coerce : Coef -> % if Coef has COMRING ---R coerce : % -> % if Coef has INTDOM --R coerce : Fraction(Integer) -> % if Coef has ALGEBRA(FRAC(INT)) --R cos : % -> % if Coef has ALGEBRA(FRAC(INT)) --R cosh : % -> % if Coef has ALGEBRA(FRAC(INT)) @@ -146803,16 +153013,18 @@ UnivariateFormalPowerSeries(Coef: Ring) == --R------------------------------- Operations -------------------------------- --R ?*? : (Coef,%) -> % ?*? : (%,Coef) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ?=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % center : % -> Coef ---R coefficient : (%,Integer) -> Coef coerce : Variable(var) -> % ---R coerce : Integer -> % coerce : % -> OutputForm ---R complete : % -> % degree : % -> Integer ---R ?.? : (%,Integer) -> Coef extend : (%,Integer) -> % ---R hash : % -> SingleInteger latex : % -> String +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R center : % -> Coef coefficient : (%,Integer) -> Coef +--R coerce : Variable(var) -> % coerce : Integer -> % +--R coerce : % -> OutputForm complete : % -> % +--R degree : % -> Integer ?.? : (%,Integer) -> Coef +--R extend : (%,Integer) -> % hash : % -> SingleInteger +--R inv : % -> % if Coef has FIELD latex : % -> String --R leadingCoefficient : % -> Coef leadingMonomial : % -> % --R map : ((Coef -> Coef),%) -> % monomial : (Coef,Integer) -> % --R monomial? : % -> Boolean one? : % -> Boolean @@ -146826,11 +153038,9 @@ UnivariateFormalPowerSeries(Coef: Ring) == --R ?*? : (Fraction(Integer),%) -> % if Coef has ALGEBRA(FRAC(INT)) --R ?*? : (UnivariateTaylorSeries(Coef,var,cen),%) -> % if Coef has FIELD --R ?*? : (%,UnivariateTaylorSeries(Coef,var,cen)) -> % if Coef has FIELD ---R ?*? : (NonNegativeInteger,%) -> % --R ?**? : (%,Fraction(Integer)) -> % if Coef has ALGEBRA(FRAC(INT)) --R ?**? : (%,%) -> % if Coef has ALGEBRA(FRAC(INT)) --R ?**? : (%,Integer) -> % if Coef has FIELD ---R ?**? : (%,NonNegativeInteger) -> % --R ?/? : (UnivariateTaylorSeries(Coef,var,cen),UnivariateTaylorSeries(Coef,var,cen)) -> % if Coef has FIELD --R ?/? : (%,%) -> % if Coef has FIELD --R ?/? : (%,Coef) -> % if Coef has FIELD @@ -146847,7 +153057,6 @@ UnivariateFormalPowerSeries(Coef: Ring) == --R D : (%,(UnivariateTaylorSeries(Coef,var,cen) -> UnivariateTaylorSeries(Coef,var,cen)),NonNegativeInteger) -> % if Coef has FIELD --R D : (%,(UnivariateTaylorSeries(Coef,var,cen) -> UnivariateTaylorSeries(Coef,var,cen))) -> % if Coef has FIELD --R ?^? : (%,Integer) -> % if Coef has FIELD ---R ?^? : (%,NonNegativeInteger) -> % --R abs : % -> % if UnivariateTaylorSeries(Coef,var,cen) has OINTDOM and Coef has FIELD --R acos : % -> % if Coef has ALGEBRA(FRAC(INT)) --R acosh : % -> % if Coef has ALGEBRA(FRAC(INT)) @@ -146922,7 +153131,6 @@ UnivariateFormalPowerSeries(Coef: Ring) == --R integrate : (%,Variable(var)) -> % if Coef has ALGEBRA(FRAC(INT)) --R integrate : (%,Symbol) -> % if Coef has integrate: (Coef,Symbol) -> Coef and Coef has variables: Coef -> List(Symbol) and Coef has ALGEBRA(FRAC(INT)) or Coef has ACFS(INT) and Coef has ALGEBRA(FRAC(INT)) and Coef has PRIMCAT and Coef has TRANFUN --R integrate : % -> % if Coef has ALGEBRA(FRAC(INT)) ---R inv : % -> % if Coef has FIELD --R laurent : (Integer,UnivariateTaylorSeries(Coef,var,cen)) -> % --R lcm : (%,%) -> % if Coef has FIELD --R lcm : List(%) -> % if Coef has FIELD @@ -147330,36 +153538,38 @@ UnivariateLaurentSeries(Coef,var,cen): Exports == Implementation where --R------------------------------- Operations -------------------------------- --R ?*? : (Coef,%) -> % ?*? : (%,Coef) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ?=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % center : % -> Coef ---R coefficient : (%,Integer) -> Coef coerce : UTS -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R center : % -> Coef coefficient : (%,Integer) -> Coef +--R coerce : % -> % if Coef has INTDOM coerce : UTS -> % --R coerce : Integer -> % coerce : % -> OutputForm --R complete : % -> % degree : % -> Integer ---R ?.? : (%,Integer) -> Coef extend : (%,Integer) -> % ---R hash : % -> SingleInteger latex : % -> String +--R denom : % -> UTS if Coef has FIELD ?.? : (%,Integer) -> Coef +--R extend : (%,Integer) -> % hash : % -> SingleInteger +--R inv : % -> % if Coef has FIELD latex : % -> String --R laurent : (Integer,UTS) -> % leadingCoefficient : % -> Coef --R leadingMonomial : % -> % map : ((Coef -> Coef),%) -> % --R monomial : (Coef,Integer) -> % monomial? : % -> Boolean ---R one? : % -> Boolean order : (%,Integer) -> Integer ---R order : % -> Integer pole? : % -> Boolean ---R recip : % -> Union(%,"failed") reductum : % -> % ---R removeZeroes : (Integer,%) -> % removeZeroes : % -> % ---R retract : % -> UTS sample : () -> % ---R taylor : % -> UTS taylorRep : % -> UTS ---R truncate : (%,Integer) -> % variable : % -> Symbol ---R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R numer : % -> UTS if Coef has FIELD one? : % -> Boolean +--R order : (%,Integer) -> Integer order : % -> Integer +--R pole? : % -> Boolean recip : % -> Union(%,"failed") +--R reductum : % -> % removeZeroes : (Integer,%) -> % +--R removeZeroes : % -> % retract : % -> UTS +--R sample : () -> % taylor : % -> UTS +--R taylorRep : % -> UTS truncate : (%,Integer) -> % +--R variable : % -> Symbol zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean --R ?*? : (%,Fraction(Integer)) -> % if Coef has ALGEBRA(FRAC(INT)) --R ?*? : (Fraction(Integer),%) -> % if Coef has ALGEBRA(FRAC(INT)) --R ?*? : (UTS,%) -> % if Coef has FIELD --R ?*? : (%,UTS) -> % if Coef has FIELD ---R ?*? : (NonNegativeInteger,%) -> % --R ?**? : (%,Fraction(Integer)) -> % if Coef has ALGEBRA(FRAC(INT)) --R ?**? : (%,%) -> % if Coef has ALGEBRA(FRAC(INT)) --R ?**? : (%,Integer) -> % if Coef has FIELD ---R ?**? : (%,NonNegativeInteger) -> % --R ?/? : (UTS,UTS) -> % if Coef has FIELD --R ?/? : (%,%) -> % if Coef has FIELD --R ?/? : (%,Coef) -> % if Coef has FIELD @@ -147376,7 +153586,6 @@ UnivariateLaurentSeries(Coef,var,cen): Exports == Implementation where --R D : (%,(UTS -> UTS),NonNegativeInteger) -> % if Coef has FIELD --R D : (%,(UTS -> UTS)) -> % if Coef has FIELD --R ?^? : (%,Integer) -> % if Coef has FIELD ---R ?^? : (%,NonNegativeInteger) -> % --R abs : % -> % if UTS has OINTDOM and Coef has FIELD --R acos : % -> % if Coef has ALGEBRA(FRAC(INT)) --R acosh : % -> % if Coef has ALGEBRA(FRAC(INT)) @@ -147395,7 +153604,6 @@ UnivariateLaurentSeries(Coef,var,cen): Exports == Implementation where --R ceiling : % -> UTS if UTS has INS and Coef has FIELD --R characteristic : () -> NonNegativeInteger --R charthRoot : % -> Union(%,"failed") if $ has CHARNZ and UTS has PFECAT and Coef has FIELD or UTS has CHARNZ and Coef has FIELD or Coef has CHARNZ ---R coerce : % -> % if Coef has INTDOM --R coerce : Fraction(Integer) -> % if Coef has ALGEBRA(FRAC(INT)) --R coerce : Symbol -> % if UTS has RETRACT(SYMBOL) and Coef has FIELD --R coerce : Coef -> % if Coef has COMRING @@ -147411,7 +153619,6 @@ UnivariateLaurentSeries(Coef,var,cen): Exports == Implementation where --R coth : % -> % if Coef has ALGEBRA(FRAC(INT)) --R csc : % -> % if Coef has ALGEBRA(FRAC(INT)) --R csch : % -> % if Coef has ALGEBRA(FRAC(INT)) ---R denom : % -> UTS if Coef has FIELD --R denominator : % -> % if Coef has FIELD --R differentiate : (%,Symbol) -> % if UTS has PDRING(SYMBOL) and Coef has FIELD or Coef has *: (Integer,Coef) -> Coef and Coef has PDRING(SYMBOL) --R differentiate : (%,List(Symbol)) -> % if UTS has PDRING(SYMBOL) and Coef has FIELD or Coef has *: (Integer,Coef) -> Coef and Coef has PDRING(SYMBOL) @@ -147448,7 +153655,6 @@ UnivariateLaurentSeries(Coef,var,cen): Exports == Implementation where --R init : () -> % if UTS has STEP and Coef has FIELD --R integrate : (%,Symbol) -> % if Coef has integrate: (Coef,Symbol) -> Coef and Coef has variables: Coef -> List(Symbol) and Coef has ALGEBRA(FRAC(INT)) or Coef has ACFS(INT) and Coef has ALGEBRA(FRAC(INT)) and Coef has PRIMCAT and Coef has TRANFUN --R integrate : % -> % if Coef has ALGEBRA(FRAC(INT)) ---R inv : % -> % if Coef has FIELD --R lcm : (%,%) -> % if Coef has FIELD --R lcm : List(%) -> % if Coef has FIELD --R lcmCoef : (%,%) -> Record(llcmres: %,coeff1: %,coeff2: %) if Coef has FIELD @@ -147464,7 +153670,6 @@ UnivariateLaurentSeries(Coef,var,cen): Exports == Implementation where --R negative? : % -> Boolean if UTS has OINTDOM and Coef has FIELD --R nextItem : % -> Union(%,"failed") if UTS has STEP and Coef has FIELD --R nthRoot : (%,Integer) -> % if Coef has ALGEBRA(FRAC(INT)) ---R numer : % -> UTS if Coef has FIELD --R numerator : % -> % if Coef has FIELD --R patternMatch : (%,Pattern(Integer),PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if UTS has PATMAB(INT) and Coef has FIELD --R patternMatch : (%,Pattern(Float),PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if UTS has PATMAB(FLOAT) and Coef has FIELD @@ -148139,13 +154344,14 @@ UnivariateLaurentSeriesConstructor(Coef,UTS):_ )set message test on )set message auto off )clear all ---S 1 of 35 + +--S 1 of 36 (p,q) : UP(x,INT) --R --R Type: Void --E 1 ---S 2 of 35 +--S 2 of 36 p := (3*x-1)**2 * (2*x + 8) --R --R @@ -148154,7 +154360,7 @@ p := (3*x-1)**2 * (2*x + 8) --R Type: UnivariatePolynomial(x,Integer) --E 2 ---S 3 of 35 +--S 3 of 36 q := (1 - 6*x + 9*x**2)**2 --R --R @@ -148163,7 +154369,7 @@ q := (1 - 6*x + 9*x**2)**2 --R Type: UnivariatePolynomial(x,Integer) --E 3 ---S 4 of 35 +--S 4 of 36 p**2 + p*q --R --R @@ -148172,7 +154378,7 @@ p**2 + p*q --R Type: UnivariatePolynomial(x,Integer) --E 4 ---S 5 of 35 +--S 5 of 36 leadingCoefficient p --R --R @@ -148180,7 +154386,7 @@ leadingCoefficient p --R Type: PositiveInteger --E 5 ---S 6 of 35 +--S 6 of 36 degree p --R --R @@ -148188,7 +154394,7 @@ degree p --R Type: PositiveInteger --E 6 ---S 7 of 35 +--S 7 of 36 reductum p --R --R @@ -148197,7 +154403,7 @@ reductum p --R Type: UnivariatePolynomial(x,Integer) --E 7 ---S 8 of 35 +--S 8 of 36 gcd(p,q) --R --R @@ -148206,7 +154412,7 @@ gcd(p,q) --R Type: UnivariatePolynomial(x,Integer) --E 8 ---S 9 of 35 +--S 9 of 36 lcm(p,q) --R --R @@ -148215,7 +154421,7 @@ lcm(p,q) --R Type: UnivariatePolynomial(x,Integer) --E 9 ---S 10 of 35 +--S 10 of 36 resultant(p,q) --R --R @@ -148223,7 +154429,7 @@ resultant(p,q) --R Type: NonNegativeInteger --E 10 ---S 11 of 35 +--S 11 of 36 D p --R --R @@ -148232,7 +154438,7 @@ D p --R Type: UnivariatePolynomial(x,Integer) --E 11 ---S 12 of 35 +--S 12 of 36 p(2) --R --R @@ -148240,7 +154446,7 @@ p(2) --R Type: PositiveInteger --E 12 ---S 13 of 35 +--S 13 of 36 p(q) --R --R @@ -148255,7 +154461,7 @@ p(q) --R Type: UnivariatePolynomial(x,Integer) --E 13 ---S 14 of 35 +--S 14 of 36 q(p) --R --R @@ -148271,7 +154477,7 @@ q(p) --R Type: UnivariatePolynomial(x,Integer) --E 14 ---S 15 of 35 +--S 15 of 36 l := coefficients p --R --R @@ -148279,7 +154485,7 @@ l := coefficients p --R Type: List(Integer) --E 15 ---S 16 of 35 +--S 16 of 36 reduce(gcd,l) --R --R @@ -148287,7 +154493,7 @@ reduce(gcd,l) --R Type: PositiveInteger --E 16 ---S 17 of 35 +--S 17 of 36 content p --R --R @@ -148295,7 +154501,7 @@ content p --R Type: PositiveInteger --E 17 ---S 18 of 35 +--S 18 of 36 ux := (x**4+2*x+3)::UP(x,INT) --R --R @@ -148304,7 +154510,7 @@ ux := (x**4+2*x+3)::UP(x,INT) --R Type: UnivariatePolynomial(x,Integer) --E 18 ---S 19 of 35 +--S 19 of 36 vectorise(ux,5) --R --R @@ -148312,13 +154518,13 @@ vectorise(ux,5) --R Type: Vector(Integer) --E 19 ---S 20 of 35 +--S 20 of 36 squareTerms(p) == reduce(+,[t**2 for t in monomials p]) --R --R Type: Void --E 20 ---S 21 of 35 +--S 21 of 36 p --R --R @@ -148327,7 +154533,7 @@ p --R Type: UnivariatePolynomial(x,Integer) --E 21 ---S 22 of 35 +--S 22 of 36 squareTerms p --R --R Compiling function squareTerms with type UnivariatePolynomial(x, @@ -148338,13 +154544,13 @@ squareTerms p --R Type: UnivariatePolynomial(x,Integer) --E 22 ---S 23 of 35 +--S 23 of 36 (r,s) : UP(a1,FRAC INT) --R --R Type: Void --E 23 ---S 24 of 35 +--S 24 of 36 r := a1**2 - 2/3 --R --R @@ -148354,7 +154560,7 @@ r := a1**2 - 2/3 --R Type: UnivariatePolynomial(a1,Fraction(Integer)) --E 24 ---S 25 of 35 +--S 25 of 36 s := a1 + 4 --R --R @@ -148362,7 +154568,7 @@ s := a1 + 4 --R Type: UnivariatePolynomial(a1,Fraction(Integer)) --E 25 ---S 26 of 35 +--S 26 of 36 r quo s --R --R @@ -148370,7 +154576,7 @@ r quo s --R Type: UnivariatePolynomial(a1,Fraction(Integer)) --E 26 ---S 27 of 35 +--S 27 of 36 r rem s --R --R @@ -148380,7 +154586,7 @@ r rem s --R Type: UnivariatePolynomial(a1,Fraction(Integer)) --E 27 ---S 28 of 35 +--S 28 of 36 d := divide(r, s) --R --R @@ -148390,7 +154596,7 @@ d := divide(r, s) --IType: Record(quotient: UnivariatePolynomial(a1,Fraction(Integer)),... --E 28 ---S 29 of 35 +--S 29 of 36 r - (d.quotient * s + d.remainder) --R --R @@ -148398,7 +154604,7 @@ r - (d.quotient * s + d.remainder) --R Type: UnivariatePolynomial(a1,Fraction(Integer)) --E 29 ---S 30 of 35 +--S 30 of 36 integrate r --R --R @@ -148408,7 +154614,7 @@ integrate r --R Type: UnivariatePolynomial(a1,Fraction(Integer)) --E 30 ---S 31 of 35 +--S 31 of 36 integrate s --R --R @@ -148418,13 +154624,13 @@ integrate s --R Type: UnivariatePolynomial(a1,Fraction(Integer)) --E 31 ---S 32 of 35 +--S 32 of 36 t : UP(a1,FRAC POLY INT) --R --R Type: Void --E 32 ---S 33 of 35 +--S 33 of 36 t := a1**2 - a1/b2 + (b1**2-b1)/(b2+3) --R --R @@ -148435,7 +154641,7 @@ t := a1**2 - a1/b2 + (b1**2-b1)/(b2+3) --R Type: UnivariatePolynomial(a1,Fraction(Polynomial(Integer))) --E 33 ---S 34 of 35 +--S 34 of 36 u : FRAC POLY INT := t --R --R @@ -148447,7 +154653,7 @@ u : FRAC POLY INT := t --R Type: Fraction(Polynomial(Integer)) --E 34 ---S 35 of 35 +--S 35 of 36 u :: UP(b1,?) --R --R @@ -148457,6 +154663,182 @@ u :: UP(b1,?) --R b2 + 3 b2 + 3 b2 --R Type: UnivariatePolynomial(b1,Fraction(Polynomial(Integer))) --E 35 + +--S 36 of 36 +)show UnivariatePolynomial +--R +--R UnivariatePolynomial(x: Symbol,R: Ring) is a domain constructor +--R Abbreviation for UnivariatePolynomial is UP +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for UP +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,R) -> % ?*? : (R,%) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?/? : (%,R) -> % if R has FIELD +--R ?=? : (%,%) -> Boolean D : (%,(R -> R)) -> % +--R D : % -> % D : (%,NonNegativeInteger) -> % +--R D : (%,SingletonAsOrderedSet) -> % 1 : () -> % +--R 0 : () -> % ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,PositiveInteger) -> % coefficients : % -> List(R) +--R coerce : % -> % if R has INTDOM coerce : Variable(x) -> % +--R coerce : SingletonAsOrderedSet -> % coerce : R -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R content : % -> R if R has GCDDOM degree : % -> NonNegativeInteger +--R differentiate : (%,(R -> R)) -> % differentiate : % -> % +--R ?.? : (%,%) -> % ?.? : (%,R) -> R +--R eval : (%,List(%),List(%)) -> % eval : (%,%,%) -> % +--R eval : (%,Equation(%)) -> % eval : (%,List(Equation(%))) -> % +--R gcd : (%,%) -> % if R has GCDDOM gcd : List(%) -> % if R has GCDDOM +--R ground : % -> R ground? : % -> Boolean +--R hash : % -> SingleInteger init : () -> % if R has STEP +--R latex : % -> String lcm : (%,%) -> % if R has GCDDOM +--R lcm : List(%) -> % if R has GCDDOM leadingCoefficient : % -> R +--R leadingMonomial : % -> % map : ((R -> R),%) -> % +--R max : (%,%) -> % if R has ORDSET min : (%,%) -> % if R has ORDSET +--R monomial? : % -> Boolean monomials : % -> List(%) +--R one? : % -> Boolean primitiveMonomials : % -> List(%) +--R pseudoRemainder : (%,%) -> % ?quo? : (%,%) -> % if R has FIELD +--R recip : % -> Union(%,"failed") reductum : % -> % +--R ?rem? : (%,%) -> % if R has FIELD retract : % -> R +--R sample : () -> % unvectorise : Vector(R) -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (Fraction(Integer),%) -> % if R has ALGEBRA(FRAC(INT)) +--R ?*? : (%,Fraction(Integer)) -> % if R has ALGEBRA(FRAC(INT)) +--R ? Boolean if R has ORDSET +--R ?<=? : (%,%) -> Boolean if R has ORDSET +--R ?>? : (%,%) -> Boolean if R has ORDSET +--R ?>=? : (%,%) -> Boolean if R has ORDSET +--R D : (%,(R -> R),NonNegativeInteger) -> % +--R D : (%,List(Symbol),List(NonNegativeInteger)) -> % if R has PDRING(SYMBOL) +--R D : (%,Symbol,NonNegativeInteger) -> % if R has PDRING(SYMBOL) +--R D : (%,List(Symbol)) -> % if R has PDRING(SYMBOL) +--R D : (%,Symbol) -> % if R has PDRING(SYMBOL) +--R D : (%,List(SingletonAsOrderedSet),List(NonNegativeInteger)) -> % +--R D : (%,SingletonAsOrderedSet,NonNegativeInteger) -> % +--R D : (%,List(SingletonAsOrderedSet)) -> % +--R associates? : (%,%) -> Boolean if R has INTDOM +--R binomThmExpt : (%,%,NonNegativeInteger) -> % if R has COMRING +--R characteristic : () -> NonNegativeInteger +--R charthRoot : % -> Union(%,"failed") if $ has CHARNZ and R has PFECAT or R has CHARNZ +--R coefficient : (%,List(SingletonAsOrderedSet),List(NonNegativeInteger)) -> % +--R coefficient : (%,SingletonAsOrderedSet,NonNegativeInteger) -> % +--R coefficient : (%,NonNegativeInteger) -> R +--R coerce : Fraction(Integer) -> % if R has ALGEBRA(FRAC(INT)) or R has RETRACT(FRAC(INT)) +--R composite : (Fraction(%),%) -> Union(Fraction(%),"failed") if R has INTDOM +--R composite : (%,%) -> Union(%,"failed") if R has INTDOM +--R conditionP : Matrix(%) -> Union(Vector(%),"failed") if $ has CHARNZ and R has PFECAT +--R content : (%,SingletonAsOrderedSet) -> % if R has GCDDOM +--R convert : % -> InputForm if SingletonAsOrderedSet has KONVERT(INFORM) and R has KONVERT(INFORM) +--R convert : % -> Pattern(Integer) if SingletonAsOrderedSet has KONVERT(PATTERN(INT)) and R has KONVERT(PATTERN(INT)) +--R convert : % -> Pattern(Float) if SingletonAsOrderedSet has KONVERT(PATTERN(FLOAT)) and R has KONVERT(PATTERN(FLOAT)) +--R degree : (%,List(SingletonAsOrderedSet)) -> List(NonNegativeInteger) +--R degree : (%,SingletonAsOrderedSet) -> NonNegativeInteger +--R differentiate : (%,(R -> R),%) -> % +--R differentiate : (%,(R -> R),NonNegativeInteger) -> % +--R differentiate : (%,List(Symbol),List(NonNegativeInteger)) -> % if R has PDRING(SYMBOL) +--R differentiate : (%,Symbol,NonNegativeInteger) -> % if R has PDRING(SYMBOL) +--R differentiate : (%,List(Symbol)) -> % if R has PDRING(SYMBOL) +--R differentiate : (%,Symbol) -> % if R has PDRING(SYMBOL) +--R differentiate : (%,NonNegativeInteger) -> % +--R differentiate : (%,List(SingletonAsOrderedSet),List(NonNegativeInteger)) -> % +--R differentiate : (%,SingletonAsOrderedSet,NonNegativeInteger) -> % +--R differentiate : (%,List(SingletonAsOrderedSet)) -> % +--R differentiate : (%,SingletonAsOrderedSet) -> % +--R discriminant : % -> R if R has COMRING +--R discriminant : (%,SingletonAsOrderedSet) -> % if R has COMRING +--R divide : (%,%) -> Record(quotient: %,remainder: %) if R has FIELD +--R divideExponents : (%,NonNegativeInteger) -> Union(%,"failed") +--R ?.? : (%,Fraction(%)) -> Fraction(%) if R has INTDOM +--R elt : (Fraction(%),R) -> R if R has FIELD +--R elt : (Fraction(%),Fraction(%)) -> Fraction(%) if R has INTDOM +--R euclideanSize : % -> NonNegativeInteger if R has FIELD +--R eval : (%,List(SingletonAsOrderedSet),List(%)) -> % +--R eval : (%,SingletonAsOrderedSet,%) -> % +--R eval : (%,List(SingletonAsOrderedSet),List(R)) -> % +--R eval : (%,SingletonAsOrderedSet,R) -> % +--R expressIdealMember : (List(%),%) -> Union(List(%),"failed") if R has FIELD +--R exquo : (%,%) -> Union(%,"failed") if R has INTDOM +--R exquo : (%,R) -> Union(%,"failed") if R has INTDOM +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) if R has FIELD +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") if R has FIELD +--R factor : % -> Factored(%) if R has PFECAT +--R factorPolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has PFECAT +--R factorSquareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has PFECAT +--R fmecg : (%,NonNegativeInteger,R,%) -> % +--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) if R has GCDDOM +--R integrate : % -> % if R has ALGEBRA(FRAC(INT)) +--R isExpt : % -> Union(Record(var: SingletonAsOrderedSet,exponent: NonNegativeInteger),"failed") +--R isPlus : % -> Union(List(%),"failed") +--R isTimes : % -> Union(List(%),"failed") +--R karatsubaDivide : (%,NonNegativeInteger) -> Record(quotient: %,remainder: %) +--R lcmCoef : (%,%) -> Record(llcmres: %,coeff1: %,coeff2: %) if R has GCDDOM +--R mainVariable : % -> Union(SingletonAsOrderedSet,"failed") +--R makeSUP : % -> SparseUnivariatePolynomial(R) +--R mapExponents : ((NonNegativeInteger -> NonNegativeInteger),%) -> % +--R minimumDegree : (%,List(SingletonAsOrderedSet)) -> List(NonNegativeInteger) +--R minimumDegree : (%,SingletonAsOrderedSet) -> NonNegativeInteger +--R minimumDegree : % -> NonNegativeInteger +--R monicDivide : (%,%) -> Record(quotient: %,remainder: %) +--R monicDivide : (%,%,SingletonAsOrderedSet) -> Record(quotient: %,remainder: %) +--R monomial : (%,List(SingletonAsOrderedSet),List(NonNegativeInteger)) -> % +--R monomial : (%,SingletonAsOrderedSet,NonNegativeInteger) -> % +--R monomial : (R,NonNegativeInteger) -> % +--R multiEuclidean : (List(%),%) -> Union(List(%),"failed") if R has FIELD +--R multiplyExponents : (%,NonNegativeInteger) -> % +--R multivariate : (SparseUnivariatePolynomial(%),SingletonAsOrderedSet) -> % +--R multivariate : (SparseUnivariatePolynomial(R),SingletonAsOrderedSet) -> % +--R nextItem : % -> Union(%,"failed") if R has STEP +--R numberOfMonomials : % -> NonNegativeInteger +--R order : (%,%) -> NonNegativeInteger if R has INTDOM +--R patternMatch : (%,Pattern(Integer),PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if SingletonAsOrderedSet has PATMAB(INT) and R has PATMAB(INT) +--R patternMatch : (%,Pattern(Float),PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if SingletonAsOrderedSet has PATMAB(FLOAT) and R has PATMAB(FLOAT) +--R pomopo! : (%,R,NonNegativeInteger,%) -> % +--R prime? : % -> Boolean if R has PFECAT +--R primitivePart : (%,SingletonAsOrderedSet) -> % if R has GCDDOM +--R primitivePart : % -> % if R has GCDDOM +--R principalIdeal : List(%) -> Record(coef: List(%),generator: %) if R has FIELD +--R pseudoDivide : (%,%) -> Record(coef: R,quotient: %,remainder: %) if R has INTDOM +--R pseudoQuotient : (%,%) -> % if R has INTDOM +--R reducedSystem : Matrix(%) -> Matrix(R) +--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(R),vec: Vector(R)) +--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(Integer),vec: Vector(Integer)) if R has LINEXP(INT) +--R reducedSystem : Matrix(%) -> Matrix(Integer) if R has LINEXP(INT) +--R resultant : (%,%) -> R if R has COMRING +--R resultant : (%,%,SingletonAsOrderedSet) -> % if R has COMRING +--R retract : % -> SingletonAsOrderedSet +--R retract : % -> Integer if R has RETRACT(INT) +--R retract : % -> Fraction(Integer) if R has RETRACT(FRAC(INT)) +--R retractIfCan : % -> Union(SingletonAsOrderedSet,"failed") +--R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT(INT) +--R retractIfCan : % -> Union(Fraction(Integer),"failed") if R has RETRACT(FRAC(INT)) +--R retractIfCan : % -> Union(R,"failed") +--R separate : (%,%) -> Record(primePart: %,commonPart: %) if R has GCDDOM +--R shiftLeft : (%,NonNegativeInteger) -> % +--R shiftRight : (%,NonNegativeInteger) -> % +--R sizeLess? : (%,%) -> Boolean if R has FIELD +--R solveLinearPolynomialEquation : (List(SparseUnivariatePolynomial(%)),SparseUnivariatePolynomial(%)) -> Union(List(SparseUnivariatePolynomial(%)),"failed") if R has PFECAT +--R squareFree : % -> Factored(%) if R has GCDDOM +--R squareFreePart : % -> % if R has GCDDOM +--R squareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has PFECAT +--R subResultantGcd : (%,%) -> % if R has INTDOM +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R totalDegree : (%,List(SingletonAsOrderedSet)) -> NonNegativeInteger +--R totalDegree : % -> NonNegativeInteger +--R unit? : % -> Boolean if R has INTDOM +--R unitCanonical : % -> % if R has INTDOM +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) if R has INTDOM +--R univariate : % -> SparseUnivariatePolynomial(R) +--R univariate : (%,SingletonAsOrderedSet) -> SparseUnivariatePolynomial(%) +--R unmakeSUP : SparseUnivariatePolynomial(R) -> % +--R variables : % -> List(SingletonAsOrderedSet) +--R vectorise : (%,NonNegativeInteger) -> Vector(R) +--R +--E 36 + )spool )lisp (bye) \end{chunk} @@ -148935,14 +155317,17 @@ UnivariatePolynomial(x:Symbol, R:Ring): --R------------------------------- Operations -------------------------------- --R ?*? : (Coef,%) -> % ?*? : (%,Coef) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ?=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % center : % -> Coef +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R center : % -> Coef coerce : % -> % if Coef has INTDOM --R coerce : Variable(var) -> % coerce : Integer -> % --R coerce : % -> OutputForm complete : % -> % ---R degree : % -> Fraction(Integer) hash : % -> SingleInteger +--R degree : % -> Fraction(Integer) ?.? : (%,Fraction(Integer)) -> Coef +--R hash : % -> SingleInteger inv : % -> % if Coef has FIELD --R latex : % -> String leadingCoefficient : % -> Coef --R leadingMonomial : % -> % map : ((Coef -> Coef),%) -> % --R monomial? : % -> Boolean one? : % -> Boolean @@ -148952,11 +155337,9 @@ UnivariatePolynomial(x:Symbol, R:Ring): --R zero? : % -> Boolean ?~=? : (%,%) -> Boolean --R ?*? : (%,Fraction(Integer)) -> % if Coef has ALGEBRA(FRAC(INT)) --R ?*? : (Fraction(Integer),%) -> % if Coef has ALGEBRA(FRAC(INT)) ---R ?*? : (NonNegativeInteger,%) -> % --R ?**? : (%,Fraction(Integer)) -> % if Coef has ALGEBRA(FRAC(INT)) --R ?**? : (%,%) -> % if Coef has ALGEBRA(FRAC(INT)) --R ?**? : (%,Integer) -> % if Coef has FIELD ---R ?**? : (%,NonNegativeInteger) -> % --R ?/? : (%,%) -> % if Coef has FIELD --R ?/? : (%,Coef) -> % if Coef has FIELD --R D : % -> % if Coef has *: (Fraction(Integer),Coef) -> Coef @@ -148966,7 +155349,6 @@ UnivariatePolynomial(x:Symbol, R:Ring): --R D : (%,Symbol,NonNegativeInteger) -> % if Coef has *: (Fraction(Integer),Coef) -> Coef and Coef has PDRING(SYMBOL) --R D : (%,List(Symbol),List(NonNegativeInteger)) -> % if Coef has *: (Fraction(Integer),Coef) -> Coef and Coef has PDRING(SYMBOL) --R ?^? : (%,Integer) -> % if Coef has FIELD ---R ?^? : (%,NonNegativeInteger) -> % --R acos : % -> % if Coef has ALGEBRA(FRAC(INT)) --R acosh : % -> % if Coef has ALGEBRA(FRAC(INT)) --R acot : % -> % if Coef has ALGEBRA(FRAC(INT)) @@ -148984,7 +155366,6 @@ UnivariatePolynomial(x:Symbol, R:Ring): --R characteristic : () -> NonNegativeInteger --R charthRoot : % -> Union(%,"failed") if Coef has CHARNZ --R coefficient : (%,Fraction(Integer)) -> Coef ---R coerce : % -> % if Coef has INTDOM --R coerce : Fraction(Integer) -> % if Coef has ALGEBRA(FRAC(INT)) --R coerce : UnivariateTaylorSeries(Coef,var,cen) -> % --R coerce : UnivariateLaurentSeries(Coef,var,cen) -> % @@ -149004,7 +155385,6 @@ UnivariatePolynomial(x:Symbol, R:Ring): --R differentiate : (%,List(Symbol),List(NonNegativeInteger)) -> % if Coef has *: (Fraction(Integer),Coef) -> Coef and Coef has PDRING(SYMBOL) --R divide : (%,%) -> Record(quotient: %,remainder: %) if Coef has FIELD --R ?.? : (%,%) -> % if Fraction(Integer) has SGROUP ---R ?.? : (%,Fraction(Integer)) -> Coef --R euclideanSize : % -> NonNegativeInteger if Coef has FIELD --R eval : (%,Coef) -> Stream(Coef) if Coef has **: (Coef,Fraction(Integer)) -> Coef --R exp : % -> % if Coef has ALGEBRA(FRAC(INT)) @@ -149020,7 +155400,6 @@ UnivariatePolynomial(x:Symbol, R:Ring): --R integrate : (%,Variable(var)) -> % if Coef has ALGEBRA(FRAC(INT)) --R integrate : (%,Symbol) -> % if Coef has integrate: (Coef,Symbol) -> Coef and Coef has variables: Coef -> List(Symbol) and Coef has ALGEBRA(FRAC(INT)) or Coef has ACFS(INT) and Coef has ALGEBRA(FRAC(INT)) and Coef has PRIMCAT and Coef has TRANFUN --R integrate : % -> % if Coef has ALGEBRA(FRAC(INT)) ---R inv : % -> % if Coef has FIELD --R laurent : % -> UnivariateLaurentSeries(Coef,var,cen) --R laurentIfCan : % -> Union(UnivariateLaurentSeries(Coef,var,cen),"failed") --R laurentRep : % -> UnivariateLaurentSeries(Coef,var,cen) @@ -149378,14 +155757,17 @@ UnivariatePuiseuxSeries(Coef,var,cen): Exports == Implementation where --R------------------------------- Operations -------------------------------- --R ?*? : (Coef,%) -> % ?*? : (%,Coef) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ?=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % center : % -> Coef +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R center : % -> Coef coerce : % -> % if Coef has INTDOM --R coerce : ULS -> % coerce : Integer -> % --R coerce : % -> OutputForm complete : % -> % ---R degree : % -> Fraction(Integer) hash : % -> SingleInteger +--R degree : % -> Fraction(Integer) ?.? : (%,Fraction(Integer)) -> Coef +--R hash : % -> SingleInteger inv : % -> % if Coef has FIELD --R latex : % -> String laurent : % -> ULS --R laurentRep : % -> ULS leadingCoefficient : % -> Coef --R leadingMonomial : % -> % map : ((Coef -> Coef),%) -> % @@ -149397,11 +155779,9 @@ UnivariatePuiseuxSeries(Coef,var,cen): Exports == Implementation where --R ?~=? : (%,%) -> Boolean --R ?*? : (%,Fraction(Integer)) -> % if Coef has ALGEBRA(FRAC(INT)) --R ?*? : (Fraction(Integer),%) -> % if Coef has ALGEBRA(FRAC(INT)) ---R ?*? : (NonNegativeInteger,%) -> % --R ?**? : (%,Fraction(Integer)) -> % if Coef has ALGEBRA(FRAC(INT)) --R ?**? : (%,%) -> % if Coef has ALGEBRA(FRAC(INT)) --R ?**? : (%,Integer) -> % if Coef has FIELD ---R ?**? : (%,NonNegativeInteger) -> % --R ?/? : (%,%) -> % if Coef has FIELD --R ?/? : (%,Coef) -> % if Coef has FIELD --R D : % -> % if Coef has *: (Fraction(Integer),Coef) -> Coef @@ -149411,7 +155791,6 @@ UnivariatePuiseuxSeries(Coef,var,cen): Exports == Implementation where --R D : (%,Symbol,NonNegativeInteger) -> % if Coef has *: (Fraction(Integer),Coef) -> Coef and Coef has PDRING(SYMBOL) --R D : (%,List(Symbol),List(NonNegativeInteger)) -> % if Coef has *: (Fraction(Integer),Coef) -> Coef and Coef has PDRING(SYMBOL) --R ?^? : (%,Integer) -> % if Coef has FIELD ---R ?^? : (%,NonNegativeInteger) -> % --R acos : % -> % if Coef has ALGEBRA(FRAC(INT)) --R acosh : % -> % if Coef has ALGEBRA(FRAC(INT)) --R acot : % -> % if Coef has ALGEBRA(FRAC(INT)) @@ -149429,7 +155808,6 @@ UnivariatePuiseuxSeries(Coef,var,cen): Exports == Implementation where --R characteristic : () -> NonNegativeInteger --R charthRoot : % -> Union(%,"failed") if Coef has CHARNZ --R coefficient : (%,Fraction(Integer)) -> Coef ---R coerce : % -> % if Coef has INTDOM --R coerce : Fraction(Integer) -> % if Coef has ALGEBRA(FRAC(INT)) --R coerce : Coef -> % if Coef has COMRING --R cos : % -> % if Coef has ALGEBRA(FRAC(INT)) @@ -149446,7 +155824,6 @@ UnivariatePuiseuxSeries(Coef,var,cen): Exports == Implementation where --R differentiate : (%,List(Symbol),List(NonNegativeInteger)) -> % if Coef has *: (Fraction(Integer),Coef) -> Coef and Coef has PDRING(SYMBOL) --R divide : (%,%) -> Record(quotient: %,remainder: %) if Coef has FIELD --R ?.? : (%,%) -> % if Fraction(Integer) has SGROUP ---R ?.? : (%,Fraction(Integer)) -> Coef --R euclideanSize : % -> NonNegativeInteger if Coef has FIELD --R eval : (%,Coef) -> Stream(Coef) if Coef has **: (Coef,Fraction(Integer)) -> Coef --R exp : % -> % if Coef has ALGEBRA(FRAC(INT)) @@ -149461,7 +155838,6 @@ UnivariatePuiseuxSeries(Coef,var,cen): Exports == Implementation where --R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) if Coef has FIELD --R integrate : (%,Symbol) -> % if Coef has integrate: (Coef,Symbol) -> Coef and Coef has variables: Coef -> List(Symbol) and Coef has ALGEBRA(FRAC(INT)) or Coef has ACFS(INT) and Coef has ALGEBRA(FRAC(INT)) and Coef has PRIMCAT and Coef has TRANFUN --R integrate : % -> % if Coef has ALGEBRA(FRAC(INT)) ---R inv : % -> % if Coef has FIELD --R laurentIfCan : % -> Union(ULS,"failed") --R lcm : (%,%) -> % if Coef has FIELD --R lcm : List(%) -> % if Coef has FIELD @@ -150007,27 +156383,26 @@ UnivariatePuiseuxSeriesConstructor(Coef,ULS):_ --R --R------------------------------- Operations -------------------------------- --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ?=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % associates? : (%,%) -> Boolean ---R coerce : % -> % coerce : Integer -> % ---R coerce : % -> OutputForm ground? : % -> Boolean ---R hash : % -> SingleInteger latex : % -> String ---R leadingMonomial : % -> % monomial? : % -> Boolean ---R one? : % -> Boolean recip : % -> Union(%,"failed") ---R reductum : % -> % sample : () -> % ---R unit? : % -> Boolean unitCanonical : % -> % ---R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R associates? : (%,%) -> Boolean coerce : % -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R ground? : % -> Boolean hash : % -> SingleInteger +--R latex : % -> String leadingMonomial : % -> % +--R monomial? : % -> Boolean one? : % -> Boolean +--R recip : % -> Union(%,"failed") reductum : % -> % +--R sample : () -> % unit? : % -> Boolean +--R unitCanonical : % -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean --R ?*? : (%,Fraction(Integer)) -> % if UnivariatePuiseuxSeries(FE,var,cen) has ALGEBRA(FRAC(INT)) --R ?*? : (Fraction(Integer),%) -> % if UnivariatePuiseuxSeries(FE,var,cen) has ALGEBRA(FRAC(INT)) --R ?*? : (UnivariatePuiseuxSeries(FE,var,cen),%) -> % --R ?*? : (%,UnivariatePuiseuxSeries(FE,var,cen)) -> % ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % --R ?/? : (%,UnivariatePuiseuxSeries(FE,var,cen)) -> % if UnivariatePuiseuxSeries(FE,var,cen) has FIELD ---R ?^? : (%,NonNegativeInteger) -> % --R binomThmExpt : (%,%,NonNegativeInteger) -> % if UnivariatePuiseuxSeries(FE,var,cen) has COMRING --R characteristic : () -> NonNegativeInteger --R charthRoot : % -> Union(%,"failed") if UnivariatePuiseuxSeries(FE,var,cen) has CHARNZ @@ -150737,26 +157112,24 @@ x^2*a --R------------------------------- Operations -------------------------------- --R ?*? : (R,%) -> % ?*? : (%,R) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ?=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % apply : (%,R,R) -> R ---R coefficients : % -> List(R) coerce : Variable(x) -> % ---R coerce : R -> % coerce : Integer -> % ---R coerce : % -> OutputForm degree : % -> NonNegativeInteger +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R apply : (%,R,R) -> R coefficients : % -> List(R) +--R coerce : Variable(x) -> % coerce : R -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R content : % -> R if R has GCDDOM degree : % -> NonNegativeInteger --R hash : % -> SingleInteger latex : % -> String --R leadingCoefficient : % -> R one? : % -> Boolean --R recip : % -> Union(%,"failed") reductum : % -> % --R retract : % -> R sample : () -> % --R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R ?^? : (%,NonNegativeInteger) -> % --R characteristic : () -> NonNegativeInteger --R coefficient : (%,NonNegativeInteger) -> R --R coerce : Fraction(Integer) -> % if R has RETRACT(FRAC(INT)) ---R content : % -> R if R has GCDDOM --R exquo : (%,R) -> Union(%,"failed") if R has INTDOM --R leftDivide : (%,%) -> Record(quotient: %,remainder: %) if R has FIELD --R leftExactQuotient : (%,%) -> Union(%,"failed") if R has FIELD @@ -150785,6 +157158,7 @@ x^2*a --R subtractIfCan : (%,%) -> Union(%,"failed") --R --E 33 + )set expose drop constructor SquareMatrix )spool @@ -151185,12 +157559,14 @@ UnivariateSkewPolynomial(x:Symbol,R:Ring,sigma:Automorphism R,delta: R -> R): --R------------------------------- Operations -------------------------------- --R ?*? : (Coef,%) -> % ?*? : (%,Coef) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ?=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % center : % -> Coef ---R coefficients : % -> Stream(Coef) coerce : Variable(var) -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R center : % -> Coef coefficients : % -> Stream(Coef) +--R coerce : Variable(var) -> % coerce : % -> % if Coef has INTDOM --R coerce : Integer -> % coerce : % -> OutputForm --R complete : % -> % degree : % -> NonNegativeInteger --R evenlambert : % -> % hash : % -> SingleInteger @@ -151206,11 +157582,9 @@ UnivariateSkewPolynomial(x:Symbol,R:Ring,sigma:Automorphism R,delta: R -> R): --R zero? : % -> Boolean ?~=? : (%,%) -> Boolean --R ?*? : (%,Fraction(Integer)) -> % if Coef has ALGEBRA(FRAC(INT)) --R ?*? : (Fraction(Integer),%) -> % if Coef has ALGEBRA(FRAC(INT)) ---R ?*? : (NonNegativeInteger,%) -> % --R ?**? : (%,Fraction(Integer)) -> % if Coef has ALGEBRA(FRAC(INT)) --R ?**? : (%,%) -> % if Coef has ALGEBRA(FRAC(INT)) --R ?**? : (%,Coef) -> % if Coef has FIELD ---R ?**? : (%,NonNegativeInteger) -> % --R ?/? : (%,Coef) -> % if Coef has FIELD --R D : % -> % if Coef has *: (NonNegativeInteger,Coef) -> Coef --R D : (%,NonNegativeInteger) -> % if Coef has *: (NonNegativeInteger,Coef) -> Coef @@ -151218,7 +157592,6 @@ UnivariateSkewPolynomial(x:Symbol,R:Ring,sigma:Automorphism R,delta: R -> R): --R D : (%,List(Symbol)) -> % if Coef has *: (NonNegativeInteger,Coef) -> Coef and Coef has PDRING(SYMBOL) --R D : (%,Symbol,NonNegativeInteger) -> % if Coef has *: (NonNegativeInteger,Coef) -> Coef and Coef has PDRING(SYMBOL) --R D : (%,List(Symbol),List(NonNegativeInteger)) -> % if Coef has *: (NonNegativeInteger,Coef) -> Coef and Coef has PDRING(SYMBOL) ---R ?^? : (%,NonNegativeInteger) -> % --R acos : % -> % if Coef has ALGEBRA(FRAC(INT)) --R acosh : % -> % if Coef has ALGEBRA(FRAC(INT)) --R acot : % -> % if Coef has ALGEBRA(FRAC(INT)) @@ -151238,7 +157611,6 @@ UnivariateSkewPolynomial(x:Symbol,R:Ring,sigma:Automorphism R,delta: R -> R): --R coefficient : (%,NonNegativeInteger) -> Coef --R coerce : UnivariatePolynomial(var,Coef) -> % --R coerce : Coef -> % if Coef has COMRING ---R coerce : % -> % if Coef has INTDOM --R coerce : Fraction(Integer) -> % if Coef has ALGEBRA(FRAC(INT)) --R cos : % -> % if Coef has ALGEBRA(FRAC(INT)) --R cosh : % -> % if Coef has ALGEBRA(FRAC(INT)) @@ -151703,12 +158075,14 @@ UnivariateTaylorSeries(Coef,var,cen): Exports == Implementation where --R------------------------------- Operations -------------------------------- --R ?*? : (Coef,%) -> % ?*? : (%,Coef) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ?=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % center : % -> Coef ---R coefficients : % -> Stream(Coef) coerce : Variable(var) -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R center : % -> Coef coefficients : % -> Stream(Coef) +--R coerce : Variable(var) -> % coerce : % -> % if Coef has INTDOM --R coerce : Integer -> % coerce : % -> OutputForm --R complete : % -> % degree : % -> NonNegativeInteger --R evenlambert : % -> % hash : % -> SingleInteger @@ -151724,11 +158098,9 @@ UnivariateTaylorSeries(Coef,var,cen): Exports == Implementation where --R zero? : % -> Boolean ?~=? : (%,%) -> Boolean --R ?*? : (%,Fraction(Integer)) -> % if Coef has ALGEBRA(FRAC(INT)) --R ?*? : (Fraction(Integer),%) -> % if Coef has ALGEBRA(FRAC(INT)) ---R ?*? : (NonNegativeInteger,%) -> % --R ?**? : (%,Fraction(Integer)) -> % if Coef has ALGEBRA(FRAC(INT)) --R ?**? : (%,%) -> % if Coef has ALGEBRA(FRAC(INT)) --R ?**? : (%,Coef) -> % if Coef has FIELD ---R ?**? : (%,NonNegativeInteger) -> % --R ?/? : (%,Coef) -> % if Coef has FIELD --R D : % -> % if Coef has *: (NonNegativeInteger,Coef) -> Coef --R D : (%,NonNegativeInteger) -> % if Coef has *: (NonNegativeInteger,Coef) -> Coef @@ -151736,7 +158108,6 @@ UnivariateTaylorSeries(Coef,var,cen): Exports == Implementation where --R D : (%,List(Symbol)) -> % if Coef has *: (NonNegativeInteger,Coef) -> Coef and Coef has PDRING(SYMBOL) --R D : (%,Symbol,NonNegativeInteger) -> % if Coef has *: (NonNegativeInteger,Coef) -> Coef and Coef has PDRING(SYMBOL) --R D : (%,List(Symbol),List(NonNegativeInteger)) -> % if Coef has *: (NonNegativeInteger,Coef) -> Coef and Coef has PDRING(SYMBOL) ---R ?^? : (%,NonNegativeInteger) -> % --R acos : % -> % if Coef has ALGEBRA(FRAC(INT)) --R acosh : % -> % if Coef has ALGEBRA(FRAC(INT)) --R acot : % -> % if Coef has ALGEBRA(FRAC(INT)) @@ -151756,7 +158127,6 @@ UnivariateTaylorSeries(Coef,var,cen): Exports == Implementation where --R coefficient : (%,NonNegativeInteger) -> Coef --R coerce : UnivariatePolynomial(var,Coef) -> % --R coerce : Coef -> % if Coef has COMRING ---R coerce : % -> % if Coef has INTDOM --R coerce : Fraction(Integer) -> % if Coef has ALGEBRA(FRAC(INT)) --R cos : % -> % if Coef has ALGEBRA(FRAC(INT)) --R cosh : % -> % if Coef has ALGEBRA(FRAC(INT)) @@ -152185,7 +158555,8 @@ UnivariateTaylorSeriesCZero(Coef,var): Exports == Implementation where )set message test on )set message auto off )clear all ---S 1 of 9 + +--S 1 of 10 pints := 1.. --R --R @@ -152193,7 +158564,7 @@ pints := 1.. --R Type: UniversalSegment(PositiveInteger) --E 1 ---S 2 of 9 +--S 2 of 10 nevens := (0..) by -2 --R --R @@ -152201,7 +158572,7 @@ nevens := (0..) by -2 --R Type: UniversalSegment(NonNegativeInteger) --E 2 ---S 3 of 9 +--S 3 of 10 useg: UniversalSegment(Integer) := 3..10 --R --R @@ -152209,7 +158580,7 @@ useg: UniversalSegment(Integer) := 3..10 --R Type: UniversalSegment(Integer) --E 3 ---S 4 of 9 +--S 4 of 10 hasHi pints --R --R @@ -152217,7 +158588,7 @@ hasHi pints --R Type: Boolean --E 4 ---S 5 of 9 +--S 5 of 10 hasHi nevens --R --R @@ -152225,7 +158596,7 @@ hasHi nevens --R Type: Boolean --E 5 ---S 6 of 9 +--S 6 of 10 hasHi useg --R --R @@ -152233,7 +158604,7 @@ hasHi useg --R Type: Boolean --E 6 ---S 7 of 9 +--S 7 of 10 expand pints --R --R @@ -152241,7 +158612,7 @@ expand pints --R Type: Stream(Integer) --E 7 ---S 8 of 9 +--S 8 of 10 expand nevens --R --R @@ -152249,13 +158620,40 @@ expand nevens --R Type: Stream(Integer) --E 8 ---S 9 of 9 +--S 9 of 10 expand [1, 3, 10..15, 100..] --R --R --R (9) [1,3,10,11,12,13,14,15,100,101,...] --R Type: Stream(Integer) --E 9 + +--S 10 of 10 +)show UniversalSegment +--R +--R UniversalSegment(S: Type) is a domain constructor +--R Abbreviation for UniversalSegment is UNISEG +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for UNISEG +--R +--R------------------------------- Operations -------------------------------- +--R BY : (%,Integer) -> % ?SEGMENT : S -> % +--R ?..? : (S,S) -> % coerce : Segment(S) -> % +--R convert : S -> % hasHi : % -> Boolean +--R hi : % -> S high : % -> S +--R incr : % -> Integer latex : % -> String if S has SETCAT +--R lo : % -> S low : % -> S +--R segment : S -> % segment : (S,S) -> % +--R ?=? : (%,%) -> Boolean if S has SETCAT +--R coerce : % -> OutputForm if S has SETCAT +--R expand : List(%) -> Stream(S) if S has ORDRING +--R expand : % -> Stream(S) if S has ORDRING +--R hash : % -> SingleInteger if S has SETCAT +--R map : ((S -> S),%) -> Stream(S) if S has ORDRING +--R ?~=? : (%,%) -> Boolean if S has SETCAT +--R +--E 10 + )spool )lisp (bye) \end{chunk} @@ -152497,11 +158895,12 @@ UniversalSegment(S: Type): SegmentCategory(S) with --R ?*? : (U8Vector,%) -> U8Vector ?*? : (%,U8Vector) -> U8Vector --R ?*? : (Integer,%) -> % ?*? : (%,Integer) -> % --R ?*? : (Integer,%) -> % ?*? : (%,%) -> % ---R ?+? : (%,%) -> % -? : % -> % ---R ?-? : (%,%) -> % antisymmetric? : % -> Boolean ---R coerce : U8Vector -> % column : (%,Integer) -> U8Vector ---R copy : % -> % diagonal? : % -> Boolean ---R diagonalMatrix : List(%) -> % empty : () -> % +--R ?**? : (%,NonNegativeInteger) -> % ?+? : (%,%) -> % +--R -? : % -> % ?-? : (%,%) -> % +--R antisymmetric? : % -> Boolean coerce : U8Vector -> % +--R column : (%,Integer) -> U8Vector copy : % -> % +--R diagonal? : % -> Boolean diagonalMatrix : List(%) -> % +--R diagonalMatrix : List(Integer) -> % empty : () -> % --R empty? : % -> Boolean eq? : (%,%) -> Boolean --R fill! : (%,Integer) -> % horizConcat : (%,%) -> % --R matrix : List(List(Integer)) -> % maxColIndex : % -> Integer @@ -152515,7 +158914,6 @@ UniversalSegment(S: Type): SegmentCategory(S) with --R vertConcat : (%,%) -> % --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R ?**? : (%,Integer) -> % if Integer has FIELD ---R ?**? : (%,NonNegativeInteger) -> % --R ?/? : (%,Integer) -> % if Integer has FIELD --R ?=? : (%,%) -> Boolean if Integer has SETCAT --R any? : ((Integer -> Boolean),%) -> Boolean if $ has finiteAggregate @@ -152524,7 +158922,6 @@ UniversalSegment(S: Type): SegmentCategory(S) with --R count : (Integer,%) -> NonNegativeInteger if $ has finiteAggregate and Integer has SETCAT --R count : ((Integer -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate --R determinant : % -> Integer if Integer has commutative(*) ---R diagonalMatrix : List(Integer) -> % --R elt : (%,List(Integer),List(Integer)) -> % --R elt : (%,Integer,Integer,Integer) -> Integer --R elt : (%,Integer,Integer) -> Integer @@ -152732,6 +159129,7 @@ U8Matrix : MatrixCategory(Integer, --S 1 of 1 )show U16Matrix +--R --R U16Matrix is a domain constructor --R Abbreviation for U16Matrix is U16MAT --R This constructor is exposed in this frame. @@ -152741,11 +159139,12 @@ U8Matrix : MatrixCategory(Integer, --R ?*? : (U16Vector,%) -> U16Vector ?*? : (%,U16Vector) -> U16Vector --R ?*? : (Integer,%) -> % ?*? : (%,Integer) -> % --R ?*? : (Integer,%) -> % ?*? : (%,%) -> % ---R ?+? : (%,%) -> % -? : % -> % ---R ?-? : (%,%) -> % antisymmetric? : % -> Boolean ---R coerce : U16Vector -> % column : (%,Integer) -> U16Vector ---R copy : % -> % diagonal? : % -> Boolean ---R diagonalMatrix : List(%) -> % empty : () -> % +--R ?**? : (%,NonNegativeInteger) -> % ?+? : (%,%) -> % +--R -? : % -> % ?-? : (%,%) -> % +--R antisymmetric? : % -> Boolean coerce : U16Vector -> % +--R column : (%,Integer) -> U16Vector copy : % -> % +--R diagonal? : % -> Boolean diagonalMatrix : List(%) -> % +--R diagonalMatrix : List(Integer) -> % empty : () -> % --R empty? : % -> Boolean eq? : (%,%) -> Boolean --R fill! : (%,Integer) -> % horizConcat : (%,%) -> % --R matrix : List(List(Integer)) -> % maxColIndex : % -> Integer @@ -152759,7 +159158,6 @@ U8Matrix : MatrixCategory(Integer, --R vertConcat : (%,%) -> % --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R ?**? : (%,Integer) -> % if Integer has FIELD ---R ?**? : (%,NonNegativeInteger) -> % --R ?/? : (%,Integer) -> % if Integer has FIELD --R ?=? : (%,%) -> Boolean if Integer has SETCAT --R any? : ((Integer -> Boolean),%) -> Boolean if $ has finiteAggregate @@ -152768,7 +159166,6 @@ U8Matrix : MatrixCategory(Integer, --R count : (Integer,%) -> NonNegativeInteger if $ has finiteAggregate and Integer has SETCAT --R count : ((Integer -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate --R determinant : % -> Integer if Integer has commutative(*) ---R diagonalMatrix : List(Integer) -> % --R elt : (%,List(Integer),List(Integer)) -> % --R elt : (%,Integer,Integer,Integer) -> Integer --R elt : (%,Integer,Integer) -> Integer @@ -152976,6 +159373,7 @@ U16Matrix : MatrixCategory(Integer, --S 1 of 1 )show U32Matrix +--R --R U32Matrix is a domain constructor --R Abbreviation for U32Matrix is U32MAT --R This constructor is exposed in this frame. @@ -152985,11 +159383,12 @@ U16Matrix : MatrixCategory(Integer, --R ?*? : (U32Vector,%) -> U32Vector ?*? : (%,U32Vector) -> U32Vector --R ?*? : (Integer,%) -> % ?*? : (%,Integer) -> % --R ?*? : (Integer,%) -> % ?*? : (%,%) -> % ---R ?+? : (%,%) -> % -? : % -> % ---R ?-? : (%,%) -> % antisymmetric? : % -> Boolean ---R coerce : U32Vector -> % column : (%,Integer) -> U32Vector ---R copy : % -> % diagonal? : % -> Boolean ---R diagonalMatrix : List(%) -> % empty : () -> % +--R ?**? : (%,NonNegativeInteger) -> % ?+? : (%,%) -> % +--R -? : % -> % ?-? : (%,%) -> % +--R antisymmetric? : % -> Boolean coerce : U32Vector -> % +--R column : (%,Integer) -> U32Vector copy : % -> % +--R diagonal? : % -> Boolean diagonalMatrix : List(%) -> % +--R diagonalMatrix : List(Integer) -> % empty : () -> % --R empty? : % -> Boolean eq? : (%,%) -> Boolean --R fill! : (%,Integer) -> % horizConcat : (%,%) -> % --R matrix : List(List(Integer)) -> % maxColIndex : % -> Integer @@ -153003,7 +159402,6 @@ U16Matrix : MatrixCategory(Integer, --R vertConcat : (%,%) -> % --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R ?**? : (%,Integer) -> % if Integer has FIELD ---R ?**? : (%,NonNegativeInteger) -> % --R ?/? : (%,Integer) -> % if Integer has FIELD --R ?=? : (%,%) -> Boolean if Integer has SETCAT --R any? : ((Integer -> Boolean),%) -> Boolean if $ has finiteAggregate @@ -153012,7 +159410,6 @@ U16Matrix : MatrixCategory(Integer, --R count : (Integer,%) -> NonNegativeInteger if $ has finiteAggregate and Integer has SETCAT --R count : ((Integer -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate --R determinant : % -> Integer if Integer has commutative(*) ---R diagonalMatrix : List(Integer) -> % --R elt : (%,List(Integer),List(Integer)) -> % --R elt : (%,Integer,Integer,Integer) -> Integer --R elt : (%,Integer,Integer) -> Integer @@ -153297,6 +159694,7 @@ t8:=fill!(t2,7) --S 12 of 12 )show U8Vector +--R --R U8Vector is a domain constructor --R Abbreviation for U8Vector is U8VEC --R This constructor is exposed in this frame. @@ -153310,8 +159708,9 @@ t8:=fill!(t2,7) --R empty : () -> % empty? : % -> Boolean --R entries : % -> List(Integer) eq? : (%,%) -> Boolean --R index? : (Integer,%) -> Boolean indices : % -> List(Integer) ---R insert : (%,%,Integer) -> % qelt : (%,Integer) -> Integer ---R reverse : % -> % sample : () -> % +--R insert : (%,%,Integer) -> % insert : (Integer,%,Integer) -> % +--R qelt : (%,Integer) -> Integer reverse : % -> % +--R sample : () -> % --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R ? Boolean if Integer has ORDSET --R ?<=? : (%,%) -> Boolean if Integer has ORDSET @@ -153337,7 +159736,6 @@ t8:=fill!(t2,7) --R find : ((Integer -> Boolean),%) -> Union(Integer,"failed") --R first : % -> Integer if Integer has ORDSET --R hash : % -> SingleInteger if Integer has SETCAT ---R insert : (Integer,%,Integer) -> % --R latex : % -> String if Integer has SETCAT --R less? : (%,NonNegativeInteger) -> Boolean --R map : (((Integer,Integer) -> Integer),%,%) -> % @@ -153667,6 +160065,7 @@ t8:=fill!(t2,7) --S 12 of 12 )show U16Vector +--R --R U16Vector is a domain constructor --R Abbreviation for U16Vector is U16VEC --R This constructor is exposed in this frame. @@ -153680,8 +160079,9 @@ t8:=fill!(t2,7) --R empty : () -> % empty? : % -> Boolean --R entries : % -> List(Integer) eq? : (%,%) -> Boolean --R index? : (Integer,%) -> Boolean indices : % -> List(Integer) ---R insert : (%,%,Integer) -> % qelt : (%,Integer) -> Integer ---R reverse : % -> % sample : () -> % +--R insert : (%,%,Integer) -> % insert : (Integer,%,Integer) -> % +--R qelt : (%,Integer) -> Integer reverse : % -> % +--R sample : () -> % --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R ? Boolean if Integer has ORDSET --R ?<=? : (%,%) -> Boolean if Integer has ORDSET @@ -153707,7 +160107,6 @@ t8:=fill!(t2,7) --R find : ((Integer -> Boolean),%) -> Union(Integer,"failed") --R first : % -> Integer if Integer has ORDSET --R hash : % -> SingleInteger if Integer has SETCAT ---R insert : (Integer,%,Integer) -> % --R latex : % -> String if Integer has SETCAT --R less? : (%,NonNegativeInteger) -> Boolean --R map : (((Integer,Integer) -> Integer),%,%) -> % @@ -154051,8 +160450,9 @@ t8:=fill!(t2,7) --R empty : () -> % empty? : % -> Boolean --R entries : % -> List(Integer) eq? : (%,%) -> Boolean --R index? : (Integer,%) -> Boolean indices : % -> List(Integer) ---R insert : (%,%,Integer) -> % qelt : (%,Integer) -> Integer ---R reverse : % -> % sample : () -> % +--R insert : (%,%,Integer) -> % insert : (Integer,%,Integer) -> % +--R qelt : (%,Integer) -> Integer reverse : % -> % +--R sample : () -> % --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R ? Boolean if Integer has ORDSET --R ?<=? : (%,%) -> Boolean if Integer has ORDSET @@ -154078,7 +160478,6 @@ t8:=fill!(t2,7) --R find : ((Integer -> Boolean),%) -> Union(Integer,"failed") --R first : % -> Integer if Integer has ORDSET --R hash : % -> SingleInteger if Integer has SETCAT ---R insert : (Integer,%,Integer) -> % --R latex : % -> String if Integer has SETCAT --R less? : (%,NonNegativeInteger) -> Boolean --R map : (((Integer,Integer) -> Integer),%,%) -> % @@ -154413,7 +160812,8 @@ Variable(sym:Symbol): Join(SetCategory, CoercibleTo Symbol) with )set message test on )set message auto off )clear all ---S 1 of 11 + +--S 1 of 12 u : VECTOR INT := new(5,12) --R --R @@ -154421,7 +160821,7 @@ u : VECTOR INT := new(5,12) --R Type: Vector(Integer) --E 1 ---S 2 of 11 +--S 2 of 12 v : VECTOR INT := vector([1,2,3,4,5]) --R --R @@ -154429,7 +160829,7 @@ v : VECTOR INT := vector([1,2,3,4,5]) --R Type: Vector(Integer) --E 2 ---S 3 of 11 +--S 3 of 12 #(v) --R --R @@ -154437,7 +160837,7 @@ v : VECTOR INT := vector([1,2,3,4,5]) --R Type: PositiveInteger --E 3 ---S 4 of 11 +--S 4 of 12 v.2 --R --R @@ -154445,7 +160845,7 @@ v.2 --R Type: PositiveInteger --E 4 ---S 5 of 11 +--S 5 of 12 v.3 := 99 --R --R @@ -154453,7 +160853,7 @@ v.3 := 99 --R Type: PositiveInteger --E 5 ---S 6 of 11 +--S 6 of 12 v --R --R @@ -154461,7 +160861,7 @@ v --R Type: Vector(Integer) --E 6 ---S 7 of 11 +--S 7 of 12 5 * v --R --R @@ -154469,7 +160869,7 @@ v --R Type: Vector(Integer) --E 7 ---S 8 of 11 +--S 8 of 12 v * 7 --R --R @@ -154477,7 +160877,7 @@ v * 7 --R Type: Vector(Integer) --E 8 ---S 9 of 11 +--S 9 of 12 w : VECTOR INT := vector([2,3,4,5,6]) --R --R @@ -154485,7 +160885,7 @@ w : VECTOR INT := vector([2,3,4,5,6]) --R Type: Vector(Integer) --E 9 ---S 10 of 11 +--S 10 of 12 v + w --R --R @@ -154493,13 +160893,104 @@ v + w --R Type: Vector(Integer) --E 10 ---S 11 of 11 +--S 11 of 12 v - w --R --R --R (11) [- 1,- 1,95,- 1,- 1] --R Type: Vector(Integer) --E 11 + +--S 12 of 12 +)show Vector +--R +--R Vector(R: Type) is a domain constructor +--R Abbreviation for Vector is VECTOR +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for VECTOR +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,R) -> % if R has MONOID ?*? : (R,%) -> % if R has MONOID +--R ?+? : (%,%) -> % if R has ABELSG ?-? : (%,%) -> % if R has ABELGRP +--R -? : % -> % if R has ABELGRP concat : List(%) -> % +--R concat : (%,%) -> % concat : (R,%) -> % +--R concat : (%,R) -> % construct : List(R) -> % +--R copy : % -> % cross : (%,%) -> % if R has RING +--R delete : (%,Integer) -> % dot : (%,%) -> R if R has RING +--R ?.? : (%,Integer) -> R elt : (%,Integer,R) -> R +--R empty : () -> % empty? : % -> Boolean +--R entries : % -> List(R) eq? : (%,%) -> Boolean +--R index? : (Integer,%) -> Boolean indices : % -> List(Integer) +--R insert : (%,%,Integer) -> % insert : (R,%,Integer) -> % +--R latex : % -> String if R has SETCAT map : (((R,R) -> R),%,%) -> % +--R map : ((R -> R),%) -> % max : (%,%) -> % if R has ORDSET +--R min : (%,%) -> % if R has ORDSET new : (NonNegativeInteger,R) -> % +--R qelt : (%,Integer) -> R reverse : % -> % +--R sample : () -> % sort : % -> % if R has ORDSET +--R sort : (((R,R) -> Boolean),%) -> % vector : List(R) -> % +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R ?*? : (Integer,%) -> % if R has ABELGRP +--R ? Boolean if R has ORDSET +--R ?<=? : (%,%) -> Boolean if R has ORDSET +--R ?=? : (%,%) -> Boolean if R has SETCAT +--R ?>? : (%,%) -> Boolean if R has ORDSET +--R ?>=? : (%,%) -> Boolean if R has ORDSET +--R any? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate +--R coerce : % -> OutputForm if R has SETCAT +--R convert : % -> InputForm if R has KONVERT(INFORM) +--R copyInto! : (%,%,Integer) -> % if $ has shallowlyMutable +--R count : (R,%) -> NonNegativeInteger if $ has finiteAggregate and R has SETCAT +--R count : ((R -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R delete : (%,UniversalSegment(Integer)) -> % +--R ?.? : (%,UniversalSegment(Integer)) -> % +--R entry? : (R,%) -> Boolean if $ has finiteAggregate and R has SETCAT +--R eval : (%,List(R),List(R)) -> % if R has EVALAB(R) and R has SETCAT +--R eval : (%,R,R) -> % if R has EVALAB(R) and R has SETCAT +--R eval : (%,Equation(R)) -> % if R has EVALAB(R) and R has SETCAT +--R eval : (%,List(Equation(R))) -> % if R has EVALAB(R) and R has SETCAT +--R every? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate +--R fill! : (%,R) -> % if $ has shallowlyMutable +--R find : ((R -> Boolean),%) -> Union(R,"failed") +--R first : % -> R if Integer has ORDSET +--R hash : % -> SingleInteger if R has SETCAT +--R length : % -> R if R has RADCAT and R has RING +--R less? : (%,NonNegativeInteger) -> Boolean +--R magnitude : % -> R if R has RADCAT and R has RING +--R map! : ((R -> R),%) -> % if $ has shallowlyMutable +--R maxIndex : % -> Integer if Integer has ORDSET +--R member? : (R,%) -> Boolean if $ has finiteAggregate and R has SETCAT +--R members : % -> List(R) if $ has finiteAggregate +--R merge : (%,%) -> % if R has ORDSET +--R merge : (((R,R) -> Boolean),%,%) -> % +--R minIndex : % -> Integer if Integer has ORDSET +--R more? : (%,NonNegativeInteger) -> Boolean +--R outerProduct : (%,%) -> Matrix(R) if R has RING +--R parts : % -> List(R) if $ has finiteAggregate +--R position : (R,%,Integer) -> Integer if R has SETCAT +--R position : (R,%) -> Integer if R has SETCAT +--R position : ((R -> Boolean),%) -> Integer +--R qsetelt! : (%,Integer,R) -> R if $ has shallowlyMutable +--R reduce : (((R,R) -> R),%) -> R if $ has finiteAggregate +--R reduce : (((R,R) -> R),%,R) -> R if $ has finiteAggregate +--R reduce : (((R,R) -> R),%,R,R) -> R if $ has finiteAggregate and R has SETCAT +--R remove : ((R -> Boolean),%) -> % if $ has finiteAggregate +--R remove : (R,%) -> % if $ has finiteAggregate and R has SETCAT +--R removeDuplicates : % -> % if $ has finiteAggregate and R has SETCAT +--R reverse! : % -> % if $ has shallowlyMutable +--R select : ((R -> Boolean),%) -> % if $ has finiteAggregate +--R setelt : (%,UniversalSegment(Integer),R) -> R if $ has shallowlyMutable +--R setelt : (%,Integer,R) -> R if $ has shallowlyMutable +--R size? : (%,NonNegativeInteger) -> Boolean +--R sort! : % -> % if $ has shallowlyMutable and R has ORDSET +--R sort! : (((R,R) -> Boolean),%) -> % if $ has shallowlyMutable +--R sorted? : % -> Boolean if R has ORDSET +--R sorted? : (((R,R) -> Boolean),%) -> Boolean +--R swap! : (%,Integer,Integer) -> Void if $ has shallowlyMutable +--R zero : NonNegativeInteger -> % if R has ABELMON +--R ?~=? : (%,%) -> Boolean if R has SETCAT +--R +--E 12 + )spool )lisp (bye) \end{chunk} @@ -154720,7 +161211,8 @@ Vector(R:Type): Exports == Implementation where )set message test on )set message auto off )clear all ---S 1 of 5 + +--S 1 of 6 r := (a; b; if c then d else e; f) --R --R @@ -154729,7 +161221,7 @@ r := (a; b; if c then d else e; f) --R have written one that does not. --E 1 ---S 2 of 5 +--S 2 of 6 a : Integer --R --R Type: Void @@ -154737,7 +161229,7 @@ a : Integer )set message void on ---S 3 of 5 +--S 3 of 6 b : Fraction Integer --R --R @@ -154747,13 +161239,13 @@ b : Fraction Integer )set message void off ---S 4 of 5 +--S 4 of 6 3::Void --R --R Type: Void --E 4 ---S 5 of 5 +--S 5 of 6 % :: PositiveInteger --R --R @@ -154762,6 +161254,20 @@ b : Fraction Integer --R "()" --R --E 5 + +--S 6 of 6 +)show Void +--R +--R Void is a domain constructor +--R Abbreviation for Void is VOID +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for VOID +--R +--R------------------------------- Operations -------------------------------- +--R coerce : % -> OutputForm void : () -> % +--R +--E 6 + )spool )lisp (bye) \end{chunk} @@ -154869,26 +161375,23 @@ Void: with --R Issue )edit bookvol10.3.pamphlet to see algebra source code for WP --R --R------------------------------- Operations -------------------------------- +--R ?*? : (%,R) -> % if R has COMRING ?*? : (R,%) -> % if R has COMRING --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ?=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % coerce : P -> % +--R ?^? : (%,NonNegativeInteger) -> % ?^? : (%,PositiveInteger) -> % +--R coerce : R -> % if R has COMRING coerce : P -> % --R coerce : % -> P coerce : Integer -> % --R coerce : % -> OutputForm hash : % -> SingleInteger --R latex : % -> String one? : % -> Boolean --R recip : % -> Union(%,"failed") sample : () -> % --R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (%,R) -> % if R has COMRING ---R ?*? : (R,%) -> % if R has COMRING ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % --R ?/? : (%,%) -> Union(%,"failed") if R has FIELD ---R ?^? : (%,NonNegativeInteger) -> % --R changeWeightLevel : NonNegativeInteger -> Void --R characteristic : () -> NonNegativeInteger ---R coerce : R -> % if R has COMRING --R subtractIfCan : (%,%) -> Union(%,"failed") --R --E 1 @@ -155056,7 +161559,8 @@ WeightedPolynomials(R:Ring,VarSet: OrderedSet, E:OrderedAbelianMonoidSup, )set message test on )set message auto off )clear all ---S 1 of 16 + +--S 1 of 17 R := Integer --R --R @@ -155064,7 +161568,7 @@ R := Integer --R Type: Domain --E 1 ---S 2 of 16 +--S 2 of 17 ls : List Symbol := [x,y,z,t] --R --R @@ -155072,7 +161576,7 @@ ls : List Symbol := [x,y,z,t] --R Type: List(Symbol) --E 2 ---S 3 of 16 +--S 3 of 17 V := OVAR(ls) --R --R @@ -155080,7 +161584,7 @@ V := OVAR(ls) --R Type: Domain --E 3 ---S 4 of 16 +--S 4 of 17 E := IndexedExponents V --R --R @@ -155088,7 +161592,7 @@ E := IndexedExponents V --R Type: Domain --E 4 ---S 5 of 16 +--S 5 of 17 P := NSMP(R, V) --R --R @@ -155097,7 +161601,7 @@ P := NSMP(R, V) --R Type: Domain --E 5 ---S 6 of 16 +--S 6 of 17 x: P := 'x --R --R @@ -155105,7 +161609,7 @@ x: P := 'x --RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList([x,y,z,t])) --E 6 ---S 7 of 16 +--S 7 of 17 y: P := 'y --R --R @@ -155113,7 +161617,7 @@ y: P := 'y --RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList([x,y,z,t])) --E 7 ---S 8 of 16 +--S 8 of 17 z: P := 'z --R --R @@ -155121,7 +161625,7 @@ z: P := 'z --RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList([x,y,z,t])) --E 8 ---S 9 of 16 +--S 9 of 17 t: P := 't --R --R @@ -155129,7 +161633,7 @@ t: P := 't --RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList([x,y,z,t])) --E 9 ---S 10 of 16 +--S 10 of 17 T := WUTSET(R,E,V,P) --R --R @@ -155140,7 +161644,7 @@ T := WUTSET(R,E,V,P) --R Type: Domain --E 10 ---S 11 of 16 +--S 11 of 17 p1 := x ** 31 - x ** 6 - x - y --R --R @@ -155149,7 +161653,7 @@ p1 := x ** 31 - x ** 6 - x - y --RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList([x,y,z,t])) --E 11 ---S 12 of 16 +--S 12 of 17 p2 := x ** 8 - z --R --R @@ -155158,7 +161662,7 @@ p2 := x ** 8 - z --RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList([x,y,z,t])) --E 12 ---S 13 of 16 +--S 13 of 17 p3 := x ** 10 - t --R --R @@ -155167,7 +161671,7 @@ p3 := x ** 10 - t --RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList([x,y,z,t])) --E 13 ---S 14 of 16 +--S 14 of 17 lp := [p1, p2, p3] --R --R @@ -155176,7 +161680,7 @@ lp := [p1, p2, p3] --RType: List(NewSparseMultivariatePolynomial(Integer,OrderedVariableList([x,y,z,t]))) --E 14 ---S 15 of 16 +--S 15 of 17 characteristicSet(lp)$T --R --R @@ -155186,7 +161690,7 @@ characteristicSet(lp)$T --IType: Union(WuWenTsunTriangularSet(Integer,IndexedExponents(... --E 15 ---S 16 of 16 +--S 16 of 17 zeroSetSplit(lp)$T --R --R @@ -155197,6 +161701,95 @@ zeroSetSplit(lp)$T --R {z - t ,t z y + 2t z y + (- t + 2t - t)z + t z,(t - 1)z x - z y - t }] --IType: List(WuWenTsunTriangularSet(Integer,IndexedExponents(... --E 16 + +--S 17 of 17 +)show WuWenTsunTriangularSet +--R +--R WuWenTsunTriangularSet(R: IntegralDomain,E: OrderedAbelianMonoidSup,V: OrderedSet,P: RecursivePolynomialCategory(R,E,V)) is a domain constructor +--R Abbreviation for WuWenTsunTriangularSet is WUTSET +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for WUTSET +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean algebraic? : (V,%) -> Boolean +--R algebraicVariables : % -> List(V) coerce : % -> List(P) +--R coerce : % -> OutputForm collect : (%,V) -> % +--R collectQuasiMonic : % -> % collectUnder : (%,V) -> % +--R collectUpper : (%,V) -> % construct : List(P) -> % +--R copy : % -> % degree : % -> NonNegativeInteger +--R empty : () -> % empty? : % -> Boolean +--R eq? : (%,%) -> Boolean extend : (%,P) -> % +--R first : % -> Union(P,"failed") hash : % -> SingleInteger +--R headReduce : (P,%) -> P headReduced? : % -> Boolean +--R headReduced? : (P,%) -> Boolean infRittWu? : (%,%) -> Boolean +--R initiallyReduce : (P,%) -> P initiallyReduced? : % -> Boolean +--R initials : % -> List(P) last : % -> Union(P,"failed") +--R latex : % -> String mainVariable? : (V,%) -> Boolean +--R mainVariables : % -> List(V) map : ((P -> P),%) -> % +--R mvar : % -> V normalized? : % -> Boolean +--R normalized? : (P,%) -> Boolean reduceByQuasiMonic : (P,%) -> P +--R removeZero : (P,%) -> P rest : % -> Union(%,"failed") +--R retract : List(P) -> % sample : () -> % +--R select : (%,V) -> Union(P,"failed") stronglyReduce : (P,%) -> P +--R stronglyReduced? : % -> Boolean stronglyReduced? : (P,%) -> Boolean +--R trivialIdeal? : % -> Boolean variables : % -> List(V) +--R zeroSetSplit : List(P) -> List(%) ?~=? : (%,%) -> Boolean +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R any? : ((P -> Boolean),%) -> Boolean if $ has finiteAggregate +--R autoReduced? : (%,((P,List(P)) -> Boolean)) -> Boolean +--R basicSet : (List(P),(P -> Boolean),((P,P) -> Boolean)) -> Union(Record(bas: %,top: List(P)),"failed") +--R basicSet : (List(P),((P,P) -> Boolean)) -> Union(Record(bas: %,top: List(P)),"failed") +--R characteristicSerie : List(P) -> List(%) +--R characteristicSerie : (List(P),((P,P) -> Boolean),((P,P) -> P)) -> List(%) +--R characteristicSet : List(P) -> Union(%,"failed") +--R characteristicSet : (List(P),((P,P) -> Boolean),((P,P) -> P)) -> Union(%,"failed") +--R coHeight : % -> NonNegativeInteger if V has FINITE +--R convert : % -> InputForm if P has KONVERT(INFORM) +--R count : ((P -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R count : (P,%) -> NonNegativeInteger if $ has finiteAggregate and P has SETCAT +--R eval : (%,List(Equation(P))) -> % if P has EVALAB(P) and P has SETCAT +--R eval : (%,Equation(P)) -> % if P has EVALAB(P) and P has SETCAT +--R eval : (%,P,P) -> % if P has EVALAB(P) and P has SETCAT +--R eval : (%,List(P),List(P)) -> % if P has EVALAB(P) and P has SETCAT +--R every? : ((P -> Boolean),%) -> Boolean if $ has finiteAggregate +--R extendIfCan : (%,P) -> Union(%,"failed") +--R find : ((P -> Boolean),%) -> Union(P,"failed") +--R headRemainder : (P,%) -> Record(num: P,den: R) if R has INTDOM +--R initiallyReduced? : (P,%) -> Boolean +--R less? : (%,NonNegativeInteger) -> Boolean +--R map! : ((P -> P),%) -> % if $ has shallowlyMutable +--R medialSet : List(P) -> Union(%,"failed") +--R medialSet : (List(P),((P,P) -> Boolean),((P,P) -> P)) -> Union(%,"failed") +--R member? : (P,%) -> Boolean if $ has finiteAggregate and P has SETCAT +--R members : % -> List(P) if $ has finiteAggregate +--R more? : (%,NonNegativeInteger) -> Boolean +--R parts : % -> List(P) if $ has finiteAggregate +--R quasiComponent : % -> Record(close: List(P),open: List(P)) +--R reduce : (P,%,((P,P) -> P),((P,P) -> Boolean)) -> P +--R reduce : (((P,P) -> P),%) -> P if $ has finiteAggregate +--R reduce : (((P,P) -> P),%,P) -> P if $ has finiteAggregate +--R reduce : (((P,P) -> P),%,P,P) -> P if $ has finiteAggregate and P has SETCAT +--R reduced? : (P,%,((P,P) -> Boolean)) -> Boolean +--R remainder : (P,%) -> Record(rnum: R,polnum: P,den: R) if R has INTDOM +--R remove : ((P -> Boolean),%) -> % if $ has finiteAggregate +--R remove : (P,%) -> % if $ has finiteAggregate and P has SETCAT +--R removeDuplicates : % -> % if $ has finiteAggregate and P has SETCAT +--R retractIfCan : List(P) -> Union(%,"failed") +--R rewriteIdealWithHeadRemainder : (List(P),%) -> List(P) if R has INTDOM +--R rewriteIdealWithRemainder : (List(P),%) -> List(P) if R has INTDOM +--R rewriteSetWithReduction : (List(P),%,((P,P) -> P),((P,P) -> Boolean)) -> List(P) +--R roughBase? : % -> Boolean if R has INTDOM +--R roughEqualIdeals? : (%,%) -> Boolean if R has INTDOM +--R roughSubIdeal? : (%,%) -> Boolean if R has INTDOM +--R roughUnitIdeal? : % -> Boolean if R has INTDOM +--R select : ((P -> Boolean),%) -> % if $ has finiteAggregate +--R size? : (%,NonNegativeInteger) -> Boolean +--R sort : (%,V) -> Record(under: %,floor: %,upper: %) +--R triangular? : % -> Boolean if R has INTDOM +--R zeroSetSplitIntoTriangularSystems : List(P) -> List(Record(close: %,open: List(P))) +--R +--E 17 + )spool )lisp (bye) \end{chunk} @@ -155727,47 +162320,43 @@ equivalent for the --R------------------------------- Operations -------------------------------- --R ?*? : (%,%) -> % ?*? : (vl,%) -> % --R ?*? : (%,R) -> % ?*? : (R,%) -> % ---R ?*? : (Integer,%) -> % ?*? : (PositiveInteger,%) -> % ---R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % +--R ?*? : (Integer,%) -> % ?*? : (NonNegativeInteger,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?+? : (%,%) -> % --R ?-? : (%,%) -> % -? : % -> % --R ?=? : (%,%) -> Boolean 1 : () -> % --R 0 : () -> % ?^? : (%,PositiveInteger) -> % ---R coef : (%,%) -> R coefficients : % -> List(R) ---R coerce : Integer -> % coerce : R -> % ---R coerce : vl -> % coerce : % -> OutputForm +--R ?^? : (%,NonNegativeInteger) -> % coef : (%,%) -> R +--R coefficients : % -> List(R) coerce : Integer -> % +--R coerce : R -> % coerce : vl -> % +--R coerce : OrderedFreeMonoid(vl) -> % coerce : % -> OutputForm --R constant : % -> R constant? : % -> Boolean --R degree : % -> NonNegativeInteger hash : % -> SingleInteger --R latex : % -> String leadingCoefficient : % -> R --R lquo : (%,vl) -> % lquo : (%,%) -> % ---R map : ((R -> R),%) -> % mirror : % -> % +--R map : ((R -> R),%) -> % maxdeg : % -> OrderedFreeMonoid(vl) +--R mindeg : % -> OrderedFreeMonoid(vl) mirror : % -> % --R monomial? : % -> Boolean monomials : % -> List(%) --R one? : % -> Boolean quasiRegular : % -> % --R quasiRegular? : % -> Boolean recip : % -> Union(%,"failed") --R reductum : % -> % rquo : (%,vl) -> % --R rquo : (%,%) -> % sample : () -> % ---R varList : % -> List(vl) zero? : % -> Boolean ---R ?~=? : (%,%) -> Boolean +--R sh : (%,%) -> % if R has COMRING varList : % -> List(vl) +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean --R ?*? : (R,OrderedFreeMonoid(vl)) -> % ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % ---R ?^? : (%,NonNegativeInteger) -> % --R characteristic : () -> NonNegativeInteger --R coef : (%,OrderedFreeMonoid(vl)) -> R --R coefficient : (%,OrderedFreeMonoid(vl)) -> R ---R coerce : OrderedFreeMonoid(vl) -> % --R leadingMonomial : % -> OrderedFreeMonoid(vl) --R leadingTerm : % -> Record(k: OrderedFreeMonoid(vl),c: R) --R listOfTerms : % -> List(Record(k: OrderedFreeMonoid(vl),c: R)) --R lquo : (%,OrderedFreeMonoid(vl)) -> % ---R maxdeg : % -> OrderedFreeMonoid(vl) ---R mindeg : % -> OrderedFreeMonoid(vl) --R mindegTerm : % -> Record(k: OrderedFreeMonoid(vl),c: R) --R monom : (OrderedFreeMonoid(vl),R) -> % --R numberOfMonomials : % -> NonNegativeInteger --R retract : % -> OrderedFreeMonoid(vl) --R retractIfCan : % -> Union(OrderedFreeMonoid(vl),"failed") --R rquo : (%,OrderedFreeMonoid(vl)) -> % ---R sh : (%,%) -> % if R has COMRING --R sh : (%,NonNegativeInteger) -> % if R has COMRING --R subtractIfCan : (%,%) -> Union(%,"failed") --R trunc : (%,NonNegativeInteger) -> % @@ -155961,7 +162550,8 @@ XDistributedPolynomial(vl:OrderedSet,R:Ring): XDPcat == XDPdef where )set message test on )set message auto off )clear all ---S 1 of 39 + +--S 1 of 40 a:Symbol := 'a --R --R @@ -155969,7 +162559,7 @@ a:Symbol := 'a --R Type: Symbol --E 1 ---S 2 of 39 +--S 2 of 40 b:Symbol := 'b --R --R @@ -155977,7 +162567,7 @@ b:Symbol := 'b --R Type: Symbol --E 2 ---S 3 of 39 +--S 3 of 40 RN := Fraction(Integer) --R --R @@ -155985,7 +162575,7 @@ RN := Fraction(Integer) --R Type: Domain --E 3 ---S 4 of 39 +--S 4 of 40 word := OrderedFreeMonoid Symbol --R --R @@ -155993,7 +162583,7 @@ word := OrderedFreeMonoid Symbol --R Type: Domain --E 4 ---S 5 of 39 +--S 5 of 40 lword := LyndonWord(Symbol) --R --R @@ -156001,7 +162591,7 @@ lword := LyndonWord(Symbol) --R Type: Domain --E 5 ---S 6 of 39 +--S 6 of 40 base := PoincareBirkhoffWittLyndonBasis Symbol --R --R @@ -156009,7 +162599,7 @@ base := PoincareBirkhoffWittLyndonBasis Symbol --R Type: Domain --E 6 ---S 7 of 39 +--S 7 of 40 dpoly := XDistributedPolynomial(Symbol, RN) --R --R @@ -156017,7 +162607,7 @@ dpoly := XDistributedPolynomial(Symbol, RN) --R Type: Domain --E 7 ---S 8 of 39 +--S 8 of 40 rpoly := XRecursivePolynomial(Symbol, RN) --R --R @@ -156025,7 +162615,7 @@ rpoly := XRecursivePolynomial(Symbol, RN) --R Type: Domain --E 8 ---S 9 of 39 +--S 9 of 40 lpoly := LiePolynomial(Symbol, RN) --R --R @@ -156033,7 +162623,7 @@ lpoly := LiePolynomial(Symbol, RN) --R Type: Domain --E 9 ---S 10 of 39 +--S 10 of 40 poly := XPBWPolynomial(Symbol, RN) --R --R @@ -156041,7 +162631,7 @@ poly := XPBWPolynomial(Symbol, RN) --R Type: Domain --E 10 ---S 11 of 39 +--S 11 of 40 liste : List lword := LyndonWordsList([a,b], 6) --R --R @@ -156055,7 +162645,7 @@ liste : List lword := LyndonWordsList([a,b], 6) --R Type: List(LyndonWord(Symbol)) --E 11 ---S 12 of 39 +--S 12 of 40 0$poly --R --R @@ -156063,7 +162653,7 @@ liste : List lword := LyndonWordsList([a,b], 6) --R Type: XPBWPolynomial(Symbol,Fraction(Integer)) --E 12 ---S 13 of 39 +--S 13 of 40 1$poly --R --R @@ -156071,7 +162661,7 @@ liste : List lword := LyndonWordsList([a,b], 6) --R Type: XPBWPolynomial(Symbol,Fraction(Integer)) --E 13 ---S 14 of 39 +--S 14 of 40 p : poly := a --R --R @@ -156079,7 +162669,7 @@ p : poly := a --R Type: XPBWPolynomial(Symbol,Fraction(Integer)) --E 14 ---S 15 of 39 +--S 15 of 40 q : poly := b --R --R @@ -156087,7 +162677,7 @@ q : poly := b --R Type: XPBWPolynomial(Symbol,Fraction(Integer)) --E 15 ---S 16 of 39 +--S 16 of 40 pq: poly := p*q --R --R @@ -156095,7 +162685,7 @@ pq: poly := p*q --R Type: XPBWPolynomial(Symbol,Fraction(Integer)) --E 16 ---S 17 of 39 +--S 17 of 40 pq :: dpoly --R --R @@ -156103,7 +162693,7 @@ pq :: dpoly --R Type: XDistributedPolynomial(Symbol,Fraction(Integer)) --E 17 ---S 18 of 39 +--S 18 of 40 mirror pq --R --R @@ -156111,7 +162701,7 @@ mirror pq --R Type: XPBWPolynomial(Symbol,Fraction(Integer)) --E 18 ---S 19 of 39 +--S 19 of 40 listOfTerms pq --R --R @@ -156119,7 +162709,7 @@ listOfTerms pq --RType: List(Record(k: PoincareBirkhoffWittLyndonBasis(Symbol),c: Fraction(Integer))) --E 19 ---S 20 of 39 +--S 20 of 40 reductum pq --R --R @@ -156127,7 +162717,7 @@ reductum pq --R Type: XPBWPolynomial(Symbol,Fraction(Integer)) --E 20 ---S 21 of 39 +--S 21 of 40 leadingMonomial pq --R --R @@ -156135,7 +162725,7 @@ leadingMonomial pq --R Type: PoincareBirkhoffWittLyndonBasis(Symbol) --E 21 ---S 22 of 39 +--S 22 of 40 coefficients pq --R --R @@ -156143,7 +162733,7 @@ coefficients pq --R Type: List(Fraction(Integer)) --E 22 ---S 23 of 39 +--S 23 of 40 leadingTerm pq --R --R @@ -156151,7 +162741,7 @@ leadingTerm pq --RType: Record(k: PoincareBirkhoffWittLyndonBasis(Symbol),c: Fraction(Integer)) --E 23 ---S 24 of 39 +--S 24 of 40 degree pq --R --R @@ -156159,7 +162749,7 @@ degree pq --R Type: PositiveInteger --E 24 ---S 25 of 39 +--S 25 of 40 pq4:=exp(pq,4) --R --R @@ -156174,7 +162764,7 @@ pq4:=exp(pq,4) --R Type: XPBWPolynomial(Symbol,Fraction(Integer)) --E 25 ---S 26 of 39 +--S 26 of 40 log(pq4,4) - pq --R --R @@ -156182,7 +162772,7 @@ log(pq4,4) - pq --R Type: XPBWPolynomial(Symbol,Fraction(Integer)) --E 26 ---S 27 of 39 +--S 27 of 40 lp1 :lpoly := LiePoly liste.10 --R --R @@ -156191,7 +162781,7 @@ lp1 :lpoly := LiePoly liste.10 --R Type: LiePolynomial(Symbol,Fraction(Integer)) --E 27 ---S 28 of 39 +--S 28 of 40 lp2 :lpoly := LiePoly liste.11 --R --R @@ -156200,7 +162790,7 @@ lp2 :lpoly := LiePoly liste.11 --R Type: LiePolynomial(Symbol,Fraction(Integer)) --E 28 ---S 29 of 39 +--S 29 of 40 lp :lpoly := [lp1, lp2] --R --R @@ -156209,7 +162799,7 @@ lp :lpoly := [lp1, lp2] --R Type: LiePolynomial(Symbol,Fraction(Integer)) --E 29 ---S 30 of 39 +--S 30 of 40 lpd1: dpoly := lp1 --R --R @@ -156218,7 +162808,7 @@ lpd1: dpoly := lp1 --R Type: XDistributedPolynomial(Symbol,Fraction(Integer)) --E 30 ---S 31 of 39 +--S 31 of 40 lpd2: dpoly := lp2 --R --R @@ -156231,7 +162821,7 @@ lpd2: dpoly := lp2 --R Type: XDistributedPolynomial(Symbol,Fraction(Integer)) --E 31 ---S 32 of 39 +--S 32 of 40 lpd : dpoly := lpd1 * lpd2 - lpd2 * lpd1 --R --R @@ -156292,7 +162882,7 @@ lpd : dpoly := lpd1 * lpd2 - lpd2 * lpd1 --R Type: XDistributedPolynomial(Symbol,Fraction(Integer)) --E 32 ---S 33 of 39 +--S 33 of 40 lp :: dpoly - lpd --R --R @@ -156300,7 +162890,7 @@ lp :: dpoly - lpd --R Type: XDistributedPolynomial(Symbol,Fraction(Integer)) --E 33 ---S 34 of 39 +--S 34 of 40 p := 3 * lp --R --R @@ -156309,7 +162899,7 @@ p := 3 * lp --R Type: XPBWPolynomial(Symbol,Fraction(Integer)) --E 34 ---S 35 of 39 +--S 35 of 40 q := lp1 --R --R @@ -156318,7 +162908,7 @@ q := lp1 --R Type: XPBWPolynomial(Symbol,Fraction(Integer)) --E 35 ---S 36 of 39 +--S 36 of 40 pq:= p * q --R --R @@ -156327,7 +162917,7 @@ pq:= p * q --R Type: XPBWPolynomial(Symbol,Fraction(Integer)) --E 36 ---S 37 of 39 +--S 37 of 40 pr:rpoly := p :: rpoly --R --R @@ -156426,7 +163016,7 @@ pr:rpoly := p :: rpoly --R Type: XRecursivePolynomial(Symbol,Fraction(Integer)) --E 37 ---S 38 of 39 +--S 38 of 40 qr:rpoly := q :: rpoly --R --R @@ -156437,13 +163027,81 @@ qr:rpoly := q :: rpoly --R Type: XRecursivePolynomial(Symbol,Fraction(Integer)) --E 38 ---S 39 of 39 +--S 39 of 40 pq :: rpoly - pr*qr --R --R --R (39) 0 --R Type: XRecursivePolynomial(Symbol,Fraction(Integer)) --E 39 + +--S 40 of 40 +)show XPBWPolynomial +--R +--R XPBWPolynomial(VarSet: OrderedSet,R: CommutativeRing) is a domain constructor +--R Abbreviation for XPBWPolynomial is XPBWPOLY +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for XPBWPOLY +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (VarSet,%) -> % ?*? : (%,R) -> % +--R ?*? : (R,%) -> % ?*? : (%,%) -> % +--R ?*? : (Integer,%) -> % ?*? : (NonNegativeInteger,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,NonNegativeInteger) -> % +--R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % +--R ?-? : (%,%) -> % -? : % -> % +--R ?=? : (%,%) -> Boolean 1 : () -> % +--R 0 : () -> % ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,PositiveInteger) -> % coef : (%,%) -> R +--R coefficients : % -> List(R) coerce : VarSet -> % +--R coerce : R -> % coerce : Integer -> % +--R coerce : % -> OutputForm constant : % -> R +--R constant? : % -> Boolean degree : % -> NonNegativeInteger +--R hash : % -> SingleInteger latex : % -> String +--R leadingCoefficient : % -> R lquo : (%,%) -> % +--R lquo : (%,VarSet) -> % map : ((R -> R),%) -> % +--R mirror : % -> % monomial? : % -> Boolean +--R monomials : % -> List(%) one? : % -> Boolean +--R quasiRegular : % -> % quasiRegular? : % -> Boolean +--R recip : % -> Union(%,"failed") reductum : % -> % +--R rquo : (%,%) -> % rquo : (%,VarSet) -> % +--R sample : () -> % sh : (%,%) -> % if R has COMRING +--R varList : % -> List(VarSet) zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R ?*? : (R,PoincareBirkhoffWittLyndonBasis(VarSet)) -> % +--R LiePolyIfCan : % -> Union(LiePolynomial(VarSet,R),"failed") +--R characteristic : () -> NonNegativeInteger +--R coef : (%,OrderedFreeMonoid(VarSet)) -> R +--R coefficient : (%,PoincareBirkhoffWittLyndonBasis(VarSet)) -> R +--R coerce : % -> XRecursivePolynomial(VarSet,R) +--R coerce : % -> XDistributedPolynomial(VarSet,R) +--R coerce : LiePolynomial(VarSet,R) -> % +--R coerce : PoincareBirkhoffWittLyndonBasis(VarSet) -> % +--R coerce : OrderedFreeMonoid(VarSet) -> % +--R exp : (%,NonNegativeInteger) -> % if R has MODULE(FRAC(INT)) +--R leadingMonomial : % -> PoincareBirkhoffWittLyndonBasis(VarSet) +--R leadingTerm : % -> Record(k: PoincareBirkhoffWittLyndonBasis(VarSet),c: R) +--R listOfTerms : % -> List(Record(k: PoincareBirkhoffWittLyndonBasis(VarSet),c: R)) +--R log : (%,NonNegativeInteger) -> % if R has MODULE(FRAC(INT)) +--R lquo : (%,OrderedFreeMonoid(VarSet)) -> % +--R maxdeg : % -> OrderedFreeMonoid(VarSet) +--R mindeg : % -> OrderedFreeMonoid(VarSet) +--R mindegTerm : % -> Record(k: OrderedFreeMonoid(VarSet),c: R) +--R monom : (PoincareBirkhoffWittLyndonBasis(VarSet),R) -> % +--R monom : (OrderedFreeMonoid(VarSet),R) -> % +--R numberOfMonomials : % -> NonNegativeInteger +--R product : (%,%,NonNegativeInteger) -> % +--R retract : % -> PoincareBirkhoffWittLyndonBasis(VarSet) +--R retract : % -> OrderedFreeMonoid(VarSet) +--R retractIfCan : % -> Union(PoincareBirkhoffWittLyndonBasis(VarSet),"failed") +--R retractIfCan : % -> Union(OrderedFreeMonoid(VarSet),"failed") +--R rquo : (%,OrderedFreeMonoid(VarSet)) -> % +--R sh : (%,NonNegativeInteger) -> % if R has COMRING +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R trunc : (%,NonNegativeInteger) -> % +--R +--E 40 + )spool )lisp (bye) \end{chunk} @@ -157098,7 +163756,8 @@ XPBWPolynomial(VarSet:OrderedSet,R:CommutativeRing): XDPcat == XDPdef where )set message test on )set message auto off )clear all ---S 1 of 14 + +--S 1 of 15 poly := XPolynomial(Integer) --R --R @@ -157106,7 +163765,7 @@ poly := XPolynomial(Integer) --R Type: Domain --E 1 ---S 2 of 14 +--S 2 of 15 pr: poly := 2*x + 3*y-5 --R --R @@ -157114,7 +163773,7 @@ pr: poly := 2*x + 3*y-5 --R Type: XPolynomial(Integer) --E 2 ---S 3 of 14 +--S 3 of 15 pr2: poly := pr*pr --R --R @@ -157122,7 +163781,7 @@ pr2: poly := pr*pr --R Type: XPolynomial(Integer) --E 3 ---S 4 of 14 +--S 4 of 15 pd := expand pr --R --R @@ -157130,7 +163789,7 @@ pd := expand pr --R Type: XDistributedPolynomial(Symbol,Integer) --E 4 ---S 5 of 14 +--S 5 of 15 pd2 := pd*pd --R --R @@ -157139,7 +163798,7 @@ pd2 := pd*pd --R Type: XDistributedPolynomial(Symbol,Integer) --E 5 ---S 6 of 14 +--S 6 of 15 expand(pr2) - pd2 --R --R @@ -157147,7 +163806,7 @@ expand(pr2) - pd2 --R Type: XDistributedPolynomial(Symbol,Integer) --E 6 ---S 7 of 14 +--S 7 of 15 qr := pr**3 --R --R @@ -157158,7 +163817,7 @@ qr := pr**3 --R Type: XPolynomial(Integer) --E 7 ---S 8 of 14 +--S 8 of 15 qd := pd**3 --R --R @@ -157171,7 +163830,7 @@ qd := pd**3 --R Type: XDistributedPolynomial(Symbol,Integer) --E 8 ---S 9 of 14 +--S 9 of 15 trunc(qd,2) --R --R @@ -157180,7 +163839,7 @@ trunc(qd,2) --R Type: XDistributedPolynomial(Symbol,Integer) --E 9 ---S 10 of 14 +--S 10 of 15 trunc(qr,2) --R --R @@ -157188,7 +163847,7 @@ trunc(qr,2) --R Type: XPolynomial(Integer) --E 10 ---S 11 of 14 +--S 11 of 15 Word := OrderedFreeMonoid Symbol --R --R @@ -157196,7 +163855,7 @@ Word := OrderedFreeMonoid Symbol --R Type: Domain --E 11 ---S 12 of 14 +--S 12 of 15 w: Word := x*y**2 --R --R @@ -157205,7 +163864,7 @@ w: Word := x*y**2 --R Type: OrderedFreeMonoid(Symbol) --E 12 ---S 13 of 14 +--S 13 of 15 rquo(qr,w) --R --R @@ -157213,13 +163872,65 @@ rquo(qr,w) --R Type: XPolynomial(Integer) --E 13 ---S 14 of 14 +--S 14 of 15 sh(pr,w::poly) --R --R --R (14) x(x y y 4 + y(x y 2 + y(- 5 + x 2 + y 9))) + y x y y 3 --R Type: XPolynomial(Integer) --E 14 + +--S 15 of 15 +)show XPolynomial +--R +--R XPolynomial(R: Ring) is a domain constructor +--R Abbreviation for XPolynomial is XPOLY +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for XPOLY +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (Symbol,%) -> % ?*? : (%,R) -> % +--R ?*? : (R,%) -> % ?*? : (%,%) -> % +--R ?*? : (Integer,%) -> % ?*? : (NonNegativeInteger,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,NonNegativeInteger) -> % +--R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % +--R ?-? : (%,%) -> % -? : % -> % +--R ?=? : (%,%) -> Boolean 1 : () -> % +--R 0 : () -> % ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,PositiveInteger) -> % coef : (%,%) -> R +--R coerce : Symbol -> % coerce : R -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R constant : % -> R constant? : % -> Boolean +--R degree : % -> NonNegativeInteger hash : % -> SingleInteger +--R latex : % -> String lquo : (%,%) -> % +--R lquo : (%,Symbol) -> % map : ((R -> R),%) -> % +--R mirror : % -> % monomial? : % -> Boolean +--R one? : % -> Boolean quasiRegular : % -> % +--R quasiRegular? : % -> Boolean recip : % -> Union(%,"failed") +--R rquo : (%,%) -> % rquo : (%,Symbol) -> % +--R sample : () -> % sh : (%,%) -> % if R has COMRING +--R varList : % -> List(Symbol) zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R RemainderList : % -> List(Record(k: Symbol,c: %)) +--R characteristic : () -> NonNegativeInteger +--R coef : (%,OrderedFreeMonoid(Symbol)) -> R +--R coerce : OrderedFreeMonoid(Symbol) -> % +--R expand : % -> XDistributedPolynomial(Symbol,R) +--R lquo : (%,OrderedFreeMonoid(Symbol)) -> % +--R maxdeg : % -> OrderedFreeMonoid(Symbol) +--R mindeg : % -> OrderedFreeMonoid(Symbol) +--R mindegTerm : % -> Record(k: OrderedFreeMonoid(Symbol),c: R) +--R monom : (OrderedFreeMonoid(Symbol),R) -> % +--R retract : % -> OrderedFreeMonoid(Symbol) +--R retractIfCan : % -> Union(OrderedFreeMonoid(Symbol),"failed") +--R rquo : (%,OrderedFreeMonoid(Symbol)) -> % +--R sh : (%,NonNegativeInteger) -> % if R has COMRING +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R trunc : (%,NonNegativeInteger) -> % +--R unexpand : XDistributedPolynomial(Symbol,R) -> % +--R +--E 15 + )spool )lisp (bye) \end{chunk} @@ -157422,7 +164133,8 @@ XPolynomial(R:Ring) == XRecursivePolynomial(Symbol, R) )set message test on )set message auto off )clear all ---S 1 of 15 + +--S 1 of 16 Word := OrderedFreeMonoid(Symbol) --R --R @@ -157430,7 +164142,7 @@ Word := OrderedFreeMonoid(Symbol) --R Type: Domain --E 1 ---S 2 of 15 +--S 2 of 16 poly:= XPR(Integer,Word) --R --R @@ -157438,7 +164150,7 @@ poly:= XPR(Integer,Word) --R Type: Domain --E 2 ---S 3 of 15 +--S 3 of 16 p:poly := 2 * x - 3 * y + 1 --R --R @@ -157446,7 +164158,7 @@ p:poly := 2 * x - 3 * y + 1 --R Type: XPolynomialRing(Integer,OrderedFreeMonoid(Symbol)) --E 3 ---S 4 of 15 +--S 4 of 16 q:poly := 2 * x + 1 --R --R @@ -157454,7 +164166,7 @@ q:poly := 2 * x + 1 --R Type: XPolynomialRing(Integer,OrderedFreeMonoid(Symbol)) --E 4 ---S 5 of 15 +--S 5 of 16 p + q --R --R @@ -157462,7 +164174,7 @@ p + q --R Type: XPolynomialRing(Integer,OrderedFreeMonoid(Symbol)) --E 5 ---S 6 of 15 +--S 6 of 16 p * q --R --R @@ -157471,7 +164183,7 @@ p * q --R Type: XPolynomialRing(Integer,OrderedFreeMonoid(Symbol)) --E 6 ---S 7 of 15 +--S 7 of 16 (p+q)**2-p**2-q**2-2*p*q --R --R @@ -157479,7 +164191,7 @@ p * q --R Type: XPolynomialRing(Integer,OrderedFreeMonoid(Symbol)) --E 7 ---S 8 of 15 +--S 8 of 16 M := SquareMatrix(2,Fraction Integer) --R --R @@ -157487,7 +164199,7 @@ M := SquareMatrix(2,Fraction Integer) --R Type: Domain --E 8 ---S 9 of 15 +--S 9 of 16 poly1:= XPR(M,Word) --R --R @@ -157496,7 +164208,7 @@ poly1:= XPR(M,Word) --R Type: Domain --E 9 ---S 10 of 15 +--S 10 of 16 m1:M := matrix [ [i*j**2 for i in 1..2] for j in 1..2] --R --R @@ -157506,7 +164218,7 @@ m1:M := matrix [ [i*j**2 for i in 1..2] for j in 1..2] --R Type: SquareMatrix(2,Fraction(Integer)) --E 10 ---S 11 of 15 +--S 11 of 16 m2:M := m1 - 5/4 --R --R @@ -157520,7 +164232,7 @@ m2:M := m1 - 5/4 --R Type: SquareMatrix(2,Fraction(Integer)) --E 11 ---S 12 of 15 +--S 12 of 16 m3: M := m2**2 --R --R @@ -157534,7 +164246,7 @@ m3: M := m2**2 --R Type: SquareMatrix(2,Fraction(Integer)) --E 12 ---S 13 of 15 +--S 13 of 16 pm:poly1 := m1*x + m2*y + m3*z - 2/3 --R --R @@ -157548,7 +164260,7 @@ pm:poly1 := m1*x + m2*y + m3*z - 2/3 --RType: XPolynomialRing(SquareMatrix(2,Fraction(Integer)),OrderedFreeMonoid(Symbol)) --E 13 ---S 14 of 15 +--S 14 of 16 qm:poly1 := pm - m1*x --R --R @@ -157562,7 +164274,7 @@ qm:poly1 := pm - m1*x --RType: XPolynomialRing(SquareMatrix(2,Fraction(Integer)),OrderedFreeMonoid(Symbol)) --E 14 ---S 15 of 15 +--S 15 of 16 qm**3 --R --R @@ -157608,6 +164320,49 @@ qm**3 --R + 64 1024 + + 128 4096 + --RType: XPolynomialRing(SquareMatrix(2,Fraction(Integer)),OrderedFreeMonoid(Symbol)) --E 15 + +--S 16 of 16 +)show XPolynomialRing +--R +--R XPolynomialRing(R: Ring,E: OrderedMonoid) is a domain constructor +--R Abbreviation for XPolynomialRing is XPR +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for XPR +--R +--R------------------------------- Operations -------------------------------- +--R #? : % -> NonNegativeInteger ?*? : (R,E) -> % +--R ?*? : (%,R) -> % ?*? : (R,%) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (NonNegativeInteger,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?/? : (%,R) -> % if R has FIELD +--R ?=? : (%,%) -> Boolean 1 : () -> % +--R 0 : () -> % ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,PositiveInteger) -> % coef : (%,E) -> R +--R coefficient : (%,E) -> R coefficients : % -> List(R) +--R coerce : E -> % coerce : R -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R constant : % -> R constant? : % -> Boolean +--R hash : % -> SingleInteger latex : % -> String +--R leadingCoefficient : % -> R leadingMonomial : % -> E +--R map : ((R -> R),%) -> % maxdeg : % -> E +--R mindeg : % -> E monom : (E,R) -> % +--R monomial? : % -> Boolean monomials : % -> List(%) +--R one? : % -> Boolean quasiRegular : % -> % +--R quasiRegular? : % -> Boolean recip : % -> Union(%,"failed") +--R reductum : % -> % retract : % -> E +--R sample : () -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R characteristic : () -> NonNegativeInteger +--R leadingTerm : % -> Record(k: E,c: R) +--R listOfTerms : % -> List(Record(k: E,c: R)) +--R numberOfMonomials : % -> NonNegativeInteger +--R retractIfCan : % -> Union(E,"failed") +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R +--E 16 + )spool )lisp (bye) \end{chunk} @@ -158028,28 +164783,27 @@ XPolynomialRing(R:Ring,E:OrderedMonoid): T == C where --R------------------------------- Operations -------------------------------- --R ?*? : (VarSet,%) -> % ?*? : (%,R) -> % --R ?*? : (R,%) -> % ?*? : (%,%) -> % ---R ?*? : (Integer,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?*? : (Integer,%) -> % ?*? : (NonNegativeInteger,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,NonNegativeInteger) -> % --R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % --R ?-? : (%,%) -> % -? : % -> % --R ?=? : (%,%) -> Boolean 1 : () -> % ---R 0 : () -> % ?^? : (%,PositiveInteger) -> % ---R coef : (%,%) -> R coerce : VarSet -> % ---R coerce : R -> % coerce : Integer -> % ---R coerce : % -> OutputForm constant : % -> R ---R constant? : % -> Boolean degree : % -> NonNegativeInteger ---R hash : % -> SingleInteger latex : % -> String ---R lquo : (%,%) -> % lquo : (%,VarSet) -> % ---R map : ((R -> R),%) -> % mirror : % -> % ---R monomial? : % -> Boolean one? : % -> Boolean ---R quasiRegular : % -> % quasiRegular? : % -> Boolean ---R recip : % -> Union(%,"failed") rquo : (%,%) -> % ---R rquo : (%,VarSet) -> % sample : () -> % +--R 0 : () -> % ?^? : (%,NonNegativeInteger) -> % +--R ?^? : (%,PositiveInteger) -> % coef : (%,%) -> R +--R coerce : VarSet -> % coerce : R -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R constant : % -> R constant? : % -> Boolean +--R degree : % -> NonNegativeInteger hash : % -> SingleInteger +--R latex : % -> String lquo : (%,%) -> % +--R lquo : (%,VarSet) -> % map : ((R -> R),%) -> % +--R mirror : % -> % monomial? : % -> Boolean +--R one? : % -> Boolean quasiRegular : % -> % +--R quasiRegular? : % -> Boolean recip : % -> Union(%,"failed") +--R rquo : (%,%) -> % rquo : (%,VarSet) -> % +--R sample : () -> % sh : (%,%) -> % if R has COMRING --R varList : % -> List(VarSet) zero? : % -> Boolean --R ?~=? : (%,%) -> Boolean ---R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,NonNegativeInteger) -> % --R RemainderList : % -> List(Record(k: VarSet,c: %)) ---R ?^? : (%,NonNegativeInteger) -> % --R characteristic : () -> NonNegativeInteger --R coef : (%,OrderedFreeMonoid(VarSet)) -> R --R coerce : OrderedFreeMonoid(VarSet) -> % @@ -158063,7 +164817,6 @@ XPolynomialRing(R:Ring,E:OrderedMonoid): T == C where --R retractIfCan : % -> Union(OrderedFreeMonoid(VarSet),"failed") --R rquo : (%,OrderedFreeMonoid(VarSet)) -> % --R sh : (%,NonNegativeInteger) -> % if R has COMRING ---R sh : (%,%) -> % if R has COMRING --R subtractIfCan : (%,%) -> Union(%,"failed") --R trunc : (%,NonNegativeInteger) -> % --R unexpand : XDistributedPolynomial(VarSet,R) -> % diff --git a/books/bookvol10.4.pamphlet b/books/bookvol10.4.pamphlet index c461cd7..debf906 100644 --- a/books/bookvol10.4.pamphlet +++ b/books/bookvol10.4.pamphlet @@ -470,6 +470,22 @@ AffineAlgebraicSetComputeWithResultant(K,symb,PolyRing,E,ProjPt):Ex==Impl where --S 1 of 1 )show AlgebraicFunction +--R +--R AlgebraicFunction(R: Join(OrderedSet,IntegralDomain),F: FunctionSpace(R)) is a package constructor +--R Abbreviation for AlgebraicFunction is AF +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for AF +--R +--R------------------------------- Operations -------------------------------- +--R belong? : BasicOperator -> Boolean droot : List(F) -> OutputForm +--R ?**? : (F,Fraction(Integer)) -> F if R has RETRACT(INT) +--R definingPolynomial : F -> F if R has RETRACT(INT) +--R inrootof : (SparseUnivariatePolynomial(F),F) -> F +--R iroot : (R,Integer) -> F if R has RETRACT(INT) +--R minPoly : Kernel(F) -> SparseUnivariatePolynomial(F) if R has RETRACT(INT) +--R operator : BasicOperator -> BasicOperator +--R rootOf : (SparseUnivariatePolynomial(F),Symbol) -> F +--R --E 1 )spool @@ -769,6 +785,15 @@ AlgebraicFunction(R, F): Exports == Implementation where --S 1 of 1 )show AlgebraicHermiteIntegration +--R +--R AlgebraicHermiteIntegration(F: Field,UP: UnivariatePolynomialCategory(F),UPUP: UnivariatePolynomialCategory(Fraction(UP)),R: FunctionFieldCategory(F,UP,UPUP)) is a package constructor +--R Abbreviation for AlgebraicHermiteIntegration is INTHERAL +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for INTHERAL +--R +--R------------------------------- Operations -------------------------------- +--R HermiteIntegrate : (R,(UP -> UP)) -> Record(answer: R,logpart: R) +--R --E 1 )spool @@ -884,6 +909,17 @@ AlgebraicHermiteIntegration(F,UP,UPUP,R):Exports == Implementation where --S 1 of 1 )show AlgebraicIntegrate +--R +--R AlgebraicIntegrate(R0: Join(OrderedSet,IntegralDomain,RetractableTo(Integer)),F: Join(AlgebraicallyClosedField,FunctionSpace(R0)),UP: UnivariatePolynomialCategory(F),UPUP: UnivariatePolynomialCategory(Fraction(UP)),R: FunctionFieldCategory(F,UP,UPUP)) is a package constructor +--R Abbreviation for AlgebraicIntegrate is INTALG +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for INTALG +--R +--R------------------------------- Operations -------------------------------- +--R algintegrate : (R,(UP -> UP)) -> IntegrationResult(R) +--R palginfieldint : (R,(UP -> UP)) -> Union(R,"failed") +--R palgintegrate : (R,(UP -> UP)) -> IntegrationResult(R) +--R --E 1 )spool @@ -1233,6 +1269,15 @@ AlgebraicIntegrate(R0, F, UP, UPUP, R): Exports == Implementation where --S 1 of 1 )show AlgebraicIntegration +--R +--R AlgebraicIntegration(R: Join(OrderedSet,IntegralDomain),F: Join(AlgebraicallyClosedField,FunctionSpace(R))) is a package constructor +--R Abbreviation for AlgebraicIntegration is INTAF +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for INTAF +--R +--R------------------------------- Operations -------------------------------- +--R algint : (F,Kernel(F),Kernel(F),(SparseUnivariatePolynomial(F) -> SparseUnivariatePolynomial(F))) -> IntegrationResult(F) +--R --E 1 )spool @@ -1351,6 +1396,26 @@ AlgebraicIntegration(R, F): Exports == Implementation where --S 1 of 1 )show AlgebraicManipulations +--R +--R AlgebraicManipulations(R: IntegralDomain,F)where +--R F: Join(Field,ExpressionSpace)with +--R numer : % -> SparseMultivariatePolynomial(R,Kernel(%)) +--R denom : % -> SparseMultivariatePolynomial(R,Kernel(%)) +--R coerce : SparseMultivariatePolynomial(R,Kernel(%)) -> % is a package constructor +--R Abbreviation for AlgebraicManipulations is ALGMANIP +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for ALGMANIP +--R +--R------------------------------- Operations -------------------------------- +--R ratDenom : F -> F ratDenom : (F,F) -> F +--R ratDenom : (F,List(F)) -> F ratDenom : (F,List(Kernel(F))) -> F +--R rootSplit : F -> F +--R ratPoly : F -> SparseUnivariatePolynomial(F) +--R rootKerSimp : (BasicOperator,F,NonNegativeInteger) -> F if F has FS(R) and R has GCDDOM and R has ORDSET and R has RETRACT(INT) +--R rootPower : F -> F if F has FS(R) and R has GCDDOM and R has ORDSET and R has RETRACT(INT) +--R rootProduct : F -> F if F has FS(R) and R has GCDDOM and R has ORDSET and R has RETRACT(INT) +--R rootSimp : F -> F if F has FS(R) and R has GCDDOM and R has ORDSET and R has RETRACT(INT) +--R --E 1 )spool @@ -1605,6 +1670,16 @@ AlgebraicManipulations(R, F): Exports == Implementation where --S 1 of 1 )show AlgebraicMultFact +--R +--R AlgebraicMultFact(OV: OrderedSet,E: OrderedAbelianMonoidSup,P: PolynomialCategory(AlgebraicNumber,E,OV)) is a package constructor +--R Abbreviation for AlgebraicMultFact is ALGMFACT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for ALGMFACT +--R +--R------------------------------- Operations -------------------------------- +--R factor : (P,List(AlgebraicNumber)) -> Factored(P) +--R factor : (SparseUnivariatePolynomial(P),List(AlgebraicNumber)) -> Factored(SparseUnivariatePolynomial(P)) +--R --E 1 )spool @@ -1697,6 +1772,27 @@ AlgebraicMultFact(OV,E,P) : C == T --S 1 of 1 )show AlgebraPackage +--R +--R AlgebraPackage(R: IntegralDomain,A: FramedNonAssociativeAlgebra(R)) is a package constructor +--R Abbreviation for AlgebraPackage is ALGPKG +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for ALGPKG +--R +--R------------------------------- Operations -------------------------------- +--R basisOfCenter : () -> List(A) basisOfLeftNucleus : () -> List(A) +--R basisOfMiddleNucleus : () -> List(A) basisOfNucleus : () -> List(A) +--R basisOfRightNucleus : () -> List(A) biRank : A -> NonNegativeInteger +--R doubleRank : A -> NonNegativeInteger leftRank : A -> NonNegativeInteger +--R rightRank : A -> NonNegativeInteger weakBiRank : A -> NonNegativeInteger +--R basis : Vector(A) -> Vector(A) if R has EUCDOM +--R basisOfCentroid : () -> List(Matrix(R)) +--R basisOfCommutingElements : () -> List(A) +--R basisOfLeftAnnihilator : A -> List(A) +--R basisOfLeftNucloid : () -> List(Matrix(R)) +--R basisOfRightAnnihilator : A -> List(A) +--R basisOfRightNucloid : () -> List(Matrix(R)) +--R radicalOfLeftTraceForm : () -> List(A) +--R --E 1 )spool @@ -2214,6 +2310,17 @@ AlgebraPackage(R:IntegralDomain, A: FramedNonAssociativeAlgebra(R)): _ --S 1 of 1 )show AlgFactor +--R +--R AlgFactor(UP: UnivariatePolynomialCategory(AlgebraicNumber)) is a package constructor +--R Abbreviation for AlgFactor is ALGFACT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for ALGFACT +--R +--R------------------------------- Operations -------------------------------- +--R doublyTransitive? : UP -> Boolean factor : UP -> Factored(UP) +--R split : UP -> Factored(UP) +--R factor : (UP,List(AlgebraicNumber)) -> Factored(UP) +--R --E 1 )spool @@ -2359,6 +2466,27 @@ AlgFactor(UP): Exports == Implementation where --S 1 of 1 )show AnnaNumericalIntegrationPackage +--R +--R AnnaNumericalIntegrationPackage is a package constructor +--R Abbreviation for AnnaNumericalIntegrationPackage is INTPACK +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for INTPACK +--R +--R------------------------------- Operations -------------------------------- +--R integrate : (Expression(Float),Segment(OrderedCompletion(Float)),Float,Float,RoutinesTable) -> Result +--R integrate : NumericalIntegrationProblem -> Result +--R integrate : (Expression(Float),Segment(OrderedCompletion(Float)),Float,Float) -> Result +--R integrate : (Expression(Float),Segment(OrderedCompletion(Float)),Float) -> Result +--R integrate : (Expression(Float),Segment(OrderedCompletion(Float))) -> Result +--R integrate : (Expression(Float),List(Segment(OrderedCompletion(Float)))) -> Result +--R integrate : (Expression(Float),List(Segment(OrderedCompletion(Float))),Float) -> Result +--R integrate : (Expression(Float),List(Segment(OrderedCompletion(Float))),Float,Float) -> Result +--R integrate : (Expression(Float),List(Segment(OrderedCompletion(Float))),Float,Float,RoutinesTable) -> Result +--R integrate : (Expression(Float),SegmentBinding(OrderedCompletion(Float)),String) -> Union(Result,"failed") +--R integrate : (Expression(Float),SegmentBinding(OrderedCompletion(Float)),Symbol) -> Union(Result,"failed") +--R measure : NumericalIntegrationProblem -> Record(measure: Float,name: String,explanations: List(String),extra: Result) +--R measure : (NumericalIntegrationProblem,RoutinesTable) -> Record(measure: Float,name: String,explanations: List(String),extra: Result) +--R --E 1 )spool @@ -2902,6 +3030,24 @@ AnnaNumericalIntegrationPackage(): EE == II where --S 1 of 1 )show AnnaNumericalOptimizationPackage +--R +--R AnnaNumericalOptimizationPackage is a package constructor +--R Abbreviation for AnnaNumericalOptimizationPackage is OPTPACK +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for OPTPACK +--R +--R------------------------------- Operations -------------------------------- +--R goodnessOfFit : NumericalOptimizationProblem -> Result +--R goodnessOfFit : (List(Expression(Float)),List(Float)) -> Result +--R measure : NumericalOptimizationProblem -> Record(measure: Float,name: String,explanations: List(String)) +--R measure : (NumericalOptimizationProblem,RoutinesTable) -> Record(measure: Float,name: String,explanations: List(String)) +--R optimize : (NumericalOptimizationProblem,RoutinesTable) -> Result +--R optimize : NumericalOptimizationProblem -> Result +--R optimize : (Expression(Float),List(Float),List(OrderedCompletion(Float)),List(Expression(Float)),List(OrderedCompletion(Float))) -> Result +--R optimize : (Expression(Float),List(Float),List(OrderedCompletion(Float)),List(OrderedCompletion(Float))) -> Result +--R optimize : (Expression(Float),List(Float)) -> Result +--R optimize : (List(Expression(Float)),List(Float)) -> Result +--R --E 1 )spool @@ -3342,6 +3488,24 @@ AnnaNumericalOptimizationPackage(): EE == II where --S 1 of 1 )show AnnaOrdinaryDifferentialEquationPackage +--R +--R AnnaOrdinaryDifferentialEquationPackage is a package constructor +--R Abbreviation for AnnaOrdinaryDifferentialEquationPackage is ODEPACK +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for ODEPACK +--R +--R------------------------------- Operations -------------------------------- +--R measure : NumericalODEProblem -> Record(measure: Float,name: String,explanations: List(String)) +--R measure : (NumericalODEProblem,RoutinesTable) -> Record(measure: Float,name: String,explanations: List(String)) +--R solve : NumericalODEProblem -> Result +--R solve : (NumericalODEProblem,RoutinesTable) -> Result +--R solve : (Vector(Expression(Float)),Float,Float,List(Float)) -> Result +--R solve : (Vector(Expression(Float)),Float,Float,List(Float),Float) -> Result +--R solve : (Vector(Expression(Float)),Float,Float,List(Float),Expression(Float),Float) -> Result +--R solve : (Vector(Expression(Float)),Float,Float,List(Float),List(Float),Float) -> Result +--R solve : (Vector(Expression(Float)),Float,Float,List(Float),Expression(Float),List(Float),Float) -> Result +--R solve : (Vector(Expression(Float)),Float,Float,List(Float),Expression(Float),List(Float),Float,Float) -> Result +--R --E 1 )spool @@ -3792,6 +3956,20 @@ AnnaOrdinaryDifferentialEquationPackage(): EE == II where --S 1 of 1 )show AnnaPartialDifferentialEquationPackage +--R +--R AnnaPartialDifferentialEquationPackage is a package constructor +--R Abbreviation for AnnaPartialDifferentialEquationPackage is PDEPACK +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for PDEPACK +--R +--R------------------------------- Operations -------------------------------- +--R measure : NumericalPDEProblem -> Record(measure: Float,name: String,explanations: List(String)) +--R measure : (NumericalPDEProblem,RoutinesTable) -> Record(measure: Float,name: String,explanations: List(String)) +--R solve : NumericalPDEProblem -> Result +--R solve : (NumericalPDEProblem,RoutinesTable) -> Result +--R solve : (Float,Float,Float,Float,NonNegativeInteger,NonNegativeInteger,List(Expression(Float)),List(List(Expression(Float))),String,DoubleFloat) -> Result +--R solve : (Float,Float,Float,Float,NonNegativeInteger,NonNegativeInteger,List(Expression(Float)),List(List(Expression(Float))),String) -> Result +--R --E 1 )spool @@ -4090,6 +4268,17 @@ AnnaPartialDifferentialEquationPackage(): EE == II where --S 1 of 1 )show AnyFunctions1 +--R +--R AnyFunctions1(S: Type) is a package constructor +--R Abbreviation for AnyFunctions1 is ANY1 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for ANY1 +--R +--R------------------------------- Operations -------------------------------- +--R coerce : S -> Any retract : Any -> S +--R retractable? : Any -> Boolean +--R retractIfCan : Any -> Union(S,"failed") +--R --E 1 )spool @@ -4175,6 +4364,7 @@ AnyFunctions1(S:Type): with )set message test on )set message auto off )clear all + --S 1 of 9 getDomains 'Collection --R @@ -4306,16 +4496,14 @@ summary() --S 5 of 9 )show API ---R --R ApplicationProgramInterface is a package constructor --R Abbreviation for ApplicationProgramInterface is API --R This constructor is exposed in this frame. --R Issue )edit bookvol10.4.pamphlet to see algebra source code for API --R --R------------------------------- Operations -------------------------------- ---R credits : () -> Void getDomains : Symbol -> Set(Symbol) ---R summary : () -> Void ---R getAncestors : Symbol -> Set(Symbol) +--R credits : () -> Void getAncestors : Symbol -> Set(Symbol) +--R getDomains : Symbol -> Set(Symbol) summary : () -> Void --R reportInstantiations : Boolean -> Void --R --E 5 @@ -4576,6 +4764,17 @@ ApplicationProgramInterface(): Exports == Implementation where --S 1 of 1 )show ApplyRules +--R +--R ApplyRules(Base: SetCategory,R: Join(Ring,PatternMatchable(Base),OrderedSet,ConvertibleTo(Pattern(Base))),F: Join(FunctionSpace(R),PatternMatchable(Base),ConvertibleTo(Pattern(Base)))) is a package constructor +--R Abbreviation for ApplyRules is APPRULE +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for APPRULE +--R +--R------------------------------- Operations -------------------------------- +--R localUnquote : (F,List(Symbol)) -> F +--R applyRules : (List(RewriteRule(Base,R,F)),F) -> F +--R applyRules : (List(RewriteRule(Base,R,F)),F,PositiveInteger) -> F +--R --E 1 )spool @@ -4738,6 +4937,15 @@ ApplyRules(Base, R, F): Exports == Implementation where --S 1 of 1 )show ApplyUnivariateSkewPolynomial +--R +--R ApplyUnivariateSkewPolynomial(R: Ring,M: LeftModule(R),P: UnivariateSkewPolynomialCategory(R)) is a package constructor +--R Abbreviation for ApplyUnivariateSkewPolynomial is APPLYORE +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for APPLYORE +--R +--R------------------------------- Operations -------------------------------- +--R apply : (P,(M -> M),M) -> M +--R --E 1 )spool @@ -4804,6 +5012,17 @@ ApplyUnivariateSkewPolynomial(R:Ring, M: LeftModule R, --S 1 of 1 )show AssociatedEquations +--R +--R AssociatedEquations(R: IntegralDomain,L: LinearOrdinaryDifferentialOperatorCategory(R)) is a package constructor +--R Abbreviation for AssociatedEquations is ASSOCEQ +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for ASSOCEQ +--R +--R------------------------------- Operations -------------------------------- +--R associatedEquations : (L,PositiveInteger) -> Record(minor: List(PositiveInteger),eq: L,minors: List(List(PositiveInteger)),ops: List(L)) if R has FIELD +--R associatedSystem : (L,PositiveInteger) -> Record(mat: Matrix(R),vec: Vector(List(PositiveInteger))) +--R uncouplingMatrices : Matrix(R) -> Vector(Matrix(R)) +--R --E 1 )spool @@ -4958,6 +5177,16 @@ AssociatedEquations(R, L):Exports == Implementation where --S 1 of 1 )show AttachPredicates +--R +--R AttachPredicates(D: Type) is a package constructor +--R Abbreviation for AttachPredicates is PMPRED +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for PMPRED +--R +--R------------------------------- Operations -------------------------------- +--R suchThat : (Symbol,(D -> Boolean)) -> Expression(Integer) +--R suchThat : (Symbol,List((D -> Boolean))) -> Expression(Integer) +--R --E 1 )spool @@ -5026,6 +5255,17 @@ AttachPredicates(D:Type): Exports == Implementation where --S 1 of 1 )show AxiomServer +--R +--R AxiomServer is a package constructor +--R Abbreviation for AxiomServer is AXSERV +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for AXSERV +--R +--R------------------------------- Operations -------------------------------- +--R multiServ : SExpression -> Void +--R axServer : (Integer,(SExpression -> Void)) -> Void +--R getDatabase : (String,String) -> String +--R --E 1 )spool @@ -5763,6 +6003,16 @@ input. --S 1 of 1 )show BalancedFactorisation +--R +--R BalancedFactorisation(R: Join(GcdDomain,CharacteristicZero),UP: UnivariatePolynomialCategory(R)) is a package constructor +--R Abbreviation for BalancedFactorisation is BALFACT +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for BALFACT +--R +--R------------------------------- Operations -------------------------------- +--R balancedFactorisation : (UP,UP) -> Factored(UP) +--R balancedFactorisation : (UP,List(UP)) -> Factored(UP) +--R --E 1 )spool @@ -5849,6 +6099,23 @@ BalancedFactorisation(R, UP): Exports == Implementation where --S 1 of 1 )show BasicOperatorFunctions1 +--R +--R BasicOperatorFunctions1(A: SetCategory) is a package constructor +--R Abbreviation for BasicOperatorFunctions1 is BOP1 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for BOP1 +--R +--R------------------------------- Operations -------------------------------- +--R constantOpIfCan : BasicOperator -> Union(A,"failed") if A has ORDSET +--R constantOperator : A -> BasicOperator if A has ORDSET +--R derivative : (BasicOperator,List((List(A) -> A))) -> BasicOperator +--R derivative : (BasicOperator,(A -> A)) -> BasicOperator +--R derivative : BasicOperator -> Union(List((List(A) -> A)),"failed") +--R evaluate : (BasicOperator,List(A)) -> Union(A,"failed") +--R evaluate : (BasicOperator,(List(A) -> A)) -> BasicOperator +--R evaluate : (BasicOperator,(A -> A)) -> BasicOperator +--R evaluate : BasicOperator -> Union((List(A) -> A),"failed") +--R --E 1 )spool @@ -6015,14 +6282,15 @@ BasicOperatorFunctions1(A:SetCategory): Exports == Implementation where )set message test on )set message auto off )clear all ---S 1 of 9 + +--S 1 of 10 n:=linearBezier([2.0,2.0],[4.0,4.0]) --R --I (1) theMap(BEZIER;linearBezier;2LM;1!0,707) --R Type: (Float -> List(Float)) --E 1 ---S 2 of 9 +--S 2 of 10 [n(t/10.0) for t in 0..10 by 1] --R --R (2) @@ -6031,14 +6299,14 @@ n:=linearBezier([2.0,2.0],[4.0,4.0]) --R Type: List(List(Float)) --E 2 ---S 3 of 9 +--S 3 of 10 n:=quadraticBezier([2.0,2.0],[4.0,4.0],[6.0,2.0]) --R --I (3) theMap(BEZIER;quadraticBezier;3LM;2!0,291) --R Type: (Float -> List(Float)) --E 3 ---S 4 of 9 +--S 4 of 10 [n(t/10.0) for t in 0..10 by 1] --R --R (4) @@ -6047,14 +6315,14 @@ n:=quadraticBezier([2.0,2.0],[4.0,4.0],[6.0,2.0]) --R Type: List(List(Float)) --E 4 ---S 5 of 9 +--S 5 of 10 n:=cubicBezier([2.0,2.0],[2.0,4.0],[6.0,4.0],[6.0,2.0]) --R --I (5) theMap(BEZIER;cubicBezier;4LM;3!0,915) --R Type: (Float -> List(Float)) --E 5 ---S 6 of 9 +--S 6 of 10 [n(t/10.0) for t in 0..10 by 1] --R --R (6) @@ -6064,7 +6332,7 @@ n:=cubicBezier([2.0,2.0],[2.0,4.0],[6.0,4.0],[6.0,2.0]) --R Type: List(List(Float)) --E 6 ---S 7 of 9 +--S 7 of 10 line:=[[i::Float,4.0] for i in -4..4 by 1] --R --R @@ -6074,7 +6342,7 @@ line:=[[i::Float,4.0] for i in -4..4 by 1] --R Type: List(List(Float)) --E 7 ---S 8 of 9 +--S 8 of 10 functions:=[quadraticBezier([2.0,2.0],m,[6.0,2.0]) for m in line] --R --R @@ -6091,7 +6359,7 @@ functions:=[quadraticBezier([2.0,2.0],m,[6.0,2.0]) for m in line] --R Type: List((Float -> List(Float))) --E 8 ---S 9 of 9 +--S 9 of 10 graphs:=[[point(((functions.i)(j/100.0))::LIST(DFLOAT)) _ for j in 0..100] for i in 1..9] --R @@ -6732,6 +7000,21 @@ graphs:=[[point(((functions.i)(j/100.0))::LIST(DFLOAT)) _ --R Type: List(List(Point(DoubleFloat))) --E 9 +--S 10 of 10 +)show Bezier +--R +--R Bezier(R: Ring) is a package constructor +--R Abbreviation for Bezier is BEZIER +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for BEZIER +--R +--R------------------------------- Operations -------------------------------- +--R cubicBezier : (List(R),List(R),List(R),List(R)) -> (R -> List(R)) +--R linearBezier : (List(R),List(R)) -> (R -> List(R)) +--R quadraticBezier : (List(R),List(R),List(R)) -> (R -> List(R)) +--R +--E 10 + -- We do not do these during testing since graphics is not available -- The resulting image is in the Bezier section of Volume 10.4 @@ -6930,6 +7213,17 @@ Bezier(R:Ring): with --S 1 of 1 )show BezoutMatrix +--R +--R BezoutMatrix(R: Ring,UP: UnivariatePolynomialCategory(R),M: MatrixCategory(R,Row,Col),Row: FiniteLinearAggregate(R),Col: FiniteLinearAggregate(R)) is a package constructor +--R Abbreviation for BezoutMatrix is BEZOUT +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for BEZOUT +--R +--R------------------------------- Operations -------------------------------- +--R bezoutMatrix : (UP,UP) -> M sylvesterMatrix : (UP,UP) -> M +--R bezoutDiscriminant : UP -> R if R has commutative(*) +--R bezoutResultant : (UP,UP) -> R if R has commutative(*) +--R --E 1 )spool @@ -7462,6 +7756,15 @@ BlowUpPackage(K,symb,PolyRing,E, BLMET):Exports == Implementation where --S 1 of 1 )show BoundIntegerRoots +--R +--R BoundIntegerRoots(F: Join(Field,RetractableTo(Fraction(Integer))),UP: UnivariatePolynomialCategory(F)) is a package constructor +--R Abbreviation for BoundIntegerRoots is BOUNDZRO +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for BOUNDZRO +--R +--R------------------------------- Operations -------------------------------- +--R integerBound : UP -> Integer +--R --E 1 )spool @@ -7587,6 +7890,19 @@ BoundIntegerRoots(F, UP): Exports == Implementation where --S 1 of 1 )show BrillhartTests +--R +--R BrillhartTests(UP: UnivariatePolynomialCategory(Integer)) is a package constructor +--R Abbreviation for BrillhartTests is BRILL +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for BRILL +--R +--R------------------------------- Operations -------------------------------- +--R noLinearFactor? : UP -> Boolean +--R brillhartIrreducible? : UP -> Boolean +--R brillhartIrreducible? : (UP,Boolean) -> Boolean +--R brillhartTrials : () -> NonNegativeInteger +--R brillhartTrials : NonNegativeInteger -> NonNegativeInteger +--R --E 1 )spool @@ -7741,6 +8057,16 @@ BrillhartTests(UP): Exports == Implementation where --S 1 of 1 )show CartesianTensorFunctions2 +--R +--R CartesianTensorFunctions2(minix: Integer,dim: NonNegativeInteger,S: CommutativeRing,T$: CommutativeRing) is a package constructor +--R Abbreviation for CartesianTensorFunctions2 is CARTEN2 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for CARTEN2 +--R +--R------------------------------- Operations -------------------------------- +--R map : ((S -> T$),CartesianTensor(minix,dim,S)) -> CartesianTensor(minix,dim,T$) +--R reshape : (List(T$),CartesianTensor(minix,dim,S)) -> CartesianTensor(minix,dim,T$) +--R --E 1 )spool @@ -7813,6 +8139,20 @@ CartesianTensorFunctions2(minix, dim, S, T): CTPcat == CTPdef where --S 1 of 1 )show ChangeOfVariable +--R +--R ChangeOfVariable(F: UniqueFactorizationDomain,UP: UnivariatePolynomialCategory(F),UPUP: UnivariatePolynomialCategory(Fraction(UP))) is a package constructor +--R Abbreviation for ChangeOfVariable is CHVAR +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for CHVAR +--R +--R------------------------------- Operations -------------------------------- +--R goodPoint : (UPUP,UPUP) -> F +--R chvar : (UPUP,UPUP) -> Record(func: UPUP,poly: UPUP,c1: Fraction(UP),c2: Fraction(UP),deg: NonNegativeInteger) +--R eval : (UPUP,Fraction(UP),Fraction(UP)) -> UPUP +--R mkIntegral : UPUP -> Record(coef: Fraction(UP),poly: UPUP) +--R radPoly : UPUP -> Union(Record(radicand: Fraction(UP),deg: NonNegativeInteger),"failed") +--R rootPoly : (Fraction(UP),NonNegativeInteger) -> Record(exponent: NonNegativeInteger,coef: Fraction(UP),radicand: UP) +--R --E 1 )spool @@ -7990,6 +8330,15 @@ ChangeOfVariable(F, UP, UPUP): Exports == Implementation where --S 1 of 1 )show CharacteristicPolynomialInMonogenicalAlgebra +--R +--R CharacteristicPolynomialInMonogenicalAlgebra(R: CommutativeRing,PolR: UnivariatePolynomialCategory(R),E: MonogenicAlgebra(R,PolR)) is a package constructor +--R Abbreviation for CharacteristicPolynomialInMonogenicalAlgebra is CPIMA +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for CPIMA +--R +--R------------------------------- Operations -------------------------------- +--R characteristicPolynomial : E -> PolR +--R --E 1 )spool @@ -8061,6 +8410,15 @@ CharacteristicPolynomialInMonogenicalAlgebra(R : CommutativeRing, --S 1 of 1 )show CharacteristicPolynomialPackage +--R +--R CharacteristicPolynomialPackage(R: CommutativeRing) is a package constructor +--R Abbreviation for CharacteristicPolynomialPackage is CHARPOL +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for CHARPOL +--R +--R------------------------------- Operations -------------------------------- +--R characteristicPolynomial : (Matrix(R),R) -> R +--R --E 1 )spool @@ -8131,6 +8489,17 @@ CharacteristicPolynomialPackage(R:CommutativeRing):C == T where --S 1 of 1 )show ChineseRemainderToolsForIntegralBases +--R +--R ChineseRemainderToolsForIntegralBases(K: FiniteFieldCategory,R: UnivariatePolynomialCategory(K),UP: UnivariatePolynomialCategory(R)) is a package constructor +--R Abbreviation for ChineseRemainderToolsForIntegralBases is IBACHIN +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for IBACHIN +--R +--R------------------------------- Operations -------------------------------- +--R chineseRemainder : (List(UP),List(Record(basis: Matrix(R),basisDen: R,basisInv: Matrix(R))),NonNegativeInteger) -> Record(basis: Matrix(R),basisDen: R,basisInv: Matrix(R)) +--R factorList : (K,NonNegativeInteger,NonNegativeInteger,NonNegativeInteger) -> List(SparseUnivariatePolynomial(K)) +--R listConjugateBases : (Record(basis: Matrix(R),basisDen: R,basisInv: Matrix(R)),NonNegativeInteger,NonNegativeInteger) -> List(Record(basis: Matrix(R),basisDen: R,basisInv: Matrix(R))) +--R --E 1 )spool @@ -8346,6 +8715,16 @@ ChineseRemainderToolsForIntegralBases(K,R,UP): Exports == Implementation where --S 1 of 1 )show CoerceVectorMatrixPackage +--R +--R CoerceVectorMatrixPackage(R: CommutativeRing) is a package constructor +--R Abbreviation for CoerceVectorMatrixPackage is CVMP +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for CVMP +--R +--R------------------------------- Operations -------------------------------- +--R coerce : Vector(Matrix(R)) -> Vector(Matrix(Fraction(Polynomial(R)))) +--R coerceP : Vector(Matrix(R)) -> Vector(Matrix(Polynomial(R))) +--R --E 1 )spool @@ -8436,7 +8815,8 @@ CoerceVectorMatrixPackage(R : CommutativeRing): public == private where )set message test on )set message auto off )clear all ---S 1 of 6 + +--S 1 of 7 f := operator 'f --R --R @@ -8444,7 +8824,7 @@ f := operator 'f --R Type: BasicOperator --E 1 ---S 2 of 6 +--S 2 of 7 D(product(f(i,x),i=1..m),x) --R --R @@ -8456,25 +8836,25 @@ D(product(f(i,x),i=1..m),x) --R Type: Expression(Integer) --E 2 ---S 3 of 6 +--S 3 of 7 )set expose add constructor OutputForm --R --I OutputForm is already explicitly exposed in frame frame0 --E 3 ---S 4 of 6 +--S 4 of 7 pascalRow(n) == [right(binomial(n,i),4) for i in 0..n] --R --R Type: Void --E 4 ---S 5 of 6 +--S 5 of 7 displayRow(n)==output center blankSeparate pascalRow(n) --R --R Type: Void --E 5 ---S 6 of 6 +--S 6 of 7 for i in 0..7 repeat displayRow i --R --R Compiling function pascalRow with type NonNegativeInteger -> List( @@ -8491,6 +8871,27 @@ for i in 0..7 repeat displayRow i --R Type: Void --E 6 +--S 7 of 7 +--R +--R CombinatorialFunction(R: Join(OrderedSet,IntegralDomain),F: FunctionSpace(R)) is a package constructor +--R Abbreviation for CombinatorialFunction is COMBF +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for COMBF +--R +--R------------------------------- Operations -------------------------------- +--R ?**? : (F,F) -> F belong? : BasicOperator -> Boolean +--R binomial : (F,F) -> F factorial : F -> F +--R factorials : F -> F factorials : (F,Symbol) -> F +--R iibinom : List(F) -> F iidprod : List(F) -> F +--R iidsum : List(F) -> F iifact : F -> F +--R iiperm : List(F) -> F iipow : List(F) -> F +--R ipow : List(F) -> F permutation : (F,F) -> F +--R product : (F,Symbol) -> F product : (F,SegmentBinding(F)) -> F +--R summation : (F,Symbol) -> F +--R operator : BasicOperator -> BasicOperator +--R summation : (F,SegmentBinding(F)) -> F +--R +--E 7 )spool )lisp (bye) @@ -9171,6 +9572,16 @@ CombinatorialFunction(R, F): Exports == Implementation where --S 1 of 1 )show CommonDenominator +--R +--R CommonDenominator(R: IntegralDomain,Q: QuotientFieldCategory(R),A: FiniteLinearAggregate(Q)) is a package constructor +--R Abbreviation for CommonDenominator is CDEN +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for CDEN +--R +--R------------------------------- Operations -------------------------------- +--R clearDenominator : A -> A commonDenominator : A -> R +--R splitDenominator : A -> Record(num: A,den: R) +--R --E 1 )spool @@ -9262,6 +9673,15 @@ CommonDenominator(R, Q, A): Exports == Implementation where --S 1 of 1 )show CommonOperators +--R +--R CommonOperators is a package constructor +--R Abbreviation for CommonOperators is COMMONOP +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for COMMONOP +--R +--R------------------------------- Operations -------------------------------- +--R operator : Symbol -> BasicOperator +--R --E 1 )spool @@ -9505,6 +9925,15 @@ CommonOperators(): Exports == Implementation where --S 1 of 1 )show CommuteUnivariatePolynomialCategory +--R +--R CommuteUnivariatePolynomialCategory(R: Ring,UP: UnivariatePolynomialCategory(R),UPUP: UnivariatePolynomialCategory(UP)) is a package constructor +--R Abbreviation for CommuteUnivariatePolynomialCategory is COMMUPC +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for COMMUPC +--R +--R------------------------------- Operations -------------------------------- +--R swap : UPUP -> UPUP +--R --E 1 )spool @@ -9584,6 +10013,15 @@ CommuteUnivariatePolynomialCategory(R, UP, UPUP): Exports == Impl where --S 1 of 1 )show ComplexFactorization +--R +--R ComplexFactorization(RR: EuclideanDomain,PR: UnivariatePolynomialCategory(Complex(RR))) is a package constructor +--R Abbreviation for ComplexFactorization is COMPFACT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for COMPFACT +--R +--R------------------------------- Operations -------------------------------- +--R factor : PR -> Factored(PR) +--R --E 1 )spool @@ -9706,6 +10144,15 @@ ComplexFactorization(RR,PR) : C == T where --S 1 of 1 )show ComplexFunctions2 +--R +--R ComplexFunctions2(R: CommutativeRing,S: CommutativeRing) is a package constructor +--R Abbreviation for ComplexFunctions2 is COMPLEX2 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for COMPLEX2 +--R +--R------------------------------- Operations -------------------------------- +--R map : ((R -> S),Complex(R)) -> Complex(S) +--R --E 1 )spool @@ -9760,6 +10207,15 @@ ComplexFunctions2(R:CommutativeRing, S:CommutativeRing): with --S 1 of 1 )show ComplexIntegerSolveLinearPolynomialEquation +--R +--R ComplexIntegerSolveLinearPolynomialEquation(R: IntegerNumberSystem,CR: ComplexCategory(R)) is a package constructor +--R Abbreviation for ComplexIntegerSolveLinearPolynomialEquation is CINTSLPE +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for CINTSLPE +--R +--R------------------------------- Operations -------------------------------- +--R solveLinearPolynomialEquation : (List(SparseUnivariatePolynomial(CR)),SparseUnivariatePolynomial(CR)) -> Union(List(SparseUnivariatePolynomial(CR)),"failed") +--R --E 1 )spool @@ -9845,6 +10301,15 @@ ComplexIntegerSolveLinearPolynomialEquation(R,CR): C == T --S 1 of 1 )show ComplexPattern +--R +--R ComplexPattern(R: SetCategory,S: Join(ConvertibleTo(Pattern(R)),CommutativeRing),CS: ComplexCategory(S)) is a package constructor +--R Abbreviation for ComplexPattern is COMPLPAT +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for COMPLPAT +--R +--R------------------------------- Operations -------------------------------- +--R convert : CS -> Pattern(R) +--R --E 1 )spool @@ -9909,6 +10374,15 @@ ComplexPattern(R, S, CS) : C == T where --S 1 of 1 )show ComplexPatternMatch +--R +--R ComplexPatternMatch(R: SetCategory,S: Join(PatternMatchable(R),CommutativeRing),CS: ComplexCategory(S)) is a package constructor +--R Abbreviation for ComplexPatternMatch is CPMATCH +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for CPMATCH +--R +--R------------------------------- Operations -------------------------------- +--R patternMatch : (CS,Pattern(R),PatternMatchResult(R,CS)) -> PatternMatchResult(R,CS) if Polynomial(S) has PATMAB(R) +--R --E 1 )spool @@ -9994,6 +10468,27 @@ ComplexPatternMatch(R, S, CS) : C == T where --S 1 of 1 )show ComplexRootFindingPackage +--R +--R ComplexRootFindingPackage(R: Join(Field,OrderedRing),UP: UnivariatePolynomialCategory(Complex(R))) is a package constructor +--R Abbreviation for ComplexRootFindingPackage is CRFP +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for CRFP +--R +--R------------------------------- Operations -------------------------------- +--R factor : (UP,R) -> Factored(UP) factor : UP -> Factored(UP) +--R graeffe : UP -> UP norm : UP -> R +--R reciprocalPolynomial : UP -> UP rootRadius : (UP,R) -> R +--R rootRadius : UP -> R schwerpunkt : UP -> Complex(R) +--R setErrorBound : R -> R +--R complexZeros : UP -> List(Complex(R)) +--R complexZeros : (UP,R) -> List(Complex(R)) +--R divisorCascade : (UP,UP,Boolean) -> List(Record(factors: List(UP),error: R)) +--R divisorCascade : (UP,UP) -> List(Record(factors: List(UP),error: R)) +--R factor : (UP,R,Boolean) -> Factored(UP) +--R pleskenSplit : (UP,R,Boolean) -> Factored(UP) +--R pleskenSplit : (UP,R) -> Factored(UP) +--R startPolynomial : UP -> Record(start: UP,factors: Factored(UP)) +--R --E 1 )spool @@ -10643,6 +11138,15 @@ ComplexRootFindingPackage(R, UP): public == private where --S 1 of 1 )show ComplexRootPackage +--R +--R ComplexRootPackage(UP: UnivariatePolynomialCategory(Complex(Integer)),Par: Join(Field,OrderedRing)) is a package constructor +--R Abbreviation for ComplexRootPackage is CMPLXRT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for CMPLXRT +--R +--R------------------------------- Operations -------------------------------- +--R complexZeros : (UP,Par) -> List(Complex(Par)) +--R --E 1 )spool @@ -10736,6 +11240,19 @@ ComplexRootPackage(UP,Par) : T == C where --S 1 of 1 )show ComplexTrigonometricManipulations +--R +--R ComplexTrigonometricManipulations(R: Join(IntegralDomain,OrderedSet,RetractableTo(Integer)),F: Join(AlgebraicallyClosedField,TranscendentalFunctionCategory,FunctionSpace(Complex(R)))) is a package constructor +--R Abbreviation for ComplexTrigonometricManipulations is CTRIGMNP +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for CTRIGMNP +--R +--R------------------------------- Operations -------------------------------- +--R complexElementary : F -> F complexElementary : (F,Symbol) -> F +--R complexNormalize : F -> F complexNormalize : (F,Symbol) -> F +--R imag : F -> Expression(R) real : F -> Expression(R) +--R real? : F -> Boolean trigs : F -> F +--R complexForm : F -> Complex(Expression(R)) +--R --E 1 )spool @@ -10891,6 +11408,15 @@ ComplexTrigonometricManipulations(R, F): Exports == Implementation where --S 1 of 1 )show ConstantLODE +--R +--R ConstantLODE(R: Join(OrderedSet,EuclideanDomain,RetractableTo(Integer),LinearlyExplicitRingOver(Integer),CharacteristicZero),F: Join(AlgebraicallyClosedFunctionSpace(R),TranscendentalFunctionCategory,PrimitiveFunctionCategory),L: LinearOrdinaryDifferentialOperatorCategory(F)) is a package constructor +--R Abbreviation for ConstantLODE is ODECONST +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for ODECONST +--R +--R------------------------------- Operations -------------------------------- +--R constDsolve : (L,F,Symbol) -> Record(particular: F,basis: List(F)) +--R --E 1 )spool @@ -11015,6 +11541,26 @@ ConstantLODE(R, F, L): Exports == Implementation where --S 1 of 1 )show CoordinateSystems +--R +--R CoordinateSystems(R: Join(Field,TranscendentalFunctionCategory,RadicalCategory)) is a package constructor +--R Abbreviation for CoordinateSystems is COORDSYS +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for COORDSYS +--R +--R------------------------------- Operations -------------------------------- +--R cartesian : Point(R) -> Point(R) cylindrical : Point(R) -> Point(R) +--R parabolic : Point(R) -> Point(R) paraboloidal : Point(R) -> Point(R) +--R polar : Point(R) -> Point(R) spherical : Point(R) -> Point(R) +--R bipolar : R -> (Point(R) -> Point(R)) +--R bipolarCylindrical : R -> (Point(R) -> Point(R)) +--R conical : (R,R) -> (Point(R) -> Point(R)) +--R elliptic : R -> (Point(R) -> Point(R)) +--R ellipticCylindrical : R -> (Point(R) -> Point(R)) +--R oblateSpheroidal : R -> (Point(R) -> Point(R)) +--R parabolicCylindrical : Point(R) -> Point(R) +--R prolateSpheroidal : R -> (Point(R) -> Point(R)) +--R toroidal : R -> (Point(R) -> Point(R)) +--R --E 1 )spool @@ -11260,6 +11806,18 @@ CoordinateSystems(R): Exports == Implementation where --S 1 of 1 )show CRApackage +--R +--R CRApackage(R: EuclideanDomain) is a package constructor +--R Abbreviation for CRApackage is CRAPACK +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for CRAPACK +--R +--R------------------------------- Operations -------------------------------- +--R modTree : (R,List(R)) -> List(R) +--R chineseRemainder : (List(R),List(R)) -> R +--R chineseRemainder : (List(List(R)),List(R)) -> List(R) +--R multiEuclideanTree : (List(R),R) -> List(R) +--R --E 1 )spool @@ -11379,7 +11937,8 @@ CRApackage(R:EuclideanDomain): Exports == Implementation where )set message test on )set message auto off )clear all ---S 1 of 47 + +--S 1 of 48 complete 1 --R --R @@ -11387,7 +11946,7 @@ complete 1 --R Type: SymmetricPolynomial(Fraction(Integer)) --E 1 ---S 2 of 47 +--S 2 of 48 complete 2 --R --R @@ -11397,7 +11956,7 @@ complete 2 --R Type: SymmetricPolynomial(Fraction(Integer)) --E 2 ---S 3 of 47 +--S 3 of 48 complete 3 --R --R @@ -11407,7 +11966,7 @@ complete 3 --R Type: SymmetricPolynomial(Fraction(Integer)) --E 3 ---S 4 of 47 +--S 4 of 48 complete 7 --R --R @@ -11426,7 +11985,7 @@ complete 7 --R Type: SymmetricPolynomial(Fraction(Integer)) --E 4 ---S 5 of 47 +--S 5 of 48 elementary 7 --R --R @@ -11445,7 +12004,7 @@ elementary 7 --R Type: SymmetricPolynomial(Fraction(Integer)) --E 5 ---S 6 of 47 +--S 6 of 48 alternating 7 --R --R @@ -11460,7 +12019,7 @@ alternating 7 --R Type: SymmetricPolynomial(Fraction(Integer)) --E 6 ---S 7 of 47 +--S 7 of 48 cyclic 7 --R --R @@ -11470,7 +12029,7 @@ cyclic 7 --R Type: SymmetricPolynomial(Fraction(Integer)) --E 7 ---S 8 of 47 +--S 8 of 48 dihedral 7 --R --R @@ -11480,7 +12039,7 @@ dihedral 7 --R Type: SymmetricPolynomial(Fraction(Integer)) --E 8 ---S 9 of 47 +--S 9 of 48 graphs 5 --R --R @@ -11491,7 +12050,7 @@ graphs 5 --R Type: SymmetricPolynomial(Fraction(Integer)) --E 9 ---S 10 of 47 +--S 10 of 48 cap(complete 2**2, complete 2*complete 1**2) --R --R @@ -11499,7 +12058,7 @@ cap(complete 2**2, complete 2*complete 1**2) --R Type: Fraction(Integer) --E 10 ---S 11 of 47 +--S 11 of 48 cap(elementary 2**2, complete 2*complete 1**2) --R --R @@ -11507,7 +12066,7 @@ cap(elementary 2**2, complete 2*complete 1**2) --R Type: Fraction(Integer) --E 11 ---S 12 of 47 +--S 12 of 48 cap(complete 3*complete 2*complete 1,complete 2**2*complete 1**2) --R --R @@ -11515,7 +12074,7 @@ cap(complete 3*complete 2*complete 1,complete 2**2*complete 1**2) --R Type: Fraction(Integer) --E 12 ---S 13 of 47 +--S 13 of 48 cap(elementary 3*elementary 2*elementary 1,complete 2**2*complete 1**2) --R --R @@ -11523,7 +12082,7 @@ cap(elementary 3*elementary 2*elementary 1,complete 2**2*complete 1**2) --R Type: Fraction(Integer) --E 13 ---S 14 of 47 +--S 14 of 48 cap(complete 3*complete 2*complete 1,elementary 2**2*elementary 1**2) --R --R @@ -11531,7 +12090,7 @@ cap(complete 3*complete 2*complete 1,elementary 2**2*elementary 1**2) --R Type: Fraction(Integer) --E 14 ---S 15 of 47 +--S 15 of 48 eval(cup(complete 3*complete 2*complete 1, _ cup(complete 2**2*complete 1**2,complete 2**3))) --R @@ -11540,7 +12099,7 @@ eval(cup(complete 3*complete 2*complete 1, _ --R Type: Fraction(Integer) --E 15 ---S 16 of 47 +--S 16 of 48 square:=dihedral 4 --R --R @@ -11550,7 +12109,7 @@ square:=dihedral 4 --R Type: SymmetricPolynomial(Fraction(Integer)) --E 16 ---S 17 of 47 +--S 17 of 48 cap(complete 2**2,square) --R --R @@ -11558,7 +12117,7 @@ cap(complete 2**2,square) --R Type: Fraction(Integer) --E 17 ---S 18 of 47 +--S 18 of 48 cap(complete 3*complete 2**2,dihedral 7) --R --R @@ -11566,7 +12125,7 @@ cap(complete 3*complete 2**2,dihedral 7) --R Type: Fraction(Integer) --E 18 ---S 19 of 47 +--S 19 of 48 cap(graphs 5,complete 7*complete 3) --R --R @@ -11574,13 +12133,13 @@ cap(graphs 5,complete 7*complete 3) --R Type: Fraction(Integer) --E 19 ---S 20 of 47 +--S 20 of 48 s(x) == powerSum(x) --R --R Type: Void --E 20 ---S 21 of 47 +--S 21 of 48 cube:=(1/24)*(s 1**8+9*s 2**4 + 8*s 3**2*s 1**2+6*s 4**2) --R --R Compiling function s with type PositiveInteger -> @@ -11592,7 +12151,7 @@ cube:=(1/24)*(s 1**8+9*s 2**4 + 8*s 3**2*s 1**2+6*s 4**2) --R Type: SymmetricPolynomial(Fraction(Integer)) --E 21 ---S 22 of 47 +--S 22 of 48 cap(complete 4**2,cube) --R --R @@ -11600,7 +12159,7 @@ cap(complete 4**2,cube) --R Type: Fraction(Integer) --E 22 ---S 23 of 47 +--S 23 of 48 cap(complete 2**3*complete 1**2,wreath(elementary 4,elementary 2)) --R --R @@ -11608,7 +12167,7 @@ cap(complete 2**3*complete 1**2,wreath(elementary 4,elementary 2)) --R Type: Fraction(Integer) --E 23 ---S 24 of 47 +--S 24 of 48 cap(complete 2**3*complete 1**2,wreath(elementary 4,complete 2)) --R --R @@ -11616,7 +12175,7 @@ cap(complete 2**3*complete 1**2,wreath(elementary 4,complete 2)) --R Type: Fraction(Integer) --E 24 ---S 25 of 47 +--S 25 of 48 cap(complete 2**3*complete 1**2,wreath(complete 4,elementary 2)) --R --R @@ -11624,7 +12183,7 @@ cap(complete 2**3*complete 1**2,wreath(complete 4,elementary 2)) --R Type: Fraction(Integer) --E 25 ---S 26 of 47 +--S 26 of 48 cap(complete 2**3*complete 1**2,wreath(complete 4,complete 2)) --R --R @@ -11632,7 +12191,7 @@ cap(complete 2**3*complete 1**2,wreath(complete 4,complete 2)) --R Type: Fraction(Integer) --E 26 ---S 27 of 47 +--S 27 of 48 x: ULS(FRAC INT,'x,0) := 'x --R --R @@ -11640,25 +12199,25 @@ x: ULS(FRAC INT,'x,0) := 'x --R Type: UnivariateLaurentSeries(Fraction(Integer),x,0) --E 27 ---S 28 of 47 +--S 28 of 48 ZeroOrOne: INT -> ULS(FRAC INT, 'x, 0) --R --R Type: Void --E 28 ---S 29 of 47 +--S 29 of 48 Integers: INT -> ULS(FRAC INT, 'x, 0) --R --R Type: Void --E 29 ---S 30 of 47 +--S 30 of 48 ZeroOrOne n == 1+x**n --R --R Type: Void --E 30 ---S 31 of 47 +--S 31 of 48 ZeroOrOne 5 --R --R Compiling function ZeroOrOne with type Integer -> @@ -11669,13 +12228,13 @@ ZeroOrOne 5 --R Type: UnivariateLaurentSeries(Fraction(Integer),x,0) --E 31 ---S 32 of 47 +--S 32 of 48 Integers n == 1/(1-x**n) --R --R Type: Void --E 32 ---S 33 of 47 +--S 33 of 48 Integers 5 --R --R Compiling function Integers with type Integer -> @@ -11686,13 +12245,13 @@ Integers 5 --R Type: UnivariateLaurentSeries(Fraction(Integer),x,0) --E 33 ---S 34 of 47 +--S 34 of 48 )expose EVALCYC --R --I EvaluateCycleIndicators is now explicitly exposed in frame frame0 --E 34 ---S 35 of 47 +--S 35 of 48 eval(ZeroOrOne, graphs 5) --R --R @@ -11701,7 +12260,7 @@ eval(ZeroOrOne, graphs 5) --R Type: UnivariateLaurentSeries(Fraction(Integer),x,0) --E 35 ---S 36 of 47 +--S 36 of 48 eval(ZeroOrOne,dihedral 8) --R --R @@ -11710,7 +12269,7 @@ eval(ZeroOrOne,dihedral 8) --R Type: UnivariateLaurentSeries(Fraction(Integer),x,0) --E 36 ---S 37 of 47 +--S 37 of 48 eval(Integers,complete 4) --R --R @@ -11720,7 +12279,7 @@ eval(Integers,complete 4) --R Type: UnivariateLaurentSeries(Fraction(Integer),x,0) --E 37 ---S 38 of 47 +--S 38 of 48 eval(Integers,elementary 4) --R --R @@ -11733,7 +12292,7 @@ eval(Integers,elementary 4) --R Type: UnivariateLaurentSeries(Fraction(Integer),x,0) --E 38 ---S 39 of 47 +--S 39 of 48 eval(ZeroOrOne,cube) --R --R @@ -11742,7 +12301,7 @@ eval(ZeroOrOne,cube) --R Type: UnivariateLaurentSeries(Fraction(Integer),x,0) --E 39 ---S 40 of 47 +--S 40 of 48 eval(Integers,cube) --R --R @@ -11755,7 +12314,7 @@ eval(Integers,cube) --R Type: UnivariateLaurentSeries(Fraction(Integer),x,0) --E 40 ---S 41 of 47 +--S 41 of 48 eval(Integers,graphs 5) --R --R @@ -11768,7 +12327,7 @@ eval(Integers,graphs 5) --R Type: UnivariateLaurentSeries(Fraction(Integer),x,0) --E 41 ---S 42 of 47 +--S 42 of 48 eval(ZeroOrOne ,graphs 15) --R --R @@ -11781,7 +12340,7 @@ eval(ZeroOrOne ,graphs 15) --R Type: UnivariateLaurentSeries(Fraction(Integer),x,0) --E 42 ---S 43 of 47 +--S 43 of 48 cap(dihedral 30,complete 7*complete 8*complete 5*complete 10) --R --R @@ -11789,7 +12348,7 @@ cap(dihedral 30,complete 7*complete 8*complete 5*complete 10) --R Type: Fraction(Integer) --E 43 ---S 44 of 47 +--S 44 of 48 sf3221:= SFunction [3,2,2,1] --R --R @@ -11808,7 +12367,7 @@ sf3221:= SFunction [3,2,2,1] --R Type: SymmetricPolynomial(Fraction(Integer)) --E 44 ---S 45 of 47 +--S 45 of 48 cap(sf3221,complete 2**4) --R --R @@ -11816,7 +12375,7 @@ cap(sf3221,complete 2**4) --R Type: Fraction(Integer) --E 45 ---S 46 of 47 +--S 46 of 48 cap(sf3221, powerSum 1**8) --R --R @@ -11824,7 +12383,7 @@ cap(sf3221, powerSum 1**8) --R Type: Fraction(Integer) --E 46 ---S 47 of 47 +--S 47 of 48 eval(Integers, sf3221) --R --R @@ -11836,6 +12395,32 @@ eval(Integers, sf3221) --R 432x + O(x ) --R Type: UnivariateLaurentSeries(Fraction(Integer),x,0) --E 47 + +--S 48 of 48 +)show CycleIndicators +--R +--R CycleIndicators is a package constructor +--R Abbreviation for CycleIndicators is CYCLES +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for CYCLES +--R +--R------------------------------- Operations -------------------------------- +--R SFunction : List(Integer) -> SymmetricPolynomial(Fraction(Integer)) +--R alternating : Integer -> SymmetricPolynomial(Fraction(Integer)) +--R cap : (SymmetricPolynomial(Fraction(Integer)),SymmetricPolynomial(Fraction(Integer))) -> Fraction(Integer) +--R complete : Integer -> SymmetricPolynomial(Fraction(Integer)) +--R cup : (SymmetricPolynomial(Fraction(Integer)),SymmetricPolynomial(Fraction(Integer))) -> SymmetricPolynomial(Fraction(Integer)) +--R cyclic : Integer -> SymmetricPolynomial(Fraction(Integer)) +--R dihedral : Integer -> SymmetricPolynomial(Fraction(Integer)) +--R elementary : Integer -> SymmetricPolynomial(Fraction(Integer)) +--R eval : SymmetricPolynomial(Fraction(Integer)) -> Fraction(Integer) +--R graphs : Integer -> SymmetricPolynomial(Fraction(Integer)) +--R powerSum : Integer -> SymmetricPolynomial(Fraction(Integer)) +--R skewSFunction : (List(Integer),List(Integer)) -> SymmetricPolynomial(Fraction(Integer)) +--R wreath : (SymmetricPolynomial(Fraction(Integer)),SymmetricPolynomial(Fraction(Integer))) -> SymmetricPolynomial(Fraction(Integer)) +--R +--E 48 + )spool )lisp (bye) \end{chunk} @@ -12541,6 +13126,16 @@ CycleIndicators: Exports == Implementation where --S 1 of 1 )show CyclicStreamTools +--R +--R CyclicStreamTools(S: Type,ST: LazyStreamAggregate(S)) is a package constructor +--R Abbreviation for CyclicStreamTools is CSTTOOLS +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for CSTTOOLS +--R +--R------------------------------- Operations -------------------------------- +--R computeCycleEntry : (ST,ST) -> ST cycleElt : ST -> Union(ST,"failed") +--R computeCycleLength : ST -> NonNegativeInteger +--R --E 1 )spool @@ -12651,6 +13246,17 @@ CyclicStreamTools(S,ST): Exports == Implementation where --S 1 of 1 )show CyclotomicPolynomialPackage +--R +--R CyclotomicPolynomialPackage is a package constructor +--R Abbreviation for CyclotomicPolynomialPackage is CYCLOTOM +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for CYCLOTOM +--R +--R------------------------------- Operations -------------------------------- +--R cyclotomic : Integer -> SparseUnivariatePolynomial(Integer) +--R cyclotomicDecomposition : Integer -> List(SparseUnivariatePolynomial(Integer)) +--R cyclotomicFactorization : Integer -> Factored(SparseUnivariatePolynomial(Integer)) +--R --E 1 )spool @@ -12751,6 +13357,22 @@ CyclotomicPolynomialPackage: public == private where --S 1 of 1 )show CylindricalAlgebraicDecompositionPackage +--R +--R CylindricalAlgebraicDecompositionPackage(TheField: RealClosedField) is a package constructor +--R Abbreviation for CylindricalAlgebraicDecompositionPackage is CAD +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for CAD +--R +--R------------------------------- Operations -------------------------------- +--R coefficientSet : SparseUnivariatePolynomial(Polynomial(TheField)) -> List(Polynomial(TheField)) +--R cylindricalDecomposition : List(Polynomial(TheField)) -> List(Cell(TheField)) +--R cylindricalDecomposition : (List(Polynomial(TheField)),List(Symbol)) -> List(Cell(TheField)) +--R discriminantSet : List(SparseUnivariatePolynomial(Polynomial(TheField))) -> List(Polynomial(TheField)) +--R principalSubResultantSet : (SparseUnivariatePolynomial(Polynomial(TheField)),SparseUnivariatePolynomial(Polynomial(TheField))) -> List(Polynomial(TheField)) +--R projectionSet : List(SparseUnivariatePolynomial(Polynomial(TheField))) -> List(Polynomial(TheField)) +--R resultantSet : List(SparseUnivariatePolynomial(Polynomial(TheField))) -> List(Polynomial(TheField)) +--R specialise : (List(Polynomial(TheField)),Cell(TheField)) -> List(SparseUnivariatePolynomial(TheField)) +--R --E 1 )spool @@ -12940,6 +13562,16 @@ the same roots than the original polynomials. --S 1 of 1 )show CylindricalAlgebraicDecompositionUtilities +--R +--R CylindricalAlgebraicDecompositionUtilities(R: GcdDomain,P: UnivariatePolynomialCategory(R)) is a package constructor +--R Abbreviation for CylindricalAlgebraicDecompositionUtilities is CADU +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for CADU +--R +--R------------------------------- Operations -------------------------------- +--R gcdBasis : List(P) -> List(P) gcdBasisAdd : (P,List(P)) -> List(P) +--R squareFreeBasis : List(P) -> List(P) +--R --E 1 )spool @@ -13037,6 +13669,18 @@ CylindricalAlgebraicDecompositionUtilities(R,P) : PUB == PRIV where --S 1 of 1 )show DefiniteIntegrationTools +--R +--R DefiniteIntegrationTools(R: Join(GcdDomain,OrderedSet,RetractableTo(Integer),LinearlyExplicitRingOver(Integer)),F: Join(TranscendentalFunctionCategory,AlgebraicallyClosedFunctionSpace(R))) is a package constructor +--R Abbreviation for DefiniteIntegrationTools is DFINTTLS +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for DFINTTLS +--R +--R------------------------------- Operations -------------------------------- +--R ignore? : String -> Boolean +--R checkForZero : (Polynomial(R),Symbol,OrderedCompletion(F),OrderedCompletion(F),Boolean) -> Union(Boolean,"failed") +--R checkForZero : (SparseUnivariatePolynomial(F),OrderedCompletion(F),OrderedCompletion(F),Boolean) -> Union(Boolean,"failed") +--R computeInt : (Kernel(F),F,OrderedCompletion(F),OrderedCompletion(F),Boolean) -> Union(OrderedCompletion(F),"failed") +--R --E 1 )spool @@ -13333,6 +13977,16 @@ DefiniteIntegrationTools(R, F): Exports == Implementation where --S 1 of 1 )show DegreeReductionPackage +--R +--R DegreeReductionPackage(R1: Ring,R2: Join(IntegralDomain,OrderedSet)) is a package constructor +--R Abbreviation for DegreeReductionPackage is DEGRED +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for DEGRED +--R +--R------------------------------- Operations -------------------------------- +--R expand : (Expression(R2),PositiveInteger) -> List(Expression(R2)) +--R reduce : SparseUnivariatePolynomial(R1) -> Record(pol: SparseUnivariatePolynomial(R1),deg: PositiveInteger) +--R --E 1 )spool @@ -13431,11 +14085,10 @@ DegreeReductionPackage(R1, R2): Cat == Capsule where --R Issue )edit bookvol10.4.pamphlet to see algebra source code for DTP --R --R------------------------------- Operations -------------------------------- ---R fullParamInit : DesTree -> Void genusNeg : PolyRing -> Integer ---R initParLocLeaves : DesTree -> Void +--R blowUpWithExcpDiv : DesTree -> Void fullParamInit : DesTree -> Void +--R genusNeg : PolyRing -> Integer initParLocLeaves : DesTree -> Void --R adjunctionDivisor : DesTree -> DIVISOR --R blowUp : InfClsPoint -> List(InfClsPoint) ---R blowUpWithExcpDiv : DesTree -> Void --R desingTree : PolyRing -> List(DesTree) --R desingTreeAtPoint : (ProjPt,PolyRing) -> DesTree --R divisorAtDesingTree : (PolyRing,DesTree) -> DIVISOR @@ -13927,6 +14580,15 @@ DesingTreePackage(K, --S 1 of 1 )show DiophantineSolutionPackage +--R +--R DiophantineSolutionPackage is a package constructor +--R Abbreviation for DiophantineSolutionPackage is DIOSP +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for DIOSP +--R +--R------------------------------- Operations -------------------------------- +--R dioSolve : Equation(Polynomial(Integer)) -> Record(varOrder: List(Symbol),inhom: Union(List(Vector(NonNegativeInteger)),"failed"),hom: List(Vector(NonNegativeInteger))) +--R --E 1 )spool @@ -14151,6 +14813,17 @@ DiophantineSolutionPackage(): Cat == Capsule where --S 1 of 1 )show DirectProductFunctions2 +--R +--R DirectProductFunctions2(dim: NonNegativeInteger,A: Type,B: Type) is a package constructor +--R Abbreviation for DirectProductFunctions2 is DIRPROD2 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for DIRPROD2 +--R +--R------------------------------- Operations -------------------------------- +--R map : ((A -> B),DirectProduct(dim,A)) -> DirectProduct(dim,B) +--R reduce : (((A,B) -> B),DirectProduct(dim,A),B) -> B +--R scan : (((A,B) -> B),DirectProduct(dim,A),B) -> DirectProduct(dim,B) +--R --E 1 )spool @@ -14237,6 +14910,17 @@ DirectProductFunctions2(dim, A, B): Exports == Implementation where --S 1 of 1 )show DiscreteLogarithmPackage +--R +--R DiscreteLogarithmPackage(M)where +--R M: Join(Monoid,Finite)with +--R ?**? : (M,Integer) -> M is a package constructor +--R Abbreviation for DiscreteLogarithmPackage is DLP +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for DLP +--R +--R------------------------------- Operations -------------------------------- +--R shanksDiscLogAlgorithm : (M,M,NonNegativeInteger) -> Union(NonNegativeInteger,"failed") +--R --E 1 )spool @@ -14354,6 +15038,21 @@ DiscreteLogarithmPackage(M): public == private where --S 1 of 1 )show DisplayPackage +--R +--R DisplayPackage is a package constructor +--R Abbreviation for DisplayPackage is DISPLAY +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for DISPLAY +--R +--R------------------------------- Operations -------------------------------- +--R bright : String -> List(String) copies : (Integer,String) -> String +--R newLine : () -> String say : String -> Void +--R say : List(String) -> Void sayLength : String -> Integer +--R sayLength : List(String) -> Integer +--R bright : List(String) -> List(String) +--R center : (String,Integer,String) -> String +--R center : (List(String),Integer,String) -> List(String) +--R --E 1 )spool @@ -14513,6 +15212,22 @@ DisplayPackage: public == private where --S 1 of 1 )show DistinctDegreeFactorize +--R +--R DistinctDegreeFactorize(F: FiniteFieldCategory,FP: UnivariatePolynomialCategory(F)) is a package constructor +--R Abbreviation for DistinctDegreeFactorize is DDFACT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for DDFACT +--R +--R------------------------------- Operations -------------------------------- +--R factor : FP -> Factored(FP) irreducible? : FP -> Boolean +--R distdfact : (FP,Boolean) -> Record(cont: F,factors: List(Record(irr: FP,pow: Integer))) +--R exptMod : (FP,NonNegativeInteger,FP) -> FP +--R factorSquareFree : FP -> Factored(FP) +--R separateDegrees : FP -> List(Record(deg: NonNegativeInteger,prod: FP)) +--R separateFactors : List(Record(deg: NonNegativeInteger,prod: FP)) -> List(FP) +--R trace2PowMod : (FP,NonNegativeInteger,FP) -> FP +--R tracePowMod : (FP,NonNegativeInteger,FP) -> FP +--R --E 1 )spool @@ -14826,8 +15541,9 @@ generalized version. --R Issue )edit bookvol10.4.pamphlet to see algebra source code for DFSFUN --R --R------------------------------- Operations -------------------------------- ---R Gamma : DoubleFloat -> DoubleFloat fresnelC : Float -> Float ---R fresnelS : Float -> Float +--R Gamma : DoubleFloat -> DoubleFloat airyAi : DoubleFloat -> DoubleFloat +--R airyBi : DoubleFloat -> DoubleFloat digamma : DoubleFloat -> DoubleFloat +--R fresnelC : Float -> Float fresnelS : Float -> Float --R Beta : (DoubleFloat,DoubleFloat) -> DoubleFloat --R Beta : (Complex(DoubleFloat),Complex(DoubleFloat)) -> Complex(DoubleFloat) --R E1 : DoubleFloat -> OnePointCompletion(DoubleFloat) @@ -14841,8 +15557,6 @@ generalized version. --R En : (Integer,DoubleFloat) -> OnePointCompletion(DoubleFloat) --R Gamma : Complex(DoubleFloat) -> Complex(DoubleFloat) --R airyAi : Complex(DoubleFloat) -> Complex(DoubleFloat) ---R airyAi : DoubleFloat -> DoubleFloat ---R airyBi : DoubleFloat -> DoubleFloat --R airyBi : Complex(DoubleFloat) -> Complex(DoubleFloat) --R besselI : (DoubleFloat,DoubleFloat) -> DoubleFloat --R besselI : (Complex(DoubleFloat),Complex(DoubleFloat)) -> Complex(DoubleFloat) @@ -14852,7 +15566,6 @@ generalized version. --R besselK : (Complex(DoubleFloat),Complex(DoubleFloat)) -> Complex(DoubleFloat) --R besselY : (DoubleFloat,DoubleFloat) -> DoubleFloat --R besselY : (Complex(DoubleFloat),Complex(DoubleFloat)) -> Complex(DoubleFloat) ---R digamma : DoubleFloat -> DoubleFloat --R digamma : Complex(DoubleFloat) -> Complex(DoubleFloat) --R hypergeometric0F1 : (DoubleFloat,DoubleFloat) -> DoubleFloat --R hypergeometric0F1 : (Complex(DoubleFloat),Complex(DoubleFloat)) -> Complex(DoubleFloat) @@ -17783,6 +18496,15 @@ Axiom uses the power series at the zero point: --S 1 of 1 )show DoubleResultantPackage +--R +--R DoubleResultantPackage(F: Field,UP: UnivariatePolynomialCategory(F),UPUP: UnivariatePolynomialCategory(Fraction(UP)),R: FunctionFieldCategory(F,UP,UPUP)) is a package constructor +--R Abbreviation for DoubleResultantPackage is DBLRESP +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for DBLRESP +--R +--R------------------------------- Operations -------------------------------- +--R doubleResultant : (R,(UP -> UP)) -> UP +--R --E 1 )spool @@ -17876,6 +18598,18 @@ DoubleResultantPackage(F, UP, UPUP, R): Exports == Implementation where --S 1 of 1 )show DrawComplex +--R +--R DrawComplex is a package constructor +--R Abbreviation for DrawComplex is DRAWCX +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for DRAWCX +--R +--R------------------------------- Operations -------------------------------- +--R setImagSteps : Integer -> Integer setRealSteps : Integer -> Integer +--R drawComplex : ((Complex(DoubleFloat) -> Complex(DoubleFloat)),Segment(DoubleFloat),Segment(DoubleFloat),Boolean) -> ThreeDimensionalViewport +--R drawComplexVectorField : ((Complex(DoubleFloat) -> Complex(DoubleFloat)),Segment(DoubleFloat),Segment(DoubleFloat)) -> ThreeDimensionalViewport +--R setClipValue : DoubleFloat -> DoubleFloat +--R --E 1 )spool @@ -18097,6 +18831,15 @@ DrawComplex(): Exports == Implementation where --S 1 of 1 )show DrawNumericHack +--R +--R DrawNumericHack(R: Join(OrderedSet,IntegralDomain,ConvertibleTo(Float))) is a package constructor +--R Abbreviation for DrawNumericHack is DRAWHACK +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for DRAWHACK +--R +--R------------------------------- Operations -------------------------------- +--R coerce : SegmentBinding(Expression(R)) -> SegmentBinding(Float) +--R --E 1 )spool @@ -18167,6 +18910,30 @@ DrawNumericHack(R:Join(OrderedSet,IntegralDomain,ConvertibleTo Float)): --S 1 of 1 )show DrawOptionFunctions0 +--R +--R DrawOptionFunctions0 is a package constructor +--R Abbreviation for DrawOptionFunctions0 is DROPT0 +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for DROPT0 +--R +--R------------------------------- Operations -------------------------------- +--R adaptive : (List(DrawOption),Boolean) -> Boolean +--R clipBoolean : (List(DrawOption),Boolean) -> Boolean +--R coord : (List(DrawOption),(Point(DoubleFloat) -> Point(DoubleFloat))) -> (Point(DoubleFloat) -> Point(DoubleFloat)) +--R curveColorPalette : (List(DrawOption),Palette) -> Palette +--R pointColorPalette : (List(DrawOption),Palette) -> Palette +--R ranges : (List(DrawOption),List(Segment(Float))) -> List(Segment(Float)) +--R space : List(DrawOption) -> ThreeSpace(DoubleFloat) +--R style : (List(DrawOption),String) -> String +--R title : (List(DrawOption),String) -> String +--R toScale : (List(DrawOption),Boolean) -> Boolean +--R tubePoints : (List(DrawOption),PositiveInteger) -> PositiveInteger +--R tubeRadius : (List(DrawOption),Float) -> Float +--R units : (List(DrawOption),List(Float)) -> List(Float) +--R var1Steps : (List(DrawOption),PositiveInteger) -> PositiveInteger +--R var2Steps : (List(DrawOption),PositiveInteger) -> PositiveInteger +--R viewpoint : (List(DrawOption),Record(theta: DoubleFloat,phi: DoubleFloat,scale: DoubleFloat,scaleX: DoubleFloat,scaleY: DoubleFloat,scaleZ: DoubleFloat,deltaX: DoubleFloat,deltaY: DoubleFloat)) -> Record(theta: DoubleFloat,phi: DoubleFloat,scale: DoubleFloat,scaleX: DoubleFloat,scaleY: DoubleFloat,scaleZ: DoubleFloat,deltaX: DoubleFloat,deltaY: DoubleFloat) +--R --E 1 )spool @@ -18393,6 +19160,15 @@ DrawOptionFunctions0(): Exports == Implementation where --S 1 of 1 )show DrawOptionFunctions1 +--R +--R DrawOptionFunctions1(S: Type) is a package constructor +--R Abbreviation for DrawOptionFunctions1 is DROPT1 +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for DROPT1 +--R +--R------------------------------- Operations -------------------------------- +--R option : (List(DrawOption),Symbol) -> Union(S,"failed") +--R --E 1 )spool @@ -18458,7 +19234,7 @@ DrawOptionFunctions1(S:Type): Exports == Implementation where )clear all ---S 1 of 1 +--S 1 of 136 )show d01AgentsPackage --R --R d01AgentsPackage is a package constructor @@ -18484,7 +19260,7 @@ DrawOptionFunctions1(S:Type): Exports == Implementation where )clear all ---S 2 +--S 2 of 136 showArrayValues true --R --R @@ -18492,7 +19268,7 @@ showArrayValues true --R Type: Boolean --E 2 ---S 3 +--S 3 of 136 showScalarValues true --R --R @@ -18500,7 +19276,7 @@ showScalarValues true --R Type: Boolean --E 3 ---S 4 +--S 4 of 136 e:EXPR FLOAT:=(X*sin(30*X)/(sqrt(1-(X/(2*%pi))^2))) --R --R @@ -18512,7 +19288,7 @@ e:EXPR FLOAT:=(X*sin(30*X)/(sqrt(1-(X/(2*%pi))^2))) --R Type: Expression(Float) --E 4 ---S 5 +--S 5 of 136 f:ASP1(F):=retract e --R --R @@ -18520,7 +19296,7 @@ f:ASP1(F):=retract e --R Type: Asp1(F) --E 5 ---S 6 +--S 6 of 136 a:SF:=0.0 --R --R @@ -18528,7 +19304,7 @@ a:SF:=0.0 --R Type: DoubleFloat --E 6 ---S 7 +--S 7 of 136 b:SF:=%pi*2 --R --R @@ -18536,7 +19312,7 @@ b:SF:=%pi*2 --R Type: DoubleFloat --E 7 ---S 8 +--S 8 of 136 epsabs:SF:=0.0 --R --R @@ -18544,7 +19320,7 @@ epsabs:SF:=0.0 --R Type: DoubleFloat --E 8 ---S 9 +--S 9 of 136 epsrel:SF:=1.0e-4 --R --R @@ -18552,7 +19328,7 @@ epsrel:SF:=1.0e-4 --R Type: DoubleFloat --E 9 ---S 10 +--S 10 of 136 liw:=200 --R --R @@ -18560,7 +19336,7 @@ liw:=200 --R Type: PositiveInteger --E 10 ---S 11 +--S 11 of 136 lw:=4*liw --R --R @@ -18568,13 +19344,13 @@ lw:=4*liw --R Type: PositiveInteger --E 11 ---S 12 +--S 12 of 136 -- result:=d01ajf(a,b,epsabs,epsrel,lw,liw,-1,f) --E 12 )clear all ---S 13 +--S 13 of 136 showArrayValues true --R --R @@ -18582,7 +19358,7 @@ showArrayValues true --R Type: Boolean --E 13 ---S 14 +--S 14 of 136 showScalarValues true --R --R @@ -18590,7 +19366,7 @@ showScalarValues true --R Type: Boolean --E 14 ---S 15 +--S 15 of 136 e:EXPR FLOAT:=X*sin(30*X)*cos(X) --R --R @@ -18598,7 +19374,7 @@ e:EXPR FLOAT:=X*sin(30*X)*cos(X) --R Type: Expression(Float) --E 15 ---S 16 +--S 16 of 136 f:ASP1(F):=retract e --R --R @@ -18606,7 +19382,7 @@ f:ASP1(F):=retract e --R Type: Asp1(F) --E 16 ---S 17 +--S 17 of 136 a:SF:=0.0 --R --R @@ -18614,7 +19390,7 @@ a:SF:=0.0 --R Type: DoubleFloat --E 17 ---S 18 +--S 18 of 136 b:SF:=%pi*2 --R --R @@ -18622,7 +19398,7 @@ b:SF:=%pi*2 --R Type: DoubleFloat --E 18 ---S 19 +--S 19 of 136 epsabs:SF:=0.0 --R --R @@ -18630,7 +19406,7 @@ epsabs:SF:=0.0 --R Type: DoubleFloat --E 19 ---S 20 +--S 20 of 136 epsrel:SF:=1.0e-4 --R --R @@ -18638,7 +19414,7 @@ epsrel:SF:=1.0e-4 --R Type: DoubleFloat --E 20 ---S 21 +--S 21 of 136 liw:=200 --R --R @@ -18646,7 +19422,7 @@ liw:=200 --R Type: PositiveInteger --E 21 ---S 22 +--S 22 of 136 lw:=4*liw --R --R @@ -18654,13 +19430,13 @@ lw:=4*liw --R Type: PositiveInteger --E 22 ---S 23 +--S 23 of 136 -- result:=d01akf(a,b,epsabs,epsrel,lw,liw,-1,f) --E 23 )clear all ---S 24 +--S 24 of 136 showArrayValues true --R --R @@ -18668,7 +19444,7 @@ showArrayValues true --R Type: Boolean --E 24 ---S 25 +--S 25 of 136 showScalarValues true --R --R @@ -18676,7 +19452,7 @@ showScalarValues true --R Type: Boolean --E 25 ---S 26 +--S 26 of 136 e:EXPR FLOAT:=1/sqrt(abs(X-1/7)) --R --R @@ -18687,7 +19463,7 @@ e:EXPR FLOAT:=1/sqrt(abs(X-1/7)) --R Type: Expression(Float) --E 26 ---S 27 +--S 27 of 136 f:ASP1(F):= retract e --R --R @@ -18695,7 +19471,7 @@ f:ASP1(F):= retract e --R Type: Asp1(F) --E 27 ---S 28 +--S 28 of 136 a:SF:=0.0 --R --R @@ -18703,7 +19479,7 @@ a:SF:=0.0 --R Type: DoubleFloat --E 28 ---S 29 +--S 29 of 136 b:SF:=1.0 --R --R @@ -18711,7 +19487,7 @@ b:SF:=1.0 --R Type: DoubleFloat --E 29 ---S 30 +--S 30 of 136 points:Matrix SF:=[[1/7]] --R --R @@ -18719,7 +19495,7 @@ points:Matrix SF:=[[1/7]] --R Type: Matrix(DoubleFloat) --E 30 ---S 31 +--S 31 of 136 npts:=ncols points --R --R @@ -18727,7 +19503,7 @@ npts:=ncols points --R Type: PositiveInteger --E 31 ---S 32 +--S 32 of 136 epsabs:SF:=0.0 --R --R @@ -18735,7 +19511,7 @@ epsabs:SF:=0.0 --R Type: DoubleFloat --E 32 ---S 33 +--S 33 of 136 epsrel:SF:=1.0e-4 --R --R @@ -18743,7 +19519,7 @@ epsrel:SF:=1.0e-4 --R Type: DoubleFloat --E 33 ---S 34 +--S 34 of 136 liw:=max(npts+4,400) --R --R @@ -18751,7 +19527,7 @@ liw:=max(npts+4,400) --R Type: PositiveInteger --E 34 ---S 35 +--S 35 of 136 lw:=max(2*npts+8,2*liw) --R --R @@ -18759,13 +19535,13 @@ lw:=max(2*npts+8,2*liw) --R Type: PositiveInteger --E 35 ---S 36 +--S 36 of 136 -- result:=d01alf(a,b,npts,points,epsabs,epsrel,lw,liw,-1,f) --E 36 )clear all ---S 37 +--S 37 of 136 showArrayValues true --R --R @@ -18773,7 +19549,7 @@ showArrayValues true --R Type: Boolean --E 37 ---S 38 +--S 38 of 136 showScalarValues true --R --R @@ -18781,7 +19557,7 @@ showScalarValues true --R Type: Boolean --E 38 ---S 39 +--S 39 of 136 e:EXPR FLOAT:=1/((X+1)*sqrt(X)) --R --R @@ -18792,7 +19568,7 @@ e:EXPR FLOAT:=1/((X+1)*sqrt(X)) --R Type: Expression(Float) --E 39 ---S 40 +--S 40 of 136 f:ASP1(F):=retract e --R --R @@ -18800,7 +19576,7 @@ f:ASP1(F):=retract e --R Type: Asp1(F) --E 40 ---S 41 +--S 41 of 136 a:SF:=0.0 --R --R @@ -18808,7 +19584,7 @@ a:SF:=0.0 --R Type: DoubleFloat --E 41 ---S 42 +--S 42 of 136 epsabs:SF:=0.0 --R --R @@ -18816,7 +19592,7 @@ epsabs:SF:=0.0 --R Type: DoubleFloat --E 42 ---S 43 +--S 43 of 136 epsrel:SF:=1.0e-4 --R --R @@ -18824,7 +19600,7 @@ epsrel:SF:=1.0e-4 --R Type: DoubleFloat --E 43 ---S 44 +--S 44 of 136 liw:=200 --R --R @@ -18832,7 +19608,7 @@ liw:=200 --R Type: PositiveInteger --E 44 ---S 45 +--S 45 of 136 lw:=4*liw --R --R @@ -18840,13 +19616,13 @@ lw:=4*liw --R Type: PositiveInteger --E 45 ---S 46 +--S 46 of 136 -- result:=d01amf(a,1,epsabs,epsrel,lw,liw,-1,f) --E 46 )clear all ---S 47 +--S 47 of 136 showArrayValues true --R --R @@ -18854,7 +19630,7 @@ showArrayValues true --R Type: Boolean --E 47 ---S 48 +--S 48 of 136 showScalarValues true --R --R @@ -18862,7 +19638,7 @@ showScalarValues true --R Type: Boolean --E 48 ---S 49 +--S 49 of 136 e:EXPR FLOAT:=log(X) --R --R @@ -18870,7 +19646,7 @@ e:EXPR FLOAT:=log(X) --R Type: Expression(Float) --E 49 ---S 50 +--S 50 of 136 f:ASP1(G):=retract e --R --R @@ -18878,7 +19654,7 @@ f:ASP1(G):=retract e --R Type: Asp1(G) --E 50 ---S 51 +--S 51 of 136 a:SF:=1.0e-6 --R --R @@ -18886,7 +19662,7 @@ a:SF:=1.0e-6 --R Type: DoubleFloat --E 51 ---S 52 +--S 52 of 136 b:SF:=1.0 --R --R @@ -18894,7 +19670,7 @@ b:SF:=1.0 --R Type: DoubleFloat --E 52 ---S 53 +--S 53 of 136 epsabs:SF:=0.0 --R --R @@ -18902,7 +19678,7 @@ epsabs:SF:=0.0 --R Type: DoubleFloat --E 53 ---S 54 +--S 54 of 136 epsrel:SF:=1.0e-4 --R --R @@ -18910,7 +19686,7 @@ epsrel:SF:=1.0e-4 --R Type: DoubleFloat --E 54 ---S 55 +--S 55 of 136 omega:SF:=10*%pi --R --R @@ -18918,7 +19694,7 @@ omega:SF:=10*%pi --R Type: DoubleFloat --E 55 ---S 56 +--S 56 of 136 liw:=max(400,2) --R --R @@ -18926,7 +19702,7 @@ liw:=max(400,2) --R Type: PositiveInteger --E 56 ---S 57 +--S 57 of 136 lw:=max(2*liw,4) --R --R @@ -18934,13 +19710,13 @@ lw:=max(2*liw,4) --R Type: PositiveInteger --E 57 ---S 58 +--S 58 of 136 -- result:=d01anf(a,b,omega,2,epsabs,epsrel,lw,liw,-1,f) --E 58 )clear all ---S 59 +--S 59 of 136 showArrayValues true --R --R @@ -18948,7 +19724,7 @@ showArrayValues true --R Type: Boolean --E 59 ---S 60 +--S 60 of 136 showScalarValues true --R --R @@ -18956,7 +19732,7 @@ showScalarValues true --R Type: Boolean --E 60 ---S 61 +--S 61 of 136 e:Expression Float:=sin(10*X) --R --R @@ -18964,7 +19740,7 @@ e:Expression Float:=sin(10*X) --R Type: Expression(Float) --E 61 ---S 62 +--S 62 of 136 f:ASP1(G):=retract e --R --R @@ -18972,7 +19748,7 @@ f:ASP1(G):=retract e --R Type: Asp1(G) --E 62 ---S 63 +--S 63 of 136 a:SF:=1.0e-6 --R --R @@ -18980,7 +19756,7 @@ a:SF:=1.0e-6 --R Type: DoubleFloat --E 63 ---S 64 +--S 64 of 136 b:SF:=1.0 --R --R @@ -18988,7 +19764,7 @@ b:SF:=1.0 --R Type: DoubleFloat --E 64 ---S 65 +--S 65 of 136 alpha:SF:=-0.5 --R --R @@ -18996,7 +19772,7 @@ alpha:SF:=-0.5 --R Type: DoubleFloat --E 65 ---S 66 +--S 66 of 136 beta:SF:=-0.5 --R --R @@ -19004,7 +19780,7 @@ beta:SF:=-0.5 --R Type: DoubleFloat --E 66 ---S 67 +--S 67 of 136 epsabs:SF:=0.0 --R --R @@ -19012,7 +19788,7 @@ epsabs:SF:=0.0 --R Type: DoubleFloat --E 67 ---S 68 +--S 68 of 136 epsrel:SF:=1.0e-4 --R --R @@ -19020,7 +19796,7 @@ epsrel:SF:=1.0e-4 --R Type: DoubleFloat --E 68 ---S 69 +--S 69 of 136 key:=1 --R --R @@ -19028,7 +19804,7 @@ key:=1 --R Type: PositiveInteger --E 69 ---S 70 +--S 70 of 136 liw:=200 --R --R @@ -19036,7 +19812,7 @@ liw:=200 --R Type: PositiveInteger --E 70 ---S 71 +--S 71 of 136 lw:=4*liw --R --R @@ -19044,13 +19820,13 @@ lw:=4*liw --R Type: PositiveInteger --E 71 ---S 72 +--S 72 of 136 -- result:=d01apf(a,b,alpha,beta,key,epsabs,epsrel,lw,liw,-1,f) --E 72 )clear all ---S 73 +--S 73 of 136 showArrayValues true --R --R @@ -19058,7 +19834,7 @@ showArrayValues true --R Type: Boolean --E 73 ---S 74 +--S 74 of 136 showScalarValues true --R --R @@ -19066,7 +19842,7 @@ showScalarValues true --R Type: Boolean --E 74 ---S 75 +--S 75 of 136 e:Expression Float:=(X^2+0.01^2)^-1 --R --R @@ -19077,7 +19853,7 @@ e:Expression Float:=(X^2+0.01^2)^-1 --R Type: Expression(Float) --E 75 ---S 76 +--S 76 of 136 f:ASP1(G):=retract e --R --R @@ -19085,7 +19861,7 @@ f:ASP1(G):=retract e --R Type: Asp1(G) --E 76 ---S 77 +--S 77 of 136 a:SF:=-1.0 --R --R @@ -19093,7 +19869,7 @@ a:SF:=-1.0 --R Type: DoubleFloat --E 77 ---S 78 +--S 78 of 136 b:SF:=1.0 --R --R @@ -19101,7 +19877,7 @@ b:SF:=1.0 --R Type: DoubleFloat --E 78 ---S 79 +--S 79 of 136 c:SF:=0.5 --R --R @@ -19109,7 +19885,7 @@ c:SF:=0.5 --R Type: DoubleFloat --E 79 ---S 80 +--S 80 of 136 epsabs:SF:=0.0 --R --R @@ -19117,7 +19893,7 @@ epsabs:SF:=0.0 --R Type: DoubleFloat --E 80 ---S 81 +--S 81 of 136 epsrel:SF:=1.0e-4 --R --R @@ -19125,7 +19901,7 @@ epsrel:SF:=1.0e-4 --R Type: DoubleFloat --E 81 ---S 82 +--S 82 of 136 liw:=200 --R --R @@ -19133,7 +19909,7 @@ liw:=200 --R Type: PositiveInteger --E 82 ---S 83 +--S 83 of 136 lw:=4*200 --R --R @@ -19141,13 +19917,13 @@ lw:=4*200 --R Type: PositiveInteger --E 83 ---S 84 +--S 84 of 136 -- result:=d01aqf(a,b,c,epsabs,epsrel,lw,liw,-1,f) --E 84 )clear all ---S 85 +--S 85 of 136 showArrayValues true --R --R @@ -19155,7 +19931,7 @@ showArrayValues true --R Type: Boolean --E 85 ---S 86 +--S 86 of 136 showScalarValues true --R --R @@ -19163,7 +19939,7 @@ showScalarValues true --R Type: Boolean --E 86 ---S 87 +--S 87 of 136 e:Expression Float:=1/sqrt(X) --R --R @@ -19174,7 +19950,7 @@ e:Expression Float:=1/sqrt(X) --R Type: Expression(Float) --E 87 ---S 88 +--S 88 of 136 f:ASP1(G):=retract e --R --R @@ -19182,7 +19958,7 @@ f:ASP1(G):=retract e --R Type: Asp1(G) --E 88 ---S 89 +--S 89 of 136 a:SF:=1.0e-12 --R --R @@ -19190,7 +19966,7 @@ a:SF:=1.0e-12 --R Type: DoubleFloat --E 89 ---S 90 +--S 90 of 136 omega:SF:=%pi/2 --R --R @@ -19198,7 +19974,7 @@ omega:SF:=%pi/2 --R Type: DoubleFloat --E 90 ---S 91 +--S 91 of 136 key:=1 --R --R @@ -19206,7 +19982,7 @@ key:=1 --R Type: PositiveInteger --E 91 ---S 92 +--S 92 of 136 epsabs:SF:=1.0e-3 --R --R @@ -19214,7 +19990,7 @@ epsabs:SF:=1.0e-3 --R Type: DoubleFloat --E 92 ---S 93 +--S 93 of 136 limlst:=50 --R --R @@ -19222,7 +19998,7 @@ limlst:=50 --R Type: PositiveInteger --E 93 ---S 94 +--S 94 of 136 liw:=400 --R --R @@ -19230,7 +20006,7 @@ liw:=400 --R Type: PositiveInteger --E 94 ---S 95 +--S 95 of 136 lw:=2*liw --R --R @@ -19238,13 +20014,13 @@ lw:=2*liw --R Type: PositiveInteger --E 95 ---S 96 +--S 96 of 136 -- result:=d01asf(a,omega,key,epsabs,limlst,lw,liw,-1,f) --E 96 )clear all ---S 97 +--S 97 of 136 showArrayValues true --R --R @@ -19252,7 +20028,7 @@ showArrayValues true --R Type: Boolean --E 97 ---S 98 +--S 98 of 136 showScalarValues true --R --R @@ -19260,7 +20036,7 @@ showScalarValues true --R Type: Boolean --E 98 ---S 99 +--S 99 of 136 a:SF:=0.0 --R --R @@ -19268,7 +20044,7 @@ a:SF:=0.0 --R Type: DoubleFloat --E 99 ---S 100 +--S 100 of 136 b:SF:=1.0 --R --R @@ -19276,7 +20052,7 @@ b:SF:=1.0 --R Type: DoubleFloat --E 100 ---S 101 +--S 101 of 136 itype:=1 --R --R @@ -19284,7 +20060,7 @@ itype:=1 --R Type: PositiveInteger --E 101 ---S 102 +--S 102 of 136 n:=6 --R --R @@ -19292,7 +20068,7 @@ n:=6 --R Type: PositiveInteger --E 102 ---S 103 +--S 103 of 136 kind:=0 --R --R @@ -19300,13 +20076,13 @@ kind:=0 --R Type: NonNegativeInteger --E 103 ---S 104 +--S 104 of 136 -- result:=d01bbf(a,b,itype,n,kind,-1) --E 104 )clear all ---S 105 +--S 105 of 136 showArrayValues true --R --R @@ -19314,7 +20090,7 @@ showArrayValues true --R Type: Boolean --E 105 ---S 106 +--S 106 of 136 showScalarValues true --R --R @@ -19322,7 +20098,7 @@ showScalarValues true --R Type: Boolean --E 106 ---S 107 +--S 107 of 136 e:= (4.0*X[1]*X[3]*X[3]*exp(2.0*X[1]*X[3])/((1.0+X[2]+X[4])^2))::EXPR FLOAT --R --R @@ -19337,7 +20113,7 @@ e:= (4.0*X[1]*X[3]*X[3]*exp(2.0*X[1]*X[3])/((1.0+X[2]+X[4])^2))::EXPR FLOAT --R Type: Expression(Float) --E 107 ---S 108 +--S 108 of 136 f:ASP4(FUNCTN):=retract e --R --R @@ -19345,7 +20121,7 @@ f:ASP4(FUNCTN):=retract e --R Type: Asp4(FUNCTN) --E 108 ---S 109 +--S 109 of 136 ndim:=4 --R --R @@ -19353,7 +20129,7 @@ ndim:=4 --R Type: PositiveInteger --E 109 ---S 110 +--S 110 of 136 a:Matrix SF:=[[0.0,0.0,0.0,0.0]] --R --R @@ -19361,7 +20137,7 @@ a:Matrix SF:=[[0.0,0.0,0.0,0.0]] --R Type: Matrix(DoubleFloat) --E 110 ---S 111 +--S 111 of 136 b:Matrix SF:=[[1.0,1.0,1.0,1.0]] --R --R @@ -19369,7 +20145,7 @@ b:Matrix SF:=[[1.0,1.0,1.0,1.0]] --R Type: Matrix(DoubleFloat) --E 111 ---S 112 +--S 112 of 136 alpha:=2^ndim+2*ndim^2+2*ndim+1 --R --R @@ -19377,7 +20153,7 @@ alpha:=2^ndim+2*ndim^2+2*ndim+1 --R Type: PositiveInteger --E 112 ---S 113 +--S 113 of 136 minpts:=1000 --R --R @@ -19385,7 +20161,7 @@ minpts:=1000 --R Type: PositiveInteger --E 113 ---S 114 +--S 114 of 136 maxpts:=5700 --R --R @@ -19393,7 +20169,7 @@ maxpts:=5700 --R Type: PositiveInteger --E 114 ---S 115 +--S 115 of 136 eps:=0.0001 --R --R @@ -19401,7 +20177,7 @@ eps:=0.0001 --R Type: Float --E 115 ---S 116 +--S 116 of 136 lenwrk:=606 --R --R @@ -19409,13 +20185,13 @@ lenwrk:=606 --R Type: PositiveInteger --E 116 ---S 117 +--S 117 of 136 -- result:=d01fcf(ndim,a,b,maxpts,eps,lenwrk,minpts,-1,f) --E 117 )clear all ---S 118 +--S 118 of 136 showArrayValues true --R --R @@ -19423,7 +20199,7 @@ showArrayValues true --R Type: Boolean --E 118 ---S 119 +--S 119 of 136 showScalarValues true --R --R @@ -19431,7 +20207,7 @@ showScalarValues true --R Type: Boolean --E 119 ---S 120 +--S 120 of 136 n:=21 --R --R @@ -19439,7 +20215,7 @@ n:=21 --R Type: PositiveInteger --E 120 ---S 121 +--S 121 of 136 x:Matrix SF:= [[0.00 ,0.04 ,0.08 ,0.12 ,0.22 ,0.26 ,0.30 ,_ 0.38 ,0.39 ,0.42 ,0.45 ,0.46 ,0.60 ,0.68 ,_ @@ -19458,7 +20234,7 @@ x:Matrix SF:= --R Type: Matrix(DoubleFloat) --E 121 ---S 122 +--S 122 of 136 y:Matrix SF:= [[4.0000 ,3.9936 ,3.9746 ,3.9432 ,3.8153 ,3.7467 ,3.6697 ,_ 3.4943 ,3.4719 ,3.4002 ,3.3264 ,3.3014 ,2.9412 ,2.7352 ,_ @@ -19477,13 +20253,13 @@ y:Matrix SF:= --R Type: Matrix(DoubleFloat) --E 122 ---S 123 +--S 123 of 136 -- result:=d01gaf(x,y,n,-1) --E 123 )clear all ---S 124 +--S 124 of 136 showArrayValues true --R --R @@ -19491,7 +20267,7 @@ showArrayValues true --R Type: Boolean --E 124 ---S 125 +--S 125 of 136 showScalarValues true --R --R @@ -19499,7 +20275,7 @@ showScalarValues true --R Type: Boolean --E 125 ---S 126 +--S 126 of 136 ndim:=4 --R --R @@ -19507,7 +20283,7 @@ ndim:=4 --R Type: PositiveInteger --E 126 ---S 127 +--S 127 of 136 e:=(4.0*X[1]*X[3]*X[3]*exp(2.0*X[1]*X[3])/((1.0+X[2]+X[4])^2)) --R --R @@ -19522,7 +20298,7 @@ e:=(4.0*X[1]*X[3]*X[3]*exp(2.0*X[1]*X[3])/((1.0+X[2]+X[4])^2)) --R Type: Expression(Float) --E 127 ---S 128 +--S 128 of 136 f:ASP4(FUNCTN):=retract e --R --R @@ -19530,7 +20306,7 @@ f:ASP4(FUNCTN):=retract e --R Type: Asp4(FUNCTN) --E 128 ---S 129 +--S 129 of 136 a:Matrix SF:=[[0.0,0.0,0.0,0.0]] --R --R @@ -19538,7 +20314,7 @@ a:Matrix SF:=[[0.0,0.0,0.0,0.0]] --R Type: Matrix(DoubleFloat) --E 129 ---S 130 +--S 130 of 136 b:Matrix SF:=[[1.0,1.0,1.0,1.0]] --R --R @@ -19546,7 +20322,7 @@ b:Matrix SF:=[[1.0,1.0,1.0,1.0]] --R Type: Matrix(DoubleFloat) --E 130 ---S 131 +--S 131 of 136 maxcls:=20000 --R --R @@ -19554,7 +20330,7 @@ maxcls:=20000 --R Type: PositiveInteger --E 131 ---S 132 +--S 132 of 136 eps:=0.01 --R --R @@ -19562,7 +20338,7 @@ eps:=0.01 --R Type: Float --E 132 ---S 133 +--S 133 of 136 lenwrk:=500 --R --R @@ -19570,14 +20346,14 @@ lenwrk:=500 --R Type: PositiveInteger --E 133 ---S 134 +--S 134 of 136 wrk:Matrix SF:=new(1,lenwrk,0.0); --R --R --R Type: Matrix(DoubleFloat) --E 134 ---S 135 +--S 135 of 136 mincls:=1000 --R --R @@ -19585,7 +20361,7 @@ mincls:=1000 --R Type: PositiveInteger --E 135 ---S 136 +--S 136 of 136 -- result:=d01gbf(ndim,a,b,maxcls,eps,lenwrk,mincls,wrk,-1,f) --E 136 @@ -19922,6 +20698,17 @@ d01AgentsPackage(): E == I where --S 1 of 1 )show d01WeightsPackage +--R +--R d01WeightsPackage is a package constructor +--R Abbreviation for d01WeightsPackage is D01WGTS +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for D01WGTS +--R +--R------------------------------- Operations -------------------------------- +--R exprHasAlgebraicWeight : Record(var: Symbol,fn: Expression(DoubleFloat),range: Segment(OrderedCompletion(DoubleFloat)),abserr: DoubleFloat,relerr: DoubleFloat) -> Union(List(DoubleFloat),"failed") +--R exprHasLogarithmicWeights : Record(var: Symbol,fn: Expression(DoubleFloat),range: Segment(OrderedCompletion(DoubleFloat)),abserr: DoubleFloat,relerr: DoubleFloat) -> Integer +--R exprHasWeightCosWXorSinWX : Record(var: Symbol,fn: Expression(DoubleFloat),range: Segment(OrderedCompletion(DoubleFloat)),abserr: DoubleFloat,relerr: DoubleFloat) -> Union(Record(op: BasicOperator,w: DoubleFloat),"failed") +--R --E 1 )spool @@ -22699,6 +23486,22 @@ d03AgentsPackage(): E == I where --S 1 of 1 )show EigenPackage +--R +--R EigenPackage(R: GcdDomain) is a package constructor +--R Abbreviation for EigenPackage is EP +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for EP +--R +--R------------------------------- Operations -------------------------------- +--R characteristicPolynomial : (Matrix(Fraction(Polynomial(R))),Symbol) -> Polynomial(R) +--R characteristicPolynomial : Matrix(Fraction(Polynomial(R))) -> Polynomial(R) +--R eigenvalues : Matrix(Fraction(Polynomial(R))) -> List(Union(Fraction(Polynomial(R)),SuchThat(Symbol,Polynomial(R)))) +--R eigenvector : (Union(Fraction(Polynomial(R)),SuchThat(Symbol,Polynomial(R))),Matrix(Fraction(Polynomial(R)))) -> List(Matrix(Fraction(Polynomial(R)))) +--R eigenvectors : Matrix(Fraction(Polynomial(R))) -> List(Record(eigval: Union(Fraction(Polynomial(R)),SuchThat(Symbol,Polynomial(R))),eigmult: NonNegativeInteger,eigvec: List(Matrix(Fraction(Polynomial(R)))))) +--R generalizedEigenvector : (Union(Fraction(Polynomial(R)),SuchThat(Symbol,Polynomial(R))),Matrix(Fraction(Polynomial(R))),NonNegativeInteger,NonNegativeInteger) -> List(Matrix(Fraction(Polynomial(R)))) +--R generalizedEigenvector : (Record(eigval: Union(Fraction(Polynomial(R)),SuchThat(Symbol,Polynomial(R))),eigmult: NonNegativeInteger,eigvec: List(Matrix(Fraction(Polynomial(R))))),Matrix(Fraction(Polynomial(R)))) -> List(Matrix(Fraction(Polynomial(R)))) +--R generalizedEigenvectors : Matrix(Fraction(Polynomial(R))) -> List(Record(eigval: Union(Fraction(Polynomial(R)),SuchThat(Symbol,Polynomial(R))),geneigvec: List(Matrix(Fraction(Polynomial(R)))))) +--R --E 1 )spool @@ -22989,7 +23792,7 @@ EigenPackage(R) : C == T )set message auto off )clear all ---S 1 of 32 +--S 1 of 33 )trace EF --R --R @@ -22997,7 +23800,7 @@ EigenPackage(R) : C == T --R EF --E 1 ---S 2 of 32 +--S 2 of 33 D(cos(3*x+6*y),x) --I --I1 (1 0 . 6) (0 1 # (1 0 . 3))) 0 . 1) @@ -23029,7 +23832,7 @@ D(cos(3*x+6*y),x) --R Type: Expression(Integer) --E 2 ---S 3 of 32 +--S 3 of 33 )trace )off --R --R @@ -23038,7 +23841,7 @@ D(cos(3*x+6*y),x) --E 3 ---S 4 of 32 +--S 4 of 33 D(sin(3*x+6*y),x) --R --R @@ -23046,7 +23849,7 @@ D(sin(3*x+6*y),x) --R Type: Expression(Integer) --E 4 ---S 5 of 32 +--S 5 of 33 D(cos(3*x+6*y),x) --R --R @@ -23060,7 +23863,7 @@ $3 sec(3*x+6*y)^2$ but Maple returns the same result as Axiom. They are equivalent results. \begin{chunk}{ElementaryFunction.input} ---S 6 of 32 +--S 6 of 33 D(tan(3*x+6*y),x) --R --R @@ -23069,7 +23872,7 @@ D(tan(3*x+6*y),x) --R Type: Expression(Integer) --E 6 ---S 7 of 32 +--S 7 of 33 simplify ((3*tan(6*y+3*x)^2+3) - (3*sec(3*x+6*y)^2)) --R --R @@ -23082,7 +23885,7 @@ Note that Mathematica and Maxima return $-3 csc(3x+6y)^2$ and Maple returns the same form as Axiom. They are equivalent. \begin{chunk}{ElementaryFunction.input} ---S 8 of 32 +--S 8 of 33 D(cot(3*x+6*y),x) --R --R @@ -23091,7 +23894,7 @@ D(cot(3*x+6*y),x) --R Type: Expression(Integer) --E 8 ---S 9 of 32 +--S 9 of 33 simplify ((-3*cot(6*y+3*x)^2-3) -(-3*csc(3*x+6*y)^2)) --R --R @@ -23099,7 +23902,7 @@ simplify ((-3*cot(6*y+3*x)^2-3) -(-3*csc(3*x+6*y)^2)) --R Type: Expression(Integer) --E 9 ---S 10 of 32 +--S 10 of 33 D(sec(3*x+6*y),x) --R --R @@ -23107,7 +23910,7 @@ D(sec(3*x+6*y),x) --R Type: Expression(Integer) --E 10 ---S 11 of 32 +--S 11 of 33 D(csc(3*x+6*y),x) --R --R @@ -23115,7 +23918,7 @@ D(csc(3*x+6*y),x) --R Type: Expression(Integer) --E 11 ---S 12 of 32 +--S 12 of 33 D(asin(3*x+6*y),x) --R --R @@ -23127,7 +23930,7 @@ D(asin(3*x+6*y),x) --R Type: Expression(Integer) --E 12 ---S 13 of 32 +--S 13 of 33 D(acos(3*x+6*y),x) --R --R @@ -23139,7 +23942,7 @@ D(acos(3*x+6*y),x) --R Type: Expression(Integer) --E 13 ---S 14 of 32 +--S 14 of 33 D(atan(3*x+6*y),x) --R --R @@ -23150,7 +23953,7 @@ D(atan(3*x+6*y),x) --R Type: Expression(Integer) --E 14 ---S 15 of 32 +--S 15 of 33 D(acot(3*x+6*y),x) --R --R @@ -23168,7 +23971,7 @@ which proceeds directly from the formula for the derivative of asec: \[\frac{d}{dx}arcsec(x) = \frac{1}{x\sqrt{x^2-1}}\] \begin{chunk}{ElementaryFunction.input} ---S 16 of 32 +--S 16 of 33 D(asec(3*x+6*y),x) --R --R @@ -23185,7 +23988,7 @@ If we use the same formula for this example: \[\frac{1}{(3*x+6*y)\sqrt{(3*x+6*y)^2-1}} d(3*x+6*y)/dx\] \begin{chunk}{ElementaryFunction.input} ---S 17 of 32 +--S 17 of 33 3/((3*x+6*y)*sqrt((3*x+6*y)^2-1)) --R --R @@ -23204,7 +24007,7 @@ which is just the negative of the above result and we can see that the same analysis applies to explain the results. \begin{chunk}{ElementaryFunction.input} ---S 18 of 32 +--S 18 of 33 D(acsc(3*x+6*y),x) --R --R @@ -23216,7 +24019,7 @@ D(acsc(3*x+6*y),x) --R Type: Expression(Integer) --E 18 ---S 19 of 32 +--S 19 of 33 D(sinh(3*x+6*y),x) --R --R @@ -23224,7 +24027,7 @@ D(sinh(3*x+6*y),x) --R Type: Expression(Integer) --E 19 ---S 20 of 32 +--S 20 of 33 D(cosh(3*x+6*y),x) --R --R @@ -23238,7 +24041,7 @@ Mathematica and Maxima return Maple returns Axiom's answer. Both are equivalent. \begin{chunk}{ElementaryFunction.input} ---S 21 of 32 +--S 21 of 33 D(tanh(3*x+6*y),x) --R --R @@ -23247,7 +24050,7 @@ D(tanh(3*x+6*y),x) --R Type: Expression(Integer) --E 21 ---S 22 of 32 +--S 22 of 33 simplify ((-3*tanh(6*y+3*x)^2+3)-(3*sech(3*x+6*y)^2)) --R --R @@ -23261,7 +24064,7 @@ Mathematica and Maxima return Maple returns Axiom's answer. Both are equivalent. \begin{chunk}{ElementaryFunction.input} ---S 23 of 32 +--S 23 of 33 D(coth(3*x+6*y),x) --R --R @@ -23270,7 +24073,7 @@ D(coth(3*x+6*y),x) --R Type: Expression(Integer) --E 23 ---S 24 of 32 +--S 24 of 33 simplify ((-3*coth(6*y+3*x)^2+3) - (-3*csch(3*x+6*y)^2)) --R --R @@ -23278,7 +24081,7 @@ simplify ((-3*coth(6*y+3*x)^2+3) - (-3*csch(3*x+6*y)^2)) --R Type: Expression(Integer) --E 24 ---S 25 of 32 +--S 25 of 33 D(sech(3*x+6*y),x) --R --R @@ -23286,7 +24089,7 @@ D(sech(3*x+6*y),x) --R Type: Expression(Integer) --E 25 ---S 26 of 32 +--S 26 of 33 D(csch(3*x+6*y),x) --R --R @@ -23294,7 +24097,7 @@ D(csch(3*x+6*y),x) --R Type: Expression(Integer) --E 26 ---S 27 of 32 +--S 27 of 33 D(asinh(3*x+6*y),x) --R --R @@ -23312,7 +24115,7 @@ Mathematica and Maple show Maxima gives Axiom's answer. Both are equivalent, just factored forms. \begin{chunk}{ElementaryFunction.input} ---S 28 of 32 +--S 28 of 33 D(acosh(3*x+6*y),x) --R --R @@ -23324,7 +24127,7 @@ D(acosh(3*x+6*y),x) --R Type: Expression(Integer) --E 28 ---S 29 of 32 +--S 29 of 33 D(atanh(3*x+6*y),x) --R --R @@ -23335,7 +24138,7 @@ D(atanh(3*x+6*y),x) --R Type: Expression(Integer) --E 29 ---S 30 of 32 +--S 30 of 33 D(acoth(3*x+6*y),x) --R --R @@ -23358,7 +24161,7 @@ Axiom cannot simplify these differences to zero but Maxima does which shows they are all equivalent answers. \begin{chunk}{ElementaryFunction.input} ---S 31 of 32 +--S 31 of 33 D(asech(3*x+6*y),x) --R --R @@ -23378,7 +24181,7 @@ Axiom cannot simplify these differences to zero but Maxima does which shows they are all equivalent answers. \begin{chunk}{ElementaryFunction.input} ---S 32 of 32 +--S 32 of 33 D(acsch(3*x+6*y),x) --R --R @@ -23390,6 +24193,49 @@ D(acsch(3*x+6*y),x) --R Type: Expression(Integer) --E 32 +--S 33 of 33 +)show ElementaryFunction +--R +--R ElementaryFunction(R: Join(OrderedSet,IntegralDomain),F: Join(FunctionSpace(R),RadicalCategory)) is a package constructor +--R Abbreviation for ElementaryFunction is EF +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for EF +--R +--R------------------------------- Operations -------------------------------- +--R acos : F -> F acosh : F -> F +--R acot : F -> F acoth : F -> F +--R acsc : F -> F acsch : F -> F +--R asec : F -> F asech : F -> F +--R asin : F -> F asinh : F -> F +--R atan : F -> F atanh : F -> F +--R belong? : BasicOperator -> Boolean cos : F -> F +--R cosh : F -> F cot : F -> F +--R coth : F -> F csc : F -> F +--R csch : F -> F exp : F -> F +--R iiacos : F -> F iiacosh : F -> F +--R iiacot : F -> F iiacoth : F -> F +--R iiacsc : F -> F iiacsch : F -> F +--R iiasec : F -> F iiasech : F -> F +--R iiasin : F -> F iiasinh : F -> F +--R iiatan : F -> F iiatanh : F -> F +--R iicos : F -> F iicosh : F -> F +--R iicot : F -> F iicoth : F -> F +--R iicsc : F -> F iicsch : F -> F +--R iiexp : F -> F iilog : F -> F +--R iisec : F -> F iisech : F -> F +--R iisin : F -> F iisinh : F -> F +--R iisqrt2 : () -> F iisqrt3 : () -> F +--R iitan : F -> F iitanh : F -> F +--R localReal? : F -> Boolean log : F -> F +--R pi : () -> F sec : F -> F +--R sech : F -> F sin : F -> F +--R sinh : F -> F tan : F -> F +--R tanh : F -> F +--R operator : BasicOperator -> BasicOperator +--R specialTrigs : (F,List(Record(func: F,pole: Boolean))) -> Union(F,"failed") +--R +--E 33 + )spool )lisp (bye) \end{chunk} @@ -24466,6 +25312,17 @@ ElementaryFunction(R, F): Exports == Implementation where --S 1 of 1 )show ElementaryFunctionDefiniteIntegration +--R +--R ElementaryFunctionDefiniteIntegration(R: Join(EuclideanDomain,OrderedSet,CharacteristicZero,RetractableTo(Integer),LinearlyExplicitRingOver(Integer)),F: Join(TranscendentalFunctionCategory,PrimitiveFunctionCategory,AlgebraicallyClosedFunctionSpace(R))) is a package constructor +--R Abbreviation for ElementaryFunctionDefiniteIntegration is DEFINTEF +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for DEFINTEF +--R +--R------------------------------- Operations -------------------------------- +--R innerint : (F,Symbol,OrderedCompletion(F),OrderedCompletion(F),Boolean) -> Union(f1: OrderedCompletion(F),f2: List(OrderedCompletion(F)),fail: failed,pole: potentialPole) +--R integrate : (F,SegmentBinding(OrderedCompletion(F))) -> Union(f1: OrderedCompletion(F),f2: List(OrderedCompletion(F)),fail: failed,pole: potentialPole) +--R integrate : (F,SegmentBinding(OrderedCompletion(F)),String) -> Union(f1: OrderedCompletion(F),f2: List(OrderedCompletion(F)),fail: failed,pole: potentialPole) +--R --E 1 )spool @@ -24723,6 +25580,16 @@ ElementaryFunctionDefiniteIntegration(R, F): Exports == Implementation where --S 1 of 1 )show ElementaryFunctionLODESolver +--R +--R ElementaryFunctionLODESolver(R: Join(OrderedSet,EuclideanDomain,RetractableTo(Integer),LinearlyExplicitRingOver(Integer),CharacteristicZero),F: Join(AlgebraicallyClosedFunctionSpace(R),TranscendentalFunctionCategory,PrimitiveFunctionCategory),L: LinearOrdinaryDifferentialOperatorCategory(F)) is a package constructor +--R Abbreviation for ElementaryFunctionLODESolver is LODEEF +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for LODEEF +--R +--R------------------------------- Operations -------------------------------- +--R solve : (L,F,Symbol) -> Union(Record(particular: F,basis: List(F)),"failed") +--R solve : (L,F,Symbol,F,List(F)) -> Union(F,"failed") +--R --E 1 )spool @@ -25021,6 +25888,22 @@ ElementaryFunctionLODESolver(R, F, L): Exports == Implementation where --S 1 of 1 )show ElementaryFunctionODESolver +--R +--R ElementaryFunctionODESolver(R: Join(OrderedSet,EuclideanDomain,RetractableTo(Integer),LinearlyExplicitRingOver(Integer),CharacteristicZero),F: Join(AlgebraicallyClosedFunctionSpace(R),TranscendentalFunctionCategory,PrimitiveFunctionCategory)) is a package constructor +--R Abbreviation for ElementaryFunctionODESolver is ODEEF +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for ODEEF +--R +--R------------------------------- Operations -------------------------------- +--R solve : (Matrix(F),Vector(F),Symbol) -> Union(Record(particular: Vector(F),basis: List(Vector(F))),"failed") +--R solve : (Matrix(F),Symbol) -> Union(List(Vector(F)),"failed") +--R solve : (List(Equation(F)),List(BasicOperator),Symbol) -> Union(Record(particular: Vector(F),basis: List(Vector(F))),"failed") +--R solve : (List(F),List(BasicOperator),Symbol) -> Union(Record(particular: Vector(F),basis: List(Vector(F))),"failed") +--R solve : (Equation(F),BasicOperator,Symbol) -> Union(Record(particular: F,basis: List(F)),F,"failed") +--R solve : (F,BasicOperator,Symbol) -> Union(Record(particular: F,basis: List(F)),F,"failed") +--R solve : (Equation(F),BasicOperator,Equation(F),List(F)) -> Union(F,"failed") +--R solve : (F,BasicOperator,Equation(F),List(F)) -> Union(F,"failed") +--R --E 1 )spool @@ -25325,6 +26208,17 @@ ElementaryFunctionODESolver(R, F): Exports == Implementation where --S 1 of 1 )show ElementaryFunctionSign +--R +--R ElementaryFunctionSign(R: Join(IntegralDomain,OrderedSet,RetractableTo(Integer),LinearlyExplicitRingOver(Integer),GcdDomain),F: Join(AlgebraicallyClosedField,TranscendentalFunctionCategory,FunctionSpace(R))) is a package constructor +--R Abbreviation for ElementaryFunctionSign is SIGNEF +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for SIGNEF +--R +--R------------------------------- Operations -------------------------------- +--R sign : F -> Union(Integer,"failed") +--R sign : (F,Symbol,OrderedCompletion(F)) -> Union(Integer,"failed") +--R sign : (F,Symbol,F,String) -> Union(Integer,"failed") +--R --E 1 )spool @@ -25552,6 +26446,19 @@ ElementaryFunctionSign(R,F): Exports == Implementation where --S 1 of 1 )show ElementaryFunctionStructurePackage +--R +--R ElementaryFunctionStructurePackage(R: Join(IntegralDomain,OrderedSet,RetractableTo(Integer),LinearlyExplicitRingOver(Integer)),F: Join(AlgebraicallyClosedField,TranscendentalFunctionCategory,FunctionSpace(R))) is a package constructor +--R Abbreviation for ElementaryFunctionStructurePackage is EFSTRUC +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for EFSTRUC +--R +--R------------------------------- Operations -------------------------------- +--R normalize : F -> F normalize : (F,Symbol) -> F +--R realElementary : F -> F realElementary : (F,Symbol) -> F +--R rootNormalize : (F,Kernel(F)) -> F tanQ : (Fraction(Integer),F) -> F +--R rischNormalize : (F,Symbol) -> Record(func: F,kers: List(Kernel(F)),vals: List(F)) +--R validExponential : (List(Kernel(F)),F,Symbol) -> Union(F,"failed") +--R --E 1 )spool @@ -25998,6 +26905,19 @@ ElementaryFunctionStructurePackage(R,F): Exports == Implementation where --S 1 of 1 )show ElementaryIntegration +--R +--R ElementaryIntegration(R: Join(GcdDomain,OrderedSet,CharacteristicZero,RetractableTo(Integer),LinearlyExplicitRingOver(Integer)),F: Join(AlgebraicallyClosedField,TranscendentalFunctionCategory,FunctionSpace(R))) is a package constructor +--R Abbreviation for ElementaryIntegration is INTEF +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for INTEF +--R +--R------------------------------- Operations -------------------------------- +--R lfextendedint : (F,Symbol,F) -> Union(Record(ratpart: F,coeff: F),"failed") +--R lfextlimint : (F,Symbol,Kernel(F),List(Kernel(F))) -> Union(Record(ratpart: F,coeff: F),"failed") +--R lfinfieldint : (F,Symbol) -> Union(F,"failed") +--R lfintegrate : (F,Symbol) -> IntegrationResult(F) +--R lflimitedint : (F,Symbol,List(F)) -> Union(Record(mainpart: F,limitedlogs: List(Record(coeff: F,logand: F))),"failed") +--R --E 1 )spool @@ -26450,6 +27370,15 @@ See the above discussion for why this causes an infinite loop. --S 1 of 1 )show ElementaryRischDE +--R +--R ElementaryRischDE(R: Join(GcdDomain,OrderedSet,CharacteristicZero,RetractableTo(Integer),LinearlyExplicitRingOver(Integer)),F: Join(TranscendentalFunctionCategory,AlgebraicallyClosedField,FunctionSpace(R))) is a package constructor +--R Abbreviation for ElementaryRischDE is RDEEF +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for RDEEF +--R +--R------------------------------- Operations -------------------------------- +--R rischDE : (Integer,F,F,Symbol,((F,List(F)) -> Union(Record(mainpart: F,limitedlogs: List(Record(coeff: F,logand: F))),"failed")),((F,F) -> Union(Record(ratpart: F,coeff: F),"failed"))) -> Record(ans: F,right: F,sol?: Boolean) +--R --E 1 )spool @@ -26866,6 +27795,15 @@ ElementaryRischDE(R, F): Exports == Implementation where --S 1 of 1 )show ElementaryRischDESystem +--R +--R ElementaryRischDESystem(R: Join(GcdDomain,OrderedSet,CharacteristicZero,RetractableTo(Integer),LinearlyExplicitRingOver(Integer)),F: Join(TranscendentalFunctionCategory,AlgebraicallyClosedField,FunctionSpace(R))) is a package constructor +--R Abbreviation for ElementaryRischDESystem is RDEEFS +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for RDEEFS +--R +--R------------------------------- Operations -------------------------------- +--R rischDEsys : (Integer,F,F,F,Symbol,((F,List(F)) -> Union(Record(mainpart: F,limitedlogs: List(Record(coeff: F,logand: F))),"failed")),((F,F) -> Union(Record(ratpart: F,coeff: F),"failed"))) -> Union(List(F),"failed") +--R --E 1 )spool @@ -27001,6 +27939,17 @@ ElementaryRischDESystem(R, F): Exports == Implementation where --S 1 of 1 )show EllipticFunctionsUnivariateTaylorSeries +--R +--R EllipticFunctionsUnivariateTaylorSeries(Coef: Field,UTS: UnivariateTaylorSeriesCategory(Coef)) is a package constructor +--R Abbreviation for EllipticFunctionsUnivariateTaylorSeries is ELFUTS +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for ELFUTS +--R +--R------------------------------- Operations -------------------------------- +--R cn : (UTS,Coef) -> UTS dn : (UTS,Coef) -> UTS +--R sn : (UTS,Coef) -> UTS +--R sncndn : (Stream(Coef),Coef) -> List(Stream(Coef)) +--R --E 1 )spool @@ -27098,6 +28047,15 @@ EllipticFunctionsUnivariateTaylorSeries(Coef,UTS): --S 1 of 1 )show EquationFunctions2 +--R +--R EquationFunctions2(S: Type,R: Type) is a package constructor +--R Abbreviation for EquationFunctions2 is EQ2 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for EQ2 +--R +--R------------------------------- Operations -------------------------------- +--R map : ((S -> R),Equation(S)) -> Equation(R) +--R --E 1 )spool @@ -27151,6 +28109,17 @@ EquationFunctions2(S: Type, R: Type): with --S 1 of 1 )show ErrorFunctions +--R +--R ErrorFunctions is a package constructor +--R Abbreviation for ErrorFunctions is ERROR +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for ERROR +--R +--R------------------------------- Operations -------------------------------- +--R error : String -> Exit error : List(String) -> Exit +--R error : (String,String) -> Exit +--R error : (String,List(String)) -> Exit +--R --E 1 )spool @@ -27307,7 +28276,8 @@ ErrorFunctions() : Exports == Implementation where )set message test on )set message auto off )clear all ---S 1 of 24 + +--S 1 of 25 a1:DMP([y,x],INT):= (9*x**2 + 5*x - 3)+ y*(3*x**2 + 2*x + 1) --R --R 2 2 @@ -27315,7 +28285,7 @@ a1:DMP([y,x],INT):= (9*x**2 + 5*x - 3)+ y*(3*x**2 + 2*x + 1) --R Type: DistributedMultivariatePolynomial([y,x],Integer) --E 1 ---S 2 of 24 +--S 2 of 25 a2:DMP([y,x],INT):= (6*x**3 - 2*x**2 - 3*x +3) + y*(2*x**3 - x - 1) --R --R 3 3 2 @@ -27323,7 +28293,7 @@ a2:DMP([y,x],INT):= (6*x**3 - 2*x**2 - 3*x +3) + y*(2*x**3 - x - 1) --R Type: DistributedMultivariatePolynomial([y,x],Integer) --E 2 ---S 3 of 24 +--S 3 of 25 a3:DMP([y,x],INT):= (3*x**3 + 2*x**2) + y*(x**3 + x**2) --R --R 3 2 3 2 @@ -27331,7 +28301,7 @@ a3:DMP([y,x],INT):= (3*x**3 + 2*x**2) + y*(x**3 + x**2) --R Type: DistributedMultivariatePolynomial([y,x],Integer) --E 3 ---S 4 of 24 +--S 4 of 25 an:=[a1,a2,a3] --R --R (4) @@ -27342,7 +28312,7 @@ an:=[a1,a2,a3] --R Type: List(DistributedMultivariatePolynomial([y,x],Integer)) --E 4 ---S 5 of 24 +--S 5 of 25 euclideanGroebner(an) --R --R 2 3 2 @@ -27350,7 +28320,7 @@ euclideanGroebner(an) --R Type: List(DistributedMultivariatePolynomial([y,x],Integer)) --E 5 ---S 6 of 24 +--S 6 of 25 euclideanGroebner(an,"redcrit") --R --R @@ -27444,7 +28414,7 @@ euclideanGroebner(an,"redcrit") --R Type: List(DistributedMultivariatePolynomial([y,x],Integer)) --E 6 ---S 7 of 24 +--S 7 of 25 euclideanGroebner(an,"info") --R --R you choose option -info- @@ -27517,7 +28487,7 @@ euclideanGroebner(an,"info") --R Type: List(DistributedMultivariatePolynomial([y,x],Integer)) --E 7 ---S 8 of 24 +--S 8 of 25 euclideanGroebner(an,"info","redcrit") --R --R @@ -27675,7 +28645,7 @@ euclideanGroebner(an,"info","redcrit") --R Type: List(DistributedMultivariatePolynomial([y,x],Integer)) --E 8 ---S 9 of 24 +--S 9 of 25 b1:HDMP([y,x],INT):= (9*x**2 + 5*x - 3)+ y*(3*x**2 + 2*x + 1) --R --R 2 2 @@ -27683,7 +28653,7 @@ b1:HDMP([y,x],INT):= (9*x**2 + 5*x - 3)+ y*(3*x**2 + 2*x + 1) --R Type: HomogeneousDistributedMultivariatePolynomial([y,x],Integer) --E 9 ---S 10 of 24 +--S 10 of 25 b2:HDMP([y,x],INT):= (6*x**3 - 2*x**2 - 3*x +3) + y*(2*x**3 - x - 1) --R --R 3 3 2 @@ -27691,7 +28661,7 @@ b2:HDMP([y,x],INT):= (6*x**3 - 2*x**2 - 3*x +3) + y*(2*x**3 - x - 1) --R Type: HomogeneousDistributedMultivariatePolynomial([y,x],Integer) --E 10 ---S 11 of 24 +--S 11 of 25 b3:HDMP([y,x],INT):= (3*x**3 + 2*x**2) + y*(x**3 + x**2) --R --R 3 2 3 2 @@ -27699,7 +28669,7 @@ b3:HDMP([y,x],INT):= (3*x**3 + 2*x**2) + y*(x**3 + x**2) --R Type: HomogeneousDistributedMultivariatePolynomial([y,x],Integer) --E 11 ---S 12 of 24 +--S 12 of 25 bn:=[b1,b2,b3] --R --R (12) @@ -27710,7 +28680,7 @@ bn:=[b1,b2,b3] --R Type: List(HomogeneousDistributedMultivariatePolynomial([y,x],Integer)) --E 12 ---S 13 of 24 +--S 13 of 25 euclideanGroebner(bn) --R --R 2 2 @@ -27718,7 +28688,7 @@ euclideanGroebner(bn) --R Type: List(HomogeneousDistributedMultivariatePolynomial([y,x],Integer)) --E 13 ---S 14 of 24 +--S 14 of 25 euclideanGroebner(bn,"redcrit") --R --R @@ -27795,7 +28765,7 @@ euclideanGroebner(bn,"redcrit") --R Type: List(HomogeneousDistributedMultivariatePolynomial([y,x],Integer)) --E 14 ---S 15 of 24 +--S 15 of 25 euclideanGroebner(bn,"info") --R --R you choose option -info- @@ -27861,7 +28831,7 @@ euclideanGroebner(bn,"info") --R Type: List(HomogeneousDistributedMultivariatePolynomial([y,x],Integer)) --E 15 ---S 16 of 24 +--S 16 of 25 euclideanGroebner(bn,"info","redcrit") --R --R @@ -27995,7 +28965,7 @@ euclideanGroebner(bn,"info","redcrit") --R Type: List(HomogeneousDistributedMultivariatePolynomial([y,x],Integer)) --E 16 ---S 17 of 24 +--S 17 of 25 c1:GDMP([y,x],INT,DIRPROD(2,NNI)):= (9*x**2 + 5*x - 3)+ y*(3*x**2 + 2*x + 1) --R --R 2 2 @@ -28003,7 +28973,7 @@ c1:GDMP([y,x],INT,DIRPROD(2,NNI)):= (9*x**2 + 5*x - 3)+ y*(3*x**2 + 2*x + 1) --IType: GeneralDistributedMultivariatePolynomial([y,x],Integer,... --E 17 ---S 18 of 24 +--S 18 of 25 c2:GDMP([y,x],INT,DIRPROD(2,NNI)):= (6*x**3 - 2*x**2 - 3*x +3) + y*(2*x**3 - x - 1) --R --R 3 3 2 @@ -28011,7 +28981,7 @@ c2:GDMP([y,x],INT,DIRPROD(2,NNI)):= (6*x**3 - 2*x**2 - 3*x +3) + y*(2*x**3 - x - --IType: GeneralDistributedMultivariatePolynomial([y,x],Integer,... --E 18 ---S 19 of 24 +--S 19 of 25 c3:GDMP([y,x],INT,DIRPROD(2,NNI)):= (3*x**3 + 2*x**2) + y*(x**3 + x**2) --R --R 3 2 3 2 @@ -28019,7 +28989,7 @@ c3:GDMP([y,x],INT,DIRPROD(2,NNI)):= (3*x**3 + 2*x**2) + y*(x**3 + x**2) --IType: GeneralDistributedMultivariatePolynomial([y,x],Integer,... --E 19 ---S 20 of 24 +--S 20 of 25 cn:=[c1,c2,c3] --R --R (20) @@ -28030,7 +29000,7 @@ cn:=[c1,c2,c3] --IType: List(GeneralDistributedMultivariatePolynomial([y,x],Integer,... --E 20 ---S 21 of 24 +--S 21 of 25 euclideanGroebner(cn) --R --R 2 3 2 @@ -28038,7 +29008,7 @@ euclideanGroebner(cn) --IType: List(GeneralDistributedMultivariatePolynomial([y,x],Integer,... --E 21 ---S 22 of 24 +--S 22 of 25 euclideanGroebner(cn,"redcrit") --R --R @@ -28132,7 +29102,7 @@ euclideanGroebner(cn,"redcrit") --IType: List(GeneralDistributedMultivariatePolynomial([y,x],Integer,... --E 22 ---S 23 of 24 +--S 23 of 25 euclideanGroebner(cn,"info") --R --R you choose option -info- @@ -28205,7 +29175,7 @@ euclideanGroebner(cn,"info") --IType: List(GeneralDistributedMultivariatePolynomial([y,x],Integer,... --E 23 ---S 24 of 24 +--S 24 of 25 euclideanGroebner(cn,"info","redcrit") --R --R @@ -28363,12 +29333,28 @@ euclideanGroebner(cn,"info","redcrit") --IType: List(GeneralDistributedMultivariatePolynomial([y,x],Integer,... --E 24 +--S 25 of 25 +)show EuclideanGroebnerBasisPackage +--R +--R EuclideanGroebnerBasisPackage(Dom: EuclideanDomain,Expon: OrderedAbelianMonoidSup,VarSet: OrderedSet,Dpol: PolynomialCategory(Dom,Expon,VarSet)) is a package constructor +--R Abbreviation for EuclideanGroebnerBasisPackage is GBEUCLID +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for GBEUCLID +--R +--R------------------------------- Operations -------------------------------- +--R euclideanGroebner : List(Dpol) -> List(Dpol) +--R euclideanGroebner : (List(Dpol),String) -> List(Dpol) +--R euclideanGroebner : (List(Dpol),String,String) -> List(Dpol) +--R euclideanNormalForm : (Dpol,List(Dpol)) -> Dpol +--R +--E 25 + )spool )lisp (bye) \end{chunk} \begin{chunk}{EuclideanGroebnerBasisPackage.help} ==================================================================== -euclideanGroebner examples +EuclideanGroebnerBasisPackage examples ==================================================================== EuclideanGroebnerBasisPackage computes groebner bases for polynomial @@ -29003,6 +29989,15 @@ EuclideanGroebnerBasisPackage(Dom, Expon, VarSet, Dpol): T == C where --S 1 of 1 )show EvaluateCycleIndicators +--R +--R EvaluateCycleIndicators(F: Algebra(Fraction(Integer))) is a package constructor +--R Abbreviation for EvaluateCycleIndicators is EVALCYC +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for EVALCYC +--R +--R------------------------------- Operations -------------------------------- +--R eval : ((Integer -> F),SymmetricPolynomial(Fraction(Integer))) -> F +--R --E 1 )spool @@ -29082,6 +30077,25 @@ EvaluateCycleIndicators(F):T==C where --S 1 of 1 )show ExpertSystemContinuityPackage +--R +--R ExpertSystemContinuityPackage is a package constructor +--R Abbreviation for ExpertSystemContinuityPackage is ESCONT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for ESCONT +--R +--R------------------------------- Operations -------------------------------- +--R df2st : DoubleFloat -> String +--R functionIsFracPolynomial? : Record(var: Symbol,fn: Expression(DoubleFloat),range: Segment(OrderedCompletion(DoubleFloat)),abserr: DoubleFloat,relerr: DoubleFloat) -> Boolean +--R gethi : Segment(OrderedCompletion(DoubleFloat)) -> DoubleFloat +--R getlo : Segment(OrderedCompletion(DoubleFloat)) -> DoubleFloat +--R ldf2lst : List(DoubleFloat) -> List(String) +--R polynomialZeros : (Polynomial(Fraction(Integer)),Symbol,Segment(OrderedCompletion(DoubleFloat))) -> List(DoubleFloat) +--R problemPoints : (Expression(DoubleFloat),Symbol,Segment(OrderedCompletion(DoubleFloat))) -> List(DoubleFloat) +--R sdf2lst : Stream(DoubleFloat) -> List(String) +--R singularitiesOf : (Expression(DoubleFloat),List(Symbol),Segment(OrderedCompletion(DoubleFloat))) -> Stream(DoubleFloat) +--R singularitiesOf : (Vector(Expression(DoubleFloat)),List(Symbol),Segment(OrderedCompletion(DoubleFloat))) -> Stream(DoubleFloat) +--R zerosOf : (Expression(DoubleFloat),List(Symbol),Segment(OrderedCompletion(DoubleFloat))) -> Stream(DoubleFloat) +--R --E 1 )spool @@ -29386,6 +30400,15 @@ ExpertSystemContinuityPackage(): E == I where --S 1 of 1 )show ExpertSystemContinuityPackage1 +--R +--R ExpertSystemContinuityPackage1(A: DoubleFloat,B: DoubleFloat) is a package constructor +--R Abbreviation for ExpertSystemContinuityPackage1 is ESCONT1 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for ESCONT1 +--R +--R------------------------------- Operations -------------------------------- +--R in? : DoubleFloat -> Boolean +--R --E 1 )spool @@ -29471,6 +30494,48 @@ ExpertSystemContinuityPackage1(A:DF,B:DF): E == I where --S 1 of 1 )show ExpertSystemToolsPackage +--R +--R ExpertSystemToolsPackage is a package constructor +--R Abbreviation for ExpertSystemToolsPackage is ESTOOLS +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for ESTOOLS +--R +--R------------------------------- Operations -------------------------------- +--R concat : (Result,Result) -> Result concat : List(Result) -> Result +--R df2mf : DoubleFloat -> MachineFloat df2st : DoubleFloat -> String +--R f2df : Float -> DoubleFloat f2st : Float -> String +--R outputMeasure : Float -> String +--R att2Result : Record(endPointContinuity: Union(continuous: Continuous at the end points,lowerSingular: There is a singularity at the lower end point,upperSingular: There is a singularity at the upper end point,bothSingular: There are singularities at both end points,notEvaluated: End point continuity not yet evaluated),singularitiesStream: Union(str: Stream(DoubleFloat),notEvaluated: Internal singularities not yet evaluated),range: Union(finite: The range is finite,lowerInfinite: The bottom of range is infinite,upperInfinite: The top of range is infinite,bothInfinite: Both top and bottom points are infinite,notEvaluated: Range not yet evaluated)) -> Result +--R convert : List(Segment(OrderedCompletion(Float))) -> List(Segment(OrderedCompletion(DoubleFloat))) +--R df2ef : DoubleFloat -> Expression(Float) +--R df2fi : DoubleFloat -> Fraction(Integer) +--R dfRange : Segment(OrderedCompletion(DoubleFloat)) -> Segment(OrderedCompletion(DoubleFloat)) +--R dflist : List(Record(left: Fraction(Integer),right: Fraction(Integer))) -> List(DoubleFloat) +--R edf2df : Expression(DoubleFloat) -> DoubleFloat +--R edf2ef : Expression(DoubleFloat) -> Expression(Float) +--R edf2efi : Expression(DoubleFloat) -> Expression(Fraction(Integer)) +--R edf2fi : Expression(DoubleFloat) -> Fraction(Integer) +--R ef2edf : Expression(Float) -> Expression(DoubleFloat) +--R expenseOfEvaluation : Vector(Expression(DoubleFloat)) -> Float +--R fi2df : Fraction(Integer) -> DoubleFloat +--R gethi : Segment(OrderedCompletion(DoubleFloat)) -> DoubleFloat +--R getlo : Segment(OrderedCompletion(DoubleFloat)) -> DoubleFloat +--R iflist2Result : Record(stiffness: Float,stability: Float,expense: Float,accuracy: Float,intermediateResults: Float) -> Result +--R in? : (DoubleFloat,Segment(OrderedCompletion(DoubleFloat))) -> Boolean +--R isQuotient : Expression(DoubleFloat) -> Union(Expression(DoubleFloat),"failed") +--R ldf2lst : List(DoubleFloat) -> List(String) +--R ldf2vmf : List(DoubleFloat) -> Vector(MachineFloat) +--R mat : (List(DoubleFloat),NonNegativeInteger) -> Matrix(DoubleFloat) +--R measure2Result : Record(measure: Float,name: String,explanations: List(String)) -> Result +--R measure2Result : Record(measure: Float,name: String,explanations: List(String),extra: Result) -> Result +--R numberOfOperations : Vector(Expression(DoubleFloat)) -> Record(additions: Integer,multiplications: Integer,exponentiations: Integer,functionCalls: Integer) +--R ocf2ocdf : OrderedCompletion(Float) -> OrderedCompletion(DoubleFloat) +--R pdf2df : Polynomial(DoubleFloat) -> DoubleFloat +--R pdf2ef : Polynomial(DoubleFloat) -> Expression(Float) +--R sdf2lst : Stream(DoubleFloat) -> List(String) +--R socf2socdf : Segment(OrderedCompletion(Float)) -> Segment(OrderedCompletion(DoubleFloat)) +--R vedf2vef : Vector(Expression(DoubleFloat)) -> Vector(Expression(Float)) +--R --E 1 )spool @@ -29921,6 +30986,15 @@ ExpertSystemToolsPackage():E == I where --S 1 of 1 )show ExpertSystemToolsPackage1 +--R +--R ExpertSystemToolsPackage1(R1: OrderedRing) is a package constructor +--R Abbreviation for ExpertSystemToolsPackage1 is ESTOOLS1 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for ESTOOLS1 +--R +--R------------------------------- Operations -------------------------------- +--R neglist : List(R1) -> List(R1) +--R --E 1 )spool @@ -29980,6 +31054,15 @@ ExpertSystemToolsPackage1(R1:OR): E == I where --S 1 of 1 )show ExpertSystemToolsPackage2 +--R +--R ExpertSystemToolsPackage2(R1: Ring,R2: Ring) is a package constructor +--R Abbreviation for ExpertSystemToolsPackage2 is ESTOOLS2 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for ESTOOLS2 +--R +--R------------------------------- Operations -------------------------------- +--R map : ((R1 -> R2),Matrix(R1)) -> Matrix(R2) +--R --E 1 )spool @@ -30043,6 +31126,15 @@ ExpertSystemToolsPackage2(R1:R,R2:R): E == I where --S 1 of 1 )show ExpressionFunctions2 +--R +--R ExpressionFunctions2(R: OrderedSet,S: OrderedSet) is a package constructor +--R Abbreviation for ExpressionFunctions2 is EXPR2 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for EXPR2 +--R +--R------------------------------- Operations -------------------------------- +--R map : ((R -> S),Expression(R)) -> Expression(S) +--R --E 1 )spool @@ -30135,6 +31227,16 @@ works. This is probably due to missing ``/'' in UFPS. --S 1 of 1 )show ExpressionSolve +--R +--R ExpressionSolve(R: Join(OrderedSet,IntegralDomain,ConvertibleTo(InputForm)),F: FunctionSpace(R),UTSF: UnivariateTaylorSeriesCategory(F),UTSSUPF: UnivariateTaylorSeriesCategory(SparseUnivariatePolynomialExpressions(F))) is a package constructor +--R Abbreviation for ExpressionSolve is EXPRSOL +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for EXPRSOL +--R +--R------------------------------- Operations -------------------------------- +--R replaceDiffs : (F,BasicOperator,Symbol) -> F +--R seriesSolve : (F,BasicOperator,Symbol,List(F)) -> UTSF +--R --E 1 )spool @@ -30260,6 +31362,15 @@ coefficient ring, since it will complain otherwise. --S 1 of 1 )show ExpressionSpaceFunctions1 +--R +--R ExpressionSpaceFunctions1(F: ExpressionSpace,S: Type) is a package constructor +--R Abbreviation for ExpressionSpaceFunctions1 is ES1 +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for ES1 +--R +--R------------------------------- Operations -------------------------------- +--R map : ((F -> S),String,Kernel(F)) -> S +--R --E 1 )spool @@ -30327,6 +31438,15 @@ ExpressionSpaceFunctions1(F:ExpressionSpace, S:Type): with --S 1 of 1 )show ExpressionSpaceFunctions2 +--R +--R ExpressionSpaceFunctions2(E: ExpressionSpace,F: ExpressionSpace) is a package constructor +--R Abbreviation for ExpressionSpaceFunctions2 is ES2 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for ES2 +--R +--R------------------------------- Operations -------------------------------- +--R map : ((E -> F),Kernel(E)) -> F +--R --E 1 )spool @@ -30390,6 +31510,24 @@ ExpressionSpaceFunctions2(E:ExpressionSpace, F:ExpressionSpace): with --S 1 of 1 )show ExpressionSpaceODESolver +--R +--R ExpressionSpaceODESolver(R: Join(OrderedSet,IntegralDomain,ConvertibleTo(InputForm)),F: FunctionSpace(R)) is a package constructor +--R Abbreviation for ExpressionSpaceODESolver is EXPRODE +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for EXPRODE +--R +--R------------------------------- Operations -------------------------------- +--R seriesSolve : (Equation(F),BasicOperator,Equation(F),Equation(F)) -> Any +--R seriesSolve : (Equation(F),BasicOperator,Equation(F),List(F)) -> Any +--R seriesSolve : (List(Equation(F)),List(BasicOperator),Equation(F),List(Equation(F))) -> Any +--R seriesSolve : (List(Equation(F)),List(BasicOperator),Equation(F),List(F)) -> Any +--R seriesSolve : (List(F),List(BasicOperator),Equation(F),List(F)) -> Any +--R seriesSolve : (List(F),List(BasicOperator),Equation(F),List(Equation(F))) -> Any +--R seriesSolve : (Equation(F),BasicOperator,Equation(F),F) -> Any +--R seriesSolve : (F,BasicOperator,Equation(F),F) -> Any +--R seriesSolve : (F,BasicOperator,Equation(F),Equation(F)) -> Any +--R seriesSolve : (F,BasicOperator,Equation(F),List(F)) -> Any +--R --E 1 )spool @@ -30631,6 +31769,18 @@ ExpressionSpaceODESolver(R, F): Exports == Implementation where --S 1 of 1 )show ExpressionToOpenMath +--R +--R ExpressionToOpenMath(R: Join(OpenMath,OrderedSet,Ring)) is a package constructor +--R Abbreviation for ExpressionToOpenMath is OMEXPR +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for OMEXPR +--R +--R------------------------------- Operations -------------------------------- +--R OMwrite : Expression(R) -> String +--R OMwrite : (Expression(R),Boolean) -> String +--R OMwrite : (OpenMathDevice,Expression(R)) -> Void +--R OMwrite : (OpenMathDevice,Expression(R),Boolean) -> Void +--R --E 1 )spool @@ -30942,6 +32092,28 @@ ExpressionToOpenMath(R: Join(OpenMath, OrderedSet, Ring)): with --S 1 of 1 )show ExpressionToUnivariatePowerSeries +--R +--R ExpressionToUnivariatePowerSeries(R: Join(GcdDomain,OrderedSet,RetractableTo(Integer),LinearlyExplicitRingOver(Integer)),FE: Join(AlgebraicallyClosedField,TranscendentalFunctionCategory,FunctionSpace(R))) is a package constructor +--R Abbreviation for ExpressionToUnivariatePowerSeries is EXPR2UPS +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for EXPR2UPS +--R +--R------------------------------- Operations -------------------------------- +--R laurent : Symbol -> Any laurent : FE -> Any +--R laurent : (FE,Integer) -> Any laurent : (FE,Equation(FE)) -> Any +--R puiseux : Symbol -> Any puiseux : FE -> Any +--R puiseux : (FE,Equation(FE)) -> Any series : Symbol -> Any +--R series : FE -> Any series : (FE,Equation(FE)) -> Any +--R taylor : Symbol -> Any taylor : FE -> Any +--R taylor : (FE,Equation(FE)) -> Any +--R laurent : (FE,Equation(FE),Integer) -> Any +--R puiseux : (FE,Fraction(Integer)) -> Any +--R puiseux : (FE,Equation(FE),Fraction(Integer)) -> Any +--R series : (FE,Fraction(Integer)) -> Any +--R series : (FE,Equation(FE),Fraction(Integer)) -> Any +--R taylor : (FE,NonNegativeInteger) -> Any +--R taylor : (FE,Equation(FE),NonNegativeInteger) -> Any +--R --E 1 )spool @@ -31309,6 +32481,19 @@ ExpressionToUnivariatePowerSeries(R,FE): Exports == Implementation where --S 1 of 1 )show ExpressionTubePlot +--R +--R ExpressionTubePlot is a package constructor +--R Abbreviation for ExpressionTubePlot is EXPRTUBE +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for EXPRTUBE +--R +--R------------------------------- Operations -------------------------------- +--R constantToUnaryFunction : DoubleFloat -> (DoubleFloat -> DoubleFloat) +--R tubePlot : (Expression(Integer),Expression(Integer),Expression(Integer),(DoubleFloat -> DoubleFloat),Segment(DoubleFloat),(DoubleFloat -> DoubleFloat),Integer) -> TubePlot(Plot3D) +--R tubePlot : (Expression(Integer),Expression(Integer),Expression(Integer),(DoubleFloat -> DoubleFloat),Segment(DoubleFloat),(DoubleFloat -> DoubleFloat),Integer,String) -> TubePlot(Plot3D) +--R tubePlot : (Expression(Integer),Expression(Integer),Expression(Integer),(DoubleFloat -> DoubleFloat),Segment(DoubleFloat),DoubleFloat,Integer) -> TubePlot(Plot3D) +--R tubePlot : (Expression(Integer),Expression(Integer),Expression(Integer),(DoubleFloat -> DoubleFloat),Segment(DoubleFloat),DoubleFloat,Integer,String) -> TubePlot(Plot3D) +--R --E 1 )spool @@ -31528,6 +32713,7 @@ ExpressionTubePlot(): Exports == Implementation where --S 1 of 1 )show Export3D +--R --R Export3D is a package constructor --R Abbreviation for Export3D is EXP3D --R This constructor is exposed in this frame. @@ -31676,6 +32862,30 @@ Export3D(): with --S 1 of 1 )show e04AgentsPackage +--R +--R e04AgentsPackage is a package constructor +--R Abbreviation for e04AgentsPackage is E04AGNT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for E04AGNT +--R +--R------------------------------- Operations -------------------------------- +--R changeNameToObjf : (Symbol,Result) -> Result +--R expenseOfEvaluation : Record(lfn: List(Expression(DoubleFloat)),init: List(DoubleFloat)) -> Float +--R finiteBound : (List(OrderedCompletion(DoubleFloat)),DoubleFloat) -> List(DoubleFloat) +--R linear? : List(Expression(DoubleFloat)) -> Boolean +--R linear? : Expression(DoubleFloat) -> Boolean +--R linearMatrix : (List(Expression(DoubleFloat)),NonNegativeInteger) -> Matrix(DoubleFloat) +--R linearPart : List(Expression(DoubleFloat)) -> List(Expression(DoubleFloat)) +--R nonLinearPart : List(Expression(DoubleFloat)) -> List(Expression(DoubleFloat)) +--R optAttributes : Union(noa: Record(fn: Expression(DoubleFloat),init: List(DoubleFloat),lb: List(OrderedCompletion(DoubleFloat)),cf: List(Expression(DoubleFloat)),ub: List(OrderedCompletion(DoubleFloat))),lsa: Record(lfn: List(Expression(DoubleFloat)),init: List(DoubleFloat))) -> List(String) +--R quadratic? : Expression(DoubleFloat) -> Boolean +--R simpleBounds? : List(Expression(DoubleFloat)) -> Boolean +--R sortConstraints : Record(fn: Expression(DoubleFloat),init: List(DoubleFloat),lb: List(OrderedCompletion(DoubleFloat)),cf: List(Expression(DoubleFloat)),ub: List(OrderedCompletion(DoubleFloat))) -> Record(fn: Expression(DoubleFloat),init: List(DoubleFloat),lb: List(OrderedCompletion(DoubleFloat)),cf: List(Expression(DoubleFloat)),ub: List(OrderedCompletion(DoubleFloat))) +--R splitLinear : Expression(DoubleFloat) -> Expression(DoubleFloat) +--R sumOfSquares : Expression(DoubleFloat) -> Union(Expression(DoubleFloat),"failed") +--R varList : (Expression(DoubleFloat),NonNegativeInteger) -> List(Symbol) +--R variables : Record(lfn: List(Expression(DoubleFloat)),init: List(DoubleFloat)) -> List(Symbol) +--R --E 1 )spool @@ -31994,6 +33204,16 @@ e04AgentsPackage(): E == I where --S 1 of 1 )show FactoredFunctions +--R +--R FactoredFunctions(M: IntegralDomain) is a package constructor +--R Abbreviation for FactoredFunctions is FACTFUNC +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for FACTFUNC +--R +--R------------------------------- Operations -------------------------------- +--R log : Factored(M) -> List(Record(coef: NonNegativeInteger,logand: M)) +--R nthRoot : (Factored(M),NonNegativeInteger) -> Record(exponent: NonNegativeInteger,coef: M,radicand: List(M)) +--R --E 1 )spool @@ -32079,13 +33299,14 @@ FactoredFunctions(M:IntegralDomain): Exports == Implementation where )set message test on )set message auto off )clear all ---S 1 of 6 + +--S 1 of 7 double(x) == x + x --R --R Type: Void --E 1 ---S 2 of 6 +--S 2 of 7 f := factor(720) --R --R @@ -32094,7 +33315,7 @@ f := factor(720) --R Type: Factored(Integer) --E 2 ---S 3 of 6 +--S 3 of 7 map(double,f) --R --R Compiling function double with type Integer -> Integer @@ -32104,13 +33325,13 @@ map(double,f) --R Type: Factored(Integer) --E 3 ---S 4 of 6 +--S 4 of 7 makePoly(b) == x + b --R --R Type: Void --E 4 ---S 5 of 6 +--S 5 of 7 g := map(makePoly,f) --R --R Compiling function makePoly with type Integer -> Polynomial(Integer) @@ -32121,13 +33342,27 @@ g := map(makePoly,f) --R Type: Factored(Polynomial(Integer)) --E 5 ---S 6 of 6 +--S 6 of 7 nthFlag(g,1) --R --R --R (6) "nil" --R Type: Union("nil",...) --E 6 + +--S 7 of 7 +)show FactoredFunctions2 +--R +--R FactoredFunctions2(R: IntegralDomain,S: IntegralDomain) is a package constructor +--R Abbreviation for FactoredFunctions2 is FR2 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for FR2 +--R +--R------------------------------- Operations -------------------------------- +--R map : ((R -> S),Factored(R)) -> Factored(S) +--R +--E 7 + )spool )lisp (bye) \end{chunk} @@ -32242,6 +33477,16 @@ FactoredFunctions2(R, S): Exports == Implementation where --S 1 of 1 )show FactoredFunctionUtilities +--R +--R FactoredFunctionUtilities(R: IntegralDomain) is a package constructor +--R Abbreviation for FactoredFunctionUtilities is FRUTIL +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for FRUTIL +--R +--R------------------------------- Operations -------------------------------- +--R mergeFactors : (Factored(R),Factored(R)) -> Factored(R) +--R refine : (Factored(R),(R -> Factored(R))) -> Factored(R) +--R --E 1 )spool @@ -32335,6 +33580,21 @@ FactoredFunctionUtilities(R): Exports == Implementation where --S 1 of 1 )show FactoringUtilities +--R +--R FactoringUtilities(E: OrderedAbelianMonoidSup,OV: OrderedSet,R: Ring,P: PolynomialCategory(R,E,OV)) is a package constructor +--R Abbreviation for FactoringUtilities is FACUTIL +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for FACUTIL +--R +--R------------------------------- Operations -------------------------------- +--R ran : Integer -> R +--R completeEval : (SparseUnivariatePolynomial(P),List(OV),List(R)) -> SparseUnivariatePolynomial(R) +--R degree : (SparseUnivariatePolynomial(P),List(OV)) -> List(NonNegativeInteger) +--R lowerPolynomial : SparseUnivariatePolynomial(P) -> SparseUnivariatePolynomial(R) +--R normalDeriv : (SparseUnivariatePolynomial(P),Integer) -> SparseUnivariatePolynomial(P) +--R raisePolynomial : SparseUnivariatePolynomial(R) -> SparseUnivariatePolynomial(P) +--R variables : SparseUnivariatePolynomial(P) -> List(OV) +--R --E 1 )spool @@ -32838,6 +34098,17 @@ FactorisationOverPseudoAlgebraicClosureOfRationalNumber(K):Exports == --S 1 of 1 )show FGLMIfCanPackage +--R +--R FGLMIfCanPackage(R: GcdDomain,ls: List(Symbol)) is a package constructor +--R Abbreviation for FGLMIfCanPackage is FGLMICPK +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for FGLMICPK +--R +--R------------------------------- Operations -------------------------------- +--R fglmIfCan : List(Polynomial(R)) -> Union(List(Polynomial(R)),"failed") +--R groebner : List(Polynomial(R)) -> List(Polynomial(R)) +--R zeroDimensional? : List(Polynomial(R)) -> Boolean +--R --E 1 )spool @@ -32969,6 +34240,15 @@ FGLMIfCanPackage(R,ls): Exports == Implementation where --S 1 of 1 )show FindOrderFinite +--R +--R FindOrderFinite(F: Join(Finite,Field),UP: UnivariatePolynomialCategory(F),UPUP: UnivariatePolynomialCategory(Fraction(UP)),R: FunctionFieldCategory(F,UP,UPUP)) is a package constructor +--R Abbreviation for FindOrderFinite is FORDER +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for FORDER +--R +--R------------------------------- Operations -------------------------------- +--R order : FiniteDivisor(F,UP,UPUP,R) -> NonNegativeInteger +--R --E 1 )spool @@ -33034,6 +34314,15 @@ FindOrderFinite(F, UP, UPUP, R): Exports == Implementation where --S 1 of 1 )show FiniteAbelianMonoidRingFunctions2 +--R +--R FiniteAbelianMonoidRingFunctions2(E: OrderedAbelianMonoid,R1: Ring,A1: FiniteAbelianMonoidRing(R1,E),R2: Ring,A2: FiniteAbelianMonoidRing(R2,E)) is a package constructor +--R Abbreviation for FiniteAbelianMonoidRingFunctions2 is FAMR2 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for FAMR2 +--R +--R------------------------------- Operations -------------------------------- +--R map : ((R1 -> R2),A1) -> A2 +--R --E 1 )spool @@ -33105,6 +34394,15 @@ FiniteAbelianMonoidRingFunctions2(E: OrderedAbelianMonoid, --S 1 of 1 )show FiniteDivisorFunctions2 +--R +--R FiniteDivisorFunctions2(R1: Field,UP1: UnivariatePolynomialCategory(R1),UPUP1: UnivariatePolynomialCategory(Fraction(UP1)),F1: FunctionFieldCategory(R1,UP1,UPUP1),R2: Field,UP2: UnivariatePolynomialCategory(R2),UPUP2: UnivariatePolynomialCategory(Fraction(UP2)),F2: FunctionFieldCategory(R2,UP2,UPUP2)) is a package constructor +--R Abbreviation for FiniteDivisorFunctions2 is FDIV2 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for FDIV2 +--R +--R------------------------------- Operations -------------------------------- +--R map : ((R1 -> R2),FiniteDivisor(R1,UP1,UPUP1,F1)) -> FiniteDivisor(R2,UP2,UPUP2,F2) +--R --E 1 )spool @@ -33182,6 +34480,7 @@ FiniteDivisorFunctions2(R1, UP1, UPUP1, F1, R2, UP2, UPUP2, F2): --S 1 of 1 )show FiniteFieldFactorization +--R --R FiniteFieldFactorization(K: FiniteFieldCategory,PolK: UnivariatePolynomialCategory(K)) is a package constructor --R Abbreviation for FiniteFieldFactorization is FFFACTOR --R This constructor is exposed in this frame. @@ -33747,6 +35046,20 @@ FiniteFieldFactorizationWithSizeParseBySideEffect(K : FiniteFieldCategory, --S 1 of 1 )show FiniteFieldFunctions +--R +--R FiniteFieldFunctions(GF: FiniteFieldCategory) is a package constructor +--R Abbreviation for FiniteFieldFunctions is FFF +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for FFF +--R +--R------------------------------- Operations -------------------------------- +--R createLowComplexityNormalBasis : PositiveInteger -> Union(SparseUnivariatePolynomial(GF),Vector(List(Record(value: GF,index: SingleInteger)))) +--R createLowComplexityTable : PositiveInteger -> Union(Vector(List(Record(value: GF,index: SingleInteger))),"failed") +--R createMultiplicationMatrix : Vector(List(Record(value: GF,index: SingleInteger))) -> Matrix(GF) +--R createMultiplicationTable : SparseUnivariatePolynomial(GF) -> Vector(List(Record(value: GF,index: SingleInteger))) +--R createZechTable : SparseUnivariatePolynomial(GF) -> PrimitiveArray(SingleInteger) +--R sizeMultiplication : Vector(List(Record(value: GF,index: SingleInteger))) -> NonNegativeInteger +--R --E 1 )spool @@ -34031,6 +35344,15 @@ FiniteFieldFunctions(GF): Exports == Implementation where --S 1 of 1 )show FiniteFieldHomomorphisms +--R +--R FiniteFieldHomomorphisms(F1: FiniteAlgebraicExtensionField(GF),GF: FiniteFieldCategory,F2: FiniteAlgebraicExtensionField(GF)) is a package constructor +--R Abbreviation for FiniteFieldHomomorphisms is FFHOM +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for FFHOM +--R +--R------------------------------- Operations -------------------------------- +--R coerce : F1 -> F2 coerce : F2 -> F1 +--R --E 1 )spool @@ -34432,6 +35754,33 @@ FiniteFieldHomomorphisms(F1,GF,F2): Exports == Implementation where --S 1 of 1 )show FiniteFieldPolynomialPackage +--R +--R FiniteFieldPolynomialPackage(GF: FiniteFieldCategory) is a package constructor +--R Abbreviation for FiniteFieldPolynomialPackage is FFPOLY +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for FFPOLY +--R +--R------------------------------- Operations -------------------------------- +--R createIrreduciblePoly : PositiveInteger -> SparseUnivariatePolynomial(GF) +--R createNormalPoly : PositiveInteger -> SparseUnivariatePolynomial(GF) +--R createNormalPrimitivePoly : PositiveInteger -> SparseUnivariatePolynomial(GF) +--R createPrimitiveNormalPoly : PositiveInteger -> SparseUnivariatePolynomial(GF) +--R createPrimitivePoly : PositiveInteger -> SparseUnivariatePolynomial(GF) +--R leastAffineMultiple : SparseUnivariatePolynomial(GF) -> SparseUnivariatePolynomial(GF) +--R nextIrreduciblePoly : SparseUnivariatePolynomial(GF) -> Union(SparseUnivariatePolynomial(GF),"failed") +--R nextNormalPoly : SparseUnivariatePolynomial(GF) -> Union(SparseUnivariatePolynomial(GF),"failed") +--R nextNormalPrimitivePoly : SparseUnivariatePolynomial(GF) -> Union(SparseUnivariatePolynomial(GF),"failed") +--R nextPrimitiveNormalPoly : SparseUnivariatePolynomial(GF) -> Union(SparseUnivariatePolynomial(GF),"failed") +--R nextPrimitivePoly : SparseUnivariatePolynomial(GF) -> Union(SparseUnivariatePolynomial(GF),"failed") +--R normal? : SparseUnivariatePolynomial(GF) -> Boolean +--R numberOfIrreduciblePoly : PositiveInteger -> PositiveInteger +--R numberOfNormalPoly : PositiveInteger -> PositiveInteger +--R numberOfPrimitivePoly : PositiveInteger -> PositiveInteger +--R primitive? : SparseUnivariatePolynomial(GF) -> Boolean +--R random : PositiveInteger -> SparseUnivariatePolynomial(GF) +--R random : (PositiveInteger,PositiveInteger) -> SparseUnivariatePolynomial(GF) +--R reducedQPowers : SparseUnivariatePolynomial(GF) -> PrimitiveArray(SparseUnivariatePolynomial(GF)) +--R --E 1 )spool @@ -35463,6 +36812,20 @@ FiniteFieldPolynomialPackage GF : Exports == Implementation where --S 1 of 1 )show FiniteFieldPolynomialPackage2 +--R +--R FiniteFieldPolynomialPackage2(F,GF: FiniteFieldCategory)where +--R F: FieldOfPrimeCharacteristicwith +--R coerce : GF -> F +--R lookup : F -> PositiveInteger +--R basis : PositiveInteger -> Vector(F) +--R Frobenius : F -> F is a package constructor +--R Abbreviation for FiniteFieldPolynomialPackage2 is FFPOLY2 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for FFPOLY2 +--R +--R------------------------------- Operations -------------------------------- +--R rootOfIrreduciblePoly : SparseUnivariatePolynomial(GF) -> F +--R --E 1 )spool @@ -35617,6 +36980,15 @@ FiniteFieldPolynomialPackage2(F,GF):Exports == Implementation where --S 1 of 1 )show FiniteFieldSolveLinearPolynomialEquation +--R +--R FiniteFieldSolveLinearPolynomialEquation(F: FiniteFieldCategory,FP: UnivariatePolynomialCategory(F),FPP: UnivariatePolynomialCategory(FP)) is a package constructor +--R Abbreviation for FiniteFieldSolveLinearPolynomialEquation is FFSLPE +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for FFSLPE +--R +--R------------------------------- Operations -------------------------------- +--R solveLinearPolynomialEquation : (List(FPP),FPP) -> Union(List(FPP),"failed") +--R --E 1 )spool @@ -35852,6 +37224,16 @@ FiniteFieldSquareFreeDecomposition (K : FiniteFieldCategory, --S 1 of 1 )show FiniteLinearAggregateFunctions2 +--R +--R FiniteLinearAggregateFunctions2(S: Type,A: FiniteLinearAggregate(S),R: Type,B: FiniteLinearAggregate(R)) is a package constructor +--R Abbreviation for FiniteLinearAggregateFunctions2 is FLAGG2 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for FLAGG2 +--R +--R------------------------------- Operations -------------------------------- +--R map : ((S -> R),A) -> B reduce : (((S,R) -> R),A,R) -> R +--R scan : (((S,R) -> R),A,R) -> B +--R --E 1 )spool @@ -36010,6 +37392,19 @@ FiniteLinearAggregateFunctions2(S, A, R, B): --S 1 of 1 )show FiniteLinearAggregateSort +--R +--R FiniteLinearAggregateSort(S: Type,V)where +--R V: FiniteLinearAggregate(S)with +--R shallowlyMutable is a package constructor +--R Abbreviation for FiniteLinearAggregateSort is FLASORT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for FLASORT +--R +--R------------------------------- Operations -------------------------------- +--R heapSort : (((S,S) -> Boolean),V) -> V +--R quickSort : (((S,S) -> Boolean),V) -> V +--R shellSort : (((S,S) -> Boolean),V) -> V +--R --E 1 )spool @@ -36154,6 +37549,16 @@ FiniteLinearAggregateSort(S, V): Exports == Implementation where --S 1 of 1 )show FiniteSetAggregateFunctions2 +--R +--R FiniteSetAggregateFunctions2(S: SetCategory,A: FiniteSetAggregate(S),R: SetCategory,B: FiniteSetAggregate(R)) is a package constructor +--R Abbreviation for FiniteSetAggregateFunctions2 is FSAGG2 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for FSAGG2 +--R +--R------------------------------- Operations -------------------------------- +--R map : ((S -> R),A) -> B reduce : (((S,R) -> R),A,R) -> R +--R scan : (((S,R) -> R),A,R) -> B +--R --E 1 )spool @@ -36249,6 +37654,20 @@ FiniteSetAggregateFunctions2(S, A, R, B): Exports == Implementation where --S 1 of 1 )show FloatingComplexPackage +--R +--R FloatingComplexPackage(Par: Join(Field,OrderedRing)) is a package constructor +--R Abbreviation for FloatingComplexPackage is FLOATCP +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for FLOATCP +--R +--R------------------------------- Operations -------------------------------- +--R complexRoots : (Fraction(Polynomial(Complex(Integer))),Par) -> List(Complex(Par)) +--R complexRoots : (List(Fraction(Polynomial(Complex(Integer)))),List(Symbol),Par) -> List(List(Complex(Par))) +--R complexSolve : (List(Fraction(Polynomial(Complex(Integer)))),Par) -> List(List(Equation(Polynomial(Complex(Par))))) +--R complexSolve : (List(Equation(Fraction(Polynomial(Complex(Integer))))),Par) -> List(List(Equation(Polynomial(Complex(Par))))) +--R complexSolve : (Fraction(Polynomial(Complex(Integer))),Par) -> List(Equation(Polynomial(Complex(Par)))) +--R complexSolve : (Equation(Fraction(Polynomial(Complex(Integer)))),Par) -> List(Equation(Polynomial(Complex(Par)))) +--R --E 1 )spool @@ -36408,6 +37827,20 @@ FloatingComplexPackage(Par): Cat == Cap where --S 1 of 1 )show FloatingRealPackage +--R +--R FloatingRealPackage(Par: Join(OrderedRing,Field)) is a package constructor +--R Abbreviation for FloatingRealPackage is FLOATRP +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for FLOATRP +--R +--R------------------------------- Operations -------------------------------- +--R realRoots : (List(Fraction(Polynomial(Integer))),List(Symbol),Par) -> List(List(Par)) +--R realRoots : (Fraction(Polynomial(Integer)),Par) -> List(Par) +--R solve : (List(Fraction(Polynomial(Integer))),Par) -> List(List(Equation(Polynomial(Par)))) +--R solve : (List(Equation(Fraction(Polynomial(Integer)))),Par) -> List(List(Equation(Polynomial(Par)))) +--R solve : (Fraction(Polynomial(Integer)),Par) -> List(Equation(Polynomial(Par))) +--R solve : (Equation(Fraction(Polynomial(Integer))),Par) -> List(Equation(Polynomial(Par))) +--R --E 1 )spool @@ -36565,6 +37998,19 @@ FloatingRealPackage(Par): Cat == Cap where --S 1 of 1 )show FortranCodePackage1 +--R +--R FortranCodePackage1 is a package constructor +--R Abbreviation for FortranCodePackage1 is FCPAK1 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for FCPAK1 +--R +--R------------------------------- Operations -------------------------------- +--R identitySquareMatrix : (Symbol,Polynomial(Integer)) -> FortranCode +--R zeroMatrix : (Symbol,Polynomial(Integer),Polynomial(Integer)) -> FortranCode +--R zeroMatrix : (Symbol,SegmentBinding(Polynomial(Integer)),SegmentBinding(Polynomial(Integer))) -> FortranCode +--R zeroSquareMatrix : (Symbol,Polynomial(Integer)) -> FortranCode +--R zeroVector : (Symbol,Polynomial(Integer)) -> FortranCode +--R --E 1 )spool @@ -36757,6 +38203,19 @@ FortranCodePackage1: Exports == Implementation where --S 1 of 1 )show FortranOutputStackPackage +--R +--R FortranOutputStackPackage is a package constructor +--R Abbreviation for FortranOutputStackPackage is FOP +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for FOP +--R +--R------------------------------- Operations -------------------------------- +--R popFortranOutputStack : () -> Void topFortranOutputStack : () -> String +--R clearFortranOutputStack : () -> Stack(String) +--R pushFortranOutputStack : FileName -> Void +--R pushFortranOutputStack : String -> Void +--R showFortranOutputStack : () -> Stack(String) +--R --E 1 )spool @@ -36880,6 +38339,19 @@ FortranOutputStackPackage() : specification == implementation where --S 1 of 1 )show FortranPackage +--R +--R FortranPackage is a package constructor +--R Abbreviation for FortranPackage is FORT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for FORT +--R +--R------------------------------- Operations -------------------------------- +--R outputAsFortran : FileName -> Void +--R linkToFortran : (Symbol,List(Union(array: List(Symbol),scalar: Symbol)),List(List(Union(array: List(Symbol),scalar: Symbol))),List(Symbol)) -> SExpression +--R linkToFortran : (Symbol,List(Union(array: List(Symbol),scalar: Symbol)),List(List(Union(array: List(Symbol),scalar: Symbol))),List(Symbol),Symbol) -> SExpression +--R linkToFortran : (Symbol,List(Symbol),TheSymbolTable,List(Symbol)) -> SExpression +--R setLegalFortranSourceExtensions : List(String) -> List(String) +--R --E 1 )spool @@ -37013,6 +38485,15 @@ FortranPackage(): Exports == Implementation where --S 1 of 1 )show FractionalIdealFunctions2 +--R +--R FractionalIdealFunctions2(R1: EuclideanDomain,F1: QuotientFieldCategory(R1),U1: UnivariatePolynomialCategory(F1),A1: Join(FramedAlgebra(F1,U1),RetractableTo(F1)),R2: EuclideanDomain,F2: QuotientFieldCategory(R2),U2: UnivariatePolynomialCategory(F2),A2: Join(FramedAlgebra(F2,U2),RetractableTo(F2))) is a package constructor +--R Abbreviation for FractionalIdealFunctions2 is FRIDEAL2 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for FRIDEAL2 +--R +--R------------------------------- Operations -------------------------------- +--R map : ((R1 -> R2),FractionalIdeal(R1,F1,U1,A1)) -> FractionalIdeal(R2,F2,U2,A2) +--R --E 1 )spool @@ -37090,6 +38571,26 @@ FractionalIdealFunctions2(R1, F1, U1, A1, R2, F2, U2, A2): --S 1 of 1 )show FractionFreeFastGaussian +--R +--R FractionFreeFastGaussian(D: Join(IntegralDomain,GcdDomain),V: AbelianMonoidRing(D,NonNegativeInteger)) is a package constructor +--R Abbreviation for FractionFreeFastGaussian is FFFG +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for FFFG +--R +--R------------------------------- Operations -------------------------------- +--R DiffAction : (NonNegativeInteger,NonNegativeInteger,V) -> D +--R DiffC : NonNegativeInteger -> List(D) +--R ShiftAction : (NonNegativeInteger,NonNegativeInteger,V) -> D +--R ShiftC : NonNegativeInteger -> List(D) +--R fffg : (List(D),((NonNegativeInteger,Vector(SparseUnivariatePolynomial(D))) -> D),List(NonNegativeInteger)) -> Matrix(SparseUnivariatePolynomial(D)) +--R generalCoefficient : (((NonNegativeInteger,NonNegativeInteger,V) -> D),Vector(V),NonNegativeInteger,Vector(SparseUnivariatePolynomial(D))) -> D +--R generalInterpolation : (List(D),((NonNegativeInteger,NonNegativeInteger,V) -> D),Vector(V),List(NonNegativeInteger)) -> Matrix(SparseUnivariatePolynomial(D)) +--R generalInterpolation : (List(D),((NonNegativeInteger,NonNegativeInteger,V) -> D),Vector(V),NonNegativeInteger,NonNegativeInteger) -> Stream(Matrix(SparseUnivariatePolynomial(D))) +--R interpolate : (List(D),List(D),NonNegativeInteger) -> Fraction(SparseUnivariatePolynomial(D)) +--R interpolate : (List(Fraction(D)),List(Fraction(D)),NonNegativeInteger) -> Fraction(SparseUnivariatePolynomial(D)) +--R qShiftAction : (D,NonNegativeInteger,NonNegativeInteger,V) -> D +--R qShiftC : (D,NonNegativeInteger) -> List(D) +--R --E 1 )spool @@ -37628,6 +39129,16 @@ $c_{\sigma,\sigma}$. --S 1 of 1 )show FractionFreeFastGaussianFractions +--R +--R FractionFreeFastGaussianFractions(D: Join(IntegralDomain,GcdDomain),V: FiniteAbelianMonoidRing(D,NonNegativeInteger),VF: FiniteAbelianMonoidRing(Fraction(D),NonNegativeInteger)) is a package constructor +--R Abbreviation for FractionFreeFastGaussianFractions is FFFGF +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for FFFGF +--R +--R------------------------------- Operations -------------------------------- +--R generalInterpolation : (List(D),((NonNegativeInteger,NonNegativeInteger,V) -> D),Vector(VF),List(NonNegativeInteger)) -> Matrix(SparseUnivariatePolynomial(D)) +--R generalInterpolation : (List(D),((NonNegativeInteger,NonNegativeInteger,V) -> D),Vector(VF),NonNegativeInteger,NonNegativeInteger) -> Stream(Matrix(SparseUnivariatePolynomial(D))) +--R --E 1 )spool @@ -37772,6 +39283,15 @@ FractionFreeFastGaussianFractions(D, V, VF): Exports == Implementation where --S 1 of 1 )show FractionFunctions2 +--R +--R FractionFunctions2(A: IntegralDomain,B: IntegralDomain) is a package constructor +--R Abbreviation for FractionFunctions2 is FRAC2 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for FRAC2 +--R +--R------------------------------- Operations -------------------------------- +--R map : ((A -> B),Fraction(A)) -> Fraction(B) +--R --E 1 )spool @@ -37836,6 +39356,15 @@ FractionFunctions2(A, B): Exports == Impl where --S 1 of 1 )show FramedNonAssociativeAlgebraFunctions2 +--R +--R FramedNonAssociativeAlgebraFunctions2(AR: FramedNonAssociativeAlgebra(R),R: CommutativeRing,AS: FramedNonAssociativeAlgebra(S),S: CommutativeRing) is a package constructor +--R Abbreviation for FramedNonAssociativeAlgebraFunctions2 is FRNAAF2 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for FRNAAF2 +--R +--R------------------------------- Operations -------------------------------- +--R map : ((R -> S),AR) -> AS +--R --E 1 )spool @@ -37920,6 +39449,27 @@ Gregory Vanuxem supplied the fix below. --S 1 of 1 )show FunctionalSpecialFunction +--R +--R FunctionalSpecialFunction(R: Join(OrderedSet,IntegralDomain),F: FunctionSpace(R)) is a package constructor +--R Abbreviation for FunctionalSpecialFunction is FSPECF +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for FSPECF +--R +--R------------------------------- Operations -------------------------------- +--R Beta : (F,F) -> F Gamma : F -> F +--R Gamma : (F,F) -> F abs : F -> F +--R airyAi : F -> F airyBi : F -> F +--R belong? : BasicOperator -> Boolean besselI : (F,F) -> F +--R besselJ : (F,F) -> F besselK : (F,F) -> F +--R besselY : (F,F) -> F digamma : F -> F +--R iiAiryAi : F -> F iiAiryBi : F -> F +--R iiBesselI : List(F) -> F iiBesselJ : List(F) -> F +--R iiBesselK : List(F) -> F iiBesselY : List(F) -> F +--R iiBeta : List(F) -> F iiGamma : F -> F +--R iiabs : F -> F iidigamma : F -> F +--R iipolygamma : List(F) -> F polygamma : (F,F) -> F +--R operator : BasicOperator -> BasicOperator +--R --E 1 )spool @@ -38371,6 +39921,15 @@ integrate(D(besselJ(a,x),a),a). --S 1 of 1 )show FunctionFieldCategoryFunctions2 +--R +--R FunctionFieldCategoryFunctions2(R1: UniqueFactorizationDomain,UP1: UnivariatePolynomialCategory(R1),UPUP1: UnivariatePolynomialCategory(Fraction(UP1)),F1: FunctionFieldCategory(R1,UP1,UPUP1),R2: UniqueFactorizationDomain,UP2: UnivariatePolynomialCategory(R2),UPUP2: UnivariatePolynomialCategory(Fraction(UP2)),F2: FunctionFieldCategory(R2,UP2,UPUP2)) is a package constructor +--R Abbreviation for FunctionFieldCategoryFunctions2 is FFCAT2 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for FFCAT2 +--R +--R------------------------------- Operations -------------------------------- +--R map : ((R1 -> R2),F1) -> F2 +--R --E 1 )spool @@ -38439,6 +39998,18 @@ FunctionFieldCategoryFunctions2(R1, UP1, UPUP1, F1, R2, UP2, UPUP2, F2): --S 1 of 1 )show FunctionFieldIntegralBasis +--R +--R FunctionFieldIntegralBasis(R,UP: UnivariatePolynomialCategory(R),F: FramedAlgebra(R,UP))where +--R R: EuclideanDomainwith +--R squareFree : % -> Factored(%) is a package constructor +--R Abbreviation for FunctionFieldIntegralBasis is FFINTBAS +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for FFINTBAS +--R +--R------------------------------- Operations -------------------------------- +--R integralBasis : () -> Record(basis: Matrix(R),basisDen: R,basisInv: Matrix(R)) +--R localIntegralBasis : R -> Record(basis: Matrix(R),basisDen: R,basisInv: Matrix(R)) +--R --E 1 )spool @@ -38605,6 +40176,16 @@ FunctionFieldIntegralBasis(R,UP,F): Exports == Implementation where --S 1 of 1 )show FunctionSpaceAssertions +--R +--R FunctionSpaceAssertions(R: OrderedSet,F: FunctionSpace(R)) is a package constructor +--R Abbreviation for FunctionSpaceAssertions is PMASSFS +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for PMASSFS +--R +--R------------------------------- Operations -------------------------------- +--R assert : (F,String) -> F constant : F -> F +--R multiple : F -> F optional : F -> F +--R --E 1 )spool @@ -38722,6 +40303,16 @@ FunctionSpaceAssertions(R, F): Exports == Implementation where --S 1 of 1 )show FunctionSpaceAttachPredicates +--R +--R FunctionSpaceAttachPredicates(R: OrderedSet,F: FunctionSpace(R),D: Type) is a package constructor +--R Abbreviation for FunctionSpaceAttachPredicates is PMPREDFS +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for PMPREDFS +--R +--R------------------------------- Operations -------------------------------- +--R suchThat : (F,(D -> Boolean)) -> F +--R suchThat : (F,List((D -> Boolean))) -> F +--R --E 1 )spool @@ -38811,6 +40402,17 @@ FunctionSpaceAttachPredicates(R, F, D): Exports == Implementation where --S 1 of 1 )show FunctionSpaceComplexIntegration +--R +--R FunctionSpaceComplexIntegration(R: Join(EuclideanDomain,OrderedSet,CharacteristicZero,RetractableTo(Integer),LinearlyExplicitRingOver(Integer)),F: Join(TranscendentalFunctionCategory,AlgebraicallyClosedFunctionSpace(R))) is a package constructor +--R Abbreviation for FunctionSpaceComplexIntegration is FSCINT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for FSCINT +--R +--R------------------------------- Operations -------------------------------- +--R complexIntegrate : (F,Symbol) -> F +--R internalIntegrate : (F,Symbol) -> IntegrationResult(F) +--R internalIntegrate0 : (F,Symbol) -> IntegrationResult(F) +--R --E 1 )spool @@ -38931,6 +40533,15 @@ FunctionSpaceComplexIntegration(R, F): Exports == Implementation where --S 1 of 1 )show FunctionSpaceFunctions2 +--R +--R FunctionSpaceFunctions2(R: Join(Ring,OrderedSet),A: FunctionSpace(R),S: Join(Ring,OrderedSet),B: FunctionSpace(S)) is a package constructor +--R Abbreviation for FunctionSpaceFunctions2 is FS2 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for FS2 +--R +--R------------------------------- Operations -------------------------------- +--R map : ((R -> S),A) -> B +--R --E 1 )spool @@ -39012,6 +40623,15 @@ FunctionSpaceFunctions2(R, A, S, B): Exports == Implementation where --S 1 of 1 )show FunctionSpaceIntegration +--R +--R FunctionSpaceIntegration(R: Join(EuclideanDomain,OrderedSet,CharacteristicZero,RetractableTo(Integer),LinearlyExplicitRingOver(Integer)),F: Join(TranscendentalFunctionCategory,PrimitiveFunctionCategory,AlgebraicallyClosedFunctionSpace(R))) is a package constructor +--R Abbreviation for FunctionSpaceIntegration is FSINT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for FSINT +--R +--R------------------------------- Operations -------------------------------- +--R integrate : (F,Symbol) -> Union(F,List(F)) +--R --E 1 )spool @@ -39184,6 +40804,16 @@ FunctionSpaceIntegration(R, F): Exports == Implementation where --S 1 of 1 )show FunctionSpacePrimitiveElement +--R +--R FunctionSpacePrimitiveElement(R: Join(IntegralDomain,OrderedSet,CharacteristicZero),F: FunctionSpace(R)) is a package constructor +--R Abbreviation for FunctionSpacePrimitiveElement is FSPRMELT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for FSPRMELT +--R +--R------------------------------- Operations -------------------------------- +--R primitiveElement : List(F) -> Record(primelt: F,poly: List(SparseUnivariatePolynomial(F)),prim: SparseUnivariatePolynomial(F)) +--R primitiveElement : (F,F) -> Record(primelt: F,pol1: SparseUnivariatePolynomial(F),pol2: SparseUnivariatePolynomial(F),prim: SparseUnivariatePolynomial(F)) if F has ACF +--R --E 1 )spool @@ -39332,6 +40962,16 @@ FunctionSpacePrimitiveElement(R, F): Exports == Implementation where --S 1 of 1 )show FunctionSpaceReduce +--R +--R FunctionSpaceReduce(R: Join(OrderedSet,IntegralDomain,RetractableTo(Integer)),F: FunctionSpace(R)) is a package constructor +--R Abbreviation for FunctionSpaceReduce is FSRED +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for FSRED +--R +--R------------------------------- Operations -------------------------------- +--R bringDown : F -> Fraction(Integer) newReduc : () -> Void +--R bringDown : (F,Kernel(F)) -> SparseUnivariatePolynomial(Fraction(Integer)) +--R --E 1 )spool @@ -39437,6 +41077,15 @@ FunctionSpaceReduce(R, F): Exports == Implementation where --S 1 of 1 )show FunctionSpaceSum +--R +--R FunctionSpaceSum(R: Join(IntegralDomain,OrderedSet,RetractableTo(Integer),LinearlyExplicitRingOver(Integer)),F: Join(FunctionSpace(R),CombinatorialOpsCategory,AlgebraicallyClosedField,TranscendentalFunctionCategory)) is a package constructor +--R Abbreviation for FunctionSpaceSum is SUMFS +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for SUMFS +--R +--R------------------------------- Operations -------------------------------- +--R sum : (F,Symbol) -> F sum : (F,SegmentBinding(F)) -> F +--R --E 1 )spool @@ -39535,6 +41184,16 @@ FunctionSpaceSum(R, F): Exports == Implementation where --S 1 of 1 )show FunctionSpaceToExponentialExpansion +--R +--R FunctionSpaceToExponentialExpansion(R: Join(GcdDomain,OrderedSet,RetractableTo(Integer),LinearlyExplicitRingOver(Integer)),FE: Join(AlgebraicallyClosedField,TranscendentalFunctionCategory,FunctionSpace(R)),x: Symbol,cen: FE) is a package constructor +--R Abbreviation for FunctionSpaceToExponentialExpansion is FS2EXPXP +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for FS2EXPXP +--R +--R------------------------------- Operations -------------------------------- +--R localAbs : FE -> FE +--R exprToXXP : (FE,Boolean) -> Union(%expansion: ExponentialExpansion(R,FE,x,cen),%problem: Record(func: String,prob: String)) +--R --E 1 )spool @@ -40116,6 +41775,22 @@ FunctionSpaceToExponentialExpansion(R,FE,x,cen):_ --S 1 of 1 )show FunctionSpaceToUnivariatePowerSeries +--R +--R FunctionSpaceToUnivariatePowerSeries(R: Join(GcdDomain,OrderedSet,RetractableTo(Integer),LinearlyExplicitRingOver(Integer)),FE,Expon: OrderedRing,UPS,TRAN: PartialTranscendentalFunctions(UPS),x: Symbol)where +--R FE: Join(AlgebraicallyClosedField,TranscendentalFunctionCategory,FunctionSpace(R))with +--R coerce : Expon -> % +--R UPS: Join(UnivariatePowerSeriesCategory(FE,Expon),Field,TranscendentalFunctionCategory)with +--R differentiate : % -> % +--R integrate : % -> % is a package constructor +--R Abbreviation for FunctionSpaceToUnivariatePowerSeries is FS2UPS +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for FS2UPS +--R +--R------------------------------- Operations -------------------------------- +--R localAbs : FE -> FE +--R exprToGenUPS : (FE,Boolean,String) -> Union(%series: UPS,%problem: Record(func: String,prob: String)) +--R exprToUPS : (FE,Boolean,String) -> Union(%series: UPS,%problem: Record(func: String,prob: String)) +--R --E 1 )spool @@ -40922,6 +42597,18 @@ FunctionSpaceToUnivariatePowerSeries(R,FE,Expon,UPS,TRAN,x):_ --S 1 of 1 )show FunctionSpaceUnivariatePolynomialFactor +--R +--R FunctionSpaceUnivariatePolynomialFactor(R: Join(IntegralDomain,OrderedSet,RetractableTo(Integer)),F: FunctionSpace(R),UP: UnivariatePolynomialCategory(F)) is a package constructor +--R Abbreviation for FunctionSpaceUnivariatePolynomialFactor is FSUPFACT +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for FSUPFACT +--R +--R------------------------------- Operations -------------------------------- +--R ffactor : UP -> Factored(UP) +--R UP2ifCan : UP -> Union(overq: SparseUnivariatePolynomial(Fraction(Integer)),overan: SparseUnivariatePolynomial(AlgebraicNumber),failed: Boolean) +--R anfactor : UP -> Union(Factored(SparseUnivariatePolynomial(AlgebraicNumber)),"failed") if F has RETRACT(AN) +--R qfactor : UP -> Union(Factored(SparseUnivariatePolynomial(Fraction(Integer))),"failed") +--R --E 1 )spool @@ -41110,6 +42797,21 @@ FunctionSpaceUnivariatePolynomialFactor(R, F, UP): --S 1 of 1 )show GaloisGroupFactorizationUtilities +--R +--R GaloisGroupFactorizationUtilities(R: Ring,UP: UnivariatePolynomialCategory(R),F: Join(FloatingPointSystem,RetractableTo(R),Field,TranscendentalFunctionCategory,ElementaryFunctionCategory)) is a package constructor +--R Abbreviation for GaloisGroupFactorizationUtilities is GALFACTU +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for GALFACTU +--R +--R------------------------------- Operations -------------------------------- +--R beauzamyBound : UP -> Integer bombieriNorm : UP -> F +--R height : UP -> F infinityNorm : UP -> F +--R length : UP -> F norm : (UP,PositiveInteger) -> F +--R quadraticNorm : UP -> F rootBound : UP -> Integer +--R singleFactorBound : UP -> Integer +--R bombieriNorm : (UP,PositiveInteger) -> F +--R singleFactorBound : (UP,NonNegativeInteger) -> Integer +--R --E 1 )spool @@ -41315,6 +43017,45 @@ GaloisGroupFactorizationUtilities(R,UP,F): Exports == Implementation where --S 1 of 1 )show GaloisGroupFactorizer +--R +--R GaloisGroupFactorizer(UP: UnivariatePolynomialCategory(Integer)) is a package constructor +--R Abbreviation for GaloisGroupFactorizer is GALFACT +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for GALFACT +--R +--R------------------------------- Operations -------------------------------- +--R factor : UP -> Factored(UP) musserTrials : () -> PositiveInteger +--R btwFact : (UP,Boolean,Set(NonNegativeInteger),NonNegativeInteger) -> Record(contp: Integer,factors: List(Record(irr: UP,pow: Integer))) +--R degreePartition : List(Record(factor: UP,degree: Integer)) -> Multiset(NonNegativeInteger) +--R eisensteinIrreducible? : UP -> Boolean +--R factor : (UP,NonNegativeInteger) -> Factored(UP) +--R factor : (UP,List(NonNegativeInteger)) -> Factored(UP) +--R factor : (UP,List(NonNegativeInteger),NonNegativeInteger) -> Factored(UP) +--R factor : (UP,NonNegativeInteger,NonNegativeInteger) -> Factored(UP) +--R factorOfDegree : (PositiveInteger,UP) -> Union(UP,"failed") +--R factorOfDegree : (PositiveInteger,UP,NonNegativeInteger) -> Union(UP,"failed") +--R factorOfDegree : (PositiveInteger,UP,List(NonNegativeInteger)) -> Union(UP,"failed") +--R factorOfDegree : (PositiveInteger,UP,List(NonNegativeInteger),NonNegativeInteger) -> Union(UP,"failed") +--R factorOfDegree : (PositiveInteger,UP,List(NonNegativeInteger),NonNegativeInteger,Boolean) -> Union(UP,"failed") +--R factorSquareFree : UP -> Factored(UP) +--R factorSquareFree : (UP,NonNegativeInteger) -> Factored(UP) +--R factorSquareFree : (UP,List(NonNegativeInteger)) -> Factored(UP) +--R factorSquareFree : (UP,List(NonNegativeInteger),NonNegativeInteger) -> Factored(UP) +--R factorSquareFree : (UP,NonNegativeInteger,NonNegativeInteger) -> Factored(UP) +--R henselFact : (UP,Boolean) -> Record(contp: Integer,factors: List(Record(irr: UP,pow: Integer))) +--R makeFR : Record(contp: Integer,factors: List(Record(irr: UP,pow: Integer))) -> Factored(UP) +--R modularFactor : UP -> Record(prime: Integer,factors: List(UP)) +--R musserTrials : PositiveInteger -> PositiveInteger +--R numberOfFactors : List(Record(factor: UP,degree: Integer)) -> NonNegativeInteger +--R stopMusserTrials : () -> PositiveInteger +--R stopMusserTrials : PositiveInteger -> PositiveInteger +--R tryFunctionalDecomposition : Boolean -> Boolean +--R tryFunctionalDecomposition? : () -> Boolean +--R useEisensteinCriterion : Boolean -> Boolean +--R useEisensteinCriterion? : () -> Boolean +--R useSingleFactorBound : Boolean -> Boolean +--R useSingleFactorBound? : () -> Boolean +--R --E 1 )spool @@ -42172,6 +43913,20 @@ GaloisGroupFactorizer(UP): Exports == Implementation where --S 1 of 1 )show GaloisGroupPolynomialUtilities +--R +--R GaloisGroupPolynomialUtilities(R: Ring,UP: UnivariatePolynomialCategory(R)) is a package constructor +--R Abbreviation for GaloisGroupPolynomialUtilities is GALPOLYU +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for GALPOLYU +--R +--R------------------------------- Operations -------------------------------- +--R monic? : UP -> Boolean reverse : UP -> UP +--R scaleRoots : (UP,R) -> UP shiftRoots : (UP,R) -> UP +--R unvectorise : Vector(R) -> UP +--R degreePartition : Factored(UP) -> Multiset(NonNegativeInteger) +--R factorOfDegree : (PositiveInteger,Factored(UP)) -> UP +--R factorsOfDegree : (PositiveInteger,Factored(UP)) -> List(UP) +--R --E 1 )spool @@ -42317,6 +44072,23 @@ GaloisGroupPolynomialUtilities(R,UP): Exports == Implementation where --S 1 of 1 )show GaloisGroupUtilities +--R +--R GaloisGroupUtilities(R: Ring) is a package constructor +--R Abbreviation for GaloisGroupUtilities is GALUTIL +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for GALUTIL +--R +--R------------------------------- Operations -------------------------------- +--R fillPascalTriangle : () -> Void +--R pascalTriangle : (NonNegativeInteger,Integer) -> R +--R rangePascalTriangle : NonNegativeInteger -> NonNegativeInteger +--R rangePascalTriangle : () -> NonNegativeInteger +--R safeCeiling : R -> Integer if R has FPS +--R safeFloor : R -> Integer if R has FPS +--R safetyMargin : NonNegativeInteger -> NonNegativeInteger if R has FPS +--R safetyMargin : () -> NonNegativeInteger if R has FPS +--R sizePascalTriangle : () -> NonNegativeInteger +--R --E 1 )spool @@ -42477,6 +44249,17 @@ GaloisGroupUtilities(R): Exports == Implementation where --S 1 of 1 )show GaussianFactorizationPackage +--R +--R GaussianFactorizationPackage is a package constructor +--R Abbreviation for GaussianFactorizationPackage is GAUSSFAC +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for GAUSSFAC +--R +--R------------------------------- Operations -------------------------------- +--R prime? : Complex(Integer) -> Boolean +--R factor : Complex(Integer) -> Factored(Complex(Integer)) +--R sumSquares : Integer -> List(Integer) +--R --E 1 )spool @@ -42693,6 +44476,17 @@ GaussianFactorizationPackage() : C == T --S 1 of 1 )show GeneralHenselPackage +--R +--R GeneralHenselPackage(RP: EuclideanDomain,TP: UnivariatePolynomialCategory(RP)) is a package constructor +--R Abbreviation for GeneralHenselPackage is GHENSEL +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for GHENSEL +--R +--R------------------------------- Operations -------------------------------- +--R reduction : (TP,RP) -> TP +--R HenselLift : (TP,List(TP),RP,PositiveInteger) -> Record(plist: List(TP),modulo: RP) +--R completeHensel : (TP,List(TP),RP,PositiveInteger) -> List(TP) +--R --E 1 )spool @@ -42886,6 +44680,18 @@ GeneralHenselPackage(RP,TP):C == T where --S 1 of 1 )show GeneralizedMultivariateFactorize +--R +--R GeneralizedMultivariateFactorize(OV,E: OrderedAbelianMonoidSup,S: IntegralDomain,R: IntegralDomain,P: PolynomialCategory(R,E,OV))where +--R OV: OrderedSetwith +--R convert : % -> Symbol +--R variable : Symbol -> Union(%,"failed") is a package constructor +--R Abbreviation for GeneralizedMultivariateFactorize is GENMFACT +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for GENMFACT +--R +--R------------------------------- Operations -------------------------------- +--R factor : P -> Factored(P) +--R --E 1 )spool @@ -42977,10 +44783,12 @@ GeneralizedMultivariateFactorize(OV,E,S,R,P) : C == T --R --R------------------------------- Operations -------------------------------- --R adjunctionDivisor : () -> DIVISOR desingTree : () -> List(DesTree) ---R eval : (PolyRing,Plc) -> K genus : () -> NonNegativeInteger ---R genusNeg : () -> Integer placesAbove : ProjPt -> List(Plc) ---R pointDominateBy : Plc -> ProjPt printInfo : List(Boolean) -> Void ---R reset : () -> Void setCurve : PolyRing -> PolyRing +--R eval : (PolyRing,Plc) -> K eval : (PolyRing,PolyRing,Plc) -> K +--R eval : (Fraction(PolyRing),Plc) -> K genus : () -> NonNegativeInteger +--R genusNeg : () -> Integer parametrize : (PolyRing,Plc) -> PCS +--R placesAbove : ProjPt -> List(Plc) pointDominateBy : Plc -> ProjPt +--R printInfo : List(Boolean) -> Void reset : () -> Void +--R setCurve : PolyRing -> PolyRing singularPoints : () -> List(ProjPt) --R theCurve : () -> PolyRing --R LPolynomial : () -> SparseUnivariatePolynomial(Integer) if K has FINITE --R LPolynomial : PositiveInteger -> SparseUnivariatePolynomial(Integer) if K has FINITE @@ -42988,8 +44796,6 @@ GeneralizedMultivariateFactorize(OV,E,S,R,P) : C == T --R ZetaFunction : PositiveInteger -> UnivariateTaylorSeriesCZero(Integer,t) if K has FINITE --R classNumber : () -> Integer if K has FINITE --R desingTreeWoFullParam : () -> List(DesTree) ---R eval : (PolyRing,PolyRing,Plc) -> K ---R eval : (Fraction(PolyRing),Plc) -> K --R evalIfCan : (PolyRing,Plc) -> Union(K,"failed") --R evalIfCan : (PolyRing,PolyRing,Plc) -> Union(K,"failed") --R evalIfCan : (Fraction(PolyRing),Plc) -> Union(K,"failed") @@ -43002,12 +44808,10 @@ GeneralizedMultivariateFactorize(OV,E,S,R,P) : C == T --R numberOfPlacesOfDegree : PositiveInteger -> Integer if K has FINITE --R numberPlacesDegExtDeg : (PositiveInteger,PositiveInteger) -> Integer if K has FINITE --R numberRatPlacesExtDeg : PositiveInteger -> Integer if K has FINITE ---R parametrize : (PolyRing,Plc) -> PCS --R placesOfDegree : PositiveInteger -> List(Plc) if K has FINITE --R rationalPlaces : () -> List(Plc) if K has FINITE --R rationalPoints : () -> List(ProjPt) if K has FINITE --R setSingularPoints : List(ProjPt) -> List(ProjPt) ---R singularPoints : () -> List(ProjPt) --R --E 1 @@ -43750,6 +45554,16 @@ GeneralPackageForAlgebraicFunctionField( K, --S 1 of 1 )show GeneralPolynomialGcdPackage +--R +--R GeneralPolynomialGcdPackage(E: OrderedAbelianMonoidSup,OV: OrderedSet,R: PolynomialFactorizationExplicit,P: PolynomialCategory(R,E,OV)) is a package constructor +--R Abbreviation for GeneralPolynomialGcdPackage is GENPGCD +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for GENPGCD +--R +--R------------------------------- Operations -------------------------------- +--R randomR : () -> R +--R gcdPolynomial : (SparseUnivariatePolynomial(P),SparseUnivariatePolynomial(P)) -> SparseUnivariatePolynomial(P) +--R --E 1 )spool @@ -44428,6 +46242,28 @@ GeneralPolynomialGcdPackage(E,OV,R,P):C == T where --S 1 of 1 )show GenerateUnivariatePowerSeries +--R +--R GenerateUnivariatePowerSeries(R: Join(IntegralDomain,OrderedSet,RetractableTo(Integer),LinearlyExplicitRingOver(Integer)),FE: Join(AlgebraicallyClosedField,TranscendentalFunctionCategory,FunctionSpace(R))) is a package constructor +--R Abbreviation for GenerateUnivariatePowerSeries is GENUPS +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for GENUPS +--R +--R------------------------------- Operations -------------------------------- +--R laurent : ((Integer -> FE),Equation(FE),UniversalSegment(Integer)) -> Any +--R laurent : (FE,Symbol,Equation(FE),UniversalSegment(Integer)) -> Any +--R puiseux : ((Fraction(Integer) -> FE),Equation(FE),UniversalSegment(Fraction(Integer)),Fraction(Integer)) -> Any +--R puiseux : (FE,Symbol,Equation(FE),UniversalSegment(Fraction(Integer)),Fraction(Integer)) -> Any +--R series : ((Integer -> FE),Equation(FE)) -> Any +--R series : (FE,Symbol,Equation(FE)) -> Any +--R series : ((Integer -> FE),Equation(FE),UniversalSegment(Integer)) -> Any +--R series : (FE,Symbol,Equation(FE),UniversalSegment(Integer)) -> Any +--R series : ((Fraction(Integer) -> FE),Equation(FE),UniversalSegment(Fraction(Integer)),Fraction(Integer)) -> Any +--R series : (FE,Symbol,Equation(FE),UniversalSegment(Fraction(Integer)),Fraction(Integer)) -> Any +--R taylor : ((Integer -> FE),Equation(FE)) -> Any +--R taylor : (FE,Symbol,Equation(FE)) -> Any +--R taylor : ((Integer -> FE),Equation(FE),UniversalSegment(NonNegativeInteger)) -> Any +--R taylor : (FE,Symbol,Equation(FE),UniversalSegment(NonNegativeInteger)) -> Any +--R --E 1 )spool @@ -44666,6 +46502,19 @@ GenerateUnivariatePowerSeries(R,FE): Exports == Implementation where --S 1 of 1 )show GenExEuclid +--R +--R GenExEuclid(R: EuclideanDomain,BP: UnivariatePolynomialCategory(R)) is a package constructor +--R Abbreviation for GenExEuclid is GENEEZ +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for GENEEZ +--R +--R------------------------------- Operations -------------------------------- +--R reduction : (BP,R) -> BP +--R compBound : (BP,List(BP)) -> NonNegativeInteger +--R solveid : (BP,R,Vector(List(BP))) -> Union(List(BP),"failed") +--R tablePow : (NonNegativeInteger,R,List(BP)) -> Union(Vector(List(BP)),"failed") +--R testModulus : (R,List(BP)) -> Boolean +--R --E 1 )spool @@ -44909,6 +46758,15 @@ GenExEuclid(R,BP) : C == T --S 1 of 1 )show GenUFactorize +--R +--R GenUFactorize(R: EuclideanDomain) is a package constructor +--R Abbreviation for GenUFactorize is GENUFACT +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for GENUFACT +--R +--R------------------------------- Operations -------------------------------- +--R factor : SparseUnivariatePolynomial(R) -> Factored(SparseUnivariatePolynomial(R)) +--R --E 1 )spool @@ -45016,6 +46874,27 @@ GenUFactorize(R) : public == private where --S 1 of 1 )show GenusZeroIntegration +--R +--R GenusZeroIntegration(R: Join(GcdDomain,RetractableTo(Integer),OrderedSet,CharacteristicZero,LinearlyExplicitRingOver(Integer)),F: Join(FunctionSpace(R),AlgebraicallyClosedField,TranscendentalFunctionCategory),L: SetCategory) is a package constructor +--R Abbreviation for GenusZeroIntegration is INTG0 +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for INTG0 +--R +--R------------------------------- Operations -------------------------------- +--R lift : (SparseUnivariatePolynomial(F),Kernel(F)) -> SparseUnivariatePolynomial(Fraction(SparseUnivariatePolynomial(F))) +--R multivariate : (SparseUnivariatePolynomial(Fraction(SparseUnivariatePolynomial(F))),Kernel(F),F) -> F +--R palgLODE0 : (L,F,Kernel(F),Kernel(F),F,SparseUnivariatePolynomial(F)) -> Record(particular: Union(F,"failed"),basis: List(F)) if L has LODOCAT(F) +--R palgLODE0 : (L,F,Kernel(F),Kernel(F),Kernel(F),F,Fraction(SparseUnivariatePolynomial(F))) -> Record(particular: Union(F,"failed"),basis: List(F)) if L has LODOCAT(F) +--R palgRDE0 : (F,F,Kernel(F),Kernel(F),((F,F,Symbol) -> Union(F,"failed")),F,SparseUnivariatePolynomial(F)) -> Union(F,"failed") +--R palgRDE0 : (F,F,Kernel(F),Kernel(F),((F,F,Symbol) -> Union(F,"failed")),Kernel(F),F,Fraction(SparseUnivariatePolynomial(F))) -> Union(F,"failed") +--R palgextint0 : (F,Kernel(F),Kernel(F),F,F,SparseUnivariatePolynomial(F)) -> Union(Record(ratpart: F,coeff: F),"failed") +--R palgextint0 : (F,Kernel(F),Kernel(F),F,Kernel(F),F,Fraction(SparseUnivariatePolynomial(F))) -> Union(Record(ratpart: F,coeff: F),"failed") +--R palgint0 : (F,Kernel(F),Kernel(F),F,SparseUnivariatePolynomial(F)) -> IntegrationResult(F) +--R palgint0 : (F,Kernel(F),Kernel(F),Kernel(F),F,Fraction(SparseUnivariatePolynomial(F))) -> IntegrationResult(F) +--R palglimint0 : (F,Kernel(F),Kernel(F),List(F),F,SparseUnivariatePolynomial(F)) -> Union(Record(mainpart: F,limitedlogs: List(Record(coeff: F,logand: F))),"failed") +--R palglimint0 : (F,Kernel(F),Kernel(F),List(F),Kernel(F),F,Fraction(SparseUnivariatePolynomial(F))) -> Union(Record(mainpart: F,limitedlogs: List(Record(coeff: F,logand: F))),"failed") +--R univariate : (F,Kernel(F),Kernel(F),SparseUnivariatePolynomial(F)) -> SparseUnivariatePolynomial(Fraction(SparseUnivariatePolynomial(F))) +--R --E 1 )spool @@ -45333,6 +47212,7 @@ GenusZeroIntegration(R, F, L): Exports == Implementation where )set message test on )set message auto off )clear all + --S 1 of 1 )show GnuDraw --R @@ -45477,6 +47357,19 @@ GnuDraw(): Exports == Implementation where --S 1 of 1 )show GosperSummationMethod +--R +--R GosperSummationMethod(E: OrderedAbelianMonoidSup,V: OrderedSet,R: IntegralDomain,P: PolynomialCategory(R,E,V),Q)where +--R Q: Join(RetractableTo(Fraction(Integer)),Field)with +--R coerce : P -> % +--R numer : % -> P +--R denom : % -> P is a package constructor +--R Abbreviation for GosperSummationMethod is GOSPER +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for GOSPER +--R +--R------------------------------- Operations -------------------------------- +--R GospersMethod : (Q,V,(() -> V)) -> Union(Q,"failed") +--R --E 1 )spool @@ -45730,6 +47623,21 @@ GosperSummationMethod(E, V, R, P, Q): Exports == Impl where --S 1 of 1 )show GraphicsDefaults +--R +--R GraphicsDefaults is a package constructor +--R Abbreviation for GraphicsDefaults is GRDEF +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for GRDEF +--R +--R------------------------------- Operations -------------------------------- +--R adaptive : () -> Boolean adaptive : Boolean -> Boolean +--R clipPointsDefault : () -> Boolean drawToScale : () -> Boolean +--R drawToScale : Boolean -> Boolean maxPoints : () -> Integer +--R maxPoints : Integer -> Integer minPoints : () -> Integer +--R minPoints : Integer -> Integer screenResolution : () -> Integer +--R clipPointsDefault : Boolean -> Boolean +--R screenResolution : Integer -> Integer +--R --E 1 )spool @@ -45910,7 +47818,7 @@ dot2eps "NeuralNet" --R --R------------------------------- Operations -------------------------------- --R dot2eps : String -> Void dotview : (String,String) -> Void ---R sampleDotGraph : () -> List(String) +--R sampleDotGraph : () -> List(String) --R standardDotHeader : () -> List(String) --R writeDotGraph : (List(String),List(String),String) -> Void --R @@ -46130,6 +48038,16 @@ Graphviz(): Exports == Implementation where --S 1 of 1 )show GrayCode +--R +--R GrayCode is a package constructor +--R Abbreviation for GrayCode is GRAY +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for GRAY +--R +--R------------------------------- Operations -------------------------------- +--R firstSubsetGray : PositiveInteger -> Vector(Vector(Integer)) +--R nextSubsetGray : (Vector(Vector(Integer)),PositiveInteger) -> Vector(Vector(Integer)) +--R --E 1 )spool @@ -46242,6 +48160,7 @@ GrayCode: public == private where )set message test on )set message auto off )clear all + --S 1 of 3 mfzn : SQMATRIX(6,DMP([x,y,z],Fraction INT)) := [ [0,1,1,1,1,1], [1,0,1,8/3,x,8/3], [1,1,0,1,8/3,y], [1,8/3,1,0,1,8/3], [1,x,8/3,1,0,1], [1,8/3,y,8/3,1,0] ] --R @@ -46311,6 +48230,25 @@ groebnerFactorize [eq,eval(eq, [x,y,z],[y,z,x]), eval(eq,[x,y,z],[z,x,y])] --R 3 3 3 --RType: List(List(DistributedMultivariatePolynomial([x,y,z],Fraction(Integer)))) --E 3 + +--S 4 of 4 +)show GroebnerFactorizationPackage +--R +--R GroebnerFactorizationPackage(Dom: Join(EuclideanDomain,CharacteristicZero),Expon: OrderedAbelianMonoidSup,VarSet: OrderedSet,Dpol: PolynomialCategory(Dom,Expon,VarSet)) is a package constructor +--R Abbreviation for GroebnerFactorizationPackage is GBF +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for GBF +--R +--R------------------------------- Operations -------------------------------- +--R factorGroebnerBasis : List(Dpol) -> List(List(Dpol)) +--R factorGroebnerBasis : (List(Dpol),Boolean) -> List(List(Dpol)) +--R groebnerFactorize : (List(Dpol),List(Dpol)) -> List(List(Dpol)) +--R groebnerFactorize : (List(Dpol),List(Dpol),Boolean) -> List(List(Dpol)) +--R groebnerFactorize : List(Dpol) -> List(List(Dpol)) +--R groebnerFactorize : (List(Dpol),Boolean) -> List(List(Dpol)) +--R +--E 4 + )spool )lisp (bye) \end{chunk} @@ -46814,6 +48752,34 @@ GroebnerFactorizationPackage(Dom, Expon, VarSet, Dpol): T == C where --S 1 of 1 )show GroebnerInternalPackage +--R +--R GroebnerInternalPackage(Dom: GcdDomain,Expon: OrderedAbelianMonoidSup,VarSet: OrderedSet,Dpol: PolynomialCategory(Dom,Expon,VarSet)) is a package constructor +--R Abbreviation for GroebnerInternalPackage is GBINTERN +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for GBINTERN +--R +--R------------------------------- Operations -------------------------------- +--R credPol : (Dpol,List(Dpol)) -> Dpol critM : (Expon,Expon) -> Boolean +--R hMonic : Dpol -> Dpol lepol : Dpol -> Integer +--R minGbasis : List(Dpol) -> List(Dpol) prinb : Integer -> Void +--R prinpolINFO : List(Dpol) -> Void prinshINFO : Dpol -> Void +--R redPol : (Dpol,List(Dpol)) -> Dpol +--R critB : (Expon,Expon,Expon,Expon) -> Boolean +--R critBonD : (Dpol,List(Record(lcmfij: Expon,totdeg: NonNegativeInteger,poli: Dpol,polj: Dpol))) -> List(Record(lcmfij: Expon,totdeg: NonNegativeInteger,poli: Dpol,polj: Dpol)) +--R critMTonD1 : List(Record(lcmfij: Expon,totdeg: NonNegativeInteger,poli: Dpol,polj: Dpol)) -> List(Record(lcmfij: Expon,totdeg: NonNegativeInteger,poli: Dpol,polj: Dpol)) +--R critMonD1 : (Expon,List(Record(lcmfij: Expon,totdeg: NonNegativeInteger,poli: Dpol,polj: Dpol))) -> List(Record(lcmfij: Expon,totdeg: NonNegativeInteger,poli: Dpol,polj: Dpol)) +--R critT : Record(lcmfij: Expon,totdeg: NonNegativeInteger,poli: Dpol,polj: Dpol) -> Boolean +--R critpOrder : (Record(lcmfij: Expon,totdeg: NonNegativeInteger,poli: Dpol,polj: Dpol),Record(lcmfij: Expon,totdeg: NonNegativeInteger,poli: Dpol,polj: Dpol)) -> Boolean +--R fprindINFO : (Record(lcmfij: Expon,totdeg: NonNegativeInteger,poli: Dpol,polj: Dpol),Dpol,Dpol,Integer,Integer,Integer,Integer) -> Integer +--R gbasis : (List(Dpol),Integer,Integer) -> List(Dpol) +--R makeCrit : (Record(totdeg: NonNegativeInteger,pol: Dpol),Dpol,NonNegativeInteger) -> Record(lcmfij: Expon,totdeg: NonNegativeInteger,poli: Dpol,polj: Dpol) +--R prindINFO : (Record(lcmfij: Expon,totdeg: NonNegativeInteger,poli: Dpol,polj: Dpol),Dpol,Dpol,Integer,Integer,Integer) -> Integer +--R redPo : (Dpol,List(Dpol)) -> Record(poly: Dpol,mult: Dom) +--R sPol : Record(lcmfij: Expon,totdeg: NonNegativeInteger,poli: Dpol,polj: Dpol) -> Dpol +--R updatD : (List(Record(lcmfij: Expon,totdeg: NonNegativeInteger,poli: Dpol,polj: Dpol)),List(Record(lcmfij: Expon,totdeg: NonNegativeInteger,poli: Dpol,polj: Dpol))) -> List(Record(lcmfij: Expon,totdeg: NonNegativeInteger,poli: Dpol,polj: Dpol)) +--R updatF : (Dpol,NonNegativeInteger,List(Record(totdeg: NonNegativeInteger,pol: Dpol))) -> List(Record(totdeg: NonNegativeInteger,pol: Dpol)) +--R virtualDegree : Dpol -> NonNegativeInteger +--R --E 1 )spool @@ -47332,21 +49298,22 @@ GroebnerInternalPackage(Dom, Expon, VarSet, Dpol): T == C where )set message test on )set message auto off )clear all ---S 1 of 24 + +--S 1 of 25 s1:DMP([w,p,z,t,s,b],FRAC(INT)):= 45*p + 35*s - 165*b - 36 --R --R (1) 45p + 35s - 165b - 36 --R Type: DistributedMultivariatePolynomial([w,p,z,t,s,b],Fraction(Integer)) --E 1 ---S 2 of 24 +--S 2 of 25 s2:DMP([w,p,z,t,s,b],FRAC(INT)):= 35*p + 40*z + 25*t - 27*s --R --R (2) 35p + 40z + 25t - 27s --R Type: DistributedMultivariatePolynomial([w,p,z,t,s,b],Fraction(Integer)) --E 2 ---S 3 of 24 +--S 3 of 25 s3:DMP([w,p,z,t,s,b],FRAC(INT)):= 15*w + 25*p*s + 30*z - 18*t - 165*b**2 --R --R 2 @@ -47354,14 +49321,14 @@ s3:DMP([w,p,z,t,s,b],FRAC(INT)):= 15*w + 25*p*s + 30*z - 18*t - 165*b**2 --R Type: DistributedMultivariatePolynomial([w,p,z,t,s,b],Fraction(Integer)) --E 3 ---S 4 of 24 +--S 4 of 25 s4:DMP([w,p,z,t,s,b],FRAC(INT)):= -9*w + 15*p*t + 20*z*s --R --R (4) - 9w + 15p t + 20z s --R Type: DistributedMultivariatePolynomial([w,p,z,t,s,b],Fraction(Integer)) --E 4 ---S 5 of 24 +--S 5 of 25 s5:DMP([w,p,z,t,s,b],FRAC(INT)):= w*p + 2*z*t - 11*b**3 --R --R 3 @@ -47369,7 +49336,7 @@ s5:DMP([w,p,z,t,s,b],FRAC(INT)):= w*p + 2*z*t - 11*b**3 --R Type: DistributedMultivariatePolynomial([w,p,z,t,s,b],Fraction(Integer)) --E 5 ---S 6 of 24 +--S 6 of 25 s6:DMP([w,p,z,t,s,b],FRAC(INT)):= 99*w - 11*b*s + 3*b**2 --R --R 2 @@ -47377,7 +49344,7 @@ s6:DMP([w,p,z,t,s,b],FRAC(INT)):= 99*w - 11*b*s + 3*b**2 --R Type: DistributedMultivariatePolynomial([w,p,z,t,s,b],Fraction(Integer)) --E 6 ---S 7 of 24 +--S 7 of 25 s7:DMP([w,p,z,t,s,b],FRAC(INT)):= b**2 + 33/50*b + 2673/10000 --R --R 2 33 2673 @@ -47386,7 +49353,7 @@ s7:DMP([w,p,z,t,s,b],FRAC(INT)):= b**2 + 33/50*b + 2673/10000 --R Type: DistributedMultivariatePolynomial([w,p,z,t,s,b],Fraction(Integer)) --E 7 ---S 8 of 24 +--S 8 of 25 sn7:=[s1,s2,s3,s4,s5,s6,s7] --R --R (8) @@ -47399,7 +49366,7 @@ sn7:=[s1,s2,s3,s4,s5,s6,s7] --RType: List(DistributedMultivariatePolynomial([w,p,z,t,s,b],Fraction(Integer))) --E 8 ---S 9 of 24 +--S 9 of 25 groebner(sn7) --R --R (9) @@ -47412,7 +49379,7 @@ groebner(sn7) --RType: List(DistributedMultivariatePolynomial([w,p,z,t,s,b],Fraction(Integer))) --E 9 ---S 10 of 24 +--S 10 of 25 groebner(sn7,"redcrit") --R --R @@ -47542,7 +49509,7 @@ groebner(sn7,"redcrit") --RType: List(DistributedMultivariatePolynomial([w,p,z,t,s,b],Fraction(Integer))) --E 10 ---S 11 of 24 +--S 11 of 25 groebner(sn7,"info") --R --R you choose option -info- @@ -47621,7 +49588,7 @@ groebner(sn7,"info") --RType: List(DistributedMultivariatePolynomial([w,p,z,t,s,b],Fraction(Integer))) --E 11 ---S 12 of 24 +--S 12 of 25 groebner(sn7,"redcrit","info") --R --R @@ -47816,35 +49783,35 @@ groebner(sn7,"redcrit","info") --RType: List(DistributedMultivariatePolynomial([w,p,z,t,s,b],Fraction(Integer))) --E 12 ---S 13 of 24 +--S 13 of 25 hs1:HDMP([w,p,z,t,s,b],FRAC(INT)):= 45*p + 35*s - 165*b - 36 --R --R (13) 45p + 35s - 165b - 36 --RType: HomogeneousDistributedMultivariatePolynomial([w,p,z,t,s,b],Fraction(Integer)) --E 13 ---S 14 of 24 +--S 14 of 25 hs2:HDMP([w,p,z,t,s,b],FRAC(INT)):= 35*p + 40*z + 25*t - 27*s --R --R (14) 35p + 40z + 25t - 27s --RType: HomogeneousDistributedMultivariatePolynomial([w,p,z,t,s,b],Fraction(Integer)) --E 14 ---S 15 of 24 +--S 15 of 25 hs3:HDMP([w,p,z,t,s,b],FRAC(INT)):= 15*w + 25*p*s + 30*z - 18*t - 165*b**2 --R 2 --R (15) 25p s - 165b + 15w + 30z - 18t --RType: HomogeneousDistributedMultivariatePolynomial([w,p,z,t,s,b],Fraction(Integer)) --E 15 ---S 16 of 24 +--S 16 of 25 hs4:HDMP([w,p,z,t,s,b],FRAC(INT)):= -9*w + 15*p*t + 20*z*s --R --R (16) 15p t + 20z s - 9w --RType: HomogeneousDistributedMultivariatePolynomial([w,p,z,t,s,b],Fraction(Integer)) --E 16 ---S 17 of 24 +--S 17 of 25 hs5:HDMP([w,p,z,t,s,b],FRAC(INT)):= w*p + 2*z*t - 11*b**3 --R --R 3 @@ -47852,7 +49819,7 @@ hs5:HDMP([w,p,z,t,s,b],FRAC(INT)):= w*p + 2*z*t - 11*b**3 --RType: HomogeneousDistributedMultivariatePolynomial([w,p,z,t,s,b],Fraction(Integer)) --E 17 ---S 18 of 24 +--S 18 of 25 hs6:HDMP([w,p,z,t,s,b],FRAC(INT)):= 99*w - 11*b*s + 3*b**2 --R --R 2 @@ -47860,7 +49827,7 @@ hs6:HDMP([w,p,z,t,s,b],FRAC(INT)):= 99*w - 11*b*s + 3*b**2 --RType: HomogeneousDistributedMultivariatePolynomial([w,p,z,t,s,b],Fraction(Integer)) --E 18 ---S 19 of 24 +--S 19 of 25 hs7:HDMP([w,p,z,t,s,b],FRAC(INT)):= b**2 + 33/50*b + 2673/10000 --R --R 2 33 2673 @@ -47869,7 +49836,7 @@ hs7:HDMP([w,p,z,t,s,b],FRAC(INT)):= b**2 + 33/50*b + 2673/10000 --RType: HomogeneousDistributedMultivariatePolynomial([w,p,z,t,s,b],Fraction(Integer)) --E 19 ---S 20 of 24 +--S 20 of 25 hsn7:=[hs1,hs2,hs3,hs4,hs5,hs6,hs7] --R --R (20) @@ -47882,7 +49849,7 @@ hsn7:=[hs1,hs2,hs3,hs4,hs5,hs6,hs7] --RType: List(HomogeneousDistributedMultivariatePolynomial([w,p,z,t,s,b],Fraction(Integer))) --E 20 ---S 21 of 24 +--S 21 of 25 groebner(hsn7) --R --R (21) @@ -47895,7 +49862,7 @@ groebner(hsn7) --RType: List(HomogeneousDistributedMultivariatePolynomial([w,p,z,t,s,b],Fraction(Integer))) --E 21 ---S 22 of 24 +--S 22 of 25 groebner(hsn7,"redcrit") --R --R @@ -48115,7 +50082,7 @@ groebner(hsn7,"redcrit") --RType: List(HomogeneousDistributedMultivariatePolynomial([w,p,z,t,s,b],Fraction(Integer))) --E 22 ---S 23 of 24 +--S 23 of 25 groebner(hsn7,"info") --R --R you choose option -info- @@ -48237,7 +50204,7 @@ groebner(hsn7,"info") --RType: List(HomogeneousDistributedMultivariatePolynomial([w,p,z,t,s,b],Fraction(Integer))) --E 23 ---S 24 of 24 +--S 24 of 25 groebner(hsn7,"redcrit","info") --R --R @@ -48565,12 +50532,28 @@ groebner(hsn7,"redcrit","info") --RType: List(HomogeneousDistributedMultivariatePolynomial([w,p,z,t,s,b],Fraction(Integer))) --E 24 +--S 25 of 25 +)show GroebnerPackage +--R +--R GroebnerPackage(Dom: GcdDomain,Expon: OrderedAbelianMonoidSup,VarSet: OrderedSet,Dpol: PolynomialCategory(Dom,Expon,VarSet)) is a package constructor +--R Abbreviation for GroebnerPackage is GB +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for GB +--R +--R------------------------------- Operations -------------------------------- +--R groebner : List(Dpol) -> List(Dpol) +--R groebner : (List(Dpol),String) -> List(Dpol) +--R groebner : (List(Dpol),String,String) -> List(Dpol) +--R normalForm : (Dpol,List(Dpol)) -> Dpol if Dom has FIELD +--R +--E 25 + )spool )lisp (bye) \end{chunk} \begin{chunk}{GroebnerPackage.help} ==================================================================== -groebner examples +GroebnerPackage examples ==================================================================== GroebnerPackage computes groebner bases for polynomial ideals. The basic @@ -48813,6 +50796,17 @@ GroebnerPackage(Dom, Expon, VarSet, Dpol): T == C where --S 1 of 1 )show GroebnerSolve +--R +--R GroebnerSolve(lv: List(Symbol),F: GcdDomain,R: GcdDomain) is a package constructor +--R Abbreviation for GroebnerSolve is GROEBSOL +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for GROEBSOL +--R +--R------------------------------- Operations -------------------------------- +--R genericPosition : (List(DistributedMultivariatePolynomial(lv,F)),List(OrderedVariableList(lv))) -> Record(dpolys: List(DistributedMultivariatePolynomial(lv,F)),coords: List(Integer)) +--R groebSolve : (List(DistributedMultivariatePolynomial(lv,F)),List(OrderedVariableList(lv))) -> List(List(DistributedMultivariatePolynomial(lv,F))) +--R testDim : (List(HomogeneousDistributedMultivariatePolynomial(lv,F)),List(OrderedVariableList(lv))) -> Union(List(HomogeneousDistributedMultivariatePolynomial(lv,F)),"failed") +--R --E 1 )spool @@ -49053,6 +51047,54 @@ GroebnerSolve(lv,F,R) : C == T --S 1 of 1 )show Guess +--R +--R Guess(F: Field,S: GcdDomain,EXPRR,R: Join(OrderedSet,IntegralDomain),retract: (R -> F),coerce: (F -> EXPRR))where +--R EXPRR: Join(FunctionSpace(Integer),IntegralDomain,RetractableTo(R),RetractableTo(Symbol),RetractableTo(Integer),CombinatorialOpsCategory,PartialDifferentialRing(Symbol))with +--R ?*? : (%,%) -> % +--R ?/? : (%,%) -> % +--R ?**? : (%,%) -> % +--R numerator : % -> % +--R denominator : % -> % +--R ground? : % -> Boolean is a package constructor +--R Abbreviation for Guess is GUESS +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for GUESS +--R +--R------------------------------- Operations -------------------------------- +--R diffHP : List(GuessOption) -> Record(guessStream: (UnivariateFormalPowerSeries(F) -> Stream(UnivariateFormalPowerSeries(F))),degreeStream: Stream(NonNegativeInteger),testStream: (UnivariateFormalPowerSeries(SparseUnivariatePolynomial(F)) -> Stream(UnivariateFormalPowerSeries(SparseUnivariatePolynomial(F)))),exprStream: ((EXPRR,Symbol) -> Stream(EXPRR)),A: ((NonNegativeInteger,NonNegativeInteger,SparseUnivariatePolynomial(S)) -> S),AF: ((NonNegativeInteger,NonNegativeInteger,UnivariateFormalPowerSeries(SparseUnivariatePolynomial(F))) -> SparseUnivariatePolynomial(F)),AX: ((NonNegativeInteger,Symbol,EXPRR) -> EXPRR),C: (NonNegativeInteger -> List(S))) +--R diffHP : Symbol -> (List(GuessOption) -> Record(guessStream: (UnivariateFormalPowerSeries(F) -> Stream(UnivariateFormalPowerSeries(F))),degreeStream: Stream(NonNegativeInteger),testStream: (UnivariateFormalPowerSeries(SparseUnivariatePolynomial(F)) -> Stream(UnivariateFormalPowerSeries(SparseUnivariatePolynomial(F)))),exprStream: ((EXPRR,Symbol) -> Stream(EXPRR)),A: ((NonNegativeInteger,NonNegativeInteger,SparseUnivariatePolynomial(S)) -> S),AF: ((NonNegativeInteger,NonNegativeInteger,UnivariateFormalPowerSeries(SparseUnivariatePolynomial(F))) -> SparseUnivariatePolynomial(F)),AX: ((NonNegativeInteger,Symbol,EXPRR) -> EXPRR),C: (NonNegativeInteger -> List(S)))) if F has RETRACT(SYMBOL) and S has RETRACT(SYMBOL) +--R guess : List(F) -> List(Record(function: EXPRR,order: NonNegativeInteger)) +--R guess : (List(F),List(GuessOption)) -> List(Record(function: EXPRR,order: NonNegativeInteger)) +--R guess : (List(F),List(((List(F),List(GuessOption)) -> List(Record(function: EXPRR,order: NonNegativeInteger)))),List(Symbol)) -> List(Record(function: EXPRR,order: NonNegativeInteger)) +--R guess : (List(F),List(((List(F),List(GuessOption)) -> List(Record(function: EXPRR,order: NonNegativeInteger)))),List(Symbol),List(GuessOption)) -> List(Record(function: EXPRR,order: NonNegativeInteger)) +--R guessADE : List(F) -> List(Record(function: EXPRR,order: NonNegativeInteger)) +--R guessADE : (List(F),List(GuessOption)) -> List(Record(function: EXPRR,order: NonNegativeInteger)) +--R guessADE : Symbol -> ((List(F),List(GuessOption)) -> List(Record(function: EXPRR,order: NonNegativeInteger))) if F has RETRACT(SYMBOL) and S has RETRACT(SYMBOL) +--R guessAlg : List(F) -> List(Record(function: EXPRR,order: NonNegativeInteger)) +--R guessAlg : (List(F),List(GuessOption)) -> List(Record(function: EXPRR,order: NonNegativeInteger)) +--R guessBinRat : List(F) -> List(Record(function: EXPRR,order: NonNegativeInteger)) +--R guessBinRat : (List(F),List(GuessOption)) -> List(Record(function: EXPRR,order: NonNegativeInteger)) +--R guessBinRat : Symbol -> ((List(F),List(GuessOption)) -> List(Record(function: EXPRR,order: NonNegativeInteger))) if F has RETRACT(SYMBOL) and S has RETRACT(SYMBOL) +--R guessExpRat : List(F) -> List(Record(function: EXPRR,order: NonNegativeInteger)) +--R guessExpRat : (List(F),List(GuessOption)) -> List(Record(function: EXPRR,order: NonNegativeInteger)) +--R guessExpRat : Symbol -> ((List(F),List(GuessOption)) -> List(Record(function: EXPRR,order: NonNegativeInteger))) if F has RETRACT(SYMBOL) and S has RETRACT(SYMBOL) +--R guessHP : (List(GuessOption) -> Record(guessStream: (UnivariateFormalPowerSeries(F) -> Stream(UnivariateFormalPowerSeries(F))),degreeStream: Stream(NonNegativeInteger),testStream: (UnivariateFormalPowerSeries(SparseUnivariatePolynomial(F)) -> Stream(UnivariateFormalPowerSeries(SparseUnivariatePolynomial(F)))),exprStream: ((EXPRR,Symbol) -> Stream(EXPRR)),A: ((NonNegativeInteger,NonNegativeInteger,SparseUnivariatePolynomial(S)) -> S),AF: ((NonNegativeInteger,NonNegativeInteger,UnivariateFormalPowerSeries(SparseUnivariatePolynomial(F))) -> SparseUnivariatePolynomial(F)),AX: ((NonNegativeInteger,Symbol,EXPRR) -> EXPRR),C: (NonNegativeInteger -> List(S)))) -> ((List(F),List(GuessOption)) -> List(Record(function: EXPRR,order: NonNegativeInteger))) +--R guessHolo : List(F) -> List(Record(function: EXPRR,order: NonNegativeInteger)) +--R guessHolo : (List(F),List(GuessOption)) -> List(Record(function: EXPRR,order: NonNegativeInteger)) +--R guessPRec : (List(F),List(GuessOption)) -> List(Record(function: EXPRR,order: NonNegativeInteger)) +--R guessPRec : List(F) -> List(Record(function: EXPRR,order: NonNegativeInteger)) +--R guessPRec : Symbol -> ((List(F),List(GuessOption)) -> List(Record(function: EXPRR,order: NonNegativeInteger))) if F has RETRACT(SYMBOL) and S has RETRACT(SYMBOL) +--R guessPade : (List(F),List(GuessOption)) -> List(Record(function: EXPRR,order: NonNegativeInteger)) +--R guessPade : List(F) -> List(Record(function: EXPRR,order: NonNegativeInteger)) +--R guessRat : (List(F),List(GuessOption)) -> List(Record(function: EXPRR,order: NonNegativeInteger)) +--R guessRat : List(F) -> List(Record(function: EXPRR,order: NonNegativeInteger)) +--R guessRat : Symbol -> ((List(F),List(GuessOption)) -> List(Record(function: EXPRR,order: NonNegativeInteger))) if F has RETRACT(SYMBOL) and S has RETRACT(SYMBOL) +--R guessRec : List(F) -> List(Record(function: EXPRR,order: NonNegativeInteger)) +--R guessRec : (List(F),List(GuessOption)) -> List(Record(function: EXPRR,order: NonNegativeInteger)) +--R guessRec : Symbol -> ((List(F),List(GuessOption)) -> List(Record(function: EXPRR,order: NonNegativeInteger))) if F has RETRACT(SYMBOL) and S has RETRACT(SYMBOL) +--R shiftHP : List(GuessOption) -> Record(guessStream: (UnivariateFormalPowerSeries(F) -> Stream(UnivariateFormalPowerSeries(F))),degreeStream: Stream(NonNegativeInteger),testStream: (UnivariateFormalPowerSeries(SparseUnivariatePolynomial(F)) -> Stream(UnivariateFormalPowerSeries(SparseUnivariatePolynomial(F)))),exprStream: ((EXPRR,Symbol) -> Stream(EXPRR)),A: ((NonNegativeInteger,NonNegativeInteger,SparseUnivariatePolynomial(S)) -> S),AF: ((NonNegativeInteger,NonNegativeInteger,UnivariateFormalPowerSeries(SparseUnivariatePolynomial(F))) -> SparseUnivariatePolynomial(F)),AX: ((NonNegativeInteger,Symbol,EXPRR) -> EXPRR),C: (NonNegativeInteger -> List(S))) +--R shiftHP : Symbol -> (List(GuessOption) -> Record(guessStream: (UnivariateFormalPowerSeries(F) -> Stream(UnivariateFormalPowerSeries(F))),degreeStream: Stream(NonNegativeInteger),testStream: (UnivariateFormalPowerSeries(SparseUnivariatePolynomial(F)) -> Stream(UnivariateFormalPowerSeries(SparseUnivariatePolynomial(F)))),exprStream: ((EXPRR,Symbol) -> Stream(EXPRR)),A: ((NonNegativeInteger,NonNegativeInteger,SparseUnivariatePolynomial(S)) -> S),AF: ((NonNegativeInteger,NonNegativeInteger,UnivariateFormalPowerSeries(SparseUnivariatePolynomial(F))) -> SparseUnivariatePolynomial(F)),AX: ((NonNegativeInteger,Symbol,EXPRR) -> EXPRR),C: (NonNegativeInteger -> List(S)))) if F has RETRACT(SYMBOL) and S has RETRACT(SYMBOL) +--R --E 1 )spool @@ -50853,6 +52895,47 @@ Guess(F, S, EXPRR, R, retract, coerce): Exports == Implementation where --S 1 of 1 )show GuessAlgebraicNumber +--R +--R GuessAlgebraicNumber is a package constructor +--R Abbreviation for GuessAlgebraicNumber is GUESSAN +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for GUESSAN +--R +--R------------------------------- Operations -------------------------------- +--R diffHP : List(GuessOption) -> Record(guessStream: (UnivariateFormalPowerSeries(AlgebraicNumber) -> Stream(UnivariateFormalPowerSeries(AlgebraicNumber))),degreeStream: Stream(NonNegativeInteger),testStream: (UnivariateFormalPowerSeries(SparseUnivariatePolynomial(AlgebraicNumber)) -> Stream(UnivariateFormalPowerSeries(SparseUnivariatePolynomial(AlgebraicNumber)))),exprStream: ((Expression(Integer),Symbol) -> Stream(Expression(Integer))),A: ((NonNegativeInteger,NonNegativeInteger,SparseUnivariatePolynomial(AlgebraicNumber)) -> AlgebraicNumber),AF: ((NonNegativeInteger,NonNegativeInteger,UnivariateFormalPowerSeries(SparseUnivariatePolynomial(AlgebraicNumber))) -> SparseUnivariatePolynomial(AlgebraicNumber)),AX: ((NonNegativeInteger,Symbol,Expression(Integer)) -> Expression(Integer)),C: (NonNegativeInteger -> List(AlgebraicNumber))) +--R diffHP : Symbol -> (List(GuessOption) -> Record(guessStream: (UnivariateFormalPowerSeries(AlgebraicNumber) -> Stream(UnivariateFormalPowerSeries(AlgebraicNumber))),degreeStream: Stream(NonNegativeInteger),testStream: (UnivariateFormalPowerSeries(SparseUnivariatePolynomial(AlgebraicNumber)) -> Stream(UnivariateFormalPowerSeries(SparseUnivariatePolynomial(AlgebraicNumber)))),exprStream: ((Expression(Integer),Symbol) -> Stream(Expression(Integer))),A: ((NonNegativeInteger,NonNegativeInteger,SparseUnivariatePolynomial(AlgebraicNumber)) -> AlgebraicNumber),AF: ((NonNegativeInteger,NonNegativeInteger,UnivariateFormalPowerSeries(SparseUnivariatePolynomial(AlgebraicNumber))) -> SparseUnivariatePolynomial(AlgebraicNumber)),AX: ((NonNegativeInteger,Symbol,Expression(Integer)) -> Expression(Integer)),C: (NonNegativeInteger -> List(AlgebraicNumber)))) if AlgebraicNumber has RETRACT(SYMBOL) +--R guess : List(AlgebraicNumber) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guess : (List(AlgebraicNumber),List(GuessOption)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guess : (List(AlgebraicNumber),List(((List(AlgebraicNumber),List(GuessOption)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)))),List(Symbol)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guess : (List(AlgebraicNumber),List(((List(AlgebraicNumber),List(GuessOption)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)))),List(Symbol),List(GuessOption)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guessADE : List(AlgebraicNumber) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guessADE : (List(AlgebraicNumber),List(GuessOption)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guessADE : Symbol -> ((List(AlgebraicNumber),List(GuessOption)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger))) if AlgebraicNumber has RETRACT(SYMBOL) +--R guessAlg : List(AlgebraicNumber) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guessAlg : (List(AlgebraicNumber),List(GuessOption)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guessBinRat : List(AlgebraicNumber) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guessBinRat : (List(AlgebraicNumber),List(GuessOption)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guessBinRat : Symbol -> ((List(AlgebraicNumber),List(GuessOption)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger))) if AlgebraicNumber has RETRACT(SYMBOL) +--R guessExpRat : List(AlgebraicNumber) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guessExpRat : (List(AlgebraicNumber),List(GuessOption)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guessExpRat : Symbol -> ((List(AlgebraicNumber),List(GuessOption)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger))) if AlgebraicNumber has RETRACT(SYMBOL) +--R guessHP : (List(GuessOption) -> Record(guessStream: (UnivariateFormalPowerSeries(AlgebraicNumber) -> Stream(UnivariateFormalPowerSeries(AlgebraicNumber))),degreeStream: Stream(NonNegativeInteger),testStream: (UnivariateFormalPowerSeries(SparseUnivariatePolynomial(AlgebraicNumber)) -> Stream(UnivariateFormalPowerSeries(SparseUnivariatePolynomial(AlgebraicNumber)))),exprStream: ((Expression(Integer),Symbol) -> Stream(Expression(Integer))),A: ((NonNegativeInteger,NonNegativeInteger,SparseUnivariatePolynomial(AlgebraicNumber)) -> AlgebraicNumber),AF: ((NonNegativeInteger,NonNegativeInteger,UnivariateFormalPowerSeries(SparseUnivariatePolynomial(AlgebraicNumber))) -> SparseUnivariatePolynomial(AlgebraicNumber)),AX: ((NonNegativeInteger,Symbol,Expression(Integer)) -> Expression(Integer)),C: (NonNegativeInteger -> List(AlgebraicNumber)))) -> ((List(AlgebraicNumber),List(GuessOption)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger))) +--R guessHolo : List(AlgebraicNumber) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guessHolo : (List(AlgebraicNumber),List(GuessOption)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guessPRec : (List(AlgebraicNumber),List(GuessOption)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guessPRec : List(AlgebraicNumber) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guessPRec : Symbol -> ((List(AlgebraicNumber),List(GuessOption)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger))) if AlgebraicNumber has RETRACT(SYMBOL) +--R guessPade : (List(AlgebraicNumber),List(GuessOption)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guessPade : List(AlgebraicNumber) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guessRat : (List(AlgebraicNumber),List(GuessOption)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guessRat : List(AlgebraicNumber) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guessRat : Symbol -> ((List(AlgebraicNumber),List(GuessOption)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger))) if AlgebraicNumber has RETRACT(SYMBOL) +--R guessRec : List(AlgebraicNumber) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guessRec : (List(AlgebraicNumber),List(GuessOption)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guessRec : Symbol -> ((List(AlgebraicNumber),List(GuessOption)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger))) if AlgebraicNumber has RETRACT(SYMBOL) +--R shiftHP : List(GuessOption) -> Record(guessStream: (UnivariateFormalPowerSeries(AlgebraicNumber) -> Stream(UnivariateFormalPowerSeries(AlgebraicNumber))),degreeStream: Stream(NonNegativeInteger),testStream: (UnivariateFormalPowerSeries(SparseUnivariatePolynomial(AlgebraicNumber)) -> Stream(UnivariateFormalPowerSeries(SparseUnivariatePolynomial(AlgebraicNumber)))),exprStream: ((Expression(Integer),Symbol) -> Stream(Expression(Integer))),A: ((NonNegativeInteger,NonNegativeInteger,SparseUnivariatePolynomial(AlgebraicNumber)) -> AlgebraicNumber),AF: ((NonNegativeInteger,NonNegativeInteger,UnivariateFormalPowerSeries(SparseUnivariatePolynomial(AlgebraicNumber))) -> SparseUnivariatePolynomial(AlgebraicNumber)),AX: ((NonNegativeInteger,Symbol,Expression(Integer)) -> Expression(Integer)),C: (NonNegativeInteger -> List(AlgebraicNumber))) +--R shiftHP : Symbol -> (List(GuessOption) -> Record(guessStream: (UnivariateFormalPowerSeries(AlgebraicNumber) -> Stream(UnivariateFormalPowerSeries(AlgebraicNumber))),degreeStream: Stream(NonNegativeInteger),testStream: (UnivariateFormalPowerSeries(SparseUnivariatePolynomial(AlgebraicNumber)) -> Stream(UnivariateFormalPowerSeries(SparseUnivariatePolynomial(AlgebraicNumber)))),exprStream: ((Expression(Integer),Symbol) -> Stream(Expression(Integer))),A: ((NonNegativeInteger,NonNegativeInteger,SparseUnivariatePolynomial(AlgebraicNumber)) -> AlgebraicNumber),AF: ((NonNegativeInteger,NonNegativeInteger,UnivariateFormalPowerSeries(SparseUnivariatePolynomial(AlgebraicNumber))) -> SparseUnivariatePolynomial(AlgebraicNumber)),AX: ((NonNegativeInteger,Symbol,Expression(Integer)) -> Expression(Integer)),C: (NonNegativeInteger -> List(AlgebraicNumber)))) if AlgebraicNumber has RETRACT(SYMBOL) +--R --E 1 )spool @@ -50919,6 +53002,47 @@ GuessAlgebraicNumber() == Guess(AlgebraicNumber, AlgebraicNumber, --S 1 of 1 )show GuessFinite +--R +--R GuessFinite(F: Join(FiniteFieldCategory,ConvertibleTo(Integer))) is a package constructor +--R Abbreviation for GuessFinite is GUESSF +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for GUESSF +--R +--R------------------------------- Operations -------------------------------- +--R diffHP : List(GuessOption) -> Record(guessStream: (UnivariateFormalPowerSeries(F) -> Stream(UnivariateFormalPowerSeries(F))),degreeStream: Stream(NonNegativeInteger),testStream: (UnivariateFormalPowerSeries(SparseUnivariatePolynomial(F)) -> Stream(UnivariateFormalPowerSeries(SparseUnivariatePolynomial(F)))),exprStream: ((Expression(Integer),Symbol) -> Stream(Expression(Integer))),A: ((NonNegativeInteger,NonNegativeInteger,SparseUnivariatePolynomial(F)) -> F),AF: ((NonNegativeInteger,NonNegativeInteger,UnivariateFormalPowerSeries(SparseUnivariatePolynomial(F))) -> SparseUnivariatePolynomial(F)),AX: ((NonNegativeInteger,Symbol,Expression(Integer)) -> Expression(Integer)),C: (NonNegativeInteger -> List(F))) +--R diffHP : Symbol -> (List(GuessOption) -> Record(guessStream: (UnivariateFormalPowerSeries(F) -> Stream(UnivariateFormalPowerSeries(F))),degreeStream: Stream(NonNegativeInteger),testStream: (UnivariateFormalPowerSeries(SparseUnivariatePolynomial(F)) -> Stream(UnivariateFormalPowerSeries(SparseUnivariatePolynomial(F)))),exprStream: ((Expression(Integer),Symbol) -> Stream(Expression(Integer))),A: ((NonNegativeInteger,NonNegativeInteger,SparseUnivariatePolynomial(F)) -> F),AF: ((NonNegativeInteger,NonNegativeInteger,UnivariateFormalPowerSeries(SparseUnivariatePolynomial(F))) -> SparseUnivariatePolynomial(F)),AX: ((NonNegativeInteger,Symbol,Expression(Integer)) -> Expression(Integer)),C: (NonNegativeInteger -> List(F)))) if F has RETRACT(SYMBOL) +--R guess : List(F) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guess : (List(F),List(GuessOption)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guess : (List(F),List(((List(F),List(GuessOption)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)))),List(Symbol)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guess : (List(F),List(((List(F),List(GuessOption)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)))),List(Symbol),List(GuessOption)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guessADE : List(F) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guessADE : (List(F),List(GuessOption)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guessADE : Symbol -> ((List(F),List(GuessOption)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger))) if F has RETRACT(SYMBOL) +--R guessAlg : List(F) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guessAlg : (List(F),List(GuessOption)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guessBinRat : List(F) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guessBinRat : (List(F),List(GuessOption)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guessBinRat : Symbol -> ((List(F),List(GuessOption)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger))) if F has RETRACT(SYMBOL) +--R guessExpRat : List(F) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guessExpRat : (List(F),List(GuessOption)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guessExpRat : Symbol -> ((List(F),List(GuessOption)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger))) if F has RETRACT(SYMBOL) +--R guessHP : (List(GuessOption) -> Record(guessStream: (UnivariateFormalPowerSeries(F) -> Stream(UnivariateFormalPowerSeries(F))),degreeStream: Stream(NonNegativeInteger),testStream: (UnivariateFormalPowerSeries(SparseUnivariatePolynomial(F)) -> Stream(UnivariateFormalPowerSeries(SparseUnivariatePolynomial(F)))),exprStream: ((Expression(Integer),Symbol) -> Stream(Expression(Integer))),A: ((NonNegativeInteger,NonNegativeInteger,SparseUnivariatePolynomial(F)) -> F),AF: ((NonNegativeInteger,NonNegativeInteger,UnivariateFormalPowerSeries(SparseUnivariatePolynomial(F))) -> SparseUnivariatePolynomial(F)),AX: ((NonNegativeInteger,Symbol,Expression(Integer)) -> Expression(Integer)),C: (NonNegativeInteger -> List(F)))) -> ((List(F),List(GuessOption)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger))) +--R guessHolo : List(F) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guessHolo : (List(F),List(GuessOption)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guessPRec : (List(F),List(GuessOption)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guessPRec : List(F) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guessPRec : Symbol -> ((List(F),List(GuessOption)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger))) if F has RETRACT(SYMBOL) +--R guessPade : (List(F),List(GuessOption)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guessPade : List(F) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guessRat : (List(F),List(GuessOption)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guessRat : List(F) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guessRat : Symbol -> ((List(F),List(GuessOption)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger))) if F has RETRACT(SYMBOL) +--R guessRec : List(F) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guessRec : (List(F),List(GuessOption)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guessRec : Symbol -> ((List(F),List(GuessOption)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger))) if F has RETRACT(SYMBOL) +--R shiftHP : List(GuessOption) -> Record(guessStream: (UnivariateFormalPowerSeries(F) -> Stream(UnivariateFormalPowerSeries(F))),degreeStream: Stream(NonNegativeInteger),testStream: (UnivariateFormalPowerSeries(SparseUnivariatePolynomial(F)) -> Stream(UnivariateFormalPowerSeries(SparseUnivariatePolynomial(F)))),exprStream: ((Expression(Integer),Symbol) -> Stream(Expression(Integer))),A: ((NonNegativeInteger,NonNegativeInteger,SparseUnivariatePolynomial(F)) -> F),AF: ((NonNegativeInteger,NonNegativeInteger,UnivariateFormalPowerSeries(SparseUnivariatePolynomial(F))) -> SparseUnivariatePolynomial(F)),AX: ((NonNegativeInteger,Symbol,Expression(Integer)) -> Expression(Integer)),C: (NonNegativeInteger -> List(F))) +--R shiftHP : Symbol -> (List(GuessOption) -> Record(guessStream: (UnivariateFormalPowerSeries(F) -> Stream(UnivariateFormalPowerSeries(F))),degreeStream: Stream(NonNegativeInteger),testStream: (UnivariateFormalPowerSeries(SparseUnivariatePolynomial(F)) -> Stream(UnivariateFormalPowerSeries(SparseUnivariatePolynomial(F)))),exprStream: ((Expression(Integer),Symbol) -> Stream(Expression(Integer))),A: ((NonNegativeInteger,NonNegativeInteger,SparseUnivariatePolynomial(F)) -> F),AF: ((NonNegativeInteger,NonNegativeInteger,UnivariateFormalPowerSeries(SparseUnivariatePolynomial(F))) -> SparseUnivariatePolynomial(F)),AX: ((NonNegativeInteger,Symbol,Expression(Integer)) -> Expression(Integer)),C: (NonNegativeInteger -> List(F)))) if F has RETRACT(SYMBOL) +--R --E 1 )spool @@ -50983,6 +53107,15 @@ GuessFinite(F:Join(FiniteFieldCategory, ConvertibleTo Integer)) == --S 1 of 1 )show GuessFiniteFunctions +--R +--R GuessFiniteFunctions(F: Join(FiniteFieldCategory,ConvertibleTo(Integer))) is a package constructor +--R Abbreviation for GuessFiniteFunctions is GUESSF1 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for GUESSF1 +--R +--R------------------------------- Operations -------------------------------- +--R F2EXPRR : F -> Expression(Integer) +--R --E 1 )spool @@ -51042,6 +53175,47 @@ GuessFiniteFunctions(F:Join(FiniteFieldCategory, ConvertibleTo Integer)): --S 1 of 1 )show GuessInteger +--R +--R GuessInteger is a package constructor +--R Abbreviation for GuessInteger is GUESSINT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for GUESSINT +--R +--R------------------------------- Operations -------------------------------- +--R diffHP : List(GuessOption) -> Record(guessStream: (UnivariateFormalPowerSeries(Fraction(Integer)) -> Stream(UnivariateFormalPowerSeries(Fraction(Integer)))),degreeStream: Stream(NonNegativeInteger),testStream: (UnivariateFormalPowerSeries(SparseUnivariatePolynomial(Fraction(Integer))) -> Stream(UnivariateFormalPowerSeries(SparseUnivariatePolynomial(Fraction(Integer))))),exprStream: ((Expression(Integer),Symbol) -> Stream(Expression(Integer))),A: ((NonNegativeInteger,NonNegativeInteger,SparseUnivariatePolynomial(Integer)) -> Integer),AF: ((NonNegativeInteger,NonNegativeInteger,UnivariateFormalPowerSeries(SparseUnivariatePolynomial(Fraction(Integer)))) -> SparseUnivariatePolynomial(Fraction(Integer))),AX: ((NonNegativeInteger,Symbol,Expression(Integer)) -> Expression(Integer)),C: (NonNegativeInteger -> List(Integer))) +--R diffHP : Symbol -> (List(GuessOption) -> Record(guessStream: (UnivariateFormalPowerSeries(Fraction(Integer)) -> Stream(UnivariateFormalPowerSeries(Fraction(Integer)))),degreeStream: Stream(NonNegativeInteger),testStream: (UnivariateFormalPowerSeries(SparseUnivariatePolynomial(Fraction(Integer))) -> Stream(UnivariateFormalPowerSeries(SparseUnivariatePolynomial(Fraction(Integer))))),exprStream: ((Expression(Integer),Symbol) -> Stream(Expression(Integer))),A: ((NonNegativeInteger,NonNegativeInteger,SparseUnivariatePolynomial(Integer)) -> Integer),AF: ((NonNegativeInteger,NonNegativeInteger,UnivariateFormalPowerSeries(SparseUnivariatePolynomial(Fraction(Integer)))) -> SparseUnivariatePolynomial(Fraction(Integer))),AX: ((NonNegativeInteger,Symbol,Expression(Integer)) -> Expression(Integer)),C: (NonNegativeInteger -> List(Integer)))) if Fraction(Integer) has RETRACT(SYMBOL) and Integer has RETRACT(SYMBOL) +--R guess : List(Fraction(Integer)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guess : (List(Fraction(Integer)),List(GuessOption)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guess : (List(Fraction(Integer)),List(((List(Fraction(Integer)),List(GuessOption)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)))),List(Symbol)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guess : (List(Fraction(Integer)),List(((List(Fraction(Integer)),List(GuessOption)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)))),List(Symbol),List(GuessOption)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guessADE : List(Fraction(Integer)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guessADE : (List(Fraction(Integer)),List(GuessOption)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guessADE : Symbol -> ((List(Fraction(Integer)),List(GuessOption)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger))) if Fraction(Integer) has RETRACT(SYMBOL) and Integer has RETRACT(SYMBOL) +--R guessAlg : List(Fraction(Integer)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guessAlg : (List(Fraction(Integer)),List(GuessOption)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guessBinRat : List(Fraction(Integer)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guessBinRat : (List(Fraction(Integer)),List(GuessOption)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guessBinRat : Symbol -> ((List(Fraction(Integer)),List(GuessOption)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger))) if Fraction(Integer) has RETRACT(SYMBOL) and Integer has RETRACT(SYMBOL) +--R guessExpRat : List(Fraction(Integer)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guessExpRat : (List(Fraction(Integer)),List(GuessOption)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guessExpRat : Symbol -> ((List(Fraction(Integer)),List(GuessOption)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger))) if Fraction(Integer) has RETRACT(SYMBOL) and Integer has RETRACT(SYMBOL) +--R guessHP : (List(GuessOption) -> Record(guessStream: (UnivariateFormalPowerSeries(Fraction(Integer)) -> Stream(UnivariateFormalPowerSeries(Fraction(Integer)))),degreeStream: Stream(NonNegativeInteger),testStream: (UnivariateFormalPowerSeries(SparseUnivariatePolynomial(Fraction(Integer))) -> Stream(UnivariateFormalPowerSeries(SparseUnivariatePolynomial(Fraction(Integer))))),exprStream: ((Expression(Integer),Symbol) -> Stream(Expression(Integer))),A: ((NonNegativeInteger,NonNegativeInteger,SparseUnivariatePolynomial(Integer)) -> Integer),AF: ((NonNegativeInteger,NonNegativeInteger,UnivariateFormalPowerSeries(SparseUnivariatePolynomial(Fraction(Integer)))) -> SparseUnivariatePolynomial(Fraction(Integer))),AX: ((NonNegativeInteger,Symbol,Expression(Integer)) -> Expression(Integer)),C: (NonNegativeInteger -> List(Integer)))) -> ((List(Fraction(Integer)),List(GuessOption)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger))) +--R guessHolo : List(Fraction(Integer)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guessHolo : (List(Fraction(Integer)),List(GuessOption)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guessPRec : (List(Fraction(Integer)),List(GuessOption)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guessPRec : List(Fraction(Integer)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guessPRec : Symbol -> ((List(Fraction(Integer)),List(GuessOption)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger))) if Fraction(Integer) has RETRACT(SYMBOL) and Integer has RETRACT(SYMBOL) +--R guessPade : (List(Fraction(Integer)),List(GuessOption)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guessPade : List(Fraction(Integer)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guessRat : (List(Fraction(Integer)),List(GuessOption)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guessRat : List(Fraction(Integer)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guessRat : Symbol -> ((List(Fraction(Integer)),List(GuessOption)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger))) if Fraction(Integer) has RETRACT(SYMBOL) and Integer has RETRACT(SYMBOL) +--R guessRec : List(Fraction(Integer)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guessRec : (List(Fraction(Integer)),List(GuessOption)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guessRec : Symbol -> ((List(Fraction(Integer)),List(GuessOption)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger))) if Fraction(Integer) has RETRACT(SYMBOL) and Integer has RETRACT(SYMBOL) +--R shiftHP : List(GuessOption) -> Record(guessStream: (UnivariateFormalPowerSeries(Fraction(Integer)) -> Stream(UnivariateFormalPowerSeries(Fraction(Integer)))),degreeStream: Stream(NonNegativeInteger),testStream: (UnivariateFormalPowerSeries(SparseUnivariatePolynomial(Fraction(Integer))) -> Stream(UnivariateFormalPowerSeries(SparseUnivariatePolynomial(Fraction(Integer))))),exprStream: ((Expression(Integer),Symbol) -> Stream(Expression(Integer))),A: ((NonNegativeInteger,NonNegativeInteger,SparseUnivariatePolynomial(Integer)) -> Integer),AF: ((NonNegativeInteger,NonNegativeInteger,UnivariateFormalPowerSeries(SparseUnivariatePolynomial(Fraction(Integer)))) -> SparseUnivariatePolynomial(Fraction(Integer))),AX: ((NonNegativeInteger,Symbol,Expression(Integer)) -> Expression(Integer)),C: (NonNegativeInteger -> List(Integer))) +--R shiftHP : Symbol -> (List(GuessOption) -> Record(guessStream: (UnivariateFormalPowerSeries(Fraction(Integer)) -> Stream(UnivariateFormalPowerSeries(Fraction(Integer)))),degreeStream: Stream(NonNegativeInteger),testStream: (UnivariateFormalPowerSeries(SparseUnivariatePolynomial(Fraction(Integer))) -> Stream(UnivariateFormalPowerSeries(SparseUnivariatePolynomial(Fraction(Integer))))),exprStream: ((Expression(Integer),Symbol) -> Stream(Expression(Integer))),A: ((NonNegativeInteger,NonNegativeInteger,SparseUnivariatePolynomial(Integer)) -> Integer),AF: ((NonNegativeInteger,NonNegativeInteger,UnivariateFormalPowerSeries(SparseUnivariatePolynomial(Fraction(Integer)))) -> SparseUnivariatePolynomial(Fraction(Integer))),AX: ((NonNegativeInteger,Symbol,Expression(Integer)) -> Expression(Integer)),C: (NonNegativeInteger -> List(Integer)))) if Fraction(Integer) has RETRACT(SYMBOL) and Integer has RETRACT(SYMBOL) +--R --E 1 )spool @@ -51109,6 +53283,47 @@ GuessInteger() == Guess(Fraction Integer, Integer, Expression Integer, --S 1 of 1 )show GuessPolynomial +--R +--R GuessPolynomial is a package constructor +--R Abbreviation for GuessPolynomial is GUESSP +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for GUESSP +--R +--R------------------------------- Operations -------------------------------- +--R diffHP : List(GuessOption) -> Record(guessStream: (UnivariateFormalPowerSeries(Fraction(Polynomial(Integer))) -> Stream(UnivariateFormalPowerSeries(Fraction(Polynomial(Integer))))),degreeStream: Stream(NonNegativeInteger),testStream: (UnivariateFormalPowerSeries(SparseUnivariatePolynomial(Fraction(Polynomial(Integer)))) -> Stream(UnivariateFormalPowerSeries(SparseUnivariatePolynomial(Fraction(Polynomial(Integer)))))),exprStream: ((Expression(Integer),Symbol) -> Stream(Expression(Integer))),A: ((NonNegativeInteger,NonNegativeInteger,SparseUnivariatePolynomial(Polynomial(Integer))) -> Polynomial(Integer)),AF: ((NonNegativeInteger,NonNegativeInteger,UnivariateFormalPowerSeries(SparseUnivariatePolynomial(Fraction(Polynomial(Integer))))) -> SparseUnivariatePolynomial(Fraction(Polynomial(Integer)))),AX: ((NonNegativeInteger,Symbol,Expression(Integer)) -> Expression(Integer)),C: (NonNegativeInteger -> List(Polynomial(Integer)))) +--R diffHP : Symbol -> (List(GuessOption) -> Record(guessStream: (UnivariateFormalPowerSeries(Fraction(Polynomial(Integer))) -> Stream(UnivariateFormalPowerSeries(Fraction(Polynomial(Integer))))),degreeStream: Stream(NonNegativeInteger),testStream: (UnivariateFormalPowerSeries(SparseUnivariatePolynomial(Fraction(Polynomial(Integer)))) -> Stream(UnivariateFormalPowerSeries(SparseUnivariatePolynomial(Fraction(Polynomial(Integer)))))),exprStream: ((Expression(Integer),Symbol) -> Stream(Expression(Integer))),A: ((NonNegativeInteger,NonNegativeInteger,SparseUnivariatePolynomial(Polynomial(Integer))) -> Polynomial(Integer)),AF: ((NonNegativeInteger,NonNegativeInteger,UnivariateFormalPowerSeries(SparseUnivariatePolynomial(Fraction(Polynomial(Integer))))) -> SparseUnivariatePolynomial(Fraction(Polynomial(Integer)))),AX: ((NonNegativeInteger,Symbol,Expression(Integer)) -> Expression(Integer)),C: (NonNegativeInteger -> List(Polynomial(Integer))))) if Fraction(Polynomial(Integer)) has RETRACT(SYMBOL) and Polynomial(Integer) has RETRACT(SYMBOL) +--R guess : List(Fraction(Polynomial(Integer))) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guess : (List(Fraction(Polynomial(Integer))),List(GuessOption)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guess : (List(Fraction(Polynomial(Integer))),List(((List(Fraction(Polynomial(Integer))),List(GuessOption)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)))),List(Symbol)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guess : (List(Fraction(Polynomial(Integer))),List(((List(Fraction(Polynomial(Integer))),List(GuessOption)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)))),List(Symbol),List(GuessOption)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guessADE : List(Fraction(Polynomial(Integer))) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guessADE : (List(Fraction(Polynomial(Integer))),List(GuessOption)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guessADE : Symbol -> ((List(Fraction(Polynomial(Integer))),List(GuessOption)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger))) if Fraction(Polynomial(Integer)) has RETRACT(SYMBOL) and Polynomial(Integer) has RETRACT(SYMBOL) +--R guessAlg : List(Fraction(Polynomial(Integer))) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guessAlg : (List(Fraction(Polynomial(Integer))),List(GuessOption)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guessBinRat : List(Fraction(Polynomial(Integer))) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guessBinRat : (List(Fraction(Polynomial(Integer))),List(GuessOption)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guessBinRat : Symbol -> ((List(Fraction(Polynomial(Integer))),List(GuessOption)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger))) if Fraction(Polynomial(Integer)) has RETRACT(SYMBOL) and Polynomial(Integer) has RETRACT(SYMBOL) +--R guessExpRat : List(Fraction(Polynomial(Integer))) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guessExpRat : (List(Fraction(Polynomial(Integer))),List(GuessOption)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guessExpRat : Symbol -> ((List(Fraction(Polynomial(Integer))),List(GuessOption)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger))) if Fraction(Polynomial(Integer)) has RETRACT(SYMBOL) and Polynomial(Integer) has RETRACT(SYMBOL) +--R guessHP : (List(GuessOption) -> Record(guessStream: (UnivariateFormalPowerSeries(Fraction(Polynomial(Integer))) -> Stream(UnivariateFormalPowerSeries(Fraction(Polynomial(Integer))))),degreeStream: Stream(NonNegativeInteger),testStream: (UnivariateFormalPowerSeries(SparseUnivariatePolynomial(Fraction(Polynomial(Integer)))) -> Stream(UnivariateFormalPowerSeries(SparseUnivariatePolynomial(Fraction(Polynomial(Integer)))))),exprStream: ((Expression(Integer),Symbol) -> Stream(Expression(Integer))),A: ((NonNegativeInteger,NonNegativeInteger,SparseUnivariatePolynomial(Polynomial(Integer))) -> Polynomial(Integer)),AF: ((NonNegativeInteger,NonNegativeInteger,UnivariateFormalPowerSeries(SparseUnivariatePolynomial(Fraction(Polynomial(Integer))))) -> SparseUnivariatePolynomial(Fraction(Polynomial(Integer)))),AX: ((NonNegativeInteger,Symbol,Expression(Integer)) -> Expression(Integer)),C: (NonNegativeInteger -> List(Polynomial(Integer))))) -> ((List(Fraction(Polynomial(Integer))),List(GuessOption)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger))) +--R guessHolo : List(Fraction(Polynomial(Integer))) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guessHolo : (List(Fraction(Polynomial(Integer))),List(GuessOption)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guessPRec : (List(Fraction(Polynomial(Integer))),List(GuessOption)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guessPRec : List(Fraction(Polynomial(Integer))) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guessPRec : Symbol -> ((List(Fraction(Polynomial(Integer))),List(GuessOption)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger))) if Fraction(Polynomial(Integer)) has RETRACT(SYMBOL) and Polynomial(Integer) has RETRACT(SYMBOL) +--R guessPade : (List(Fraction(Polynomial(Integer))),List(GuessOption)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guessPade : List(Fraction(Polynomial(Integer))) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guessRat : (List(Fraction(Polynomial(Integer))),List(GuessOption)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guessRat : List(Fraction(Polynomial(Integer))) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guessRat : Symbol -> ((List(Fraction(Polynomial(Integer))),List(GuessOption)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger))) if Fraction(Polynomial(Integer)) has RETRACT(SYMBOL) and Polynomial(Integer) has RETRACT(SYMBOL) +--R guessRec : List(Fraction(Polynomial(Integer))) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guessRec : (List(Fraction(Polynomial(Integer))),List(GuessOption)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger)) +--R guessRec : Symbol -> ((List(Fraction(Polynomial(Integer))),List(GuessOption)) -> List(Record(function: Expression(Integer),order: NonNegativeInteger))) if Fraction(Polynomial(Integer)) has RETRACT(SYMBOL) and Polynomial(Integer) has RETRACT(SYMBOL) +--R shiftHP : List(GuessOption) -> Record(guessStream: (UnivariateFormalPowerSeries(Fraction(Polynomial(Integer))) -> Stream(UnivariateFormalPowerSeries(Fraction(Polynomial(Integer))))),degreeStream: Stream(NonNegativeInteger),testStream: (UnivariateFormalPowerSeries(SparseUnivariatePolynomial(Fraction(Polynomial(Integer)))) -> Stream(UnivariateFormalPowerSeries(SparseUnivariatePolynomial(Fraction(Polynomial(Integer)))))),exprStream: ((Expression(Integer),Symbol) -> Stream(Expression(Integer))),A: ((NonNegativeInteger,NonNegativeInteger,SparseUnivariatePolynomial(Polynomial(Integer))) -> Polynomial(Integer)),AF: ((NonNegativeInteger,NonNegativeInteger,UnivariateFormalPowerSeries(SparseUnivariatePolynomial(Fraction(Polynomial(Integer))))) -> SparseUnivariatePolynomial(Fraction(Polynomial(Integer)))),AX: ((NonNegativeInteger,Symbol,Expression(Integer)) -> Expression(Integer)),C: (NonNegativeInteger -> List(Polynomial(Integer)))) +--R shiftHP : Symbol -> (List(GuessOption) -> Record(guessStream: (UnivariateFormalPowerSeries(Fraction(Polynomial(Integer))) -> Stream(UnivariateFormalPowerSeries(Fraction(Polynomial(Integer))))),degreeStream: Stream(NonNegativeInteger),testStream: (UnivariateFormalPowerSeries(SparseUnivariatePolynomial(Fraction(Polynomial(Integer)))) -> Stream(UnivariateFormalPowerSeries(SparseUnivariatePolynomial(Fraction(Polynomial(Integer)))))),exprStream: ((Expression(Integer),Symbol) -> Stream(Expression(Integer))),A: ((NonNegativeInteger,NonNegativeInteger,SparseUnivariatePolynomial(Polynomial(Integer))) -> Polynomial(Integer)),AF: ((NonNegativeInteger,NonNegativeInteger,UnivariateFormalPowerSeries(SparseUnivariatePolynomial(Fraction(Polynomial(Integer))))) -> SparseUnivariatePolynomial(Fraction(Polynomial(Integer)))),AX: ((NonNegativeInteger,Symbol,Expression(Integer)) -> Expression(Integer)),C: (NonNegativeInteger -> List(Polynomial(Integer))))) if Fraction(Polynomial(Integer)) has RETRACT(SYMBOL) and Polynomial(Integer) has RETRACT(SYMBOL) +--R --E 1 )spool @@ -51175,6 +53390,47 @@ GuessPolynomial() == Guess(Fraction Polynomial Integer, Polynomial Integer, --S 1 of 1 )show GuessUnivariatePolynomial +--R +--R GuessUnivariatePolynomial(q: Symbol) is a package constructor +--R Abbreviation for GuessUnivariatePolynomial is GUESSUP +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for GUESSUP +--R +--R------------------------------- Operations -------------------------------- +--R diffHP : List(GuessOption) -> HPSPEC +--R diffHP : Symbol -> (List(GuessOption) -> HPSPEC) +--R guess : List(Fraction(MyUnivariatePolynomial(q,Integer))) -> List(Record(function: MyExpression(q,Integer),order: NonNegativeInteger)) +--R guess : (List(Fraction(MyUnivariatePolynomial(q,Integer))),List(GuessOption)) -> List(Record(function: MyExpression(q,Integer),order: NonNegativeInteger)) +--R guess : (List(Fraction(MyUnivariatePolynomial(q,Integer))),List(((List(Fraction(MyUnivariatePolynomial(q,Integer))),List(GuessOption)) -> List(Record(function: MyExpression(q,Integer),order: NonNegativeInteger)))),List(Symbol)) -> List(Record(function: MyExpression(q,Integer),order: NonNegativeInteger)) +--R guess : (List(Fraction(MyUnivariatePolynomial(q,Integer))),List(((List(Fraction(MyUnivariatePolynomial(q,Integer))),List(GuessOption)) -> List(Record(function: MyExpression(q,Integer),order: NonNegativeInteger)))),List(Symbol),List(GuessOption)) -> List(Record(function: MyExpression(q,Integer),order: NonNegativeInteger)) +--R guessADE : List(Fraction(MyUnivariatePolynomial(q,Integer))) -> List(Record(function: MyExpression(q,Integer),order: NonNegativeInteger)) +--R guessADE : (List(Fraction(MyUnivariatePolynomial(q,Integer))),List(GuessOption)) -> List(Record(function: MyExpression(q,Integer),order: NonNegativeInteger)) +--R guessADE : Symbol -> ((List(Fraction(MyUnivariatePolynomial(q,Integer))),List(GuessOption)) -> List(Record(function: MyExpression(q,Integer),order: NonNegativeInteger))) +--R guessAlg : List(Fraction(MyUnivariatePolynomial(q,Integer))) -> List(Record(function: MyExpression(q,Integer),order: NonNegativeInteger)) +--R guessAlg : (List(Fraction(MyUnivariatePolynomial(q,Integer))),List(GuessOption)) -> List(Record(function: MyExpression(q,Integer),order: NonNegativeInteger)) +--R guessBinRat : List(Fraction(MyUnivariatePolynomial(q,Integer))) -> List(Record(function: MyExpression(q,Integer),order: NonNegativeInteger)) +--R guessBinRat : (List(Fraction(MyUnivariatePolynomial(q,Integer))),List(GuessOption)) -> List(Record(function: MyExpression(q,Integer),order: NonNegativeInteger)) +--R guessBinRat : Symbol -> ((List(Fraction(MyUnivariatePolynomial(q,Integer))),List(GuessOption)) -> List(Record(function: MyExpression(q,Integer),order: NonNegativeInteger))) +--R guessExpRat : List(Fraction(MyUnivariatePolynomial(q,Integer))) -> List(Record(function: MyExpression(q,Integer),order: NonNegativeInteger)) +--R guessExpRat : (List(Fraction(MyUnivariatePolynomial(q,Integer))),List(GuessOption)) -> List(Record(function: MyExpression(q,Integer),order: NonNegativeInteger)) +--R guessExpRat : Symbol -> ((List(Fraction(MyUnivariatePolynomial(q,Integer))),List(GuessOption)) -> List(Record(function: MyExpression(q,Integer),order: NonNegativeInteger))) +--R guessHP : (List(GuessOption) -> HPSPEC) -> ((List(Fraction(MyUnivariatePolynomial(q,Integer))),List(GuessOption)) -> List(Record(function: MyExpression(q,Integer),order: NonNegativeInteger))) +--R guessHolo : List(Fraction(MyUnivariatePolynomial(q,Integer))) -> List(Record(function: MyExpression(q,Integer),order: NonNegativeInteger)) +--R guessHolo : (List(Fraction(MyUnivariatePolynomial(q,Integer))),List(GuessOption)) -> List(Record(function: MyExpression(q,Integer),order: NonNegativeInteger)) +--R guessPRec : (List(Fraction(MyUnivariatePolynomial(q,Integer))),List(GuessOption)) -> List(Record(function: MyExpression(q,Integer),order: NonNegativeInteger)) +--R guessPRec : List(Fraction(MyUnivariatePolynomial(q,Integer))) -> List(Record(function: MyExpression(q,Integer),order: NonNegativeInteger)) +--R guessPRec : Symbol -> ((List(Fraction(MyUnivariatePolynomial(q,Integer))),List(GuessOption)) -> List(Record(function: MyExpression(q,Integer),order: NonNegativeInteger))) +--R guessPade : (List(Fraction(MyUnivariatePolynomial(q,Integer))),List(GuessOption)) -> List(Record(function: MyExpression(q,Integer),order: NonNegativeInteger)) +--R guessPade : List(Fraction(MyUnivariatePolynomial(q,Integer))) -> List(Record(function: MyExpression(q,Integer),order: NonNegativeInteger)) +--R guessRat : (List(Fraction(MyUnivariatePolynomial(q,Integer))),List(GuessOption)) -> List(Record(function: MyExpression(q,Integer),order: NonNegativeInteger)) +--R guessRat : List(Fraction(MyUnivariatePolynomial(q,Integer))) -> List(Record(function: MyExpression(q,Integer),order: NonNegativeInteger)) +--R guessRat : Symbol -> ((List(Fraction(MyUnivariatePolynomial(q,Integer))),List(GuessOption)) -> List(Record(function: MyExpression(q,Integer),order: NonNegativeInteger))) +--R guessRec : List(Fraction(MyUnivariatePolynomial(q,Integer))) -> List(Record(function: MyExpression(q,Integer),order: NonNegativeInteger)) +--R guessRec : (List(Fraction(MyUnivariatePolynomial(q,Integer))),List(GuessOption)) -> List(Record(function: MyExpression(q,Integer),order: NonNegativeInteger)) +--R guessRec : Symbol -> ((List(Fraction(MyUnivariatePolynomial(q,Integer))),List(GuessOption)) -> List(Record(function: MyExpression(q,Integer),order: NonNegativeInteger))) +--R shiftHP : List(GuessOption) -> HPSPEC +--R shiftHP : Symbol -> (List(GuessOption) -> HPSPEC) +--R --E 1 )spool @@ -51448,6 +53704,17 @@ GuessUnivariatePolynomial(q: Symbol): Exports == Implementation where --S 1 of 1 )show HallBasis +--R +--R HallBasis is a package constructor +--R Abbreviation for HallBasis is HB +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for HB +--R +--R------------------------------- Operations -------------------------------- +--R lfunc : (Integer,Integer) -> Integer +--R generate : (NonNegativeInteger,NonNegativeInteger) -> Vector(List(Integer)) +--R inHallBasis? : (Integer,Integer,Integer,Integer) -> Boolean +--R --E 1 )spool @@ -51584,6 +53851,17 @@ HallBasis() : Export == Implement where --S 1 of 1 )show HeuGcd +--R +--R HeuGcd(BP: UnivariatePolynomialCategory(Integer)) is a package constructor +--R Abbreviation for HeuGcd is HEUGCD +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for HEUGCD +--R +--R------------------------------- Operations -------------------------------- +--R content : List(BP) -> List(Integer) gcd : List(BP) -> BP +--R gcdcofact : List(BP) -> List(BP) gcdcofactprim : List(BP) -> List(BP) +--R gcdprim : List(BP) -> BP lintgcd : List(Integer) -> Integer +--R --E 1 )spool @@ -51849,6 +54127,20 @@ HeuGcd (BP):C == T --S 1 of 1 )show IdealDecompositionPackage +--R +--R IdealDecompositionPackage(vl: List(Symbol),nv: NonNegativeInteger) is a package constructor +--R Abbreviation for IdealDecompositionPackage is IDECOMP +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for IDECOMP +--R +--R------------------------------- Operations -------------------------------- +--R contract : (PolynomialIdeals(Fraction(Integer),DirectProduct(nv,NonNegativeInteger),OrderedVariableList(vl),DistributedMultivariatePolynomial(vl,Fraction(Integer))),List(OrderedVariableList(vl))) -> PolynomialIdeals(Fraction(Integer),DirectProduct(nv,NonNegativeInteger),OrderedVariableList(vl),DistributedMultivariatePolynomial(vl,Fraction(Integer))) +--R primaryDecomp : PolynomialIdeals(Fraction(Integer),DirectProduct(nv,NonNegativeInteger),OrderedVariableList(vl),DistributedMultivariatePolynomial(vl,Fraction(Integer))) -> List(PolynomialIdeals(Fraction(Integer),DirectProduct(nv,NonNegativeInteger),OrderedVariableList(vl),DistributedMultivariatePolynomial(vl,Fraction(Integer)))) +--R prime? : PolynomialIdeals(Fraction(Integer),DirectProduct(nv,NonNegativeInteger),OrderedVariableList(vl),DistributedMultivariatePolynomial(vl,Fraction(Integer))) -> Boolean +--R radical : PolynomialIdeals(Fraction(Integer),DirectProduct(nv,NonNegativeInteger),OrderedVariableList(vl),DistributedMultivariatePolynomial(vl,Fraction(Integer))) -> PolynomialIdeals(Fraction(Integer),DirectProduct(nv,NonNegativeInteger),OrderedVariableList(vl),DistributedMultivariatePolynomial(vl,Fraction(Integer))) +--R zeroDimPrimary? : PolynomialIdeals(Fraction(Integer),DirectProduct(nv,NonNegativeInteger),OrderedVariableList(vl),DistributedMultivariatePolynomial(vl,Fraction(Integer))) -> Boolean +--R zeroDimPrime? : PolynomialIdeals(Fraction(Integer),DirectProduct(nv,NonNegativeInteger),OrderedVariableList(vl),DistributedMultivariatePolynomial(vl,Fraction(Integer))) -> Boolean +--R --E 1 )spool @@ -52281,6 +54573,15 @@ IdealDecompositionPackage(vl,nv) : C == T -- take away nv, now doesn't --S 1 of 1 )show IncrementingMaps +--R +--R IncrementingMaps(R: Join(Monoid,AbelianSemiGroup)) is a package constructor +--R Abbreviation for IncrementingMaps is INCRMAPS +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for INCRMAPS +--R +--R------------------------------- Operations -------------------------------- +--R increment : () -> (R -> R) incrementBy : R -> (R -> R) +--R --E 1 )spool @@ -52344,6 +54645,17 @@ IncrementingMaps(R:Join(Monoid, AbelianSemiGroup)): with --S 1 of 1 )show InfiniteProductCharacteristicZero +--R +--R InfiniteProductCharacteristicZero(Coef: Join(IntegralDomain,CharacteristicZero),UTS: UnivariateTaylorSeriesCategory(Coef)) is a package constructor +--R Abbreviation for InfiniteProductCharacteristicZero is INFPROD0 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for INFPROD0 +--R +--R------------------------------- Operations -------------------------------- +--R evenInfiniteProduct : UTS -> UTS infiniteProduct : UTS -> UTS +--R oddInfiniteProduct : UTS -> UTS +--R generalInfiniteProduct : (UTS,Integer,Integer) -> UTS +--R --E 1 )spool @@ -52433,6 +54745,17 @@ InfiniteProductCharacteristicZero(Coef,UTS):_ --S 1 of 1 )show InfiniteProductFiniteField +--R +--R InfiniteProductFiniteField(K: Join(Field,Finite,ConvertibleTo(Integer)),UP: UnivariatePolynomialCategory(K),Coef: MonogenicAlgebra(K,UP),UTS: UnivariateTaylorSeriesCategory(Coef)) is a package constructor +--R Abbreviation for InfiniteProductFiniteField is INPRODFF +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for INPRODFF +--R +--R------------------------------- Operations -------------------------------- +--R evenInfiniteProduct : UTS -> UTS infiniteProduct : UTS -> UTS +--R oddInfiniteProduct : UTS -> UTS +--R generalInfiniteProduct : (UTS,Integer,Integer) -> UTS +--R --E 1 )spool @@ -52582,6 +54905,17 @@ InfiniteProductFiniteField(K,UP,Coef,UTS):_ --S 1 of 1 )show InfiniteProductPrimeField +--R +--R InfiniteProductPrimeField(Coef: Join(Field,Finite,ConvertibleTo(Integer)),UTS: UnivariateTaylorSeriesCategory(Coef)) is a package constructor +--R Abbreviation for InfiniteProductPrimeField is INPRODPF +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for INPRODPF +--R +--R------------------------------- Operations -------------------------------- +--R evenInfiniteProduct : UTS -> UTS infiniteProduct : UTS -> UTS +--R oddInfiniteProduct : UTS -> UTS +--R generalInfiniteProduct : (UTS,Integer,Integer) -> UTS +--R --E 1 )spool @@ -52680,6 +55014,15 @@ InfiniteProductPrimeField(Coef,UTS): Exports == Implementation where --S 1 of 1 )show InfiniteTupleFunctions2 +--R +--R InfiniteTupleFunctions2(A: Type,B: Type) is a package constructor +--R Abbreviation for InfiniteTupleFunctions2 is ITFUN2 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for ITFUN2 +--R +--R------------------------------- Operations -------------------------------- +--R map : ((A -> B),InfiniteTuple(A)) -> InfiniteTuple(B) +--R --E 1 )spool @@ -52738,6 +55081,17 @@ InfiniteTupleFunctions2(A:Type,B:Type): Exports == Implementation where --S 1 of 1 )show InfiniteTupleFunctions3 +--R +--R InfiniteTupleFunctions3(A: Type,B: Type,C: Type) is a package constructor +--R Abbreviation for InfiniteTupleFunctions3 is ITFUN3 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for ITFUN3 +--R +--R------------------------------- Operations -------------------------------- +--R map : (((A,B) -> C),InfiniteTuple(A),InfiniteTuple(B)) -> InfiniteTuple(C) +--R map : (((A,B) -> C),Stream(A),InfiniteTuple(B)) -> Stream(C) +--R map : (((A,B) -> C),InfiniteTuple(A),Stream(B)) -> Stream(C) +--R --E 1 )spool @@ -52807,6 +55161,17 @@ InfiniteTupleFunctions3(A:Type, B:Type,C:Type): Exports --S 1 of 1 )show Infinity +--R +--R Infinity is a package constructor +--R Abbreviation for Infinity is INFINITY +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for INFINITY +--R +--R------------------------------- Operations -------------------------------- +--R infinity : () -> OnePointCompletion(Integer) +--R minusInfinity : () -> OrderedCompletion(Integer) +--R plusInfinity : () -> OrderedCompletion(Integer) +--R --E 1 )spool @@ -52875,6 +55240,15 @@ Infinity(): with --S 1 of 1 )show InnerAlgFactor +--R +--R InnerAlgFactor(F: Field,UP: UnivariatePolynomialCategory(F),AlExt: Join(Field,CharacteristicZero,MonogenicAlgebra(F,UP)),AlPol: UnivariatePolynomialCategory(AlExt)) is a package constructor +--R Abbreviation for InnerAlgFactor is IALGFACT +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for IALGFACT +--R +--R------------------------------- Operations -------------------------------- +--R factor : (AlPol,(UP -> Factored(UP))) -> Factored(AlPol) +--R --E 1 )spool @@ -53003,6 +55377,16 @@ InnerAlgFactor(F, UP, AlExt, AlPol): Exports == Implementation where --S 1 of 1 )show InnerCommonDenominator +--R +--R InnerCommonDenominator(R: IntegralDomain,Q: QuotientFieldCategory(R),A: FiniteLinearAggregate(R),B: FiniteLinearAggregate(Q)) is a package constructor +--R Abbreviation for InnerCommonDenominator is ICDEN +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for ICDEN +--R +--R------------------------------- Operations -------------------------------- +--R clearDenominator : B -> A commonDenominator : B -> R +--R splitDenominator : B -> Record(num: A,den: R) +--R --E 1 )spool @@ -53094,6 +55478,18 @@ InnerCommonDenominator(R, Q, A, B): Exports == Implementation where --S 1 of 1 )show InnerMatrixLinearAlgebraFunctions +--R +--R InnerMatrixLinearAlgebraFunctions(R: Field,Row: FiniteLinearAggregate(R),Col: FiniteLinearAggregate(R),M: MatrixCategory(R,Row,Col)) is a package constructor +--R Abbreviation for InnerMatrixLinearAlgebraFunctions is IMATLIN +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for IMATLIN +--R +--R------------------------------- Operations -------------------------------- +--R determinant : M -> R generalizedInverse : M -> M +--R inverse : M -> Union(M,"failed") nullity : M -> NonNegativeInteger +--R rank : M -> NonNegativeInteger rowEchelon : M -> M +--R nullSpace : M -> List(Col) if Col has shallowlyMutable +--R --E 1 )spool @@ -53353,6 +55749,16 @@ InnerMatrixLinearAlgebraFunctions(R,Row,Col,M):_ --S 1 of 1 )show InnerMatrixQuotientFieldFunctions +--R +--R InnerMatrixQuotientFieldFunctions(R: IntegralDomain,Row: FiniteLinearAggregate(R),Col: FiniteLinearAggregate(R),M: MatrixCategory(R,Row,Col),QF: QuotientFieldCategory(R),Row2: FiniteLinearAggregate(QF),Col2: FiniteLinearAggregate(QF),M2: MatrixCategory(QF,Row2,Col2)) is a package constructor +--R Abbreviation for InnerMatrixQuotientFieldFunctions is IMATQF +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for IMATQF +--R +--R------------------------------- Operations -------------------------------- +--R inverse : M -> Union(M2,"failed") rowEchelon : M -> M2 +--R nullSpace : M -> List(Col) if Col2 has shallowlyMutable +--R --E 1 )spool @@ -53453,6 +55859,16 @@ InnerMatrixQuotientFieldFunctions(R,Row,Col,M,QF,Row2,Col2,M2):_ --S 1 of 1 )show InnerModularGcd +--R +--R InnerModularGcd(R: EuclideanDomain,BP: UnivariatePolynomialCategory(R),pMod: R,nextMod: ((R,NonNegativeInteger) -> R)) is a package constructor +--R Abbreviation for InnerModularGcd is INMODGCD +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for INMODGCD +--R +--R------------------------------- Operations -------------------------------- +--R modularGcd : List(BP) -> BP modularGcdPrimitive : List(BP) -> BP +--R reduction : (BP,R) -> BP +--R --E 1 )spool @@ -53763,6 +56179,16 @@ InnerModularGcd(R,BP,pMod,nextMod):C == T --S 1 of 1 )show InnerMultFact +--R +--R InnerMultFact(OV: OrderedSet,E: OrderedAbelianMonoidSup,R: Join(EuclideanDomain,CharacteristicZero),P: PolynomialCategory(R,E,OV)) is a package constructor +--R Abbreviation for InnerMultFact is INNMFACT +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for INNMFACT +--R +--R------------------------------- Operations -------------------------------- +--R factor : (P,(SparseUnivariatePolynomial(R) -> Factored(SparseUnivariatePolynomial(R)))) -> Factored(P) +--R factor : (SparseUnivariatePolynomial(P),(SparseUnivariatePolynomial(R) -> Factored(SparseUnivariatePolynomial(R)))) -> Factored(SparseUnivariatePolynomial(P)) +--R --E 1 )spool @@ -54235,6 +56661,33 @@ InnerMultFact(OV,E,R,P) : C == T --S 1 of 1 )show InnerNormalBasisFieldFunctions +--R +--R InnerNormalBasisFieldFunctions(GF: FiniteFieldCategory) is a package constructor +--R Abbreviation for InnerNormalBasisFieldFunctions is INBFF +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for INBFF +--R +--R------------------------------- Operations -------------------------------- +--R inv : Vector(GF) -> Vector(GF) normal? : Vector(GF) -> Boolean +--R ?*? : (Vector(GF),Vector(GF)) -> Vector(GF) +--R ?**? : (Vector(GF),Integer) -> Vector(GF) +--R ?/? : (Vector(GF),Vector(GF)) -> Vector(GF) +--R basis : PositiveInteger -> Vector(Vector(GF)) +--R dAndcExp : (Vector(GF),NonNegativeInteger,SingleInteger) -> Vector(GF) +--R expPot : (Vector(GF),SingleInteger,SingleInteger) -> Vector(GF) +--R index : (PositiveInteger,PositiveInteger) -> Vector(GF) +--R lookup : Vector(GF) -> PositiveInteger +--R minimalPolynomial : Vector(GF) -> SparseUnivariatePolynomial(GF) +--R norm : (Vector(GF),PositiveInteger) -> Vector(GF) +--R normalElement : PositiveInteger -> Vector(GF) +--R pol : Vector(GF) -> SparseUnivariatePolynomial(GF) +--R qPot : (Vector(GF),Integer) -> Vector(GF) +--R random : PositiveInteger -> Vector(GF) +--R repSq : (Vector(GF),NonNegativeInteger) -> Vector(GF) +--R setFieldInfo : (Vector(List(Record(value: GF,index: SingleInteger))),GF) -> Void +--R trace : (Vector(GF),PositiveInteger) -> Vector(GF) +--R xn : NonNegativeInteger -> SparseUnivariatePolynomial(GF) +--R --E 1 )spool @@ -54644,6 +57097,17 @@ InnerNormalBasisFieldFunctions(GF): Exports == Implementation where --S 1 of 1 )show InnerNumericEigenPackage +--R +--R InnerNumericEigenPackage(K: Field,F: Field,Par: Join(Field,OrderedRing)) is a package constructor +--R Abbreviation for InnerNumericEigenPackage is INEP +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for INEP +--R +--R------------------------------- Operations -------------------------------- +--R charpol : Matrix(K) -> SparseUnivariatePolynomial(K) +--R innerEigenvectors : (Matrix(K),Par,(SparseUnivariatePolynomial(K) -> Factored(SparseUnivariatePolynomial(K)))) -> List(Record(outval: F,outmult: Integer,outvect: List(Matrix(F)))) +--R solve1 : (SparseUnivariatePolynomial(K),Par) -> List(F) +--R --E 1 )spool @@ -54883,6 +57347,18 @@ InnerNumericEigenPackage(K,F,Par) : C == T --S 1 of 1 )show InnerNumericFloatSolvePackage +--R +--R InnerNumericFloatSolvePackage(K: GcdDomain,F: Field,Par: Join(Field,OrderedRing)) is a package constructor +--R Abbreviation for InnerNumericFloatSolvePackage is INFSP +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for INFSP +--R +--R------------------------------- Operations -------------------------------- +--R innerSolve : (List(Polynomial(K)),List(Polynomial(K)),List(Symbol),Par) -> List(List(F)) +--R innerSolve1 : (SparseUnivariatePolynomial(K),Par) -> List(F) +--R innerSolve1 : (Polynomial(K),Par) -> List(F) +--R makeEq : (List(F),List(Symbol)) -> List(Equation(Polynomial(F))) +--R --E 1 )spool @@ -55123,6 +57599,17 @@ InnerNumericFloatSolvePackage(K,F,Par): Cat == Cap where --S 1 of 1 )show InnerPolySign +--R +--R InnerPolySign(R: Ring,UP: UnivariatePolynomialCategory(R)) is a package constructor +--R Abbreviation for InnerPolySign is INPSIGN +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for INPSIGN +--R +--R------------------------------- Operations -------------------------------- +--R signAround : (UP,Integer,(R -> Union(Integer,"failed"))) -> Union(Integer,"failed") +--R signAround : (UP,R,Integer,(R -> Union(Integer,"failed"))) -> Union(Integer,"failed") +--R signAround : (UP,R,(R -> Union(Integer,"failed"))) -> Union(Integer,"failed") +--R --E 1 )spool @@ -55207,6 +57694,16 @@ InnerPolySign(R, UP): Exports == Implementation where --S 1 of 1 )show InnerPolySum +--R +--R InnerPolySum(E: OrderedAbelianMonoidSup,V: OrderedSet,R: IntegralDomain,P: PolynomialCategory(R,E,V)) is a package constructor +--R Abbreviation for InnerPolySum is ISUMP +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for ISUMP +--R +--R------------------------------- Operations -------------------------------- +--R sum : (P,V,Segment(P)) -> Record(num: P,den: Integer) +--R sum : (P,V) -> Record(num: P,den: Integer) +--R --E 1 )spool @@ -55303,6 +57800,17 @@ InnerPolySum(E, V, R, P): Exports == Impl where --S 1 of 1 )show InnerTrigonometricManipulations +--R +--R InnerTrigonometricManipulations(R: Join(IntegralDomain,OrderedSet),F: Join(FunctionSpace(R),RadicalCategory,TranscendentalFunctionCategory),FG: Join(FunctionSpace(Complex(R)),RadicalCategory,TranscendentalFunctionCategory)) is a package constructor +--R Abbreviation for InnerTrigonometricManipulations is ITRIGMNP +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for ITRIGMNP +--R +--R------------------------------- Operations -------------------------------- +--R F2FG : F -> FG FG2F : FG -> F +--R GF2FG : Complex(F) -> FG explogs2trigs : FG -> Complex(F) +--R trigs2explogs : (FG,List(Kernel(FG)),List(Symbol)) -> FG +--R --E 1 )spool @@ -55518,6 +58026,15 @@ InnerTrigonometricManipulations(R,F,FG): Exports == Implementation where --S 1 of 1 )show InputFormFunctions1 +--R +--R InputFormFunctions1(R: Type) is a package constructor +--R Abbreviation for InputFormFunctions1 is INFORM1 +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for INFORM1 +--R +--R------------------------------- Operations -------------------------------- +--R interpret : InputForm -> R packageCall : Symbol -> InputForm +--R --E 1 )spool @@ -55585,6 +58102,7 @@ InputFormFunctions1(R:Type):with )set message test on )set message auto off )clear all + --S 1 of 1 )show InterfaceGroebnerPackage --R @@ -55710,6 +58228,17 @@ representation and so are much facter than using a quotient loop. --S 1 of 1 )show IntegerBits +--R +--R IntegerBits is a package constructor +--R Abbreviation for IntegerBits is INTBIT +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for INTBIT +--R +--R------------------------------- Operations -------------------------------- +--R bitLength : Integer -> Integer +--R bitCoef : (Integer,Integer) -> Integer +--R bitTruth : (Integer,Integer) -> Boolean +--R --E 1 )spool @@ -55774,25 +58303,42 @@ IntegerBits: with )set message test on )set message auto off )clear all ---S 1 of 4 + +--S 1 of 5 +)show IntegerCombinatoricFunctions +--R +--R IntegerCombinatoricFunctions(I: IntegerNumberSystem) is a package constructor +--R Abbreviation for IntegerCombinatoricFunctions is COMBINAT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for COMBINAT +--R +--R------------------------------- Operations -------------------------------- +--R binomial : (I,I) -> I factorial : I -> I +--R multinomial : (I,List(I)) -> I partition : I -> I +--R permutation : (I,I) -> I stirling1 : (I,I) -> I +--R stirling2 : (I,I) -> I +--R +--E 5 + +--S 2 of 5 )set expose add constructor OutputForm --R --I OutputForm is already explicitly exposed in frame frame0 --E 1 ---S 2 of 4 +--S 3 of 5 pascalRow(n) == [right(binomial(n,i),4) for i in 0..n] --R --R Type: Void --E 2 ---S 3 of 4 +--S 4 of 5 displayRow(n)==output center blankSeparate pascalRow(n) --R --R Type: Void --E 3 ---S 4 of 4 +--S 5 of 5 for i in 0..7 repeat displayRow i --R --R Compiling function pascalRow with type NonNegativeInteger -> List( @@ -56046,6 +58592,17 @@ IntegerCombinatoricFunctions(I:IntegerNumberSystem): EE == II where --S 1 of 1 )show IntegerFactorizationPackage +--R +--R IntegerFactorizationPackage(I: IntegerNumberSystem) is a package constructor +--R Abbreviation for IntegerFactorizationPackage is INTFACT +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for INTFACT +--R +--R------------------------------- Operations -------------------------------- +--R BasicMethod : I -> Factored(I) factor : I -> Factored(I) +--R squareFree : I -> Factored(I) +--R PollardSmallFactor : I -> Union(I,"failed") +--R --E 1 )spool @@ -56412,7 +58969,7 @@ factor t6 )set message auto off )clear all ---S 1 of 8 +--S 1 of 9 M := SQMATRIX(2,INT) --R --R @@ -56420,7 +58977,7 @@ M := SQMATRIX(2,INT) --R Type: Domain --E 1 ---S 2 of 8 +--S 2 of 9 m1: M := squareMatrix matrix [ [1, 2], [0, -1] ] --R --R @@ -56430,7 +58987,7 @@ m1: M := squareMatrix matrix [ [1, 2], [0, -1] ] --R Type: SquareMatrix(2,Integer) --E 2 ---S 3 of 8 +--S 3 of 9 m2: M := squareMatrix matrix [ [2, 3], [1, -2] ] --R --R @@ -56440,7 +58997,7 @@ m2: M := squareMatrix matrix [ [2, 3], [1, -2] ] --R Type: SquareMatrix(2,Integer) --E 3 ---S 4 of 8 +--S 4 of 9 m3: M := squareMatrix matrix [ [3, 4], [2, -3] ] --R --R @@ -56450,7 +59007,7 @@ m3: M := squareMatrix matrix [ [3, 4], [2, -3] ] --R Type: SquareMatrix(2,Integer) --E 4 ---S 5 of 8 +--S 5 of 9 linearlyDependentOverZ? vector [m1, m2, m3] --R --R @@ -56458,7 +59015,7 @@ linearlyDependentOverZ? vector [m1, m2, m3] --R Type: Boolean --E 5 ---S 6 of 8 +--S 6 of 9 c := linearDependenceOverZ vector [m1, m2, m3] --R --R @@ -56466,7 +59023,7 @@ c := linearDependenceOverZ vector [m1, m2, m3] --R Type: Union(Vector(Integer),...) --E 6 ---S 7 of 8 +--S 7 of 9 c.1 * m1 + c.2 * m2 + c.3 * m3 --R --R @@ -56476,7 +59033,7 @@ c.1 * m1 + c.2 * m2 + c.3 * m3 --R Type: SquareMatrix(2,Integer) --E 7 ---S 8 of 8 +--S 8 of 9 solveLinearlyOverQ(vector [m1, m3], m2) --R --R @@ -56485,6 +59042,22 @@ solveLinearlyOverQ(vector [m1, m3], m2) --R 2 2 --R Type: Union(Vector(Fraction(Integer)),...) --E 8 + +--S 9 of 9 +)show IntegerLinearDependence +--R +--R IntegerLinearDependence(R: LinearlyExplicitRingOver(Integer)) is a package constructor +--R Abbreviation for IntegerLinearDependence is ZLINDEP +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for ZLINDEP +--R +--R------------------------------- Operations -------------------------------- +--R linearDependenceOverZ : Vector(R) -> Union(Vector(Integer),"failed") +--R linearlyDependentOverZ? : Vector(R) -> Boolean +--R solveLinearlyOverQ : (Vector(R),R) -> Union(Vector(Fraction(Integer)),"failed") +--R +--E 9 + )spool )lisp (bye) \end{chunk} @@ -56630,7 +59203,7 @@ IntegerLinearDependence(R): Exports == Implementation where )set message auto off )clear all ---S 1 of 30 +--S 1 of 31 div144 := divisors(144) --R --R @@ -56638,7 +59211,7 @@ div144 := divisors(144) --R Type: List(Integer) --E 1 ---S 2 of 30 +--S 2 of 31 #(div144) --R --R @@ -56646,7 +59219,7 @@ div144 := divisors(144) --R Type: PositiveInteger --E 2 ---S 3 of 30 +--S 3 of 31 reduce(+,div144) --R --R @@ -56654,7 +59227,7 @@ reduce(+,div144) --R Type: PositiveInteger --E 3 ---S 4 of 30 +--S 4 of 31 numberOfDivisors(144) --R --R @@ -56662,7 +59235,7 @@ numberOfDivisors(144) --R Type: PositiveInteger --E 4 ---S 5 of 30 +--S 5 of 31 sumOfDivisors(144) --R --R @@ -56670,14 +59243,14 @@ sumOfDivisors(144) --R Type: PositiveInteger --E 5 ---S 6 of 30 +--S 6 of 31 f1(n)==reduce(+,[moebiusMu(d)*numberOfDivisors(quo(n,d))_ for d in divisors(n)]) --R --R Type: Void --E 6 ---S 7 of 30 +--S 7 of 31 f1(200) --R --R Compiling function f1 with type PositiveInteger -> Integer @@ -56686,7 +59259,7 @@ f1(200) --R Type: PositiveInteger --E 7 ---S 8 of 30 +--S 8 of 31 f1(846) --R --R @@ -56694,14 +59267,14 @@ f1(846) --R Type: PositiveInteger --E 8 ---S 9 of 30 +--S 9 of 31 f2(n) == reduce(+,[moebiusMu(d) * sumOfDivisors(quo(n,d))_ for d in divisors(n)]) --R --R Type: Void --E 9 ---S 10 of 30 +--S 10 of 31 f2(200) --R --R Compiling function f2 with type PositiveInteger -> Integer @@ -56710,7 +59283,7 @@ f2(200) --R Type: PositiveInteger --E 10 ---S 11 of 30 +--S 11 of 31 f2(846) --R --R @@ -56718,7 +59291,7 @@ f2(846) --R Type: PositiveInteger --E 11 ---S 12 of 30 +--S 12 of 31 fibonacci(25) --R --R @@ -56726,7 +59299,7 @@ fibonacci(25) --R Type: PositiveInteger --E 12 ---S 13 of 30 +--S 13 of 31 [fibonacci(n) for n in 1..15] --R --R @@ -56734,13 +59307,13 @@ fibonacci(25) --R Type: List(Integer) --E 13 ---S 14 of 30 +--S 14 of 31 fib(n) == reduce(+,[binomial(n-1-k,k) for k in 0..quo(n-1,2)]) --R --R Type: Void --E 14 ---S 15 of 30 +--S 15 of 31 fib(25) --R --R Compiling function fib with type PositiveInteger -> Integer @@ -56749,7 +59322,7 @@ fib(25) --R Type: PositiveInteger --E 15 ---S 16 of 30 +--S 16 of 31 [fib(n) for n in 1..15] --R --R @@ -56757,7 +59330,7 @@ fib(25) --R Type: List(Integer) --E 16 ---S 17 of 30 +--S 17 of 31 legendre(3,5) --R --R @@ -56765,7 +59338,7 @@ legendre(3,5) --R Type: Integer --E 17 ---S 18 of 30 +--S 18 of 31 legendre(23,691) --R --R @@ -56773,13 +59346,13 @@ legendre(23,691) --R Type: Integer --E 18 ---S 19 of 30 +--S 19 of 31 h(d) == quo(reduce(+,[jacobi(d,k) for k in 1..quo(-d, 2)]),2-jacobi(d,2)) --R --R Type: Void --E 19 ---S 20 of 30 +--S 20 of 31 h(-163) --R --R Compiling function h with type Integer -> Integer @@ -56788,7 +59361,7 @@ h(-163) --R Type: PositiveInteger --E 20 ---S 21 of 30 +--S 21 of 31 h(-499) --R --R @@ -56796,7 +59369,7 @@ h(-499) --R Type: PositiveInteger --E 21 ---S 22 of 30 +--S 22 of 31 h(-1832) --R --R @@ -56804,13 +59377,13 @@ h(-1832) --R Type: PositiveInteger --E 22 ---S 23 of 30 +--S 23 of 31 inverse:(INT,INT)->INT --R --R Type: Void --E 23 ---S 24 of 30 +--S 24 of 31 inverse(a,b) == borg:INT:=b c1:INT := 1 @@ -56827,7 +59400,7 @@ inverse(a,b) == --R Type: Void --E 24 ---S 25 of 30 +--S 25 of 31 inverse(15,26) --R --R Compiling function inverse with type (Integer,Integer) -> Integer @@ -56842,7 +59415,7 @@ inverse(15,26) --R Type: PositiveInteger --E 25 ---S 26 of 30 +--S 26 of 31 x1:=4 --R --R @@ -56850,7 +59423,7 @@ x1:=4 --R Type: PositiveInteger --E 26 ---S 27 of 30 +--S 27 of 31 m1:=5 --R --R @@ -56858,7 +59431,7 @@ m1:=5 --R Type: PositiveInteger --E 27 ---S 28 of 30 +--S 28 of 31 x2:=2 --R --R @@ -56866,7 +59439,7 @@ x2:=2 --R Type: PositiveInteger --E 28 ---S 29 of 30 +--S 29 of 31 m2:=3 --R --R @@ -56874,7 +59447,7 @@ m2:=3 --R Type: PositiveInteger --E 29 ---S 30 of 30 +--S 30 of 31 result:=chineseRemainder(x1,m1,x2,m2) --R --R @@ -56882,6 +59455,28 @@ result:=chineseRemainder(x1,m1,x2,m2) --R Type: PositiveInteger --E 30 +--S 31 of 31 +)show IntegerNumberTheoryFunctions +--R +--R IntegerNumberTheoryFunctions is a package constructor +--R Abbreviation for IntegerNumberTheoryFunctions is INTHEORY +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for INTHEORY +--R +--R------------------------------- Operations -------------------------------- +--R divisors : Integer -> List(Integer) euler : Integer -> Integer +--R eulerPhi : Integer -> Integer fibonacci : Integer -> Integer +--R moebiusMu : Integer -> Integer sumOfDivisors : Integer -> Integer +--R bernoulli : Integer -> Fraction(Integer) +--R chineseRemainder : (Integer,Integer,Integer,Integer) -> Integer +--R harmonic : Integer -> Fraction(Integer) +--R jacobi : (Integer,Integer) -> Integer +--R legendre : (Integer,Integer) -> Integer +--R numberOfDivisors : Integer -> Integer +--R sumOfKthPowerDivisors : (Integer,NonNegativeInteger) -> Integer +--R +--E 31 + )spool )lisp (bye) \end{chunk} @@ -57564,6 +60159,16 @@ We've expanded the list of small primes to include those between 1 and 10000. --S 1 of 1 )show IntegerPrimesPackage +--R +--R IntegerPrimesPackage(I: IntegerNumberSystem) is a package constructor +--R Abbreviation for IntegerPrimesPackage is PRIMES +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for PRIMES +--R +--R------------------------------- Operations -------------------------------- +--R nextPrime : I -> I prevPrime : I -> I +--R prime? : I -> Boolean primes : (I,I) -> List(I) +--R --E 1 )spool @@ -58029,6 +60634,16 @@ that is the square of the upper bound of the table range, in this case --S 1 of 1 )show IntegerRetractions +--R +--R IntegerRetractions(S: RetractableTo(Integer)) is a package constructor +--R Abbreviation for IntegerRetractions is INTRET +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for INTRET +--R +--R------------------------------- Operations -------------------------------- +--R integer : S -> Integer integer? : S -> Boolean +--R integerIfCan : S -> Union(Integer,"failed") +--R --E 1 )spool @@ -58096,6 +60711,20 @@ IntegerRetractions(S:RetractableTo(Integer)): with --S 1 of 1 )show IntegerRoots +--R +--R IntegerRoots(I: IntegerNumberSystem) is a package constructor +--R Abbreviation for IntegerRoots is IROOT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for IROOT +--R +--R------------------------------- Operations -------------------------------- +--R approxSqrt : I -> I perfectSqrt : I -> Union(I,"failed") +--R perfectSquare? : I -> Boolean +--R approxNthRoot : (I,NonNegativeInteger) -> I +--R perfectNthPower? : (I,NonNegativeInteger) -> Boolean +--R perfectNthRoot : (I,NonNegativeInteger) -> Union(I,"failed") +--R perfectNthRoot : I -> Record(base: I,exponent: NonNegativeInteger) +--R --E 1 )spool @@ -58272,6 +60901,15 @@ IntegerRoots(I:IntegerNumberSystem): Exports == Implementation where --S 1 of 1 )show IntegerSolveLinearPolynomialEquation +--R +--R IntegerSolveLinearPolynomialEquation is a package constructor +--R Abbreviation for IntegerSolveLinearPolynomialEquation is INTSLPE +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for INTSLPE +--R +--R------------------------------- Operations -------------------------------- +--R solveLinearPolynomialEquation : (List(SparseUnivariatePolynomial(Integer)),SparseUnivariatePolynomial(Integer)) -> Union(List(SparseUnivariatePolynomial(Integer)),"failed") +--R --E 1 )spool @@ -58355,6 +60993,24 @@ IntegerSolveLinearPolynomialEquation(): C ==T --S 1 of 1 )show IntegralBasisTools +--R +--R IntegralBasisTools(R,UP: UnivariatePolynomialCategory(R),F: FramedAlgebra(R,UP))where +--R R: EuclideanDomainwith +--R squareFree : % -> Factored(%) is a package constructor +--R Abbreviation for IntegralBasisTools is IBATOOL +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for IBATOOL +--R +--R------------------------------- Operations -------------------------------- +--R diagonalProduct : Matrix(R) -> R +--R divideIfCan! : (Matrix(R),Matrix(R),R,Integer) -> R +--R idealiser : (Matrix(R),Matrix(R)) -> Matrix(R) +--R idealiser : (Matrix(R),Matrix(R),R) -> Matrix(R) +--R idealiserMatrix : (Matrix(R),Matrix(R)) -> Matrix(R) +--R leastPower : (NonNegativeInteger,NonNegativeInteger) -> NonNegativeInteger +--R matrixGcd : (Matrix(R),R,NonNegativeInteger) -> R +--R moduleSum : (Record(basis: Matrix(R),basisDen: R,basisInv: Matrix(R)),Record(basis: Matrix(R),basisDen: R,basisInv: Matrix(R))) -> Record(basis: Matrix(R),basisDen: R,basisInv: Matrix(R)) +--R --E 1 )spool @@ -58541,6 +61197,19 @@ IntegralBasisTools(R,UP,F): Exports == Implementation where --S 1 of 1 )show IntegralBasisPolynomialTools +--R +--R IntegralBasisPolynomialTools(K: Ring,R: UnivariatePolynomialCategory(K),UP: UnivariatePolynomialCategory(R),L: Ring) is a package constructor +--R Abbreviation for IntegralBasisPolynomialTools is IBPTOOLS +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for IBPTOOLS +--R +--R------------------------------- Operations -------------------------------- +--R mapBivariate : ((K -> L),UP) -> SparseUnivariatePolynomial(SparseUnivariatePolynomial(L)) +--R mapMatrixIfCan : ((L -> Union(K,"failed")),Matrix(SparseUnivariatePolynomial(L))) -> Union(Matrix(R),"failed") +--R mapUnivariate : ((L -> K),SparseUnivariatePolynomial(L)) -> R +--R mapUnivariate : ((K -> L),R) -> SparseUnivariatePolynomial(L) +--R mapUnivariateIfCan : ((L -> Union(K,"failed")),SparseUnivariatePolynomial(L)) -> Union(R,"failed") +--R --E 1 )spool @@ -58670,6 +61339,18 @@ IntegralBasisPolynomialTools(K,R,UP,L): Exports == Implementation where --S 1 of 1 )show IntegrationResultFunctions2 +--R +--R IntegrationResultFunctions2(E: Field,F: Field) is a package constructor +--R Abbreviation for IntegrationResultFunctions2 is IR2 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for IR2 +--R +--R------------------------------- Operations -------------------------------- +--R map : ((E -> F),IntegrationResult(E)) -> IntegrationResult(F) +--R map : ((E -> F),Union(Record(ratpart: E,coeff: E),"failed")) -> Union(Record(ratpart: F,coeff: F),"failed") +--R map : ((E -> F),Union(E,"failed")) -> Union(F,"failed") +--R map : ((E -> F),Union(Record(mainpart: E,limitedlogs: List(Record(coeff: E,logand: E))),"failed")) -> Union(Record(mainpart: F,limitedlogs: List(Record(coeff: F,logand: F))),"failed") +--R --E 1 )spool @@ -58776,6 +61457,19 @@ IntegrationResultFunctions2(E, F): Exports == Implementation where --S 1 of 1 )show IntegrationResultRFToFunction +--R +--R IntegrationResultRFToFunction(R: Join(GcdDomain,RetractableTo(Integer),OrderedSet,LinearlyExplicitRingOver(Integer))) is a package constructor +--R Abbreviation for IntegrationResultRFToFunction is IRRF2F +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for IRRF2F +--R +--R------------------------------- Operations -------------------------------- +--R complexExpand : IntegrationResult(Fraction(Polynomial(R))) -> Expression(R) +--R complexIntegrate : (Fraction(Polynomial(R)),Symbol) -> Expression(R) if R has CHARZ +--R expand : IntegrationResult(Fraction(Polynomial(R))) -> List(Expression(R)) +--R integrate : (Fraction(Polynomial(R)),Symbol) -> Union(Expression(R),List(Expression(R))) if R has CHARZ +--R split : IntegrationResult(Fraction(Polynomial(R))) -> IntegrationResult(Fraction(Polynomial(R))) +--R --E 1 )spool @@ -58891,6 +61585,17 @@ IntegrationResultRFToFunction(R): Exports == Implementation where --S 1 of 1 )show IntegrationResultToFunction +--R +--R IntegrationResultToFunction(R: Join(GcdDomain,RetractableTo(Integer),OrderedSet,LinearlyExplicitRingOver(Integer)),F: Join(AlgebraicallyClosedFunctionSpace(R),TranscendentalFunctionCategory)) is a package constructor +--R Abbreviation for IntegrationResultToFunction is IR2F +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for IR2F +--R +--R------------------------------- Operations -------------------------------- +--R complexExpand : IntegrationResult(F) -> F +--R expand : IntegrationResult(F) -> List(F) +--R split : IntegrationResult(F) -> IntegrationResult(F) +--R --E 1 )spool @@ -59153,6 +61858,22 @@ IntegrationResultToFunction(R, F): Exports == Implementation where --S 1 of 1 )show IntegrationTools +--R +--R IntegrationTools(R: OrderedSet,F: FunctionSpace(R)) is a package constructor +--R Abbreviation for IntegrationTools is INTTOOLS +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for INTTOOLS +--R +--R------------------------------- Operations -------------------------------- +--R kmax : List(Kernel(F)) -> Kernel(F) +--R intPatternMatch : (F,Symbol,((F,Symbol) -> IntegrationResult(F)),((F,Symbol) -> Union(Record(special: F,integrand: F),"failed"))) -> IntegrationResult(F) if F has ELEMFUN and F has LFCAT and F has RETRACT(SYMBOL) and R has KONVERT(PATTERN(INT)) and R has GCDDOM and R has PATMAB(INT) +--R ksec : (Kernel(F),List(Kernel(F)),Symbol) -> Kernel(F) +--R mkPrim : (F,Symbol) -> F if F has ELEMFUN and R has GCDDOM +--R removeConstantTerm : (F,Symbol) -> F if R has INTDOM +--R union : (List(Kernel(F)),List(Kernel(F))) -> List(Kernel(F)) +--R vark : (List(F),Symbol) -> List(Kernel(F)) +--R varselect : (List(Kernel(F)),Symbol) -> List(Kernel(F)) +--R --E 1 )spool @@ -59338,6 +62059,15 @@ IntegrationTools(R:OrderedSet, F:FunctionSpace R): Exp == Impl where --S 1 of 1 )show InternalPrintPackage +--R +--R InternalPrintPackage is a package constructor +--R Abbreviation for InternalPrintPackage is IPRNTPK +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for IPRNTPK +--R +--R------------------------------- Operations -------------------------------- +--R iprint : String -> Void +--R --E 1 )spool @@ -59399,6 +62129,15 @@ InternalPrintPackage(): Exports == Implementation where --S 1 of 1 )show InternalRationalUnivariateRepresentationPackage +--R +--R InternalRationalUnivariateRepresentationPackage(R: Join(EuclideanDomain,CharacteristicZero),E: OrderedAbelianMonoidSup,V: OrderedSet,P: RecursivePolynomialCategory(R,E,V),TS: SquareFreeRegularTriangularSetCategory(R,E,V,P)) is a package constructor +--R Abbreviation for InternalRationalUnivariateRepresentationPackage is IRURPK +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for IRURPK +--R +--R------------------------------- Operations -------------------------------- +--R checkRur : (TS,List(TS)) -> Boolean rur : (TS,Boolean) -> List(TS) +--R --E 1 )spool @@ -60142,6 +62881,15 @@ IntersectionDivisorPackage(K,symb,PolyRing,E,ProjPt, PCS,Plc,DIVISOR,_ --S 1 of 1 )show IrredPolyOverFiniteField +--R +--R IrredPolyOverFiniteField(GF: FiniteFieldCategory) is a package constructor +--R Abbreviation for IrredPolyOverFiniteField is IRREDFFX +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for IRREDFFX +--R +--R------------------------------- Operations -------------------------------- +--R generateIrredPoly : PositiveInteger -> SparseUnivariatePolynomial(GF) +--R --E 1 )spool @@ -60247,6 +62995,18 @@ IrredPolyOverFiniteField(GF:FiniteFieldCategory): Exports == Impl where --S 1 of 1 )show IrrRepSymNatPackage +--R +--R IrrRepSymNatPackage is a package constructor +--R Abbreviation for IrrRepSymNatPackage is IRSN +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for IRSN +--R +--R------------------------------- Operations -------------------------------- +--R dimensionOfIrreducibleRepresentation : List(Integer) -> NonNegativeInteger +--R irreducibleRepresentation : (List(Integer),Permutation(Integer)) -> Matrix(Integer) +--R irreducibleRepresentation : List(Integer) -> List(Matrix(Integer)) +--R irreducibleRepresentation : (List(Integer),List(Permutation(Integer))) -> List(Matrix(Integer)) +--R --E 1 )spool @@ -60602,6 +63362,15 @@ IrrRepSymNatPackage(): public == private where --S 1 of 1 )show InverseLaplaceTransform +--R +--R InverseLaplaceTransform(R: Join(EuclideanDomain,OrderedSet,CharacteristicZero,RetractableTo(Integer),LinearlyExplicitRingOver(Integer)),F: Join(TranscendentalFunctionCategory,PrimitiveFunctionCategory,SpecialFunctionCategory,AlgebraicallyClosedFunctionSpace(R))) is a package constructor +--R Abbreviation for InverseLaplaceTransform is INVLAPLA +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for INVLAPLA +--R +--R------------------------------- Operations -------------------------------- +--R inverseLaplace : (F,Symbol,Symbol) -> Union(F,"failed") +--R --E 1 )spool @@ -60742,6 +63511,16 @@ InverseLaplaceTransform(R, F): Exports == Implementation where --S 1 of 1 )show KernelFunctions2 +--R +--R KernelFunctions2(R: OrderedSet,S: OrderedSet) is a package constructor +--R Abbreviation for KernelFunctions2 is KERNEL2 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for KERNEL2 +--R +--R------------------------------- Operations -------------------------------- +--R constantKernel : R -> Kernel(S) +--R constantIfCan : Kernel(S) -> Union(R,"failed") +--R --E 1 )spool @@ -60803,6 +63582,16 @@ KernelFunctions2(R:OrderedSet, S:OrderedSet): with --S 1 of 1 )show Kovacic +--R +--R Kovacic(F: Join(CharacteristicZero,AlgebraicallyClosedField,RetractableTo(Integer),RetractableTo(Fraction(Integer))),UP: UnivariatePolynomialCategory(F)) is a package constructor +--R Abbreviation for Kovacic is KOVACIC +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for KOVACIC +--R +--R------------------------------- Operations -------------------------------- +--R kovacic : (Fraction(UP),Fraction(UP),Fraction(UP)) -> Union(SparseUnivariatePolynomial(Fraction(UP)),"failed") +--R kovacic : (Fraction(UP),Fraction(UP),Fraction(UP),(UP -> Factored(UP))) -> Union(SparseUnivariatePolynomial(Fraction(UP)),"failed") +--R --E 1 )spool @@ -60940,6 +63729,15 @@ Kovacic(F, UP): Exports == Impl where --S 1 of 1 )show LaplaceTransform +--R +--R LaplaceTransform(R: Join(EuclideanDomain,OrderedSet,CharacteristicZero,RetractableTo(Integer),LinearlyExplicitRingOver(Integer)),F: Join(TranscendentalFunctionCategory,PrimitiveFunctionCategory,AlgebraicallyClosedFunctionSpace(R))) is a package constructor +--R Abbreviation for LaplaceTransform is LAPLACE +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for LAPLACE +--R +--R------------------------------- Operations -------------------------------- +--R laplace : (F,Symbol,Symbol) -> F +--R --E 1 )spool @@ -61197,7 +63995,7 @@ LaplaceTransform(R, F): Exports == Implementation where )set message auto off )clear all ---S 1 of 36 +--S 1 of 37 R := Integer --R --R @@ -61205,7 +64003,7 @@ R := Integer --R Type: Domain --E 1 ---S 2 of 36 +--S 2 of 37 ls : List Symbol := [b1,x,y,z,t,v,u,w] --R --R @@ -61213,7 +64011,7 @@ ls : List Symbol := [b1,x,y,z,t,v,u,w] --R Type: List(Symbol) --E 2 ---S 3 of 36 +--S 3 of 37 V := OVAR(ls) --R --R @@ -61221,7 +64019,7 @@ V := OVAR(ls) --R Type: Domain --E 3 ---S 4 of 36 +--S 4 of 37 E := IndexedExponents V --R --R @@ -61229,7 +64027,7 @@ E := IndexedExponents V --R Type: Domain --E 4 ---S 5 of 36 +--S 5 of 37 P := NSMP(R, V) --R --R @@ -61239,7 +64037,7 @@ P := NSMP(R, V) --R Type: Domain --E 5 ---S 6 of 36 +--S 6 of 37 b1: P := 'b1 --R --R @@ -61247,7 +64045,7 @@ b1: P := 'b1 --IType: NewSparseMultivariatePolynomial(Integer,... --E 6 ---S 7 of 36 +--S 7 of 37 x: P := 'x --R --R @@ -61255,7 +64053,7 @@ x: P := 'x --IType: NewSparseMultivariatePolynomial(Integer,... --E 7 ---S 8 of 36 +--S 8 of 37 y: P := 'y --R --R @@ -61263,7 +64061,7 @@ y: P := 'y --IType: NewSparseMultivariatePolynomial(Integer,... --E 8 ---S 9 of 36 +--S 9 of 37 z: P := 'z --R --R @@ -61271,7 +64069,7 @@ z: P := 'z --IType: NewSparseMultivariatePolynomial(Integer,... --E 9 ---S 10 of 36 +--S 10 of 37 t: P := 't --R --R @@ -61279,7 +64077,7 @@ t: P := 't --IType: NewSparseMultivariatePolynomial(Integer,... --E 10 ---S 11 of 36 +--S 11 of 37 u: P := 'u --R --R @@ -61287,7 +64085,7 @@ u: P := 'u --IType: NewSparseMultivariatePolynomial(Integer,... --E 11 ---S 12 of 36 +--S 12 of 37 v: P := 'v --R --R @@ -61295,7 +64093,7 @@ v: P := 'v --IType: NewSparseMultivariatePolynomial(Integer,... --E 12 ---S 13 of 36 +--S 13 of 37 w: P := 'w --R --R @@ -61303,7 +64101,7 @@ w: P := 'w --IType: NewSparseMultivariatePolynomial(Integer,... --E 13 ---S 14 of 36 +--S 14 of 37 T := REGSET(R,E,V,P) --R --R @@ -61314,7 +64112,7 @@ T := REGSET(R,E,V,P) --R Type: Domain --E 14 ---S 15 of 36 +--S 15 of 37 p0 := b1 + y + z - t - w --R --R @@ -61322,7 +64120,7 @@ p0 := b1 + y + z - t - w --IType: NewSparseMultivariatePolynomial(Integer,... --E 15 ---S 16 of 36 +--S 16 of 37 p1 := 2*z*u + 2*y*v + 2*t*w - 2*w**2 - w - 1 --R --R @@ -61331,7 +64129,7 @@ p1 := 2*z*u + 2*y*v + 2*t*w - 2*w**2 - w - 1 --IType: NewSparseMultivariatePolynomial(Integer,... --E 16 ---S 17 of 36 +--S 17 of 37 p2 := 3*z*u**2 + 3*y*v**2 - 3*t*w**2 + 3*w**3 + 3*w**2 - t + 4*w --R --R @@ -61340,7 +64138,7 @@ p2 := 3*z*u**2 + 3*y*v**2 - 3*t*w**2 + 3*w**3 + 3*w**2 - t + 4*w --IType: NewSparseMultivariatePolynomial(Integer,... --E 17 ---S 18 of 36 +--S 18 of 37 p3 := 6*x*z*v - 6*t*w**2 + 6*w**3 - 3*t*w + 6*w**2 - t + 4*w --R --R @@ -61349,7 +64147,7 @@ p3 := 6*x*z*v - 6*t*w**2 + 6*w**3 - 3*t*w + 6*w**2 - t + 4*w --IType: NewSparseMultivariatePolynomial(Integer,... --E 18 ---S 19 of 36 +--S 19 of 37 p4 := 4*z*u**3+ 4*y*v**3+ 4*t*w**3- 4*w**4 - 6*w**3+ 4*t*w- 10*w**2- w- 1 --R --R @@ -61358,7 +64156,7 @@ p4 := 4*z*u**3+ 4*y*v**3+ 4*t*w**3- 4*w**4 - 6*w**3+ 4*t*w- 10*w**2- w- 1 --IType: NewSparseMultivariatePolynomial(Integer,... --E 19 ---S 20 of 36 +--S 20 of 37 p5 := 8*x*z*u*v +8*t*w**3 -8*w**4 +4*t*w**2 -12*w**3 +4*t*w -14*w**2 -3*w -1 --R --R @@ -61367,7 +64165,7 @@ p5 := 8*x*z*u*v +8*t*w**3 -8*w**4 +4*t*w**2 -12*w**3 +4*t*w -14*w**2 -3*w -1 --IType: NewSparseMultivariatePolynomial(Integer,... --E 20 ---S 21 of 36 +--S 21 of 37 p6 := 12*x*z*v**2+12*t*w**3 -12*w**4 +12*t*w**2 -18*w**3 +8*t*w -14*w**2 -w -1 --R --R @@ -61376,7 +64174,7 @@ p6 := 12*x*z*v**2+12*t*w**3 -12*w**4 +12*t*w**2 -18*w**3 +8*t*w -14*w**2 -w -1 --IType: NewSparseMultivariatePolynomial(Integer,... --E 21 ---S 22 of 36 +--S 22 of 37 p7 := -24*t*w**3 + 24*w**4 - 24*t*w**2 + 36*w**3 - 8*t*w + 26*w**2 + 7*w + 1 --R --R @@ -61385,7 +64183,7 @@ p7 := -24*t*w**3 + 24*w**4 - 24*t*w**2 + 36*w**3 - 8*t*w + 26*w**2 + 7*w + 1 --IType: NewSparseMultivariatePolynomial(Integer,... --E 22 ---S 23 of 36 +--S 23 of 37 lp := [p0, p1, p2, p3, p4, p5, p6, p7] --R --R @@ -61407,7 +64205,7 @@ lp := [p0, p1, p2, p3, p4, p5, p6, p7] --IType: List(NewSparseMultivariatePolynomial(Integer,... --E 23 ---S 24 of 36 +--S 24 of 37 lts := zeroSetSplit(lp,false)$T --R --R @@ -61438,7 +64236,7 @@ lts := zeroSetSplit(lp,false)$T --IType: List(RegularTriangularSet(Integer,... --E 24 ---S 25 of 36 +--S 25 of 37 [coHeight(ts) for ts in lts] --R --R @@ -61446,7 +64244,7 @@ lts := zeroSetSplit(lp,false)$T --R Type: List(NonNegativeInteger) --E 25 ---S 26 of 36 +--S 26 of 37 ST := SREGSET(R,E,V,P) --R --R @@ -61457,7 +64255,7 @@ ST := SREGSET(R,E,V,P) --R Type: Domain --E 26 ---S 27 of 36 +--S 27 of 37 pack := LAZM3PK(R,E,V,P,T,ST) --R --R @@ -61474,7 +64272,7 @@ pack := LAZM3PK(R,E,V,P,T,ST) --R Type: Domain --E 27 ---S 28 of 36 +--S 28 of 37 zeroSetSplit(lp,false)$pack --R --R @@ -61499,7 +64297,7 @@ zeroSetSplit(lp,false)$pack --IType: List(SquareFreeRegularTriangularSet(Integer,... --E 28 ---S 29 of 36 +--S 29 of 37 f0 := (w - v) ** 2 + (u - t) ** 2 - 1 --R --R @@ -61508,7 +64306,7 @@ f0 := (w - v) ** 2 + (u - t) ** 2 - 1 --IType: NewSparseMultivariatePolynomial(Integer,... --E 29 ---S 30 of 36 +--S 30 of 37 f1 := t ** 2 - v ** 3 --R --R @@ -61517,7 +64315,7 @@ f1 := t ** 2 - v ** 3 --IType: NewSparseMultivariatePolynomial(Integer,... --E 30 ---S 31 of 36 +--S 31 of 37 f2 := 2 * t * (w - v) + 3 * v ** 2 * (u - t) --R --R @@ -61526,7 +64324,7 @@ f2 := 2 * t * (w - v) + 3 * v ** 2 * (u - t) --IType: NewSparseMultivariatePolynomial(Integer,... --E 31 ---S 32 of 36 +--S 32 of 37 f3 := (3 * z * v ** 2 - 1) * (2 * z * t - 1) --R --R @@ -61535,7 +64333,7 @@ f3 := (3 * z * v ** 2 - 1) * (2 * z * t - 1) --IType: NewSparseMultivariatePolynomial(Integer,... --E 32 ---S 33 of 36 +--S 33 of 37 lf := [f0, f1, f2, f3] --R --R @@ -61547,7 +64345,7 @@ lf := [f0, f1, f2, f3] --IType: List(NewSparseMultivariatePolynomial(Integer,... --E 33 ---S 34 of 36 +--S 34 of 37 zeroSetSplit(lf,true)$T --R --R @@ -61581,7 +64379,7 @@ zeroSetSplit(lf,true)$T --IType: List(RegularTriangularSet(Integer,IndexedExponents(... --E 34 ---S 35 of 36 +--S 35 of 37 zeroSetSplit(lf,false)$T --R --R @@ -61651,7 +64449,7 @@ zeroSetSplit(lf,false)$T --IType: List(RegularTriangularSet(Integer,IndexedExponents(... --E 35 ---S 36 of 36 +--S 36 of 37 zeroSetSplit(lf,false)$pack --R --R @@ -61745,6 +64543,20 @@ zeroSetSplit(lf,false)$pack --IType: List(SquareFreeRegularTriangularSet(Integer,... --E 36 +--S 37 of 37 +)show LazardSetSolvingPackage +--R +--R LazardSetSolvingPackage(R: GcdDomain,E: OrderedAbelianMonoidSup,V: OrderedSet,P: RecursivePolynomialCategory(R,E,V),TS: RegularTriangularSetCategory(R,E,V,P),ST: SquareFreeRegularTriangularSetCategory(R,E,V,P)) is a package constructor +--R Abbreviation for LazardSetSolvingPackage is LAZM3PK +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for LAZM3PK +--R +--R------------------------------- Operations -------------------------------- +--R normalizeIfCan : ST -> ST +--R zeroSetSplit : (List(P),Boolean) -> List(ST) +--R +--E 37 + )spool )lisp (bye) \end{chunk} @@ -62343,6 +65155,16 @@ LazardSetSolvingPackage(R,E,V,P,TS,ST): Exports == Implementation where --S 1 of 1 )show LeadingCoefDetermination +--R +--R LeadingCoefDetermination(OV: OrderedSet,E: OrderedAbelianMonoidSup,Z: EuclideanDomain,P: PolynomialCategory(Z,E,OV)) is a package constructor +--R Abbreviation for LeadingCoefDetermination is LEADCDET +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for LEADCDET +--R +--R------------------------------- Operations -------------------------------- +--R distFact : (Z,List(SparseUnivariatePolynomial(Z)),Record(contp: Z,factors: List(Record(irr: P,pow: Integer))),List(Z),List(OV),List(Z)) -> Union(Record(polfac: List(P),correct: Z,corrfact: List(SparseUnivariatePolynomial(Z))),"failed") +--R polCase : (Z,NonNegativeInteger,List(Z)) -> Boolean +--R --E 1 )spool @@ -62496,7 +65318,8 @@ LeadingCoefDetermination(OV,E,Z,P) : C == T )set message test on )set message auto off )clear all ---S 1 of 22 + +--S 1 of 23 R := Integer --R --R @@ -62504,7 +65327,7 @@ R := Integer --R Type: Domain --E 1 ---S 2 of 22 +--S 2 of 23 ls : List Symbol := [a,b,c,d,e,f] --R --R @@ -62512,7 +65335,7 @@ ls : List Symbol := [a,b,c,d,e,f] --R Type: List(Symbol) --E 2 ---S 3 of 22 +--S 3 of 23 V := OVAR(ls) --R --R @@ -62520,7 +65343,7 @@ V := OVAR(ls) --R Type: Domain --E 3 ---S 4 of 22 +--S 4 of 23 P := NSMP(R, V) --R --R @@ -62529,7 +65352,7 @@ P := NSMP(R, V) --R Type: Domain --E 4 ---S 5 of 22 +--S 5 of 23 p1: P := a*b*c*d*e*f - 1 --R --R @@ -62537,7 +65360,7 @@ p1: P := a*b*c*d*e*f - 1 --RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList([a,b,c,d,e,f])) --E 5 ---S 6 of 22 +--S 6 of 23 p2: P := a*b*c*d*e +a*b*c*d*f +a*b*c*e*f +a*b*d*e*f +a*c*d*e*f +b*c*d*e*f --R --R @@ -62545,7 +65368,7 @@ p2: P := a*b*c*d*e +a*b*c*d*f +a*b*c*e*f +a*b*d*e*f +a*c*d*e*f +b*c*d*e*f --RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList([a,b,c,d,e,f])) --E 6 ---S 7 of 22 +--S 7 of 23 p3: P := a*b*c*d + a*b*c*f + a*b*e*f + a*d*e*f + b*c*d*e + c*d*e*f --R --R @@ -62553,7 +65376,7 @@ p3: P := a*b*c*d + a*b*c*f + a*b*e*f + a*d*e*f + b*c*d*e + c*d*e*f --RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList([a,b,c,d,e,f])) --E 7 ---S 8 of 22 +--S 8 of 23 p4: P := a*b*c + a*b*f + a*e*f + b*c*d + c*d*e + d*e*f --R --R @@ -62561,7 +65384,7 @@ p4: P := a*b*c + a*b*f + a*e*f + b*c*d + c*d*e + d*e*f --RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList([a,b,c,d,e,f])) --E 8 ---S 9 of 22 +--S 9 of 23 p5: P := a*b + a*f + b*c + c*d + d*e + e*f --R --R @@ -62569,7 +65392,7 @@ p5: P := a*b + a*f + b*c + c*d + d*e + e*f --RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList([a,b,c,d,e,f])) --E 9 ---S 10 of 22 +--S 10 of 23 p6: P := a + b + c + d + e + f --R --R @@ -62577,7 +65400,7 @@ p6: P := a + b + c + d + e + f --RType: NewSparseMultivariatePolynomial(Integer,OrderedVariableList([a,b,c,d,e,f])) --E 10 ---S 11 of 22 +--S 11 of 23 lp := [p1, p2, p3, p4, p5, p6] --R --R @@ -62589,7 +65412,7 @@ lp := [p1, p2, p3, p4, p5, p6] --RType: List(NewSparseMultivariatePolynomial(Integer,OrderedVariableList([a,b,c,d,e,f]))) --E 11 ---S 12 of 22 +--S 12 of 23 lextripack := LEXTRIPK(R,ls) --R --R @@ -62597,7 +65420,7 @@ lextripack := LEXTRIPK(R,ls) --R Type: Domain --E 12 ---S 13 of 22 +--S 13 of 23 lg := groebner(lp)$lextripack --R --R @@ -63051,7 +65874,7 @@ lg := groebner(lp)$lextripack --RType: List(NewSparseMultivariatePolynomial(Integer,OrderedVariableList([a,b,c,d,e,f]))) --E 13 ---S 14 of 22 +--S 14 of 23 lexTriangular(lg,false)$lextripack --R --R @@ -63149,7 +65972,7 @@ lexTriangular(lg,false)$lextripack --R Type: List(RegularChain(Integer,[a,b,c,d,e,f])) --E 14 ---S 15 of 22 +--S 15 of 23 lts := lexTriangular(lg,true)$lextripack --R --R @@ -63247,7 +66070,7 @@ lts := lexTriangular(lg,true)$lextripack --R Type: List(RegularChain(Integer,[a,b,c,d,e,f])) --E 15 ---S 16 of 22 +--S 16 of 23 [ [init(p) for p in (ts :: List(P))] for ts in lts] --R --R @@ -63258,7 +66081,7 @@ lts := lexTriangular(lg,true)$lextripack --RType: List(List(NewSparseMultivariatePolynomial(Integer,OrderedVariableList([a,b,c,d,e,f])))) --E 16 ---S 17 of 22 +--S 17 of 23 squareFreeLexTriangular(lg,true)$lextripack --R --R @@ -63356,7 +66179,7 @@ squareFreeLexTriangular(lg,true)$lextripack --RType: List(SquareFreeRegularTriangularSet(Integer,IndexedExponents(OrderedVariableList([a,b,c,d,e,f])),OrderedVariableList([a,b,c,d,e,f]),NewSparseMultivariatePolynomial(Integer,OrderedVariableList([a,b,c,d,e,f])))) --E 17 ---S 18 of 22 +--S 18 of 23 reduce(+,[degree(ts) for ts in lts]) --R --R @@ -63364,7 +66187,7 @@ reduce(+,[degree(ts) for ts in lts]) --R Type: PositiveInteger --E 18 ---S 19 of 22 +--S 19 of 23 ls2 : List Symbol := concat(ls,new()$Symbol) --R --R @@ -63372,7 +66195,7 @@ ls2 : List Symbol := concat(ls,new()$Symbol) --R Type: List(Symbol) --E 19 ---S 20 of 22 +--S 20 of 23 zdpack := ZDSOLVE(R,ls,ls2) --R --R @@ -63380,7 +66203,7 @@ zdpack := ZDSOLVE(R,ls,ls2) --R Type: Domain --E 20 ---S 21 of 22 +--S 21 of 23 concat [univariateSolve(ts)$zdpack for ts in lts] --R --R @@ -63881,7 +66704,7 @@ concat [univariateSolve(ts)$zdpack for ts in lts] --RType: List(Record(complexRoots: SparseUnivariatePolynomial(Integer),coordinates: List(Polynomial(Integer)))) --E 21 ---S 22 of 22 +--S 22 of 23 concat [realSolve(ts)$zdpack for ts in lts] --R --R @@ -64244,6 +67067,26 @@ concat [realSolve(ts)$zdpack for ts in lts] --R [%B32,%B34,- %B34 - 4%B32,%B32,%B32,%B32]] --R Type: List(List(RealClosure(Fraction(Integer)))) --E 22 + +--S 23 of 23 +)show LexTriangularPackage +--R +--R LexTriangularPackage(R: GcdDomain,ls: List(Symbol)) is a package constructor +--R Abbreviation for LexTriangularPackage is LEXTRIPK +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for LEXTRIPK +--R +--R------------------------------- Operations -------------------------------- +--R fglmIfCan : List(NewSparseMultivariatePolynomial(R,OrderedVariableList(ls))) -> Union(List(NewSparseMultivariatePolynomial(R,OrderedVariableList(ls))),"failed") +--R groebner : List(NewSparseMultivariatePolynomial(R,OrderedVariableList(ls))) -> List(NewSparseMultivariatePolynomial(R,OrderedVariableList(ls))) +--R lexTriangular : (List(NewSparseMultivariatePolynomial(R,OrderedVariableList(ls))),Boolean) -> List(RegularChain(R,ls)) +--R squareFreeLexTriangular : (List(NewSparseMultivariatePolynomial(R,OrderedVariableList(ls))),Boolean) -> List(SquareFreeRegularTriangularSet(R,IndexedExponents(OrderedVariableList(ls)),OrderedVariableList(ls),NewSparseMultivariatePolynomial(R,OrderedVariableList(ls)))) +--R zeroDimensional? : List(NewSparseMultivariatePolynomial(R,OrderedVariableList(ls))) -> Boolean +--R zeroSetSplit : (List(NewSparseMultivariatePolynomial(R,OrderedVariableList(ls))),Boolean) -> List(RegularChain(R,ls)) +--R zeroSetSplit : (List(NewSparseMultivariatePolynomial(R,OrderedVariableList(ls))),Boolean) -> List(SquareFreeRegularTriangularSet(R,IndexedExponents(OrderedVariableList(ls)),OrderedVariableList(ls),NewSparseMultivariatePolynomial(R,OrderedVariableList(ls)))) +--R +--E 23 + )spool )lisp (bye) \end{chunk} @@ -66199,6 +69042,18 @@ LexTriangularPackage(R,ls): Exports == Implementation where --S 1 of 1 )show LinearDependence +--R +--R LinearDependence(S: IntegralDomain,R: LinearlyExplicitRingOver(S)) is a package constructor +--R Abbreviation for LinearDependence is LINDEP +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for LINDEP +--R +--R------------------------------- Operations -------------------------------- +--R linearDependence : Vector(R) -> Union(Vector(S),"failed") +--R linearlyDependent? : Vector(R) -> Boolean +--R solveLinear : (Vector(R),R) -> Union(Vector(S),"failed") if S has FIELD +--R solveLinear : (Vector(R),R) -> Union(Vector(Fraction(S)),"failed") if not(has(S,Field)) +--R --E 1 )spool @@ -66317,6 +69172,17 @@ LinearDependence(S, R): Exports == Implementation where --S 1 of 1 )show LinearOrdinaryDifferentialOperatorFactorizer +--R +--R LinearOrdinaryDifferentialOperatorFactorizer(F: Join(Field,CharacteristicZero,RetractableTo(Integer),RetractableTo(Fraction(Integer))),UP: UnivariatePolynomialCategory(F)) is a package constructor +--R Abbreviation for LinearOrdinaryDifferentialOperatorFactorizer is LODOF +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for LODOF +--R +--R------------------------------- Operations -------------------------------- +--R factor : (LinearOrdinaryDifferentialOperator1(Fraction(UP)),(UP -> List(F))) -> List(LinearOrdinaryDifferentialOperator1(Fraction(UP))) +--R factor : LinearOrdinaryDifferentialOperator1(Fraction(UP)) -> List(LinearOrdinaryDifferentialOperator1(Fraction(UP))) if F has ACF +--R factor1 : LinearOrdinaryDifferentialOperator1(Fraction(UP)) -> List(LinearOrdinaryDifferentialOperator1(Fraction(UP))) if F has ACF +--R --E 1 )spool @@ -66486,6 +69352,17 @@ LinearOrdinaryDifferentialOperatorFactorizer(F, UP): Exports == Impl where --S 1 of 1 )show LinearOrdinaryDifferentialOperatorsOps +--R +--R LinearOrdinaryDifferentialOperatorsOps(A: Field,L: LinearOrdinaryDifferentialOperatorCategory(A)) is a package constructor +--R Abbreviation for LinearOrdinaryDifferentialOperatorsOps is LODOOPS +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for LODOOPS +--R +--R------------------------------- Operations -------------------------------- +--R directSum : (L,L,(A -> A)) -> L +--R symmetricPower : (L,NonNegativeInteger,(A -> A)) -> L +--R symmetricProduct : (L,L,(A -> A)) -> L +--R --E 1 )spool @@ -66635,6 +69512,15 @@ LinearOrdinaryDifferentialOperatorsOps(A, L): Exports == Implementation where --S 1 of 1 )show LinearPolynomialEquationByFractions +--R +--R LinearPolynomialEquationByFractions(R: PolynomialFactorizationExplicit) is a package constructor +--R Abbreviation for LinearPolynomialEquationByFractions is LPEFRAC +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for LPEFRAC +--R +--R------------------------------- Operations -------------------------------- +--R solveLinearPolynomialEquationByFractions : (List(SparseUnivariatePolynomial(R)),SparseUnivariatePolynomial(R)) -> Union(List(SparseUnivariatePolynomial(R)),"failed") +--R --E 1 )spool @@ -66846,6 +69732,22 @@ LinearSystemFromPowerSeriesPackage(K,PCS):P==T where --S 1 of 1 )show LinearSystemMatrixPackage +--R +--R LinearSystemMatrixPackage(F: Field,Row,Col,M: MatrixCategory(F,Row,Col))where +--R Row: FiniteLinearAggregate(F)with +--R shallowlyMutable +--R Col: FiniteLinearAggregate(F)with +--R shallowlyMutable is a package constructor +--R Abbreviation for LinearSystemMatrixPackage is LSMP +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for LSMP +--R +--R------------------------------- Operations -------------------------------- +--R hasSolution? : (M,Col) -> Boolean rank : (M,Col) -> NonNegativeInteger +--R particularSolution : (M,Col) -> Union(Col,"failed") +--R solve : (M,Col) -> Record(particular: Union(Col,"failed"),basis: List(Col)) +--R solve : (M,List(Col)) -> List(Record(particular: Union(Col,"failed"),basis: List(Col))) +--R --E 1 )spool @@ -66978,6 +69880,21 @@ LinearSystemMatrixPackage(F, Row, Col, M): Cat == Capsule where --S 1 of 1 )show LinearSystemMatrixPackage1 +--R +--R LinearSystemMatrixPackage1(F: Field) is a package constructor +--R Abbreviation for LinearSystemMatrixPackage1 is LSMP1 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for LSMP1 +--R +--R------------------------------- Operations -------------------------------- +--R hasSolution? : (Matrix(F),Vector(F)) -> Boolean +--R particularSolution : (Matrix(F),Vector(F)) -> Union(Vector(F),"failed") +--R rank : (Matrix(F),Vector(F)) -> NonNegativeInteger +--R solve : (Matrix(F),Vector(F)) -> Record(particular: Union(Vector(F),"failed"),basis: List(Vector(F))) +--R solve : (List(List(F)),Vector(F)) -> Record(particular: Union(Vector(F),"failed"),basis: List(Vector(F))) +--R solve : (Matrix(F),List(Vector(F))) -> List(Record(particular: Union(Vector(F),"failed"),basis: List(Vector(F)))) +--R solve : (List(List(F)),List(Vector(F))) -> List(Record(particular: Union(Vector(F),"failed"),basis: List(Vector(F)))) +--R --E 1 )spool @@ -67085,6 +70002,15 @@ LinearSystemMatrixPackage1(F): Cat == Capsule where --S 1 of 1 )show LinearSystemPolynomialPackage +--R +--R LinearSystemPolynomialPackage(R: IntegralDomain,E: OrderedAbelianMonoidSup,OV: OrderedSet,P: PolynomialCategory(R,E,OV)) is a package constructor +--R Abbreviation for LinearSystemPolynomialPackage is LSPP +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for LSPP +--R +--R------------------------------- Operations -------------------------------- +--R linSolve : (List(P),List(OV)) -> Record(particular: Union(Vector(Fraction(P)),"failed"),basis: List(Vector(Fraction(P)))) +--R --E 1 )spool @@ -67184,6 +70110,25 @@ LinearSystemPolynomialPackage(R, E, OV, P): Cat == Capsule where --S 1 of 1 )show LinGroebnerPackage +--R +--R LinGroebnerPackage(lv: List(Symbol),F: GcdDomain) is a package constructor +--R Abbreviation for LinGroebnerPackage is LGROBP +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for LGROBP +--R +--R------------------------------- Operations -------------------------------- +--R anticoord : (List(F),DistributedMultivariatePolynomial(lv,F),List(DistributedMultivariatePolynomial(lv,F))) -> DistributedMultivariatePolynomial(lv,F) +--R choosemon : (DistributedMultivariatePolynomial(lv,F),List(DistributedMultivariatePolynomial(lv,F))) -> DistributedMultivariatePolynomial(lv,F) +--R computeBasis : List(HomogeneousDistributedMultivariatePolynomial(lv,F)) -> List(HomogeneousDistributedMultivariatePolynomial(lv,F)) +--R coord : (HomogeneousDistributedMultivariatePolynomial(lv,F),List(HomogeneousDistributedMultivariatePolynomial(lv,F))) -> Vector(F) +--R groebgen : List(DistributedMultivariatePolynomial(lv,F)) -> Record(glbase: List(DistributedMultivariatePolynomial(lv,F)),glval: List(Integer)) +--R intcompBasis : (OrderedVariableList(lv),List(HomogeneousDistributedMultivariatePolynomial(lv,F)),List(HomogeneousDistributedMultivariatePolynomial(lv,F))) -> List(HomogeneousDistributedMultivariatePolynomial(lv,F)) +--R linGenPos : List(HomogeneousDistributedMultivariatePolynomial(lv,F)) -> Record(gblist: List(DistributedMultivariatePolynomial(lv,F)),gvlist: List(Integer)) +--R minPol : (List(HomogeneousDistributedMultivariatePolynomial(lv,F)),List(HomogeneousDistributedMultivariatePolynomial(lv,F)),OrderedVariableList(lv)) -> HomogeneousDistributedMultivariatePolynomial(lv,F) +--R minPol : (List(HomogeneousDistributedMultivariatePolynomial(lv,F)),OrderedVariableList(lv)) -> HomogeneousDistributedMultivariatePolynomial(lv,F) +--R totolex : List(HomogeneousDistributedMultivariatePolynomial(lv,F)) -> List(DistributedMultivariatePolynomial(lv,F)) +--R transform : DistributedMultivariatePolynomial(lv,F) -> HomogeneousDistributedMultivariatePolynomial(lv,F) +--R --E 1 )spool @@ -67705,6 +70650,21 @@ LinesOpPack(K):P==T where --S 1 of 1 )show LiouvillianFunction +--R +--R LiouvillianFunction(R: Join(OrderedSet,IntegralDomain),F: Join(FunctionSpace(R),RadicalCategory,TranscendentalFunctionCategory)) is a package constructor +--R Abbreviation for LiouvillianFunction is LF +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for LF +--R +--R------------------------------- Operations -------------------------------- +--R Ci : F -> F Ei : F -> F +--R Si : F -> F belong? : BasicOperator -> Boolean +--R dilog : F -> F erf : F -> F +--R fresnelC : F -> F fresnelS : F -> F +--R integral : (F,Symbol) -> F li : F -> F +--R integral : (F,SegmentBinding(F)) -> F +--R operator : BasicOperator -> BasicOperator +--R --E 1 )spool @@ -67960,6 +70920,17 @@ LiouvillianFunction(R, F): Exports == Implementation where --S 1 of 1 )show ListFunctions2 +--R +--R ListFunctions2(A: Type,B: Type) is a package constructor +--R Abbreviation for ListFunctions2 is LIST2 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for LIST2 +--R +--R------------------------------- Operations -------------------------------- +--R map : ((A -> B),List(A)) -> List(B) +--R reduce : (((A,B) -> B),List(A),B) -> B +--R scan : (((A,B) -> B),List(A),B) -> List(B) +--R --E 1 )spool @@ -68045,6 +71016,15 @@ ListFunctions2(A:Type, B:Type): public == private where --S 1 of 1 )show ListFunctions3 +--R +--R ListFunctions3(A: Type,B: Type,C: Type) is a package constructor +--R Abbreviation for ListFunctions3 is LIST3 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for LIST3 +--R +--R------------------------------- Operations -------------------------------- +--R map : (((A,B) -> C),List(A),List(B)) -> List(C) +--R --E 1 )spool @@ -68114,6 +71094,19 @@ ListFunctions3(A:Type, B:Type, C:Type): public == private where --S 1 of 1 )show ListToMap +--R +--R ListToMap(A: SetCategory,B: Type) is a package constructor +--R Abbreviation for ListToMap is LIST2MAP +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for LIST2MAP +--R +--R------------------------------- Operations -------------------------------- +--R match : (List(A),List(B),A) -> B match : (List(A),List(B),A,B) -> B +--R match : (List(A),List(B)) -> (A -> B) +--R match : (List(A),List(B),B) -> (A -> B) +--R match : (List(A),List(B),(A -> B)) -> (A -> B) +--R match : (List(A),List(B),A,(A -> B)) -> B +--R --E 1 )spool @@ -68550,6 +71543,16 @@ LocalParametrizationOfSimplePointPackage(K,symb,PolyRing,E,ProjPt,PCS,Plc):_ --S 1 of 1 )show MakeBinaryCompiledFunction +--R +--R MakeBinaryCompiledFunction(S: ConvertibleTo(InputForm),D1: Type,D2: Type,I: Type) is a package constructor +--R Abbreviation for MakeBinaryCompiledFunction is MKBCFUNC +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for MKBCFUNC +--R +--R------------------------------- Operations -------------------------------- +--R binaryFunction : Symbol -> ((D1,D2) -> I) +--R compiledFunction : (S,Symbol,Symbol) -> ((D1,D2) -> I) +--R --E 1 )spool @@ -68634,6 +71637,16 @@ MakeBinaryCompiledFunction(S, D1, D2, I):Exports == Implementation where --S 1 of 1 )show MakeFloatCompiledFunction +--R +--R MakeFloatCompiledFunction(S: ConvertibleTo(InputForm)) is a package constructor +--R Abbreviation for MakeFloatCompiledFunction is MKFLCFN +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for MKFLCFN +--R +--R------------------------------- Operations -------------------------------- +--R makeFloatFunction : (S,Symbol) -> (DoubleFloat -> DoubleFloat) +--R makeFloatFunction : (S,Symbol,Symbol) -> ((DoubleFloat,DoubleFloat) -> DoubleFloat) +--R --E 1 )spool @@ -68799,7 +71812,8 @@ MakeFloatCompiledFunction(S): Exports == Implementation where )set message test on )set message auto off )clear all ---S 1 of 9 + +--S 1 of 10 expr := (x - exp x + 1)^2 * (sin(x^2) * x + 1)^3 --R --R @@ -68818,7 +71832,7 @@ expr := (x - exp x + 1)^2 * (sin(x^2) * x + 1)^3 --R Type: Expression(Integer) --E 1 ---S 2 of 9 +--S 2 of 10 function(expr, f, x) --R --R @@ -68826,7 +71840,7 @@ function(expr, f, x) --R Type: Symbol --E 2 ---S 3 of 9 +--S 3 of 10 tbl := [f(0.1 * i - 1) for i in 0..20] --R --R Compiling function f with type Float -> Float @@ -68845,7 +71859,7 @@ tbl := [f(0.1 * i - 1) for i in 0..20] --R Type: List(Float) --E 3 ---S 4 of 9 +--S 4 of 10 e := (x - y + 1)^2 * (x^2 * y + 1)^2 --R --R @@ -68858,7 +71872,7 @@ e := (x - y + 1)^2 * (x^2 * y + 1)^2 --R Type: Polynomial(Integer) --E 4 ---S 5 of 9 +--S 5 of 10 function(e, g, [x, y]) --R --R @@ -68866,7 +71880,7 @@ function(e, g, [x, y]) --R Type: Symbol --E 5 ---S 6 of 9 +--S 6 of 10 function(e, h, x, y) --R --R @@ -68874,7 +71888,7 @@ function(e, h, x, y) --R Type: Symbol --E 6 ---S 7 of 9 +--S 7 of 10 m1 := squareMatrix [ [1, 2], [3, 4] ] --R --R @@ -68884,7 +71898,7 @@ m1 := squareMatrix [ [1, 2], [3, 4] ] --R Type: SquareMatrix(2,Integer) --E 7 ---S 8 of 9 +--S 8 of 10 m2 := squareMatrix [ [1, 0], [-1, 1] ] --R --R @@ -68894,7 +71908,7 @@ m2 := squareMatrix [ [1, 0], [-1, 1] ] --R Type: SquareMatrix(2,Integer) --E 8 ---S 9 of 9 +--S 9 of 10 h(m1, m2) --R --R Compiling function h with type (SquareMatrix(2,Integer),SquareMatrix @@ -68905,6 +71919,23 @@ h(m1, m2) --R +- 17132 19588+ --R Type: SquareMatrix(2,Integer) --E 9 + +--S 10 of 10 +)show MakeFunction +--R +--R MakeFunction(S: ConvertibleTo(InputForm)) is a package constructor +--R Abbreviation for MakeFunction is MKFUNC +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for MKFUNC +--R +--R------------------------------- Operations -------------------------------- +--R function : (S,Symbol) -> Symbol +--R function : (S,Symbol,Symbol) -> Symbol +--R function : (S,Symbol,Symbol,Symbol) -> Symbol +--R function : (S,Symbol,List(Symbol)) -> Symbol +--R +--E 10 + )spool )lisp (bye) \end{chunk} @@ -69059,6 +72090,15 @@ MakeFunction(S:ConvertibleTo InputForm): Exports == Implementation where --S 1 of 1 )show MakeRecord +--R +--R MakeRecord(S: Type,T$: Type) is a package constructor +--R Abbreviation for MakeRecord is MKRECORD +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for MKRECORD +--R +--R------------------------------- Operations -------------------------------- +--R makeRecord : (S,T$) -> Record(part1: S,part2: T$) +--R --E 1 )spool @@ -69119,6 +72159,16 @@ MakeRecord(S: Type, T: Type): public == private where --S 1 of 1 )show MakeUnaryCompiledFunction +--R +--R MakeUnaryCompiledFunction(S: ConvertibleTo(InputForm),D: Type,I: Type) is a package constructor +--R Abbreviation for MakeUnaryCompiledFunction is MKUCFUNC +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for MKUCFUNC +--R +--R------------------------------- Operations -------------------------------- +--R unaryFunction : Symbol -> (D -> I) +--R compiledFunction : (S,Symbol) -> (D -> I) +--R --E 1 )spool @@ -69204,6 +72254,16 @@ MakeUnaryCompiledFunction(S, D, I): Exports == Implementation where --S 1 of 1 )show MappingPackageInternalHacks1 +--R +--R MappingPackageInternalHacks1(A: SetCategory) is a package constructor +--R Abbreviation for MappingPackageInternalHacks1 is MAPHACK1 +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for MAPHACK1 +--R +--R------------------------------- Operations -------------------------------- +--R iter : ((A -> A),NonNegativeInteger,A) -> A +--R recur : (((NonNegativeInteger,A) -> A),NonNegativeInteger,A) -> A +--R --E 1 )spool @@ -69275,6 +72335,15 @@ MappingPackageInternalHacks1(A: SetCategory): MPcat == MPdef where --S 1 of 1 )show MappingPackageInternalHacks2 +--R +--R MappingPackageInternalHacks2(A: SetCategory,C: SetCategory) is a package constructor +--R Abbreviation for MappingPackageInternalHacks2 is MAPHACK2 +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for MAPHACK2 +--R +--R------------------------------- Operations -------------------------------- +--R arg1 : (A,C) -> A arg2 : (A,C) -> C +--R --E 1 )spool @@ -69340,6 +72409,15 @@ MappingPackageInternalHacks2(A: SetCategory, C: SetCategory):_ --S 1 of 1 )show MappingPackageInternalHacks3 +--R +--R MappingPackageInternalHacks3(A: SetCategory,B: SetCategory,C: SetCategory) is a package constructor +--R Abbreviation for MappingPackageInternalHacks3 is MAPHACK3 +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for MAPHACK3 +--R +--R------------------------------- Operations -------------------------------- +--R comp : ((B -> C),(A -> B),A) -> C +--R --E 1 )spool @@ -69396,7 +72474,7 @@ MappingPackageInternalHacks3(A: SetCategory, B: SetCategory, C: SetCategory):_ )set message auto off )clear all ---S 1 of 26 +--S 1 of 27 power(q: FRAC INT, n: INT): FRAC INT == q**n --R --R Function declaration power : (Fraction(Integer),Integer) -> Fraction @@ -69404,7 +72482,7 @@ power(q: FRAC INT, n: INT): FRAC INT == q**n --R Type: Void --E 1 ---S 2 of 26 +--S 2 of 27 power(2,3) --R --R Compiling function power with type (Fraction(Integer),Integer) -> @@ -69414,7 +72492,7 @@ power(2,3) --R Type: Fraction(Integer) --E 2 ---S 3 of 26 +--S 3 of 27 rewop := twist power --R --R @@ -69422,7 +72500,7 @@ rewop := twist power --R Type: ((Integer,Fraction(Integer)) -> Fraction(Integer)) --E 3 ---S 4 of 26 +--S 4 of 27 rewop(3, 2) --R --R @@ -69430,13 +72508,13 @@ rewop(3, 2) --R Type: Fraction(Integer) --E 4 ---S 5 of 26 +--S 5 of 27 square: FRAC INT -> FRAC INT --R --R Type: Void --E 5 ---S 6 of 26 +--S 6 of 27 square:= curryRight(power, 2) --R --R @@ -69444,7 +72522,7 @@ square:= curryRight(power, 2) --R Type: (Fraction(Integer) -> Fraction(Integer)) --E 6 ---S 7 of 26 +--S 7 of 27 square 4 --R --R @@ -69452,7 +72530,7 @@ square 4 --R Type: Fraction(Integer) --E 7 ---S 8 of 26 +--S 8 of 27 squirrel:= constantRight(square)$MAPPKG3(FRAC INT,FRAC INT,FRAC INT) --R --R @@ -69460,7 +72538,7 @@ squirrel:= constantRight(square)$MAPPKG3(FRAC INT,FRAC INT,FRAC INT) --R Type: ((Fraction(Integer),Fraction(Integer)) -> Fraction(Integer)) --E 8 ---S 9 of 26 +--S 9 of 27 squirrel(1/2, 1/3) --R --R @@ -69470,7 +72548,7 @@ squirrel(1/2, 1/3) --R Type: Fraction(Integer) --E 9 ---S 10 of 26 +--S 10 of 27 sixteen := curry(square, 4/1) --R --R @@ -69478,7 +72556,7 @@ sixteen := curry(square, 4/1) --R Type: (() -> Fraction(Integer)) --E 10 ---S 11 of 26 +--S 11 of 27 sixteen() --R --R @@ -69486,7 +72564,7 @@ sixteen() --R Type: Fraction(Integer) --E 11 ---S 12 of 26 +--S 12 of 27 square2:=square*square --R --R @@ -69494,7 +72572,7 @@ square2:=square*square --R Type: (Fraction(Integer) -> Fraction(Integer)) --E 12 ---S 13 of 26 +--S 13 of 27 square2 3 --R --R @@ -69502,7 +72580,7 @@ square2 3 --R Type: Fraction(Integer) --E 13 ---S 14 of 26 +--S 14 of 27 sc(x: FRAC INT): FRAC INT == x + 1 --R --R Function declaration sc : Fraction(Integer) -> Fraction(Integer) has @@ -69510,7 +72588,7 @@ sc(x: FRAC INT): FRAC INT == x + 1 --R Type: Void --E 14 ---S 15 of 26 +--S 15 of 27 incfns := [sc**i for i in 0..10] --R --R Compiling function sc with type Fraction(Integer) -> Fraction( @@ -69526,7 +72604,7 @@ incfns := [sc**i for i in 0..10] --R Type: List((Fraction(Integer) -> Fraction(Integer))) --E 15 ---S 16 of 26 +--S 16 of 27 [f 4 for f in incfns] --R --R @@ -69534,7 +72612,7 @@ incfns := [sc**i for i in 0..10] --R Type: List(Fraction(Integer)) --E 16 ---S 17 of 26 +--S 17 of 27 times(n:NNI, i:INT):INT == n*i --R --R Function declaration times : (NonNegativeInteger,Integer) -> Integer @@ -69542,7 +72620,7 @@ times(n:NNI, i:INT):INT == n*i --R Type: Void --E 17 ---S 18 of 26 +--S 18 of 27 r := recur(times) --R --R Compiling function times with type (NonNegativeInteger,Integer) -> @@ -69552,7 +72630,7 @@ r := recur(times) --R Type: ((NonNegativeInteger,Integer) -> Integer) --E 18 ---S 19 of 26 +--S 19 of 27 fact := curryRight(r, 1) --R --R @@ -69560,7 +72638,7 @@ fact := curryRight(r, 1) --R Type: (NonNegativeInteger -> Integer) --E 19 ---S 20 of 26 +--S 20 of 27 fact 4 --R --R @@ -69568,7 +72646,7 @@ fact 4 --R Type: PositiveInteger --E 20 ---S 21 of 26 +--S 21 of 27 mto2ton(m, n) == raiser := square^n raiser m @@ -69576,7 +72654,7 @@ mto2ton(m, n) == --R Type: Void --E 21 ---S 22 of 26 +--S 22 of 27 mto2ton(3, 3) --R --R Compiling function mto2ton with type (PositiveInteger, @@ -69586,7 +72664,7 @@ mto2ton(3, 3) --R Type: Fraction(Integer) --E 22 ---S 23 of 26 +--S 23 of 27 shiftfib(r: List INT) : INT == t := r.1 r.1 := r.2 @@ -69598,7 +72676,7 @@ shiftfib(r: List INT) : INT == --R Type: Void --E 23 ---S 24 of 26 +--S 24 of 27 fibinit: List INT := [0, 1] --R --R @@ -69606,7 +72684,7 @@ fibinit: List INT := [0, 1] --R Type: List(Integer) --E 24 ---S 25 of 26 +--S 25 of 27 fibs := curry(shiftfib, fibinit) --R --R Compiling function shiftfib with type List(Integer) -> Integer @@ -69615,7 +72693,7 @@ fibs := curry(shiftfib, fibinit) --R Type: (() -> Integer) --E 25 ---S 26 of 26 +--S 26 of 27 [fibs() for i in 0..30] --R --R @@ -69625,6 +72703,23 @@ fibs := curry(shiftfib, fibinit) --R 317811, 514229, 832040] --R Type: List(Integer) --E 26 + +--S 27 of 27 +)show MappingPackage1 +--R +--R MappingPackage1(A: SetCategory) is a package constructor +--R Abbreviation for MappingPackage1 is MAPPKG1 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for MAPPKG1 +--R +--R------------------------------- Operations -------------------------------- +--R coerce : A -> (() -> A) fixedPoint : (A -> A) -> A +--R id : A -> A nullary : A -> (() -> A) +--R ?**? : ((A -> A),NonNegativeInteger) -> (A -> A) +--R fixedPoint : ((List(A) -> List(A)),Integer) -> List(A) +--R recur : ((NonNegativeInteger,A) -> A) -> ((NonNegativeInteger,A) -> A) +--R +--E 27 )spool )lisp (bye) @@ -69632,7 +72727,7 @@ fibs := curry(shiftfib, fibinit) \end{chunk} \begin{chunk}{MappingPackage1.help} ==================================================================== -MappingPackage examples +MappingPackage1 examples ==================================================================== Various Currying operations. @@ -69909,7 +73004,8 @@ MappingPackage1(A:SetCategory): MPcat == MPdef where )set message test on )set message auto off )clear all ---S 1 of 26 + +--S 1 of 27 power(q: FRAC INT, n: INT): FRAC INT == q**n --R --R Function declaration power : (Fraction(Integer),Integer) -> Fraction @@ -69917,7 +73013,7 @@ power(q: FRAC INT, n: INT): FRAC INT == q**n --R Type: Void --E 1 ---S 2 of 26 +--S 2 of 27 power(2,3) --R --R Compiling function power with type (Fraction(Integer),Integer) -> @@ -69927,7 +73023,7 @@ power(2,3) --R Type: Fraction(Integer) --E 2 ---S 3 of 26 +--S 3 of 27 rewop := twist power --R --R @@ -69935,7 +73031,7 @@ rewop := twist power --R Type: ((Integer,Fraction(Integer)) -> Fraction(Integer)) --E 3 ---S 4 of 26 +--S 4 of 27 rewop(3, 2) --R --R @@ -69943,13 +73039,13 @@ rewop(3, 2) --R Type: Fraction(Integer) --E 4 ---S 5 of 26 +--S 5 of 27 square: FRAC INT -> FRAC INT --R --R Type: Void --E 5 ---S 6 of 26 +--S 6 of 27 square:= curryRight(power, 2) --R --R @@ -69957,7 +73053,7 @@ square:= curryRight(power, 2) --R Type: (Fraction(Integer) -> Fraction(Integer)) --E 6 ---S 7 of 26 +--S 7 of 27 square 4 --R --R @@ -69965,7 +73061,7 @@ square 4 --R Type: Fraction(Integer) --E 7 ---S 8 of 26 +--S 8 of 27 squirrel:= constantRight(square)$MAPPKG3(FRAC INT,FRAC INT,FRAC INT) --R --R @@ -69973,7 +73069,7 @@ squirrel:= constantRight(square)$MAPPKG3(FRAC INT,FRAC INT,FRAC INT) --R Type: ((Fraction(Integer),Fraction(Integer)) -> Fraction(Integer)) --E 8 ---S 9 of 26 +--S 9 of 27 squirrel(1/2, 1/3) --R --R @@ -69983,7 +73079,7 @@ squirrel(1/2, 1/3) --R Type: Fraction(Integer) --E 9 ---S 10 of 26 +--S 10 of 27 sixteen := curry(square, 4/1) --R --R @@ -69991,7 +73087,7 @@ sixteen := curry(square, 4/1) --R Type: (() -> Fraction(Integer)) --E 10 ---S 11 of 26 +--S 11 of 27 sixteen() --R --R @@ -69999,7 +73095,7 @@ sixteen() --R Type: Fraction(Integer) --E 11 ---S 12 of 26 +--S 12 of 27 square2:=square*square --R --R @@ -70007,7 +73103,7 @@ square2:=square*square --R Type: (Fraction(Integer) -> Fraction(Integer)) --E 12 ---S 13 of 26 +--S 13 of 27 square2 3 --R --R @@ -70015,7 +73111,7 @@ square2 3 --R Type: Fraction(Integer) --E 13 ---S 14 of 26 +--S 14 of 27 sc(x: FRAC INT): FRAC INT == x + 1 --R --R Function declaration sc : Fraction(Integer) -> Fraction(Integer) has @@ -70023,7 +73119,7 @@ sc(x: FRAC INT): FRAC INT == x + 1 --R Type: Void --E 14 ---S 15 of 26 +--S 15 of 27 incfns := [sc**i for i in 0..10] --R --R Compiling function sc with type Fraction(Integer) -> Fraction( @@ -70039,7 +73135,7 @@ incfns := [sc**i for i in 0..10] --R Type: List((Fraction(Integer) -> Fraction(Integer))) --E 15 ---S 16 of 26 +--S 16 of 27 [f 4 for f in incfns] --R --R @@ -70047,7 +73143,7 @@ incfns := [sc**i for i in 0..10] --R Type: List(Fraction(Integer)) --E 16 ---S 17 of 26 +--S 17 of 27 times(n:NNI, i:INT):INT == n*i --R --R Function declaration times : (NonNegativeInteger,Integer) -> Integer @@ -70055,7 +73151,7 @@ times(n:NNI, i:INT):INT == n*i --R Type: Void --E 17 ---S 18 of 26 +--S 18 of 27 r := recur(times) --R --R Compiling function times with type (NonNegativeInteger,Integer) -> @@ -70065,7 +73161,7 @@ r := recur(times) --R Type: ((NonNegativeInteger,Integer) -> Integer) --E 18 ---S 19 of 26 +--S 19 of 27 fact := curryRight(r, 1) --R --R @@ -70073,7 +73169,7 @@ fact := curryRight(r, 1) --R Type: (NonNegativeInteger -> Integer) --E 19 ---S 20 of 26 +--S 20 of 27 fact 4 --R --R @@ -70081,7 +73177,7 @@ fact 4 --R Type: PositiveInteger --E 20 ---S 21 of 26 +--S 21 of 27 mto2ton(m, n) == raiser := square^n raiser m @@ -70089,7 +73185,7 @@ mto2ton(m, n) == --R Type: Void --E 21 ---S 22 of 26 +--S 22 of 27 mto2ton(3, 3) --R --R Compiling function mto2ton with type (PositiveInteger, @@ -70099,7 +73195,7 @@ mto2ton(3, 3) --R Type: Fraction(Integer) --E 22 ---S 23 of 26 +--S 23 of 27 shiftfib(r: List INT) : INT == t := r.1 r.1 := r.2 @@ -70111,7 +73207,7 @@ shiftfib(r: List INT) : INT == --R Type: Void --E 23 ---S 24 of 26 +--S 24 of 27 fibinit: List INT := [0, 1] --R --R @@ -70119,7 +73215,7 @@ fibinit: List INT := [0, 1] --R Type: List(Integer) --E 24 ---S 25 of 26 +--S 25 of 27 fibs := curry(shiftfib, fibinit) --R --R Compiling function shiftfib with type List(Integer) -> Integer @@ -70128,7 +73224,7 @@ fibs := curry(shiftfib, fibinit) --R Type: (() -> Integer) --E 25 ---S 26 of 26 +--S 26 of 27 [fibs() for i in 0..30] --R --R @@ -70138,12 +73234,27 @@ fibs := curry(shiftfib, fibinit) --R 317811, 514229, 832040] --R Type: List(Integer) --E 26 + +--S 27 of 27 +)show MappingPackage2 +--R +--R MappingPackage2(A: SetCategory,C: SetCategory) is a package constructor +--R Abbreviation for MappingPackage2 is MAPPKG2 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for MAPPKG2 +--R +--R------------------------------- Operations -------------------------------- +--R const : C -> (A -> C) constant : (() -> C) -> (A -> C) +--R curry : ((A -> C),A) -> (() -> C) diag : ((A,A) -> C) -> (A -> C) +--R +--E 27 + )spool )lisp (bye) \end{chunk} \begin{chunk}{MappingPackage2.help} ==================================================================== -MappingPackage examples +MappingPackage2 examples ==================================================================== Various Currying operations. @@ -70389,6 +73500,7 @@ MappingPackage2(A:SetCategory, C:SetCategory): MPcat == MPdef where )set message test on )set message auto off )clear all + --S 1 of 26 power(q: FRAC INT, n: INT): FRAC INT == q**n --R @@ -70618,12 +73730,31 @@ fibs := curry(shiftfib, fibinit) --R 317811, 514229, 832040] --R Type: List(Integer) --E 26 + +--S 27 of 27 +)show MappingPackage3 +--R +--R MappingPackage3(A: SetCategory,B: SetCategory,C: SetCategory) is a package constructor +--R Abbreviation for MappingPackage3 is MAPPKG3 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for MAPPKG3 +--R +--R------------------------------- Operations -------------------------------- +--R twist : ((A,B) -> C) -> ((B,A) -> C) +--R ?*? : ((B -> C),(A -> B)) -> (A -> C) +--R constantLeft : (B -> C) -> ((A,B) -> C) +--R constantRight : (A -> C) -> ((A,B) -> C) +--R curryLeft : (((A,B) -> C),A) -> (B -> C) +--R curryRight : (((A,B) -> C),B) -> (A -> C) +--R +--E 27 + )spool )lisp (bye) \end{chunk} \begin{chunk}{MappingPackage3.help} ==================================================================== -MappingPackage examples +MappingPackage3 examples ==================================================================== Various Currying operations. @@ -70893,7 +74024,7 @@ MappingPackage3(A:SetCategory, B:SetCategory, C:SetCategory):_ )set message auto off )clear all ---S 1 of 21 +--S 1 of 22 p:=(x:EXPR(INT)):EXPR(INT)+->3*x --R --R @@ -70901,7 +74032,7 @@ p:=(x:EXPR(INT)):EXPR(INT)+->3*x --R Type: (Expression Integer -> Expression Integer) --E 1 ---S 2 of 21 +--S 2 of 22 q:=(x:EXPR(INT)):EXPR(INT)+->2*x+3 --R --R @@ -70909,7 +74040,7 @@ q:=(x:EXPR(INT)):EXPR(INT)+->2*x+3 --R Type: (Expression Integer -> Expression Integer) --E 2 ---S 3 of 21 +--S 3 of 22 (p+q)(4)-(p(4)+q(4)) --R --R @@ -70917,7 +74048,7 @@ q:=(x:EXPR(INT)):EXPR(INT)+->2*x+3 --R Type: Expression Integer --E 3 ---S 4 of 21 +--S 4 of 22 (p+q)(x)-(p(x)+q(x)) --R --R @@ -70925,7 +74056,7 @@ q:=(x:EXPR(INT)):EXPR(INT)+->2*x+3 --R Type: Expression Integer --E 4 ---S 5 of 21 +--S 5 of 22 (p-q)(4)-(p(4)-q(4)) --R --R @@ -70933,7 +74064,7 @@ q:=(x:EXPR(INT)):EXPR(INT)+->2*x+3 --R Type: Expression Integer --E 5 ---S 6 of 21 +--S 6 of 22 (p-q)(x)-(p(x)-q(x)) --R --R @@ -70941,7 +74072,7 @@ q:=(x:EXPR(INT)):EXPR(INT)+->2*x+3 --R Type: Expression Integer --E 6 ---S 7 of 21 +--S 7 of 22 (p*q)(4)-(p(4)*q(4)) --R --R @@ -70949,7 +74080,7 @@ q:=(x:EXPR(INT)):EXPR(INT)+->2*x+3 --R Type: Expression Integer --E 7 ---S 8 of 21 +--S 8 of 22 (p*q)(x)-(p(x)*q(x)) --R --R @@ -70957,7 +74088,7 @@ q:=(x:EXPR(INT)):EXPR(INT)+->2*x+3 --R Type: Expression Integer --E 8 ---S 9 of 21 +--S 9 of 22 (p/q)(4)-(p(4)/q(4)) --R --R @@ -70965,7 +74096,7 @@ q:=(x:EXPR(INT)):EXPR(INT)+->2*x+3 --R Type: Expression Integer --E 9 ---S 10 of 21 +--S 10 of 22 (p/q)(x)-(p(x)/q(x)) --R --R @@ -70973,7 +74104,7 @@ q:=(x:EXPR(INT)):EXPR(INT)+->2*x+3 --R Type: Expression Integer --E 10 ---S 11 of 21 +--S 11 of 22 r:=(x:INT):INT+-> (x*x*x) --R --R @@ -70981,7 +74112,7 @@ r:=(x:INT):INT+-> (x*x*x) --R Type: (Integer -> Integer) --E 11 ---S 12 of 21 +--S 12 of 22 s:=(y:INT):INT+-> (y*y+3) --R --R @@ -70989,7 +74120,7 @@ s:=(y:INT):INT+-> (y*y+3) --R Type: (Integer -> Integer) --E 12 ---S 13 of 21 +--S 13 of 22 (r+s)(4)-(r(4)+s(4)) --R --R @@ -70997,7 +74128,7 @@ s:=(y:INT):INT+-> (y*y+3) --R Type: NonNegativeInteger --E 13 ---S 14 of 21 +--S 14 of 22 (r-s)(4)-(r(4)-s(4)) --R --R @@ -71005,7 +74136,7 @@ s:=(y:INT):INT+-> (y*y+3) --R Type: NonNegativeInteger --E 14 ---S 15 of 21 +--S 15 of 22 (r*s)(4)-(r(4)*s(4)) --R --R @@ -71013,7 +74144,7 @@ s:=(y:INT):INT+-> (y*y+3) --R Type: NonNegativeInteger --E 15 ---S 16 of 21 +--S 16 of 22 t:=(x:INT):EXPR(INT)+-> (x*x*x) --R --R @@ -71021,7 +74152,7 @@ t:=(x:INT):EXPR(INT)+-> (x*x*x) --R Type: (Integer -> Expression Integer) --E 16 ---S 17 of 21 +--S 17 of 22 u:=(y:INT):EXPR(INT)+-> (y*y+3) --R --R @@ -71029,7 +74160,7 @@ u:=(y:INT):EXPR(INT)+-> (y*y+3) --R Type: (Integer -> Expression Integer) --E 17 ---S 18 of 21 +--S 18 of 22 (t/u)(4)-(t(4)/u(4)) --R --R @@ -71037,27 +74168,43 @@ u:=(y:INT):EXPR(INT)+-> (y*y+3) --R Type: Expression Integer --E 18 ---S 19 of 21 +--S 19 of 22 h:=(x:EXPR(INT)):EXPR(INT)+->1 --R --R (19) theMap(Closure) --R Type: (Expression Integer -> Expression Integer) --E 19 ---S 20 of 21 +--S 20 of 22 (p/h)(x) --R --R (20) 3x --R Type: Expression Integer --E 20 ---S 21 of 21 +--S 21 of 22 (q/h)(x) --R --R (21) 2x + 3 --R Type: Expression Integer --E 21 +--S 22 of 22 +)show MappingPackage4 +--R +--R MappingPackage4(A: SetCategory,B: Ring) is a package constructor +--R Abbreviation for MappingPackage4 is MAPPKG4 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for MAPPKG4 +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : ((A -> B),(A -> B)) -> (A -> B) +--R ?+? : ((A -> B),(A -> B)) -> (A -> B) +--R ?-? : ((A -> B),(A -> B)) -> (A -> B) +--R ?/? : ((A -> Expression(Integer)),(A -> Expression(Integer))) -> (A -> Expression(Integer)) +--R +--E 22 + )spool )lisp (bye) @@ -71225,6 +74372,17 @@ MappingPackage4(A:SetCategory, B:Ring): --S 1 of 1 )show MatrixCategoryFunctions2 +--R +--R MatrixCategoryFunctions2(R1: Ring,Row1: FiniteLinearAggregate(R1),Col1: FiniteLinearAggregate(R1),M1: MatrixCategory(R1,Row1,Col1),R2: Ring,Row2: FiniteLinearAggregate(R2),Col2: FiniteLinearAggregate(R2),M2: MatrixCategory(R2,Row2,Col2)) is a package constructor +--R Abbreviation for MatrixCategoryFunctions2 is MATCAT2 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for MATCAT2 +--R +--R------------------------------- Operations -------------------------------- +--R map : ((R1 -> R2),M1) -> M2 +--R map : ((R1 -> Union(R2,"failed")),M1) -> Union(M2,"failed") +--R reduce : (((R1,R2) -> R2),M1,R2) -> R2 +--R --E 1 )spool @@ -71327,6 +74485,17 @@ MatrixCategoryFunctions2(R1,Row1,Col1,M1,R2,Row2,Col2,M2):_ --S 1 of 1 )show MatrixCommonDenominator +--R +--R MatrixCommonDenominator(R: IntegralDomain,Q: QuotientFieldCategory(R)) is a package constructor +--R Abbreviation for MatrixCommonDenominator is MCDEN +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for MCDEN +--R +--R------------------------------- Operations -------------------------------- +--R commonDenominator : Matrix(Q) -> R +--R clearDenominator : Matrix(Q) -> Matrix(R) +--R splitDenominator : Matrix(Q) -> Record(num: Matrix(R),den: R) +--R --E 1 )spool @@ -71419,6 +74588,26 @@ MatrixCommonDenominator(R, Q): Exports == Implementation where --S 1 of 1 )show MatrixLinearAlgebraFunctions +--R +--R MatrixLinearAlgebraFunctions(R: CommutativeRing,Row: FiniteLinearAggregate(R),Col: FiniteLinearAggregate(R),M: MatrixCategory(R,Row,Col)) is a package constructor +--R Abbreviation for MatrixLinearAlgebraFunctions is MATLIN +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for MATLIN +--R +--R------------------------------- Operations -------------------------------- +--R determinant : M -> R elRow1! : (M,Integer,Integer) -> M +--R elRow2! : (M,R,Integer,Integer) -> M minordet : M -> R +--R rowEchelon : M -> M if R has EUCDOM +--R adjoint : M -> Record(adjMat: M,detMat: R) if R has INTDOM +--R elColumn2! : (M,R,Integer,Integer) -> M +--R fractionFreeGauss! : M -> M if R has INTDOM +--R inverse : M -> Union(M,"failed") if R has FIELD +--R invertIfCan : M -> Union(M,"failed") if R has INTDOM +--R normalizedDivide : (R,R) -> Record(quotient: R,remainder: R) if R has EUCDOM +--R nullSpace : M -> List(Col) if R has INTDOM +--R nullity : M -> NonNegativeInteger if R has INTDOM +--R rank : M -> NonNegativeInteger if R has INTDOM +--R --E 1 )spool @@ -72260,10 +75449,9 @@ zero?(blockConcat(%) - E) --R --R------------------------------- Operations -------------------------------- --R aColumn : (M,PositiveInteger) -> M aRow : (M,PositiveInteger) -> M ---R blockConcat : List(List(M)) -> M diagonalMatrix : (M,Integer) -> M ---R diagonalMatrix : M -> M horizConcat : List(M) -> M ---R vertConcat : List(M) -> M ---R bandMatrix : (M,List(Integer)) -> M +--R bandMatrix : (M,List(Integer)) -> M blockConcat : List(List(M)) -> M +--R diagonalMatrix : (M,Integer) -> M diagonalMatrix : M -> M +--R horizConcat : List(M) -> M vertConcat : List(M) -> M --R bandMatrix : (M,Segment(Integer)) -> M --R blockSplit : (M,PositiveInteger,PositiveInteger) -> List(List(M)) --R blockSplit : (M,List(PositiveInteger),PositiveInteger) -> List(List(M)) @@ -74358,6 +77546,15 @@ MatrixManipulation(R, Row, Col, M) : Exports == Implementation where --S 1 of 1 )show MergeThing +--R +--R MergeThing(S: OrderedSet) is a package constructor +--R Abbreviation for MergeThing is MTHING +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for MTHING +--R +--R------------------------------- Operations -------------------------------- +--R mergeDifference : (List(S),List(S)) -> List(S) +--R --E 1 )spool @@ -74432,6 +77629,20 @@ MergeThing(S:OrderedSet): Exports == Implementation where --S 1 of 1 )show MeshCreationRoutinesForThreeDimensions +--R +--R MeshCreationRoutinesForThreeDimensions is a package constructor +--R Abbreviation for MeshCreationRoutinesForThreeDimensions is MESH +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for MESH +--R +--R------------------------------- Operations -------------------------------- +--R meshFun2Var : (((DoubleFloat,DoubleFloat) -> DoubleFloat),Union(((DoubleFloat,DoubleFloat,DoubleFloat) -> DoubleFloat),undefined),Segment(DoubleFloat),Segment(DoubleFloat),List(DrawOption)) -> ThreeSpace(DoubleFloat) +--R meshPar1Var : (Expression(Integer),Expression(Integer),Expression(Integer),(DoubleFloat -> DoubleFloat),Segment(DoubleFloat),List(DrawOption)) -> ThreeSpace(DoubleFloat) +--R meshPar2Var : (((DoubleFloat,DoubleFloat) -> DoubleFloat),((DoubleFloat,DoubleFloat) -> DoubleFloat),((DoubleFloat,DoubleFloat) -> DoubleFloat),Union(((DoubleFloat,DoubleFloat,DoubleFloat) -> DoubleFloat),undefined),Segment(DoubleFloat),Segment(DoubleFloat),List(DrawOption)) -> ThreeSpace(DoubleFloat) +--R meshPar2Var : (((DoubleFloat,DoubleFloat) -> Point(DoubleFloat)),Segment(DoubleFloat),Segment(DoubleFloat),List(DrawOption)) -> ThreeSpace(DoubleFloat) +--R meshPar2Var : (ThreeSpace(DoubleFloat),((DoubleFloat,DoubleFloat) -> Point(DoubleFloat)),Segment(DoubleFloat),Segment(DoubleFloat),List(DrawOption)) -> ThreeSpace(DoubleFloat) +--R ptFunc : (((DoubleFloat,DoubleFloat) -> DoubleFloat),((DoubleFloat,DoubleFloat) -> DoubleFloat),((DoubleFloat,DoubleFloat) -> DoubleFloat),((DoubleFloat,DoubleFloat,DoubleFloat) -> DoubleFloat)) -> ((DoubleFloat,DoubleFloat) -> Point(DoubleFloat)) +--R --E 1 )spool @@ -74612,6 +77823,18 @@ MeshCreationRoutinesForThreeDimensions():Exports == Implementation where --S 1 of 1 )show ModularDistinctDegreeFactorizer +--R +--R ModularDistinctDegreeFactorizer(U: UnivariatePolynomialCategory(Integer)) is a package constructor +--R Abbreviation for ModularDistinctDegreeFactorizer is MDDFACT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for MDDFACT +--R +--R------------------------------- Operations -------------------------------- +--R exptMod : (U,Integer,U,Integer) -> U factor : (U,Integer) -> List(U) +--R gcd : (U,U,Integer) -> U linears : (U,Integer) -> U +--R ddFact : (U,Integer) -> List(Record(factor: U,degree: Integer)) +--R separateFactors : (List(Record(factor: U,degree: Integer)),Integer) -> List(U) +--R --E 1 )spool @@ -74881,6 +78104,19 @@ ModularDistinctDegreeFactorizer(U):C == T where --S 1 of 1 )show ModularHermitianRowReduction +--R +--R ModularHermitianRowReduction(R: EuclideanDomain) is a package constructor +--R Abbreviation for ModularHermitianRowReduction is MHROWRED +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for MHROWRED +--R +--R------------------------------- Operations -------------------------------- +--R rowEch : Matrix(R) -> Matrix(R) +--R normalizedDivide : (R,R) -> Record(quotient: R,remainder: R) +--R rowEchLocal : (Matrix(R),R) -> Matrix(R) +--R rowEchelon : (Matrix(R),R) -> Matrix(R) +--R rowEchelonLocal : (Matrix(R),R,R) -> Matrix(R) +--R --E 1 )spool @@ -75169,6 +78405,15 @@ ModularHermitianRowReduction(R): Exports == Implementation where --S 1 of 1 )show MonoidRingFunctions2 +--R +--R MonoidRingFunctions2(R: Ring,S: Ring,M: Monoid) is a package constructor +--R Abbreviation for MonoidRingFunctions2 is MRF2 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for MRF2 +--R +--R------------------------------- Operations -------------------------------- +--R map : ((R -> S),MonoidRing(R,M)) -> MonoidRing(S,M) +--R --E 1 )spool @@ -75238,6 +78483,18 @@ MonoidRingFunctions2(R,S,M) : Exports == Implementation where --S 1 of 1 )show MonomialExtensionTools +--R +--R MonomialExtensionTools(F: Field,UP: UnivariatePolynomialCategory(F)) is a package constructor +--R Abbreviation for MonomialExtensionTools is MONOTOOL +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for MONOTOOL +--R +--R------------------------------- Operations -------------------------------- +--R decompose : (Fraction(UP),(UP -> UP)) -> Record(poly: UP,normal: Fraction(UP),special: Fraction(UP)) +--R normalDenom : (Fraction(UP),(UP -> UP)) -> UP +--R split : (UP,(UP -> UP)) -> Record(normal: UP,special: UP) +--R splitSquarefree : (UP,(UP -> UP)) -> Record(normal: Factored(UP),special: Factored(UP)) +--R --E 1 )spool @@ -75356,6 +78613,15 @@ MonomialExtensionTools(F, UP): Exports == Implementation where --S 1 of 1 )show MoreSystemCommands +--R +--R MoreSystemCommands is a package constructor +--R Abbreviation for MoreSystemCommands is MSYSCMD +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for MSYSCMD +--R +--R------------------------------- Operations -------------------------------- +--R systemCommand : String -> Void +--R --E 1 )spool @@ -75422,6 +78688,18 @@ MoreSystemCommands: public == private where --S 1 of 1 )show MPolyCatPolyFactorizer +--R +--R MPolyCatPolyFactorizer(E: OrderedAbelianMonoidSup,OV,R: EuclideanDomain,PPR: PolynomialCategory(Polynomial(R),E,OV))where +--R OV: OrderedSetwith +--R convert : % -> Symbol +--R variable : Symbol -> Union(%,"failed") is a package constructor +--R Abbreviation for MPolyCatPolyFactorizer is MPCPF +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for MPCPF +--R +--R------------------------------- Operations -------------------------------- +--R factor : PPR -> Factored(PPR) +--R --E 1 )spool @@ -75521,6 +78799,22 @@ MPolyCatPolyFactorizer(E,OV,R,PPR) : C == T --S 1 of 1 )show MPolyCatRationalFunctionFactorizer +--R +--R MPolyCatRationalFunctionFactorizer(E: OrderedAbelianMonoidSup,OV,R: IntegralDomain,PRF: PolynomialCategory(Fraction(Polynomial(R)),E,OV))where +--R OV: OrderedSetwith +--R convert : % -> Symbol is a package constructor +--R Abbreviation for MPolyCatRationalFunctionFactorizer is MPRFF +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for MPRFF +--R +--R------------------------------- Operations -------------------------------- +--R factor : PRF -> Factored(PRF) pushdown : (PRF,OV) -> PRF +--R pushup : (PRF,OV) -> PRF +--R pushdterm : (SparseUnivariatePolynomial(PRF),OV) -> PRF +--R pushucoef : (SparseUnivariatePolynomial(Polynomial(R)),OV) -> PRF +--R pushuconst : (Fraction(Polynomial(R)),OV) -> PRF +--R totalfract : PRF -> Record(sup: Polynomial(R),inf: Polynomial(R)) +--R --E 1 )spool @@ -75712,6 +79006,15 @@ MPolyCatRationalFunctionFactorizer(E,OV,R,PRF) : C == T --S 1 of 1 )show MPolyCatFunctions2 +--R +--R MPolyCatFunctions2(VarSet: OrderedSet,E1: OrderedAbelianMonoidSup,E2: OrderedAbelianMonoidSup,R: Ring,S: Ring,PR: PolynomialCategory(R,E1,VarSet),PS: PolynomialCategory(S,E2,VarSet)) is a package constructor +--R Abbreviation for MPolyCatFunctions2 is MPC2 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for MPC2 +--R +--R------------------------------- Operations -------------------------------- +--R map : ((R -> S),PR) -> PS reshape : (List(S),PR) -> PS +--R --E 1 )spool @@ -75799,6 +79102,15 @@ MPolyCatFunctions2(VarSet,E1,E2,R,S,PR,PS) : public == private where --S 1 of 1 )show MPolyCatFunctions3 +--R +--R MPolyCatFunctions3(Vars1: OrderedSet,Vars2: OrderedSet,E1: OrderedAbelianMonoidSup,E2: OrderedAbelianMonoidSup,R: Ring,PR1: PolynomialCategory(R,E1,Vars1),PR2: PolynomialCategory(R,E2,Vars2)) is a package constructor +--R Abbreviation for MPolyCatFunctions3 is MPC3 +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for MPC3 +--R +--R------------------------------- Operations -------------------------------- +--R map : ((Vars1 -> Vars2),PR1) -> PR2 +--R --E 1 )spool @@ -75872,6 +79184,15 @@ MPolyCatFunctions3(Vars1,Vars2,E1,E2,R,PR1,PR2): C == T where --S 1 of 1 )show MRationalFactorize +--R +--R MRationalFactorize(E: OrderedAbelianMonoidSup,OV: OrderedSet,R: Join(EuclideanDomain,CharacteristicZero),P: PolynomialCategory(Fraction(R),E,OV)) is a package constructor +--R Abbreviation for MRationalFactorize is MRATFAC +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for MRATFAC +--R +--R------------------------------- Operations -------------------------------- +--R factor : P -> Factored(P) +--R --E 1 )spool @@ -75959,6 +79280,16 @@ MRationalFactorize(E,OV,R,P) : C == T --S 1 of 1 )show MultFiniteFactorize +--R +--R MultFiniteFactorize(OV: OrderedSet,E: OrderedAbelianMonoidSup,F: FiniteFieldCategory,PG: PolynomialCategory(F,E,OV)) is a package constructor +--R Abbreviation for MultFiniteFactorize is MFINFACT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for MFINFACT +--R +--R------------------------------- Operations -------------------------------- +--R factor : PG -> Factored(PG) +--R factor : SparseUnivariatePolynomial(PG) -> Factored(SparseUnivariatePolynomial(PG)) +--R --E 1 )spool @@ -76486,6 +79817,15 @@ MultFiniteFactorize(OV,E,F,PG) : C == T --S 1 of 1 )show MultipleMap +--R +--R MultipleMap(R1: IntegralDomain,UP1: UnivariatePolynomialCategory(R1),UPUP1: UnivariatePolynomialCategory(Fraction(UP1)),R2: IntegralDomain,UP2: UnivariatePolynomialCategory(R2),UPUP2: UnivariatePolynomialCategory(Fraction(UP2))) is a package constructor +--R Abbreviation for MultipleMap is MMAP +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for MMAP +--R +--R------------------------------- Operations -------------------------------- +--R map : ((R1 -> R2),UPUP1) -> UPUP2 +--R --E 1 )spool @@ -76561,6 +79901,21 @@ MultipleMap(R1,UP1,UPUP1,R2,UP2,UPUP2): Exports == Implementation where --S 1 of 1 )show MultiVariableCalculusFunctions +--R +--R MultiVariableCalculusFunctions(S: SetCategory,F: PartialDifferentialRing(S),FLAF: FiniteLinearAggregate(F),FLAS)where +--R FLAS: FiniteLinearAggregate(S)with +--R finiteAggregate is a package constructor +--R Abbreviation for MultiVariableCalculusFunctions is MCALCFN +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for MCALCFN +--R +--R------------------------------- Operations -------------------------------- +--R divergence : (FLAF,FLAS) -> F gradient : (F,FLAS) -> Vector(F) +--R hessian : (F,FLAS) -> Matrix(F) jacobian : (FLAF,FLAS) -> Matrix(F) +--R laplacian : (F,FLAS) -> F +--R bandedHessian : (F,FLAS,NonNegativeInteger) -> Matrix(F) +--R bandedJacobian : (FLAF,FLAS,NonNegativeInteger,NonNegativeInteger) -> Matrix(F) +--R --E 1 )spool @@ -76767,6 +80122,16 @@ MultiVariableCalculusFunctions(S,F,FLAF,FLAS) : Exports == Implementation where --S 1 of 1 )show MultivariateFactorize +--R +--R MultivariateFactorize(OV: OrderedSet,E: OrderedAbelianMonoidSup,R: Join(EuclideanDomain,CharacteristicZero),P: PolynomialCategory(R,E,OV)) is a package constructor +--R Abbreviation for MultivariateFactorize is MULTFACT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for MULTFACT +--R +--R------------------------------- Operations -------------------------------- +--R factor : P -> Factored(P) +--R factor : SparseUnivariatePolynomial(P) -> Factored(SparseUnivariatePolynomial(P)) +--R --E 1 )spool @@ -76857,6 +80222,17 @@ MultivariateFactorize(OV,E,R,P) : C == T --S 1 of 1 )show MultivariateLifting +--R +--R MultivariateLifting(E: OrderedAbelianMonoidSup,OV: OrderedSet,R: EuclideanDomain,P: PolynomialCategory(R,E,OV)) is a package constructor +--R Abbreviation for MultivariateLifting is MLIFT +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for MLIFT +--R +--R------------------------------- Operations -------------------------------- +--R corrPoly : (SparseUnivariatePolynomial(P),List(OV),List(R),List(NonNegativeInteger),List(SparseUnivariatePolynomial(P)),Vector(List(SparseUnivariatePolynomial(R))),R) -> Union(List(SparseUnivariatePolynomial(P)),"failed") +--R lifting : (SparseUnivariatePolynomial(P),List(OV),List(SparseUnivariatePolynomial(R)),List(R),List(P),List(NonNegativeInteger),R) -> Union(List(SparseUnivariatePolynomial(P)),"failed") +--R lifting1 : (SparseUnivariatePolynomial(P),List(OV),List(SparseUnivariatePolynomial(P)),List(R),List(P),List(List(Record(expt: NonNegativeInteger,pcoef: P))),List(NonNegativeInteger),Vector(List(SparseUnivariatePolynomial(R))),R) -> Union(List(SparseUnivariatePolynomial(P)),"failed") +--R --E 1 )spool @@ -77117,6 +80493,26 @@ MultivariateLifting(E,OV,R,P) : C == T --S 1 of 1 )show MultivariateSquareFree +--R +--R MultivariateSquareFree(E: OrderedAbelianMonoidSup,OV: OrderedSet,R: EuclideanDomain,P: PolynomialCategory(R,E,OV)) is a package constructor +--R Abbreviation for MultivariateSquareFree is MULTSQFR +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for MULTSQFR +--R +--R------------------------------- Operations -------------------------------- +--R squareFree : P -> Factored(P) squareFreePrim : P -> Factored(P) +--R univcase : (P,OV) -> Factored(P) +--R check : (List(Record(factor: SparseUnivariatePolynomial(R),exponent: Integer)),List(Record(factor: SparseUnivariatePolynomial(R),exponent: Integer))) -> Boolean +--R coefChoose : (Integer,Factored(P)) -> P +--R compdegd : List(Record(factor: SparseUnivariatePolynomial(R),exponent: Integer)) -> Integer +--R consnewpol : (SparseUnivariatePolynomial(P),SparseUnivariatePolynomial(R),Integer) -> Record(pol: SparseUnivariatePolynomial(P),polval: SparseUnivariatePolynomial(R)) +--R intChoose : (SparseUnivariatePolynomial(P),List(OV),List(List(R))) -> Record(upol: SparseUnivariatePolynomial(R),Lval: List(R),Lfact: List(Record(factor: SparseUnivariatePolynomial(R),exponent: Integer)),ctpol: R) +--R lift : (SparseUnivariatePolynomial(P),SparseUnivariatePolynomial(R),SparseUnivariatePolynomial(R),P,List(OV),List(NonNegativeInteger),List(R)) -> Union(List(SparseUnivariatePolynomial(P)),"failed") +--R myDegree : (SparseUnivariatePolynomial(P),List(OV),NonNegativeInteger) -> List(NonNegativeInteger) +--R normDeriv2 : (SparseUnivariatePolynomial(R),Integer) -> SparseUnivariatePolynomial(R) +--R nsqfree : (SparseUnivariatePolynomial(P),List(OV),List(List(R))) -> Record(unitPart: P,suPart: List(Record(factor: SparseUnivariatePolynomial(P),exponent: Integer))) +--R squareFree : SparseUnivariatePolynomial(P) -> Factored(SparseUnivariatePolynomial(P)) +--R --E 1 )spool @@ -92272,7 +95668,7 @@ NagFittingPackage(): Exports == Implementation where )set message auto off )clear all ---S 1 of 164 +--S 1 of 165 showArrayValues true --R --R @@ -92280,7 +95676,7 @@ showArrayValues true --R Type: Boolean --E 1 ---S 2 of 164 +--S 2 of 165 showScalarValues true --R --R @@ -92288,7 +95684,7 @@ showScalarValues true --R Type: Boolean --E 2 ---S 3 of 164 +--S 3 of 165 ia:=3 --R --R @@ -92296,7 +95692,7 @@ ia:=3 --R Type: PositiveInteger --E 3 ---S 4 of 164 +--S 4 of 165 b:Matrix Complex SF:= [[1 ,0 ,0 ]] --R --R @@ -92304,7 +95700,7 @@ b:Matrix Complex SF:= [[1 ,0 ,0 ]] --R Type: Matrix(Complex(DoubleFloat)) --E 4 ---S 5 of 164 +--S 5 of 165 ib:=3 --R --R @@ -92312,7 +95708,7 @@ ib:=3 --R Type: PositiveInteger --E 5 ---S 6 of 164 +--S 6 of 165 n:=3 --R --R @@ -92320,7 +95716,7 @@ n:=3 --R Type: PositiveInteger --E 6 ---S 7 of 164 +--S 7 of 165 m:=1 --R --R @@ -92328,7 +95724,7 @@ m:=1 --R Type: PositiveInteger --E 7 ---S 8 of 164 +--S 8 of 165 ic:=3 --R --R @@ -92336,7 +95732,7 @@ ic:=3 --R Type: PositiveInteger --E 8 ---S 9 of 164 +--S 9 of 165 a:Matrix Complex SF:= [[1,1 + 2*%i,2 + 10*%i],_ [1 + %i,3*%i,-5 + 14*%i],_ @@ -92351,13 +95747,13 @@ a:Matrix Complex SF:= --R Type: Matrix(Complex(DoubleFloat)) --E 9 ---S 10 of 164 +--S 10 of 165 -- result:=f04adf(ia,b,ib,n,m,ic,a,-1) --E 10 )clear all ---S 11 of 164 +--S 11 of 165 showArrayValues true --R --R @@ -92365,7 +95761,7 @@ showArrayValues true --R Type: Boolean --E 11 ---S 12 of 164 +--S 12 of 165 showScalarValues true --R --R @@ -92373,7 +95769,7 @@ showScalarValues true --R Type: Boolean --E 12 ---S 13 of 164 +--S 13 of 165 ia:=8 --R --R @@ -92381,7 +95777,7 @@ ia:=8 --R Type: PositiveInteger --E 13 ---S 14 of 164 +--S 14 of 165 b:Matrix SF:= [[-359 ,281 ,85 ]] --R --R @@ -92389,7 +95785,7 @@ b:Matrix SF:= [[-359 ,281 ,85 ]] --R Type: Matrix(DoubleFloat) --E 14 ---S 15 of 164 +--S 15 of 165 n:=3 --R --R @@ -92397,7 +95793,7 @@ n:=3 --R Type: PositiveInteger --E 15 ---S 16 of 164 +--S 16 of 165 a:Matrix SF:= [[33,16,72],_ [-24,-10,-57],_ @@ -92427,13 +95823,13 @@ a:Matrix SF:= --R Type: Matrix(DoubleFloat) --E 16 ---S 17 of 164 +--S 17 of 165 -- result:=f04arf(ia,b,n,a,-1) --E 17 )clear all ---S 18 of 164 +--S 18 of 165 showArrayValues true --R --R @@ -92441,7 +95837,7 @@ showArrayValues true --R Type: Boolean --E 18 ---S 19 of 164 +--S 19 of 165 showScalarValues true --R --R @@ -92449,7 +95845,7 @@ showScalarValues true --R Type: Boolean --E 19 ---S 20 of 164 +--S 20 of 165 ia:=8 --R --R @@ -92457,7 +95853,7 @@ ia:=8 --R Type: PositiveInteger --E 20 ---S 21 of 164 +--S 21 of 165 b:Matrix SF:= [[23 ,32 ,33 ,31 ]] --R --R @@ -92465,7 +95861,7 @@ b:Matrix SF:= [[23 ,32 ,33 ,31 ]] --R Type: Matrix(DoubleFloat) --E 21 ---S 22 of 164 +--S 22 of 165 n:=4 --R --R @@ -92473,7 +95869,7 @@ n:=4 --R Type: PositiveInteger --E 22 ---S 23 of 164 +--S 23 of 165 a:Matrix SF:= [[5,7,6,5],_ [7,10,8,7],_ @@ -92503,13 +95899,13 @@ a:Matrix SF:= --R Type: Matrix(DoubleFloat) --E 23 ---S 24 of 164 +--S 24 of 165 -- result:=f04asf(ia,b,n,a,-1) --E 24 )clear all ---S 25 of 164 +--S 25 of 165 showArrayValues true --R --R @@ -92517,7 +95913,7 @@ showArrayValues true --R Type: Boolean --E 25 ---S 26 of 164 +--S 26 of 165 showScalarValues true --R --R @@ -92525,7 +95921,7 @@ showScalarValues true --R Type: Boolean --E 26 ---S 27 of 164 +--S 27 of 165 a:Matrix SF:= [[33,16,72],_ [-24,-10,-57],_ @@ -92555,7 +95951,7 @@ a:Matrix SF:= --R Type: Matrix(DoubleFloat) --E 27 ---S 28 of 164 +--S 28 of 165 ia:=8 --R --R @@ -92563,7 +95959,7 @@ ia:=8 --R Type: PositiveInteger --E 28 ---S 29 of 164 +--S 29 of 165 b:Matrix SF:= [[-359 ,281 ,85 ]] --R --R @@ -92571,7 +95967,7 @@ b:Matrix SF:= [[-359 ,281 ,85 ]] --R Type: Matrix(DoubleFloat) --E 29 ---S 30 of 164 +--S 30 of 165 n:=3 --R --R @@ -92579,7 +95975,7 @@ n:=3 --R Type: PositiveInteger --E 30 ---S 31 of 164 +--S 31 of 165 iaa:=8 --R --R @@ -92587,13 +95983,13 @@ iaa:=8 --R Type: PositiveInteger --E 31 ---S 32 of 164 +--S 32 of 165 -- result:=f04atf(a,ia,b,n,iaa,-1) --E 32 )clear all ---S 33 of 164 +--S 33 of 165 showArrayValues true --R --R @@ -92601,7 +95997,7 @@ showArrayValues true --R Type: Boolean --E 33 ---S 34 of 164 +--S 34 of 165 showScalarValues true --R --R @@ -92609,7 +96005,7 @@ showScalarValues true --R Type: Boolean --E 34 ---S 35 of 164 +--S 35 of 165 n := 6 --R --R @@ -92617,7 +96013,7 @@ n := 6 --R Type: PositiveInteger --E 35 ---S 36 of 164 +--S 36 of 165 nz := 15 --R --R @@ -92625,7 +96021,7 @@ nz := 15 --R Type: PositiveInteger --E 36 ---S 37 of 164 +--S 37 of 165 nzmax := 50 --R --R @@ -92633,7 +96029,7 @@ nzmax := 50 --R Type: PositiveInteger --E 37 ---S 38 of 164 +--S 38 of 165 licn := 3*nzmax --R --R @@ -92641,7 +96037,7 @@ licn := 3*nzmax --R Type: PositiveInteger --E 38 ---S 39 of 164 +--S 39 of 165 t1 := [0.0 for i in 1..(licn-nz)] --R --R @@ -92658,7 +96054,7 @@ t1 := [0.0 for i in 1..(licn-nz)] --R Type: List(Float) --E 39 ---S 40 of 164 +--S 40 of 165 t2 := [5.0,2.0,-1.0,2.0,3.0,-2.0,1.0,1.0,-1.0,-1.0,2.0,-3.0,-1.0,-1.0,6.0] --R --R @@ -92667,7 +96063,7 @@ t2 := [5.0,2.0,-1.0,2.0,3.0,-2.0,1.0,1.0,-1.0,-1.0,2.0,-3.0,-1.0,-1.0,6.0] --R Type: List(Float) --E 40 ---S 41 of 164 +--S 41 of 165 t3 := concat(t2,t1) --R --R @@ -92686,7 +96082,7 @@ t3 := concat(t2,t1) --R Type: List(Float) --E 41 ---S 42 of 164 +--S 42 of 165 a := [t3] :: Matrix SF --R --R @@ -92705,7 +96101,7 @@ a := [t3] :: Matrix SF --R Type: Matrix(DoubleFloat) --E 42 ---S 43 of 164 +--S 43 of 165 lirn := (3*nzmax/2)::Integer --R --R @@ -92713,7 +96109,7 @@ lirn := (3*nzmax/2)::Integer --R Type: Integer --E 43 ---S 44 of 164 +--S 44 of 165 t1 := [0.0 for i in 1..(lirn-nz)] --R --R @@ -92725,7 +96121,7 @@ t1 := [0.0 for i in 1..(lirn-nz)] --R Type: List(Float) --E 44 ---S 45 of 164 +--S 45 of 165 t2 := [1,2,2,2,3,4,4,4,5,5,5,5,6,6,6] --R --R @@ -92733,7 +96129,7 @@ t2 := [1,2,2,2,3,4,4,4,5,5,5,5,6,6,6] --R Type: List(PositiveInteger) --E 45 ---S 46 of 164 +--S 46 of 165 t3 := concat(t2,t1) --R --R @@ -92746,7 +96142,7 @@ t3 := concat(t2,t1) --R Type: List(Float) --E 46 ---S 47 of 164 +--S 47 of 165 irn := [t3] :: Matrix Integer --R --R @@ -92760,7 +96156,7 @@ irn := [t3] :: Matrix Integer --R Type: Matrix(Integer) --E 47 ---S 48 of 164 +--S 48 of 165 t1 := [0.0 for i in 1..(licn-nz)] --R --R @@ -92777,7 +96173,7 @@ t1 := [0.0 for i in 1..(licn-nz)] --R Type: List(Float) --E 48 ---S 49 of 164 +--S 49 of 165 t2 := [1,2,3,4,3,1,4,5,1,4,5,6,1,2,6] --R --R @@ -92785,7 +96181,7 @@ t2 := [1,2,3,4,3,1,4,5,1,4,5,6,1,2,6] --R Type: List(PositiveInteger) --E 49 ---S 50 of 164 +--S 50 of 165 t3 := concat(t2,t1) --R --R @@ -92803,7 +96199,7 @@ t3 := concat(t2,t1) --R Type: List(Float) --E 50 ---S 51 of 164 +--S 51 of 165 icn := [t3] :: Matrix Integer --R --R @@ -92820,7 +96216,7 @@ icn := [t3] :: Matrix Integer --R Type: Matrix(Integer) --E 51 ---S 52 of 164 +--S 52 of 165 pivot := 0.1 --R --R @@ -92828,7 +96224,7 @@ pivot := 0.1 --R Type: Float --E 52 ---S 53 of 164 +--S 53 of 165 lblock := true --R --R @@ -92836,7 +96232,7 @@ lblock := true --R Type: Boolean --E 53 ---S 54 of 164 +--S 54 of 165 grow := true --R --R @@ -92844,7 +96240,7 @@ grow := true --R Type: Boolean --E 54 ---S 55 of 164 +--S 55 of 165 abort := [true,true,false,true] --R --R @@ -92852,7 +96248,7 @@ abort := [true,true,false,true] --R Type: List(Boolean) --E 55 ---S 56 of 164 +--S 56 of 165 ifail := 1 --R --R @@ -92860,23 +96256,23 @@ ifail := 1 --R Type: PositiveInteger --E 56 ---S 57 of 164 +--S 57 of 165 -- res1:=f01brf(n,nz,licn,lirn,pivot,lblock,grow,abort,a,irn,icn,ifail) --E 57 ---S 58 of 164 +--S 58 of 165 --a := (res1)."a" --E 58 ---S 59 of 164 +--S 59 of 165 -- icn := (res1)."icn" --E 59 ---S 60 of 164 +--S 60 of 165 -- ikeep := (res1)."ikeep" --E 60 ---S 61 of 164 +--S 61 of 165 rhs := [[15,12,18,3,-6,0]] --R --R @@ -92884,11 +96280,11 @@ rhs := [[15,12,18,3,-6,0]] --R Type: List(List(Integer)) --E 61 ---S 62 of 164 +--S 62 of 165 -- idisp := (res1)."idisp" --E 62 ---S 63 of 164 +--S 63 of 165 mtype := 1 --R --R @@ -92896,13 +96292,13 @@ mtype := 1 --R Type: PositiveInteger --E 63 ---S 64 of 164 +--S 64 of 165 -- result:=f04axf(n,a,licn,icn,ikeep,mtype,[[idisp(1,1),idisp(1,2)]],rhs) --E 64 )clear all ---S 65 of 164 +--S 65 of 165 showArrayValues true --R --R @@ -92910,7 +96306,7 @@ showArrayValues true --R Type: Boolean --E 65 ---S 66 of 164 +--S 66 of 165 showScalarValues true --R --R @@ -92918,7 +96314,7 @@ showScalarValues true --R Type: Boolean --E 66 ---S 67 of 164 +--S 67 of 165 job:=0 --R --R @@ -92926,7 +96322,7 @@ job:=0 --R Type: NonNegativeInteger --E 67 ---S 68 of 164 +--S 68 of 165 n:=5 --R --R @@ -92934,7 +96330,7 @@ n:=5 --R Type: PositiveInteger --E 68 ---S 69 of 164 +--S 69 of 165 d:Matrix SF:= [[4 ,10 ,29 ,25 ,5 ]] --R --R @@ -92942,7 +96338,7 @@ d:Matrix SF:= [[4 ,10 ,29 ,25 ,5 ]] --R Type: Matrix(DoubleFloat) --E 69 ---S 70 of 164 +--S 70 of 165 e:Matrix SF:= [[0,-2 ,-6 ,15 ,8 ]] --R --R @@ -92950,7 +96346,7 @@ e:Matrix SF:= [[0,-2 ,-6 ,15 ,8 ]] --R Type: Matrix(DoubleFloat) --E 70 ---S 71 of 164 +--S 71 of 165 b:Matrix SF:= [[6 ,9 ,2 ,14 ,7 ]] --R --R @@ -92958,13 +96354,13 @@ b:Matrix SF:= [[6 ,9 ,2 ,14 ,7 ]] --R Type: Matrix(DoubleFloat) --E 71 ---S 72 of 164 +--S 72 of 165 -- result:=f04faf(job,n,d,e,b,-1) --E 72 )clear all ---S 73 of 164 +--S 73 of 165 showArrayValues true --R --R @@ -92972,7 +96368,7 @@ showArrayValues true --R Type: Boolean --E 73 ---S 74 of 164 +--S 74 of 165 showScalarValues true --R --R @@ -92980,7 +96376,7 @@ showScalarValues true --R Type: Boolean --E 74 ---S 75 of 164 +--S 75 of 165 m:=6 --R --R @@ -92988,7 +96384,7 @@ m:=6 --R Type: PositiveInteger --E 75 ---S 76 of 164 +--S 76 of 165 n:=4 --R --R @@ -92996,7 +96392,7 @@ n:=4 --R Type: PositiveInteger --E 76 ---S 77 of 164 +--S 77 of 165 nra:=8 --R --R @@ -93004,7 +96400,7 @@ nra:=8 --R Type: PositiveInteger --E 77 ---S 78 of 164 +--S 78 of 165 tol:= 5.0e-4 --R --R @@ -93012,7 +96408,7 @@ tol:= 5.0e-4 --R Type: Float --E 78 ---S 79 of 164 +--S 79 of 165 lwork:=32 --R --R @@ -93020,7 +96416,7 @@ lwork:=32 --R Type: PositiveInteger --E 79 ---S 80 of 164 +--S 80 of 165 a:Matrix SF:= [[0.05 ,0.05 ,0.25 ,-0.25 ],_ [0.25 ,0.25 ,0.05 ,-0.05 ],_ @@ -93049,7 +96445,7 @@ a:Matrix SF:= --R Type: Matrix(DoubleFloat) --E 80 ---S 81 of 164 +--S 81 of 165 b:Matrix SF:= [[1 ,2 ,3 ,4 ,5 ,6 ]] --R --R @@ -93057,13 +96453,13 @@ b:Matrix SF:= [[1 ,2 ,3 ,4 ,5 ,6 ]] --R Type: Matrix(DoubleFloat) --E 81 ---S 82 of 164 +--S 82 of 165 -- result:=f04jgf(m,n,nra,tol,lwork,a,b,-1) --E 82 )clear all ---S 83 of 164 +--S 83 of 165 showArrayValues true --R --R @@ -93071,7 +96467,7 @@ showArrayValues true --R Type: Boolean --E 83 ---S 84 of 164 +--S 84 of 165 showScalarValues true --R --R @@ -93079,70 +96475,70 @@ showScalarValues true --R Type: Boolean --E 84 ---S 85 of 164 +--S 85 of 165 n := 4; --R --R --R Type: PositiveInteger --E 85 ---S 86 of 164 +--S 86 of 165 m := 4; --R --R --R Type: PositiveInteger --E 86 ---S 87 of 164 +--S 87 of 165 nn := n*m; --R --R --R Type: PositiveInteger --E 87 ---S 88 of 164 +--S 88 of 165 licn := 90; --R --R --R Type: PositiveInteger --E 88 ---S 89 of 164 +--S 89 of 165 lirn := 50; --R --R --R Type: PositiveInteger --E 89 ---S 90 of 164 +--S 90 of 165 a := new(1,licn,0.0)$Matrix DoubleFloat; --R --R --R Type: Matrix(DoubleFloat) --E 90 ---S 91 of 164 +--S 91 of 165 irn := new(1,lirn,0)$Matrix Integer; --R --R --R Type: Matrix(Integer) --E 91 ---S 92 of 164 +--S 92 of 165 icn := new(1,licn,0)$Matrix Integer; --R --R --R Type: Matrix(Integer) --E 92 ---S 93 of 164 +--S 93 of 165 k := 0; --R --R --R Type: NonNegativeInteger --E 93 ---S 94 of 164 +--S 94 of 165 for i in 1..nn repeat k := k + 1 a(1,k) := 1 @@ -93152,7 +96548,7 @@ for i in 1..nn repeat --R Type: Void --E 94 ---S 95 of 164 +--S 95 of 165 for i in 1..n repeat for j in 1..(m-1) repeat k := k + 1 @@ -93164,7 +96560,7 @@ for i in 1..n repeat --R Type: Void --E 95 ---S 96 of 164 +--S 96 of 165 for i in (n+1)..nn repeat k := k + 1 a(1,k) := -0.25 @@ -93174,58 +96570,58 @@ for i in (n+1)..nn repeat --R Type: Void --E 96 ---S 97 of 164 +--S 97 of 165 nz := k; --R --R --R Type: NonNegativeInteger --E 97 ---S 98 of 164 +--S 98 of 165 abort := [true,true,true]; --R --R --R Type: List(Boolean) --E 98 ---S 99 of 164 +--S 99 of 165 droptl := 0.1; --R --R --R Type: Float --E 99 ---S 100 of 164 +--S 100 of 165 densw := 0.8; --R --R --R Type: Float --E 100 ---S 101 of 164 +--S 101 of 165 ifail := 111; --R --R --R Type: PositiveInteger --E 101 ---S 102 of 164 +--S 102 of 165 -- res1:=f01maf(nn,nz,licn,lirn,abort,a,irn,icn,droptl,densw,ifail) --E 102 ---S 103 of 164 +--S 103 of 165 -- a := res1."avals" --E 103 ---S 104 of 164 +--S 104 of 165 -- irn := res1."irn" --E 104 ---S 105 of 164 +--S 105 of 165 -- icn := res1."icn" --E 105 ---S 106 of 164 +--S 106 of 165 b := [[0.5,0.25,0.25,0.5,0.25,0,0,0.25,0.25,0,0,0.25,0.5,0.25,0.25,0.5]] --R --R @@ -93234,7 +96630,7 @@ b := [[0.5,0.25,0.25,0.5,0.25,0,0,0.25,0.25,0,0,0.25,0.5,0.25,0.25,0.5]] --R Type: List(List(Float)) --E 106 ---S 107 of 164 +--S 107 of 165 acc := [[0.0001,0]] --R --R @@ -93242,7 +96638,7 @@ acc := [[0.0001,0]] --R Type: List(List(Float)) --E 107 ---S 108 of 164 +--S 108 of 165 noits := [[50,0]] --R --R @@ -93250,26 +96646,26 @@ noits := [[50,0]] --R Type: List(List(NonNegativeInteger)) --E 108 ---S 109 of 164 +--S 109 of 165 -- wkeep := res1."wkeep" --E 109 ---S 110 of 164 +--S 110 of 165 -- ikeep := res1."ikeep" --E 110 ---S 111 of 164 +--S 111 of 165 -- inform := res1."inform" --E 111 ---S 112 of 164 +--S 112 of 165 -- result:= -- f04maf(nn,nz,a,licn,irn,lirn,icn,wkeep,ikeep,inform,b,acc,noits,ifail) --E 112 )clear all ---S 113 of 164 +--S 113 of 165 showArrayValues true --R --R @@ -93277,7 +96673,7 @@ showArrayValues true --R Type: Boolean --E 113 ---S 114 of 164 +--S 114 of 165 showScalarValues true --R --R @@ -93285,7 +96681,7 @@ showScalarValues true --R Type: Boolean --E 114 ---S 115 of 164 +--S 115 of 165 n := 10 --R --R @@ -93293,14 +96689,14 @@ n := 10 --R Type: PositiveInteger --E 115 ---S 116 of 164 +--S 116 of 165 b := new(1,n,0.0)$Matrix DoubleFloat; --R --R --R Type: Matrix(DoubleFloat) --E 116 ---S 117 of 164 +--S 117 of 165 b(1,1) := 6 --R --R @@ -93308,14 +96704,14 @@ b(1,1) := 6 --R Type: DoubleFloat --E 117 ---S 118 of 164 +--S 118 of 165 for i in 2..n-1 repeat b(1,i) := 4 --R --R Type: Void --E 118 ---S 119 of 164 +--S 119 of 165 b(1,n) := 6 --R --R @@ -93323,7 +96719,7 @@ b(1,n) := 6 --R Type: DoubleFloat --E 119 ---S 120 of 164 +--S 120 of 165 precon := true --R --R @@ -93331,7 +96727,7 @@ precon := true --R Type: Boolean --E 120 ---S 121 of 164 +--S 121 of 165 shft := 0 --R --R @@ -93343,7 +96739,7 @@ shft := 0 -- by the ASPs. They may be useful if a user -- supplies FORTRAN code directly. ---S 122 of 164 +--S 122 of 165 lrwork:=1 --R --R @@ -93351,7 +96747,7 @@ lrwork:=1 --R Type: PositiveInteger --E 122 ---S 123 of 164 +--S 123 of 165 liwork:=1 --R --R @@ -93359,7 +96755,7 @@ liwork:=1 --R Type: PositiveInteger --E 123 ---S 124 of 164 +--S 124 of 165 rtol := 0.00001 --R --R @@ -93367,7 +96763,7 @@ rtol := 0.00001 --R Type: Float --E 124 ---S 125 of 164 +--S 125 of 165 itnlim := 100 --R --R @@ -93375,7 +96771,7 @@ itnlim := 100 --R Type: PositiveInteger --E 125 ---S 126 of 164 +--S 126 of 165 msglvl := 1 --R --R @@ -93383,7 +96779,7 @@ msglvl := 1 --R Type: PositiveInteger --E 126 ---S 127 of 164 +--S 127 of 165 ifail := 1 --R --R @@ -93391,14 +96787,14 @@ ifail := 1 --R Type: PositiveInteger --E 127 ---S 128 of 164 +--S 128 of 165 z:=new(10,10,0.0)$Matrix MFLOAT; --R --R --R Type: Matrix(MachineFloat) --E 128 ---S 129 of 164 +--S 129 of 165 z(1,1):=2;z(1,2):=1;z(1,10):=3 --R --R @@ -93406,7 +96802,7 @@ z(1,1):=2;z(1,2):=1;z(1,10):=3 --R Type: MachineFloat --E 129 ---S 130 of 164 +--S 130 of 165 z(10,1):=3;z(10,9):=1;z(10,10):=2 --R --R @@ -93414,7 +96810,7 @@ z(10,1):=3;z(10,9):=1;z(10,10):=2 --R Type: MachineFloat --E 130 ---S 131 of 164 +--S 131 of 165 for i in 2..(n-1) repeat z(i,i-1):=1 z(i,i):=2 @@ -93423,7 +96819,7 @@ for i in 2..(n-1) repeat --R Type: Void --E 131 ---S 132 of 164 +--S 132 of 165 z --R --R @@ -93449,7 +96845,7 @@ z --R Type: Matrix(MachineFloat) --E 132 ---S 133 of 164 +--S 133 of 165 m :Matrix MFLOAT:= [[2,1,0,0,0,0,0,0,0,0],[1,2,1,0,0,0,0,0,0,0],_ [0,1,2,1,0,0,0,0,0,0],[0,0,1,2,1,0,0,0,0,0],[0,0,0,1,2,1,0,0,0,0],_ [0,0,0,0,1,2,1,0,0,0],[0,0,0,0,0,1,2,1,0,0],[0,0,0,0,0,0,1,2,1,0],_ @@ -93478,14 +96874,14 @@ m :Matrix MFLOAT:= [[2,1,0,0,0,0,0,0,0,0],[1,2,1,0,0,0,0,0,0,0],_ --R Type: Matrix(MachineFloat) --E 133 ---S 134 of 164 +--S 134 of 165 -- result:=f04mbf(n,b,precon,shft,itnlim,msglvl,lrwork,liwork,_ -- rtol,ifail,z::ASP28(APROD),(m::ASP34(MSOLVE))) --E 134 )clear all ---S 135 of 164 +--S 135 of 165 showArrayValues true --R --R @@ -93493,7 +96889,7 @@ showArrayValues true --R Type: Boolean --E 135 ---S 136 of 164 +--S 136 of 165 showScalarValues true --R --R @@ -93501,7 +96897,7 @@ showScalarValues true --R Type: Boolean --E 136 ---S 137 of 164 +--S 137 of 165 n:=6 --R --R @@ -93509,7 +96905,7 @@ n:=6 --R Type: PositiveInteger --E 137 ---S 138 of 164 +--S 138 of 165 al:Matrix SF:= [[1.0 ,2.0 ,1.0 ,3.0 ,1.0 ,1.0 ,5.0 ,4.0 ,1.5 ,0.5 ,1.0 ,1.5 ,5.0,1.0 ]] --R @@ -93518,7 +96914,7 @@ al:Matrix SF:= --R Type: Matrix(DoubleFloat) --E 138 ---S 139 of 164 +--S 139 of 165 lal:=14 --R --R @@ -93526,7 +96922,7 @@ lal:=14 --R Type: PositiveInteger --E 139 ---S 140 of 164 +--S 140 of 165 d:Matrix SF:= [[1.0 ,1.0 ,4.0 ,16.0 ,1.0 ,16.0 ]] --R --R @@ -93534,7 +96930,7 @@ d:Matrix SF:= [[1.0 ,1.0 ,4.0 ,16.0 ,1.0 ,16.0 ]] --R Type: Matrix(DoubleFloat) --E 140 ---S 141 of 164 +--S 141 of 165 nrow:Matrix Integer:= [[1 ,2 ,2 ,1 ,5 ,3 ]] --R --R @@ -93542,7 +96938,7 @@ nrow:Matrix Integer:= [[1 ,2 ,2 ,1 ,5 ,3 ]] --R Type: Matrix(Integer) --E 141 ---S 142 of 164 +--S 142 of 165 ir:=2 --R --R @@ -93550,7 +96946,7 @@ ir:=2 --R Type: PositiveInteger --E 142 ---S 143 of 164 +--S 143 of 165 b:Matrix SF:= [[6 ,-10 ],_ [15 ,-21 ],_ @@ -93574,7 +96970,7 @@ b:Matrix SF:= --R Type: Matrix(DoubleFloat) --E 143 ---S 144 of 164 +--S 144 of 165 nrb:=6 --R --R @@ -93582,7 +96978,7 @@ nrb:=6 --R Type: PositiveInteger --E 144 ---S 145 of 164 +--S 145 of 165 iselct:=1 --R --R @@ -93590,7 +96986,7 @@ iselct:=1 --R Type: PositiveInteger --E 145 ---S 146 of 164 +--S 146 of 165 nrx:=6 --R --R @@ -93598,13 +96994,13 @@ nrx:=6 --R Type: PositiveInteger --E 146 ---S 147 of 164 +--S 147 of 165 -- result:=f04mcf(n,al,lal,d,nrow,ir,b,nrb,iselct,nrx,-1) --E 147 )clear all ---S 148 of 164 +--S 148 of 165 showArrayValues true --R --R @@ -93612,7 +97008,7 @@ showArrayValues true --R Type: Boolean --E 148 ---S 149 of 164 +--S 149 of 165 showScalarValues true --R --R @@ -93620,7 +97016,7 @@ showScalarValues true --R Type: Boolean --E 149 ---S 150 of 164 +--S 150 of 165 n := 12 --R --R @@ -93628,7 +97024,7 @@ n := 12 --R Type: PositiveInteger --E 150 ---S 151 of 164 +--S 151 of 165 m := 13 --R --R @@ -93636,7 +97032,7 @@ m := 13 --R Type: PositiveInteger --E 151 ---S 152 of 164 +--S 152 of 165 h:SF := 0.1 --R --R @@ -93644,7 +97040,7 @@ h:SF := 0.1 --R Type: DoubleFloat --E 152 ---S 153 of 164 +--S 153 of 165 b :Matrix SF:= -h^2 * [[0],[0],[0],[1],[1],[0],[0],[1],[1],[0],[0],[0],[-h^-3]] --R --R @@ -93676,7 +97072,7 @@ b :Matrix SF:= -h^2 * [[0],[0],[0],[1],[1],[0],[0],[1],[1],[0],[0],[0],[-h^-3]] --R Type: Matrix(DoubleFloat) --E 153 ---S 154 of 164 +--S 154 of 165 a : Matrix MachineFloat:= [[1,0,0,-1,0,0,0,0,0,0,0,0],_ [0,1,0,0,-1,0,0,0,0,0,0,0],_ @@ -93710,7 +97106,7 @@ a : Matrix MachineFloat:= --R Type: Matrix(MachineFloat) --E 154 ---S 155 of 164 +--S 155 of 165 damp := 0.0 --R --R @@ -93718,7 +97114,7 @@ damp := 0.0 --R Type: Float --E 155 ---S 156 of 164 +--S 156 of 165 atol := 1.0e-5 --R --R @@ -93726,7 +97122,7 @@ atol := 1.0e-5 --R Type: Float --E 156 ---S 157 of 164 +--S 157 of 165 btol := 1.0e-4 --R --R @@ -93734,7 +97130,7 @@ btol := 1.0e-4 --R Type: Float --E 157 ---S 158 of 164 +--S 158 of 165 conlim := 1/atol --R --R @@ -93742,7 +97138,7 @@ conlim := 1/atol --R Type: Float --E 158 ---S 159 of 164 +--S 159 of 165 itnlim := 100 --R --R @@ -93750,7 +97146,7 @@ itnlim := 100 --R Type: PositiveInteger --E 159 ---S 160 of 164 +--S 160 of 165 msglvl := 1 --R --R @@ -93758,7 +97154,7 @@ msglvl := 1 --R Type: PositiveInteger --E 160 ---S 161 of 164 +--S 161 of 165 liwork := 1 --R --R @@ -93766,7 +97162,7 @@ liwork := 1 --R Type: PositiveInteger --E 161 ---S 162 of 164 +--S 162 of 165 lrwork := 1 --R --R @@ -93774,7 +97170,7 @@ lrwork := 1 --R Type: PositiveInteger --E 162 ---S 163 of 164 +--S 163 of 165 ifail :=1 --R --R @@ -93782,12 +97178,33 @@ ifail :=1 --R Type: PositiveInteger --E 163 ---S 164 of 164 +--S 164 of 165 -- result:=f04qaf(m,n,damp,atol,btol,conlim,itnlim,msglvl,lrwork,_ -- liwork,b,ifail,a::ASP30(APROD)) --E 164 - +--S 165 of 165 +)show NagLinearEquationSolvingPackage +--R +--R NagLinearEquationSolvingPackage is a package constructor +--R Abbreviation for NagLinearEquationSolvingPackage is NAGF04 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for NAGF04 +--R +--R------------------------------- Operations -------------------------------- +--R f04adf : (Integer,Matrix(Complex(DoubleFloat)),Integer,Integer,Integer,Integer,Matrix(Complex(DoubleFloat)),Integer) -> Result +--R f04arf : (Integer,Matrix(DoubleFloat),Integer,Matrix(DoubleFloat),Integer) -> Result +--R f04asf : (Integer,Matrix(DoubleFloat),Integer,Matrix(DoubleFloat),Integer) -> Result +--R f04atf : (Matrix(DoubleFloat),Integer,Matrix(DoubleFloat),Integer,Integer,Integer) -> Result +--R f04axf : (Integer,Matrix(DoubleFloat),Integer,Matrix(Integer),Matrix(Integer),Integer,Matrix(Integer),Matrix(DoubleFloat)) -> Result +--R f04faf : (Integer,Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),Integer) -> Result +--R f04jgf : (Integer,Integer,Integer,DoubleFloat,Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Integer) -> Result +--R f04maf : (Integer,Integer,Matrix(DoubleFloat),Integer,Matrix(Integer),Integer,Matrix(Integer),Matrix(DoubleFloat),Matrix(Integer),Matrix(Integer),Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(Integer),Integer) -> Result +--R f04mbf : (Integer,Matrix(DoubleFloat),Boolean,DoubleFloat,Integer,Integer,Integer,Integer,DoubleFloat,Integer,Union(fn: FileName,fp: Asp28(APROD)),Union(fn: FileName,fp: Asp34(MSOLVE))) -> Result +--R f04mcf : (Integer,Matrix(DoubleFloat),Integer,Matrix(DoubleFloat),Matrix(Integer),Integer,Matrix(DoubleFloat),Integer,Integer,Integer,Integer) -> Result +--R f04qaf : (Integer,Integer,DoubleFloat,DoubleFloat,DoubleFloat,DoubleFloat,Integer,Integer,Integer,Integer,Matrix(DoubleFloat),Integer,Union(fn: FileName,fp: Asp30(APROD))) -> Result +--R +--E 165 )spool )lisp (bye) @@ -97480,6 +100897,19 @@ NagLinearEquationSolvingPackage(): Exports == Implementation where --S 1 of 1 )show NAGLinkSupportPackage +--R +--R NAGLinkSupportPackage is a package constructor +--R Abbreviation for NAGLinkSupportPackage is NAGSP +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for NAGSP +--R +--R------------------------------- Operations -------------------------------- +--R aspFilename : String -> String checkPrecision : () -> Boolean +--R fortranCompilerName : () -> String fortranLinkerArgs : () -> String +--R restorePrecision : () -> Void +--R dimensionsOf : (Symbol,Matrix(DoubleFloat)) -> SExpression +--R dimensionsOf : (Symbol,Matrix(Integer)) -> SExpression +--R --E 1 )spool @@ -97597,6 +101027,26 @@ NAGLinkSupportPackage() : exports == implementation where --S 1 of 1 )show NagIntegrationPackage +--R +--R NagIntegrationPackage is a package constructor +--R Abbreviation for NagIntegrationPackage is NAGD01 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for NAGD01 +--R +--R------------------------------- Operations -------------------------------- +--R d01ajf : (DoubleFloat,DoubleFloat,DoubleFloat,DoubleFloat,Integer,Integer,Integer,Union(fn: FileName,fp: Asp1(F))) -> Result +--R d01akf : (DoubleFloat,DoubleFloat,DoubleFloat,DoubleFloat,Integer,Integer,Integer,Union(fn: FileName,fp: Asp1(F))) -> Result +--R d01alf : (DoubleFloat,DoubleFloat,Integer,Matrix(DoubleFloat),DoubleFloat,DoubleFloat,Integer,Integer,Integer,Union(fn: FileName,fp: Asp1(F))) -> Result +--R d01amf : (DoubleFloat,Integer,DoubleFloat,DoubleFloat,Integer,Integer,Integer,Union(fn: FileName,fp: Asp1(F))) -> Result +--R d01anf : (DoubleFloat,DoubleFloat,DoubleFloat,Integer,DoubleFloat,DoubleFloat,Integer,Integer,Integer,Union(fn: FileName,fp: Asp1(G))) -> Result +--R d01apf : (DoubleFloat,DoubleFloat,DoubleFloat,DoubleFloat,Integer,DoubleFloat,DoubleFloat,Integer,Integer,Integer,Union(fn: FileName,fp: Asp1(G))) -> Result +--R d01aqf : (DoubleFloat,DoubleFloat,DoubleFloat,DoubleFloat,DoubleFloat,Integer,Integer,Integer,Union(fn: FileName,fp: Asp1(G))) -> Result +--R d01asf : (DoubleFloat,DoubleFloat,Integer,DoubleFloat,Integer,Integer,Integer,Integer,Union(fn: FileName,fp: Asp1(G))) -> Result +--R d01bbf : (DoubleFloat,DoubleFloat,Integer,Integer,Integer,Integer) -> Result +--R d01fcf : (Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Integer,DoubleFloat,Integer,Integer,Integer,Union(fn: FileName,fp: Asp4(FUNCTN))) -> Result +--R d01gaf : (Matrix(DoubleFloat),Matrix(DoubleFloat),Integer,Integer) -> Result +--R d01gbf : (Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Integer,DoubleFloat,Integer,Integer,Matrix(DoubleFloat),Integer,Union(fn: FileName,fp: Asp4(FUNCTN))) -> Result +--R --E 1 )spool @@ -120461,6 +123911,23 @@ NagOptimisationPackage(): Exports == Implementation where --S 1 of 1 )show NagOrdinaryDifferentialEquationsPackage +--R +--R NagOrdinaryDifferentialEquationsPackage is a package constructor +--R Abbreviation for NagOrdinaryDifferentialEquationsPackage is NAGD02 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for NAGD02 +--R +--R------------------------------- Operations -------------------------------- +--R d02bbf : (DoubleFloat,Integer,Integer,Integer,DoubleFloat,Matrix(DoubleFloat),DoubleFloat,Integer,Union(fn: FileName,fp: Asp7(FCN)),Union(fn: FileName,fp: Asp8(OUTPUT))) -> Result +--R d02bhf : (DoubleFloat,Integer,Integer,DoubleFloat,DoubleFloat,Matrix(DoubleFloat),DoubleFloat,Integer,Union(fn: FileName,fp: Asp9(G)),Union(fn: FileName,fp: Asp7(FCN))) -> Result +--R d02cjf : (DoubleFloat,Integer,Integer,DoubleFloat,String,DoubleFloat,Matrix(DoubleFloat),Integer,Union(fn: FileName,fp: Asp9(G)),Union(fn: FileName,fp: Asp7(FCN)),Union(fn: FileName,fp: Asp8(OUTPUT))) -> Result +--R d02ejf : (DoubleFloat,Integer,Integer,String,Integer,DoubleFloat,Matrix(DoubleFloat),DoubleFloat,Integer,Union(fn: FileName,fp: Asp9(G)),Union(fn: FileName,fp: Asp7(FCN)),Union(fn: FileName,fp: Asp31(PEDERV)),Union(fn: FileName,fp: Asp8(OUTPUT))) -> Result +--R d02gaf : (Matrix(DoubleFloat),Matrix(DoubleFloat),Integer,DoubleFloat,DoubleFloat,DoubleFloat,Integer,Integer,Integer,Matrix(DoubleFloat),Integer,Integer,Union(fn: FileName,fp: Asp7(FCN))) -> Result +--R d02gbf : (DoubleFloat,DoubleFloat,Integer,DoubleFloat,Integer,Integer,Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),Integer,Integer,Union(fn: FileName,fp: Asp77(FCNF)),Union(fn: FileName,fp: Asp78(FCNG))) -> Result +--R d02kef : (Matrix(DoubleFloat),Integer,Integer,DoubleFloat,Integer,Integer,DoubleFloat,DoubleFloat,Matrix(DoubleFloat),Integer,Integer,Union(fn: FileName,fp: Asp10(COEFFN)),Union(fn: FileName,fp: Asp80(BDYVAL))) -> Result +--R d02kef : (Matrix(DoubleFloat),Integer,Integer,DoubleFloat,Integer,Integer,DoubleFloat,DoubleFloat,Matrix(DoubleFloat),Integer,Integer,Union(fn: FileName,fp: Asp10(COEFFN)),Union(fn: FileName,fp: Asp80(BDYVAL)),FileName,FileName) -> Result +--R d02raf : (Integer,Integer,Integer,Integer,DoubleFloat,Integer,Integer,Integer,Integer,Integer,Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),DoubleFloat,Integer,Union(fn: FileName,fp: Asp41(FCN,JACOBF,JACEPS)),Union(fn: FileName,fp: Asp42(G,JACOBG,JACGEP))) -> Result +--R --E 1 )spool @@ -125473,6 +128940,17 @@ NagOrdinaryDifferentialEquationsPackage(): Exports == Implementation where --S 1 of 1 )show NagPartialDifferentialEquationsPackage +--R +--R NagPartialDifferentialEquationsPackage is a package constructor +--R Abbreviation for NagPartialDifferentialEquationsPackage is NAGD03 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for NAGD03 +--R +--R------------------------------- Operations -------------------------------- +--R d03edf : (Integer,Integer,Integer,Integer,DoubleFloat,Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),Integer) -> Result +--R d03eef : (DoubleFloat,DoubleFloat,DoubleFloat,DoubleFloat,Integer,Integer,Integer,String,Integer,Union(fn: FileName,fp: Asp73(PDEF)),Union(fn: FileName,fp: Asp74(BNDY))) -> Result +--R d03faf : (DoubleFloat,DoubleFloat,Integer,Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),DoubleFloat,DoubleFloat,Integer,Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),DoubleFloat,DoubleFloat,Integer,Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),DoubleFloat,Integer,Integer,Integer,ThreeDimensionalMatrix(DoubleFloat),Integer) -> Result +--R --E 1 )spool @@ -141294,6 +144772,15 @@ NagSpecialFunctionsPackage(): Exports == Implementation where --S 1 of 1 )show NewSparseUnivariatePolynomialFunctions2 +--R +--R NewSparseUnivariatePolynomialFunctions2(R: Ring,S: Ring) is a package constructor +--R Abbreviation for NewSparseUnivariatePolynomialFunctions2 is NSUP2 +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for NSUP2 +--R +--R------------------------------- Operations -------------------------------- +--R map : ((R -> S),NewSparseUnivariatePolynomial(R)) -> NewSparseUnivariatePolynomial(S) +--R --E 1 )spool @@ -141359,6 +144846,15 @@ NewSparseUnivariatePolynomialFunctions2(R:Ring, S:Ring): with --S 1 of 1 )show NewtonInterpolation +--R +--R NewtonInterpolation(F: IntegralDomain) is a package constructor +--R Abbreviation for NewtonInterpolation is NEWTON +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for NEWTON +--R +--R------------------------------- Operations -------------------------------- +--R newton : List(F) -> SparseUnivariatePolynomial(F) +--R --E 1 )spool @@ -141708,6 +145204,18 @@ NewtonPolygon(K,PolyRing,E,dim):Exports == Implementation where --S 1 of 1 )show NonCommutativeOperatorDivision +--R +--R NonCommutativeOperatorDivision(P: MonogenicLinearOperator(F),F: Field) is a package constructor +--R Abbreviation for NonCommutativeOperatorDivision is NCODIV +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for NCODIV +--R +--R------------------------------- Operations -------------------------------- +--R leftGcd : (P,P) -> P leftLcm : (P,P) -> P +--R leftQuotient : (P,P) -> P leftRemainder : (P,P) -> P +--R leftDivide : (P,P) -> Record(quotient: P,remainder: P) +--R leftExactQuotient : (P,P) -> Union(P,"failed") +--R --E 1 )spool @@ -141849,6 +145357,15 @@ NonCommutativeOperatorDivision(P, F): PDcat == PDdef where --S 1 of 1 )show NoneFunctions1 +--R +--R NoneFunctions1(S: Type) is a package constructor +--R Abbreviation for NoneFunctions1 is NONE1 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for NONE1 +--R +--R------------------------------- Operations -------------------------------- +--R coerce : S -> None +--R --E 1 )spool @@ -141908,6 +145425,15 @@ NoneFunctions1(S:Type): Exports == Implementation where --S 1 of 1 )show NonLinearFirstOrderODESolver +--R +--R NonLinearFirstOrderODESolver(R: Join(OrderedSet,EuclideanDomain,RetractableTo(Integer),LinearlyExplicitRingOver(Integer),CharacteristicZero),F: Join(AlgebraicallyClosedFunctionSpace(R),TranscendentalFunctionCategory,PrimitiveFunctionCategory)) is a package constructor +--R Abbreviation for NonLinearFirstOrderODESolver is NODE1 +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for NODE1 +--R +--R------------------------------- Operations -------------------------------- +--R solve : (F,F,BasicOperator,Symbol) -> Union(F,"failed") +--R --E 1 )spool @@ -142100,6 +145626,18 @@ NonLinearFirstOrderODESolver(R, F): Exports == Implementation where --S 1 of 1 )show NonLinearSolvePackage +--R +--R NonLinearSolvePackage(R: IntegralDomain) is a package constructor +--R Abbreviation for NonLinearSolvePackage is NLINSOL +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for NLINSOL +--R +--R------------------------------- Operations -------------------------------- +--R solve : (List(Polynomial(R)),List(Symbol)) -> List(List(Equation(Fraction(Polynomial(R))))) +--R solve : List(Polynomial(R)) -> List(List(Equation(Fraction(Polynomial(R))))) +--R solveInField : (List(Polynomial(R)),List(Symbol)) -> List(List(Equation(Fraction(Polynomial(R))))) +--R solveInField : List(Polynomial(R)) -> List(List(Equation(Fraction(Polynomial(R))))) +--R --E 1 )spool @@ -142245,6 +145783,19 @@ NonLinearSolvePackage(R:IntegralDomain): Exports == Implementation where --S 1 of 1 )show NormalizationPackage +--R +--R NormalizationPackage(R: GcdDomain,E: OrderedAbelianMonoidSup,V: OrderedSet,P: RecursivePolynomialCategory(R,E,V),TS: RegularTriangularSetCategory(R,E,V,P)) is a package constructor +--R Abbreviation for NormalizationPackage is NORMPK +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for NORMPK +--R +--R------------------------------- Operations -------------------------------- +--R normalizedAssociate : (P,TS) -> P +--R normInvertible? : (P,TS) -> List(Record(val: Boolean,tower: TS)) +--R normalize : (P,TS) -> List(Record(val: P,tower: TS)) +--R outputArgs : (String,String,P,TS) -> Void +--R recip : (P,TS) -> Record(num: P,den: P) +--R --E 1 )spool @@ -142484,6 +146035,15 @@ NormalizationPackage(R,E,V,P,TS): Exports == Implementation where --S 1 of 1 )show NormInMonogenicAlgebra +--R +--R NormInMonogenicAlgebra(R: GcdDomain,PolR: UnivariatePolynomialCategory(R),E: MonogenicAlgebra(R,PolR),PolE: UnivariatePolynomialCategory(E)) is a package constructor +--R Abbreviation for NormInMonogenicAlgebra is NORMMA +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for NORMMA +--R +--R------------------------------- Operations -------------------------------- +--R norm : PolE -> PolR +--R --E 1 )spool @@ -142563,6 +146123,16 @@ NormInMonogenicAlgebra(R, PolR, E, PolE): Exports == Implementation where --S 1 of 1 )show NormRetractPackage +--R +--R NormRetractPackage(F: FiniteFieldCategory,ExtF: FiniteAlgebraicExtensionField(F),SUEx: UnivariatePolynomialCategory(ExtF),ExtP: UnivariatePolynomialCategory(SUEx),n: PositiveInteger) is a package constructor +--R Abbreviation for NormRetractPackage is NORMRETR +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for NORMRETR +--R +--R------------------------------- Operations -------------------------------- +--R Frobenius : ExtP -> ExtP normFactors : ExtP -> List(ExtP) +--R retractIfCan : ExtP -> Union(SparseUnivariatePolynomial(SparseUnivariatePolynomial(F)),"failed") +--R --E 1 )spool @@ -142664,6 +146234,16 @@ NormRetractPackage(F, ExtF, SUEx, ExtP, n):C == T where --S 1 of 1 )show NPCoef +--R +--R NPCoef(BP: UnivariatePolynomialCategory(R),E: OrderedAbelianMonoidSup,OV: OrderedSet,R: EuclideanDomain,P: PolynomialCategory(R,E,OV)) is a package constructor +--R Abbreviation for NPCoef is NPCOEF +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for NPCOEF +--R +--R------------------------------- Operations -------------------------------- +--R listexp : BP -> List(NonNegativeInteger) +--R npcoef : (SparseUnivariatePolynomial(P),List(BP),List(P)) -> Record(deter: List(SparseUnivariatePolynomial(P)),dterm: List(List(Record(expt: NonNegativeInteger,pcoef: P))),nfacts: List(BP),nlead: List(P)) +--R --E 1 )spool @@ -142868,6 +146448,17 @@ NPCoef(BP,E,OV,R,P) : C == T where --S 1 of 1 )show NumberFieldIntegralBasis +--R +--R NumberFieldIntegralBasis(UP: UnivariatePolynomialCategory(Integer),F: FramedAlgebra(Integer,UP)) is a package constructor +--R Abbreviation for NumberFieldIntegralBasis is NFINTBAS +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for NFINTBAS +--R +--R------------------------------- Operations -------------------------------- +--R discriminant : () -> Integer +--R integralBasis : () -> Record(basis: Matrix(Integer),basisDen: Integer,basisInv: Matrix(Integer)) +--R localIntegralBasis : Integer -> Record(basis: Matrix(Integer),basisDen: Integer,basisInv: Matrix(Integer)) +--R --E 1 )spool @@ -143137,6 +146728,20 @@ NumberFieldIntegralBasis(UP,F): Exports == Implementation where --S 1 of 1 )show NumberFormats +--R +--R NumberFormats is a package constructor +--R Abbreviation for NumberFormats is NUMFMT +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for NUMFMT +--R +--R------------------------------- Operations -------------------------------- +--R FormatArabic : PositiveInteger -> String +--R FormatRoman : PositiveInteger -> String +--R ScanArabic : String -> PositiveInteger +--R ScanFloatIgnoreSpaces : String -> Float +--R ScanFloatIgnoreSpacesIfCan : String -> Union(Float,"failed") +--R ScanRoman : String -> PositiveInteger +--R --E 1 )spool @@ -143377,6 +146982,17 @@ NumberFormats(): NFexports == NFimplementation where --S 1 of 1 )show NumberTheoreticPolynomialFunctions +--R +--R NumberTheoreticPolynomialFunctions(R: CommutativeRing) is a package constructor +--R Abbreviation for NumberTheoreticPolynomialFunctions is NTPOLFN +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for NTPOLFN +--R +--R------------------------------- Operations -------------------------------- +--R bernoulliB : (NonNegativeInteger,R) -> R if R has ALGEBRA(FRAC(INT)) +--R cyclotomic : (NonNegativeInteger,R) -> R +--R eulerE : (NonNegativeInteger,R) -> R if R has ALGEBRA(FRAC(INT)) +--R --E 1 )spool @@ -143483,6 +147099,55 @@ NumberTheoreticPolynomialFunctions(R: CommutativeRing): Exports == Impl where --S 1 of 1 )show Numeric +--R +--R Numeric(S: ConvertibleTo(Float)) is a package constructor +--R Abbreviation for Numeric is NUMERIC +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for NUMERIC +--R +--R------------------------------- Operations -------------------------------- +--R complexNumeric : S -> Complex(Float) numeric : S -> Float +--R complexNumeric : (S,PositiveInteger) -> Complex(Float) +--R complexNumeric : Complex(S) -> Complex(Float) if S has COMRING +--R complexNumeric : (Complex(S),PositiveInteger) -> Complex(Float) if S has COMRING +--R complexNumeric : Polynomial(Complex(S)) -> Complex(Float) if S has COMRING +--R complexNumeric : (Polynomial(Complex(S)),PositiveInteger) -> Complex(Float) if S has COMRING +--R complexNumeric : Polynomial(S) -> Complex(Float) if S has RING +--R complexNumeric : (Polynomial(S),PositiveInteger) -> Complex(Float) if S has RING +--R complexNumeric : Fraction(Polynomial(S)) -> Complex(Float) if S has INTDOM +--R complexNumeric : (Fraction(Polynomial(S)),PositiveInteger) -> Complex(Float) if S has INTDOM +--R complexNumeric : Fraction(Polynomial(Complex(S))) -> Complex(Float) if S has INTDOM +--R complexNumeric : (Fraction(Polynomial(Complex(S))),PositiveInteger) -> Complex(Float) if S has INTDOM +--R complexNumeric : Expression(S) -> Complex(Float) if S has INTDOM and S has ORDSET +--R complexNumeric : (Expression(S),PositiveInteger) -> Complex(Float) if S has INTDOM and S has ORDSET +--R complexNumeric : Expression(Complex(S)) -> Complex(Float) if S has INTDOM and S has ORDSET +--R complexNumeric : (Expression(Complex(S)),PositiveInteger) -> Complex(Float) if S has INTDOM and S has ORDSET +--R complexNumericIfCan : Polynomial(Complex(S)) -> Union(Complex(Float),"failed") if S has COMRING +--R complexNumericIfCan : (Polynomial(Complex(S)),PositiveInteger) -> Union(Complex(Float),"failed") if S has COMRING +--R complexNumericIfCan : Polynomial(S) -> Union(Complex(Float),"failed") if S has RING +--R complexNumericIfCan : (Polynomial(S),PositiveInteger) -> Union(Complex(Float),"failed") if S has RING +--R complexNumericIfCan : Fraction(Polynomial(S)) -> Union(Complex(Float),"failed") if S has INTDOM +--R complexNumericIfCan : (Fraction(Polynomial(S)),PositiveInteger) -> Union(Complex(Float),"failed") if S has INTDOM +--R complexNumericIfCan : Fraction(Polynomial(Complex(S))) -> Union(Complex(Float),"failed") if S has INTDOM +--R complexNumericIfCan : (Fraction(Polynomial(Complex(S))),PositiveInteger) -> Union(Complex(Float),"failed") if S has INTDOM +--R complexNumericIfCan : Expression(S) -> Union(Complex(Float),"failed") if S has INTDOM and S has ORDSET +--R complexNumericIfCan : (Expression(S),PositiveInteger) -> Union(Complex(Float),"failed") if S has INTDOM and S has ORDSET +--R complexNumericIfCan : Expression(Complex(S)) -> Union(Complex(Float),"failed") if S has INTDOM and S has ORDSET +--R complexNumericIfCan : (Expression(Complex(S)),PositiveInteger) -> Union(Complex(Float),"failed") if S has INTDOM and S has ORDSET +--R numeric : (S,PositiveInteger) -> Float +--R numeric : Polynomial(S) -> Float if S has RING +--R numeric : (Polynomial(S),PositiveInteger) -> Float if S has RING +--R numeric : Fraction(Polynomial(S)) -> Float if S has INTDOM +--R numeric : (Fraction(Polynomial(S)),PositiveInteger) -> Float if S has INTDOM +--R numeric : Expression(S) -> Float if S has INTDOM and S has ORDSET +--R numeric : (Expression(S),PositiveInteger) -> Float if S has INTDOM and S has ORDSET +--R numericIfCan : Polynomial(S) -> Union(Float,"failed") if S has RING +--R numericIfCan : (Polynomial(S),PositiveInteger) -> Union(Float,"failed") if S has RING +--R numericIfCan : Fraction(Polynomial(S)) -> Union(Float,"failed") if S has INTDOM +--R numericIfCan : (Fraction(Polynomial(S)),PositiveInteger) -> Union(Float,"failed") if S has INTDOM +--R numericIfCan : Expression(S) -> Union(Float,"failed") if S has INTDOM and S has ORDSET +--R numericIfCan : (Expression(S),PositiveInteger) -> Union(Float,"failed") if S has INTDOM and S has ORDSET +--R --E 1 )spool @@ -143958,6 +147623,20 @@ Numeric(S:ConvertibleTo Float): with --S 1 of 1 )show NumericalOrdinaryDifferentialEquations +--R +--R NumericalOrdinaryDifferentialEquations is a package constructor +--R Abbreviation for NumericalOrdinaryDifferentialEquations is NUMODE +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for NUMODE +--R +--R------------------------------- Operations -------------------------------- +--R rk4 : (Vector(Float),Integer,Float,Float,((Vector(Float),Vector(Float),Float) -> Void)) -> Void +--R rk4 : (Vector(Float),Integer,Float,Float,((Vector(Float),Vector(Float),Float) -> Void),Vector(Float),Vector(Float),Vector(Float),Vector(Float)) -> Void +--R rk4a : (Vector(Float),Integer,Float,Float,Float,Float,Integer,((Vector(Float),Vector(Float),Float) -> Void)) -> Void +--R rk4f : (Vector(Float),Integer,Float,Float,Integer,((Vector(Float),Vector(Float),Float) -> Void)) -> Void +--R rk4qc : (Vector(Float),Integer,Float,Record(try: Float,did: Float,next: Float),Float,Vector(Float),((Vector(Float),Vector(Float),Float) -> Void)) -> Void +--R rk4qc : (Vector(Float),Integer,Float,Record(try: Float,did: Float,next: Float),Float,Vector(Float),((Vector(Float),Vector(Float),Float) -> Void),Vector(Float),Vector(Float),Vector(Float),Vector(Float),Vector(Float),Vector(Float),Vector(Float)) -> Void +--R --E 1 )spool @@ -144479,6 +148158,23 @@ NumericalOrdinaryDifferentialEquations(): Exports == Implementation where --S 1 of 1 )show NumericalQuadrature +--R +--R NumericalQuadrature is a package constructor +--R Abbreviation for NumericalQuadrature is NUMQUAD +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for NUMQUAD +--R +--R------------------------------- Operations -------------------------------- +--R aromberg : ((Float -> Float),Float,Float,Float,Float,Integer,Integer,Integer) -> Record(value: Float,error: Float,totalpts: Integer,success: Boolean) +--R asimpson : ((Float -> Float),Float,Float,Float,Float,Integer,Integer,Integer) -> Record(value: Float,error: Float,totalpts: Integer,success: Boolean) +--R atrapezoidal : ((Float -> Float),Float,Float,Float,Float,Integer,Integer,Integer) -> Record(value: Float,error: Float,totalpts: Integer,success: Boolean) +--R romberg : ((Float -> Float),Float,Float,Float,Float,Integer,Integer) -> Record(value: Float,error: Float,totalpts: Integer,success: Boolean) +--R rombergo : ((Float -> Float),Float,Float,Float,Float,Integer,Integer) -> Record(value: Float,error: Float,totalpts: Integer,success: Boolean) +--R simpson : ((Float -> Float),Float,Float,Float,Float,Integer,Integer) -> Record(value: Float,error: Float,totalpts: Integer,success: Boolean) +--R simpsono : ((Float -> Float),Float,Float,Float,Float,Integer,Integer) -> Record(value: Float,error: Float,totalpts: Integer,success: Boolean) +--R trapezoidal : ((Float -> Float),Float,Float,Float,Float,Integer,Integer) -> Record(value: Float,error: Float,totalpts: Integer,success: Boolean) +--R trapezoidalo : ((Float -> Float),Float,Float,Float,Float,Integer,Integer) -> Record(value: Float,error: Float,totalpts: Integer,success: Boolean) +--R --E 1 )spool @@ -145132,6 +148828,18 @@ NumericalQuadrature(): Exports == Implementation where --S 1 of 1 )show NumericComplexEigenPackage +--R +--R NumericComplexEigenPackage(Par: Join(Field,OrderedRing)) is a package constructor +--R Abbreviation for NumericComplexEigenPackage is NCEP +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for NCEP +--R +--R------------------------------- Operations -------------------------------- +--R characteristicPolynomial : Matrix(Complex(Fraction(Integer))) -> Polynomial(Complex(Fraction(Integer))) +--R characteristicPolynomial : (Matrix(Complex(Fraction(Integer))),Symbol) -> Polynomial(Complex(Fraction(Integer))) +--R complexEigenvalues : (Matrix(Complex(Fraction(Integer))),Par) -> List(Complex(Par)) +--R complexEigenvectors : (Matrix(Complex(Fraction(Integer))),Par) -> List(Record(outval: Complex(Par),outmult: Integer,outvect: List(Matrix(Complex(Par))))) +--R --E 1 )spool @@ -145254,6 +148962,15 @@ NumericComplexEigenPackage(Par) : C == T --S 1 of 1 )show NumericContinuedFraction +--R +--R NumericContinuedFraction(F: FloatingPointSystem) is a package constructor +--R Abbreviation for NumericContinuedFraction is NCNTFRAC +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for NCNTFRAC +--R +--R------------------------------- Operations -------------------------------- +--R continuedFraction : F -> ContinuedFraction(Integer) +--R --E 1 )spool @@ -145332,6 +149049,18 @@ NumericContinuedFraction(F): Exports == Implementation where --S 1 of 1 )show NumericRealEigenPackage +--R +--R NumericRealEigenPackage(Par: Join(Field,OrderedRing)) is a package constructor +--R Abbreviation for NumericRealEigenPackage is NREP +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for NREP +--R +--R------------------------------- Operations -------------------------------- +--R characteristicPolynomial : Matrix(Fraction(Integer)) -> Polynomial(Fraction(Integer)) +--R characteristicPolynomial : (Matrix(Fraction(Integer)),Symbol) -> Polynomial(Fraction(Integer)) +--R realEigenvalues : (Matrix(Fraction(Integer)),Par) -> List(Par) +--R realEigenvectors : (Matrix(Fraction(Integer)),Par) -> List(Record(outval: Par,outmult: Integer,outvect: List(Matrix(Par)))) +--R --E 1 )spool @@ -145452,6 +149181,15 @@ NumericRealEigenPackage(Par) : C == T --S 1 of 1 )show NumericTubePlot +--R +--R NumericTubePlot(Curve: PlottableSpaceCurveCategory) is a package constructor +--R Abbreviation for NumericTubePlot is NUMTUBE +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for NUMTUBE +--R +--R------------------------------- Operations -------------------------------- +--R tube : (Curve,DoubleFloat,Integer) -> TubePlot(Curve) +--R --E 1 )spool @@ -145599,6 +149337,15 @@ NumericTubePlot(Curve): Exports == Implementation where --S 1 of 1 )show OctonionCategoryFunctions2 +--R +--R OctonionCategoryFunctions2(OR: OctonionCategory(R),R: CommutativeRing,OS: OctonionCategory(S),S: CommutativeRing) is a package constructor +--R Abbreviation for OctonionCategoryFunctions2 is OCTCT2 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for OCTCT2 +--R +--R------------------------------- Operations -------------------------------- +--R map : ((R -> S),OR) -> OS +--R --E 1 )spool @@ -145667,6 +149414,16 @@ OctonionCategoryFunctions2(OR,R,OS,S) : Exports == --S 1 of 1 )show ODEIntegration +--R +--R ODEIntegration(R: Join(OrderedSet,EuclideanDomain,RetractableTo(Integer),LinearlyExplicitRingOver(Integer),CharacteristicZero),F: Join(AlgebraicallyClosedFunctionSpace(R),TranscendentalFunctionCategory,PrimitiveFunctionCategory)) is a package constructor +--R Abbreviation for ODEIntegration is ODEINT +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for ODEINT +--R +--R------------------------------- Operations -------------------------------- +--R diff : Symbol -> (F -> F) expint : (F,Symbol) -> F +--R int : (F,Symbol) -> F +--R --E 1 )spool @@ -145805,6 +149562,18 @@ ODEIntegration(R, F): Exports == Implementation where --S 1 of 1 )show ODETools +--R +--R ODETools(F: Field,LODO: LinearOrdinaryDifferentialOperatorCategory(F)) is a package constructor +--R Abbreviation for ODETools is ODETOOLS +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for ODETOOLS +--R +--R------------------------------- Operations -------------------------------- +--R particularSolution : (LODO,F,List(F),(F -> F)) -> Union(F,"failed") +--R variationOfParameters : (LODO,F,List(F)) -> Union(Vector(F),"failed") +--R wronskianMatrix : List(F) -> Matrix(F) +--R wronskianMatrix : (List(F),NonNegativeInteger) -> Matrix(F) +--R --E 1 )spool @@ -145917,6 +149686,17 @@ ODETools(F, LODO): Exports == Implementation where --S 1 of 1 )show OneDimensionalArrayFunctions2 +--R +--R OneDimensionalArrayFunctions2(A: Type,B: Type) is a package constructor +--R Abbreviation for OneDimensionalArrayFunctions2 is ARRAY12 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for ARRAY12 +--R +--R------------------------------- Operations -------------------------------- +--R map : ((A -> B),OneDimensionalArray(A)) -> OneDimensionalArray(B) +--R reduce : (((A,B) -> B),OneDimensionalArray(A),B) -> B +--R scan : (((A,B) -> B),OneDimensionalArray(A),B) -> OneDimensionalArray(B) +--R --E 1 )spool @@ -146014,6 +149794,16 @@ OneDimensionalArrayFunctions2(A, B): Exports == Implementation where --S 1 of 1 )show OnePointCompletionFunctions2 +--R +--R OnePointCompletionFunctions2(R: SetCategory,S: SetCategory) is a package constructor +--R Abbreviation for OnePointCompletionFunctions2 is ONECOMP2 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for ONECOMP2 +--R +--R------------------------------- Operations -------------------------------- +--R map : ((R -> S),OnePointCompletion(R)) -> OnePointCompletion(S) +--R map : ((R -> S),OnePointCompletion(R),OnePointCompletion(S)) -> OnePointCompletion(S) +--R --E 1 )spool @@ -146086,6 +149876,20 @@ OnePointCompletionFunctions2(R, S): Exports == Implementation where --S 1 of 1 )show OpenMathPackage +--R +--R OpenMathPackage is a package constructor +--R Abbreviation for OpenMathPackage is OMPKG +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for OMPKG +--R +--R------------------------------- Operations -------------------------------- +--R OMlistCDs : () -> List(String) OMread : OpenMathDevice -> Any +--R OMreadFile : String -> Any OMreadStr : String -> Any +--R OMsupportsCD? : String -> Boolean +--R OMlistSymbols : String -> List(String) +--R OMsupportsSymbol? : (String,String) -> Boolean +--R OMunhandledSymbol : (String,String) -> Exit +--R --E 1 )spool @@ -146206,6 +150010,17 @@ OpenMathPackage(): with --S 1 of 1 )show OpenMathServerPackage +--R +--R OpenMathServerPackage is a package constructor +--R Abbreviation for OpenMathServerPackage is OMSERVER +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for OMSERVER +--R +--R------------------------------- Operations -------------------------------- +--R OMreceive : OpenMathConnection -> Any +--R OMsend : (OpenMathConnection,Any) -> Void +--R OMserve : (SingleInteger,SingleInteger) -> Void +--R --E 1 )spool @@ -146312,6 +150127,15 @@ OpenMathServerPackage(): with --S 1 of 1 )show OperationsQuery +--R +--R OperationsQuery is a package constructor +--R Abbreviation for OperationsQuery is OPQUERY +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for OPQUERY +--R +--R------------------------------- Operations -------------------------------- +--R getDatabase : String -> Database(IndexCard) +--R --E 1 )spool @@ -146367,6 +150191,16 @@ OperationsQuery(): Exports == Implementation where --S 1 of 1 )show OrderedCompletionFunctions2 +--R +--R OrderedCompletionFunctions2(R: SetCategory,S: SetCategory) is a package constructor +--R Abbreviation for OrderedCompletionFunctions2 is ORDCOMP2 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for ORDCOMP2 +--R +--R------------------------------- Operations -------------------------------- +--R map : ((R -> S),OrderedCompletion(R)) -> OrderedCompletion(S) +--R map : ((R -> S),OrderedCompletion(R),OrderedCompletion(S),OrderedCompletion(S)) -> OrderedCompletion(S) +--R --E 1 )spool @@ -146442,6 +150276,17 @@ OrderedCompletionFunctions2(R, S): Exports == Implementation where --S 1 of 1 )show OrderingFunctions +--R +--R OrderingFunctions(dim: NonNegativeInteger,S: OrderedAbelianMonoid) is a package constructor +--R Abbreviation for OrderingFunctions is ORDFUNS +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for ORDFUNS +--R +--R------------------------------- Operations -------------------------------- +--R pureLex : (Vector(S),Vector(S)) -> Boolean +--R reverseLex : (Vector(S),Vector(S)) -> Boolean +--R totalLex : (Vector(S),Vector(S)) -> Boolean +--R --E 1 )spool @@ -146551,6 +150396,20 @@ OrderingFunctions(dim,S) : T == C where --S 1 of 1 )show OrthogonalPolynomialFunctions +--R +--R OrthogonalPolynomialFunctions(R: CommutativeRing) is a package constructor +--R Abbreviation for OrthogonalPolynomialFunctions is ORTHPOL +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for ORTHPOL +--R +--R------------------------------- Operations -------------------------------- +--R chebyshevT : (NonNegativeInteger,R) -> R +--R chebyshevU : (NonNegativeInteger,R) -> R +--R hermiteH : (NonNegativeInteger,R) -> R +--R laguerreL : (NonNegativeInteger,R) -> R +--R laguerreL : (NonNegativeInteger,NonNegativeInteger,R) -> R +--R legendreP : (NonNegativeInteger,R) -> R if R has ALGEBRA(FRAC(INT)) +--R --E 1 )spool @@ -146697,6 +150556,16 @@ OrthogonalPolynomialFunctions(R: CommutativeRing): Exports == Impl where --S 1 of 1 )show OutputPackage +--R +--R OutputPackage is a package constructor +--R Abbreviation for OutputPackage is OUT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for OUT +--R +--R------------------------------- Operations -------------------------------- +--R output : String -> Void output : OutputForm -> Void +--R output : (String,OutputForm) -> Void outputList : List(Any) -> Void +--R --E 1 )spool @@ -147680,14 +151549,13 @@ PackageForAlgebraicFunctionFieldOverFiniteField(K,symb,BLMET):Exp == Impl where --R --R------------------------------- Operations -------------------------------- --R constant : PolyRing -> R firstExponent : PolyRing -> E +--R listAllMonoExp : Integer -> List(E) listVariable : () -> List(PolyRing) --R minimalForm : PolyRing -> PolyRing --R degOneCoef : (PolyRing,PositiveInteger) -> R --R degree : (PolyRing,Integer) -> NonNegativeInteger --R degreeOfMinimalForm : PolyRing -> NonNegativeInteger --R homogenize : (PolyRing,Integer) -> PolyRing --R listAllMono : NonNegativeInteger -> List(PolyRing) ---R listAllMonoExp : Integer -> List(E) ---R listVariable : () -> List(PolyRing) --R mapExponents : ((E -> E),PolyRing) -> PolyRing --R monomials : PolyRing -> List(PolyRing) --R replaceVarByOne : (PolyRing,Integer) -> PolyRing @@ -148056,6 +151924,16 @@ PackageForPoly(R,PolyRing,E,dim): public == private where --S 1 of 1 )show PadeApproximantPackage +--R +--R PadeApproximantPackage(R: Field,x: Symbol,pt: R) is a package constructor +--R Abbreviation for PadeApproximantPackage is PADEPAC +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for PADEPAC +--R +--R------------------------------- Operations -------------------------------- +--R pade : (NonNegativeInteger,NonNegativeInteger,UnivariateTaylorSeries(R,x,pt),UnivariateTaylorSeries(R,x,pt)) -> Union(Fraction(UnivariatePolynomial(x,R)),"failed") +--R pade : (NonNegativeInteger,NonNegativeInteger,UnivariateTaylorSeries(R,x,pt)) -> Union(Fraction(UnivariatePolynomial(x,R)),"failed") +--R --E 1 )spool @@ -148341,6 +152219,17 @@ PadeApproximants(R,PS,UP): Exports == Implementation where --S 1 of 1 )show PAdicWildFunctionFieldIntegralBasis +--R +--R PAdicWildFunctionFieldIntegralBasis(K: FiniteFieldCategory,R: UnivariatePolynomialCategory(K),UP: UnivariatePolynomialCategory(R),F: MonogenicAlgebra(R,UP)) is a package constructor +--R Abbreviation for PAdicWildFunctionFieldIntegralBasis is PWFFINTB +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for PWFFINTB +--R +--R------------------------------- Operations -------------------------------- +--R reducedDiscriminant : UP -> R +--R integralBasis : () -> Record(basis: Matrix(R),basisDen: R,basisInv: Matrix(R)) +--R localIntegralBasis : R -> Record(basis: Matrix(R),basisDen: R,basisInv: Matrix(R)) +--R --E 1 )spool @@ -148631,6 +152520,16 @@ PAdicWildFunctionFieldIntegralBasis(K,R,UP,F): Exports == Implementation where --S 1 of 1 )show ParadoxicalCombinatorsForStreams +--R +--R ParadoxicalCombinatorsForStreams(A: Type) is a package constructor +--R Abbreviation for ParadoxicalCombinatorsForStreams is YSTREAM +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for YSTREAM +--R +--R------------------------------- Operations -------------------------------- +--R Y : (Stream(A) -> Stream(A)) -> Stream(A) +--R Y : ((List(Stream(A)) -> List(Stream(A))),Integer) -> List(Stream(A)) +--R --E 1 )spool @@ -148711,6 +152610,48 @@ ParadoxicalCombinatorsForStreams(A):Exports == Implementation where --S 1 of 1 )show ParametricLinearEquations +--R +--R ParametricLinearEquations(R: Join(EuclideanDomain,CharacteristicZero),Var: Join(OrderedSet,ConvertibleTo(Symbol)),Expon: OrderedAbelianMonoidSup,GR: PolynomialCategory(R,Expon,Var)) is a package constructor +--R Abbreviation for ParametricLinearEquations is PLEQN +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for PLEQN +--R +--R------------------------------- Operations -------------------------------- +--R factorset : GR -> List(GR) inconsistent? : List(GR) -> Boolean +--R pr2dmp : Polynomial(R) -> GR sqfree : GR -> GR +--R B1solve : Record(mat: Matrix(Fraction(Polynomial(R))),vec: List(Fraction(Polynomial(R))),rank: NonNegativeInteger,rows: List(Integer),cols: List(Integer)) -> Record(partsol: Vector(Fraction(Polynomial(R))),basis: List(Vector(Fraction(Polynomial(R))))) +--R ParCond : (Matrix(GR),NonNegativeInteger) -> List(Record(det: GR,rows: List(Integer),cols: List(Integer))) +--R ParCondList : (Matrix(GR),NonNegativeInteger) -> List(Record(rank: NonNegativeInteger,eqns: List(Record(det: GR,rows: List(Integer),cols: List(Integer))),fgb: List(GR))) +--R bsolve : (Matrix(GR),List(Fraction(Polynomial(R))),NonNegativeInteger,String,Integer) -> Record(rgl: List(Record(eqzro: List(GR),neqzro: List(GR),wcond: List(Polynomial(R)),bsoln: Record(partsol: Vector(Fraction(Polynomial(R))),basis: List(Vector(Fraction(Polynomial(R))))))),rgsz: Integer) +--R dmp2rfi : GR -> Fraction(Polynomial(R)) +--R dmp2rfi : Matrix(GR) -> Matrix(Fraction(Polynomial(R))) +--R dmp2rfi : List(GR) -> List(Fraction(Polynomial(R))) +--R hasoln : (List(GR),List(GR)) -> Record(sysok: Boolean,z0: List(GR),n0: List(GR)) +--R inconsistent? : List(Polynomial(R)) -> Boolean +--R maxrank : List(Record(rank: NonNegativeInteger,eqns: List(Record(det: GR,rows: List(Integer),cols: List(Integer))),fgb: List(GR))) -> NonNegativeInteger +--R minrank : List(Record(rank: NonNegativeInteger,eqns: List(Record(det: GR,rows: List(Integer),cols: List(Integer))),fgb: List(GR))) -> NonNegativeInteger +--R minset : List(List(GR)) -> List(List(GR)) +--R nextSublist : (Integer,Integer) -> List(List(Integer)) +--R overset? : (List(GR),List(List(GR))) -> Boolean +--R psolve : (Matrix(GR),List(GR)) -> List(Record(eqzro: List(GR),neqzro: List(GR),wcond: List(Polynomial(R)),bsoln: Record(partsol: Vector(Fraction(Polynomial(R))),basis: List(Vector(Fraction(Polynomial(R))))))) +--R psolve : (Matrix(GR),List(Symbol)) -> List(Record(eqzro: List(GR),neqzro: List(GR),wcond: List(Polynomial(R)),bsoln: Record(partsol: Vector(Fraction(Polynomial(R))),basis: List(Vector(Fraction(Polynomial(R))))))) +--R psolve : Matrix(GR) -> List(Record(eqzro: List(GR),neqzro: List(GR),wcond: List(Polynomial(R)),bsoln: Record(partsol: Vector(Fraction(Polynomial(R))),basis: List(Vector(Fraction(Polynomial(R))))))) +--R psolve : (Matrix(GR),List(GR),PositiveInteger) -> List(Record(eqzro: List(GR),neqzro: List(GR),wcond: List(Polynomial(R)),bsoln: Record(partsol: Vector(Fraction(Polynomial(R))),basis: List(Vector(Fraction(Polynomial(R))))))) +--R psolve : (Matrix(GR),List(Symbol),PositiveInteger) -> List(Record(eqzro: List(GR),neqzro: List(GR),wcond: List(Polynomial(R)),bsoln: Record(partsol: Vector(Fraction(Polynomial(R))),basis: List(Vector(Fraction(Polynomial(R))))))) +--R psolve : (Matrix(GR),PositiveInteger) -> List(Record(eqzro: List(GR),neqzro: List(GR),wcond: List(Polynomial(R)),bsoln: Record(partsol: Vector(Fraction(Polynomial(R))),basis: List(Vector(Fraction(Polynomial(R))))))) +--R psolve : (Matrix(GR),List(GR),String) -> Integer +--R psolve : (Matrix(GR),List(Symbol),String) -> Integer +--R psolve : (Matrix(GR),String) -> Integer +--R psolve : (Matrix(GR),List(GR),PositiveInteger,String) -> Integer +--R psolve : (Matrix(GR),List(Symbol),PositiveInteger,String) -> Integer +--R psolve : (Matrix(GR),PositiveInteger,String) -> Integer +--R rdregime : String -> List(Record(eqzro: List(GR),neqzro: List(GR),wcond: List(Polynomial(R)),bsoln: Record(partsol: Vector(Fraction(Polynomial(R))),basis: List(Vector(Fraction(Polynomial(R))))))) +--R redmat : (Matrix(GR),List(GR)) -> Matrix(GR) +--R redpps : (Record(partsol: Vector(Fraction(Polynomial(R))),basis: List(Vector(Fraction(Polynomial(R))))),List(GR)) -> Record(partsol: Vector(Fraction(Polynomial(R))),basis: List(Vector(Fraction(Polynomial(R))))) +--R regime : (Record(det: GR,rows: List(Integer),cols: List(Integer)),Matrix(GR),List(Fraction(Polynomial(R))),List(List(GR)),NonNegativeInteger,NonNegativeInteger,Integer) -> Record(eqzro: List(GR),neqzro: List(GR),wcond: List(Polynomial(R)),bsoln: Record(partsol: Vector(Fraction(Polynomial(R))),basis: List(Vector(Fraction(Polynomial(R)))))) +--R se2rfi : List(Symbol) -> List(Fraction(Polynomial(R))) +--R wrregime : (List(Record(eqzro: List(GR),neqzro: List(GR),wcond: List(Polynomial(R)),bsoln: Record(partsol: Vector(Fraction(Polynomial(R))),basis: List(Vector(Fraction(Polynomial(R))))))),String) -> Integer +--R --E 1 )spool @@ -149431,6 +153372,15 @@ ParametricLinearEquations(R,Var,Expon,GR): --S 1 of 1 )show ParametricPlaneCurveFunctions2 +--R +--R ParametricPlaneCurveFunctions2(CF1: Type,CF2: Type) is a package constructor +--R Abbreviation for ParametricPlaneCurveFunctions2 is PARPC2 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for PARPC2 +--R +--R------------------------------- Operations -------------------------------- +--R map : ((CF1 -> CF2),ParametricPlaneCurve(CF1)) -> ParametricPlaneCurve(CF2) +--R --E 1 )spool @@ -149483,6 +153433,15 @@ ParametricPlaneCurveFunctions2(CF1: Type, CF2:Type): with --S 1 of 1 )show ParametricSpaceCurveFunctions2 +--R +--R ParametricSpaceCurveFunctions2(CF1: Type,CF2: Type) is a package constructor +--R Abbreviation for ParametricSpaceCurveFunctions2 is PARSC2 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for PARSC2 +--R +--R------------------------------- Operations -------------------------------- +--R map : ((CF1 -> CF2),ParametricSpaceCurve(CF1)) -> ParametricSpaceCurve(CF2) +--R --E 1 )spool @@ -149535,6 +153494,15 @@ ParametricSpaceCurveFunctions2(CF1: Type, CF2:Type): with --S 1 of 1 )show ParametricSurfaceFunctions2 +--R +--R ParametricSurfaceFunctions2(CF1: Type,CF2: Type) is a package constructor +--R Abbreviation for ParametricSurfaceFunctions2 is PARSU2 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for PARSU2 +--R +--R------------------------------- Operations -------------------------------- +--R map : ((CF1 -> CF2),ParametricSurface(CF1)) -> ParametricSurface(CF2) +--R --E 1 )spool @@ -149594,8 +153562,8 @@ ParametricSurfaceFunctions2(CF1: Type, CF2:Type): with --R Issue )edit bookvol10.4.pamphlet to see algebra source code for PARAMP --R --R------------------------------- Operations -------------------------------- +--R parametrize : (PolyRing,Plc) -> PCS --R parametrize : (PolyRing,List(PCS)) -> PCS ---R parametrize : (PolyRing,Plc) -> PCS --R parametrize : (PolyRing,PolyRing,Plc) -> PCS --R parametrize : (PolyRing,Plc,Integer) -> PCS --R @@ -149715,7 +153683,7 @@ ParametrizationPackage(K,symb,PolyRing,E,ProjPt,PCS,Plc):Exp == Impl where )set message auto off )clear all ---S 1 of 4 +--S 1 of 5 a:=x+1/(y+1) --R --R x y + x + 1 @@ -149724,7 +153692,7 @@ a:=x+1/(y+1) --R Type: Fraction(Polynomial(Integer)) --E 1 ---S 2 of 4 +--S 2 of 5 partialFraction(a,y)$PFRPAC(INT) --R --R 1 @@ -149733,7 +153701,7 @@ partialFraction(a,y)$PFRPAC(INT) --R Type: PartialFraction(UnivariatePolynomial(y,Fraction(Polynomial(Integer)))) --E 2 ---S 3 of 4 +--S 3 of 5 b:=y+1/(x+1) --R --R (x + 1)y + 1 @@ -149742,7 +153710,7 @@ b:=y+1/(x+1) --R Type: Fraction(Polynomial(Integer)) --E 3 ---S 4 of 4 +--S 4 of 5 partialFraction(b,x)$PFRPAC(INT) --R --R 1 @@ -149751,6 +153719,20 @@ partialFraction(b,x)$PFRPAC(INT) --R Type: PartialFraction(UnivariatePolynomial(x,Fraction(Polynomial(Integer)))) --E 4 +--S 5 of 5 +)show PartialFractionPackage +--R +--R PartialFractionPackage(R: Join(EuclideanDomain,CharacteristicZero)) is a package constructor +--R Abbreviation for PartialFractionPackage is PFRPAC +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for PFRPAC +--R +--R------------------------------- Operations -------------------------------- +--R partialFraction : (Fraction(Polynomial(R)),Symbol) -> Any +--R partialFraction : (Polynomial(R),Factored(Polynomial(R)),Symbol) -> Any +--R +--E 5 + )spool )lisp (bye) @@ -149877,6 +153859,24 @@ PartialFractionPackage(R): Cat == Capsule where --S 1 of 1 )show PartitionsAndPermutations +--R +--R PartitionsAndPermutations is a package constructor +--R Abbreviation for PartitionsAndPermutations is PARTPERM +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for PARTPERM +--R +--R------------------------------- Operations -------------------------------- +--R conjugate : List(Integer) -> List(Integer) +--R conjugates : Stream(List(Integer)) -> Stream(List(Integer)) +--R partitions : (Integer,Integer,Integer) -> Stream(List(Integer)) +--R partitions : Integer -> Stream(List(Integer)) +--R partitions : (Integer,Integer) -> Stream(List(Integer)) +--R permutations : Integer -> Stream(List(Integer)) +--R sequences : (List(Integer),List(Integer)) -> Stream(List(Integer)) +--R sequences : List(Integer) -> Stream(List(Integer)) +--R shuffle : (List(Integer),List(Integer)) -> Stream(List(Integer)) +--R shufflein : (List(Integer),Stream(List(Integer))) -> Stream(List(Integer)) +--R --E 1 )spool @@ -150036,6 +154036,21 @@ PartitionsAndPermutations: Exports == Implementation where --S 1 of 1 )show PatternFunctions1 +--R +--R PatternFunctions1(R: SetCategory,D: Type) is a package constructor +--R Abbreviation for PatternFunctions1 is PATTERN1 +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for PATTERN1 +--R +--R------------------------------- Operations -------------------------------- +--R badValues : Pattern(R) -> List(D) satisfy? : (D,Pattern(R)) -> Boolean +--R addBadValue : (Pattern(R),D) -> Pattern(R) +--R predicate : Pattern(R) -> (D -> Boolean) +--R satisfy? : (List(D),Pattern(R)) -> Boolean +--R suchThat : (Pattern(R),(D -> Boolean)) -> Pattern(R) +--R suchThat : (Pattern(R),List((D -> Boolean))) -> Pattern(R) +--R suchThat : (Pattern(R),List(Symbol),(List(D) -> Boolean)) -> Pattern(R) +--R --E 1 )spool @@ -150149,6 +154164,15 @@ PatternFunctions1(R:SetCategory, D:Type): with --S 1 of 1 )show PatternFunctions2 +--R +--R PatternFunctions2(R: SetCategory,S: SetCategory) is a package constructor +--R Abbreviation for PatternFunctions2 is PATTERN2 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for PATTERN2 +--R +--R------------------------------- Operations -------------------------------- +--R map : ((R -> S),Pattern(R)) -> Pattern(S) +--R --E 1 )spool @@ -150227,6 +154251,19 @@ PatternFunctions2(R:SetCategory, S:SetCategory): with --S 1 of 1 )show PatternMatch +--R +--R PatternMatch(Base: SetCategory,Subject: PatternMatchable(Base),Pat: ConvertibleTo(Pattern(Base))) is a package constructor +--R Abbreviation for PatternMatch is PATMATCH +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for PATMATCH +--R +--R------------------------------- Operations -------------------------------- +--R is? : (Subject,Pat) -> Boolean is? : (List(Subject),Pat) -> Boolean +--R Is : (List(Subject),Pat) -> PatternMatchListResult(Base,Subject,List(Subject)) +--R Is : (Subject,Pat) -> List(Equation(Subject)) if Subject has RETRACT(SYMBOL) +--R Is : (Subject,Pat) -> List(Equation(Polynomial(Subject))) if Subject has RING and not(has(Subject,RetractableTo(Symbol))) +--R Is : (Subject,Pat) -> PatternMatchResult(Base,Subject) if not(has(Subject,RetractableTo(Symbol))) and not(has(Subject,Ring)) +--R --E 1 )spool @@ -150348,6 +154385,18 @@ PatternMatch(Base, Subject, Pat): Exports == Implementation where --S 1 of 1 )show PatternMatchAssertions +--R +--R PatternMatchAssertions is a package constructor +--R Abbreviation for PatternMatchAssertions is PMASS +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for PMASS +--R +--R------------------------------- Operations -------------------------------- +--R assert : (Symbol,String) -> Expression(Integer) +--R constant : Symbol -> Expression(Integer) +--R multiple : Symbol -> Expression(Integer) +--R optional : Symbol -> Expression(Integer) +--R --E 1 )spool @@ -150430,6 +154479,15 @@ PatternMatchAssertions(): Exports == Implementation where --S 1 of 1 )show PatternMatchFunctionSpace +--R +--R PatternMatchFunctionSpace(S: SetCategory,R: Join(IntegralDomain,OrderedSet,PatternMatchable(S)),F: Join(FunctionSpace(R),ConvertibleTo(Pattern(S)),PatternMatchable(S),RetractableTo(Kernel($)))) is a package constructor +--R Abbreviation for PatternMatchFunctionSpace is PMFS +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for PMFS +--R +--R------------------------------- Operations -------------------------------- +--R patternMatch : (F,Pattern(S),PatternMatchResult(S,F)) -> PatternMatchResult(S,F) +--R --E 1 )spool @@ -150543,6 +154601,15 @@ PatternMatchFunctionSpace(S, R, F): Exports== Implementation where --S 1 of 1 )show PatternMatchIntegerNumberSystem +--R +--R PatternMatchIntegerNumberSystem(I: IntegerNumberSystem) is a package constructor +--R Abbreviation for PatternMatchIntegerNumberSystem is PMINS +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for PMINS +--R +--R------------------------------- Operations -------------------------------- +--R patternMatch : (I,Pattern(Integer),PatternMatchResult(Integer,I)) -> PatternMatchResult(Integer,I) +--R --E 1 )spool @@ -150662,6 +154729,18 @@ PatternMatchIntegerNumberSystem(I:IntegerNumberSystem): with --S 1 of 1 )show PatternMatchIntegration +--R +--R PatternMatchIntegration(R: Join(OrderedSet,RetractableTo(Integer),GcdDomain,LinearlyExplicitRingOver(Integer)),F: Join(AlgebraicallyClosedField,TranscendentalFunctionCategory,FunctionSpace(R))) is a package constructor +--R Abbreviation for PatternMatchIntegration is INTPM +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for INTPM +--R +--R------------------------------- Operations -------------------------------- +--R pmComplexintegrate : (F,Symbol) -> Union(Record(special: F,integrand: F),"failed") if F has LFCAT and R has KONVERT(PATTERN(INT)) and R has PATMAB(INT) +--R pmintegrate : (F,Symbol) -> Union(Record(special: F,integrand: F),"failed") if F has LFCAT and R has KONVERT(PATTERN(INT)) and R has PATMAB(INT) +--R pmintegrate : (F,Symbol,OrderedCompletion(F),OrderedCompletion(F)) -> Union(F,"failed") if F has SPFCAT and R has KONVERT(PATTERN(INT)) and R has PATMAB(INT) +--R splitConstant : (F,Symbol) -> Record(const: F,nconst: F) +--R --E 1 )spool @@ -151033,6 +155112,15 @@ PatternMatchIntegration(R, F): Exports == Implementation where --S 1 of 1 )show PatternMatchKernel +--R +--R PatternMatchKernel(S: SetCategory,E: Join(OrderedSet,RetractableTo(Kernel($)),ConvertibleTo(Pattern(S)),PatternMatchable(S))) is a package constructor +--R Abbreviation for PatternMatchKernel is PMKERNEL +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for PMKERNEL +--R +--R------------------------------- Operations -------------------------------- +--R patternMatch : (Kernel(E),Pattern(S),PatternMatchResult(S,E)) -> PatternMatchResult(S,E) +--R --E 1 )spool @@ -151168,6 +155256,15 @@ PatternMatchKernel(S, E): Exports == Implementation where --S 1 of 1 )show PatternMatchListAggregate +--R +--R PatternMatchListAggregate(S: SetCategory,R: PatternMatchable(S),L: ListAggregate(R)) is a package constructor +--R Abbreviation for PatternMatchListAggregate is PMLSAGG +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for PMLSAGG +--R +--R------------------------------- Operations -------------------------------- +--R patternMatch : (L,Pattern(S),PatternMatchListResult(S,R,L)) -> PatternMatchListResult(S,R,L) +--R --E 1 )spool @@ -151252,6 +155349,16 @@ PatternMatchListAggregate(S, R, L): Exports == Implementation where --S 1 of 1 )show PatternMatchPolynomialCategory +--R +--R PatternMatchPolynomialCategory(S: SetCategory,E: OrderedAbelianMonoidSup,V: OrderedSet,R: Join(Ring,OrderedSet,PatternMatchable(S)),P: Join(PolynomialCategory(R,E,V),ConvertibleTo(Pattern(S)))) is a package constructor +--R Abbreviation for PatternMatchPolynomialCategory is PMPLCAT +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for PMPLCAT +--R +--R------------------------------- Operations -------------------------------- +--R patternMatch : (P,Pattern(S),PatternMatchResult(S,P),((V,Pattern(S),PatternMatchResult(S,P)) -> PatternMatchResult(S,P))) -> PatternMatchResult(S,P) +--R patternMatch : (P,Pattern(S),PatternMatchResult(S,P)) -> PatternMatchResult(S,P) if V has PATMAB(S) +--R --E 1 )spool @@ -151374,6 +155481,16 @@ PatternMatchPolynomialCategory(S,E,V,R,P):Exports== Implementation where --S 1 of 1 )show PatternMatchPushDown +--R +--R PatternMatchPushDown(S: SetCategory,A: PatternMatchable(S),B: Join(SetCategory,RetractableTo(A))) is a package constructor +--R Abbreviation for PatternMatchPushDown is PMDOWN +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for PMDOWN +--R +--R------------------------------- Operations -------------------------------- +--R fixPredicate : (B -> Boolean) -> (A -> Boolean) +--R patternMatch : (A,Pattern(S),PatternMatchResult(S,B)) -> PatternMatchResult(S,B) +--R --E 1 )spool @@ -151515,6 +155632,15 @@ PatternMatchPushDown(S, A, B): Exports == Implementation where --S 1 of 1 )show PatternMatchQuotientFieldCategory +--R +--R PatternMatchQuotientFieldCategory(S: SetCategory,R: Join(IntegralDomain,PatternMatchable(S),ConvertibleTo(Pattern(S))),Q: QuotientFieldCategory(R)) is a package constructor +--R Abbreviation for PatternMatchQuotientFieldCategory is PMQFCAT +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for PMQFCAT +--R +--R------------------------------- Operations -------------------------------- +--R patternMatch : (Q,Pattern(S),PatternMatchResult(S,Q)) -> PatternMatchResult(S,Q) +--R --E 1 )spool @@ -151591,6 +155717,15 @@ PatternMatchQuotientFieldCategory(S,R,Q):Exports == Implementation where --S 1 of 1 )show PatternMatchResultFunctions2 +--R +--R PatternMatchResultFunctions2(R: SetCategory,A: SetCategory,B: SetCategory) is a package constructor +--R Abbreviation for PatternMatchResultFunctions2 is PATRES2 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for PATRES2 +--R +--R------------------------------- Operations -------------------------------- +--R map : ((A -> B),PatternMatchResult(R,A)) -> PatternMatchResult(R,B) +--R --E 1 )spool @@ -151657,6 +155792,15 @@ PatternMatchResultFunctions2(R, A, B): Exports == Implementation where --S 1 of 1 )show PatternMatchSymbol +--R +--R PatternMatchSymbol(S: SetCategory) is a package constructor +--R Abbreviation for PatternMatchSymbol is PMSYM +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for PMSYM +--R +--R------------------------------- Operations -------------------------------- +--R patternMatch : (Symbol,Pattern(S),PatternMatchResult(S,Symbol)) -> PatternMatchResult(S,Symbol) +--R --E 1 )spool @@ -151723,6 +155867,16 @@ PatternMatchSymbol(S:SetCategory): with --S 1 of 1 )show PatternMatchTools +--R +--R PatternMatchTools(S: SetCategory,R: Join(Ring,OrderedSet),P: Join(Ring,ConvertibleTo(Pattern(S)),RetractableTo(R))) is a package constructor +--R Abbreviation for PatternMatchTools is PMTOOLS +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for PMTOOLS +--R +--R------------------------------- Operations -------------------------------- +--R patternMatch : (List(P),List(Pattern(S)),(List(P) -> P),PatternMatchResult(S,P),((P,Pattern(S),PatternMatchResult(S,P)) -> PatternMatchResult(S,P))) -> PatternMatchResult(S,P) +--R patternMatchTimes : (List(P),List(Pattern(S)),PatternMatchResult(S,P),((P,Pattern(S),PatternMatchResult(S,P)) -> PatternMatchResult(S,P))) -> PatternMatchResult(S,P) +--R --E 1 )spool @@ -151926,7 +156080,8 @@ PatternMatchTools(S, R, P): Exports == Implementation where )set message test on )set message auto off )clear all ---S 1 of 3 + +--S 1 of 4 kn n == r : MATRIX INT := new(n,n,1) for i in 1..n repeat @@ -151936,7 +156091,7 @@ kn n == --R Type: Void --E 1 ---S 2 of 3 +--S 2 of 4 permanent(kn(5) :: SQMATRIX(5,INT)) --R --R Compiling function kn with type PositiveInteger -> Matrix(Integer) @@ -151945,7 +156100,7 @@ permanent(kn(5) :: SQMATRIX(5,INT)) --R Type: PositiveInteger --E 2 ---S 3 of 3 +--S 3 of 4 [permanent(kn(n) :: SQMATRIX(n,INT)) for n in 1..13] --R --R Cannot compile conversion for types involving local variables. In @@ -151957,6 +156112,22 @@ permanent(kn(5) :: SQMATRIX(5,INT)) --R [0,1,2,9,44,265,1854,14833,133496,1334961,14684570,176214841,2290792932] --R Type: List(NonNegativeInteger) --E 3 + +--S 4 of 4 +)show Permanent +--R +--R Permanent(n: PositiveInteger,R)where +--R R: Ringwith +--R commutative("*") is a package constructor +--R Abbreviation for Permanent is PERMAN +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for PERMAN +--R +--R------------------------------- Operations -------------------------------- +--R permanent : SquareMatrix(n,R) -> R +--R +--E 4 + )spool )lisp (bye) \end{chunk} @@ -152202,6 +156373,38 @@ Permanent(n : PositiveInteger, R : Ring with commutative("*")): --S 1 of 1 )show PermutationGroupExamples +--R +--R PermutationGroupExamples is a package constructor +--R Abbreviation for PermutationGroupExamples is PGE +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for PGE +--R +--R------------------------------- Operations -------------------------------- +--R abelianGroup : List(PositiveInteger) -> PermutationGroup(Integer) +--R alternatingGroup : PositiveInteger -> PermutationGroup(Integer) +--R alternatingGroup : List(Integer) -> PermutationGroup(Integer) +--R cyclicGroup : PositiveInteger -> PermutationGroup(Integer) +--R cyclicGroup : List(Integer) -> PermutationGroup(Integer) +--R dihedralGroup : PositiveInteger -> PermutationGroup(Integer) +--R dihedralGroup : List(Integer) -> PermutationGroup(Integer) +--R janko2 : List(Integer) -> PermutationGroup(Integer) +--R janko2 : () -> PermutationGroup(Integer) +--R mathieu11 : List(Integer) -> PermutationGroup(Integer) +--R mathieu11 : () -> PermutationGroup(Integer) +--R mathieu12 : List(Integer) -> PermutationGroup(Integer) +--R mathieu12 : () -> PermutationGroup(Integer) +--R mathieu22 : List(Integer) -> PermutationGroup(Integer) +--R mathieu22 : () -> PermutationGroup(Integer) +--R mathieu23 : List(Integer) -> PermutationGroup(Integer) +--R mathieu23 : () -> PermutationGroup(Integer) +--R mathieu24 : List(Integer) -> PermutationGroup(Integer) +--R mathieu24 : () -> PermutationGroup(Integer) +--R rubiksGroup : () -> PermutationGroup(Integer) +--R symmetricGroup : PositiveInteger -> PermutationGroup(Integer) +--R symmetricGroup : List(Integer) -> PermutationGroup(Integer) +--R youngGroup : List(Integer) -> PermutationGroup(Integer) +--R youngGroup : Partition -> PermutationGroup(Integer) +--R --E 1 )spool @@ -152629,6 +156832,15 @@ PermutationGroupExamples():public == private where --S 1 of 1 )show PiCoercions +--R +--R PiCoercions(R: Join(OrderedSet,IntegralDomain)) is a package constructor +--R Abbreviation for PiCoercions is PICOERCE +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for PICOERCE +--R +--R------------------------------- Operations -------------------------------- +--R coerce : Pi -> Expression(R) +--R --E 1 )spool @@ -152695,6 +156907,18 @@ PiCoercions(R:Join(OrderedSet, IntegralDomain)): with --S 1 of 1 )show PlotFunctions1 +--R +--R PlotFunctions1(S: ConvertibleTo(InputForm)) is a package constructor +--R Abbreviation for PlotFunctions1 is PLOT1 +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for PLOT1 +--R +--R------------------------------- Operations -------------------------------- +--R plotPolar : (S,Symbol) -> Plot +--R plot : (S,Symbol,Segment(DoubleFloat)) -> Plot +--R plot : (S,S,Symbol,Segment(DoubleFloat)) -> Plot +--R plotPolar : (S,Symbol,Segment(DoubleFloat)) -> Plot +--R --E 1 )spool @@ -152771,6 +156995,15 @@ PlotFunctions1(S:ConvertibleTo InputForm): with --S 1 of 1 )show PlotTools +--R +--R PlotTools is a package constructor +--R Abbreviation for PlotTools is PLOTTOOL +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for PLOTTOOL +--R +--R------------------------------- Operations -------------------------------- +--R calcRanges : List(List(Point(DoubleFloat))) -> List(Segment(DoubleFloat)) +--R --E 1 )spool @@ -153106,6 +157339,15 @@ ProjectiveAlgebraicSetPackage(K,symb,PolyRing,E,ProjPt):_ --S 1 of 1 )show PointFunctions2 +--R +--R PointFunctions2(R1: Ring,R2: Ring) is a package constructor +--R Abbreviation for PointFunctions2 is PTFUNC2 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for PTFUNC2 +--R +--R------------------------------- Operations -------------------------------- +--R map : ((R1 -> R2),Point(R1)) -> Point(R2) +--R --E 1 )spool @@ -153167,6 +157409,19 @@ PointFunctions2(R1:Ring,R2:Ring):Exports == Implementation where --S 1 of 1 )show PointPackage +--R +--R PointPackage(R: Ring) is a package constructor +--R Abbreviation for PointPackage is PTPACK +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for PTPACK +--R +--R------------------------------- Operations -------------------------------- +--R color : Point(R) -> R hue : Point(R) -> R +--R phiCoord : Point(R) -> R rCoord : Point(R) -> R +--R shade : Point(R) -> R thetaCoord : Point(R) -> R +--R xCoord : Point(R) -> R yCoord : Point(R) -> R +--R zCoord : Point(R) -> R +--R --E 1 )spool @@ -153306,6 +157561,17 @@ PointPackage(R:Ring):Exports == Implementation where --S 1 of 1 )show PointsOfFiniteOrder +--R +--R PointsOfFiniteOrder(R0: Join(OrderedSet,IntegralDomain,RetractableTo(Integer)),F: FunctionSpace(R0),UP: UnivariatePolynomialCategory(F),UPUP: UnivariatePolynomialCategory(Fraction(UP)),R: FunctionFieldCategory(F,UP,UPUP)) is a package constructor +--R Abbreviation for PointsOfFiniteOrder is PFO +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for PFO +--R +--R------------------------------- Operations -------------------------------- +--R order : FiniteDivisor(F,UP,UPUP,R) -> Union(NonNegativeInteger,"failed") +--R torsion? : FiniteDivisor(F,UP,UPUP,R) -> Boolean +--R torsionIfCan : FiniteDivisor(F,UP,UPUP,R) -> Union(Record(order: NonNegativeInteger,function: R),"failed") +--R --E 1 )spool @@ -153630,6 +157896,17 @@ PointsOfFiniteOrder(R0, F, UP, UPUP, R): Exports == Implementation where --S 1 of 1 )show PointsOfFiniteOrderRational +--R +--R PointsOfFiniteOrderRational(UP: UnivariatePolynomialCategory(Fraction(Integer)),UPUP: UnivariatePolynomialCategory(Fraction(UP)),R: FunctionFieldCategory(Fraction(Integer),UP,UPUP)) is a package constructor +--R Abbreviation for PointsOfFiniteOrderRational is PFOQ +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for PFOQ +--R +--R------------------------------- Operations -------------------------------- +--R order : FiniteDivisor(Fraction(Integer),UP,UPUP,R) -> Union(NonNegativeInteger,"failed") +--R torsion? : FiniteDivisor(Fraction(Integer),UP,UPUP,R) -> Boolean +--R torsionIfCan : FiniteDivisor(Fraction(Integer),UP,UPUP,R) -> Union(Record(order: NonNegativeInteger,function: R),"failed") +--R --E 1 )spool @@ -153754,6 +158031,19 @@ PointsOfFiniteOrderRational(UP, UPUP, R): Exports == Implementation where --S 1 of 1 )show PointsOfFiniteOrderTools +--R +--R PointsOfFiniteOrderTools(UP: UnivariatePolynomialCategory(Fraction(Integer)),UPUP: UnivariatePolynomialCategory(Fraction(UP))) is a package constructor +--R Abbreviation for PointsOfFiniteOrderTools is PFOTOOLS +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for PFOTOOLS +--R +--R------------------------------- Operations -------------------------------- +--R badNum : UPUP -> Integer doubleDisc : UPUP -> Integer +--R polyred : UPUP -> UPUP +--R badNum : UP -> Record(den: Integer,gcdnum: Integer) +--R getGoodPrime : Integer -> PositiveInteger +--R mix : List(Record(den: Integer,gcdnum: Integer)) -> Integer +--R --E 1 )spool @@ -154009,6 +158299,20 @@ PolynomialPackageForCurve(K,PolyRing,E,dim,ProjPt):Exp == Impl where --S 1 of 1 )show PolToPol +--R +--R PolToPol(lv: List(Symbol),R: Ring) is a package constructor +--R Abbreviation for PolToPol is POLTOPOL +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for POLTOPOL +--R +--R------------------------------- Operations -------------------------------- +--R dmpToHdmp : DistributedMultivariatePolynomial(lv,R) -> HomogeneousDistributedMultivariatePolynomial(lv,R) +--R dmpToP : DistributedMultivariatePolynomial(lv,R) -> Polynomial(R) +--R hdmpToDmp : HomogeneousDistributedMultivariatePolynomial(lv,R) -> DistributedMultivariatePolynomial(lv,R) +--R hdmpToP : HomogeneousDistributedMultivariatePolynomial(lv,R) -> Polynomial(R) +--R pToDmp : Polynomial(R) -> DistributedMultivariatePolynomial(lv,R) +--R pToHdmp : Polynomial(R) -> HomogeneousDistributedMultivariatePolynomial(lv,R) +--R --E 1 )spool @@ -154128,6 +158432,16 @@ PolToPol(lv,R) : C == T --S 1 of 1 )show PolyGroebner +--R +--R PolyGroebner(F: GcdDomain) is a package constructor +--R Abbreviation for PolyGroebner is PGROEB +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for PGROEB +--R +--R------------------------------- Operations -------------------------------- +--R lexGroebner : (List(Polynomial(F)),List(Symbol)) -> List(Polynomial(F)) +--R totalGroebner : (List(Polynomial(F)),List(Symbol)) -> List(Polynomial(F)) +--R --E 1 )spool @@ -154239,6 +158553,16 @@ PolyGroebner(F) : C == T --S 1 of 1 )show PolynomialAN2Expression +--R +--R PolynomialAN2Expression is a package constructor +--R Abbreviation for PolynomialAN2Expression is PAN2EXPR +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for PAN2EXPR +--R +--R------------------------------- Operations -------------------------------- +--R coerce : Polynomial(AlgebraicNumber) -> Expression(Integer) +--R coerce : Fraction(Polynomial(AlgebraicNumber)) -> Expression(Integer) +--R --E 1 )spool @@ -154311,6 +158635,19 @@ PolynomialAN2Expression():Target == Implementation where --S 1 of 1 )show PolynomialCategoryLifting +--R +--R PolynomialCategoryLifting(E: OrderedAbelianMonoidSup,Vars: OrderedSet,R: Ring,P: PolynomialCategory(R,E,Vars),S)where +--R S: SetCategorywith +--R ?+? : (%,%) -> % +--R ?*? : (%,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % is a package constructor +--R Abbreviation for PolynomialCategoryLifting is POLYLIFT +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for POLYLIFT +--R +--R------------------------------- Operations -------------------------------- +--R map : ((Vars -> S),(R -> S),P) -> S +--R --E 1 )spool @@ -154393,6 +158730,27 @@ PolynomialCategoryLifting(E,Vars,R,P,S): Exports == Implementation where --S 1 of 1 )show PolynomialCategoryQuotientFunctions +--R +--R PolynomialCategoryQuotientFunctions(E: OrderedAbelianMonoidSup,V: OrderedSet,R: Ring,P: PolynomialCategory(R,E,V),F)where +--R F: Fieldwith +--R coerce : P -> % +--R numer : % -> P +--R denom : % -> P is a package constructor +--R Abbreviation for PolynomialCategoryQuotientFunctions is POLYCATQ +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for POLYCATQ +--R +--R------------------------------- Operations -------------------------------- +--R variables : F -> List(V) +--R isExpt : F -> Union(Record(var: V,exponent: Integer),"failed") +--R isPlus : F -> Union(List(F),"failed") +--R isPower : F -> Union(Record(val: F,exponent: Integer),"failed") +--R isTimes : F -> Union(List(F),"failed") +--R mainVariable : F -> Union(V,"failed") +--R multivariate : (Fraction(SparseUnivariatePolynomial(F)),V) -> F +--R univariate : (F,V) -> Fraction(SparseUnivariatePolynomial(F)) +--R univariate : (F,V,SparseUnivariatePolynomial(F)) -> SparseUnivariatePolynomial(F) +--R --E 1 )spool @@ -154575,6 +158933,15 @@ PolynomialCategoryQuotientFunctions(E, V, R, P, F): --S 1 of 1 )show PolynomialComposition +--R +--R PolynomialComposition(UP: UnivariatePolynomialCategory(R),R: Ring) is a package constructor +--R Abbreviation for PolynomialComposition is PCOMP +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for PCOMP +--R +--R------------------------------- Operations -------------------------------- +--R compose : (UP,UP) -> UP +--R --E 1 )spool @@ -154636,6 +159003,18 @@ PolynomialComposition(UP: UnivariatePolynomialCategory(R), R: Ring): with --S 1 of 1 )show PolynomialDecomposition +--R +--R PolynomialDecomposition(UP: UnivariatePolynomialCategory(F),F: Field) is a package constructor +--R Abbreviation for PolynomialDecomposition is PDECOMP +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for PDECOMP +--R +--R------------------------------- Operations -------------------------------- +--R decompose : UP -> List(UP) +--R decompose : (UP,NonNegativeInteger,NonNegativeInteger) -> Union(Record(left: UP,right: UP),"failed") +--R leftFactor : (UP,UP) -> Union(UP,"failed") +--R rightFactorCandidate : (UP,NonNegativeInteger) -> UP +--R --E 1 )spool @@ -154744,6 +159123,20 @@ PolynomialDecomposition(UP, F): PDcat == PDdef where --S 1 of 1 )show PolynomialFactorizationByRecursion +--R +--R PolynomialFactorizationByRecursion(R: PolynomialFactorizationExplicit,E: OrderedAbelianMonoidSup,VarSet: OrderedSet,S: PolynomialCategory(R,E,VarSet)) is a package constructor +--R Abbreviation for PolynomialFactorizationByRecursion is PFBR +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for PFBR +--R +--R------------------------------- Operations -------------------------------- +--R randomR : () -> R +--R bivariateSLPEBR : (List(SparseUnivariatePolynomial(S)),SparseUnivariatePolynomial(S),VarSet) -> Union(List(SparseUnivariatePolynomial(S)),"failed") +--R factorByRecursion : SparseUnivariatePolynomial(S) -> Factored(SparseUnivariatePolynomial(S)) +--R factorSFBRlcUnit : (List(VarSet),SparseUnivariatePolynomial(S)) -> Factored(SparseUnivariatePolynomial(S)) +--R factorSquareFreeByRecursion : SparseUnivariatePolynomial(S) -> Factored(SparseUnivariatePolynomial(S)) +--R solveLinearPolynomialEquationByRecursion : (List(SparseUnivariatePolynomial(S)),SparseUnivariatePolynomial(S)) -> Union(List(SparseUnivariatePolynomial(S)),"failed") +--R --E 1 )spool @@ -155088,6 +159481,19 @@ PolynomialFactorizationByRecursion(R,E, VarSet:OrderedSet, S): public == --S 1 of 1 )show PolynomialFactorizationByRecursionUnivariate +--R +--R PolynomialFactorizationByRecursionUnivariate(R: PolynomialFactorizationExplicit,S: UnivariatePolynomialCategory(R)) is a package constructor +--R Abbreviation for PolynomialFactorizationByRecursionUnivariate is PFBRU +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for PFBRU +--R +--R------------------------------- Operations -------------------------------- +--R randomR : () -> R +--R factorByRecursion : SparseUnivariatePolynomial(S) -> Factored(SparseUnivariatePolynomial(S)) +--R factorSFBRlcUnit : SparseUnivariatePolynomial(S) -> Factored(SparseUnivariatePolynomial(S)) +--R factorSquareFreeByRecursion : SparseUnivariatePolynomial(S) -> Factored(SparseUnivariatePolynomial(S)) +--R solveLinearPolynomialEquationByRecursion : (List(SparseUnivariatePolynomial(S)),SparseUnivariatePolynomial(S)) -> Union(List(SparseUnivariatePolynomial(S)),"failed") +--R --E 1 )spool @@ -155380,6 +159786,15 @@ PolynomialFactorizationByRecursionUnivariate(R, S): public == private where --S 1 of 1 )show PolynomialFunctions2 +--R +--R PolynomialFunctions2(R: Ring,S: Ring) is a package constructor +--R Abbreviation for PolynomialFunctions2 is POLY2 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for POLY2 +--R +--R------------------------------- Operations -------------------------------- +--R map : ((R -> S),Polynomial(R)) -> Polynomial(S) +--R --E 1 )spool @@ -155438,6 +159853,19 @@ PolynomialFunctions2(R:Ring, S:Ring): with --S 1 of 1 )show PolynomialGcdPackage +--R +--R PolynomialGcdPackage(E: OrderedAbelianMonoidSup,OV: OrderedSet,R: EuclideanDomain,P: PolynomialCategory(R,E,OV)) is a package constructor +--R Abbreviation for PolynomialGcdPackage is PGCD +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for PGCD +--R +--R------------------------------- Operations -------------------------------- +--R gcd : (P,P) -> P gcd : List(P) -> P +--R gcdPrimitive : (P,P) -> P gcdPrimitive : List(P) -> P +--R gcd : (SparseUnivariatePolynomial(P),SparseUnivariatePolynomial(P)) -> SparseUnivariatePolynomial(P) +--R gcd : List(SparseUnivariatePolynomial(P)) -> SparseUnivariatePolynomial(P) +--R gcdPrimitive : (SparseUnivariatePolynomial(P),SparseUnivariatePolynomial(P)) -> SparseUnivariatePolynomial(P) +--R --E 1 )spool @@ -155953,6 +160381,16 @@ See Volume 10.1 for more details. --S 1 of 1 )show PolynomialInterpolation +--R +--R PolynomialInterpolation(xx: Symbol,F: Field) is a package constructor +--R Abbreviation for PolynomialInterpolation is PINTERP +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for PINTERP +--R +--R------------------------------- Operations -------------------------------- +--R interpolate : (UnivariatePolynomial(xx,F),List(F),List(F)) -> UnivariatePolynomial(xx,F) +--R interpolate : (List(F),List(F)) -> SparseUnivariatePolynomial(F) +--R --E 1 )spool @@ -156021,6 +160459,15 @@ PolynomialInterpolation(xx, F): Cat == Body where --S 1 of 1 )show PolynomialInterpolationAlgorithms +--R +--R PolynomialInterpolationAlgorithms(F: Field,P: UnivariatePolynomialCategory(F)) is a package constructor +--R Abbreviation for PolynomialInterpolationAlgorithms is PINTERPA +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for PINTERPA +--R +--R------------------------------- Operations -------------------------------- +--R LagrangeInterpolation : (List(F),List(F)) -> P +--R --E 1 )spool @@ -156089,6 +160536,23 @@ PolynomialInterpolationAlgorithms(F, P): Cat == Body where --S 1 of 1 )show PolynomialNumberTheoryFunctions +--R +--R PolynomialNumberTheoryFunctions is a package constructor +--R Abbreviation for PolynomialNumberTheoryFunctions is PNTHEORY +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for PNTHEORY +--R +--R------------------------------- Operations -------------------------------- +--R bernoulli : Integer -> SparseUnivariatePolynomial(Fraction(Integer)) +--R chebyshevT : Integer -> SparseUnivariatePolynomial(Integer) +--R chebyshevU : Integer -> SparseUnivariatePolynomial(Integer) +--R cyclotomic : Integer -> SparseUnivariatePolynomial(Integer) +--R euler : Integer -> SparseUnivariatePolynomial(Fraction(Integer)) +--R fixedDivisor : SparseUnivariatePolynomial(Integer) -> Integer +--R hermite : Integer -> SparseUnivariatePolynomial(Integer) +--R laguerre : Integer -> SparseUnivariatePolynomial(Integer) +--R legendre : Integer -> SparseUnivariatePolynomial(Fraction(Integer)) +--R --E 1 )spool @@ -156346,6 +160810,22 @@ PolynomialNumberTheoryFunctions(): Exports == Implementation where --S 1 of 1 )show PolynomialRoots +--R +--R PolynomialRoots(E: OrderedAbelianMonoidSup,V: OrderedSet,R: IntegralDomain,P: PolynomialCategory(R,E,V),F)where +--R F: Fieldwith +--R numer : % -> P +--R denom : % -> P +--R coerce : P -> % is a package constructor +--R Abbreviation for PolynomialRoots is POLYROOT +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for POLYROOT +--R +--R------------------------------- Operations -------------------------------- +--R froot : (F,NonNegativeInteger) -> Record(exponent: NonNegativeInteger,coef: F,radicand: F) if R has GCDDOM +--R nthr : (P,NonNegativeInteger) -> Record(exponent: NonNegativeInteger,coef: P,radicand: List(P)) +--R qroot : (Fraction(Integer),NonNegativeInteger) -> Record(exponent: NonNegativeInteger,coef: F,radicand: F) +--R rroot : (R,NonNegativeInteger) -> Record(exponent: NonNegativeInteger,coef: F,radicand: F) +--R --E 1 )spool @@ -156520,6 +161000,49 @@ PolynomialRoots(E, V, R, P, F):Exports == Implementation where --S 1 of 1 )show PolynomialSetUtilitiesPackage +--R +--R PolynomialSetUtilitiesPackage(R: IntegralDomain,E: OrderedAbelianMonoidSup,V: OrderedSet,P: RecursivePolynomialCategory(R,E,V)) is a package constructor +--R Abbreviation for PolynomialSetUtilitiesPackage is PSETPK +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for PSETPK +--R +--R------------------------------- Operations -------------------------------- +--R bivariate? : P -> Boolean crushedSet : List(P) -> List(P) +--R interReduce : List(P) -> List(P) linear? : P -> Boolean +--R univariate? : P -> Boolean +--R bivariatePolynomials : List(P) -> Record(goodPols: List(P),badPols: List(P)) +--R certainlySubVariety? : (List(P),List(P)) -> Boolean +--R irreducibleFactors : List(P) -> List(P) if R has CHARZ and R has EUCDOM +--R lazyIrreducibleFactors : List(P) -> List(P) if R has CHARZ and R has EUCDOM +--R linearPolynomials : List(P) -> Record(goodPols: List(P),badPols: List(P)) +--R possiblyNewVariety? : (List(P),List(List(P))) -> Boolean +--R probablyZeroDim? : List(P) -> Boolean +--R quasiMonicPolynomials : List(P) -> Record(goodPols: List(P),badPols: List(P)) +--R removeIrreducibleRedundantFactors : (List(P),List(P)) -> List(P) if R has CHARZ and R has EUCDOM +--R removeRedundantFactors : List(P) -> List(P) +--R removeRedundantFactors : (P,P) -> List(P) +--R removeRedundantFactors : (List(P),P) -> List(P) +--R removeRedundantFactors : (List(P),List(P)) -> List(P) +--R removeRedundantFactors : (List(P),List(P),(List(P) -> List(P))) -> List(P) +--R removeRedundantFactorsInContents : (List(P),List(P)) -> List(P) if R has GCDDOM +--R removeRedundantFactorsInPols : (List(P),List(P)) -> List(P) if R has GCDDOM +--R removeRoughlyRedundantFactorsInContents : (List(P),List(P)) -> List(P) if R has GCDDOM +--R removeRoughlyRedundantFactorsInPol : (P,List(P)) -> P +--R removeRoughlyRedundantFactorsInPols : (List(P),List(P)) -> List(P) +--R removeRoughlyRedundantFactorsInPols : (List(P),List(P),Boolean) -> List(P) +--R removeSquaresIfCan : List(P) -> List(P) +--R rewriteIdealWithQuasiMonicGenerators : (List(P),((P,P) -> Boolean),((P,P) -> P)) -> List(P) +--R rewriteSetByReducingWithParticularGenerators : (List(P),(P -> Boolean),((P,P) -> Boolean),((P,P) -> P)) -> List(P) +--R roughBasicSet : List(P) -> Union(Record(bas: GeneralTriangularSet(R,E,V,P),top: List(P)),"failed") +--R selectAndPolynomials : (List((P -> Boolean)),List(P)) -> Record(goodPols: List(P),badPols: List(P)) +--R selectOrPolynomials : (List((P -> Boolean)),List(P)) -> Record(goodPols: List(P),badPols: List(P)) +--R selectPolynomials : ((P -> Boolean),List(P)) -> Record(goodPols: List(P),badPols: List(P)) +--R squareFreeFactors : P -> List(P) if R has GCDDOM +--R univariatePolynomials : List(P) -> Record(goodPols: List(P),badPols: List(P)) +--R univariatePolynomialsGcds : List(P) -> List(P) if R has GCDDOM +--R univariatePolynomialsGcds : (List(P),Boolean) -> List(P) if R has GCDDOM +--R unprotectedRemoveRedundantFactors : (P,P) -> List(P) +--R --E 1 )spool @@ -157405,6 +161928,24 @@ PolynomialSetUtilitiesPackage (R,E,V,P) : Exports == Implementation where --S 1 of 1 )show PolynomialSolveByFormulas +--R +--R PolynomialSolveByFormulas(UP: UnivariatePolynomialCategory(F),F)where +--R F: Fieldwith +--R ?**? : (%,Fraction(Integer)) -> % is a package constructor +--R Abbreviation for PolynomialSolveByFormulas is SOLVEFOR +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for SOLVEFOR +--R +--R------------------------------- Operations -------------------------------- +--R aCubic : (F,F,F,F) -> F aLinear : (F,F) -> F +--R aQuadratic : (F,F,F) -> F aQuartic : (F,F,F,F,F) -> F +--R cubic : UP -> List(F) cubic : (F,F,F,F) -> List(F) +--R linear : UP -> List(F) linear : (F,F) -> List(F) +--R particularSolution : UP -> F quadratic : UP -> List(F) +--R quadratic : (F,F,F) -> List(F) quartic : UP -> List(F) +--R quartic : (F,F,F,F,F) -> List(F) solve : UP -> List(F) +--R mapSolve : (UP,(F -> F)) -> Record(solns: List(F),maps: List(Record(arg: F,res: F))) +--R --E 1 )spool @@ -157730,6 +162271,15 @@ PolynomialSolveByFormulas(UP, F): PSFcat == PSFdef where --S 1 of 1 )show PolynomialSquareFree +--R +--R PolynomialSquareFree(VarSet: OrderedSet,E: OrderedAbelianMonoidSup,RC: GcdDomain,P: PolynomialCategory(RC,E,VarSet)) is a package constructor +--R Abbreviation for PolynomialSquareFree is PSQFR +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for PSQFR +--R +--R------------------------------- Operations -------------------------------- +--R squareFree : P -> Factored(P) +--R --E 1 )spool @@ -157894,6 +162444,15 @@ PolynomialSquareFree(VarSet:OrderedSet,E,RC:GcdDomain,P):C == T where --S 1 of 1 )show PolynomialToUnivariatePolynomial +--R +--R PolynomialToUnivariatePolynomial(x: Symbol,R: Ring) is a package constructor +--R Abbreviation for PolynomialToUnivariatePolynomial is POLY2UP +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for POLY2UP +--R +--R------------------------------- Operations -------------------------------- +--R univariate : (Polynomial(R),Variable(x)) -> UnivariatePolynomial(x,Polynomial(R)) +--R --E 1 )spool @@ -157959,6 +162518,17 @@ PolynomialToUnivariatePolynomial(x:Symbol, R:Ring): with --S 1 of 1 )show PowerSeriesLimitPackage +--R +--R PowerSeriesLimitPackage(R: Join(GcdDomain,OrderedSet,RetractableTo(Integer),LinearlyExplicitRingOver(Integer)),FE: Join(AlgebraicallyClosedField,TranscendentalFunctionCategory,FunctionSpace(R))) is a package constructor +--R Abbreviation for PowerSeriesLimitPackage is LIMITPS +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for LIMITPS +--R +--R------------------------------- Operations -------------------------------- +--R complexLimit : (FE,Equation(OnePointCompletion(FE))) -> Union(OnePointCompletion(FE),"failed") +--R limit : (FE,Equation(OrderedCompletion(FE))) -> Union(OrderedCompletion(FE),Record(leftHandLimit: Union(OrderedCompletion(FE),"failed"),rightHandLimit: Union(OrderedCompletion(FE),"failed")),"failed") +--R limit : (FE,Equation(FE),String) -> Union(OrderedCompletion(FE),"failed") +--R --E 1 )spool @@ -158524,6 +163094,15 @@ PowerSeriesLimitPackage(R,FE): Exports == Implementation where --S 1 of 1 )show PrecomputedAssociatedEquations +--R +--R PrecomputedAssociatedEquations(R: IntegralDomain,L: LinearOrdinaryDifferentialOperatorCategory(R)) is a package constructor +--R Abbreviation for PrecomputedAssociatedEquations is PREASSOC +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for PREASSOC +--R +--R------------------------------- Operations -------------------------------- +--R firstUncouplingMatrix : (L,PositiveInteger) -> Union(Matrix(R),"failed") +--R --E 1 )spool @@ -158664,6 +163243,17 @@ PrecomputedAssociatedEquations(R, L): Exports == Implementation where --S 1 of 1 )show PrimitiveArrayFunctions2 +--R +--R PrimitiveArrayFunctions2(A: Type,B: Type) is a package constructor +--R Abbreviation for PrimitiveArrayFunctions2 is PRIMARR2 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for PRIMARR2 +--R +--R------------------------------- Operations -------------------------------- +--R map : ((A -> B),PrimitiveArray(A)) -> PrimitiveArray(B) +--R reduce : (((A,B) -> B),PrimitiveArray(A),B) -> B +--R scan : (((A,B) -> B),PrimitiveArray(A),B) -> PrimitiveArray(B) +--R --E 1 )spool @@ -158760,6 +163350,17 @@ PrimitiveArrayFunctions2(A, B): Exports == Implementation where --S 1 of 1 )show PrimitiveElement +--R +--R PrimitiveElement(F: Join(Field,CharacteristicZero)) is a package constructor +--R Abbreviation for PrimitiveElement is PRIMELT +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for PRIMELT +--R +--R------------------------------- Operations -------------------------------- +--R primitiveElement : (Polynomial(F),Symbol,Polynomial(F),Symbol) -> Record(coef1: Integer,coef2: Integer,prim: SparseUnivariatePolynomial(F)) +--R primitiveElement : (List(Polynomial(F)),List(Symbol)) -> Record(coef: List(Integer),poly: List(SparseUnivariatePolynomial(F)),prim: SparseUnivariatePolynomial(F)) +--R primitiveElement : (List(Polynomial(F)),List(Symbol),Symbol) -> Record(coef: List(Integer),poly: List(SparseUnivariatePolynomial(F)),prim: SparseUnivariatePolynomial(F)) +--R --E 1 )spool @@ -158905,6 +163506,22 @@ PrimitiveElement(F): Exports == Implementation where --S 1 of 1 )show PrimitiveRatDE +--R +--R PrimitiveRatDE(F: Join(Field,CharacteristicZero,RetractableTo(Fraction(Integer))),UP: UnivariatePolynomialCategory(F),L: LinearOrdinaryDifferentialOperatorCategory(UP),LQ: LinearOrdinaryDifferentialOperatorCategory(Fraction(UP))) is a package constructor +--R Abbreviation for PrimitiveRatDE is ODEPRIM +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for ODEPRIM +--R +--R------------------------------- Operations -------------------------------- +--R indicialEquation : (L,F) -> UP indicialEquation : (LQ,F) -> UP +--R denomLODE : (L,Fraction(UP)) -> Union(UP,"failed") +--R denomLODE : (L,List(Fraction(UP))) -> UP +--R indicialEquations : L -> List(Record(center: UP,equation: UP)) +--R indicialEquations : (L,UP) -> List(Record(center: UP,equation: UP)) +--R indicialEquations : LQ -> List(Record(center: UP,equation: UP)) +--R indicialEquations : (LQ,UP) -> List(Record(center: UP,equation: UP)) +--R splitDenominator : (LQ,List(Fraction(UP))) -> Record(eq: L,rh: List(Fraction(UP))) +--R --E 1 )spool @@ -159130,6 +163747,20 @@ PrimitiveRatDE(F, UP, L, LQ): Exports == Implementation where --S 1 of 1 )show PrimitiveRatRicDE +--R +--R PrimitiveRatRicDE(F: Join(Field,CharacteristicZero,RetractableTo(Fraction(Integer))),UP: UnivariatePolynomialCategory(F),L: LinearOrdinaryDifferentialOperatorCategory(UP),LQ: LinearOrdinaryDifferentialOperatorCategory(Fraction(UP))) is a package constructor +--R Abbreviation for PrimitiveRatRicDE is ODEPRRIC +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for ODEPRRIC +--R +--R------------------------------- Operations -------------------------------- +--R changeVar : (L,UP) -> L changeVar : (L,Fraction(UP)) -> L +--R denomRicDE : L -> UP +--R constantCoefficientRicDE : (L,(UP -> List(F))) -> List(Record(constant: F,eq: L)) +--R leadingCoefficientRicDE : L -> List(Record(deg: NonNegativeInteger,eq: UP)) +--R polyRicDE : (L,(UP -> List(F))) -> List(Record(poly: UP,eq: L)) +--R singRicDE : (L,((UP,SparseUnivariatePolynomial(UP)) -> List(UP)),(UP -> Factored(UP))) -> List(Record(frac: Fraction(UP),eq: L)) +--R --E 1 )spool @@ -159436,6 +164067,15 @@ PrimitiveRatRicDE(F, UP, L, LQ): Exports == Implementation where --S 1 of 1 )show PrintPackage +--R +--R PrintPackage is a package constructor +--R Abbreviation for PrintPackage is PRINT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for PRINT +--R +--R------------------------------- Operations -------------------------------- +--R print : OutputForm -> Void +--R --E 1 )spool @@ -159491,6 +164131,17 @@ PrintPackage(): with --S 1 of 1 )show PseudoLinearNormalForm +--R +--R PseudoLinearNormalForm(K: Field) is a package constructor +--R Abbreviation for PseudoLinearNormalForm is PSEUDLIN +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for PSEUDLIN +--R +--R------------------------------- Operations -------------------------------- +--R changeBase : (Matrix(K),Matrix(K),Automorphism(K),(K -> K)) -> Matrix(K) +--R companionBlocks : (Matrix(K),Vector(K)) -> List(Record(C: Matrix(K),g: Vector(K))) +--R normalForm : (Matrix(K),Automorphism(K),(K -> K)) -> Record(R: Matrix(K),A: Matrix(K),Ainv: Matrix(K)) +--R --E 1 )spool @@ -159690,6 +164341,49 @@ PseudoLinearNormalForm(K:Field): Exports == Implementation where --S 1 of 1 )show PseudoRemainderSequence +--R +--R PseudoRemainderSequence(R: IntegralDomain,polR: UnivariatePolynomialCategory(R)) is a package constructor +--R Abbreviation for PseudoRemainderSequence is PRS +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for PRS +--R +--R------------------------------- Operations -------------------------------- +--R discriminant : polR -> R resultant : (polR,polR) -> R +--R resultantnaif : (polR,polR) -> R +--R ?*? : (R,Vector(polR)) -> Vector(polR) +--R Lazard : (R,R,NonNegativeInteger) -> R +--R Lazard2 : (polR,R,R,NonNegativeInteger) -> polR +--R chainSubResultants : (polR,polR) -> List(polR) +--R degreeSubResultant : (polR,polR,NonNegativeInteger) -> polR +--R degreeSubResultantEuclidean : (polR,polR,NonNegativeInteger) -> Record(coef1: polR,coef2: polR,subResultant: polR) +--R discriminantEuclidean : polR -> Record(coef1: polR,coef2: polR,discriminant: R) +--R divide : (polR,polR) -> Record(quotient: polR,remainder: polR) +--R exquo : (Vector(polR),R) -> Vector(polR) +--R gcd : (polR,polR) -> polR if R has GCDDOM +--R indiceSubResultant : (polR,polR,NonNegativeInteger) -> polR +--R indiceSubResultantEuclidean : (polR,polR,NonNegativeInteger) -> Record(coef1: polR,coef2: polR,subResultant: polR) +--R lastSubResultant : (polR,polR) -> polR +--R lastSubResultantEuclidean : (polR,polR) -> Record(coef1: polR,coef2: polR,subResultant: polR) +--R nextsousResultant2 : (polR,polR,polR,R) -> polR +--R pseudoDivide : (polR,polR) -> Record(coef: R,quotient: polR,remainder: polR) +--R resultantEuclidean : (polR,polR) -> Record(coef1: polR,coef2: polR,resultant: R) +--R resultantEuclideannaif : (polR,polR) -> Record(coef1: polR,coef2: polR,resultant: R) +--R resultantReduit : (polR,polR) -> R if R has GCDDOM +--R resultantReduitEuclidean : (polR,polR) -> Record(coef1: polR,coef2: polR,resultantReduit: R) if R has GCDDOM +--R schema : (polR,polR) -> List(NonNegativeInteger) +--R semiDegreeSubResultantEuclidean : (polR,polR,NonNegativeInteger) -> Record(coef2: polR,subResultant: polR) +--R semiDiscriminantEuclidean : polR -> Record(coef2: polR,discriminant: R) +--R semiIndiceSubResultantEuclidean : (polR,polR,NonNegativeInteger) -> Record(coef2: polR,subResultant: polR) +--R semiLastSubResultantEuclidean : (polR,polR) -> Record(coef2: polR,subResultant: polR) +--R semiResultantEuclidean1 : (polR,polR) -> Record(coef1: polR,resultant: R) +--R semiResultantEuclidean2 : (polR,polR) -> Record(coef2: polR,resultant: R) +--R semiResultantEuclideannaif : (polR,polR) -> Record(coef2: polR,resultant: R) +--R semiResultantReduitEuclidean : (polR,polR) -> Record(coef2: polR,resultantReduit: R) if R has GCDDOM +--R semiSubResultantGcdEuclidean1 : (polR,polR) -> Record(coef1: polR,gcd: polR) +--R semiSubResultantGcdEuclidean2 : (polR,polR) -> Record(coef2: polR,gcd: polR) +--R subResultantGcd : (polR,polR) -> polR +--R subResultantGcdEuclidean : (polR,polR) -> Record(coef1: polR,coef2: polR,gcd: polR) +--R --E 1 )spool @@ -160688,6 +165382,19 @@ PseudoRemainderSequence(R, polR) : Specification == Implementation where --S 1 of 1 )show PureAlgebraicIntegration +--R +--R PureAlgebraicIntegration(R: Join(GcdDomain,RetractableTo(Integer),OrderedSet,CharacteristicZero,LinearlyExplicitRingOver(Integer)),F: Join(FunctionSpace(R),AlgebraicallyClosedField,TranscendentalFunctionCategory),L: SetCategory) is a package constructor +--R Abbreviation for PureAlgebraicIntegration is INTPAF +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for INTPAF +--R +--R------------------------------- Operations -------------------------------- +--R palgLODE : (L,F,Kernel(F),Kernel(F),Symbol) -> Record(particular: Union(F,"failed"),basis: List(F)) if L has LODOCAT(F) +--R palgRDE : (F,F,F,Kernel(F),Kernel(F),((F,F,Symbol) -> Union(F,"failed"))) -> Union(F,"failed") +--R palgextint : (F,Kernel(F),Kernel(F),F) -> Union(Record(ratpart: F,coeff: F),"failed") +--R palgint : (F,Kernel(F),Kernel(F)) -> IntegrationResult(F) +--R palglimint : (F,Kernel(F),Kernel(F),List(F)) -> Union(Record(mainpart: F,limitedlogs: List(Record(coeff: F,logand: F))),"failed") +--R --E 1 )spool @@ -161208,6 +165915,20 @@ PureAlgebraicLODE(F, UP, UPUP, R): Exports == Implementation where --S 1 of 1 )show PushVariables +--R +--R PushVariables(R: Ring,E: OrderedAbelianMonoidSup,OV,PPR: PolynomialCategory(Polynomial(R),E,OV))where +--R OV: OrderedSetwith +--R convert : % -> Symbol +--R variable : Symbol -> Union(%,"failed") is a package constructor +--R Abbreviation for PushVariables is PUSHVAR +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for PUSHVAR +--R +--R------------------------------- Operations -------------------------------- +--R pushdown : (PPR,OV) -> PPR pushdown : (PPR,List(OV)) -> PPR +--R pushup : (PPR,OV) -> PPR pushup : (PPR,List(OV)) -> PPR +--R map : ((Polynomial(R) -> PPR),PPR) -> PPR +--R --E 1 )spool @@ -161318,6 +166039,15 @@ PushVariables(R,E,OV,PPR):C == T where --S 1 of 1 )show QuasiAlgebraicSet2 +--R +--R QuasiAlgebraicSet2(vl: List(Symbol),nv: NonNegativeInteger) is a package constructor +--R Abbreviation for QuasiAlgebraicSet2 is QALGSET2 +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for QALGSET2 +--R +--R------------------------------- Operations -------------------------------- +--R radicalSimplify : QuasiAlgebraicSet(Fraction(Integer),OrderedVariableList(vl),DirectProduct(nv,NonNegativeInteger),DistributedMultivariatePolynomial(vl,Fraction(Integer))) -> QuasiAlgebraicSet(Fraction(Integer),OrderedVariableList(vl),DirectProduct(nv,NonNegativeInteger),DistributedMultivariatePolynomial(vl,Fraction(Integer))) +--R --E 1 )spool @@ -161486,6 +166216,30 @@ QuasiAlgebraicSet2(vl,nv) : C == T where --S 1 of 1 )show QuasiComponentPackage +--R +--R QuasiComponentPackage(R: GcdDomain,E: OrderedAbelianMonoidSup,V: OrderedSet,P: RecursivePolynomialCategory(R,E,V),TS: RegularTriangularSetCategory(R,E,V,P)) is a package constructor +--R Abbreviation for QuasiComponentPackage is QCMPACK +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for QCMPACK +--R +--R------------------------------- Operations -------------------------------- +--R algebraicSort : List(TS) -> List(TS) moreAlgebraic? : (TS,TS) -> Boolean +--R stopTable! : () -> Void subTriSet? : (TS,TS) -> Boolean +--R branchIfCan : (List(P),TS,List(P),Boolean,Boolean,Boolean,Boolean,Boolean) -> Union(Record(eq: List(P),tower: TS,ineq: List(P)),"failed") +--R infRittWu? : (List(P),List(P)) -> Boolean +--R internalInfRittWu? : (List(P),List(P)) -> Boolean +--R internalSubPolSet? : (List(P),List(P)) -> Boolean +--R internalSubQuasiComponent? : (TS,TS) -> Union(Boolean,"failed") +--R prepareDecompose : (List(P),List(TS),Boolean,Boolean) -> List(Record(eq: List(P),tower: TS,ineq: List(P))) +--R removeSuperfluousCases : List(Record(val: List(P),tower: TS)) -> List(Record(val: List(P),tower: TS)) +--R removeSuperfluousQuasiComponents : List(TS) -> List(TS) +--R startTable! : (String,String,String) -> Void +--R subCase? : (Record(val: List(P),tower: TS),Record(val: List(P),tower: TS)) -> Boolean +--R subPolSet? : (List(P),List(P)) -> Boolean +--R subQuasiComponent? : (TS,TS) -> Boolean +--R subQuasiComponent? : (TS,List(TS)) -> Boolean +--R supDimElseRittWu? : (TS,TS) -> Boolean +--R --E 1 )spool @@ -161924,6 +166678,15 @@ QuasiComponentPackage(R,E,V,P,TS): Exports == Implementation where --S 1 of 1 )show QuotientFieldCategoryFunctions2 +--R +--R QuotientFieldCategoryFunctions2(A: IntegralDomain,B: IntegralDomain,R: QuotientFieldCategory(A),S: QuotientFieldCategory(B)) is a package constructor +--R Abbreviation for QuotientFieldCategoryFunctions2 is QFCAT2 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for QFCAT2 +--R +--R------------------------------- Operations -------------------------------- +--R map : ((A -> B),R) -> S +--R --E 1 )spool @@ -162123,6 +166886,21 @@ QuaternionCategoryFunctions2(QR,R,QS,S) : Exports == --S 1 of 1 )show RadicalEigenPackage +--R +--R RadicalEigenPackage is a package constructor +--R Abbreviation for RadicalEigenPackage is REP +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for REP +--R +--R------------------------------- Operations -------------------------------- +--R eigenMatrix : Matrix(Fraction(Polynomial(Integer))) -> Union(Matrix(Expression(Integer)),"failed") +--R gramschmidt : List(Matrix(Expression(Integer))) -> List(Matrix(Expression(Integer))) +--R normalise : Matrix(Expression(Integer)) -> Matrix(Expression(Integer)) +--R orthonormalBasis : Matrix(Fraction(Polynomial(Integer))) -> List(Matrix(Expression(Integer))) +--R radicalEigenvalues : Matrix(Fraction(Polynomial(Integer))) -> List(Expression(Integer)) +--R radicalEigenvector : (Expression(Integer),Matrix(Fraction(Polynomial(Integer)))) -> List(Matrix(Expression(Integer))) +--R radicalEigenvectors : Matrix(Fraction(Polynomial(Integer))) -> List(Record(radval: Expression(Integer),radmult: Integer,radvect: List(Matrix(Expression(Integer))))) +--R --E 1 )spool @@ -162759,6 +167537,30 @@ t4^3+t4^2-7 --R Type: Expression(Integer) --E 21 +--S 22 of 22 +)show RadicalSolvePackage +--R +--R RadicalSolvePackage(R: Join(EuclideanDomain,OrderedSet,CharacteristicZero)) is a package constructor +--R Abbreviation for RadicalSolvePackage is SOLVERAD +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for SOLVERAD +--R +--R------------------------------- Operations -------------------------------- +--R contractSolve : (Equation(Fraction(Polynomial(R))),Symbol) -> SuchThat(List(Expression(R)),List(Equation(Expression(R)))) +--R contractSolve : (Fraction(Polynomial(R)),Symbol) -> SuchThat(List(Expression(R)),List(Equation(Expression(R)))) +--R radicalRoots : (Fraction(Polynomial(R)),Symbol) -> List(Expression(R)) +--R radicalRoots : (List(Fraction(Polynomial(R))),List(Symbol)) -> List(List(Expression(R))) +--R radicalSolve : (Fraction(Polynomial(R)),Symbol) -> List(Equation(Expression(R))) +--R radicalSolve : Fraction(Polynomial(R)) -> List(Equation(Expression(R))) +--R radicalSolve : (Equation(Fraction(Polynomial(R))),Symbol) -> List(Equation(Expression(R))) +--R radicalSolve : Equation(Fraction(Polynomial(R))) -> List(Equation(Expression(R))) +--R radicalSolve : (List(Fraction(Polynomial(R))),List(Symbol)) -> List(List(Equation(Expression(R)))) +--R radicalSolve : List(Fraction(Polynomial(R))) -> List(List(Equation(Expression(R)))) +--R radicalSolve : (List(Equation(Fraction(Polynomial(R)))),List(Symbol)) -> List(List(Equation(Expression(R)))) +--R radicalSolve : List(Equation(Fraction(Polynomial(R)))) -> List(List(Equation(Expression(R)))) +--R +--E 22 + )spool \end{chunk} @@ -163316,6 +168118,15 @@ RadicalSolvePackage(R): Cat == Capsule where --S 1 of 1 )show RadixUtilities +--R +--R RadixUtilities is a package constructor +--R Abbreviation for RadixUtilities is RADUTIL +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for RADUTIL +--R +--R------------------------------- Operations -------------------------------- +--R radix : (Fraction(Integer),Integer) -> Any +--R --E 1 )spool @@ -163375,6 +168186,17 @@ RadixUtilities: Exports == Implementation where --S 1 of 1 )show RandomDistributions +--R +--R RandomDistributions(S: SetCategory) is a package constructor +--R Abbreviation for RandomDistributions is RDIST +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for RDIST +--R +--R------------------------------- Operations -------------------------------- +--R uniform : Set(S) -> (() -> S) +--R rdHack1 : (Vector(S),Vector(Integer),Integer) -> (() -> S) +--R weighted : List(Record(value: S,weight: Integer)) -> (() -> S) +--R --E 1 )spool @@ -163469,6 +168291,23 @@ RandomDistributions(S: SetCategory): with --S 1 of 1 )show RandomFloatDistributions +--R +--R RandomFloatDistributions is a package constructor +--R Abbreviation for RandomFloatDistributions is RFDIST +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for RFDIST +--R +--R------------------------------- Operations -------------------------------- +--R exponential : Float -> (() -> Float) exponential1 : () -> Float +--R normal01 : () -> Float uniform01 : () -> Float +--R Beta : (NonNegativeInteger,NonNegativeInteger) -> (() -> Float) +--R F : (NonNegativeInteger,NonNegativeInteger) -> (() -> Float) +--R chiSquare : NonNegativeInteger -> (() -> Float) +--R chiSquare1 : NonNegativeInteger -> Float +--R normal : (Float,Float) -> (() -> Float) +--R t : NonNegativeInteger -> (() -> Float) +--R uniform : (Float,Float) -> (() -> Float) +--R --E 1 )spool @@ -163614,6 +168453,19 @@ RandomFloatDistributions(): Cat == Body where --S 1 of 1 )show RandomIntegerDistributions +--R +--R RandomIntegerDistributions is a package constructor +--R Abbreviation for RandomIntegerDistributions is RIDIST +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for RIDIST +--R +--R------------------------------- Operations -------------------------------- +--R binomial : (Integer,RationalNumber) -> (() -> Integer) +--R geometric : RationalNumber -> (() -> Integer) +--R poisson : RationalNumber -> (() -> Integer) +--R ridHack1 : (Integer,Integer,Integer,Integer) -> Integer +--R uniform : Segment(Integer) -> (() -> Integer) +--R --E 1 )spool @@ -163707,6 +168559,17 @@ RandomIntegerDistributions(): with --S 1 of 1 )show RandomNumberSource +--R +--R RandomNumberSource is a package constructor +--R Abbreviation for RandomNumberSource is RANDSRC +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for RANDSRC +--R +--R------------------------------- Operations -------------------------------- +--R randnum : () -> Integer randnum : Integer -> Integer +--R reseed : Integer -> Void seed : () -> Integer +--R size : () -> Integer +--R --E 1 )spool @@ -163809,6 +168672,16 @@ RandomNumberSource(): with --S 1 of 1 )show RationalFactorize +--R +--R RationalFactorize(RP: UnivariatePolynomialCategory(Fraction(Integer))) is a package constructor +--R Abbreviation for RationalFactorize is RATFACT +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for RATFACT +--R +--R------------------------------- Operations -------------------------------- +--R factor : RP -> Factored(RP) +--R factorSquareFree : RP -> Factored(RP) +--R --E 1 )spool @@ -163917,6 +168790,23 @@ RationalFactorize(RP) : public == private where --S 1 of 1 )show RationalFunction +--R +--R RationalFunction(R: IntegralDomain) is a package constructor +--R Abbreviation for RationalFunction is RF +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for RF +--R +--R------------------------------- Operations -------------------------------- +--R coerce : R -> Fraction(Polynomial(R)) +--R eval : (Fraction(Polynomial(R)),Symbol,Fraction(Polynomial(R))) -> Fraction(Polynomial(R)) +--R eval : (Fraction(Polynomial(R)),List(Symbol),List(Fraction(Polynomial(R)))) -> Fraction(Polynomial(R)) +--R eval : (Fraction(Polynomial(R)),Equation(Fraction(Polynomial(R)))) -> Fraction(Polynomial(R)) +--R eval : (Fraction(Polynomial(R)),List(Equation(Fraction(Polynomial(R))))) -> Fraction(Polynomial(R)) +--R mainVariable : Fraction(Polynomial(R)) -> Union(Symbol,"failed") +--R multivariate : (Fraction(SparseUnivariatePolynomial(Fraction(Polynomial(R)))),Symbol) -> Fraction(Polynomial(R)) +--R univariate : (Fraction(Polynomial(R)),Symbol) -> Fraction(SparseUnivariatePolynomial(Fraction(Polynomial(R)))) +--R variables : Fraction(Polynomial(R)) -> List(Symbol) +--R --E 1 )spool @@ -164038,6 +168928,18 @@ RationalFunction(R:IntegralDomain): Exports == Implementation where --S 1 of 1 )show RationalFunctionDefiniteIntegration +--R +--R RationalFunctionDefiniteIntegration(R: Join(EuclideanDomain,OrderedSet,CharacteristicZero,RetractableTo(Integer),LinearlyExplicitRingOver(Integer))) is a package constructor +--R Abbreviation for RationalFunctionDefiniteIntegration is DEFINTRF +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for DEFINTRF +--R +--R------------------------------- Operations -------------------------------- +--R integrate : (Fraction(Polynomial(R)),SegmentBinding(OrderedCompletion(Expression(R)))) -> Union(f1: OrderedCompletion(Expression(R)),f2: List(OrderedCompletion(Expression(R))),fail: failed,pole: potentialPole) +--R integrate : (Fraction(Polynomial(R)),SegmentBinding(OrderedCompletion(Expression(R))),String) -> Union(f1: OrderedCompletion(Expression(R)),f2: List(OrderedCompletion(Expression(R))),fail: failed,pole: potentialPole) +--R integrate : (Fraction(Polynomial(R)),SegmentBinding(OrderedCompletion(Fraction(Polynomial(R))))) -> Union(f1: OrderedCompletion(Expression(R)),f2: List(OrderedCompletion(Expression(R))),fail: failed,pole: potentialPole) +--R integrate : (Fraction(Polynomial(R)),SegmentBinding(OrderedCompletion(Fraction(Polynomial(R)))),String) -> Union(f1: OrderedCompletion(Expression(R)),f2: List(OrderedCompletion(Expression(R))),fail: failed,pole: potentialPole) +--R --E 1 )spool @@ -164171,6 +169073,15 @@ RationalFunctionDefiniteIntegration(R): Exports == Implementation where --S 1 of 1 )show RationalFunctionFactor +--R +--R RationalFunctionFactor(UP: UnivariatePolynomialCategory(Fraction(Polynomial(Integer)))) is a package constructor +--R Abbreviation for RationalFunctionFactor is RFFACT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for RFFACT +--R +--R------------------------------- Operations -------------------------------- +--R factor : UP -> Factored(UP) +--R --E 1 )spool @@ -164247,6 +169158,15 @@ RationalFunctionFactor(UP): Exports == Implementation where --S 1 of 1 )show RationalFunctionFactorizer +--R +--R RationalFunctionFactorizer(R: EuclideanDomain) is a package constructor +--R Abbreviation for RationalFunctionFactorizer is RFFACTOR +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for RFFACTOR +--R +--R------------------------------- Operations -------------------------------- +--R factorFraction : Fraction(Polynomial(R)) -> Fraction(Factored(Polynomial(R))) +--R --E 1 )spool @@ -164329,6 +169249,18 @@ RationalFunctionFactorizer(R) : C == T --S 1 of 1 )show RationalFunctionIntegration +--R +--R RationalFunctionIntegration(F: Join(IntegralDomain,RetractableTo(Integer),CharacteristicZero)) is a package constructor +--R Abbreviation for RationalFunctionIntegration is INTRF +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for INTRF +--R +--R------------------------------- Operations -------------------------------- +--R extendedIntegrate : (Fraction(Polynomial(F)),Symbol,Fraction(Polynomial(F))) -> Union(Record(ratpart: Fraction(Polynomial(F)),coeff: Fraction(Polynomial(F))),"failed") +--R infieldIntegrate : (Fraction(Polynomial(F)),Symbol) -> Union(Fraction(Polynomial(F)),"failed") +--R internalIntegrate : (Fraction(Polynomial(F)),Symbol) -> IntegrationResult(Fraction(Polynomial(F))) +--R limitedIntegrate : (Fraction(Polynomial(F)),Symbol,List(Fraction(Polynomial(F)))) -> Union(Record(mainpart: Fraction(Polynomial(F)),limitedlogs: List(Record(coeff: Fraction(Polynomial(F)),logand: Fraction(Polynomial(F))))),"failed") +--R --E 1 )spool @@ -164433,6 +169365,19 @@ RationalFunctionIntegration(F): Exports == Implementation where --S 1 of 1 )show RationalFunctionLimitPackage +--R +--R RationalFunctionLimitPackage(R: GcdDomain) is a package constructor +--R Abbreviation for RationalFunctionLimitPackage is LIMITRF +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for LIMITRF +--R +--R------------------------------- Operations -------------------------------- +--R complexLimit : (Fraction(Polynomial(R)),Equation(OnePointCompletion(Polynomial(R)))) -> OnePointCompletion(Fraction(Polynomial(R))) +--R complexLimit : (Fraction(Polynomial(R)),Equation(Fraction(Polynomial(R)))) -> OnePointCompletion(Fraction(Polynomial(R))) +--R limit : (Fraction(Polynomial(R)),Equation(OrderedCompletion(Polynomial(R)))) -> Union(OrderedCompletion(Fraction(Polynomial(R))),Record(leftHandLimit: Union(OrderedCompletion(Fraction(Polynomial(R))),"failed"),rightHandLimit: Union(OrderedCompletion(Fraction(Polynomial(R))),"failed")),"failed") +--R limit : (Fraction(Polynomial(R)),Equation(Fraction(Polynomial(R)))) -> Union(OrderedCompletion(Fraction(Polynomial(R))),Record(leftHandLimit: Union(OrderedCompletion(Fraction(Polynomial(R))),"failed"),rightHandLimit: Union(OrderedCompletion(Fraction(Polynomial(R))),"failed")),"failed") +--R limit : (Fraction(Polynomial(R)),Equation(Fraction(Polynomial(R))),String) -> Union(OrderedCompletion(Fraction(Polynomial(R))),"failed") +--R --E 1 )spool @@ -164624,6 +169569,17 @@ RationalFunctionLimitPackage(R:GcdDomain):Exports==Implementation where --S 1 of 1 )show RationalFunctionSign +--R +--R RationalFunctionSign(R: GcdDomain) is a package constructor +--R Abbreviation for RationalFunctionSign is SIGNRF +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for SIGNRF +--R +--R------------------------------- Operations -------------------------------- +--R sign : Fraction(Polynomial(R)) -> Union(Integer,"failed") +--R sign : (Fraction(Polynomial(R)),Symbol,OrderedCompletion(Fraction(Polynomial(R)))) -> Union(Integer,"failed") +--R sign : (Fraction(Polynomial(R)),Symbol,Fraction(Polynomial(R)),String) -> Union(Integer,"failed") +--R --E 1 )spool @@ -164751,7 +169707,7 @@ RationalFunctionSign(R:GcdDomain): Exports == Implementation where )set message auto off )clear all ---S 1 of 13 +--S 1 of 14 sum(i::Polynomial(Integer),variable(i=1..n)) --R --R @@ -164762,7 +169718,7 @@ sum(i::Polynomial(Integer),variable(i=1..n)) --R Type: Fraction(Polynomial(Integer)) --E 1 ---S 2 of 13 +--S 2 of 14 sum(i::Fraction(Polynomial(Integer)),i::Symbol) --R --R @@ -164773,7 +169729,7 @@ sum(i::Fraction(Polynomial(Integer)),i::Symbol) --R Type: Union(Fraction(Polynomial(Integer)),...) --E 2 ---S 3 of 13 +--S 3 of 14 sum(i,i=1..n) --R --R @@ -164784,7 +169740,7 @@ sum(i,i=1..n) --R Type: Fraction(Polynomial(Integer)) --E 3 ---S 4 of 13 +--S 4 of 14 sum(i::Fraction(Polynomial(Integer)),i=1..n) --R --R @@ -164795,7 +169751,7 @@ sum(i::Fraction(Polynomial(Integer)),i=1..n) --R Type: Union(Fraction(Polynomial(Integer)),...) --E 4 ---S 5 of 13 +--S 5 of 14 s:=i=1..n --R --R @@ -164803,7 +169759,7 @@ s:=i=1..n --R Type: SegmentBinding(Polynomial(Integer)) --E 5 ---S 6 of 13 +--S 6 of 14 hiseg:=high(segment(s)) --R --R @@ -164811,7 +169767,7 @@ hiseg:=high(segment(s)) --R Type: Polynomial(Integer) --E 6 ---S 7 of 13 +--S 7 of 14 loseg:=low(segment(s)) --R --R @@ -164819,7 +169775,7 @@ loseg:=low(segment(s)) --R Type: Polynomial(Integer) --E 7 ---S 8 of 13 +--S 8 of 14 v:=variable s --R --R @@ -164827,7 +169783,7 @@ v:=variable s --R Type: Symbol --E 8 ---S 9 of 13 +--S 9 of 14 p:=i::Polynomial(Integer) --R --R @@ -164835,7 +169791,7 @@ p:=i::Polynomial(Integer) --R Type: Polynomial(Integer) --E 9 ---S 10 of 13 +--S 10 of 14 f:=sum(p,v) --R --R @@ -164846,7 +169802,7 @@ f:=sum(p,v) --R Type: Fraction(Polynomial(Integer)) --E 10 ---S 11 of 13 +--S 11 of 14 t1:=eval(f,v,(1+hiseg)) --R --R @@ -164857,7 +169813,7 @@ t1:=eval(f,v,(1+hiseg)) --R Type: Fraction(Polynomial(Integer)) --E 11 ---S 12 of 13 +--S 12 of 14 t2:=eval(f,v,loseg) --R --R @@ -164867,7 +169823,7 @@ t2:=eval(f,v,loseg) --R Type: Fraction(Polynomial(Integer)) --E 12 ---S 13 of 13 +--S 13 of 14 t1-t2 --R --R @@ -164878,6 +169834,22 @@ t1-t2 --R Type: Fraction(Polynomial(Integer)) --E 13 +--S 14 of 14 +)show RationalFunctionSum +--R +--R RationalFunctionSum(R: Join(IntegralDomain,OrderedSet,RetractableTo(Integer))) is a package constructor +--R Abbreviation for RationalFunctionSum is SUMRF +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for SUMRF +--R +--R------------------------------- Operations -------------------------------- +--R sum : (Polynomial(R),Symbol) -> Fraction(Polynomial(R)) +--R sum : (Fraction(Polynomial(R)),Symbol) -> Union(Fraction(Polynomial(R)),Expression(R)) +--R sum : (Polynomial(R),SegmentBinding(Polynomial(R))) -> Fraction(Polynomial(R)) +--R sum : (Fraction(Polynomial(R)),SegmentBinding(Fraction(Polynomial(R)))) -> Union(Fraction(Polynomial(R)),Expression(R)) +--R +--E 14 + )spool \end{chunk} @@ -165096,6 +170068,18 @@ RationalFunctionSum(R): Exports == Impl where --S 1 of 1 )show RationalIntegration +--R +--R RationalIntegration(F: Join(Field,CharacteristicZero,RetractableTo(Integer)),UP: UnivariatePolynomialCategory(F)) is a package constructor +--R Abbreviation for RationalIntegration is INTRAT +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for INTRAT +--R +--R------------------------------- Operations -------------------------------- +--R extendedint : (Fraction(UP),Fraction(UP)) -> Union(Record(ratpart: Fraction(UP),coeff: Fraction(UP)),"failed") +--R infieldint : Fraction(UP) -> Union(Fraction(UP),"failed") +--R integrate : Fraction(UP) -> IntegrationResult(Fraction(UP)) +--R limitedint : (Fraction(UP),List(Fraction(UP))) -> Union(Record(mainpart: Fraction(UP),limitedlogs: List(Record(coeff: Fraction(UP),logand: Fraction(UP)))),"failed") +--R --E 1 )spool @@ -165220,6 +170204,15 @@ where the coefficients of the rational function are in any given field. --S 1 of 1 )show RationalInterpolation +--R +--R RationalInterpolation(xx: Symbol,F: Field) is a package constructor +--R Abbreviation for RationalInterpolation is RINTERP +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for RINTERP +--R +--R------------------------------- Operations -------------------------------- +--R interpolate : (List(F),List(F),NonNegativeInteger,NonNegativeInteger) -> Fraction(Polynomial(F)) +--R --E 1 )spool @@ -165366,6 +170359,20 @@ Finally, we generate the rational function: --S 1 of 1 )show RationalLODE +--R +--R RationalLODE(F: Join(Field,CharacteristicZero,RetractableTo(Integer),RetractableTo(Fraction(Integer))),UP: UnivariatePolynomialCategory(F)) is a package constructor +--R Abbreviation for RationalLODE is ODERAT +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for ODERAT +--R +--R------------------------------- Operations -------------------------------- +--R indicialEquationAtInfinity : LinearOrdinaryDifferentialOperator1(Fraction(UP)) -> UP +--R indicialEquationAtInfinity : LinearOrdinaryDifferentialOperator2(UP,Fraction(UP)) -> UP +--R ratDsolve : (LinearOrdinaryDifferentialOperator1(Fraction(UP)),Fraction(UP)) -> Record(particular: Union(Fraction(UP),"failed"),basis: List(Fraction(UP))) +--R ratDsolve : (LinearOrdinaryDifferentialOperator1(Fraction(UP)),List(Fraction(UP))) -> Record(basis: List(Fraction(UP)),mat: Matrix(F)) +--R ratDsolve : (LinearOrdinaryDifferentialOperator2(UP,Fraction(UP)),Fraction(UP)) -> Record(particular: Union(Fraction(UP),"failed"),basis: List(Fraction(UP))) +--R ratDsolve : (LinearOrdinaryDifferentialOperator2(UP,Fraction(UP)),List(Fraction(UP))) -> Record(basis: List(Fraction(UP)),mat: Matrix(F)) +--R --E 1 )spool @@ -165641,6 +170648,16 @@ RationalLODE(F, UP): Exports == Implementation where --S 1 of 1 )show RationalRetractions +--R +--R RationalRetractions(S: RetractableTo(Fraction(Integer))) is a package constructor +--R Abbreviation for RationalRetractions is RATRET +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for RATRET +--R +--R------------------------------- Operations -------------------------------- +--R rational : S -> Fraction(Integer) rational? : S -> Boolean +--R rationalIfCan : S -> Union(Fraction(Integer),"failed") +--R --E 1 )spool @@ -165711,6 +170728,24 @@ RationalRetractions(S:RetractableTo(Fraction Integer)): with --S 1 of 1 )show RationalRicDE +--R +--R RationalRicDE(F: Join(Field,CharacteristicZero,RetractableTo(Integer),RetractableTo(Fraction(Integer))),UP: UnivariatePolynomialCategory(F)) is a package constructor +--R Abbreviation for RationalRicDE is ODERTRIC +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for ODERTRIC +--R +--R------------------------------- Operations -------------------------------- +--R polyRicDE : (LinearOrdinaryDifferentialOperator2(UP,Fraction(UP)),(UP -> List(F))) -> List(Record(poly: UP,eq: LinearOrdinaryDifferentialOperator2(UP,Fraction(UP)))) +--R ricDsolve : (LinearOrdinaryDifferentialOperator1(Fraction(UP)),(UP -> List(F))) -> List(Fraction(UP)) +--R ricDsolve : (LinearOrdinaryDifferentialOperator1(Fraction(UP)),(UP -> List(F)),(UP -> Factored(UP))) -> List(Fraction(UP)) +--R ricDsolve : (LinearOrdinaryDifferentialOperator2(UP,Fraction(UP)),(UP -> List(F))) -> List(Fraction(UP)) +--R ricDsolve : (LinearOrdinaryDifferentialOperator2(UP,Fraction(UP)),(UP -> List(F)),(UP -> Factored(UP))) -> List(Fraction(UP)) +--R ricDsolve : LinearOrdinaryDifferentialOperator1(Fraction(UP)) -> List(Fraction(UP)) if F has ACF +--R ricDsolve : (LinearOrdinaryDifferentialOperator1(Fraction(UP)),(UP -> Factored(UP))) -> List(Fraction(UP)) if F has ACF +--R ricDsolve : LinearOrdinaryDifferentialOperator2(UP,Fraction(UP)) -> List(Fraction(UP)) if F has ACF +--R ricDsolve : (LinearOrdinaryDifferentialOperator2(UP,Fraction(UP)),(UP -> Factored(UP))) -> List(Fraction(UP)) if F has ACF +--R singRicDE : (LinearOrdinaryDifferentialOperator2(UP,Fraction(UP)),(UP -> Factored(UP))) -> List(Record(frac: Fraction(UP),eq: LinearOrdinaryDifferentialOperator2(UP,Fraction(UP)))) +--R --E 1 )spool @@ -166042,6 +171077,17 @@ RationalRicDE(F, UP): Exports == Implementation where --S 1 of 1 )show RationalUnivariateRepresentationPackage +--R +--R RationalUnivariateRepresentationPackage(R: Join(EuclideanDomain,CharacteristicZero),ls: List(Symbol)) is a package constructor +--R Abbreviation for RationalUnivariateRepresentationPackage is RURPK +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for RURPK +--R +--R------------------------------- Operations -------------------------------- +--R rur : (List(Polynomial(R)),Boolean) -> List(Record(complexRoots: SparseUnivariatePolynomial(R),coordinates: List(Polynomial(R)))) +--R rur : List(Polynomial(R)) -> List(Record(complexRoots: SparseUnivariatePolynomial(R),coordinates: List(Polynomial(R)))) +--R rur : (List(Polynomial(R)),Boolean,Boolean) -> List(Record(complexRoots: SparseUnivariatePolynomial(R),coordinates: List(Polynomial(R)))) +--R --E 1 )spool @@ -166258,6 +171304,19 @@ depending on several ``real roots''. --S 1 of 1 )show RealPolynomialUtilitiesPackage +--R +--R RealPolynomialUtilitiesPackage(TheField: Field,ThePols: UnivariatePolynomialCategory(TheField)) is a package constructor +--R Abbreviation for RealPolynomialUtilitiesPackage is POLUTIL +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for POLUTIL +--R +--R------------------------------- Operations -------------------------------- +--R boundOfCauchy : ThePols -> TheField if TheField has ORDRING +--R lazyVariations : (List(TheField),Integer,Integer) -> NonNegativeInteger if TheField has ORDRING +--R sturmSequence : ThePols -> List(ThePols) +--R sturmVariationsOf : List(TheField) -> NonNegativeInteger if TheField has ORDRING +--R sylvesterSequence : (ThePols,ThePols) -> List(ThePols) +--R --E 1 )spool @@ -166408,8 +171467,9 @@ RealPolynomialUtilitiesPackage(TheField,ThePols) : PUB == PRIV where )spool RealSolvePackage.output )set message test on )set message auto off + )clear all ---S 1 of 13 +--S 1 of 14 p := 4*x^3 - 3*x^2 + 2*x - 4 --R --R @@ -166418,7 +171478,7 @@ p := 4*x^3 - 3*x^2 + 2*x - 4 --R Type: Polynomial(Integer) --E 1 ---S 2 of 13 +--S 2 of 14 ans1 := solve(p,0.01)$REALSOLV --R --R @@ -166426,7 +171486,7 @@ ans1 := solve(p,0.01)$REALSOLV --R Type: List(Float) --E 2 ---S 3 of 13 +--S 3 of 14 ans2 := solve(p::POLY(FRAC(INT)),0.01)$REALSOLV --R --R @@ -166434,7 +171494,7 @@ ans2 := solve(p::POLY(FRAC(INT)),0.01)$REALSOLV --R Type: List(Float) --E 3 ---S 4 of 13 +--S 4 of 14 R := Integer --R --R @@ -166442,7 +171502,7 @@ R := Integer --R Type: Domain --E 4 ---S 5 of 13 +--S 5 of 14 ls : List Symbol := [x,y,z,t] --R --R @@ -166450,7 +171510,7 @@ ls : List Symbol := [x,y,z,t] --R Type: List(Symbol) --E 5 ---S 6 of 13 +--S 6 of 14 ls2 : List Symbol := [x,y,z,t,new()$Symbol] --R --R @@ -166458,7 +171518,7 @@ ls2 : List Symbol := [x,y,z,t,new()$Symbol] --R Type: List(Symbol) --E 6 ---S 7 of 13 +--S 7 of 14 pack := ZDSOLVE(R,ls,ls2) --R --R @@ -166466,7 +171526,7 @@ pack := ZDSOLVE(R,ls,ls2) --R Type: Domain --E 7 ---S 8 of 13 +--S 8 of 14 p1 := x**2*y*z + y*z --R --R @@ -166475,7 +171535,7 @@ p1 := x**2*y*z + y*z --R Type: Polynomial(Integer) --E 8 ---S 9 of 13 +--S 9 of 14 p2 := x**2*y**2*z + x + z --R --R @@ -166484,7 +171544,7 @@ p2 := x**2*y**2*z + x + z --R Type: Polynomial(Integer) --E 9 ---S 10 of 13 +--S 10 of 14 p3 := x**2*y**2*z**2 + z + 1 --R --R @@ -166493,7 +171553,7 @@ p3 := x**2*y**2*z**2 + z + 1 --R Type: Polynomial(Integer) --E 10 ---S 11 of 13 +--S 11 of 14 lp := [p1, p2, p3] --R --R @@ -166502,7 +171562,7 @@ lp := [p1, p2, p3] --R Type: List(Polynomial(Integer)) --E 11 ---S 12 of 13 +--S 12 of 14 lsv:List(Symbol):=[x,y,z] --R --R @@ -166510,13 +171570,29 @@ lsv:List(Symbol):=[x,y,z] --R Type: List(Symbol) --E 12 ---S 13 of 13 +--S 13 of 14 ans3 := realSolve(lp,lsv,0.01)$REALSOLV --R --R --R (13) [[1.0,0.0,- 1.0]] --R Type: List(List(Float)) --E 13 + +--S 14 of 14 +)show RealSolvePackage +--R +--R RealSolvePackage is a package constructor +--R Abbreviation for RealSolvePackage is REALSOLV +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for REALSOLV +--R +--R------------------------------- Operations -------------------------------- +--R realSolve : (List(Polynomial(Integer)),List(Symbol),Float) -> List(List(Float)) +--R solve : (Polynomial(Fraction(Integer)),Float) -> List(Float) +--R solve : (Polynomial(Integer),Float) -> List(Float) +--R +--E 14 + )spool \end{chunk} @@ -166645,6 +171721,22 @@ RealSolvePackage(): Exports == Implementation where --S 1 of 1 )show RealZeroPackage +--R +--R RealZeroPackage(Pol: UnivariatePolynomialCategory(Integer)) is a package constructor +--R Abbreviation for RealZeroPackage is REAL0 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for REAL0 +--R +--R------------------------------- Operations -------------------------------- +--R midpoint : Record(left: Fraction(Integer),right: Fraction(Integer)) -> Fraction(Integer) +--R midpoints : List(Record(left: Fraction(Integer),right: Fraction(Integer))) -> List(Fraction(Integer)) +--R realZeros : Pol -> List(Record(left: Fraction(Integer),right: Fraction(Integer))) +--R realZeros : (Pol,Record(left: Fraction(Integer),right: Fraction(Integer))) -> List(Record(left: Fraction(Integer),right: Fraction(Integer))) +--R realZeros : (Pol,Fraction(Integer)) -> List(Record(left: Fraction(Integer),right: Fraction(Integer))) +--R realZeros : (Pol,Record(left: Fraction(Integer),right: Fraction(Integer)),Fraction(Integer)) -> List(Record(left: Fraction(Integer),right: Fraction(Integer))) +--R refine : (Pol,Record(left: Fraction(Integer),right: Fraction(Integer)),Fraction(Integer)) -> Record(left: Fraction(Integer),right: Fraction(Integer)) +--R refine : (Pol,Record(left: Fraction(Integer),right: Fraction(Integer)),Record(left: Fraction(Integer),right: Fraction(Integer))) -> Union(Record(left: Fraction(Integer),right: Fraction(Integer)),"failed") +--R --E 1 )spool @@ -166978,6 +172070,20 @@ RealZeroPackage(Pol): T == C where --S 1 of 1 )show RealZeroPackageQ +--R +--R RealZeroPackageQ(Pol: UnivariatePolynomialCategory(Fraction(Integer))) is a package constructor +--R Abbreviation for RealZeroPackageQ is REAL0Q +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for REAL0Q +--R +--R------------------------------- Operations -------------------------------- +--R realZeros : Pol -> List(Record(left: Fraction(Integer),right: Fraction(Integer))) +--R realZeros : (Pol,Record(left: Fraction(Integer),right: Fraction(Integer))) -> List(Record(left: Fraction(Integer),right: Fraction(Integer))) +--R realZeros : (Pol,Fraction(Integer)) -> List(Record(left: Fraction(Integer),right: Fraction(Integer))) +--R realZeros : (Pol,Record(left: Fraction(Integer),right: Fraction(Integer)),Fraction(Integer)) -> List(Record(left: Fraction(Integer),right: Fraction(Integer))) +--R refine : (Pol,Record(left: Fraction(Integer),right: Fraction(Integer)),Fraction(Integer)) -> Record(left: Fraction(Integer),right: Fraction(Integer)) +--R refine : (Pol,Record(left: Fraction(Integer),right: Fraction(Integer)),Record(left: Fraction(Integer),right: Fraction(Integer))) -> Union(Record(left: Fraction(Integer),right: Fraction(Integer)),"failed") +--R --E 1 )spool @@ -167091,6 +172197,16 @@ RealZeroPackageQ(Pol): T == C where --S 1 of 1 )show RectangularMatrixCategoryFunctions2 +--R +--R RectangularMatrixCategoryFunctions2(m: NonNegativeInteger,n: NonNegativeInteger,R1: Ring,Row1: DirectProductCategory(n,R1),Col1: DirectProductCategory(m,R1),M1: RectangularMatrixCategory(m,n,R1,Row1,Col1),R2: Ring,Row2: DirectProductCategory(n,R2),Col2: DirectProductCategory(m,R2),M2: RectangularMatrixCategory(m,n,R2,Row2,Col2)) is a package constructor +--R Abbreviation for RectangularMatrixCategoryFunctions2 is RMCAT2 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for RMCAT2 +--R +--R------------------------------- Operations -------------------------------- +--R map : ((R1 -> R2),M1) -> M2 +--R reduce : (((R1,R2) -> R2),M1,R2) -> R2 +--R --E 1 )spool @@ -167186,6 +172302,20 @@ RectangularMatrixCategoryFunctions2(m,n,R1,Row1,Col1,M1,R2,Row2,Col2,M2):_ --S 1 of 1 )show RecurrenceOperator +--R +--R RecurrenceOperator(R: Join(OrderedSet,IntegralDomain,ConvertibleTo(InputForm)),F: Join(FunctionSpace(R),AbelianMonoid,RetractableTo(Integer),RetractableTo(Symbol),PartialDifferentialRing(Symbol),CombinatorialOpsCategory)) is a package constructor +--R Abbreviation for RecurrenceOperator is RECOP +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for RECOP +--R +--R------------------------------- Operations -------------------------------- +--R getEq : F -> F getOp : F -> BasicOperator +--R evalADE : (BasicOperator,Symbol,F,F,F,List(F)) -> F +--R evalRec : (BasicOperator,Symbol,F,F,F,List(F)) -> F +--R getShiftRec : (BasicOperator,Kernel(F),Symbol) -> Union(Integer,"failed") if R has RING +--R numberOfValuesNeeded : (Integer,BasicOperator,Symbol,F) -> Integer +--R shiftInfoRec : (BasicOperator,Symbol,F) -> Record(max: Union(Integer,"failed"),ord: Union(Integer,"failed"),ker: Kernel(F)) if R has RING +--R --E 1 )spool @@ -167721,6 +172851,15 @@ getOrder returns the maximum derivative of op occurring in f. --S 1 of 1 )show ReducedDivisor +--R +--R ReducedDivisor(F1: Field,UP: UnivariatePolynomialCategory(F1),UPUP: UnivariatePolynomialCategory(Fraction(UP)),R: FunctionFieldCategory(F1,UP,UPUP),F2: Join(Finite,Field)) is a package constructor +--R Abbreviation for ReducedDivisor is RDIV +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for RDIV +--R +--R------------------------------- Operations -------------------------------- +--R order : (FiniteDivisor(F1,UP,UPUP,R),UPUP,(F1 -> F2)) -> NonNegativeInteger +--R --E 1 )spool @@ -167812,6 +172951,15 @@ ReducedDivisor(F1, UP, UPUP, R, F2): Exports == Implementation where --S 1 of 1 )show ReduceLODE +--R +--R ReduceLODE(F: Field,L: LinearOrdinaryDifferentialOperatorCategory(F),UP: UnivariatePolynomialCategory(F),A: MonogenicAlgebra(F,UP),LO: LinearOrdinaryDifferentialOperatorCategory(A)) is a package constructor +--R Abbreviation for ReduceLODE is ODERED +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for ODERED +--R +--R------------------------------- Operations -------------------------------- +--R reduceLODE : (LO,A) -> Record(mat: Matrix(L),vec: Vector(F)) +--R --E 1 )spool @@ -167911,6 +173059,16 @@ ReduceLODE(F, L, UP, A, LO): Exports == Implementation where --S 1 of 1 )show ReductionOfOrder +--R +--R ReductionOfOrder(F: Field,L: LinearOrdinaryDifferentialOperatorCategory(F)) is a package constructor +--R Abbreviation for ReductionOfOrder is REDORDER +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for REDORDER +--R +--R------------------------------- Operations -------------------------------- +--R ReduceOrder : (L,F) -> L +--R ReduceOrder : (L,List(F)) -> Record(eq: L,op: List(F)) +--R --E 1 )spool @@ -168018,6 +173176,27 @@ ReductionOfOrder(F, L): Exports == Impl where --S 1 of 1 )show RegularSetDecompositionPackage +--R +--R RegularSetDecompositionPackage(R: GcdDomain,E: OrderedAbelianMonoidSup,V: OrderedSet,P: RecursivePolynomialCategory(R,E,V),TS: RegularTriangularSetCategory(R,E,V,P)) is a package constructor +--R Abbreviation for RegularSetDecompositionPackage is RSDCMPK +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for RSDCMPK +--R +--R------------------------------- Operations -------------------------------- +--R KrullNumber : (List(P),List(TS)) -> NonNegativeInteger +--R algebraicDecompose : (P,TS,Boolean) -> Record(done: List(TS),todo: List(Record(val: List(P),tower: TS))) +--R convert : Record(val: List(P),tower: TS) -> String +--R decompose : (List(P),List(TS),Boolean,Boolean) -> List(TS) +--R decompose : (List(P),List(TS),Boolean,Boolean,Boolean,Boolean,Boolean) -> List(TS) +--R internalDecompose : (P,TS,NonNegativeInteger,Boolean) -> Record(done: List(TS),todo: List(Record(val: List(P),tower: TS))) +--R internalDecompose : (P,TS,NonNegativeInteger) -> Record(done: List(TS),todo: List(Record(val: List(P),tower: TS))) +--R internalDecompose : (P,TS) -> Record(done: List(TS),todo: List(Record(val: List(P),tower: TS))) +--R numberOfVariables : (List(P),List(TS)) -> NonNegativeInteger +--R printInfo : (List(Record(val: List(P),tower: TS)),NonNegativeInteger) -> Void +--R transcendentalDecompose : (P,TS,NonNegativeInteger) -> Record(done: List(TS),todo: List(Record(val: List(P),tower: TS))) +--R transcendentalDecompose : (P,TS) -> Record(done: List(TS),todo: List(Record(val: List(P),tower: TS))) +--R upDateBranches : (List(P),List(TS),List(Record(val: List(P),tower: TS)),Record(done: List(TS),todo: List(Record(val: List(P),tower: TS))),NonNegativeInteger) -> List(Record(val: List(P),tower: TS)) +--R --E 1 )spool @@ -168360,6 +173539,26 @@ RegularSetDecompositionPackage(R,E,V,P,TS): Exports == Implementation where --S 1 of 1 )show RegularTriangularSetGcdPackage +--R +--R RegularTriangularSetGcdPackage(R: GcdDomain,E: OrderedAbelianMonoidSup,V: OrderedSet,P: RecursivePolynomialCategory(R,E,V),TS: RegularTriangularSetCategory(R,E,V,P)) is a package constructor +--R Abbreviation for RegularTriangularSetGcdPackage is RSETGCD +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for RSETGCD +--R +--R------------------------------- Operations -------------------------------- +--R stopTableGcd! : () -> Void stopTableInvSet! : () -> Void +--R toseInvertible? : (P,TS) -> Boolean +--R integralLastSubResultant : (P,P,TS) -> List(Record(val: P,tower: TS)) +--R internalLastSubResultant : (P,P,TS,Boolean,Boolean) -> List(Record(val: P,tower: TS)) +--R internalLastSubResultant : (List(Record(val: List(P),tower: TS)),V,Boolean) -> List(Record(val: P,tower: TS)) +--R prepareSubResAlgo : (P,P,TS) -> List(Record(val: List(P),tower: TS)) +--R startTableGcd! : (String,String,String) -> Void +--R startTableInvSet! : (String,String,String) -> Void +--R toseInvertible? : (P,TS) -> List(Record(val: Boolean,tower: TS)) +--R toseInvertibleSet : (P,TS) -> List(TS) +--R toseLastSubResultant : (P,P,TS) -> List(Record(val: P,tower: TS)) +--R toseSquareFreePart : (P,TS) -> List(Record(val: P,tower: TS)) +--R --E 1 )spool @@ -168762,6 +173961,17 @@ RegularTriangularSetGcdPackage(R,E,V,P,TS): Exports == Implementation where --S 1 of 1 )show RepeatedDoubling +--R +--R RepeatedDoubling(S)where +--R S: SetCategorywith +--R ?+? : (%,%) -> % is a package constructor +--R Abbreviation for RepeatedDoubling is REPDB +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for REPDB +--R +--R------------------------------- Operations -------------------------------- +--R double : (PositiveInteger,S) -> S +--R --E 1 )spool @@ -168833,6 +174043,17 @@ RepeatedDoubling(S):Exports ==Implementation where --S 1 of 1 )show RepeatedSquaring +--R +--R RepeatedSquaring(S)where +--R S: SetCategorywith +--R ?*? : (%,%) -> % is a package constructor +--R Abbreviation for RepeatedSquaring is REPSQ +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for REPSQ +--R +--R------------------------------- Operations -------------------------------- +--R expt : (S,PositiveInteger) -> S +--R --E 1 )spool @@ -168916,6 +174137,27 @@ RepeatedSquaring(S): Exports == Implementation where --S 1 of 1 )show RepresentationPackage1 +--R +--R RepresentationPackage1(R: Ring) is a package constructor +--R Abbreviation for RepresentationPackage1 is REP1 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for REP1 +--R +--R------------------------------- Operations -------------------------------- +--R antisymmetricTensors : (Matrix(R),PositiveInteger) -> Matrix(R) if R has commutative(*) +--R antisymmetricTensors : (List(Matrix(R)),PositiveInteger) -> List(Matrix(R)) if R has commutative(*) +--R createGenericMatrix : NonNegativeInteger -> Matrix(Polynomial(R)) +--R permutationRepresentation : (Permutation(Integer),Integer) -> Matrix(Integer) +--R permutationRepresentation : List(Integer) -> Matrix(Integer) +--R permutationRepresentation : (List(Permutation(Integer)),Integer) -> List(Matrix(Integer)) +--R permutationRepresentation : List(List(Integer)) -> List(Matrix(Integer)) +--R symmetricTensors : (Matrix(R),PositiveInteger) -> Matrix(R) +--R symmetricTensors : (List(Matrix(R)),PositiveInteger) -> List(Matrix(R)) +--R tensorProduct : (Matrix(R),Matrix(R)) -> Matrix(R) +--R tensorProduct : (List(Matrix(R)),List(Matrix(R))) -> List(Matrix(R)) +--R tensorProduct : Matrix(R) -> Matrix(R) +--R tensorProduct : List(Matrix(R)) -> List(Matrix(R)) +--R --E 1 )spool @@ -169293,6 +174535,30 @@ RepresentationPackage1(R): public == private where --S 1 of 1 )show RepresentationPackage2 +--R +--R RepresentationPackage2(R: Ring) is a package constructor +--R Abbreviation for RepresentationPackage2 is REP2 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for REP2 +--R +--R------------------------------- Operations -------------------------------- +--R areEquivalent? : (List(Matrix(R)),List(Matrix(R)),Boolean,Integer) -> Matrix(R) if R has FIELD +--R areEquivalent? : (List(Matrix(R)),List(Matrix(R))) -> Matrix(R) if R has FIELD +--R areEquivalent? : (List(Matrix(R)),List(Matrix(R)),Integer) -> Matrix(R) if R has FIELD +--R completeEchelonBasis : Vector(Vector(R)) -> Matrix(R) +--R createRandomElement : (List(Matrix(R)),Matrix(R)) -> Matrix(R) +--R cyclicSubmodule : (List(Matrix(R)),Vector(R)) -> Vector(Vector(R)) if R has EUCDOM +--R isAbsolutelyIrreducible? : (List(Matrix(R)),Integer) -> Boolean if R has FIELD +--R isAbsolutelyIrreducible? : List(Matrix(R)) -> Boolean if R has FIELD +--R meatAxe : (List(Matrix(R)),Boolean,Integer,Integer) -> List(List(Matrix(R))) if R has FIELD and R has FINITE +--R meatAxe : List(Matrix(R)) -> List(List(Matrix(R))) if R has FIELD and R has FINITE +--R meatAxe : (List(Matrix(R)),Boolean) -> List(List(Matrix(R))) if R has FIELD and R has FINITE +--R meatAxe : (List(Matrix(R)),PositiveInteger) -> List(List(Matrix(R))) if R has FIELD and R has FINITE +--R scanOneDimSubspaces : (List(Vector(R)),Integer) -> Vector(R) if R has FIELD and R has FINITE +--R split : (List(Matrix(R)),Vector(R)) -> List(List(Matrix(R))) if R has FIELD +--R split : (List(Matrix(R)),Vector(Vector(R))) -> List(List(Matrix(R))) if R has FIELD +--R standardBasisOfCyclicSubmodule : (List(Matrix(R)),Vector(R)) -> Matrix(R) if R has EUCDOM +--R --E 1 )spool @@ -170119,6 +175385,15 @@ RepresentationPackage2(R): public == private where --S 1 of 1 )show ResolveLatticeCompletion +--R +--R ResolveLatticeCompletion(S: Type) is a package constructor +--R Abbreviation for ResolveLatticeCompletion is RESLATC +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for RESLATC +--R +--R------------------------------- Operations -------------------------------- +--R coerce : S -> Void coerce : Exit -> S +--R --E 1 )spool @@ -170186,6 +175461,15 @@ ResolveLatticeCompletion(S: Type): with --S 1 of 1 )show RetractSolvePackage +--R +--R RetractSolvePackage(Q: IntegralDomain,R: Join(IntegralDomain,RetractableTo(Q))) is a package constructor +--R Abbreviation for RetractSolvePackage is RETSOL +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for RETSOL +--R +--R------------------------------- Operations -------------------------------- +--R solveRetract : (List(Polynomial(R)),List(Symbol)) -> List(List(Equation(Fraction(Polynomial(R))))) +--R --E 1 )spool @@ -170299,10 +175583,9 @@ RetractSolvePackage(Q, R): Exports == Implementation where --R Issue )edit bookvol10.4.pamphlet to see algebra source code for RFP --R --R------------------------------- Operations -------------------------------- ---R foundZeroes : () -> List(K) +--R foundZeroes : () -> List(K) setFoundZeroes : List(K) -> List(K) --R distinguishedCommonRootsOf : (List(SparseUnivariatePolynomial(K)),K) -> Record(zeros: List(K),extDegree: Integer) --R distinguishedRootsOf : (SparseUnivariatePolynomial(K),K) -> Record(zeros: List(K),extDegree: Integer) ---R setFoundZeroes : List(K) -> List(K) --R --E 1 @@ -170474,6 +175757,15 @@ RootsFindingPackage(K):P==T where --S 1 of 1 )show SAERationalFunctionAlgFactor +--R +--R SAERationalFunctionAlgFactor(UP: UnivariatePolynomialCategory(Fraction(Polynomial(Integer))),SAE: Join(Field,CharacteristicZero,MonogenicAlgebra(Fraction(Polynomial(Integer)),UP)),UPA: UnivariatePolynomialCategory(SAE)) is a package constructor +--R Abbreviation for SAERationalFunctionAlgFactor is SAERFFC +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for SAERFFC +--R +--R------------------------------- Operations -------------------------------- +--R factor : UPA -> Factored(UPA) +--R --E 1 )spool @@ -170538,6 +175830,15 @@ SAERationalFunctionAlgFactor(UP, SAE, UPA): Exports == Implementation where --S 1 of 1 )show ScriptFormulaFormat1 +--R +--R ScriptFormulaFormat1(S: SetCategory) is a package constructor +--R Abbreviation for ScriptFormulaFormat1 is FORMULA1 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for FORMULA1 +--R +--R------------------------------- Operations -------------------------------- +--R coerce : S -> ScriptFormulaFormat +--R --E 1 )spool @@ -170610,6 +175911,15 @@ ScriptFormulaFormat1(S : SetCategory): public == private where --S 1 of 1 )show SegmentBindingFunctions2 +--R +--R SegmentBindingFunctions2(R: Type,S: Type) is a package constructor +--R Abbreviation for SegmentBindingFunctions2 is SEGBIND2 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for SEGBIND2 +--R +--R------------------------------- Operations -------------------------------- +--R map : ((R -> S),SegmentBinding(R)) -> SegmentBinding(S) +--R --E 1 )spool @@ -170665,6 +175975,16 @@ SegmentBindingFunctions2(R:Type, S:Type): with --S 1 of 1 )show SegmentFunctions2 +--R +--R SegmentFunctions2(R: Type,S: Type) is a package constructor +--R Abbreviation for SegmentFunctions2 is SEG2 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for SEG2 +--R +--R------------------------------- Operations -------------------------------- +--R map : ((R -> S),Segment(R)) -> Segment(S) +--R map : ((R -> S),Segment(R)) -> List(S) if R has ORDRING +--R --E 1 )spool @@ -170745,6 +176065,15 @@ SegmentFunctions2(R:Type, S:Type): public == private where --S 1 of 1 )show SimpleAlgebraicExtensionAlgFactor +--R +--R SimpleAlgebraicExtensionAlgFactor(UP: UnivariatePolynomialCategory(Fraction(Integer)),SAE: Join(Field,CharacteristicZero,MonogenicAlgebra(Fraction(Integer),UP)),UPA: UnivariatePolynomialCategory(SAE)) is a package constructor +--R Abbreviation for SimpleAlgebraicExtensionAlgFactor is SAEFACT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for SAEFACT +--R +--R------------------------------- Operations -------------------------------- +--R factor : UPA -> Factored(UPA) +--R --E 1 )spool @@ -170809,6 +176138,15 @@ SimpleAlgebraicExtensionAlgFactor(UP,SAE,UPA):Exports==Implementation where --S 1 of 1 )show SimplifyAlgebraicNumberConvertPackage +--R +--R SimplifyAlgebraicNumberConvertPackage is a package constructor +--R Abbreviation for SimplifyAlgebraicNumberConvertPackage is SIMPAN +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for SIMPAN +--R +--R------------------------------- Operations -------------------------------- +--R simplify : AlgebraicNumber -> Expression(Integer) +--R --E 1 )spool @@ -170864,6 +176202,18 @@ SimplifyAlgebraicNumberConvertPackage(): with --S 1 of 1 )show SmithNormalForm +--R +--R SmithNormalForm(R: EuclideanDomain,Row: FiniteLinearAggregate(R),Col: FiniteLinearAggregate(R),M: MatrixCategory(R,Row,Col)) is a package constructor +--R Abbreviation for SmithNormalForm is SMITH +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for SMITH +--R +--R------------------------------- Operations -------------------------------- +--R hermite : M -> M smith : M -> M +--R completeHermite : M -> Record(Hermite: M,eqMat: M) +--R completeSmith : M -> Record(Smith: M,leftEqMat: M,rightEqMat: M) +--R diophantineSystem : (M,Col) -> Record(particular: Union(Col,"failed"),basis: List(Col)) +--R --E 1 )spool @@ -171132,6 +176482,17 @@ SmithNormalForm(R,Row,Col,M) : Exports == Implementation where --S 1 of 1 )show SortedCache +--R +--R SortedCache(S: CachableSet) is a package constructor +--R Abbreviation for SortedCache is SCACHE +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for SCACHE +--R +--R------------------------------- Operations -------------------------------- +--R cache : () -> List(S) clearCache : () -> Void +--R enterInCache : (S,(S -> Boolean)) -> S +--R enterInCache : (S,((S,S) -> Integer)) -> S +--R --E 1 )spool @@ -171260,6 +176621,21 @@ SortedCache(S:CachableSet): Exports == Implementation where --S 1 of 1 )show SortPackage +--R +--R SortPackage(S: Type,A)where +--R A: IndexedAggregate(Integer,S)with +--R finiteAggregate +--R shallowlyMutable is a package constructor +--R Abbreviation for SortPackage is SORTPAK +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for SORTPAK +--R +--R------------------------------- Operations -------------------------------- +--R bubbleSort! : A -> A if S has ORDSET +--R bubbleSort! : (A,((S,S) -> Boolean)) -> A +--R insertionSort! : (A,((S,S) -> Boolean)) -> A +--R insertionSort! : A -> A if S has ORDSET +--R --E 1 )spool @@ -171358,6 +176734,15 @@ SortPackage(S,A) : Exports == Implementation where --S 1 of 1 )show SparseUnivariatePolynomialFunctions2 +--R +--R SparseUnivariatePolynomialFunctions2(R: Ring,S: Ring) is a package constructor +--R Abbreviation for SparseUnivariatePolynomialFunctions2 is SUP2 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for SUP2 +--R +--R------------------------------- Operations -------------------------------- +--R map : ((R -> S),SparseUnivariatePolynomial(R)) -> SparseUnivariatePolynomial(S) +--R --E 1 )spool @@ -171423,6 +176808,20 @@ SparseUnivariatePolynomialFunctions2(R:Ring, S:Ring): with --S 1 of 1 )show SpecialOutputPackage +--R +--R SpecialOutputPackage is a package constructor +--R Abbreviation for SpecialOutputPackage is SPECOUT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for SPECOUT +--R +--R------------------------------- Operations -------------------------------- +--R outputAsFortran : OutputForm -> Void outputAsScript : OutputForm -> Void +--R outputAsTex : OutputForm -> Void +--R outputAsFortran : (String,OutputForm) -> Void +--R outputAsFortran : List(OutputForm) -> Void +--R outputAsScript : List(OutputForm) -> Void +--R outputAsTex : List(OutputForm) -> Void +--R --E 1 )spool @@ -171542,6 +176941,30 @@ SpecialOutputPackage: public == private where --S 1 of 1 )show SquareFreeQuasiComponentPackage +--R +--R SquareFreeQuasiComponentPackage(R: GcdDomain,E: OrderedAbelianMonoidSup,V: OrderedSet,P: RecursivePolynomialCategory(R,E,V),TS: RegularTriangularSetCategory(R,E,V,P)) is a package constructor +--R Abbreviation for SquareFreeQuasiComponentPackage is SFQCMPK +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for SFQCMPK +--R +--R------------------------------- Operations -------------------------------- +--R algebraicSort : List(TS) -> List(TS) moreAlgebraic? : (TS,TS) -> Boolean +--R stopTable! : () -> Void subTriSet? : (TS,TS) -> Boolean +--R branchIfCan : (List(P),TS,List(P),Boolean,Boolean,Boolean,Boolean,Boolean) -> Union(Record(eq: List(P),tower: TS,ineq: List(P)),"failed") +--R infRittWu? : (List(P),List(P)) -> Boolean +--R internalInfRittWu? : (List(P),List(P)) -> Boolean +--R internalSubPolSet? : (List(P),List(P)) -> Boolean +--R internalSubQuasiComponent? : (TS,TS) -> Union(Boolean,"failed") +--R prepareDecompose : (List(P),List(TS),Boolean,Boolean) -> List(Record(eq: List(P),tower: TS,ineq: List(P))) +--R removeSuperfluousCases : List(Record(val: List(P),tower: TS)) -> List(Record(val: List(P),tower: TS)) +--R removeSuperfluousQuasiComponents : List(TS) -> List(TS) +--R startTable! : (String,String,String) -> Void +--R subCase? : (Record(val: List(P),tower: TS),Record(val: List(P),tower: TS)) -> Boolean +--R subPolSet? : (List(P),List(P)) -> Boolean +--R subQuasiComponent? : (TS,TS) -> Boolean +--R subQuasiComponent? : (TS,List(TS)) -> Boolean +--R supDimElseRittWu? : (TS,TS) -> Boolean +--R --E 1 )spool @@ -172001,6 +177424,27 @@ SquareFreeQuasiComponentPackage(R,E,V,P,TS): Exports == Implementation where --S 1 of 1 )show SquareFreeRegularSetDecompositionPackage +--R +--R SquareFreeRegularSetDecompositionPackage(R: GcdDomain,E: OrderedAbelianMonoidSup,V: OrderedSet,P: RecursivePolynomialCategory(R,E,V),TS: SquareFreeRegularTriangularSetCategory(R,E,V,P)) is a package constructor +--R Abbreviation for SquareFreeRegularSetDecompositionPackage is SRDCMPK +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for SRDCMPK +--R +--R------------------------------- Operations -------------------------------- +--R KrullNumber : (List(P),List(TS)) -> NonNegativeInteger +--R algebraicDecompose : (P,TS) -> Record(done: List(TS),todo: List(Record(val: List(P),tower: TS))) +--R convert : Record(val: List(P),tower: TS) -> String +--R decompose : (List(P),List(TS),Boolean,Boolean) -> List(TS) +--R decompose : (List(P),List(TS),Boolean,Boolean,Boolean,Boolean,Boolean) -> List(TS) +--R internalDecompose : (P,TS,NonNegativeInteger,Boolean) -> Record(done: List(TS),todo: List(Record(val: List(P),tower: TS))) +--R internalDecompose : (P,TS,NonNegativeInteger) -> Record(done: List(TS),todo: List(Record(val: List(P),tower: TS))) +--R internalDecompose : (P,TS) -> Record(done: List(TS),todo: List(Record(val: List(P),tower: TS))) +--R numberOfVariables : (List(P),List(TS)) -> NonNegativeInteger +--R printInfo : (List(Record(val: List(P),tower: TS)),NonNegativeInteger) -> Void +--R transcendentalDecompose : (P,TS,NonNegativeInteger) -> Record(done: List(TS),todo: List(Record(val: List(P),tower: TS))) +--R transcendentalDecompose : (P,TS) -> Record(done: List(TS),todo: List(Record(val: List(P),tower: TS))) +--R upDateBranches : (List(P),List(TS),List(Record(val: List(P),tower: TS)),Record(done: List(TS),todo: List(Record(val: List(P),tower: TS))),NonNegativeInteger) -> List(Record(val: List(P),tower: TS)) +--R --E 1 )spool @@ -172341,6 +177785,30 @@ SquareFreeRegularSetDecompositionPackage(R,E,V,P,TS): Exports == Implementation --S 1 of 1 )show SquareFreeRegularTriangularSetGcdPackage +--R +--R SquareFreeRegularTriangularSetGcdPackage(R: GcdDomain,E: OrderedAbelianMonoidSup,V: OrderedSet,P: RecursivePolynomialCategory(R,E,V),TS: RegularTriangularSetCategory(R,E,V,P)) is a package constructor +--R Abbreviation for SquareFreeRegularTriangularSetGcdPackage is SFRGCD +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for SFRGCD +--R +--R------------------------------- Operations -------------------------------- +--R stopTableGcd! : () -> Void stopTableInvSet! : () -> Void +--R stoseInvertible? : (P,TS) -> Boolean +--R startTableGcd! : (String,String,String) -> Void +--R startTableInvSet! : (String,String,String) -> Void +--R stoseIntegralLastSubResultant : (P,P,TS) -> List(Record(val: P,tower: TS)) +--R stoseInternalLastSubResultant : (P,P,TS,Boolean,Boolean) -> List(Record(val: P,tower: TS)) +--R stoseInternalLastSubResultant : (List(Record(val: List(P),tower: TS)),V,Boolean) -> List(Record(val: P,tower: TS)) +--R stoseInvertible? : (P,TS) -> List(Record(val: Boolean,tower: TS)) +--R stoseInvertible?reg : (P,TS) -> List(Record(val: Boolean,tower: TS)) +--R stoseInvertible?sqfreg : (P,TS) -> List(Record(val: Boolean,tower: TS)) +--R stoseInvertibleSet : (P,TS) -> List(TS) +--R stoseInvertibleSetreg : (P,TS) -> List(TS) +--R stoseInvertibleSetsqfreg : (P,TS) -> List(TS) +--R stoseLastSubResultant : (P,P,TS) -> List(Record(val: P,tower: TS)) +--R stosePrepareSubResAlgo : (P,P,TS) -> List(Record(val: List(P),tower: TS)) +--R stoseSquareFreePart : (P,TS) -> List(Record(val: P,tower: TS)) +--R --E 1 )spool @@ -172843,6 +178311,23 @@ SquareFreeRegularTriangularSetGcdPackage(R,E,V,P,TS): Exports == Implementation --S 1 of 1 )show StorageEfficientMatrixOperations +--R +--R StorageEfficientMatrixOperations(R: Ring) is a package constructor +--R Abbreviation for StorageEfficientMatrixOperations is MATSTOR +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for MATSTOR +--R +--R------------------------------- Operations -------------------------------- +--R ?**? : (Matrix(R),NonNegativeInteger) -> Matrix(R) +--R copy! : (Matrix(R),Matrix(R)) -> Matrix(R) +--R leftScalarTimes! : (Matrix(R),R,Matrix(R)) -> Matrix(R) +--R minus! : (Matrix(R),Matrix(R)) -> Matrix(R) +--R minus! : (Matrix(R),Matrix(R),Matrix(R)) -> Matrix(R) +--R plus! : (Matrix(R),Matrix(R),Matrix(R)) -> Matrix(R) +--R power! : (Matrix(R),Matrix(R),Matrix(R),Matrix(R),NonNegativeInteger) -> Matrix(R) +--R rightScalarTimes! : (Matrix(R),Matrix(R),R) -> Matrix(R) +--R times! : (Matrix(R),Matrix(R),Matrix(R)) -> Matrix(R) +--R --E 1 )spool @@ -173081,6 +178566,15 @@ StorageEfficientMatrixOperations(R): Exports == Implementation where --S 1 of 1 )show StreamFunctions1 +--R +--R StreamFunctions1(S: Type) is a package constructor +--R Abbreviation for StreamFunctions1 is STREAM1 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for STREAM1 +--R +--R------------------------------- Operations -------------------------------- +--R concat : Stream(Stream(S)) -> Stream(S) +--R --E 1 )spool @@ -173150,6 +178644,17 @@ StreamFunctions1(S:Type): Exports == Implementation where --S 1 of 1 )show StreamFunctions2 +--R +--R StreamFunctions2(A: Type,B: Type) is a package constructor +--R Abbreviation for StreamFunctions2 is STREAM2 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for STREAM2 +--R +--R------------------------------- Operations -------------------------------- +--R map : ((A -> B),Stream(A)) -> Stream(B) +--R reduce : (B,((A,B) -> B),Stream(A)) -> B +--R scan : (B,((A,B) -> B),Stream(A)) -> Stream(B) +--R --E 1 )spool @@ -173268,6 +178773,15 @@ StreamFunctions2(A:Type,B:Type): Exports == Implementation where --S 1 of 1 )show StreamFunctions3 +--R +--R StreamFunctions3(A: Type,B: Type,C: Type) is a package constructor +--R Abbreviation for StreamFunctions3 is STREAM3 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for STREAM3 +--R +--R------------------------------- Operations -------------------------------- +--R map : (((A,B) -> C),Stream(A),Stream(B)) -> Stream(C) +--R --E 1 )spool @@ -173349,6 +178863,18 @@ StreamFunctions3(A,B,C): Exports == Implementation where --S 1 of 1 )show StreamInfiniteProduct +--R +--R StreamInfiniteProduct(Coef: Join(IntegralDomain,CharacteristicZero)) is a package constructor +--R Abbreviation for StreamInfiniteProduct is STINPROD +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for STINPROD +--R +--R------------------------------- Operations -------------------------------- +--R evenInfiniteProduct : Stream(Coef) -> Stream(Coef) +--R generalInfiniteProduct : (Stream(Coef),Integer,Integer) -> Stream(Coef) +--R infiniteProduct : Stream(Coef) -> Stream(Coef) +--R oddInfiniteProduct : Stream(Coef) -> Stream(Coef) +--R --E 1 )spool @@ -173457,6 +178983,43 @@ StreamInfiniteProduct(Coef): Exports == Implementation where --S 1 of 1 )show StreamTaylorSeriesOperations +--R +--R StreamTaylorSeriesOperations(A: Ring) is a package constructor +--R Abbreviation for StreamTaylorSeriesOperations is STTAYLOR +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for STTAYLOR +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (A,Stream(A)) -> Stream(A) ?*? : (Stream(A),A) -> Stream(A) +--R -? : Stream(A) -> Stream(A) coerce : A -> Stream(A) +--R deriv : Stream(A) -> Stream(A) eval : (Stream(A),A) -> Stream(A) +--R evenlambert : Stream(A) -> Stream(A) int : A -> Stream(A) +--R lagrange : Stream(A) -> Stream(A) lambert : Stream(A) -> Stream(A) +--R monom : (A,Integer) -> Stream(A) oddlambert : Stream(A) -> Stream(A) +--R revert : Stream(A) -> Stream(A) +--R ?*? : (Stream(A),Stream(A)) -> Stream(A) +--R ?+? : (Stream(A),Stream(A)) -> Stream(A) +--R ?-? : (Stream(A),Stream(A)) -> Stream(A) +--R ?/? : (Stream(A),Stream(A)) -> Stream(A) +--R addiag : Stream(Stream(A)) -> Stream(A) +--R compose : (Stream(A),Stream(A)) -> Stream(A) +--R exquo : (Stream(A),Stream(A)) -> Union(Stream(A),"failed") +--R gderiv : ((Integer -> A),Stream(A)) -> Stream(A) +--R generalLambert : (Stream(A),Integer,Integer) -> Stream(A) +--R integers : Integer -> Stream(Integer) +--R integrate : (A,Stream(A)) -> Stream(A) if A has ALGEBRA(FRAC(INT)) +--R invmultisect : (Integer,Integer,Stream(A)) -> Stream(A) +--R lazyGintegrate : ((Integer -> A),A,(() -> Stream(A))) -> Stream(A) if A has FIELD +--R lazyIntegrate : (A,(() -> Stream(A))) -> Stream(A) if A has ALGEBRA(FRAC(INT)) +--R mapdiv : (Stream(A),Stream(A)) -> Stream(A) if A has FIELD +--R mapmult : (Stream(A),Stream(A)) -> Stream(A) +--R multisect : (Integer,Integer,Stream(A)) -> Stream(A) +--R nlde : Stream(Stream(A)) -> Stream(A) if A has ALGEBRA(FRAC(INT)) +--R oddintegers : Integer -> Stream(Integer) +--R power : (A,Stream(A)) -> Stream(A) if A has FIELD +--R powern : (Fraction(Integer),Stream(A)) -> Stream(A) if A has ALGEBRA(FRAC(INT)) +--R recip : Stream(A) -> Union(Stream(A),"failed") +--R --E 1 )spool @@ -174052,6 +179615,30 @@ StreamTensor(R: Type): with --S 1 of 1 )show StreamTranscendentalFunctions +--R +--R StreamTranscendentalFunctions(Coef: Algebra(Fraction(Integer))) is a package constructor +--R Abbreviation for StreamTranscendentalFunctions is STTF +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for STTF +--R +--R------------------------------- Operations -------------------------------- +--R acos : Stream(Coef) -> Stream(Coef) acosh : Stream(Coef) -> Stream(Coef) +--R acot : Stream(Coef) -> Stream(Coef) acoth : Stream(Coef) -> Stream(Coef) +--R acsc : Stream(Coef) -> Stream(Coef) acsch : Stream(Coef) -> Stream(Coef) +--R asec : Stream(Coef) -> Stream(Coef) asech : Stream(Coef) -> Stream(Coef) +--R asin : Stream(Coef) -> Stream(Coef) asinh : Stream(Coef) -> Stream(Coef) +--R atan : Stream(Coef) -> Stream(Coef) atanh : Stream(Coef) -> Stream(Coef) +--R cos : Stream(Coef) -> Stream(Coef) cosh : Stream(Coef) -> Stream(Coef) +--R cot : Stream(Coef) -> Stream(Coef) coth : Stream(Coef) -> Stream(Coef) +--R csc : Stream(Coef) -> Stream(Coef) csch : Stream(Coef) -> Stream(Coef) +--R exp : Stream(Coef) -> Stream(Coef) log : Stream(Coef) -> Stream(Coef) +--R sec : Stream(Coef) -> Stream(Coef) sech : Stream(Coef) -> Stream(Coef) +--R sin : Stream(Coef) -> Stream(Coef) sinh : Stream(Coef) -> Stream(Coef) +--R tan : Stream(Coef) -> Stream(Coef) tanh : Stream(Coef) -> Stream(Coef) +--R ?**? : (Stream(Coef),Stream(Coef)) -> Stream(Coef) +--R sincos : Stream(Coef) -> Record(sin: Stream(Coef),cos: Stream(Coef)) +--R sinhcosh : Stream(Coef) -> Record(sinh: Stream(Coef),cosh: Stream(Coef)) +--R --E 1 )spool @@ -174554,6 +180141,28 @@ StreamTranscendentalFunctions(Coef): Exports == Implementation where --S 1 of 1 )show StreamTranscendentalFunctionsNonCommutative +--R +--R StreamTranscendentalFunctionsNonCommutative(Coef: Algebra(Fraction(Integer))) is a package constructor +--R Abbreviation for StreamTranscendentalFunctionsNonCommutative is STTFNC +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for STTFNC +--R +--R------------------------------- Operations -------------------------------- +--R acos : Stream(Coef) -> Stream(Coef) acosh : Stream(Coef) -> Stream(Coef) +--R acot : Stream(Coef) -> Stream(Coef) acoth : Stream(Coef) -> Stream(Coef) +--R acsc : Stream(Coef) -> Stream(Coef) acsch : Stream(Coef) -> Stream(Coef) +--R asec : Stream(Coef) -> Stream(Coef) asech : Stream(Coef) -> Stream(Coef) +--R asin : Stream(Coef) -> Stream(Coef) asinh : Stream(Coef) -> Stream(Coef) +--R atan : Stream(Coef) -> Stream(Coef) atanh : Stream(Coef) -> Stream(Coef) +--R cos : Stream(Coef) -> Stream(Coef) cosh : Stream(Coef) -> Stream(Coef) +--R cot : Stream(Coef) -> Stream(Coef) coth : Stream(Coef) -> Stream(Coef) +--R csc : Stream(Coef) -> Stream(Coef) csch : Stream(Coef) -> Stream(Coef) +--R exp : Stream(Coef) -> Stream(Coef) log : Stream(Coef) -> Stream(Coef) +--R sec : Stream(Coef) -> Stream(Coef) sech : Stream(Coef) -> Stream(Coef) +--R sin : Stream(Coef) -> Stream(Coef) sinh : Stream(Coef) -> Stream(Coef) +--R tan : Stream(Coef) -> Stream(Coef) tanh : Stream(Coef) -> Stream(Coef) +--R ?**? : (Stream(Coef),Stream(Coef)) -> Stream(Coef) +--R --E 1 )spool @@ -174842,6 +180451,18 @@ StreamTranscendentalFunctionsNonCommutative(Coef): _ --S 1 of 1 )show StructuralConstantsPackage +--R +--R StructuralConstantsPackage(R: Field) is a package constructor +--R Abbreviation for StructuralConstantsPackage is SCPKG +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for SCPKG +--R +--R------------------------------- Operations -------------------------------- +--R coordinates : (Matrix(R),List(Matrix(R))) -> Vector(R) +--R structuralConstants : (List(Symbol),Matrix(Fraction(Polynomial(R)))) -> Vector(Matrix(Fraction(Polynomial(R)))) +--R structuralConstants : (List(Symbol),Matrix(Polynomial(R))) -> Vector(Matrix(Polynomial(R))) +--R structuralConstants : List(Matrix(R)) -> Vector(Matrix(R)) +--R --E 1 )spool @@ -175019,6 +180640,21 @@ must be linear polynomials in the generators" --S 1 of 1 )show SturmHabichtPackage +--R +--R SturmHabichtPackage(R: OrderedIntegralDomain,x: Symbol) is a package constructor +--R Abbreviation for SturmHabichtPackage is SHP +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for SHP +--R +--R------------------------------- Operations -------------------------------- +--R SturmHabicht : (UnivariatePolynomial(x,R),UnivariatePolynomial(x,R)) -> Integer +--R SturmHabichtCoefficients : (UnivariatePolynomial(x,R),UnivariatePolynomial(x,R)) -> List(R) +--R SturmHabichtMultiple : (UnivariatePolynomial(x,R),UnivariatePolynomial(x,R)) -> Integer if R has GCDDOM +--R SturmHabichtSequence : (UnivariatePolynomial(x,R),UnivariatePolynomial(x,R)) -> List(UnivariatePolynomial(x,R)) +--R countRealRoots : UnivariatePolynomial(x,R) -> Integer +--R countRealRootsMultiple : UnivariatePolynomial(x,R) -> Integer if R has GCDDOM +--R subresultantSequence : (UnivariatePolynomial(x,R),UnivariatePolynomial(x,R)) -> List(UnivariatePolynomial(x,R)) +--R --E 1 )spool @@ -175428,6 +181064,16 @@ SturmHabichtPackage(R,x): T == C where --S 1 of 1 )show SubResultantPackage +--R +--R SubResultantPackage(R: IntegralDomain,UP: UnivariatePolynomialCategory(R)) is a package constructor +--R Abbreviation for SubResultantPackage is SUBRESP +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for SUBRESP +--R +--R------------------------------- Operations -------------------------------- +--R primitivePart : (UP,R) -> UP if R has EUCDOM +--R subresultantVector : (UP,UP) -> PrimitiveArray(UP) +--R --E 1 )spool @@ -175604,6 +181250,16 @@ SubResultantPackage(R, UP): Exports == Implementation where --S 1 of 1 )show SupFractionFactorizer +--R +--R SupFractionFactorizer(E: OrderedAbelianMonoidSup,OV: OrderedSet,R: GcdDomain,P: PolynomialCategory(R,E,OV)) is a package constructor +--R Abbreviation for SupFractionFactorizer is SUPFRACF +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for SUPFRACF +--R +--R------------------------------- Operations -------------------------------- +--R factor : SparseUnivariatePolynomial(Fraction(P)) -> Factored(SparseUnivariatePolynomial(Fraction(P))) +--R squareFree : SparseUnivariatePolynomial(Fraction(P)) -> Factored(SparseUnivariatePolynomial(Fraction(P))) +--R --E 1 )spool @@ -175709,6 +181365,18 @@ SupFractionFactorizer(E,OV,R,P) : C == T --S 1 of 1 )show SystemODESolver +--R +--R SystemODESolver(F: Field,LO: LinearOrdinaryDifferentialOperatorCategory(F)) is a package constructor +--R Abbreviation for SystemODESolver is ODESYS +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for ODESYS +--R +--R------------------------------- Operations -------------------------------- +--R solve : (Matrix(F),Vector(F),((LO,F) -> Union(Record(particular: F,basis: List(F)),"failed"))) -> Union(Record(particular: Vector(F),basis: Matrix(F)),"failed") +--R solveInField : (Matrix(LO),Vector(F),((LO,F) -> Record(particular: Union(F,"failed"),basis: List(F)))) -> Record(particular: Union(Vector(F),"failed"),basis: List(Vector(F))) +--R triangulate : (Matrix(F),Vector(F)) -> Record(A: Matrix(F),eqs: List(Record(C: Matrix(F),g: Vector(F),eq: LO,rh: F))) +--R triangulate : (Matrix(LO),Vector(F)) -> Record(mat: Matrix(LO),vec: Vector(F)) +--R --E 1 )spool @@ -175990,6 +181658,23 @@ SystemODESolver(F, LO): Exports == Implementation where --S 1 of 1 )show SystemSolvePackage +--R +--R SystemSolvePackage(R: IntegralDomain) is a package constructor +--R Abbreviation for SystemSolvePackage is SYSSOLP +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for SYSSOLP +--R +--R------------------------------- Operations -------------------------------- +--R solve : (List(Fraction(Polynomial(R))),List(Symbol)) -> List(List(Equation(Fraction(Polynomial(R))))) +--R solve : (List(Equation(Fraction(Polynomial(R)))),List(Symbol)) -> List(List(Equation(Fraction(Polynomial(R))))) +--R solve : List(Fraction(Polynomial(R))) -> List(List(Equation(Fraction(Polynomial(R))))) +--R solve : List(Equation(Fraction(Polynomial(R)))) -> List(List(Equation(Fraction(Polynomial(R))))) +--R solve : (Fraction(Polynomial(R)),Symbol) -> List(Equation(Fraction(Polynomial(R)))) +--R solve : (Equation(Fraction(Polynomial(R))),Symbol) -> List(Equation(Fraction(Polynomial(R)))) +--R solve : Fraction(Polynomial(R)) -> List(Equation(Fraction(Polynomial(R)))) +--R solve : Equation(Fraction(Polynomial(R))) -> List(Equation(Fraction(Polynomial(R)))) +--R triangularSystems : (List(Fraction(Polynomial(R))),List(Symbol)) -> List(List(Polynomial(R))) +--R --E 1 )spool @@ -176284,6 +181969,26 @@ SystemSolvePackage(R): Cat == Cap where --S 1 of 1 )show SymmetricGroupCombinatoricFunctions +--R +--R SymmetricGroupCombinatoricFunctions is a package constructor +--R Abbreviation for SymmetricGroupCombinatoricFunctions is SGCF +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for SGCF +--R +--R------------------------------- Operations -------------------------------- +--R coleman : (List(Integer),List(Integer),List(Integer)) -> Matrix(Integer) +--R inverseColeman : (List(Integer),List(Integer),Matrix(Integer)) -> List(Integer) +--R listYoungTableaus : List(Integer) -> List(Matrix(Integer)) +--R makeYoungTableau : (List(Integer),List(Integer)) -> Matrix(Integer) +--R nextColeman : (List(Integer),List(Integer),Matrix(Integer)) -> Matrix(Integer) +--R nextLatticePermutation : (List(Integer),List(Integer),Boolean) -> List(Integer) +--R nextPartition : (Vector(Integer),Vector(Integer),Integer) -> Vector(Integer) +--R nextPartition : (List(Integer),Vector(Integer),Integer) -> Vector(Integer) +--R numberOfImproperPartitions : (Integer,Integer) -> Integer +--R subSet : (Integer,Integer,Integer) -> List(Integer) +--R unrankImproperPartitions0 : (Integer,Integer,Integer) -> List(Integer) +--R unrankImproperPartitions1 : (Integer,Integer,Integer) -> List(Integer) +--R --E 1 )spool @@ -176801,6 +182506,16 @@ SymmetricGroupCombinatoricFunctions(): public == private where --S 1 of 1 )show SymmetricFunctions +--R +--R SymmetricFunctions(R: Ring) is a package constructor +--R Abbreviation for SymmetricFunctions is SYMFUNC +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for SYMFUNC +--R +--R------------------------------- Operations -------------------------------- +--R symFunc : List(R) -> Vector(R) +--R symFunc : (R,PositiveInteger) -> Vector(R) +--R --E 1 )spool @@ -176878,6 +182593,25 @@ SymmetricFunctions(R:Ring): Exports == Implementation where --S 1 of 1 )show TableauxBumpers +--R +--R TableauxBumpers(S: OrderedSet) is a package constructor +--R Abbreviation for TableauxBumpers is TABLBUMP +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for TABLBUMP +--R +--R------------------------------- Operations -------------------------------- +--R inverse : List(S) -> List(S) lex : List(List(S)) -> List(List(S)) +--R slex : List(S) -> List(List(S)) tab : List(S) -> Tableau(List(S)) +--R bat : Tableau(List(S)) -> List(List(S)) +--R bat1 : List(List(List(S))) -> List(List(S)) +--R bumprow : (((S,S) -> Boolean),List(S),List(List(S))) -> Record(fs: Boolean,sd: List(S),td: List(List(S))) +--R bumptab : (((S,S) -> Boolean),List(S),List(List(List(S)))) -> List(List(List(S))) +--R bumptab1 : (List(S),List(List(List(S)))) -> List(List(List(S))) +--R maxrow : (List(S),List(List(List(S))),List(List(S)),List(List(List(S))),List(List(List(S))),List(List(List(S)))) -> Record(f1: List(S),f2: List(List(List(S))),f3: List(List(S)),f4: List(List(List(S)))) +--R mr : List(List(List(S))) -> Record(f1: List(S),f2: List(List(List(S))),f3: List(List(S)),f4: List(List(List(S)))) +--R tab1 : List(List(S)) -> List(List(List(S))) +--R untab : (List(List(S)),List(List(List(S)))) -> List(List(S)) +--R --E 1 )spool @@ -177056,6 +182790,20 @@ TableauxBumpers(S:OrderedSet):T==C where --S 1 of 1 )show TabulatedComputationPackage +--R +--R TabulatedComputationPackage(Key: SetCategory,Entry: SetCategory) is a package constructor +--R Abbreviation for TabulatedComputationPackage is TBCMPPK +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for TBCMPPK +--R +--R------------------------------- Operations -------------------------------- +--R clearTable! : () -> Void initTable! : () -> Void +--R insert! : (Key,Entry) -> Void makingStats? : () -> Boolean +--R printInfo! : (String,String) -> Void printStats! : () -> Void +--R printingInfo? : () -> Boolean startStats! : String -> Void +--R usingTable? : () -> Boolean +--R extractIfCan : Key -> Union(Entry,"failed") +--R --E 1 )spool @@ -177230,6 +182978,16 @@ TabulatedComputationPackage(Key ,Entry): Exports == Implementation where --S 1 of 1 )show TangentExpansions +--R +--R TangentExpansions(R: Field) is a package constructor +--R Abbreviation for TangentExpansions is TANEXP +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for TANEXP +--R +--R------------------------------- Operations -------------------------------- +--R tanNa : (R,Integer) -> R tanSum : List(R) -> R +--R tanAn : (R,PositiveInteger) -> SparseUnivariatePolynomial(R) +--R --E 1 )spool @@ -177327,6 +183085,15 @@ TangentExpansions(R:Field): Exports == Implementation where --S 1 of 1 )show TaylorSolve +--R +--R TaylorSolve(F: Field,UTSF: UnivariateTaylorSeriesCategory(F),UTSSUPF: UnivariateTaylorSeriesCategory(SparseUnivariatePolynomialExpressions(F))) is a package constructor +--R Abbreviation for TaylorSolve is UTSSOL +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for UTSSOL +--R +--R------------------------------- Operations -------------------------------- +--R seriesSolve : ((UTSSUPF -> UTSSUPF),List(F)) -> UTSF +--R --E 1 )spool @@ -177511,6 +183278,16 @@ should be unique. --S 1 of 1 )show TemplateUtilities +--R +--R TemplateUtilities is a package constructor +--R Abbreviation for TemplateUtilities is TEMUTL +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for TEMUTL +--R +--R------------------------------- Operations -------------------------------- +--R interpretString : String -> Any +--R stripCommentsAndBlanks : String -> String +--R --E 1 )spool @@ -177590,6 +183367,15 @@ TemplateUtilities(): Exports == Implementation where --S 1 of 1 )show TexFormat1 +--R +--R TexFormat1(S: SetCategory) is a package constructor +--R Abbreviation for TexFormat1 is TEX1 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for TEX1 +--R +--R------------------------------- Operations -------------------------------- +--R coerce : S -> TexFormat +--R --E 1 )spool @@ -177656,6 +183442,16 @@ TexFormat1(S : SetCategory): public == private where --S 1 of 1 )show ToolsForSign +--R +--R ToolsForSign(R: Ring) is a package constructor +--R Abbreviation for ToolsForSign is TOOLSIGN +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for TOOLSIGN +--R +--R------------------------------- Operations -------------------------------- +--R direction : String -> Integer sign : R -> Union(Integer,"failed") +--R nonQsign : R -> Union(Integer,"failed") +--R --E 1 )spool @@ -177751,6 +183547,30 @@ ToolsForSign(R:Ring): with --S 1 of 1 )show TopLevelDrawFunctions +--R +--R TopLevelDrawFunctions(Ex: Join(ConvertibleTo(InputForm),SetCategory)) is a package constructor +--R Abbreviation for TopLevelDrawFunctions is DRAW +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for DRAW +--R +--R------------------------------- Operations -------------------------------- +--R draw : (Ex,SegmentBinding(Float),List(DrawOption)) -> TwoDimensionalViewport +--R draw : (Ex,SegmentBinding(Float)) -> TwoDimensionalViewport +--R draw : (ParametricPlaneCurve(Ex),SegmentBinding(Float),List(DrawOption)) -> TwoDimensionalViewport +--R draw : (ParametricPlaneCurve(Ex),SegmentBinding(Float)) -> TwoDimensionalViewport +--R draw : (ParametricSpaceCurve(Ex),SegmentBinding(Float),List(DrawOption)) -> ThreeDimensionalViewport +--R draw : (ParametricSpaceCurve(Ex),SegmentBinding(Float)) -> ThreeDimensionalViewport +--R draw : (Ex,SegmentBinding(Float),SegmentBinding(Float),List(DrawOption)) -> ThreeDimensionalViewport +--R draw : (Ex,SegmentBinding(Float),SegmentBinding(Float)) -> ThreeDimensionalViewport +--R draw : (ParametricSurface(Ex),SegmentBinding(Float),SegmentBinding(Float),List(DrawOption)) -> ThreeDimensionalViewport +--R draw : (ParametricSurface(Ex),SegmentBinding(Float),SegmentBinding(Float)) -> ThreeDimensionalViewport +--R makeObject : (ParametricSpaceCurve(Ex),SegmentBinding(Float),List(DrawOption)) -> ThreeSpace(DoubleFloat) +--R makeObject : (ParametricSpaceCurve(Ex),SegmentBinding(Float)) -> ThreeSpace(DoubleFloat) +--R makeObject : (Ex,SegmentBinding(Float),SegmentBinding(Float),List(DrawOption)) -> ThreeSpace(DoubleFloat) +--R makeObject : (Ex,SegmentBinding(Float),SegmentBinding(Float)) -> ThreeSpace(DoubleFloat) +--R makeObject : (ParametricSurface(Ex),SegmentBinding(Float),SegmentBinding(Float),List(DrawOption)) -> ThreeSpace(DoubleFloat) +--R makeObject : (ParametricSurface(Ex),SegmentBinding(Float),SegmentBinding(Float)) -> ThreeSpace(DoubleFloat) +--R --E 1 )spool @@ -178117,6 +183937,15 @@ TopLevelDrawFunctions(Ex:Join(ConvertibleTo InputForm,SetCategory)): --S 1 of 1 )show TopLevelDrawFunctionsForAlgebraicCurves +--R +--R TopLevelDrawFunctionsForAlgebraicCurves(R: Join(IntegralDomain,OrderedSet,RetractableTo(Integer)),Ex: FunctionSpace(R)) is a package constructor +--R Abbreviation for TopLevelDrawFunctionsForAlgebraicCurves is DRAWCURV +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for DRAWCURV +--R +--R------------------------------- Operations -------------------------------- +--R draw : (Equation(Ex),Symbol,Symbol,List(DrawOption)) -> TwoDimensionalViewport +--R --E 1 )spool @@ -178275,6 +184104,39 @@ TopLevelDrawFunctionsForAlgebraicCurves(R,Ex): Exports == Implementation where --S 1 of 1 )show TopLevelDrawFunctionsForCompiledFunctions +--R +--R TopLevelDrawFunctionsForCompiledFunctions is a package constructor +--R Abbreviation for TopLevelDrawFunctionsForCompiledFunctions is DRAWCFUN +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for DRAWCFUN +--R +--R------------------------------- Operations -------------------------------- +--R draw : ((DoubleFloat -> DoubleFloat),Segment(Float),List(DrawOption)) -> TwoDimensionalViewport +--R draw : ((DoubleFloat -> DoubleFloat),Segment(Float)) -> TwoDimensionalViewport +--R draw : (ParametricPlaneCurve((DoubleFloat -> DoubleFloat)),Segment(Float),List(DrawOption)) -> TwoDimensionalViewport +--R draw : (ParametricPlaneCurve((DoubleFloat -> DoubleFloat)),Segment(Float)) -> TwoDimensionalViewport +--R draw : (ParametricSpaceCurve((DoubleFloat -> DoubleFloat)),Segment(Float),List(DrawOption)) -> ThreeDimensionalViewport +--R draw : (ParametricSpaceCurve((DoubleFloat -> DoubleFloat)),Segment(Float)) -> ThreeDimensionalViewport +--R draw : ((DoubleFloat -> Point(DoubleFloat)),Segment(Float),List(DrawOption)) -> ThreeDimensionalViewport +--R draw : ((DoubleFloat -> Point(DoubleFloat)),Segment(Float)) -> ThreeDimensionalViewport +--R draw : (((DoubleFloat,DoubleFloat) -> DoubleFloat),Segment(Float),Segment(Float),List(DrawOption)) -> ThreeDimensionalViewport +--R draw : (((DoubleFloat,DoubleFloat) -> DoubleFloat),Segment(Float),Segment(Float)) -> ThreeDimensionalViewport +--R draw : (((DoubleFloat,DoubleFloat) -> Point(DoubleFloat)),Segment(Float),Segment(Float),List(DrawOption)) -> ThreeDimensionalViewport +--R draw : (((DoubleFloat,DoubleFloat) -> Point(DoubleFloat)),Segment(Float),Segment(Float)) -> ThreeDimensionalViewport +--R draw : (ParametricSurface(((DoubleFloat,DoubleFloat) -> DoubleFloat)),Segment(Float),Segment(Float),List(DrawOption)) -> ThreeDimensionalViewport +--R draw : (ParametricSurface(((DoubleFloat,DoubleFloat) -> DoubleFloat)),Segment(Float),Segment(Float)) -> ThreeDimensionalViewport +--R makeObject : (ParametricSpaceCurve((DoubleFloat -> DoubleFloat)),Segment(Float),List(DrawOption)) -> ThreeSpace(DoubleFloat) +--R makeObject : (ParametricSpaceCurve((DoubleFloat -> DoubleFloat)),Segment(Float)) -> ThreeSpace(DoubleFloat) +--R makeObject : ((DoubleFloat -> Point(DoubleFloat)),Segment(Float),List(DrawOption)) -> ThreeSpace(DoubleFloat) +--R makeObject : ((DoubleFloat -> Point(DoubleFloat)),Segment(Float)) -> ThreeSpace(DoubleFloat) +--R makeObject : (((DoubleFloat,DoubleFloat) -> DoubleFloat),Segment(Float),Segment(Float),List(DrawOption)) -> ThreeSpace(DoubleFloat) +--R makeObject : (((DoubleFloat,DoubleFloat) -> DoubleFloat),Segment(Float),Segment(Float)) -> ThreeSpace(DoubleFloat) +--R makeObject : (((DoubleFloat,DoubleFloat) -> Point(DoubleFloat)),Segment(Float),Segment(Float),List(DrawOption)) -> ThreeSpace(DoubleFloat) +--R makeObject : (((DoubleFloat,DoubleFloat) -> Point(DoubleFloat)),Segment(Float),Segment(Float)) -> ThreeSpace(DoubleFloat) +--R makeObject : (ParametricSurface(((DoubleFloat,DoubleFloat) -> DoubleFloat)),Segment(Float),Segment(Float),List(DrawOption)) -> ThreeSpace(DoubleFloat) +--R makeObject : (ParametricSurface(((DoubleFloat,DoubleFloat) -> DoubleFloat)),Segment(Float),Segment(Float)) -> ThreeSpace(DoubleFloat) +--R recolor : (((DoubleFloat,DoubleFloat) -> Point(DoubleFloat)),((DoubleFloat,DoubleFloat,DoubleFloat) -> DoubleFloat)) -> ((DoubleFloat,DoubleFloat) -> Point(DoubleFloat)) +--R --E 1 )spool @@ -178954,6 +184816,20 @@ SingleFloat value. --S 1 of 1 )show TopLevelDrawFunctionsForPoints +--R +--R TopLevelDrawFunctionsForPoints is a package constructor +--R Abbreviation for TopLevelDrawFunctionsForPoints is DRAWPT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for DRAWPT +--R +--R------------------------------- Operations -------------------------------- +--R draw : (List(DoubleFloat),List(DoubleFloat)) -> TwoDimensionalViewport +--R draw : (List(DoubleFloat),List(DoubleFloat),List(DrawOption)) -> TwoDimensionalViewport +--R draw : List(Point(DoubleFloat)) -> TwoDimensionalViewport +--R draw : (List(Point(DoubleFloat)),List(DrawOption)) -> TwoDimensionalViewport +--R draw : (List(DoubleFloat),List(DoubleFloat),List(DoubleFloat)) -> ThreeDimensionalViewport +--R draw : (List(DoubleFloat),List(DoubleFloat),List(DoubleFloat),List(DrawOption)) -> ThreeDimensionalViewport +--R --E 1 )spool @@ -179076,6 +184952,15 @@ TopLevelDrawFunctionsForPoints(): Exports == Implementation where --S 1 of 1 )show TopLevelThreeSpace +--R +--R TopLevelThreeSpace is a package constructor +--R Abbreviation for TopLevelThreeSpace is TOPSP +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for TOPSP +--R +--R------------------------------- Operations -------------------------------- +--R createThreeSpace : () -> ThreeSpace(DoubleFloat) +--R --E 1 )spool @@ -179131,6 +185016,15 @@ TopLevelThreeSpace(): with --S 1 of 1 )show TranscendentalHermiteIntegration +--R +--R TranscendentalHermiteIntegration(F: Field,UP: UnivariatePolynomialCategory(F)) is a package constructor +--R Abbreviation for TranscendentalHermiteIntegration is INTHERTR +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for INTHERTR +--R +--R------------------------------- Operations -------------------------------- +--R HermiteIntegrate : (Fraction(UP),(UP -> UP)) -> Record(answer: Fraction(UP),logpart: Fraction(UP),specpart: Fraction(UP),polypart: UP) +--R --E 1 )spool @@ -179234,6 +185128,27 @@ TranscendentalHermiteIntegration(F, UP): Exports == Implementation where --S 1 of 1 )show TranscendentalIntegration +--R +--R TranscendentalIntegration(F: Field,UP: UnivariatePolynomialCategory(F)) is a package constructor +--R Abbreviation for TranscendentalIntegration is INTTR +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for INTTR +--R +--R------------------------------- Operations -------------------------------- +--R expextendedint : (Fraction(UP),(UP -> UP),((Integer,F) -> Record(ans: F,right: F,sol?: Boolean)),Fraction(UP)) -> Union(Record(answer: Fraction(UP),a0: F),Record(ratpart: Fraction(UP),coeff: Fraction(UP)),"failed") +--R expintegrate : (Fraction(UP),(UP -> UP),((Integer,F) -> Record(ans: F,right: F,sol?: Boolean))) -> Record(answer: IntegrationResult(Fraction(UP)),a0: F) +--R expintfldpoly : (LaurentPolynomial(F,UP),((Integer,F) -> Record(ans: F,right: F,sol?: Boolean))) -> Union(LaurentPolynomial(F,UP),"failed") +--R explimitedint : (Fraction(UP),(UP -> UP),((Integer,F) -> Record(ans: F,right: F,sol?: Boolean)),List(Fraction(UP))) -> Union(Record(answer: Record(mainpart: Fraction(UP),limitedlogs: List(Record(coeff: Fraction(UP),logand: Fraction(UP)))),a0: F),"failed") +--R monomialIntPoly : (UP,(UP -> UP)) -> Record(answer: UP,polypart: UP) +--R monomialIntegrate : (Fraction(UP),(UP -> UP)) -> Record(ir: IntegrationResult(Fraction(UP)),specpart: Fraction(UP),polypart: UP) +--R primextendedint : (Fraction(UP),(UP -> UP),(F -> Union(Record(ratpart: F,coeff: F),"failed")),Fraction(UP)) -> Union(Record(answer: Fraction(UP),a0: F),Record(ratpart: Fraction(UP),coeff: Fraction(UP)),"failed") +--R primextintfrac : (Fraction(UP),(UP -> UP),Fraction(UP)) -> Union(Record(ratpart: Fraction(UP),coeff: Fraction(UP)),"failed") +--R primintegrate : (Fraction(UP),(UP -> UP),(F -> Union(Record(ratpart: F,coeff: F),"failed"))) -> Record(answer: IntegrationResult(Fraction(UP)),a0: F) +--R primintfldpoly : (UP,(F -> Union(Record(ratpart: F,coeff: F),"failed")),F) -> Union(UP,"failed") +--R primlimintfrac : (Fraction(UP),(UP -> UP),List(Fraction(UP))) -> Union(Record(mainpart: Fraction(UP),limitedlogs: List(Record(coeff: Fraction(UP),logand: Fraction(UP)))),"failed") +--R primlimitedint : (Fraction(UP),(UP -> UP),(F -> Union(Record(ratpart: F,coeff: F),"failed")),List(Fraction(UP))) -> Union(Record(answer: Record(mainpart: Fraction(UP),limitedlogs: List(Record(coeff: Fraction(UP),logand: Fraction(UP)))),a0: F),"failed") +--R tanintegrate : (Fraction(UP),(UP -> UP),((Integer,F,F) -> Union(List(F),"failed"))) -> Record(answer: IntegrationResult(Fraction(UP)),a0: F) +--R --E 1 )spool @@ -179740,6 +185655,29 @@ TranscendentalIntegration(F, UP): Exports == Implementation where --S 1 of 1 )show TranscendentalManipulations +--R +--R TranscendentalManipulations(R: Join(OrderedSet,GcdDomain),F: Join(FunctionSpace(R),TranscendentalFunctionCategory)) is a package constructor +--R Abbreviation for TranscendentalManipulations is TRMANIP +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for TRMANIP +--R +--R------------------------------- Operations -------------------------------- +--R cos2sec : F -> F cosh2sech : F -> F +--R cot2tan : F -> F cot2trig : F -> F +--R coth2tanh : F -> F coth2trigh : F -> F +--R csc2sin : F -> F csch2sinh : F -> F +--R expand : F -> F expandLog : F -> F +--R expandPower : F -> F htrigs : F -> F +--R removeCosSq : F -> F removeCoshSq : F -> F +--R removeSinSq : F -> F removeSinhSq : F -> F +--R sec2cos : F -> F sech2cosh : F -> F +--R simplify : F -> F simplifyExp : F -> F +--R simplifyLog : F -> F sin2csc : F -> F +--R sinh2csch : F -> F tan2cot : F -> F +--R tan2trig : F -> F tanh2coth : F -> F +--R tanh2trigh : F -> F +--R expandTrigProducts : F -> F if F has KONVERT(PATTERN(R)) and F has PATMAB(R) and R has KONVERT(PATTERN(R)) and R has PATMAB(R) +--R --E 1 )spool @@ -180454,6 +186392,17 @@ so the result is 0 --S 1 of 1 )show TranscendentalRischDE +--R +--R TranscendentalRischDE(F: Join(Field,CharacteristicZero,RetractableTo(Integer)),UP: UnivariatePolynomialCategory(F)) is a package constructor +--R Abbreviation for TranscendentalRischDE is RDETR +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for RDETR +--R +--R------------------------------- Operations -------------------------------- +--R baseRDE : (Fraction(UP),Fraction(UP)) -> Record(ans: Fraction(UP),nosol: Boolean) +--R monomRDE : (Fraction(UP),Fraction(UP),(UP -> UP)) -> Union(Record(a: UP,b: Fraction(UP),c: Fraction(UP),t: UP),"failed") +--R polyRDE : (UP,UP,UP,Integer,(UP -> UP)) -> Union(ans: Record(ans: UP,nosol: Boolean),eq: Record(b: UP,c: UP,m: Integer,alpha: UP,beta: UP)) +--R --E 1 )spool @@ -180666,6 +186615,16 @@ TranscendentalRischDE(F, UP): Exports == Implementation where --S 1 of 1 )show TranscendentalRischDESystem +--R +--R TranscendentalRischDESystem(F: Join(Field,CharacteristicZero,RetractableTo(Integer)),UP: UnivariatePolynomialCategory(F)) is a package constructor +--R Abbreviation for TranscendentalRischDESystem is RDETRS +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for RDETRS +--R +--R------------------------------- Operations -------------------------------- +--R baseRDEsys : (Fraction(UP),Fraction(UP),Fraction(UP)) -> Union(List(Fraction(UP)),"failed") +--R monomRDEsys : (Fraction(UP),Fraction(UP),Fraction(UP),(UP -> UP)) -> Union(Record(a: UP,b: Fraction(UP),h: UP,c1: Fraction(UP),c2: Fraction(UP),t: UP),"failed") +--R --E 1 )spool @@ -180925,6 +186884,7 @@ TranscendentalRischDESystem(F, UP): Exports == Implementation where )set message test on )set message auto off )clear all + --S 1 of 4 solve(1/2*v*v*cos(theta+phi)*cos(theta+phi)+g*l*cos(phi)=g*l,phi) --R @@ -181759,6 +187719,16 @@ generates the error (reported as bug \# 102): --S 1 of 1 )show TransSolvePackageService +--R +--R TransSolvePackageService(R: Join(IntegralDomain,OrderedSet)) is a package constructor +--R Abbreviation for TransSolvePackageService is SOLVESER +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for SOLVESER +--R +--R------------------------------- Operations -------------------------------- +--R decomposeFunc : (Fraction(SparseUnivariatePolynomial(Expression(R))),Fraction(SparseUnivariatePolynomial(Expression(R))),Fraction(SparseUnivariatePolynomial(Expression(R)))) -> Fraction(SparseUnivariatePolynomial(Expression(R))) +--R unvectorise : (Vector(Expression(R)),Fraction(SparseUnivariatePolynomial(Expression(R))),Integer) -> Fraction(SparseUnivariatePolynomial(Expression(R))) +--R --E 1 )spool @@ -181922,6 +187892,15 @@ TransSolvePackageService(R) : Exports == Implementation where --S 1 of 1 )show TriangularMatrixOperations +--R +--R TriangularMatrixOperations(R: IntegralDomain,Row: FiniteLinearAggregate(R),Col: FiniteLinearAggregate(R),M: MatrixCategory(R,Row,Col)) is a package constructor +--R Abbreviation for TriangularMatrixOperations is TRIMAT +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for TRIMAT +--R +--R------------------------------- Operations -------------------------------- +--R LowTriBddDenomInv : (M,R) -> M UpTriBddDenomInv : (M,R) -> M +--R --E 1 )spool @@ -182034,6 +188013,19 @@ TriangularMatrixOperations(R,Row,Col,M): Exports == Implementation where --S 1 of 1 )show TrigonometricManipulations +--R +--R TrigonometricManipulations(R: Join(GcdDomain,OrderedSet,RetractableTo(Integer),LinearlyExplicitRingOver(Integer)),F: Join(AlgebraicallyClosedField,TranscendentalFunctionCategory,FunctionSpace(R))) is a package constructor +--R Abbreviation for TrigonometricManipulations is TRIGMNIP +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for TRIGMNIP +--R +--R------------------------------- Operations -------------------------------- +--R complexElementary : F -> F complexElementary : (F,Symbol) -> F +--R complexForm : F -> Complex(F) complexNormalize : F -> F +--R complexNormalize : (F,Symbol) -> F imag : F -> F +--R real : F -> F real? : F -> Boolean +--R trigs : F -> F +--R --E 1 )spool @@ -182227,6 +188219,23 @@ TrigonometricManipulations(R, F): Exports == Implementation where --S 1 of 1 )show TubePlotTools +--R +--R TubePlotTools is a package constructor +--R Abbreviation for TubePlotTools is TUBETOOL +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for TUBETOOL +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (DoubleFloat,Point(DoubleFloat)) -> Point(DoubleFloat) +--R ?+? : (Point(DoubleFloat),Point(DoubleFloat)) -> Point(DoubleFloat) +--R ?-? : (Point(DoubleFloat),Point(DoubleFloat)) -> Point(DoubleFloat) +--R cosSinInfo : Integer -> List(List(DoubleFloat)) +--R cross : (Point(DoubleFloat),Point(DoubleFloat)) -> Point(DoubleFloat) +--R dot : (Point(DoubleFloat),Point(DoubleFloat)) -> DoubleFloat +--R loopPoints : (Point(DoubleFloat),Point(DoubleFloat),Point(DoubleFloat),DoubleFloat,List(List(DoubleFloat))) -> List(Point(DoubleFloat)) +--R point : (DoubleFloat,DoubleFloat,DoubleFloat,DoubleFloat) -> Point(DoubleFloat) +--R unitVector : Point(DoubleFloat) -> Point(DoubleFloat) +--R --E 1 )spool @@ -182394,6 +188403,21 @@ TubePlotTools(): Exports == Implementation where --S 1 of 1 )show TwoDimensionalPlotClipping +--R +--R TwoDimensionalPlotClipping is a package constructor +--R Abbreviation for TwoDimensionalPlotClipping is CLIP +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for CLIP +--R +--R------------------------------- Operations -------------------------------- +--R clip : Plot -> Record(brans: List(List(Point(DoubleFloat))),xValues: Segment(DoubleFloat),yValues: Segment(DoubleFloat)) +--R clip : (Plot,Fraction(Integer),Fraction(Integer)) -> Record(brans: List(List(Point(DoubleFloat))),xValues: Segment(DoubleFloat),yValues: Segment(DoubleFloat)) +--R clip : List(Point(DoubleFloat)) -> Record(brans: List(List(Point(DoubleFloat))),xValues: Segment(DoubleFloat),yValues: Segment(DoubleFloat)) +--R clip : List(List(Point(DoubleFloat))) -> Record(brans: List(List(Point(DoubleFloat))),xValues: Segment(DoubleFloat),yValues: Segment(DoubleFloat)) +--R clipParametric : Plot -> Record(brans: List(List(Point(DoubleFloat))),xValues: Segment(DoubleFloat),yValues: Segment(DoubleFloat)) +--R clipParametric : (Plot,Fraction(Integer),Fraction(Integer)) -> Record(brans: List(List(Point(DoubleFloat))),xValues: Segment(DoubleFloat),yValues: Segment(DoubleFloat)) +--R clipWithRanges : (List(List(Point(DoubleFloat))),DoubleFloat,DoubleFloat,DoubleFloat,DoubleFloat) -> Record(brans: List(List(Point(DoubleFloat))),xValues: Segment(DoubleFloat),yValues: Segment(DoubleFloat)) +--R --E 1 )spool @@ -182726,6 +188750,17 @@ TwoDimensionalPlotClipping(): Exports == Implementation where --S 1 of 1 )show TwoFactorize +--R +--R TwoFactorize(F: FiniteFieldCategory) is a package constructor +--R Abbreviation for TwoFactorize is TWOFACT +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for TWOFACT +--R +--R------------------------------- Operations -------------------------------- +--R generalSqFr : SparseUnivariatePolynomial(SparseUnivariatePolynomial(F)) -> Factored(SparseUnivariatePolynomial(SparseUnivariatePolynomial(F))) +--R generalTwoFactor : SparseUnivariatePolynomial(SparseUnivariatePolynomial(F)) -> Factored(SparseUnivariatePolynomial(SparseUnivariatePolynomial(F))) +--R twoFactor : (SparseUnivariatePolynomial(SparseUnivariatePolynomial(F)),Integer) -> Factored(SparseUnivariatePolynomial(SparseUnivariatePolynomial(F))) +--R --E 1 )spool @@ -182997,6 +189032,17 @@ TwoFactorize(F) : C == T --S 1 of 1 )show UnivariateFactorize +--R +--R UnivariateFactorize(ZP: UnivariatePolynomialCategory(Integer)) is a package constructor +--R Abbreviation for UnivariateFactorize is UNIFACT +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for UNIFACT +--R +--R------------------------------- Operations -------------------------------- +--R factor : ZP -> Factored(ZP) +--R factorSquareFree : ZP -> Factored(ZP) +--R henselFact : (ZP,Boolean) -> Record(contp: Integer,factors: List(Record(irr: ZP,pow: Integer))) +--R --E 1 )spool @@ -183356,6 +189402,15 @@ UnivariateFactorize(ZP) : public == private where --S 1 of 1 )show UnivariateFormalPowerSeriesFunctions +--R +--R UnivariateFormalPowerSeriesFunctions(Coef: Ring) is a package constructor +--R Abbreviation for UnivariateFormalPowerSeriesFunctions is UFPS1 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for UFPS1 +--R +--R------------------------------- Operations -------------------------------- +--R hadamard : (UnivariateFormalPowerSeries(Coef),UnivariateFormalPowerSeries(Coef)) -> UnivariateFormalPowerSeries(Coef) +--R --E 1 )spool @@ -183418,6 +189473,15 @@ UnivariateFormalPowerSeriesFunctions(Coef: Ring): Exports == Implementation --S 1 of 1 )show UnivariateLaurentSeriesFunctions2 +--R +--R UnivariateLaurentSeriesFunctions2(Coef1: Ring,Coef2: Ring,var1: Symbol,var2: Symbol,cen1: Coef1,cen2: Coef2) is a package constructor +--R Abbreviation for UnivariateLaurentSeriesFunctions2 is ULS2 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for ULS2 +--R +--R------------------------------- Operations -------------------------------- +--R map : ((Coef1 -> Coef2),UnivariateLaurentSeries(Coef1,var1,cen1)) -> UnivariateLaurentSeries(Coef2,var2,cen2) +--R --E 1 )spool @@ -183496,6 +189560,15 @@ UnivariateLaurentSeriesFunctions2(Coef1,Coef2,var1,var2,cen1,cen2):_ --S 1 of 1 )show UnivariatePolynomialCategoryFunctions2 +--R +--R UnivariatePolynomialCategoryFunctions2(R: Ring,PR: UnivariatePolynomialCategory(R),S: Ring,PS: UnivariatePolynomialCategory(S)) is a package constructor +--R Abbreviation for UnivariatePolynomialCategoryFunctions2 is UPOLYC2 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for UPOLYC2 +--R +--R------------------------------- Operations -------------------------------- +--R map : ((R -> S),PR) -> PS +--R --E 1 )spool @@ -183565,6 +189638,16 @@ UnivariatePolynomialCategoryFunctions2(R,PR,S,PS): Exports == Impl where --S 1 of 1 )show UnivariatePolynomialCommonDenominator +--R +--R UnivariatePolynomialCommonDenominator(R: IntegralDomain,Q: QuotientFieldCategory(R),UP: UnivariatePolynomialCategory(Q)) is a package constructor +--R Abbreviation for UnivariatePolynomialCommonDenominator is UPCDEN +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for UPCDEN +--R +--R------------------------------- Operations -------------------------------- +--R clearDenominator : UP -> UP commonDenominator : UP -> R +--R splitDenominator : UP -> Record(num: UP,den: R) +--R --E 1 )spool @@ -183652,6 +189735,19 @@ UnivariatePolynomialCommonDenominator(R, Q, UP): Exports == Impl where --S 1 of 1 )show UnivariatePolynomialDecompositionPackage +--R +--R UnivariatePolynomialDecompositionPackage(R: Join(IntegralDomain,CharacteristicZero),UP: UnivariatePolynomialCategory(R)) is a package constructor +--R Abbreviation for UnivariatePolynomialDecompositionPackage is UPDECOMP +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for UPDECOMP +--R +--R------------------------------- Operations -------------------------------- +--R leftFactorIfCan : (UP,UP) -> Union(UP,"failed") +--R monicCompleteDecompose : UP -> List(UP) +--R monicDecomposeIfCan : UP -> Union(Record(left: UP,right: UP),"failed") +--R monicRightFactorIfCan : (UP,NonNegativeInteger) -> Union(UP,"failed") +--R rightFactorIfCan : (UP,NonNegativeInteger,R) -> Union(UP,"failed") +--R --E 1 )spool @@ -183819,6 +189915,15 @@ UnivariatePolynomialDecompositionPackage(R,UP): Exports == Implementation where --S 1 of 1 )show UnivariatePolynomialDivisionPackage +--R +--R UnivariatePolynomialDivisionPackage(R: IntegralDomain,UP: UnivariatePolynomialCategory(R)) is a package constructor +--R Abbreviation for UnivariatePolynomialDivisionPackage is UPDIVP +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for UPDIVP +--R +--R------------------------------- Operations -------------------------------- +--R divideIfCan : (UP,UP) -> Union(Record(quotient: UP,remainder: UP),"failed") +--R --E 1 )spool @@ -183899,6 +190004,15 @@ UnivariatePolynomialDivisionPackage(R,UP): Exports == Implementation where --S 1 of 1 )show UnivariatePolynomialFunctions2 +--R +--R UnivariatePolynomialFunctions2(x: Symbol,R: Ring,y: Symbol,S: Ring) is a package constructor +--R Abbreviation for UnivariatePolynomialFunctions2 is UP2 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for UP2 +--R +--R------------------------------- Operations -------------------------------- +--R map : ((R -> S),UnivariatePolynomial(x,R)) -> UnivariatePolynomial(y,S) +--R --E 1 )spool @@ -183963,6 +190077,16 @@ UnivariatePolynomialFunctions2(x:Symbol, R:Ring, y:Symbol, S:Ring): with --S 1 of 1 )show UnivariatePolynomialMultiplicationPackage +--R +--R UnivariatePolynomialMultiplicationPackage(R: Ring,U: UnivariatePolynomialCategory(R)) is a package constructor +--R Abbreviation for UnivariatePolynomialMultiplicationPackage is UPMP +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for UPMP +--R +--R------------------------------- Operations -------------------------------- +--R karatsubaOnce : (U,U) -> U noKaratsuba : (U,U) -> U +--R karatsuba : (U,U,NonNegativeInteger,NonNegativeInteger) -> U +--R --E 1 )spool @@ -184099,6 +190223,18 @@ UnivariatePolynomialMultiplicationPackage(R: Ring, U: UnivariatePolynomialCatego --S 1 of 1 )show UnivariatePolynomialSquareFree +--R +--R UnivariatePolynomialSquareFree(RC: IntegralDomain,P)where +--R P: Join(UnivariatePolynomialCategory(RC),IntegralDomain)with +--R gcd : (%,%) -> % is a package constructor +--R Abbreviation for UnivariatePolynomialSquareFree is UPSQFREE +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for UPSQFREE +--R +--R------------------------------- Operations -------------------------------- +--R squareFree : P -> Factored(P) squareFreePart : P -> P +--R BumInSepFFE : Record(flg: Union("nil","sqfr","irred","prime"),fctr: P,xpnt: Integer) -> Record(flg: Union("nil","sqfr","irred","prime"),fctr: P,xpnt: Integer) +--R --E 1 )spool @@ -184264,6 +190400,15 @@ UnivariatePolynomialSquareFree(RC:IntegralDomain,P):C == T --S 1 of 1 )show UnivariatePuiseuxSeriesFunctions2 +--R +--R UnivariatePuiseuxSeriesFunctions2(Coef1: Ring,Coef2: Ring,var1: Symbol,var2: Symbol,cen1: Coef1,cen2: Coef2) is a package constructor +--R Abbreviation for UnivariatePuiseuxSeriesFunctions2 is UPXS2 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for UPXS2 +--R +--R------------------------------- Operations -------------------------------- +--R map : ((Coef1 -> Coef2),UnivariatePuiseuxSeries(Coef1,var1,cen1)) -> UnivariatePuiseuxSeries(Coef2,var2,cen2) +--R --E 1 )spool @@ -184339,6 +190484,20 @@ UnivariatePuiseuxSeriesFunctions2(Coef1,Coef2,var1,var2,cen1,cen2):_ --S 1 of 1 )show UnivariateSkewPolynomialCategoryOps +--R +--R UnivariateSkewPolynomialCategoryOps(R: Ring,C: UnivariateSkewPolynomialCategory(R)) is a package constructor +--R Abbreviation for UnivariateSkewPolynomialCategoryOps is OREPCTO +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for OREPCTO +--R +--R------------------------------- Operations -------------------------------- +--R apply : (C,R,R,Automorphism(R),(R -> R)) -> R +--R leftDivide : (C,C,Automorphism(R)) -> Record(quotient: C,remainder: C) if R has FIELD +--R monicLeftDivide : (C,C,Automorphism(R)) -> Record(quotient: C,remainder: C) if R has INTDOM +--R monicRightDivide : (C,C,Automorphism(R)) -> Record(quotient: C,remainder: C) if R has INTDOM +--R rightDivide : (C,C,Automorphism(R)) -> Record(quotient: C,remainder: C) if R has FIELD +--R times : (C,C,Automorphism(R),(R -> R)) -> C +--R --E 1 )spool @@ -184518,6 +190677,15 @@ UnivariateSkewPolynomialCategoryOps(R, C): Exports == Implementation where --S 1 of 1 )show UnivariateTaylorSeriesFunctions2 +--R +--R UnivariateTaylorSeriesFunctions2(Coef1: Ring,Coef2: Ring,UTS1: UnivariateTaylorSeriesCategory(Coef1),UTS2: UnivariateTaylorSeriesCategory(Coef2)) is a package constructor +--R Abbreviation for UnivariateTaylorSeriesFunctions2 is UTS2 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for UTS2 +--R +--R------------------------------- Operations -------------------------------- +--R map : ((Coef1 -> Coef2),UTS1) -> UTS2 +--R --E 1 )spool @@ -184587,6 +190755,21 @@ UnivariateTaylorSeriesFunctions2(Coef1,Coef2,UTS1,UTS2):_ --S 1 of 1 )show UnivariateTaylorSeriesODESolver +--R +--R UnivariateTaylorSeriesODESolver(Coef: Algebra(Fraction(Integer)),UTS: UnivariateTaylorSeriesCategory(Coef)) is a package constructor +--R Abbreviation for UnivariateTaylorSeriesODESolver is UTSODE +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for UTSODE +--R +--R------------------------------- Operations -------------------------------- +--R fixedPointExquo : (UTS,UTS) -> UTS ode1 : ((UTS -> UTS),Coef) -> UTS +--R mpsode : (List(Coef),List((List(UTS) -> UTS))) -> List(UTS) +--R ode : ((List(UTS) -> UTS),List(Coef)) -> UTS +--R ode2 : (((UTS,UTS) -> UTS),Coef,Coef) -> UTS +--R stFunc1 : (UTS -> UTS) -> (Stream(Coef) -> Stream(Coef)) +--R stFunc2 : ((UTS,UTS) -> UTS) -> ((Stream(Coef),Stream(Coef)) -> Stream(Coef)) +--R stFuncN : (List(UTS) -> UTS) -> (List(Stream(Coef)) -> Stream(Coef)) +--R --E 1 )spool @@ -184762,6 +190945,16 @@ UnivariateTaylorSeriesODESolver(Coef,UTS):_ --S 1 of 1 )show UniversalSegmentFunctions2 +--R +--R UniversalSegmentFunctions2(R: Type,S: Type) is a package constructor +--R Abbreviation for UniversalSegmentFunctions2 is UNISEG2 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for UNISEG2 +--R +--R------------------------------- Operations -------------------------------- +--R map : ((R -> S),UniversalSegment(R)) -> UniversalSegment(S) +--R map : ((R -> S),UniversalSegment(R)) -> Stream(S) if R has ORDRING +--R --E 1 )spool @@ -184829,6 +191022,22 @@ UniversalSegmentFunctions2(R:Type, S:Type): with --S 1 of 1 )show UserDefinedPartialOrdering +--R +--R UserDefinedPartialOrdering(S: SetCategory) is a package constructor +--R Abbreviation for UserDefinedPartialOrdering is UDPO +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for UDPO +--R +--R------------------------------- Operations -------------------------------- +--R setOrder : List(S) -> Void setOrder : (List(S),List(S)) -> Void +--R userOrdered? : () -> Boolean +--R getOrder : () -> Record(low: List(S),high: List(S)) +--R largest : (List(S),((S,S) -> Boolean)) -> S +--R largest : List(S) -> S if S has ORDSET +--R less? : (S,S) -> Union(Boolean,"failed") +--R less? : (S,S,((S,S) -> Boolean)) -> Boolean +--R more? : (S,S) -> Boolean if S has ORDSET +--R --E 1 )spool @@ -184969,6 +191178,18 @@ UserDefinedPartialOrdering(S:SetCategory): with --S 1 of 1 )show UserDefinedVariableOrdering +--R +--R UserDefinedVariableOrdering is a package constructor +--R Abbreviation for UserDefinedVariableOrdering is UDVO +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for UDVO +--R +--R------------------------------- Operations -------------------------------- +--R resetVariableOrder : () -> Void +--R getVariableOrder : () -> Record(high: List(Symbol),low: List(Symbol)) +--R setVariableOrder : List(Symbol) -> Void +--R setVariableOrder : (List(Symbol),List(Symbol)) -> Void +--R --E 1 )spool @@ -185056,6 +191277,17 @@ UserDefinedVariableOrdering(): with --S 1 of 1 )show UTSodetools +--R +--R UTSodetools(F: Ring,UP: UnivariatePolynomialCategory(F),L: LinearOrdinaryDifferentialOperatorCategory(UP),UTS: UnivariateTaylorSeriesCategory(F)) is a package constructor +--R Abbreviation for UTSodetools is UTSODETL +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for UTSODETL +--R +--R------------------------------- Operations -------------------------------- +--R LODO2FUN : L -> (List(UTS) -> UTS) UP2UTS : UP -> UTS +--R RF2UTS : Fraction(UP) -> UTS if F has INTDOM +--R UTS2UP : (UTS,NonNegativeInteger) -> UP +--R --E 1 )spool @@ -185161,6 +191393,37 @@ UTSodetools(F, UP, L, UTS): Exports == Implementation where --S 1 of 1 )show U32VectorPolynomialOperations +--R +--R U32VectorPolynomialOperations is a package constructor +--R Abbreviation for U32VectorPolynomialOperations is POLYVEC +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for POLYVEC +--R +--R------------------------------- Operations -------------------------------- +--R degree : U32Vector -> Integer +--R copyfirst : (U32Vector,U32Vector,Integer) -> Void +--R copyslice : (U32Vector,U32Vector,Integer,Integer) -> Void +--R differentiate : (U32Vector,Integer) -> U32Vector +--R differentiate : (U32Vector,NonNegativeInteger,Integer) -> U32Vector +--R divide! : (U32Vector,U32Vector,U32Vector,Integer) -> Void +--R evalat : (U32Vector,Integer,Integer,Integer) -> Integer +--R extendedgcd : (U32Vector,U32Vector,Integer) -> List(U32Vector) +--R gcd : (U32Vector,U32Vector,Integer) -> U32Vector +--R gcd : (PrimitiveArray(U32Vector),Integer,Integer,Integer) -> U32Vector +--R lcm : (PrimitiveArray(U32Vector),Integer,Integer,Integer) -> U32Vector +--R mul : (U32Vector,U32Vector,Integer) -> U32Vector +--R mulbybinomial : (U32Vector,Integer,Integer) -> Void +--R mulbybinomial : (U32Vector,Integer,Integer,Integer) -> Void +--R mulbyscalar : (U32Vector,Integer,Integer,Integer) -> Void +--R pow : (U32Vector,PositiveInteger,NonNegativeInteger,Integer) -> U32Vector +--R remainder! : (U32Vector,U32Vector,Integer) -> Void +--R resultant : (U32Vector,U32Vector,Integer) -> Integer +--R tomodpa : (SparseUnivariatePolynomial(Integer),Integer) -> U32Vector +--R truncatedmuladd : (U32Vector,U32Vector,U32Vector,Integer,Integer) -> Void +--R truncatedmultiplication : (U32Vector,U32Vector,Integer,Integer) -> U32Vector +--R vectoraddmul : (U32Vector,U32Vector,Integer,Integer,Integer,Integer) -> Void +--R vectorcombination : (U32Vector,Integer,U32Vector,Integer,Integer,Integer,Integer) -> Void +--R --E 1 )spool @@ -185744,6 +192007,18 @@ U32VectorPolynomialOperations() : Export == Implementation where --S 1 of 1 )show VectorFunctions2 +--R +--R VectorFunctions2(A: Type,B: Type) is a package constructor +--R Abbreviation for VectorFunctions2 is VECTOR2 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for VECTOR2 +--R +--R------------------------------- Operations -------------------------------- +--R map : ((A -> B),Vector(A)) -> Vector(B) +--R map : ((A -> Union(B,"failed")),Vector(A)) -> Union(Vector(B),"failed") +--R reduce : (((A,B) -> B),Vector(A),B) -> B +--R scan : (((A,B) -> B),Vector(A),B) -> Vector(B) +--R --E 1 )spool @@ -185837,6 +192112,38 @@ VectorFunctions2(A, B): Exports == Implementation where --S 1 of 1 )show ViewDefaultsPackage +--R +--R ViewDefaultsPackage is a package constructor +--R Abbreviation for ViewDefaultsPackage is VIEWDEF +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for VIEWDEF +--R +--R------------------------------- Operations -------------------------------- +--R axesColorDefault : () -> Palette lineColorDefault : () -> Palette +--R pointColorDefault : () -> Palette unitsColorDefault : () -> Palette +--R viewDefaults : () -> Void +--R axesColorDefault : Palette -> Palette +--R lineColorDefault : Palette -> Palette +--R pointColorDefault : Palette -> Palette +--R pointSizeDefault : () -> PositiveInteger +--R pointSizeDefault : PositiveInteger -> PositiveInteger +--R tubePointsDefault : PositiveInteger -> PositiveInteger +--R tubePointsDefault : () -> PositiveInteger +--R tubeRadiusDefault : Float -> DoubleFloat +--R tubeRadiusDefault : () -> DoubleFloat +--R unitsColorDefault : Palette -> Palette +--R var1StepsDefault : () -> PositiveInteger +--R var1StepsDefault : PositiveInteger -> PositiveInteger +--R var2StepsDefault : () -> PositiveInteger +--R var2StepsDefault : PositiveInteger -> PositiveInteger +--R viewPosDefault : () -> List(NonNegativeInteger) +--R viewPosDefault : List(NonNegativeInteger) -> List(NonNegativeInteger) +--R viewSizeDefault : () -> List(PositiveInteger) +--R viewSizeDefault : List(PositiveInteger) -> List(PositiveInteger) +--R viewWriteAvailable : () -> List(String) +--R viewWriteDefault : () -> List(String) +--R viewWriteDefault : List(String) -> List(String) +--R --E 1 )spool @@ -186121,6 +192428,20 @@ ViewDefaultsPackage():Exports == Implementation where --S 1 of 1 )show ViewportPackage +--R +--R ViewportPackage is a package constructor +--R Abbreviation for ViewportPackage is VIEW +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for VIEW +--R +--R------------------------------- Operations -------------------------------- +--R coerce : GraphImage -> TwoDimensionalViewport +--R drawCurves : (List(List(Point(DoubleFloat))),Palette,Palette,PositiveInteger,List(DrawOption)) -> TwoDimensionalViewport +--R drawCurves : (List(List(Point(DoubleFloat))),List(DrawOption)) -> TwoDimensionalViewport +--R graphCurves : (List(List(Point(DoubleFloat))),Palette,Palette,PositiveInteger,List(DrawOption)) -> GraphImage +--R graphCurves : List(List(Point(DoubleFloat))) -> GraphImage +--R graphCurves : (List(List(Point(DoubleFloat))),List(DrawOption)) -> GraphImage +--R --E 1 )spool @@ -186268,6 +192589,20 @@ ViewportPackage():Exports == Implementation where --S 1 of 1 )show WeierstrassPreparation +--R +--R WeierstrassPreparation(R: Field) is a package constructor +--R Abbreviation for WeierstrassPreparation is WEIER +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for WEIER +--R +--R------------------------------- Operations -------------------------------- +--R cfirst : NonNegativeInteger -> (Stream(Polynomial(R)) -> Stream(Polynomial(R))) +--R clikeUniv : Symbol -> (Polynomial(R) -> SparseUnivariatePolynomial(Polynomial(R))) +--R crest : NonNegativeInteger -> (Stream(Polynomial(R)) -> Stream(Polynomial(R))) +--R qqq : (NonNegativeInteger,TaylorSeries(R),Stream(TaylorSeries(R))) -> (Stream(TaylorSeries(R)) -> Stream(TaylorSeries(R))) +--R sts2stst : (Symbol,Stream(Polynomial(R))) -> Stream(Stream(Polynomial(R))) +--R weierstrass : (Symbol,TaylorSeries(R)) -> List(TaylorSeries(R)) +--R --E 1 )spool @@ -186466,6 +192801,16 @@ WeierstrassPreparation(R): Defn == Impl where --S 1 of 1 )show WildFunctionFieldIntegralBasis +--R +--R WildFunctionFieldIntegralBasis(K: FiniteFieldCategory,R: UnivariatePolynomialCategory(K),UP: UnivariatePolynomialCategory(R),F: FramedAlgebra(R,UP)) is a package constructor +--R Abbreviation for WildFunctionFieldIntegralBasis is WFFINTBS +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for WFFINTBS +--R +--R------------------------------- Operations -------------------------------- +--R integralBasis : () -> Record(basis: Matrix(R),basisDen: R,basisInv: Matrix(R)) +--R localIntegralBasis : R -> Record(basis: Matrix(R),basisDen: R,basisInv: Matrix(R)) +--R --E 1 )spool @@ -186704,6 +193049,17 @@ WildFunctionFieldIntegralBasis(K,R,UP,F): Exports == Implementation where --S 1 of 1 )show XExponentialPackage +--R +--R XExponentialPackage(R: Join(Ring,Module(Fraction(Integer))),VarSet: OrderedSet,XPOLY: XPolynomialsCat(VarSet,R)) is a package constructor +--R Abbreviation for XExponentialPackage is XEXPPKG +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for XEXPPKG +--R +--R------------------------------- Operations -------------------------------- +--R Hausdorff : (XPOLY,XPOLY,NonNegativeInteger) -> XPOLY +--R exp : (XPOLY,NonNegativeInteger) -> XPOLY +--R log : (XPOLY,NonNegativeInteger) -> XPOLY +--R --E 1 )spool @@ -186821,7 +193177,8 @@ with finitely many solutions. )set message test on )set message auto off )clear all ---S 1 of 28 + +--S 1 of 29 R := Integer --R --R @@ -186829,7 +193186,7 @@ R := Integer --R Type: Domain --E 1 ---S 2 of 28 +--S 2 of 29 ls : List Symbol := [x,y,z,t] --R --R @@ -186837,7 +193194,7 @@ ls : List Symbol := [x,y,z,t] --R Type: List(Symbol) --E 2 ---S 3 of 28 +--S 3 of 29 ls2 : List Symbol := [x,y,z,t,new()$Symbol] --R --R @@ -186845,7 +193202,7 @@ ls2 : List Symbol := [x,y,z,t,new()$Symbol] --R Type: List(Symbol) --E 3 ---S 4 of 28 +--S 4 of 29 pack := ZDSOLVE(R,ls,ls2) --R --R @@ -186853,7 +193210,7 @@ pack := ZDSOLVE(R,ls,ls2) --R Type: Domain --E 4 ---S 5 of 28 +--S 5 of 29 p1 := x**2*y*z + x*y**2*z + x*y*z**2 + x*y*z + x*y + x*z + y*z --R --R @@ -186862,7 +193219,7 @@ p1 := x**2*y*z + x*y**2*z + x*y*z**2 + x*y*z + x*y + x*z + y*z --R Type: Polynomial(Integer) --E 5 ---S 6 of 28 +--S 6 of 29 p2 := x**2*y**2*z + x*y**2*z**2 + x**2*y*z + x*y*z + y*z + x + z --R --R @@ -186871,7 +193228,7 @@ p2 := x**2*y**2*z + x*y**2*z**2 + x**2*y*z + x*y*z + y*z + x + z --R Type: Polynomial(Integer) --E 6 ---S 7 of 28 +--S 7 of 29 p3 := x**2*y**2*z**2 + x**2*y**2*z + x*y**2*z + x*y*z + x*z + z + 1 --R --R @@ -186880,7 +193237,7 @@ p3 := x**2*y**2*z**2 + x**2*y**2*z + x*y**2*z + x*y*z + x*z + z + 1 --R Type: Polynomial(Integer) --E 7 ---S 8 of 28 +--S 8 of 29 lp := [p1, p2, p3] --R --R @@ -186894,7 +193251,7 @@ lp := [p1, p2, p3] --R Type: List(Polynomial(Integer)) --E 8 ---S 9 of 28 +--S 9 of 29 triangSolve(lp)$pack --R --R @@ -186946,7 +193303,7 @@ triangSolve(lp)$pack --R Type: List(RegularChain(Integer,[x,y,z,t])) --E 9 ---S 10 of 28 +--S 10 of 29 univariateSolve(lp)$pack --R --R @@ -186990,7 +193347,7 @@ univariateSolve(lp)$pack --RType: List(Record(complexRoots: SparseUnivariatePolynomial(Integer),coordinates: List(Polynomial(Integer)))) --E 10 ---S 11 of 28 +--S 11 of 29 lr := realSolve(lp)$pack --R --R @@ -187358,7 +193715,7 @@ lr := realSolve(lp)$pack --R Type: List(List(RealClosure(Fraction(Integer)))) --E 11 ---S 12 of 28 +--S 12 of 29 # lr --R --R @@ -187366,7 +193723,7 @@ lr := realSolve(lp)$pack --R Type: PositiveInteger --E 12 ---S 13 of 28 +--S 13 of 29 [ [approximate(r,1/1000000) for r in point] for point in lr] --R --R @@ -187600,7 +193957,7 @@ lr := realSolve(lp)$pack --R Type: List(List(Fraction(Integer))) --E 13 ---S 14 of 28 +--S 14 of 29 lpr := positiveSolve(lp)$pack --R --R @@ -187608,7 +193965,7 @@ lpr := positiveSolve(lp)$pack --R Type: List(List(RealClosure(Fraction(Integer)))) --E 14 ---S 15 of 28 +--S 15 of 29 f0 := x**3 + y + z + t- 1 --R --R @@ -187617,7 +193974,7 @@ f0 := x**3 + y + z + t- 1 --R Type: Polynomial(Integer) --E 15 ---S 16 of 28 +--S 16 of 29 f1 := x + y**3 + z + t -1 --R --R @@ -187626,7 +193983,7 @@ f1 := x + y**3 + z + t -1 --R Type: Polynomial(Integer) --E 16 ---S 17 of 28 +--S 17 of 29 f2 := x + y + z**3 + t-1 --R --R @@ -187635,7 +193992,7 @@ f2 := x + y + z**3 + t-1 --R Type: Polynomial(Integer) --E 17 ---S 18 of 28 +--S 18 of 29 f3 := x + y + z + t**3 -1 --R --R @@ -187644,7 +194001,7 @@ f3 := x + y + z + t**3 -1 --R Type: Polynomial(Integer) --E 18 ---S 19 of 28 +--S 19 of 29 lf := [f0, f1, f2, f3] --R --R @@ -187654,7 +194011,7 @@ lf := [f0, f1, f2, f3] --R Type: List(Polynomial(Integer)) --E 19 ---S 20 of 28 +--S 20 of 29 lts := triangSolve(lf)$pack --R --R @@ -187855,7 +194212,7 @@ lts := triangSolve(lf)$pack --R Type: List(RegularChain(Integer,[x,y,z,t])) --E 20 ---S 21 of 28 +--S 21 of 29 univariateSolve(lf)$pack --R --R @@ -187989,7 +194346,7 @@ univariateSolve(lf)$pack --RType: List(Record(complexRoots: SparseUnivariatePolynomial(Integer),coordinates: List(Polynomial(Integer)))) --E 21 ---S 22 of 28 +--S 22 of 29 ts := lts.1 --R --R @@ -188007,7 +194364,7 @@ ts := lts.1 --R Type: RegularChain(Integer,[x,y,z,t]) --E 22 ---S 23 of 28 +--S 23 of 29 univariateSolve(ts)$pack --R --R @@ -188041,7 +194398,7 @@ univariateSolve(ts)$pack --RType: List(Record(complexRoots: SparseUnivariatePolynomial(Integer),coordinates: List(Polynomial(Integer)))) --E 23 ---S 24 of 28 +--S 24 of 29 realSolve(ts)$pack --R --R @@ -188049,7 +194406,7 @@ realSolve(ts)$pack --R Type: List(List(RealClosure(Fraction(Integer)))) --E 24 ---S 25 of 28 +--S 25 of 29 lr2 := realSolve(lf)$pack --R --R @@ -188373,7 +194730,7 @@ lr2 := realSolve(lf)$pack --R Type: List(List(RealClosure(Fraction(Integer)))) --E 25 ---S 26 of 28 +--S 26 of 29 #lr2 --R --R @@ -188381,7 +194738,7 @@ lr2 := realSolve(lf)$pack --R Type: PositiveInteger --E 26 ---S 27 of 28 +--S 27 of 29 lpr2 := positiveSolve(lf)$pack --R --R @@ -188391,7 +194748,7 @@ lpr2 := positiveSolve(lf)$pack --R Type: List(List(RealClosure(Fraction(Integer)))) --E 27 ---S 28 of 28 +--S 28 of 29 [approximate(r,1/10**21)::Float for r in lpr2.1] --R --R @@ -188400,6 +194757,42 @@ lpr2 := positiveSolve(lf)$pack --R 0.3221853546 2608559291] --R Type: List(Float) --E 28 + +--S 29 of 29 +)show ZeroDimensionalSolvePackage +--R +--R ZeroDimensionalSolvePackage(R: Join(OrderedRing,EuclideanDomain,CharacteristicZero,RealConstant),ls: List(Symbol),ls2: List(Symbol)) is a package constructor +--R Abbreviation for ZeroDimensionalSolvePackage is ZDSOLVE +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for ZDSOLVE +--R +--R------------------------------- Operations -------------------------------- +--R convert : NewSparseMultivariatePolynomial(R,OrderedVariableList(ls)) -> NewSparseMultivariatePolynomial(R,OrderedVariableList(ls2)) +--R convert : Polynomial(R) -> Polynomial(RealClosure(Fraction(R))) +--R convert : NewSparseMultivariatePolynomial(R,OrderedVariableList(ls2)) -> Polynomial(RealClosure(Fraction(R))) +--R convert : SparseUnivariatePolynomial(R) -> SparseUnivariatePolynomial(RealClosure(Fraction(R))) +--R convert : SquareFreeRegularTriangularSet(R,IndexedExponents(OrderedVariableList(ls2)),OrderedVariableList(ls2),NewSparseMultivariatePolynomial(R,OrderedVariableList(ls2))) -> List(NewSparseMultivariatePolynomial(R,OrderedVariableList(ls2))) +--R positiveSolve : RegularChain(R,ls) -> List(List(RealClosure(Fraction(R)))) +--R positiveSolve : (List(Polynomial(R)),Boolean,Boolean) -> List(List(RealClosure(Fraction(R)))) +--R positiveSolve : (List(Polynomial(R)),Boolean) -> List(List(RealClosure(Fraction(R)))) +--R positiveSolve : List(Polynomial(R)) -> List(List(RealClosure(Fraction(R)))) +--R realSolve : RegularChain(R,ls) -> List(List(RealClosure(Fraction(R)))) +--R realSolve : (List(Polynomial(R)),Boolean,Boolean,Boolean) -> List(List(RealClosure(Fraction(R)))) +--R realSolve : (List(Polynomial(R)),Boolean,Boolean) -> List(List(RealClosure(Fraction(R)))) +--R realSolve : (List(Polynomial(R)),Boolean) -> List(List(RealClosure(Fraction(R)))) +--R realSolve : List(Polynomial(R)) -> List(List(RealClosure(Fraction(R)))) +--R squareFree : RegularChain(R,ls) -> List(SquareFreeRegularTriangularSet(R,IndexedExponents(OrderedVariableList(ls2)),OrderedVariableList(ls2),NewSparseMultivariatePolynomial(R,OrderedVariableList(ls2)))) +--R triangSolve : (List(Polynomial(R)),Boolean,Boolean) -> List(RegularChain(R,ls)) +--R triangSolve : (List(Polynomial(R)),Boolean) -> List(RegularChain(R,ls)) +--R triangSolve : List(Polynomial(R)) -> List(RegularChain(R,ls)) +--R univariateSolve : RegularChain(R,ls) -> List(Record(complexRoots: SparseUnivariatePolynomial(R),coordinates: List(Polynomial(R)))) +--R univariateSolve : (List(Polynomial(R)),Boolean,Boolean,Boolean) -> List(Record(complexRoots: SparseUnivariatePolynomial(R),coordinates: List(Polynomial(R)))) +--R univariateSolve : (List(Polynomial(R)),Boolean,Boolean) -> List(Record(complexRoots: SparseUnivariatePolynomial(R),coordinates: List(Polynomial(R)))) +--R univariateSolve : (List(Polynomial(R)),Boolean) -> List(Record(complexRoots: SparseUnivariatePolynomial(R),coordinates: List(Polynomial(R)))) +--R univariateSolve : List(Polynomial(R)) -> List(Record(complexRoots: SparseUnivariatePolynomial(R),coordinates: List(Polynomial(R)))) +--R +--E 29 + )spool )lisp (bye) \end{chunk} diff --git a/books/bookvol10.pamphlet b/books/bookvol10.pamphlet index 1d87e17..d311ee2 100644 --- a/books/bookvol10.pamphlet +++ b/books/bookvol10.pamphlet @@ -583,7 +583,7 @@ LAYER0=\ ${OUT}/ATARBPR.o ${OUT}/ATCANCL.o ${OUT}/ATCANON.o ${OUT}/ATCUNOR.o \ ${OUT}/ATFINAG.o ${OUT}/ATJACID.o ${OUT}/ATLR.o ${OUT}/ATLUNIT.o \ ${OUT}/ATMULVA.o ${OUT}/ATNOTHR.o ${OUT}/ATNULSQ.o \ - ${OUT}/ATNZDIV.o ${OUT}/ATPOSET.o \ + ${OUT}/ATNZDIV.o ${OUT}/ATPOSET.o ${OUT}/ATRUNIT.o \ ${OUT}/ATSHMUT.o \ ${OUT}/ATTREG.o ${OUT}/ATUNIKN.o \ ${OUT}/BASTYPE.o ${OUT}/BASTYPE-.o \ @@ -655,6 +655,9 @@ LAYER0=\ "ATNZDIV" [color=lightblue,href="bookvol10.2.pdf#nameddest=ATNZDIV"]; "ATNZDIV" -> "Category" +"ATRUNIT" [color=lightblue,href="bookvol10.2.pdf#nameddest=ATRUNIT"]; +"ATRUNIT" -> "Category" + "ATSHMUT" [color=lightblue,href="bookvol10.2.pdf#nameddest=ATSHMUT"]; "ATSHMUT" -> "Category" diff --git a/books/bookvol5.pamphlet b/books/bookvol5.pamphlet index abbd3dd..1d743c0 100644 --- a/books/bookvol5.pamphlet +++ b/books/bookvol5.pamphlet @@ -4608,6 +4608,7 @@ otherwise the new algebra won't be loaded by the interpreter when needed. (|RetractableTo| . RETRACT) (|RightModule| . RMODULE) (|Ring| . RING) + (|RightUnitaryAttribute| . ATRUNIT) (|Rng| . RNG) (|SegmentCategory| . SEGCAT) (|SegmentExpansionCategory| . SEGXCAT) diff --git a/changelog b/changelog index c225ca1..80de6d1 100644 --- a/changelog +++ b/changelog @@ -1,3 +1,19 @@ +20150508 tpd src/axiom-website/patches.html 20150508.02.tpd.patch +20150508 tpd books/bookvol10.2.pamphlet add more tests +20150508 tpd books/bookvol10.3.pamphlet add more tests +20150508 tpd books/bookvol10.4.pamphlet add more tests +20150508 tpd src/input/Makefile.pamphlet add more tests +20150508 tpd src/input/cmds.input.pamphlet add more tests +20150508 tpd src/interp/clam.lisp.pamphlet fix test breakage +20150508 tpd src/interp/msgdb.lisp.pamphlet fix test breakage +20150508 tpd src/interp/vmlisp.lisp.pamphlet fix test breakage +20150508 tpd books/bookvol10.pamphlet fix missing category +20150508 tpd books/bookvol5.pamphlet fix missing category +20150508 tpd src/share/algebra/browse.daase fix missing category +20150508 tpd src/share/algebra/category.daase fix missing category +20150508 tpd src/share/algebra/interp.daase fix missing category +20150508 tpd src/share/algebra/operation.daase fix missing category +20150508 tpd src/share/algebra/users.daase/index.kaf fix missing category 20150508 tpd src/axiom-website/patches.html 20150508.01.tpd.patch 20150508 tpd books/bookvolbib add Robe15 reference 20150505 tpd src/axiom-website/patches.html 20150505.02.tpd.patch diff --git a/patch b/patch index d09c818..f6661bd 100644 --- a/patch +++ b/patch @@ -1,8 +1,2 @@ -books/bookvolbib add Robe15 reference - -@misc{Robe15, - author = "Roberts, Siobhan", - title = "In Mathematics, Mistakes Aren't What They Used To Be", - year = 2015, - url = "http://nautil.us/issue/24/error/In-mathematics-mistakes-arent-what-they-used-to-be" +books/bookvol*pamphlet add more test cases diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html index 129f8e1..17d3de0 100644 --- a/src/axiom-website/patches.html +++ b/src/axiom-website/patches.html @@ -5056,6 +5056,8 @@ books/bookvolbib add Kama15 to paper collection
books/bookvol13 add Kama15 reference
20150508.01.tpd.patch books/bookvolbib add Robe15 reference
+20150508.02.tpd.patch +books/bookvol*pamphlet add more test cases
diff --git a/src/input/Makefile.pamphlet b/src/input/Makefile.pamphlet index 854df2e..8456827 100644 --- a/src/input/Makefile.pamphlet +++ b/src/input/Makefile.pamphlet @@ -505,6 +505,11 @@ regresstests: ${REGRESSTESTS} ${OUTS} @ echo src/input RUNNING REGRESSION TESTS @ echo ====================================== +moretests: ${REGRESSTESTS} ${OUTS} algebratests + @ echo ====================================== + @ echo src/input RUNNING MORE TESTS + @ echo ====================================== + alltests: regresstests algebratests catstests newrichtests richtests ${OUTS} @ echo ====================================== @ echo src/input RUNNING ALL TESTS diff --git a/src/input/cmds.input.pamphlet b/src/input/cmds.input.pamphlet index d2c9f5a..b13f59f 100644 --- a/src/input/cmds.input.pamphlet +++ b/src/input/cmds.input.pamphlet @@ -109,12 +109,13 @@ --R ATNOTHR NotherianAttribute ATNULSQ NullSquareAttribute --R ATNZDIV NoZeroDivisorsAttribute ATPOSET PartiallyOrderedSetAttribute --R ATRIG ArcTrigonometricFunctionCategory ---R ATSHMUT ShallowlyMutableAttribute ATTREG AttributeRegistry ---R ATUNIKN UnitsKnownAttribute BASTYPE BasicType ---R BGAGG BagAggregate BLMETCT BlowUpMethodCategory ---R BMODULE BiModule BRAGG BinaryRecursiveAggregate ---R BTAGG BitAggregate BTCAT BinaryTreeCategory ---R CABMON CancellationAbelianMonoid CACHSET CachableSet +--R ATRUNIT RightUnitaryAttribute ATSHMUT ShallowlyMutableAttribute +--R ATTREG AttributeRegistry ATUNIKN UnitsKnownAttribute +--R BASTYPE BasicType BGAGG BagAggregate +--R BLMETCT BlowUpMethodCategory BMODULE BiModule +--R BRAGG BinaryRecursiveAggregate BTAGG BitAggregate +--R BTCAT BinaryTreeCategory CABMON CancellationAbelianMonoid +--R CACHSET CachableSet --R CFCAT CombinatorialFunctionCategory --R CHARNZ CharacteristicNonZero CHARZ CharacteristicZero --R CLAGG Collection COMBOPC CombinatorialOpsCategory diff --git a/src/interp/clam.lisp.pamphlet b/src/interp/clam.lisp.pamphlet index df7c188..0bc8c4a 100644 --- a/src/interp/clam.lisp.pamphlet +++ b/src/interp/clam.lisp.pamphlet @@ -1996,7 +1996,7 @@ |form|) NIL))))))))) (|sayBrightly| - (CONS "Totals:" + (CONS "Totals: " (CONS |nTotal| (CONS " instantiated" (CONS "%l" diff --git a/src/interp/msgdb.lisp.pamphlet b/src/interp/msgdb.lisp.pamphlet index e338789..4b43d90 100644 --- a/src/interp/msgdb.lisp.pamphlet +++ b/src/interp/msgdb.lisp.pamphlet @@ -1852,24 +1852,11 @@ ; +/[fn y for y in x] where fn y == ; sayWidth y -(defun |sayWidth,fn| (|y|) (|sayWidth| |y|)) -(defun |sayWidth| (|x|) - (PROG () - (RETURN - (SEQ (COND - ((ATOM |x|) (|#| (|atom2String| |x|))) - (t - (PROG (G167143) - (setq G167143 0) - (RETURN - (DO ((G167148 |x| (CDR G167148)) (|y| nil)) - ((OR (ATOM G167148) - (PROGN (SETQ |y| (CAR G167148)) nil)) - G167143) - (SEQ (EXIT (SETQ G167143 - (+ G167143 - (|sayWidth,fn| |y|)))))))))))))) +(defun |sayWidth| (x) + (if (atom x) + (|#| (princ-to-string x)) + (loop for y in x sum (|sayWidth| y)))) ;pp2Cols(al) == ; while al repeat @@ -1947,36 +1934,36 @@ ; if f.1 = 0 then fill2 := fill1 else fill2 := STRCONC(fillchar,fill1) ; concat(fill1,text,fill2) -(defun |center| (|text| |argList|) - (PROG (|width| |fillchar| |u| |moreLines| |wid| |f| |fill1| |fill2|) - (declare (special $LINELENGTH)) - (RETURN - (SEQ (PROGN - (setq |width| (OR (IFCAR |argList|) $LINELENGTH)) - (setq |fillchar| - (OR (IFCAR (IFCDR |argList|)) " ")) - (COND - ((setq |u| (splitSayBrightlyArgument |text|)) - (setq |text| (CAR |u|)) - (setq |moreLines| (CDR |u|)) |u|)) - (setq |wid| (|sayBrightlyLength| |text|)) - (COND - ((>= |wid| (- |width| 2)) - (|sayBrightly| |text|)) - (t - (setq |f| - (DIVIDE (- - (- |width| |wid|) 2) - 2)) - (setq |fill1| "") - (DO ((G167248 (ELT |f| 0)) (|i| 1 (1+ |i|))) - ((QSGREATERP |i| G167248) nil) - (SEQ (EXIT (setq |fill1| - (STRCONC |fillchar| |fill1|))))) - (COND - ((EQL (ELT |f| 1) 0) (setq |fill2| |fill1|)) - (t (setq |fill2| (STRCONC |fillchar| |fill1|)))) - (|concat| |fill1| |text| |fill2|)))))))) +;(defun |center| (|text| |argList|) +; (PROG (|width| |fillchar| |u| |moreLines| |wid| |f| |fill1| |fill2|) +; (declare (special $LINELENGTH)) +; (RETURN +; (SEQ (PROGN +; (setq |width| (OR (IFCAR |argList|) $LINELENGTH)) +; (setq |fillchar| +; (OR (IFCAR (IFCDR |argList|)) " ")) +; (COND +; ((setq |u| (splitSayBrightlyArgument |text|)) +; (setq |text| (CAR |u|)) +; (setq |moreLines| (CDR |u|)) |u|)) +; (setq |wid| (|sayBrightlyLength| |text|)) +; (COND +; ((>= |wid| (- |width| 2)) +; (|sayBrightly| |text|)) +; (t +; (setq |f| +; (DIVIDE (- +; (- |width| |wid|) 2) +; 2)) +; (setq |fill1| "") +; (DO ((G167248 (ELT |f| 0)) (|i| 1 (1+ |i|))) +; ((QSGREATERP |i| G167248) nil) +; (SEQ (EXIT (setq |fill1| +; (STRCONC |fillchar| |fill1|))))) +; (COND +; ((EQL (ELT |f| 1) 0) (setq |fill2| |fill1|)) +; (t (setq |fill2| (STRCONC |fillchar| |fill1|)))) +; (|concat| |fill1| |text| |fill2|)))))))) ;splitSayBrightlyArgument u == ; atom u => nil diff --git a/src/interp/vmlisp.lisp.pamphlet b/src/interp/vmlisp.lisp.pamphlet index 2854922..99d07ba 100644 --- a/src/interp/vmlisp.lisp.pamphlet +++ b/src/interp/vmlisp.lisp.pamphlet @@ -1097,7 +1097,9 @@ can be restored. ; 24.0 Printing \end{chunk} - +\section{The StringImage Fix} +In GCL 2.5 there is a bug in the write-to-string function. +It should respect *print-escape* but it does not. That is, \begin{verbatim} In GCL 2.4.1: @@ -1109,8 +1111,12 @@ In GCL 2.5: (write-to-string '|a|) ==> "|a|" \end{verbatim} +The form2LispString function uses stringimage and fails. +The princ-to-string function assumes *print-escape* is nil +and works properly. \begin{chunk}{*} +(define-function 'stringimage #'princ-to-string) (defun |F,PRINT-ONE| (form &optional (stream *standard-output*)) (declare (ignore stream)) @@ -2973,7 +2979,7 @@ LP (COND ((NULL X) (defvar $GENNO 0) -(DEFUN GENVAR () (INTERNL "$" (princ-to-string (SETQ $GENNO (1+ $GENNO))))) +(DEFUN GENVAR () (INTERNL "$" (STRINGIMAGE (SETQ $GENNO (1+ $GENNO))))) (DEFUN IS_GENVAR (X) (AND (IDENTP X) @@ -3645,9 +3651,9 @@ terminals and empty or at-end files. In Common Lisp, we must assume record size (defmacro |assert| (x y) `(IF (NULL ,x) (|error| ,y))) (defun coerce-failure-msg (val mode) - (STRCONC (MAKE-REASONABLE (princ-to-string val)) + (STRCONC (MAKE-REASONABLE (STRINGIMAGE val)) " cannot be coerced to mode " - (princ-to-string (|devaluate| mode)))) + (STRINGIMAGE (|devaluate| mode)))) (defmacro |check-subtype| (pred submode val) `(|assert| ,pred (coerce-failure-msg ,val ,submode))) @@ -4098,7 +4104,7 @@ terminals and empty or at-end files. In Common Lisp, we must assume record size (t (COMP-NEWNAM (CAR X)) (COMP-NEWNAM (CDR X)))))) (defun make-closedfn-name () - (internl $FUNNAME "!" (princ-to-string (LENGTH $CLOSEDFNS)))) + (internl $FUNNAME "!" (STRINGIMAGE (LENGTH $CLOSEDFNS)))) (DEFUN COMP-TRAN (X) "SEXPR -> SEXPR" @@ -4320,7 +4326,7 @@ terminals and empty or at-end files. In Common Lisp, we must assume record size (LENGTH2STR min))))) (DEFUN LENGTH2STR (X &aux XLEN) - (cond ( (= 1 (SETQ XLEN (LENGTH (SETQ X (princ-to-string X))))) (STRCONC "0" X)) + (cond ( (= 1 (SETQ XLEN (LENGTH (SETQ X (STRINGIMAGE X))))) (STRCONC "0" X)) ( (= 2 XLEN) X) ( (subseq x (- XLEN 2))))) @@ -5334,12 +5340,12 @@ o there is some code at the end of SPECEVAL BOOT that puts "up" (REPEAT (IN X '( |Polynomial| |UnivariatePoly| |SquareMatrix| |QuotientField| )) -(setf (get x '|status|) (internl (strconc "status" (princ-to-string x))))) +(setf (get x '|status|) (internl (strconc "status" (stringimage x))))) (REPEAT (IN X '( |UnivariatePoly| |Matrix| |QuotientField| |Gaussian| )) -(setf (get x '|dataCoerce|) (internl (strconc "coerce" (princ-to-string x))))) +(setf (get x '|dataCoerce|) (internl (strconc "coerce" (stringimage x))))) ;; this property is checked for Integers to decide which subdomain to ;; choose at compile time. @@ -5939,6 +5945,9 @@ o there is some code at the end of SPECEVAL BOOT that puts "up" (defun |ToString| (ob) (string ob) ) +(defun |StringImage| (ob) + (format nil "~a" ob) ) + (defun |String?| (ob) (stringp ob) ) diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index 422d9d0..dc63186 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,5 +1,5 @@ -(2509984 . 3621447416) +(2526798 . 3639870122) (|OneDimensionalArrayAggregate&| A S) ((|constructor| (NIL "One-dimensional-array aggregates serves as models for one-dimensional arrays. Categorically, these aggregates are finite linear aggregates with the \\spadatt{shallowlyMutable} property, that is, any component of the array may be changed without affecting the identity of the overall array. Array data structures are typically represented by a fixed area in storage and cannot efficiently grow or shrink on demand as can list structures (see however \\spadtype{FlexibleArray} for a data structure which is a cross between a list and an array). Iteration over, and access to, elements of arrays is extremely fast (and often can be optimized to open-code). Insertion and deletion however is generally slow since an entirely new data structure must be created for the result."))) NIL @@ -141,7 +141,7 @@ NIL (((|commutative| "*") |has| |#1| (|CommutativeRing|)) (|noZeroDivisors| |has| |#1| (|IntegralDomain|)) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) NIL (|AlgebraicNumber|) -((|constructor| (NIL "Algebraic closure of the rational numbers, with mathematical =")) (|norm| (($ $ (|List| (|Kernel| $))) "\\spad{norm(f,l)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernels \\spad{l}") (($ $ (|Kernel| $)) "\\spad{norm(f,k)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernel \\spad{k}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|List| (|Kernel| $))) "\\spad{norm(p,l)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernels \\spad{l}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{norm(p,k)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernel \\spad{k}")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic numbers present in \\spad{f} by applying their defining relations.")) (|denom| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z.}")) (|numer| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z.}")) (|coerce| (($ (|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} viewed as an algebraic number."))) +((|constructor| (NIL "Algebraic closure of the rational numbers, with mathematical =")) (|norm| (($ $ (|List| (|Kernel| $))) "\\spad{norm(f,l)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernels \\spad{l}") (($ $ (|Kernel| $)) "\\spad{norm(f,k)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernel \\spad{k}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|List| (|Kernel| $))) "\\spad{norm(p,l)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernels \\spad{l}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{norm(p,k)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernel \\spad{k}")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic numbers present in \\spad{f} by applying their defining relations.")) (|denom| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\indented{1}{denom(f) returns the denominator of \\spad{f} viewed as a} \\indented{1}{polynomial in the kernels over \\spad{Z.}} \\blankline \\spad{X} t1:=sqrt(3)/sqrt(5) \\spad{X} denom \\spad{t1}")) (|numer| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\indented{1}{numer(f) returns the numerator of \\spad{f} viewed as a} \\indented{1}{polynomial in the kernels over \\spad{Z.}} \\blankline \\spad{X} t1:=sqrt(3)/sqrt(5) \\spad{X} numer \\spad{t1}")) (|coerce| (($ (|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} viewed as an algebraic number."))) ((|canonicalsClosed| . T) (|canonicalUnitNormal| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) ((|HasCategory| $ (QUOTE (|Ring|))) (|HasCategory| $ (LIST (QUOTE |RetractableTo|) (QUOTE (|Integer|))))) (|AnonymousFunction|) @@ -149,7 +149,7 @@ NIL NIL NIL (|AntiSymm| R |lVar|) -((|constructor| (NIL "The domain of antisymmetric polynomials.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,p)} changes each coefficient of \\spad{p} by the application of \\spad{f.}")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} returns the homogeneous degree of \\spad{p.}")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?(p)} tests if \\spad{p} is a 0-form, \\spadignore{i.e.} if degree(p) = 0.")) (|homogeneous?| (((|Boolean|) $) "\\spad{homogeneous?(p)} tests if all of the terms of \\spad{p} have the same degree.")) (|exp| (($ (|List| (|Integer|))) "\\spad{exp([i1,...in])} returns \\spad{u_1\\^{i_1} \\spad{...} u_n\\^{i_n}}")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(n)} returns the \\spad{n}th multiplicative generator, a basis term.")) (|coefficient| ((|#1| $ $) "\\spad{coefficient(p,u)} returns the coefficient of the term in \\spad{p} containing the basis term \\spad{u} if such a term exists, and 0 otherwise. Error: if the second argument \\spad{u} is not a basis element.")) (|reductum| (($ $) "\\spad{reductum(p)}, where \\spad{p} is an antisymmetric polynomial, returns \\spad{p} minus the leading term of \\spad{p} if \\spad{p} has at least two terms, and 0 otherwise.")) (|leadingBasisTerm| (($ $) "\\spad{leadingBasisTerm(p)} returns the leading basis term of antisymmetric polynomial \\spad{p.}")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(p)} returns the leading coefficient of antisymmetric polynomial \\spad{p.}"))) +((|constructor| (NIL "The domain of antisymmetric polynomials.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,p)} changes each coefficient of \\spad{p} by the application of \\spad{f.}")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} returns the homogeneous degree of \\spad{p.}")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?(p)} tests if \\spad{p} is a 0-form, \\spadignore{i.e.} if degree(p) = 0.")) (|homogeneous?| (((|Boolean|) $) "\\spad{homogeneous?(p)} tests if all of the terms of \\spad{p} have the same degree.")) (|exp| (($ (|List| (|Integer|))) "\\spad{exp([i1,...in])} returns \\spad{u_1\\^{i_1} \\spad{...} u_n\\^{i_n}}")) (|generator| (($ (|NonNegativeInteger|)) "\\indented{1}{generator(n) returns the \\spad{n}th multiplicative generator,} \\indented{1}{a basis term.} \\blankline \\spad{X} AS:=AntiSymm(Integer,[x,y,z]) \\spad{X} [dx,dy,dz]:=[generator(i)$AS for \\spad{i} in 1..3]")) (|coefficient| ((|#1| $ $) "\\spad{coefficient(p,u)} returns the coefficient of the term in \\spad{p} containing the basis term \\spad{u} if such a term exists, and 0 otherwise. Error: if the second argument \\spad{u} is not a basis element.")) (|reductum| (($ $) "\\spad{reductum(p)}, where \\spad{p} is an antisymmetric polynomial, returns \\spad{p} minus the leading term of \\spad{p} if \\spad{p} has at least two terms, and 0 otherwise.")) (|leadingBasisTerm| (($ $) "\\spad{leadingBasisTerm(p)} returns the leading basis term of antisymmetric polynomial \\spad{p.}")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(p)} returns the leading coefficient of antisymmetric polynomial \\spad{p.}"))) ((|unitsKnown| . T)) NIL (|AnyFunctions1| S) @@ -157,7 +157,7 @@ NIL NIL NIL (|Any|) -((|constructor| (NIL "\\spadtype{Any} implements a type that packages up objects and their types in objects of \\spadtype{Any}. Roughly speaking that means that if \\spad{s : \\spad{S}} then when converted to \\spadtype{Any}, the new object will include both the original object and its type. This is a way of converting arbitrary objects into a single type without losing any of the original information. Any object can be converted to one of \\spadtype{Any}.")) (|showTypeInOutput| (((|String|) (|Boolean|)) "\\spad{showTypeInOutput(bool)} affects the way objects of \\spadtype{Any} are displayed. If \\spad{bool} is \\spad{true} then the type of the original object that was converted to \\spadtype{Any} will be printed. If \\spad{bool} is false, it will not be printed.")) (|obj| (((|None|) $) "\\spad{obj(a)} essentially returns the original object that was converted to \\spadtype{Any} except that the type is forced to be \\spadtype{None}.")) (|dom| (((|SExpression|) $) "\\spad{dom(a)} returns a \\spadgloss{LISP} form of the type of the original object that was converted to \\spadtype{Any}.")) (|objectOf| (((|OutputForm|) $) "\\spad{objectOf(a)} returns a printable form of the original object that was converted to \\spadtype{Any}.")) (|domainOf| (((|OutputForm|) $) "\\spad{domainOf(a)} returns a printable form of the type of the original object that was converted to \\spadtype{Any}.")) (|any| (($ (|SExpression|) (|None|)) "\\spad{any(type,object)} is a technical function for creating an \\spad{object} of \\spadtype{Any}. Arugment \\spad{type} is a \\spadgloss{LISP} form for the \\spad{type} of \\spad{object}."))) +((|constructor| (NIL "\\spadtype{Any} implements a type that packages up objects and their types in objects of \\spadtype{Any}. Roughly speaking that means that if \\spad{s : \\spad{S}} then when converted to \\spadtype{Any}, the new object will include both the original object and its type. This is a way of converting arbitrary objects into a single type without losing any of the original information. Any object can be converted to one of \\spadtype{Any}.")) (|showTypeInOutput| (((|String|) (|Boolean|)) "\\indented{1}{showTypeInOutput(bool) affects the way objects of} \\indented{1}{\\spadtype{Any} are displayed. If \\spad{bool} is true} \\indented{1}{then the type of the original object that was converted} \\indented{1}{to \\spadtype{Any} will be printed. If \\spad{bool} is} \\indented{1}{false, it will not be printed.} \\blankline \\spad{X} u:=[1,7.2,3/2,x**2,\"wally\"] \\spad{X} showTypeInOutput(true) \\spad{X} \\spad{u}")) (|obj| (((|None|) $) "\\spad{obj(a)} essentially returns the original object that was converted to \\spadtype{Any} except that the type is forced to be \\spadtype{None}.")) (|dom| (((|SExpression|) $) "\\spad{dom(a)} returns a \\spadgloss{LISP} form of the type of the original object that was converted to \\spadtype{Any}.")) (|objectOf| (((|OutputForm|) $) "\\spad{objectOf(a)} returns a printable form of the original object that was converted to \\spadtype{Any}.")) (|domainOf| (((|OutputForm|) $) "\\spad{domainOf(a)} returns a printable form of the type of the original object that was converted to \\spadtype{Any}.")) (|any| (($ (|SExpression|) (|None|)) "\\spad{any(type,object)} is a technical function for creating an \\spad{object} of \\spadtype{Any}. Arugment \\spad{type} is a \\spadgloss{LISP} form for the \\spad{type} of \\spad{object}."))) NIL NIL (|ApplicationProgramInterface|) @@ -313,7 +313,7 @@ NIL NIL ((|HasCategory| |#1| (QUOTE (|Field|)))) (|ArrayStack| S) -((|constructor| (NIL "A stack represented as a flexible array.")) (|member?| (((|Boolean|) |#1| $) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,2,3,4,5] \\spad{X} member?(3,a)")) (|members| (((|List| |#1|) $) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,2,3,4,5] \\spad{X} members a")) (|parts| (((|List| |#1|) $) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,2,3,4,5] \\spad{X} parts a")) (|#| (((|NonNegativeInteger|) $) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,2,3,4,5] \\spad{X} \\#a")) (|count| (((|NonNegativeInteger|) |#1| $) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,2,3,4,5] \\spad{X} count(4,a)") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,2,3,4,5] \\spad{X} count(x+->(x>2),a)")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,2,3,4,5] \\spad{X} any?(x+->(x=4),a)")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,2,3,4,5] \\spad{X} every?(x+->(x=4),a)")) (~= (((|Boolean|) $ $) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,2,3,4,5] \\spad{X} b:=copy a \\spad{X} (a~=b)")) (= (((|Boolean|) $ $) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,2,3,4,5] \\spad{X} b:ArrayStack INT:= arrayStack [1,2,3,4,5] \\spad{X} (a=b)@Boolean")) (|coerce| (((|OutputForm|) $) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,2,3,4,5] \\spad{X} coerce a")) (|hash| (((|SingleInteger|) $) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,2,3,4,5] \\spad{X} hash a")) (|latex| (((|String|) $) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,2,3,4,5] \\spad{X} latex a")) (|map!| (($ (|Mapping| |#1| |#1|) $) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,2,3,4,5] \\spad{X} map!(x+->x+10,a) \\spad{X} a")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,2,3,4,5] \\spad{X} map(x+->x+10,a) \\spad{X} a")) (|eq?| (((|Boolean|) $ $) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,2,3,4,5] \\spad{X} b:=copy a \\spad{X} eq?(a,b)")) (|copy| (($ $) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,2,3,4,5] \\spad{X} copy a")) (|sample| (($) "\\blankline \\spad{X} sample()$ArrayStack(INT)")) (|empty| (($) "\\blankline \\spad{X} b:=empty()$(ArrayStack INT)")) (|empty?| (((|Boolean|) $) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,2,3,4,5] \\spad{X} empty? a")) (|bag| (($ (|List| |#1|)) "\\blankline \\spad{X} bag([1,2,3,4,5])$ArrayStack(INT)")) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,2,3,4,5] \\spad{X} size?(a,5)")) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,2,3,4,5] \\spad{X} more?(a,9)")) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,2,3,4,5] \\spad{X} less?(a,9)")) (|depth| (((|NonNegativeInteger|) $) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,2,3,4,5] \\spad{X} depth a")) (|top| ((|#1| $) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,2,3,4,5] \\spad{X} top a")) (|inspect| ((|#1| $) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,2,3,4,5] \\spad{X} inspect a")) (|insert!| (($ |#1| $) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,2,3,4,5] \\spad{X} insert!(8,a) \\spad{X} a")) (|push!| ((|#1| |#1| $) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,2,3,4,5] \\spad{X} push!(9,a) \\spad{X} a")) (|extract!| ((|#1| $) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,2,3,4,5] \\spad{X} extract! a \\spad{X} a")) (|pop!| ((|#1| $) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,2,3,4,5] \\spad{X} pop! a \\spad{X} a")) (|arrayStack| (($ (|List| |#1|)) "\\indented{1}{arrayStack([x,y,...,z]) creates an array stack with first (top)} \\indented{1}{element \\spad{x,} second element y,...,and last element \\spad{z.}} \\blankline \\spad{E} c:ArrayStack INT:= arrayStack [1,2,3,4,5]"))) +((|constructor| (NIL "A stack represented as a flexible array.")) (|member?| (((|Boolean|) |#1| $) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,2,3,4,5] \\spad{X} member?(3,a)")) (|members| (((|List| |#1|) $) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,2,3,4,5] \\spad{X} members a")) (|parts| (((|List| |#1|) $) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,2,3,4,5] \\spad{X} parts a")) (|#| (((|NonNegativeInteger|) $) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,2,3,4,5] \\spad{X} \\#a")) (|count| (((|NonNegativeInteger|) |#1| $) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,2,3,4,5] \\spad{X} count(4,a)") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,2,3,4,5] \\spad{X} count(x+->(x>2),a)")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,2,3,4,5] \\spad{X} any?(x+->(x=4),a)")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,2,3,4,5] \\spad{X} every?(x+->(x=4),a)")) (~= (((|Boolean|) $ $) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,2,3,4,5] \\spad{X} b:=copy a \\spad{X} (a~=b)")) (= (((|Boolean|) $ $) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,2,3,4,5] \\spad{X} b:ArrayStack INT:= arrayStack [1,2,3,4,5] \\spad{X} (a=b)@Boolean")) (|coerce| (((|OutputForm|) $) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,2,3,4,5] \\spad{X} coerce a")) (|hash| (((|SingleInteger|) $) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,2,3,4,5] \\spad{X} hash a")) (|latex| (((|String|) $) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,2,3,4,5] \\spad{X} latex a")) (|map!| (($ (|Mapping| |#1| |#1|) $) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,2,3,4,5] \\spad{X} map!(x+->x+10,a) \\spad{X} a")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,2,3,4,5] \\spad{X} map(x+->x+10,a) \\spad{X} a")) (|eq?| (((|Boolean|) $ $) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,2,3,4,5] \\spad{X} b:=copy a \\spad{X} eq?(a,b)")) (|copy| (($ $) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,2,3,4,5] \\spad{X} copy a")) (|sample| (($) "\\blankline \\spad{X} sample()$ArrayStack(INT)")) (|empty| (($) "\\blankline \\spad{X} b:=empty()$(ArrayStack INT)")) (|empty?| (((|Boolean|) $) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,2,3,4,5] \\spad{X} empty? a")) (|bag| (($ (|List| |#1|)) "\\blankline \\spad{X} bag([1,2,3,4,5])$ArrayStack(INT)")) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,2,3,4,5] \\spad{X} size?(a,5)")) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,2,3,4,5] \\spad{X} more?(a,9)")) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,2,3,4,5] \\spad{X} less?(a,9)")) (|depth| (((|NonNegativeInteger|) $) "\\indented{1}{depth returns the number of elements} \\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,2,3,4,5] \\spad{X} depth a")) (|top| ((|#1| $) "\\indented{1}{top returns the first item of the list without modifing the list} \\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,2,3,4,5] \\spad{X} top a")) (|inspect| ((|#1| $) "\\indented{1}{inspect returns the first item of the list without modifing the list} \\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,2,3,4,5] \\spad{X} inspect a")) (|insert!| (($ |#1| $) "\\indented{1}{insert! destructively modifies its argument and returns a new} \\indented{1}{list with the element add to the front of the list} \\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,2,3,4,5] \\spad{X} insert!(8,a) \\spad{X} a")) (|push!| ((|#1| |#1| $) "\\indented{1}{push! destructively modifies its argument and returns a new} \\indented{1}{list with the element add to the front of the list} \\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,2,3,4,5] \\spad{X} push!(9,a) \\spad{X} a")) (|extract!| ((|#1| $) "\\indented{1}{extract! destructively modifies its argument and returns the} \\indented{1}{first item of the argument} \\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,2,3,4,5] \\spad{X} extract! a \\spad{X} a")) (|pop!| ((|#1| $) "\\indented{1}{pop! destructively modifies its argument and returns the} \\indented{1}{first item of the argument} \\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,2,3,4,5] \\spad{X} pop! a \\spad{X} a")) (|arrayStack| (($ (|List| |#1|)) "\\indented{1}{arrayStack([x,y,...,z]) creates an array stack with first (top)} \\indented{1}{element \\spad{x,} second element y,...,and last element \\spad{z.}} \\blankline \\spad{X} c:ArrayStack INT:= arrayStack [1,2,3,4,5]"))) ((|finiteAggregate| . T) (|shallowlyMutable| . T)) ((|HasCategory| |#1| (QUOTE (|SetCategory|))) (AND (|HasCategory| |#1| (LIST (QUOTE |Evalable|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (|SetCategory|))))) (|AdditiveValuationAttribute|) @@ -396,6 +396,10 @@ NIL ((|constructor| (NIL "Category for the inverse trigonometric functions.")) (|atan| (($ $) "\\spad{atan(x)} returns the arc-tangent of \\spad{x.}")) (|asin| (($ $) "\\spad{asin(x)} returns the arc-sine of \\spad{x.}")) (|asec| (($ $) "\\spad{asec(x)} returns the arc-secant of \\spad{x.}")) (|acsc| (($ $) "\\spad{acsc(x)} returns the arc-cosecant of \\spad{x.}")) (|acot| (($ $) "\\spad{acot(x)} returns the arc-cotangent of \\spad{x.}")) (|acos| (($ $) "\\spad{acos(x)} returns the arc-cosine of \\spad{x.}"))) NIL NIL +(|RightUnitaryAttribute|) +((|constructor| (NIL "RightUnitary is \\spad{true} if \\spad{x * 1 = \\spad{x}} for all \\spad{x.}"))) +((|nil| . T)) +NIL (|ShallowlyMutableAttribute|) ((|constructor| (NIL "The class of all domains which have immediate components that are updateable in place (mutable). The properties of any component domain are irrevelant to the ShallowlyMutableAttribute."))) ((|nil| . T)) @@ -881,7 +885,7 @@ NIL ((|finiteAggregate| . T) (|shallowlyMutable| . T)) ((|HasCategory| |#1| (QUOTE (|SetCategory|))) (AND (|HasCategory| |#1| (LIST (QUOTE |Evalable|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (|SetCategory|))))) (|DeRhamComplex| |CoefRing| |listIndVar|) -((|constructor| (NIL "The deRham complex of Euclidean space, that is, the class of differential forms of arbitary degree over a coefficient ring. See Flanders, Harley, Differential Forms, With Applications to the Physical Sciences, New York, Academic Press, 1963.")) (|exteriorDifferential| (($ $) "\\spad{exteriorDifferential(df)} returns the exterior derivative (gradient, curl, divergence, ...) of the differential form \\spad{df.}")) (|totalDifferential| (($ (|Expression| |#1|)) "\\spad{totalDifferential(x)} returns the total differential (gradient) form for element \\spad{x.}")) (|map| (($ (|Mapping| (|Expression| |#1|) (|Expression| |#1|)) $) "\\spad{map(f,df)} replaces each coefficient \\spad{x} of differential form \\spad{df} by \\spad{f(x)}.")) (|degree| (((|Integer|) $) "\\spad{degree(df)} returns the homogeneous degree of differential form \\spad{df.}")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?(df)} tests if differential form \\spad{df} is a 0-form, \\spadignore{i.e.} if degree(df) = 0.")) (|homogeneous?| (((|Boolean|) $) "\\spad{homogeneous?(df)} tests if all of the terms of differential form \\spad{df} have the same degree.")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(n)} returns the \\spad{n}th basis term for a differential form.")) (|coefficient| (((|Expression| |#1|) $ $) "\\spad{coefficient(df,u)}, where \\spad{df} is a differential form, returns the coefficient of \\spad{df} containing the basis term \\spad{u} if such a term exists, and 0 otherwise.")) (|reductum| (($ $) "\\spad{reductum(df)}, where \\spad{df} is a differential form, returns \\spad{df} minus the leading term of \\spad{df} if \\spad{df} has two or more terms, and 0 otherwise.")) (|leadingBasisTerm| (($ $) "\\spad{leadingBasisTerm(df)} returns the leading basis term of differential form \\spad{df.}")) (|leadingCoefficient| (((|Expression| |#1|) $) "\\spad{leadingCoefficient(df)} returns the leading coefficient of differential form \\spad{df.}"))) +((|constructor| (NIL "The deRham complex of Euclidean space, that is, the class of differential forms of arbitary degree over a coefficient ring. See Flanders, Harley, Differential Forms, With Applications to the Physical Sciences, New York, Academic Press, 1963.")) (|lieDerivative| (($ (|Vector| (|Expression| |#1|)) $ (|SquareMatrix| (|#| |#2|) (|Expression| |#1|))) "\\indented{1}{calculates the Lie derivative L_X(a) of the differential} \\indented{1}{form a with respect to the vector field \\spad{X} (w.r.t. metric \\spad{g)}} \\blankline \\spad{X} coefRing \\spad{:=} Integer \\spad{X} \\spad{R3} : List Symbol \\spad{:=} [x,y,z] \\spad{X} \\spad{D} \\spad{:=} DERHAM(coefRing,R3) \\spad{X} [dx,dy,dz] \\spad{:=} [generator(i)$D for \\spad{i} in 1..3] \\spad{X} a : BOP \\spad{:=} operator('a) \\spad{X} \\spad{b} : BOP \\spad{:=} operator('b) \\spad{X} \\spad{c} : BOP \\spad{:=} operator('c) \\spad{X} \\spad{U} : BOP \\spad{:=} operator('U) \\spad{X} \\spad{V} : BOP \\spad{:=} operator('V) \\spad{X} \\spad{W} : BOP \\spad{:=} operator('W) \\spad{X} \\spad{v} \\spad{:=} vector[U(x,y,z),V(x,y,z),W(x,y,z)] \\spad{X} theta \\spad{:=} a(x,y,z)*dx*dy + b(x,y,z)*dx*dz + c(x,y,z)*dy*dz \\spad{X} \\spad{G} \\spad{:=} diagonalMatrix([1,1,1]) \\spad{X} eta \\spad{:=} lieDerivative(v,theta,G)")) (|interiorProduct| (($ (|Vector| (|Expression| |#1|)) $ (|SquareMatrix| (|#| |#2|) (|Expression| |#1|))) "\\indented{1}{calculates the interior product i_X(a) of the vector field \\spad{X}} \\indented{1}{with the differential form a (w.r.t. metric \\spad{g)}} \\blankline \\spad{X} coefRing \\spad{:=} Integer \\spad{X} \\spad{R3} : List Symbol \\spad{:=} [x,y,z] \\spad{X} \\spad{D} \\spad{:=} DERHAM(coefRing,R3) \\spad{X} [dx,dy,dz] \\spad{:=} [generator(i)$D for \\spad{i} in 1..3] \\spad{X} \\spad{f} : BOP \\spad{:=} operator('f) \\spad{X} \\spad{g} : BOP \\spad{:=} operator('g) \\spad{X} \\spad{h} : BOP \\spad{:=} operator('h) \\spad{X} a : BOP \\spad{:=} operator('a) \\spad{X} \\spad{b} : BOP \\spad{:=} operator('b) \\spad{X} \\spad{c} : BOP \\spad{:=} operator('c) \\spad{X} \\spad{U} : BOP \\spad{:=} operator('U) \\spad{X} \\spad{V} : BOP \\spad{:=} operator('V) \\spad{X} \\spad{W} : BOP \\spad{:=} operator('W) \\spad{X} \\spad{v} \\spad{:=} vector[U(x,y,z),V(x,y,z),W(x,y,z)] \\spad{X} sigma \\spad{:=} f(x,y,z)*dx + g(x,y,z)*dy + h(x,y,z)*dz \\spad{X} theta \\spad{:=} a(x,y,z)*dx*dy + b(x,y,z)*dx*dz + c(x,y,z)*dy*dz \\spad{X} \\spad{G} \\spad{:=} diagonalMatrix([1,1,1]) \\spad{X} interiorProduct(v,sigma,G) \\spad{X} interiorProduct(v,theta,G)")) (|proj| (($ $ (|NonNegativeInteger|)) "\\indented{1}{projection to homogeneous terms of degree \\spad{p}} \\blankline \\spad{X} coefRing \\spad{:=} Integer \\spad{X} \\spad{R3} : List Symbol \\spad{:=} [x,y,z] \\spad{X} \\spad{D} \\spad{:=} DERHAM(coefRing,R3) \\spad{X} [dx,dy,dz] \\spad{:=} [generator(i)$D for \\spad{i} in 1..3] \\spad{X} proj(dx+dy*dz+dx*dy*dz,2)")) (|dot| (((|Expression| |#1|) $ $ (|SquareMatrix| (|#| |#2|) (|Expression| |#1|))) "\\indented{1}{compute the inner product of two differential forms w.r.t. \\spad{g}} \\blankline \\spad{X} der \\spad{:=} DeRhamComplex(Integer,[x,y,z]) \\spad{X} f:BOP:=operator('f) \\spad{X} g:BOP:=operator('g) \\spad{X} h:BOP:=operator('h) \\spad{X} sigma:der:=f(x,y,z)*dx + g(x,y,z)*dy + h(x,y,z)*dz \\spad{X} G:SquareMatrix(3,Integer):=diagonalMatrix([1,1,1]) \\spad{X} dot(sigma,sigma,G)")) (|hodgeStar| (($ $ (|SquareMatrix| (|#| |#2|) (|Expression| |#1|))) "\\indented{1}{computes the Hodge dual of the differential form with respect} \\indented{1}{to the metric \\spad{g.}} \\blankline \\spad{X} der \\spad{:=} DeRhamComplex(Integer,[x,y,z]) \\spad{X} f:BOP:=operator('f) \\spad{X} g:BOP:=operator('g) \\spad{X} h:BOP:=operator('h) \\spad{X} sigma:der:=f(x,y,z)*dx + g(x,y,z)*dy + h(x,y,z)*dz \\spad{X} G:SquareMatrix(3,Integer):=diagonalMatrix([1,1,1]) \\spad{X} hodgeStar(sigma,G)")) (|dim| (((|NonNegativeInteger|) $) "\\indented{1}{dimension of the underlying space} \\indented{1}{that is, dim ExtAlg = 2^dim} \\blankline \\spad{X} der \\spad{:=} DeRhamComplex(Integer,[x,y,z]) \\spad{X} f:BOP:=operator('f) \\spad{X} g:BOP:=operator('g) \\spad{X} h:BOP:=operator('h) \\spad{X} sigma:der:=f(x,y,z)*dx + g(x,y,z)*dy + h(x,y,z)*dz \\spad{X} dim sigma")) (|exteriorDifferential| (($ $) "\\indented{2}{exteriorDifferential(df) returns the exterior} \\indented{2}{derivative (gradient, curl, divergence, ...) of} \\indented{2}{the differential form df.} \\blankline \\spad{X} der \\spad{:=} DeRhamComplex(Integer,[x,y,z]) \\spad{X} \\spad{R} \\spad{:=} Expression(Integer) \\spad{X} [dx,dy,dz] \\spad{:=} [generator(i)$der for \\spad{i} in 1..3] \\spad{X} \\spad{f} : \\spad{R} \\spad{:=} \\spad{x**2*y*z-5*x**3*y**2*z**5} \\spad{X} \\spad{g} : \\spad{R} \\spad{:=} \\spad{z**2*y*cos(z)-7*sin(x**3*y**2)*z**2} \\spad{X} \\spad{h} : \\spad{R} \\spad{:=x*y*z-2*x**3*y*z**2} \\spad{X} alpha : der \\spad{:=} f*dx + g*dy + h*dz \\spad{X} exteriorDifferential alpha")) (|totalDifferential| (($ (|Expression| |#1|)) "\\indented{2}{totalDifferential(x) returns the total differential} \\indented{2}{(gradient) form for element \\spad{x.}} \\blankline \\spad{X} der \\spad{:=} DeRhamComplex(Integer,[x,y,z]) \\spad{X} a : BOP \\spad{:=} operator('a) \\spad{X} totalDifferential(a(x,y,z))$der \\spad{X} totalDifferential(x^2+y^2+sin(x)*z^2)$der")) (|map| (($ (|Mapping| (|Expression| |#1|) (|Expression| |#1|)) $) "\\indented{2}{map(f,df) replaces each coefficient \\spad{x} of differential} \\indented{2}{form \\spad{df} by \\spad{f(x)}.} \\blankline \\spad{X} der \\spad{:=} DeRhamComplex(Integer,[x,y,z]) \\spad{X} f:BOP:=operator('f) \\spad{X} g:BOP:=operator('g) \\spad{X} h:BOP:=operator('h) \\spad{X} sigma:der:=f(x,y,z)*dx + g(x,y,z)*dy + h(x,y,z)*dz \\spad{X} \\spad{R} \\spad{:=} Expression(Integer) \\spad{X} T(x:R):R \\spad{==} \\spad{x^2} \\spad{X} map(T,sigma)")) (|degree| (((|NonNegativeInteger|) $) "\\indented{2}{degree(df) returns the homogeneous degree of differential form df.} \\blankline \\spad{X} der \\spad{:=} DeRhamComplex(Integer,[x,y,z]) \\spad{X} \\spad{t1} \\spad{:=} generator(1)$der \\spad{X} f:BOP:=operator('f) \\spad{X} g:BOP:=operator('g) \\spad{X} h:BOP:=operator('h) \\spad{X} sigma:der:=f(x,y,z)*dx + g(x,y,z)*dy + h(x,y,z)*dz \\spad{X} a:BOP:=operator('a) \\spad{X} b:BOP:=operator('b) \\spad{X} c:BOP:=operator('c) \\spad{X} theta:der:=a(x,y,z)*dx*dy + b(x,y,z)*dx*dz + c(x,y,z)*dy*dz \\spad{X} [degree \\spad{x} for \\spad{x} in [sigma,theta,t1]]")) (|retractable?| (((|Boolean|) $) "\\indented{2}{retractable?(df) tests if differential form \\spad{df} is a 0-form,} \\indented{2}{\\spadignore{i.e.} if degree(df) = 0.} \\blankline \\spad{X} der:=DERHAM(Integer,[x,y,z]) \\spad{X} [dx,dy,dz]:=[generator(i)$der for \\spad{i} in 1..3] \\spad{X} f:BOP:=operator('f) \\spad{X} g:BOP:=operator('g) \\spad{X} h:BOP:=operator('h) \\spad{X} sigma:=f(x,y,z)*dx + g(x,y,z)*dy + h(x,y,z)*dz \\spad{X} retractable? sigma")) (|homogeneous?| (((|Boolean|) $) "\\indented{2}{homogeneous?(df) tests if all of the terms of} \\indented{2}{differential form \\spad{df} have the same degree.} \\blankline \\spad{X} der:=DERHAM(Integer,[x,y,z]) \\spad{X} [dx,dy,dz]:=[generator(i)$der for \\spad{i} in 1..3] \\spad{X} f:BOP:=operator('f) \\spad{X} g:BOP:=operator('g) \\spad{X} h:BOP:=operator('h) \\spad{X} sigma:=f(x,y,z)*dx + g(x,y,z)*dy + h(x,y,z)*dz \\spad{X} homogeneous? sigma \\spad{X} a:BOP:=operator('a) \\spad{X} b:BOP:=operator('b) \\spad{X} c:BOP:=operator('c) \\spad{X} theta:=a(x,y,z)*dx*dy + b(x,y,z)*dx*dz + c(x,y,z)*dy*dz \\spad{X} homogeneous? (sigma+theta)")) (|generator| (($ (|NonNegativeInteger|)) "\\indented{1}{generator(n) returns the \\spad{n}th basis term for a differential form.} \\blankline \\spad{X} der \\spad{:=} DeRhamComplex(Integer,[x,y,z]) \\spad{X} [dx,dy,dz] \\spad{:=} [generator(i)$der for \\spad{i} in 1..3]")) (|coefficient| (((|Expression| |#1|) $ $) "\\indented{1}{coefficient(df,u), where \\spad{df} is a differential form,} \\indented{1}{returns the coefficient of \\spad{df} containing the basis term u} \\indented{1}{if such a term exists, and 0 otherwise.} \\blankline \\spad{X} der \\spad{:=} DeRhamComplex(Integer,[x,y,z]) \\spad{X} \\spad{R} \\spad{:=} Expression(Integer) \\spad{X} [dx,dy,dz] \\spad{:=} [generator(i)$der for \\spad{i} in 1..3] \\spad{X} \\spad{f} : \\spad{R} \\spad{:=} \\spad{x**2*y*z-5*x**3*y**2*z**5} \\spad{X} \\spad{g} : \\spad{R} \\spad{:=} \\spad{z**2*y*cos(z)-7*sin(x**3*y**2)*z**2} \\spad{X} \\spad{h} : \\spad{R} \\spad{:=x*y*z-2*x**3*y*z**2} \\spad{X} alpha : der \\spad{:=} f*dx + g*dy + h*dz \\spad{X} beta : der \\spad{:=} cos(tan(x*y*z)+x*y*z)*dx + x*dy \\spad{X} gamma \\spad{:=} alpha * beta \\spad{X} coefficient(gamma, dx*dy)")) (|reductum| (($ $) "\\indented{1}{reductum(df), where \\spad{df} is a differential form, returns \\spad{df} minus} \\indented{1}{the leading term of \\spad{df} if \\spad{df} has two or more terms, and} \\indented{1}{0 otherwise.} \\blankline \\spad{X} der:=DERHAM(Integer,[x,y,z]) \\spad{X} [dx,dy,dz]:=[generator(i)$der for \\spad{i} in 1..3] \\spad{X} f:BOP:=operator('f) \\spad{X} g:BOP:=operator('g) \\spad{X} h:BOP:=operator('h) \\spad{X} sigma:=f(x,y,z)*dx + g(x,y,z)*dy + h(x,y,z)*dz \\spad{X} reductum sigma")) (|leadingBasisTerm| (($ $) "\\indented{1}{leadingBasisTerm(df) returns the leading} \\indented{1}{basis term of differential form df.} \\blankline \\spad{X} der:=DERHAM(Integer,[x,y,z]) \\spad{X} [dx,dy,dz]:=[generator(i)$der for \\spad{i} in 1..3] \\spad{X} f:BOP:=operator('f) \\spad{X} g:BOP:=operator('g) \\spad{X} h:BOP:=operator('h) \\spad{X} sigma:=f(x,y,z)*dx + g(x,y,z)*dy + h(x,y,z)*dz \\spad{X} leadingBasisTerm sigma")) (|leadingCoefficient| (((|Expression| |#1|) $) "\\indented{1}{leadingCoefficient(df) returns the leading} \\indented{1}{coefficient of differential form df.} \\blankline \\spad{X} der:=DERHAM(Integer,[x,y,z]) \\spad{X} [dx,dy,dz]:=[generator(i)$der for \\spad{i} in 1..3] \\spad{X} f:BOP:=operator('f) \\spad{X} g:BOP:=operator('g) \\spad{X} h:BOP:=operator('h) \\spad{X} sigma:=f(x,y,z)*dx + g(x,y,z)*dy + h(x,y,z)*dz \\spad{X} leadingCoefficient sigma"))) ((|unitsKnown| . T)) NIL (|DefiniteIntegrationTools| R F) @@ -905,7 +909,7 @@ NIL ((|shallowlyMutable| . T) (|finiteAggregate| . T)) ((|HasCategory| (|DoubleFloat|) (QUOTE (|SetCategory|))) (|HasCategory| (|DoubleFloat|) (LIST (QUOTE |ConvertibleTo|) (QUOTE (|InputForm|)))) (|HasCategory| (|DoubleFloat|) (QUOTE (|OrderedSet|))) (OR (|HasCategory| (|DoubleFloat|) (QUOTE (|OrderedSet|))) (|HasCategory| (|DoubleFloat|) (QUOTE (|SetCategory|)))) (|HasCategory| (|Integer|) (QUOTE (|OrderedSet|))) (|HasCategory| (|DoubleFloat|) (QUOTE (|AbelianSemiGroup|))) (|HasCategory| (|DoubleFloat|) (QUOTE (|AbelianMonoid|))) (|HasCategory| (|DoubleFloat|) (QUOTE (|AbelianGroup|))) (|HasCategory| (|DoubleFloat|) (QUOTE (|Monoid|))) (|HasCategory| (|DoubleFloat|) (QUOTE (|Ring|))) (AND (|HasCategory| (|DoubleFloat|) (QUOTE (|RadicalCategory|))) (|HasCategory| (|DoubleFloat|) (QUOTE (|Ring|)))) (AND (|HasCategory| (|DoubleFloat|) (LIST (QUOTE |Evalable|) (QUOTE (|DoubleFloat|)))) (|HasCategory| (|DoubleFloat|) (QUOTE (|SetCategory|)))) (OR (AND (|HasCategory| (|DoubleFloat|) (LIST (QUOTE |Evalable|) (QUOTE (|DoubleFloat|)))) (|HasCategory| (|DoubleFloat|) (QUOTE (|OrderedSet|)))) (AND (|HasCategory| (|DoubleFloat|) (LIST (QUOTE |Evalable|) (QUOTE (|DoubleFloat|)))) (|HasCategory| (|DoubleFloat|) (QUOTE (|SetCategory|)))))) (|DenavitHartenbergMatrix| R) -((|constructor| (NIL "4x4 Matrices for coordinate transformations\\br This package contains functions to create 4x4 matrices useful for rotating and transforming coordinate systems. These matrices are useful for graphics and robotics. (Reference: Robot Manipulators Richard Paul MIT Press 1981) \\blankline A Denavit-Hartenberg Matrix is a 4x4 Matrix of the form:\\br \\tab{5}\\spad{nx ox ax px}\\br \\tab{5}\\spad{ny oy ay py}\\br \\tab{5}\\spad{nz oz az pz}\\br \\tab{5}\\spad{0 0 0 1}\\br \\spad{(n,} o, and a are the direction cosines)")) (|translate| (($ |#1| |#1| |#1|) "\\spad{translate(x,y,z)} returns a dhmatrix for translation by \\spad{x,} \\spad{y,} and \\spad{z}")) (|scale| (($ |#1| |#1| |#1|) "\\spad{scale(sx,sy,sz)} returns a dhmatrix for scaling in the \\spad{x,} \\spad{y} and \\spad{z} directions")) (|rotatez| (($ |#1|) "\\spad{rotatez(r)} returns a dhmatrix for rotation about axis \\spad{z} for \\spad{r} degrees")) (|rotatey| (($ |#1|) "\\spad{rotatey(r)} returns a dhmatrix for rotation about axis \\spad{y} for \\spad{r} degrees")) (|rotatex| (($ |#1|) "\\spad{rotatex(r)} returns a dhmatrix for rotation about axis \\spad{x} for \\spad{r} degrees")) (|identity| (($) "\\spad{identity()} create the identity dhmatrix")) (* (((|Point| |#1|) $ (|Point| |#1|)) "\\spad{t*p} applies the dhmatrix \\spad{t} to point \\spad{p}"))) +((|constructor| (NIL "4x4 Matrices for coordinate transformations\\br This package contains functions to create 4x4 matrices useful for rotating and transforming coordinate systems. These matrices are useful for graphics and robotics. (Reference: Robot Manipulators Richard Paul MIT Press 1981) \\blankline A Denavit-Hartenberg Matrix is a 4x4 Matrix of the form:\\br \\tab{5}\\spad{nx ox ax px}\\br \\tab{5}\\spad{ny oy ay py}\\br \\tab{5}\\spad{nz oz az pz}\\br \\tab{5}\\spad{0 0 0 1}\\br \\spad{(n,} o, and a are the direction cosines)")) (|translate| (($ |#1| |#1| |#1|) "\\indented{1}{translate(x,y,z) returns a dhmatrix for translation by \\spad{x,} \\spad{y,} and \\spad{z}} \\blankline \\spad{X} translate(1.0,2.0,3.0)")) (|scale| (($ |#1| |#1| |#1|) "\\indented{1}{scale(sx,sy,sz) returns a dhmatrix for scaling in the \\spad{x,} \\spad{y} and \\spad{z}} \\indented{1}{directions} \\blankline \\spad{X} scale(0.5,0.5,0.5)")) (|rotatez| (($ |#1|) "\\indented{1}{rotatez(r) returns a dhmatrix for rotation about axis \\spad{z} for \\spad{r} degrees} \\blankline \\spad{X} rotatez(30)")) (|rotatey| (($ |#1|) "\\indented{1}{rotatey(r) returns a dhmatrix for rotation about axis \\spad{y} for \\spad{r} degrees} \\blankline \\spad{X} rotatey(30)")) (|rotatex| (($ |#1|) "\\indented{1}{rotatex(r) returns a dhmatrix for rotation about axis \\spad{x} for \\spad{r} degrees} \\blankline \\spad{X} rotatex(30)")) (|identity| (($) "\\spad{identity()} create the identity dhmatrix \\blankline identity()")) (* (((|Point| |#1|) $ (|Point| |#1|)) "\\indented{1}{t*p applies the dhmatrix \\spad{t} to point \\spad{p}} \\blankline \\spad{X} rotatex(30)*point([1,2,3])"))) ((|finiteAggregate| . T) (|shallowlyMutable| . T)) ((|HasCategory| |#1| (QUOTE (|SetCategory|))) (AND (|HasCategory| |#1| (LIST (QUOTE |Evalable|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (|SetCategory|)))) (|HasCategory| |#1| (QUOTE (|EuclideanDomain|))) (|HasCategory| |#1| (QUOTE (|IntegralDomain|))) (|HasAttribute| |#1| (QUOTE (|commutative| "*"))) (|HasCategory| |#1| (QUOTE (|CommutativeRing|))) (|HasCategory| |#1| (QUOTE (|Field|)))) (|Dictionary&| A S) @@ -1189,7 +1193,7 @@ NIL ((|finiteAggregate| . T) (|shallowlyMutable| . T)) ((|HasCategory| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (LIST (QUOTE |ConvertibleTo|) (QUOTE (|InputForm|)))) (|HasCategory| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (QUOTE (|SetCategory|))) (AND (|HasCategory| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (LIST (QUOTE |Evalable|) (LIST (QUOTE |Record|) (LIST (QUOTE |:|) (QUOTE |key|) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (QUOTE (|SetCategory|)))) (|HasCategory| |#1| (QUOTE (|OrderedSet|))) (|HasCategory| |#2| (QUOTE (|SetCategory|))) (OR (|HasCategory| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (QUOTE (|SetCategory|))) (|HasCategory| |#2| (QUOTE (|SetCategory|)))) (AND (|HasCategory| |#2| (LIST (QUOTE |Evalable|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (|SetCategory|))))) (|ErrorFunctions|) -((|constructor| (NIL "ErrorFunctions implements error functions callable from the system interpreter. Typically, these functions would be called in user functions. The simple forms of the functions take one argument which is either a string (an error message) or a list of strings which all together make up a message. The list can contain formatting codes (see below). The more sophisticated versions takes two arguments where the first argument is the name of the function from which the error was invoked and the second argument is either a string or a list of strings, as above. When you use the one argument version in an interpreter function, the system will automatically insert the name of the function as the new first argument. Thus in the user interpreter function\\br \\tab{5}\\spad{f \\spad{x} \\spad{==} if \\spad{x} < 0 then error \"negative argument\" else x}\\br the call to error will actually be of the form\\br \\tab{5}\\spad{error(\"f\",\"negative argument\")}\\br because the interpreter will have created a new first argument. \\blankline Formatting codes: error messages may contain the following formatting codes (they should either start or end a string or else have blanks around them):\\br \\spad{\\%l}\\tab{6}start a new line\\br \\spad{\\%b}\\tab{6}start printing in a bold font (where available)\\br \\spad{\\%d}\\tab{6}stop printing in a bold font (where available)\\br \\spad{\\%ceon}\\tab{3}start centering message lines\\br \\spad{\\%ceoff}\\tab{2}stop centering message lines\\br \\spad{\\%rjon}\\tab{3}start displaying lines \"ragged left\"\\br \\spad{\\%rjoff}\\tab{2}stop displaying lines \"ragged left\"\\br \\spad{\\%i}\\tab{6}indent following lines 3 additional spaces\\br \\spad{\\%u}\\tab{6}unindent following lines 3 additional spaces\\br \\spad{\\%xN}\\tab{5}insert \\spad{N} blanks (eg, \\spad{\\%x10} inserts 10 blanks) \\blankline")) (|error| (((|Exit|) (|String|) (|List| (|String|))) "\\spad{error(nam,lmsg)} displays error messages \\spad{lmsg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|String|) (|String|)) "\\spad{error(nam,msg)} displays error message \\spad{msg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|List| (|String|))) "\\spad{error(lmsg)} displays error message \\spad{lmsg} and terminates.") (((|Exit|) (|String|)) "\\spad{error(msg)} displays error message \\spad{msg} and terminates."))) +((|constructor| (NIL "ErrorFunctions implements error functions callable from the system interpreter. Typically, these functions would be called in user functions. The simple forms of the functions take one argument which is either a string (an error message) or a list of strings which all together make up a message. The list can contain formatting codes (see below). The more sophisticated versions takes two arguments where the first argument is the name of the function from which the error was invoked and the second argument is either a string or a list of strings, as above. When you use the one argument version in an interpreter function, the system will automatically insert the name of the function as the new first argument. Thus in the user interpreter function\\br \\tab{5}\\spad{f \\spad{x} \\spad{==} if \\spad{x} < 0 then error \"negative argument\" else x}\\br the call to error will actually be of the form\\br \\tab{5}\\spad{error(\"f\",\"negative argument\")}\\br because the interpreter will have created a new first argument. \\blankline Formatting codes: error messages may contain the following formatting codes (they should either start or end a string or else have blanks around them):\\br \\spad{\\%l}\\tab{6}start a new line\\br \\spad{\\%ceon}\\tab{3}start centering message lines\\br \\spad{\\%ceoff}\\tab{2}stop centering message lines\\br \\spad{\\%rjon}\\tab{3}start displaying lines \"ragged left\"\\br \\spad{\\%rjoff}\\tab{2}stop displaying lines \"ragged left\"\\br \\spad{\\%i}\\tab{6}indent following lines 3 additional spaces\\br \\spad{\\%u}\\tab{6}unindent following lines 3 additional spaces\\br \\spad{\\%xN}\\tab{5}insert \\spad{N} blanks (eg, \\spad{\\%x10} inserts 10 blanks) \\blankline")) (|error| (((|Exit|) (|String|) (|List| (|String|))) "\\spad{error(nam,lmsg)} displays error messages \\spad{lmsg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|String|) (|String|)) "\\spad{error(nam,msg)} displays error message \\spad{msg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|List| (|String|))) "\\spad{error(lmsg)} displays error message \\spad{lmsg} and terminates.") (((|Exit|) (|String|)) "\\spad{error(msg)} displays error message \\spad{msg} and terminates."))) NIL NIL (|ExpressionSpaceFunctions1| F S) @@ -2029,7 +2033,7 @@ NIL NIL NIL (|HexadecimalExpansion|) -((|constructor| (NIL "This domain allows rational numbers to be presented as repeating hexadecimal expansions.")) (|hex| (($ (|Fraction| (|Integer|))) "\\spad{hex(r)} converts a rational number to a hexadecimal expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(h)} returns the fractional part of a hexadecimal expansion.")) (|coerce| (((|RadixExpansion| 16) $) "\\spad{coerce(h)} converts a hexadecimal expansion to a radix expansion with base 16.") (((|Fraction| (|Integer|)) $) "\\spad{coerce(h)} converts a hexadecimal expansion to a rational number."))) +((|constructor| (NIL "This domain allows rational numbers to be presented as repeating hexadecimal expansions.")) (|toint| (((|Integer|) (|String|)) "\\indented{1}{toint(s) converts a hex string to integer} \\blankline \\spad{X} toint(\"FE\") \\spad{X} toint(\"BFD25E8C\")")) (|hex| (($ (|Fraction| (|Integer|))) "\\spad{hex(r)} converts a rational number to a hexadecimal expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(h)} returns the fractional part of a hexadecimal expansion")) (|coerce| (((|RadixExpansion| 16) $) "\\spad{coerce(h)} converts a hexadecimal expansion to a radix expansion with base 16.") (((|Fraction| (|Integer|)) $) "\\spad{coerce(h)} converts a hexadecimal expansion to a rational number."))) ((|canonicalsClosed| . T) (|canonicalUnitNormal| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) ((|HasCategory| (|Integer|) (QUOTE (|PolynomialFactorizationExplicit|))) (|HasCategory| (|Integer|) (LIST (QUOTE |RetractableTo|) (QUOTE (|Symbol|)))) (|HasCategory| (|Integer|) (QUOTE (|CharacteristicNonZero|))) (|HasCategory| (|Integer|) (QUOTE (|CharacteristicZero|))) (|HasCategory| (|Integer|) (LIST (QUOTE |ConvertibleTo|) (QUOTE (|InputForm|)))) (|HasCategory| (|Integer|) (QUOTE (|RealConstant|))) (|HasCategory| (|Integer|) (QUOTE (|OrderedIntegralDomain|))) (|HasCategory| (|Integer|) (LIST (QUOTE |RetractableTo|) (QUOTE (|Integer|)))) (|HasCategory| (|Integer|) (QUOTE (|StepThrough|))) (|HasCategory| (|Integer|) (LIST (QUOTE |PatternMatchable|) (QUOTE (|Integer|)))) (|HasCategory| (|Integer|) (LIST (QUOTE |PatternMatchable|) (QUOTE (|Float|)))) (|HasCategory| (|Integer|) (LIST (QUOTE |ConvertibleTo|) (LIST (QUOTE |Pattern|) (QUOTE (|Float|))))) (|HasCategory| (|Integer|) (LIST (QUOTE |ConvertibleTo|) (LIST (QUOTE |Pattern|) (QUOTE (|Integer|))))) (|HasCategory| (|Integer|) (QUOTE (|DifferentialRing|))) (|HasCategory| (|Integer|) (LIST (QUOTE |PartialDifferentialRing|) (QUOTE (|Symbol|)))) (|HasCategory| (|Integer|) (LIST (QUOTE |InnerEvalable|) (QUOTE (|Symbol|)) (QUOTE (|Integer|)))) (|HasCategory| (|Integer|) (LIST (QUOTE |Evalable|) (QUOTE (|Integer|)))) (|HasCategory| (|Integer|) (LIST (QUOTE |Eltable|) (QUOTE (|Integer|)) (QUOTE (|Integer|)))) (|HasCategory| (|Integer|) (QUOTE (|EuclideanDomain|))) (|HasCategory| (|Integer|) (QUOTE (|IntegerNumberSystem|))) (|HasCategory| (|Integer|) (QUOTE (|OrderedSet|))) (OR (|HasCategory| (|Integer|) (QUOTE (|OrderedIntegralDomain|))) (|HasCategory| (|Integer|) (QUOTE (|OrderedSet|)))) (|HasCategory| (|Integer|) (LIST (QUOTE |LinearlyExplicitRingOver|) (QUOTE (|Integer|)))) (AND (|HasCategory| $ (QUOTE (|CharacteristicNonZero|))) (|HasCategory| (|Integer|) (QUOTE (|PolynomialFactorizationExplicit|)))) (OR (AND (|HasCategory| $ (QUOTE (|CharacteristicNonZero|))) (|HasCategory| (|Integer|) (QUOTE (|PolynomialFactorizationExplicit|)))) (|HasCategory| (|Integer|) (QUOTE (|CharacteristicNonZero|))))) (|HomogeneousAggregate&| A S) @@ -2501,7 +2505,7 @@ NIL NIL NIL (|LaurentPolynomial| R UP) -((|constructor| (NIL "Univariate polynomials with negative and positive exponents.")) (|separate| (((|Record| (|:| |polyPart| $) (|:| |fracPart| (|Fraction| |#2|))) (|Fraction| |#2|)) "\\spad{separate(x)} is not documented")) (|monomial| (($ |#1| (|Integer|)) "\\spad{monomial(x,n)} is not documented")) (|coefficient| ((|#1| $ (|Integer|)) "\\spad{coefficient(x,n)} is not documented")) (|trailingCoefficient| ((|#1| $) "trailingCoefficient is not documented")) (|leadingCoefficient| ((|#1| $) "leadingCoefficient is not documented")) (|reductum| (($ $) "\\spad{reductum(x)} is not documented")) (|order| (((|Integer|) $) "\\spad{order(x)} is not documented")) (|degree| (((|Integer|) $) "\\spad{degree(x)} is not documented")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} is not documented"))) +((|constructor| (NIL "Univariate polynomials with negative and positive exponents.")) (|separate| (((|Record| (|:| |polyPart| $) (|:| |fracPart| (|Fraction| |#2|))) (|Fraction| |#2|)) "\\spad{separate(x)} is not documented")) (|monomial| (($ |#1| (|Integer|)) "\\spad{monomial(x,n)} is not documented")) (|coefficient| ((|#1| $ (|Integer|)) "\\spad{coefficient(x,n)} is not documented")) (|trailingCoefficient| ((|#1| $) "trailingCoefficient is not documented")) (|leadingCoefficient| ((|#1| $) "leadingCoefficient is not documented")) (|reductum| (($ $) "\\spad{reductum(x)} is not documented")) (|order| (((|Integer|) $) "\\indented{1}{order(x) is not documented} \\blankline \\spad{X} \\spad{w:SparseUnivariateLaurentSeries(Fraction(Integer),'z,0):=0} \\spad{X} order(w,0)")) (|degree| (((|Integer|) $) "\\spad{degree(x)} is not documented")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} is not documented"))) ((|leftUnitary| . T) (|rightUnitary| . T) ((|commutative| "*") . T) (|noZeroDivisors| . T) (|unitsKnown| . T)) ((|HasCategory| |#2| (LIST (QUOTE |PartialDifferentialRing|) (QUOTE (|Symbol|)))) (|HasCategory| |#2| (QUOTE (|DifferentialRing|))) (|HasCategory| |#1| (QUOTE (|Field|))) (|HasCategory| |#1| (QUOTE (|CharacteristicNonZero|))) (|HasCategory| |#1| (QUOTE (|CharacteristicZero|))) (|HasCategory| |#1| (LIST (QUOTE |RetractableTo|) (LIST (QUOTE |Fraction|) (QUOTE (|Integer|))))) (|HasCategory| |#1| (LIST (QUOTE |RetractableTo|) (QUOTE (|Integer|))))) (|LazardSetSolvingPackage| R E V P TS ST) @@ -2721,7 +2725,7 @@ NIL NIL NIL (|MatrixManipulation| R |Row| |Col| M) -((|constructor| (NIL "Some functions for manipulating (dense) matrices. Supported are various kinds of slicing, splitting and stacking of matrices. The functions resemble operations often used in numerical linear algebra algorithms.")) (|blockSplit| (((|List| (|List| |#4|)) |#4| (|List| (|PositiveInteger|)) (|List| (|PositiveInteger|))) "\\spad{blockSplit} splits a matrix into multiple submatrices row and column wise, dividing a matrix into blocks.") (((|List| (|List| |#4|)) |#4| (|PositiveInteger|) (|List| (|PositiveInteger|))) "\\spad{blockSplit} splits a matrix into multiple submatrices row and column wise, dividing a matrix into blocks.") (((|List| (|List| |#4|)) |#4| (|List| (|PositiveInteger|)) (|PositiveInteger|)) "\\spad{blockSplit} splits a matrix into multiple submatrices row and column wise, dividing a matrix into blocks.") (((|List| (|List| |#4|)) |#4| (|PositiveInteger|) (|PositiveInteger|)) "\\spad{blockSplit} splits a matrix into multiple submatrices row and column wise, dividing a matrix into blocks.")) (|horizSplit| (((|List| |#4|) |#4| (|List| (|PositiveInteger|))) "\\spad{horizSplit} splits a matrix into multiple submatrices column wise.") (((|List| |#4|) |#4| (|PositiveInteger|)) "\\spad{horizSplit} splits a matrix into multiple submatrices column wise.")) (|vertSplit| (((|List| |#4|) |#4| (|List| (|PositiveInteger|))) "\\spad{vertSplit} splits a matrix into multiple submatrices row wise.") (((|List| |#4|) |#4| (|PositiveInteger|)) "\\spad{vertSplit} splits a matrix into multiple submatrices row wise.")) (|blockConcat| ((|#4| (|List| (|List| |#4|))) "\\spad{blockConcat} concatenates matrices row and column wise, building a block matrix. The order is row major as in \\spad{matrix}.")) (|vertConcat| ((|#4| (|List| |#4|)) "\\spad{vertConcat} concatenates matrices row wise.")) (|horizConcat| ((|#4| (|List| |#4|)) "\\spad{horizConcat} concatenates matrices column wise.")) (|bandMatrix| ((|#4| |#4| (|Segment| (|Integer|))) "\\spad{bandMatrix} returns multiple diagonals out of a matrix. The diagonals are put into a matrix of same shape as the original one. Positive integer arguments select upper off-diagonals, negative ones lower off-diagonals.") ((|#4| |#4| (|List| (|Integer|))) "\\spad{bandMatrix} returns multiple diagonals out of a matrix. The diagonals are put into a matrix of same shape as the original one. Positive integer arguments select upper off-diagonals, negative ones lower off-diagonals.")) (|diagonalMatrix| ((|#4| |#4|) "\\spad{diagonalMatrix} returns the main diagonal out of a matrix. The diagonal is put into a matrix of same shape as the original one.") ((|#4| |#4| (|Integer|)) "\\spad{diagonalMatrix} returns a diagonal out of a matrix. The diagonal is put into a matrix of same shape as the original one. Positive integer arguments select upper off-diagonals, negative ones lower off-diagonals.")) (|subMatrix| ((|#4| |#4| (|Segment| (|PositiveInteger|)) (|Segment| (|PositiveInteger|))) "\\spad{subMatrix} returns several elements out of a matrix. The elements are stacked into a submatrix.") ((|#4| |#4| (|List| (|PositiveInteger|)) (|List| (|PositiveInteger|))) "\\spad{subMatrix} returns several elements out of a matrix. The elements are stacked into a submatrix.")) (|columns| ((|#4| |#4| (|Segment| (|PositiveInteger|))) "\\spad{columns} returns several columns out of a matrix. The columns are stacked into a matrix.") ((|#4| |#4| (|List| (|PositiveInteger|))) "\\spad{columns} returns several columns out of a matrix. The columns are stacked into a matrix.")) (|aColumn| ((|#4| |#4| (|PositiveInteger|)) "\\spad{aColumn} returns a single column out of a matrix. The column is put into a one by \\spad{N} matrix.")) (|rows| ((|#4| |#4| (|Segment| (|PositiveInteger|))) "\\spad{rows} returns several rows out of a matrix. The rows are stacked into a matrix.") ((|#4| |#4| (|List| (|PositiveInteger|))) "\\spad{rows} returns several rows out of a matrix. The rows are stacked into a matrix.")) (|aRow| ((|#4| |#4| (|PositiveInteger|)) "\\spad{aRow} returns a single row out of a matrix. The row is put into a one by \\spad{N} matrix.")) (|element| ((|#4| |#4| (|PositiveInteger|) (|PositiveInteger|)) "\\spad{element} returns a single element out of a matrix. The element is put into a one by one matrix."))) +((|constructor| (NIL "Some functions for manipulating (dense) matrices. Supported are various kinds of slicing, splitting and stacking of matrices. The functions resemble operations often used in numerical linear algebra algorithms.")) (|blockSplit| (((|List| (|List| |#4|)) |#4| (|List| (|PositiveInteger|)) (|List| (|PositiveInteger|))) "\\indented{1}{\\spad{blockSplit} splits a matrix into multiple} \\indented{1}{submatrices row and column wise, dividing} \\indented{1}{a matrix into blocks.} \\blankline \\spad{X} \\spad{E} \\spad{:=} matrix([[i,a,b,c],[a,a,b,c],[b,d,e,f],[c,g,h,i]]) \\spad{X} t1:= blockSplit(E, [1,2,1], [2,2])") (((|List| (|List| |#4|)) |#4| (|PositiveInteger|) (|List| (|PositiveInteger|))) "\\indented{1}{\\spad{blockSplit} splits a matrix into multiple} \\indented{1}{submatrices row and column wise, dividing} \\indented{1}{a matrix into blocks.} \\blankline \\spad{X} \\spad{E} \\spad{:=} matrix([[i,a,b,c],[a,a,b,c],[b,d,e,f],[c,g,h,i]]) \\spad{X} t1:= blockSplit(E, 4, [2,2])") (((|List| (|List| |#4|)) |#4| (|List| (|PositiveInteger|)) (|PositiveInteger|)) "\\indented{1}{\\spad{blockSplit} splits a matrix into multiple} \\indented{1}{submatrices row and column wise, dividing} \\indented{1}{a matrix into blocks.} \\blankline \\spad{X} \\spad{E} \\spad{:=} matrix([[i,a,b,c],[a,a,b,c],[b,d,e,f],[c,g,h,i]]) \\spad{X} t1:= blockSplit(E, [2,1,1], 2)") (((|List| (|List| |#4|)) |#4| (|PositiveInteger|) (|PositiveInteger|)) "\\indented{1}{\\spad{blockSplit} splits a matrix into multiple} \\indented{1}{submatrices row and column wise, dividing} \\indented{1}{a matrix into blocks.} \\blankline \\spad{X} \\spad{E} \\spad{:=} matrix([[i,a,b,c],[a,a,b,c],[b,d,e,f],[c,g,h,i]]) \\spad{X} t1:= blockSplit(E,2,2)")) (|horizSplit| (((|List| |#4|) |#4| (|List| (|PositiveInteger|))) "\\indented{1}{\\spad{horizSplit} splits a matrix into multiple} \\indented{1}{submatrices column wise.} \\blankline \\spad{X} \\spad{E} \\spad{:=} matrix([[i,a,b,c],[a,a,b,c],[b,d,e,f],[c,g,h,i]]) \\spad{X} t1:= horizSplit(E, [2,2]) \\spad{X} t2:= horizSplit(E, [1,2,1])") (((|List| |#4|) |#4| (|PositiveInteger|)) "\\indented{1}{\\spad{horizSplit} splits a matrix into multiple} \\indented{1}{submatrices column wise.} \\blankline \\spad{X} \\spad{E} \\spad{:=} matrix([[i,a,b,c],[a,a,b,c],[b,d,e,f],[c,g,h,i]]) \\spad{X} t1:= horizSplit(E, 2)")) (|vertSplit| (((|List| |#4|) |#4| (|List| (|PositiveInteger|))) "\\indented{1}{\\spad{vertSplit} splits a matrix into multiple} \\indented{1}{submatrices row wise.} \\blankline \\spad{X} \\spad{E} \\spad{:=} matrix([[i,a,b,c],[a,a,b,c],[b,d,e,f],[c,g,h,i]]) \\spad{X} t1:= vertSplit(E, [1,2,1])") (((|List| |#4|) |#4| (|PositiveInteger|)) "\\indented{1}{\\spad{vertSplit} splits a matrix into multiple} \\indented{1}{submatrices row wise.} \\blankline \\spad{X} \\spad{E} \\spad{:=} matrix([[i,a,b,c],[a,a,b,c],[b,d,e,f],[c,g,h,i]]) \\spad{X} t1:= vertSplit(E, 2)")) (|blockConcat| ((|#4| (|List| (|List| |#4|))) "\\indented{1}{\\spad{blockConcat} concatenates matrices row and} \\indented{1}{column wise, building a block matrix. The order} \\indented{1}{is row major as in \\spad{matrix}.} \\blankline \\spad{X} A \\spad{:=} matrix([[a]]) \\spad{X} \\spad{B} \\spad{:=} matrix([[b]]) \\spad{X} \\spad{C} \\spad{:=} matrix([[c]]) \\spad{X} \\spad{A11} \\spad{:=} element(M, 3,3) \\spad{X} \\spad{A12} \\spad{:=} horizConcat([A,B,C]) \\spad{X} \\spad{A21} \\spad{:=} vertConcat([A,B,C]) \\spad{X} \\spad{M} \\spad{:=} matrix([[a,b,c],[d,e,f],[g,h,i]]) \\spad{X} \\spad{E} \\spad{:=} blockConcat([[A11,A12],[A21,M]]) \\spad{X} \\spad{t1} \\spad{:=} blockSplit(E, 4, [2,2]) \\spad{X} \\spad{t2} \\spad{:=} blockConcat \\spad{t1} \\spad{X} zero?(E-t2) \\spad{X} \\spad{t3} \\spad{:=} blockSplit(E, [1,2,1], [2,2]) \\spad{X} \\spad{t4} \\spad{:=} blockConcat \\spad{t3} \\spad{X} zero?(E-t4)")) (|vertConcat| ((|#4| (|List| |#4|)) "\\indented{1}{\\spad{vertConcat} concatenates matrices row wise.} \\blankline \\spad{X} A \\spad{:=} matrix([[a]]) \\spad{X} \\spad{B} \\spad{:=} matrix([[b]]) \\spad{X} \\spad{C} \\spad{:=} matrix([[c]]) \\spad{X} \\spad{A21} \\spad{:=} vertConcat([A,B,C])")) (|horizConcat| ((|#4| (|List| |#4|)) "\\indented{1}{\\spad{horizConcat} concatenates matrices column wise.} \\blankline \\spad{X} A \\spad{:=} matrix([[a]]) \\spad{X} \\spad{B} \\spad{:=} matrix([[b]]) \\spad{X} \\spad{C} \\spad{:=} matrix([[c]]) \\spad{X} \\spad{A12} \\spad{:=} horizConcat([A,B,C])")) (|bandMatrix| ((|#4| |#4| (|Segment| (|Integer|))) "\\indented{1}{\\spad{bandMatrix} returns multiple diagonals out of a matrix.} \\indented{1}{The diagonals are put into a matrix of same shape as the} \\indented{1}{original one. Positive integer arguments select upper} \\indented{1}{off-diagonals, negative ones lower off-diagonals.} \\blankline \\spad{X} \\spad{M} \\spad{:=} matrix([[a,b,c],[d,e,f],[g,h,i]]) \\spad{X} bandMatrix(M, -1..1)") ((|#4| |#4| (|List| (|Integer|))) "\\indented{1}{\\spad{bandMatrix} returns multiple diagonals out of a matrix.} \\indented{1}{The diagonals are put into a matrix of same shape as the} \\indented{1}{original one. Positive integer arguments select upper} \\indented{1}{off-diagonals, negative ones lower off-diagonals.} \\blankline \\spad{X} \\spad{M} \\spad{:=} matrix([[a,b,c],[d,e,f],[g,h,i]]) \\spad{X} bandMatrix(M, [-1,1]) \\spad{X} bandMatrix(M, [-1,0,1])")) (|diagonalMatrix| ((|#4| |#4|) "\\indented{1}{\\spad{diagonalMatrix} returns the main diagonal out of} \\indented{1}{a matrix. The diagonal is put into a matrix of same shape} \\indented{1}{as the original one.} \\blankline \\spad{X} \\spad{M} \\spad{:=} matrix([[a,b,c],[d,e,f],[g,h,i]]) \\spad{X} diagonalMatrix(M)") ((|#4| |#4| (|Integer|)) "\\indented{1}{\\spad{diagonalMatrix} returns a diagonal out of a matrix.} \\indented{1}{The diagonal is put into a matrix of same shape as the} \\indented{1}{original one. Positive integer arguments select upper} \\indented{1}{off-diagonals, negative ones lower off-diagonals.} \\blankline \\spad{X} \\spad{M} \\spad{:=} matrix([[a,b,c],[d,e,f],[g,h,i]]) \\spad{X} diagonalMatrix(M, 1) \\spad{X} diagonalMatrix(M, 2) \\spad{X} diagonalMatrix(M, \\spad{-1)}")) (|subMatrix| ((|#4| |#4| (|Segment| (|PositiveInteger|)) (|Segment| (|PositiveInteger|))) "\\indented{1}{\\spad{subMatrix} returns several elements out of a matrix.} \\indented{1}{The elements are stacked into a submatrix.} \\blankline \\spad{X} \\spad{M} \\spad{:=} matrix([[a,b,c],[d,e,f],[g,h,i]]) \\spad{X} subMatrix(M, 1..2,2..3)") ((|#4| |#4| (|List| (|PositiveInteger|)) (|List| (|PositiveInteger|))) "\\indented{1}{\\spad{subMatrix} returns several elements out of a matrix.} \\indented{1}{The elements are stacked into a submatrix.} \\blankline \\spad{X} \\spad{M} \\spad{:=} matrix([[a,b,c],[d,e,f],[g,h,i]]) \\spad{X} subMatrix(M, [1,2],[1,2]) \\spad{X} subMatrix(M, [1,3],[1,3])")) (|columns| ((|#4| |#4| (|Segment| (|PositiveInteger|))) "\\indented{1}{\\spad{columns} returns several columns out of a matrix.} \\indented{1}{The columns are stacked into a matrix.} \\blankline \\spad{X} \\spad{M} \\spad{:=} matrix([[a,b,c],[d,e,f],[g,h,i]]) \\spad{X} columns(M, 1..2)") ((|#4| |#4| (|List| (|PositiveInteger|))) "\\indented{1}{\\spad{columns} returns several columns out of a matrix.} \\indented{1}{The columns are stacked into a matrix.} \\blankline \\spad{X} \\spad{M} \\spad{:=} matrix([[a,b,c],[d,e,f],[g,h,i]]) \\spad{X} columns(M, [1,2]) \\spad{X} columns(M, [3,2])")) (|aColumn| ((|#4| |#4| (|PositiveInteger|)) "\\indented{1}{\\spad{aColumn} returns a single column out of a matrix.} \\indented{1}{The column is put into a one by \\spad{N} matrix.} \\blankline \\spad{X} \\spad{M} \\spad{:=} matrix([[a,b,c],[d,e,f],[g,h,i]]) \\spad{X} aColumn(M, 2)")) (|rows| ((|#4| |#4| (|Segment| (|PositiveInteger|))) "\\indented{1}{\\spad{rows} returns several rows out of a matrix.} \\indented{1}{The rows are stacked into a matrix.} \\blankline \\spad{X} \\spad{M} \\spad{:=} matrix([[a,b,c],[d,e,f],[g,h,i]]) \\spad{X} rows(M, 2..3)") ((|#4| |#4| (|List| (|PositiveInteger|))) "\\indented{1}{\\spad{rows} returns several rows out of a matrix.} \\indented{1}{The rows are stacked into a matrix.} \\blankline \\spad{X} \\spad{M} \\spad{:=} matrix([[a,b,c],[d,e,f],[g,h,i]]) \\spad{X} rows(M, [1,2]) \\spad{X} rows(M, [3,2])")) (|aRow| ((|#4| |#4| (|PositiveInteger|)) "\\indented{1}{\\spad{aRow} returns a single row out of a matrix.} \\indented{1}{The row is put into a one by \\spad{N} matrix.} \\blankline \\spad{X} \\spad{M} \\spad{:=} matrix([[a,b,c],[d,e,f],[g,h,i]]) \\spad{X} aRow(M, 1) \\spad{X} aRow(M, 2)")) (|element| ((|#4| |#4| (|PositiveInteger|) (|PositiveInteger|)) "\\indented{1}{\\spad{element} returns a single element out of a matrix.} \\indented{1}{The element is put into a one by one matrix.} \\blankline \\spad{X} \\spad{M} \\spad{:=} matrix([[a,b,c],[d,e,f],[g,h,i]]) \\spad{X} element(M,2,2)"))) NIL NIL (|MappingPackageInternalHacks1| A) @@ -3649,7 +3653,7 @@ NIL ((|unitsKnown| . T)) NIL (|PermutationGroup| S) -((|constructor| (NIL "PermutationGroup implements permutation groups acting on a set \\spad{S,} \\spadignore{i.e.} all subgroups of the symmetric group of \\spad{S,} represented as a list of permutations (generators). Note that therefore the objects are not members of the Axiom category \\spadtype{Group}. Using the idea of base and strong generators by Sims, basic routines and algorithms are implemented so that the word problem for permutation groups can be solved.")) (|initializeGroupForWordProblem| (((|Void|) $ (|Integer|) (|Integer|)) "\\spad{initializeGroupForWordProblem(gp,m,n)} initializes the group \\spad{gp} for the word problem. Notes: \\spad{(1)} with a small integer you get shorter words, but the routine takes longer than the standard routine for longer words. \\spad{(2)} be careful: invoking this routine will destroy the possibly stored information about your group (but will recompute it again). \\spad{(3)} users need not call this function normally for the soultion of the word problem.") (((|Void|) $) "\\spad{initializeGroupForWordProblem(gp)} initializes the group \\spad{gp} for the word problem. Notes: it calls the other function of this name with parameters 0 and 1: initializeGroupForWordProblem(gp,0,1). Notes: \\spad{(1)} be careful: invoking this routine will destroy the possibly information about your group (but will recompute it again) \\spad{(2)} users need not call this function normally for the soultion of the word problem.")) (<= (((|Boolean|) $ $) "\\spad{gp1 \\spad{<=} gp2} returns \\spad{true} if and only if \\spad{gp1} is a subgroup of gp2. Note: because of a bug in the parser you have to call this function explicitly by \\spad{gp1} <=$(PERMGRP \\spad{S)} gp2.")) (< (((|Boolean|) $ $) "\\spad{gp1 < gp2} returns \\spad{true} if and only if \\spad{gp1} is a proper subgroup of gp2.")) (|movedPoints| (((|Set| |#1|) $) "\\spad{movedPoints(gp)} returns the points moved by the group \\spad{gp.}")) (|wordInGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInGenerators(p,gp)} returns the word for the permutation \\spad{p} in the original generators of the group \\spad{gp,} represented by the indices of the list, given by generators.")) (|wordInStrongGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInStrongGenerators(p,gp)} returns the word for the permutation \\spad{p} in the strong generators of the group \\spad{gp,} represented by the indices of the list, given by strongGenerators.")) (|member?| (((|Boolean|) (|Permutation| |#1|) $) "\\spad{member?(pp,gp)} answers the question, whether the permutation \\spad{pp} is in the group \\spad{gp} or not.")) (|orbits| (((|Set| (|Set| |#1|)) $) "\\spad{orbits(gp)} returns the orbits of the group \\spad{gp,} \\spadignore{i.e.} it partitions the (finite) of all moved points.")) (|orbit| (((|Set| (|List| |#1|)) $ (|List| |#1|)) "\\spad{orbit(gp,ls)} returns the orbit of the ordered list \\spad{ls} under the group \\spad{gp.} Note: return type is \\spad{L} \\spad{L} \\spad{S} temporarily because FSET \\spad{L} \\spad{S} has an error.") (((|Set| (|Set| |#1|)) $ (|Set| |#1|)) "\\spad{orbit(gp,els)} returns the orbit of the unordered set \\spad{els} under the group \\spad{gp.}") (((|Set| |#1|) $ |#1|) "\\spad{orbit(gp,el)} returns the orbit of the element \\spad{el} under the group \\spad{gp,} \\spadignore{i.e.} the set of all points gained by applying each group element to el.")) (|permutationGroup| (($ (|List| (|Permutation| |#1|))) "\\spad{permutationGroup(ls)} coerces a list of permutations \\spad{ls} to the group generated by this list.")) (|wordsForStrongGenerators| (((|List| (|List| (|NonNegativeInteger|))) $) "\\spad{wordsForStrongGenerators(gp)} returns the words for the strong generators of the group \\spad{gp} in the original generators of \\spad{gp,} represented by their indices in the list, given by generators.")) (|strongGenerators| (((|List| (|Permutation| |#1|)) $) "\\spad{strongGenerators(gp)} returns strong generators for the group \\spad{gp.}")) (|base| (((|List| |#1|) $) "\\spad{base(gp)} returns a base for the group \\spad{gp.}")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(gp)} returns the number of points moved by all permutations of the group \\spad{gp.}")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(gp)} returns the order of the group \\spad{gp.}")) (|random| (((|Permutation| |#1|) $) "\\spad{random(gp)} returns a random product of maximal 20 generators of the group \\spad{gp.} Note: random(gp)=random(gp,20).") (((|Permutation| |#1|) $ (|Integer|)) "\\spad{random(gp,i)} returns a random product of maximal \\spad{i} generators of the group \\spad{gp.}")) (|elt| (((|Permutation| |#1|) $ (|NonNegativeInteger|)) "\\spad{elt(gp,i)} returns the \\spad{i}-th generator of the group \\spad{gp.}")) (|generators| (((|List| (|Permutation| |#1|)) $) "\\spad{generators(gp)} returns the generators of the group \\spad{gp.}")) (|coerce| (($ (|List| (|Permutation| |#1|))) "\\spad{coerce(ls)} coerces a list of permutations \\spad{ls} to the group generated by this list.") (((|List| (|Permutation| |#1|)) $) "\\spad{coerce(gp)} returns the generators of the group \\spad{gp.}"))) +((|constructor| (NIL "PermutationGroup implements permutation groups acting on a set \\spad{S,} \\spadignore{i.e.} all subgroups of the symmetric group of \\spad{S,} represented as a list of permutations (generators). Note that therefore the objects are not members of the Axiom category \\spadtype{Group}. Using the idea of base and strong generators by Sims, basic routines and algorithms are implemented so that the word problem for permutation groups can be solved.")) (|initializeGroupForWordProblem| (((|Void|) $ (|Integer|) (|Integer|)) "\\spad{initializeGroupForWordProblem(gp,m,n)} initializes the group \\spad{gp} for the word problem. Notes: \\spad{(1)} with a small integer you get shorter words, but the routine takes longer than the standard routine for longer words. \\spad{(2)} be careful: invoking this routine will destroy the possibly stored information about your group (but will recompute it again). \\spad{(3)} users need not call this function normally for the soultion of the word problem.") (((|Void|) $) "\\spad{initializeGroupForWordProblem(gp)} initializes the group \\spad{gp} for the word problem. Notes: it calls the other function of this name with parameters 0 and 1: initializeGroupForWordProblem(gp,0,1). Notes: \\spad{(1)} be careful: invoking this routine will destroy the possibly information about your group (but will recompute it again) \\spad{(2)} users need not call this function normally for the soultion of the word problem.")) (<= (((|Boolean|) $ $) "\\spad{gp1 \\spad{<=} gp2} returns \\spad{true} if and only if \\spad{gp1} is a subgroup of gp2. Note: because of a bug in the parser you have to call this function explicitly by \\spad{gp1} <=$(PERMGRP \\spad{S)} gp2.")) (< (((|Boolean|) $ $) "\\spad{gp1 < gp2} returns \\spad{true} if and only if \\spad{gp1} is a proper subgroup of gp2.")) (|movedPoints| (((|Set| |#1|) $) "\\indented{1}{movedPoints(gp) returns the points moved by the group gp.} \\blankline \\spad{X} \\spad{x} : PERM INT \\spad{:=} [[1,3,5],[7,11,9]] \\spad{X} \\spad{z} : PERM INT \\spad{:=} [1,3,11] \\spad{X} \\spad{g} : PERMGRP INT \\spad{:=} [ \\spad{x} ,{} \\spad{z} ] \\spad{X} movedPoints \\spad{g}")) (|wordInGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInGenerators(p,gp)} returns the word for the permutation \\spad{p} in the original generators of the group \\spad{gp,} represented by the indices of the list, given by generators.")) (|wordInStrongGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInStrongGenerators(p,gp)} returns the word for the permutation \\spad{p} in the strong generators of the group \\spad{gp,} represented by the indices of the list, given by strongGenerators.")) (|member?| (((|Boolean|) (|Permutation| |#1|) $) "\\indented{1}{member?(pp,gp) answers the question, whether the} \\indented{1}{permutation \\spad{pp} is in the group \\spad{gp} or not.} \\blankline \\spad{X} \\spad{x} : PERM INT \\spad{:=} [[1,3,5],[7,11,9]] \\spad{X} \\spad{y} : PERM INT \\spad{:=} [[3,5,7,9]] \\spad{X} \\spad{z} : PERM INT \\spad{:=} [1,3,11] \\spad{X} \\spad{g} : PERMGRP INT \\spad{:=} [ \\spad{x} ,{} \\spad{z} ] \\spad{X} member? ( \\spad{y} ,{} \\spad{g} )")) (|orbits| (((|Set| (|Set| |#1|)) $) "\\indented{1}{orbits(gp) returns the orbits of the group \\spad{gp,} \\spadignore{i.e.} \\indented{1}{it partitions the (finite) of all moved points.} \\blankline \\spad{X} \\spad{y} : PERM INT \\spad{:=} [[3,5,7,9]] \\spad{X} \\spad{z} : PERM INT \\spad{:=} [1,3,11] \\spad{X} \\spad{g} : PERMGRP INT \\spad{:=} [ \\spad{y} ,{} \\spad{z} ] \\spad{X} orbits \\spad{g}")) (|orbit| (((|Set| (|List| |#1|)) $ (|List| |#1|)) "\\indented{1}{orbit(gp,ls) returns the orbit of the ordered} \\indented{1}{list \\spad{ls} under the group gp.} \\indented{1}{Note: return type is \\spad{L} \\spad{L} \\spad{S} temporarily because FSET \\spad{L} \\spad{S} has an error.} \\blankline \\spad{X} \\spad{x} : PERM INT \\spad{:=} [[1,3,5],[7,11,9]] \\spad{X} \\spad{y} : PERM INT \\spad{:=} [[3,5,7,9]] \\spad{X} \\spad{g} : PERMGRP INT \\spad{:=} [ \\spad{x} ,{} \\spad{y} ] \\spad{X} orbit(g, 3)") (((|Set| (|Set| |#1|)) $ (|Set| |#1|)) "\\spad{orbit(gp,els)} returns the orbit of the unordered set \\spad{els} under the group \\spad{gp.}") (((|Set| |#1|) $ |#1|) "\\spad{orbit(gp,el)} returns the orbit of the element \\spad{el} under the group \\spad{gp,} \\spadignore{i.e.} the set of all points gained by applying each group element to el.")) (|permutationGroup| (($ (|List| (|Permutation| |#1|))) "\\spad{permutationGroup(ls)} coerces a list of permutations \\spad{ls} to the group generated by this list.")) (|wordsForStrongGenerators| (((|List| (|List| (|NonNegativeInteger|))) $) "\\spad{wordsForStrongGenerators(gp)} returns the words for the strong generators of the group \\spad{gp} in the original generators of \\spad{gp,} represented by their indices in the list, given by generators.")) (|strongGenerators| (((|List| (|Permutation| |#1|)) $) "\\spad{strongGenerators(gp)} returns strong generators for the group \\spad{gp.}")) (|base| (((|List| |#1|) $) "\\spad{base(gp)} returns a base for the group \\spad{gp.}")) (|degree| (((|NonNegativeInteger|) $) "\\indented{1}{degree(gp) returns the number of points moved by all permutations} \\indented{1}{of the group gp.} \\blankline \\spad{X} \\spad{y} : PERM INT \\spad{:=} [[3,5,7,9]] \\spad{X} \\spad{z} : PERM INT \\spad{:=} [1,3,11] \\spad{X} \\spad{g} : PERMGRP INT \\spad{:=} [ \\spad{y} ,{} \\spad{z} ] \\spad{X} degree \\spad{g}")) (|order| (((|NonNegativeInteger|) $) "\\indented{1}{order(gp) returns the order of the group gp.} \\blankline \\spad{X} \\spad{x} : PERM INT \\spad{:=} [[1,3,5],[7,11,9]] \\spad{X} \\spad{y} : PERM INT \\spad{:=} [[3,5,7,9]] \\spad{X} \\spad{g} : PERMGRP INT \\spad{:=} [ \\spad{x} ,{} \\spad{y} ] \\spad{X} order \\spad{g}")) (|random| (((|Permutation| |#1|) $) "\\spad{random(gp)} returns a random product of maximal 20 generators of the group \\spad{gp.} Note: random(gp)=random(gp,20).") (((|Permutation| |#1|) $ (|Integer|)) "\\spad{random(gp,i)} returns a random product of maximal \\spad{i} generators of the group \\spad{gp.}")) (|elt| (((|Permutation| |#1|) $ (|NonNegativeInteger|)) "\\spad{elt(gp,i)} returns the \\spad{i}-th generator of the group \\spad{gp.}")) (|generators| (((|List| (|Permutation| |#1|)) $) "\\spad{generators(gp)} returns the generators of the group \\spad{gp.}")) (|coerce| (($ (|List| (|Permutation| |#1|))) "\\indented{1}{coerce(ls) coerces a list of permutations \\spad{ls} to the group} \\indented{1}{generated by this list.} \\blankline \\spad{X} \\spad{y} : PERM INT \\spad{:=} [[3,5,7,9]] \\spad{X} \\spad{z} : PERM INT \\spad{:=} [1,3,11] \\spad{X} \\spad{g} : PERMGRP INT \\spad{:=} [ \\spad{y} ,{} \\spad{z} ]") (((|List| (|Permutation| |#1|)) $) "\\indented{1}{coerce(gp) returns the generators of the group gp.} \\blankline \\spad{X} \\spad{x} : PERM INT \\spad{:=} [[1,3,5],[7,11,9]]"))) NIL NIL (|Permutation| S) @@ -4525,7 +4529,7 @@ NIL (((|commutative| "*") |has| |#1| (|CommutativeRing|)) (|noZeroDivisors| |has| |#1| (|IntegralDomain|)) (|canonicalUnitNormal| |has| |#1| (ATTRIBUTE |canonicalUnitNormal|)) (|leftUnitary| . T) (|rightUnitary| . T) (|unitsKnown| . T)) ((|HasCategory| |#1| (QUOTE (|PolynomialFactorizationExplicit|))) (|HasCategory| |#1| (QUOTE (|IntegralDomain|))) (|HasCategory| |#1| (QUOTE (|CommutativeRing|))) (OR (|HasCategory| |#1| (QUOTE (|CommutativeRing|))) (|HasCategory| |#1| (QUOTE (|IntegralDomain|)))) (|HasCategory| |#1| (QUOTE (|GcdDomain|))) (OR (|HasCategory| |#1| (QUOTE (|CommutativeRing|))) (|HasCategory| |#1| (QUOTE (|GcdDomain|))) (|HasCategory| |#1| (QUOTE (|IntegralDomain|))) (|HasCategory| |#1| (QUOTE (|PolynomialFactorizationExplicit|)))) (OR (|HasCategory| |#1| (QUOTE (|GcdDomain|))) (|HasCategory| |#1| (QUOTE (|IntegralDomain|))) (|HasCategory| |#1| (QUOTE (|PolynomialFactorizationExplicit|)))) (OR (|HasCategory| |#1| (QUOTE (|GcdDomain|))) (|HasCategory| |#1| (QUOTE (|PolynomialFactorizationExplicit|)))) (AND (|HasCategory| |#1| (LIST (QUOTE |PatternMatchable|) (QUOTE (|Float|)))) (|HasCategory| |#2| (LIST (QUOTE |PatternMatchable|) (QUOTE (|Float|))))) (AND (|HasCategory| |#1| (LIST (QUOTE |PatternMatchable|) (QUOTE (|Integer|)))) (|HasCategory| |#2| (LIST (QUOTE |PatternMatchable|) (QUOTE (|Integer|))))) (AND (|HasCategory| |#1| (LIST (QUOTE |ConvertibleTo|) (LIST (QUOTE |Pattern|) (QUOTE (|Float|))))) (|HasCategory| |#2| (LIST (QUOTE |ConvertibleTo|) (LIST (QUOTE |Pattern|) (QUOTE (|Float|)))))) (AND (|HasCategory| |#1| (LIST (QUOTE |ConvertibleTo|) (LIST (QUOTE |Pattern|) (QUOTE (|Integer|))))) (|HasCategory| |#2| (LIST (QUOTE |ConvertibleTo|) (LIST (QUOTE |Pattern|) (QUOTE (|Integer|)))))) (AND (|HasCategory| |#1| (LIST (QUOTE |ConvertibleTo|) (QUOTE (|InputForm|)))) (|HasCategory| |#2| (LIST (QUOTE |ConvertibleTo|) (QUOTE (|InputForm|))))) (|HasCategory| |#1| (QUOTE (|OrderedSet|))) (|HasCategory| |#1| (LIST (QUOTE |LinearlyExplicitRingOver|) (QUOTE (|Integer|)))) (|HasCategory| |#1| (QUOTE (|CharacteristicZero|))) (|HasCategory| |#1| (QUOTE (|CharacteristicNonZero|))) (OR (|HasCategory| |#1| (QUOTE (|GcdDomain|))) (|HasCategory| |#1| (QUOTE (|IntegralDomain|)))) (|HasCategory| |#1| (LIST (QUOTE |Algebra|) (LIST (QUOTE |Fraction|) (QUOTE (|Integer|))))) (|HasCategory| |#1| (LIST (QUOTE |RetractableTo|) (QUOTE (|Integer|)))) (|HasCategory| |#1| (LIST (QUOTE |RetractableTo|) (LIST (QUOTE |Fraction|) (QUOTE (|Integer|))))) (|HasCategory| |#1| (QUOTE (|Field|))) (OR (|HasCategory| |#1| (LIST (QUOTE |Algebra|) (LIST (QUOTE |Fraction|) (QUOTE (|Integer|))))) (|HasCategory| |#1| (LIST (QUOTE |RetractableTo|) (LIST (QUOTE |Fraction|) (QUOTE (|Integer|)))))) (|HasAttribute| |#1| (QUOTE |canonicalUnitNormal|)) (AND (|HasCategory| $ (QUOTE (|CharacteristicNonZero|))) (|HasCategory| |#1| (QUOTE (|PolynomialFactorizationExplicit|)))) (OR (AND (|HasCategory| $ (QUOTE (|CharacteristicNonZero|))) (|HasCategory| |#1| (QUOTE (|PolynomialFactorizationExplicit|)))) (|HasCategory| |#1| (QUOTE (|CharacteristicNonZero|))))) (|SparseMultivariateTaylorSeries| |Coef| |Var| SMP) -((|constructor| (NIL "This domain provides multivariate Taylor series with variables from an arbitrary ordered set. A Taylor series is represented by a stream of polynomials from the polynomial domain SMP. The \\spad{n}th element of the stream is a form of degree \\spad{n.} SMTS is an internal domain.")) (|fintegrate| (($ (|Mapping| $) |#2| |#1|) "\\spad{fintegrate(f,v,c)} is the integral of \\spad{f()} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.} \\indented{1}{The evaluation of \\spad{f()} is delayed.}")) (|integrate| (($ $ |#2| |#1|) "\\spad{integrate(s,v,c)} is the integral of \\spad{s} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.}")) (|csubst| (((|Mapping| (|Stream| |#3|) |#3|) (|List| |#2|) (|List| (|Stream| |#3|))) "\\spad{csubst(a,b)} is for internal use only")) (* (($ |#3| $) "\\spad{smp*ts} multiplies a TaylorSeries by a monomial SMP.")) (|coerce| (($ |#3|) "\\spad{coerce(poly)} regroups the terms by total degree and forms a series.") (($ |#2|) "\\spad{coerce(var)} converts a variable to a Taylor series")) (|coefficient| ((|#3| $ (|NonNegativeInteger|)) "\\indented{1}{\\spad{coefficient(s, \\spad{n)}} gives the terms of total degree \\spad{n.}} \\blankline \\spad{X} xts:=x::TaylorSeries Fraction Integer \\spad{X} t1:=sin(xts) \\spad{X} coefficient(t1,3)"))) +((|constructor| (NIL "This domain provides multivariate Taylor series with variables from an arbitrary ordered set. A Taylor series is represented by a stream of polynomials from the polynomial domain SMP. The \\spad{n}th element of the stream is a form of degree \\spad{n.} SMTS is an internal domain.")) (|fintegrate| (($ (|Mapping| $) |#2| |#1|) "\\spad{fintegrate(f,v,c)} is the integral of \\spad{f()} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.} \\indented{1}{The evaluation of \\spad{f()} is delayed.}")) (|integrate| (($ $ |#2| |#1|) "\\spad{integrate(s,v,c)} is the integral of \\spad{s} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.}")) (|csubst| (((|Mapping| (|Stream| |#3|) |#3|) (|List| |#2|) (|List| (|Stream| |#3|))) "\\spad{csubst(a,b)} is for internal use only")) (* (($ |#3| $) "\\spad{smp*ts} multiplies a TaylorSeries by a monomial SMP.")) (|coerce| (($ |#3|) "\\spad{coerce(poly)} regroups the terms by total degree and forms a series.") (($ |#2|) "\\spad{coerce(var)} converts a variable to a Taylor series")) (|series| (($ (|Stream| |#3|)) "\\space(series(st)) creates a series from a stream of coefficients")) (|coefficients| (((|Stream| |#3|) $) "\\space{coefficients(s)) gives a stream of coefficients of \\spad{s,} \\spadignore{e.g.} [coefficient(s,0), coefficient(s,1), ...]")) (|coefficient| ((|#3| $ (|NonNegativeInteger|)) "\\indented{1}{\\spad{coefficient(s, \\spad{n)}} gives the terms of total degree \\spad{n.}} \\blankline \\spad{X} xts:=x::TaylorSeries Fraction Integer \\spad{X} t1:=sin(xts) \\spad{X} coefficient(t1,3)"))) (((|commutative| "*") |has| |#1| (|CommutativeRing|)) (|noZeroDivisors| |has| |#1| (|IntegralDomain|)) (|leftUnitary| . T) (|rightUnitary| . T) (|unitsKnown| . T)) ((|HasCategory| |#1| (LIST (QUOTE |Algebra|) (LIST (QUOTE |Fraction|) (QUOTE (|Integer|))))) (|HasCategory| |#1| (QUOTE (|CommutativeRing|))) (|HasCategory| |#1| (QUOTE (|CharacteristicZero|))) (|HasCategory| |#1| (QUOTE (|CharacteristicNonZero|))) (|HasCategory| |#1| (QUOTE (|IntegralDomain|))) (OR (|HasCategory| |#1| (QUOTE (|CommutativeRing|))) (|HasCategory| |#1| (QUOTE (|IntegralDomain|)))) (|HasCategory| |#1| (QUOTE (|Field|)))) (|SquareFreeNormalizedTriangularSetCategory| R E V P) @@ -4909,7 +4913,7 @@ NIL NIL NIL (|UnivariateLaurentSeriesCategory| |Coef|) -((|constructor| (NIL "\\spadtype{UnivariateLaurentSeriesCategory} is the category of Laurent series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 1. We may integrate a series when we can divide coefficients by integers.")) (|rationalFunction| (((|Fraction| (|Polynomial| |#1|)) $ (|Integer|) (|Integer|)) "\\spad{rationalFunction(f,k1,k2)} returns a rational function consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 \\spad{<=} \\spad{d} \\spad{<=} k2}.") (((|Fraction| (|Polynomial| |#1|)) $ (|Integer|)) "\\spad{rationalFunction(f,k)} returns a rational function consisting of the sum of all terms of \\spad{f} of degree \\spad{<=} \\spad{k.}")) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) "\\spad{multiplyCoefficients(f,sum(n = n0..infinity,a[n] * x**n)) = sum(n = 0..infinity,f(n) * a[n] * x**n)}. This function is used when Puiseux series are represented by a Laurent series and an exponent.")) (|series| (($ (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms, where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents."))) +((|constructor| (NIL "\\spadtype{UnivariateLaurentSeriesCategory} is the category of Laurent series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 1. We may integrate a series when we can divide coefficients by integers.")) (|rationalFunction| (((|Fraction| (|Polynomial| |#1|)) $ (|Integer|) (|Integer|)) "\\spad{rationalFunction(f,k1,k2)} returns a rational function consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 \\spad{<=} \\spad{d} \\spad{<=} k2}.") (((|Fraction| (|Polynomial| |#1|)) $ (|Integer|)) "\\indented{1}{\\spad{rationalFunction(f,k)} returns a rational function} \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<=} \\spad{k.}} \\blankline \\spad{X} \\spad{w:SparseUnivariateLaurentSeries(Fraction(Integer),'z,0):=0} \\spad{X} rationalFunction(w,0)")) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) "\\spad{multiplyCoefficients(f,sum(n = n0..infinity,a[n] * x**n)) = sum(n = 0..infinity,f(n) * a[n] * x**n)}. This function is used when Puiseux series are represented by a Laurent series and an exponent.")) (|series| (($ (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms, where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents."))) (((|commutative| "*") |has| |#1| (|CommutativeRing|)) (|noZeroDivisors| |has| |#1| (|IntegralDomain|)) (|canonicalUnitNormal| |has| |#1| (|Field|)) (|canonicalsClosed| |has| |#1| (|Field|)) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . 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(((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) |has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Evalable| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))))) (((|#2| |#2|) . T)) ((((|Integer|)) . T)) diff --git a/src/share/algebra/interp.daase b/src/share/algebra/interp.daase index 3c9b210..8ab16f5 100644 --- a/src/share/algebra/interp.daase +++ b/src/share/algebra/interp.daase @@ -1,5 +1,5 @@ -(5961098 . 3621447417) +(5965124 . 3639870124) ((|sorted?| (((|Boolean|) (|Mapping| (|Boolean|) |#2| |#2|) $) 62) (((|Boolean|) $) NIL)) (|sort!| (($ (|Mapping| (|Boolean|) |#2| |#2|) $) 17) (($ $) NIL)) (|setelt| ((|#2| $ (|Integer|) |#2|) NIL) ((|#2| $ (|UniversalSegment| (|Integer|)) |#2|) 34)) (|reverse!| (($ $) 58)) (|reduce| ((|#2| (|Mapping| |#2| |#2| |#2|) $ |#2| |#2|) 40) ((|#2| (|Mapping| |#2| |#2| |#2|) $ |#2|) 38) ((|#2| (|Mapping| |#2| |#2| |#2|) $) 37)) (|position| (((|Integer|) (|Mapping| (|Boolean|) |#2|) $) 22) (((|Integer|) |#2| $) NIL) (((|Integer|) |#2| $ (|Integer|)) 70)) (|parts| (((|List| |#2|) $) 13)) (|merge| (($ (|Mapping| (|Boolean|) |#2| |#2|) $ $) 47) (($ $ $) NIL)) (|map!| (($ (|Mapping| |#2| |#2|) $) 29)) (|map| (($ (|Mapping| |#2| |#2|) $) NIL) (($ 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(|Mapping| |#2| |#2| |#2|) |#1| |#1|)) (SIGNATURE |concat| (|#1| (|List| |#1|))) (SIGNATURE |concat| (|#1| |#1| |#1|)) (SIGNATURE |concat| (|#1| |#2| |#1|)) (SIGNATURE |concat| (|#1| |#1| |#2|)) (SIGNATURE |construct| (|#1| (|List| |#2|))) (SIGNATURE |find| ((|Union| |#2| "failed") (|Mapping| (|Boolean|) |#2|) |#1|)) (SIGNATURE |reduce| (|#2| (|Mapping| |#2| |#2| |#2|) |#1|)) (SIGNATURE |reduce| (|#2| (|Mapping| |#2| |#2| |#2|) |#1| |#2|)) (SIGNATURE |reduce| (|#2| (|Mapping| |#2| |#2| |#2|) |#1| |#2| |#2|)) (SIGNATURE |elt| (|#2| |#1| (|Integer|))) (SIGNATURE |elt| (|#2| |#1| (|Integer|) |#2|)) (SIGNATURE |setelt| (|#2| |#1| (|Integer|) |#2|)) (SIGNATURE |count| ((|NonNegativeInteger|) |#2| |#1|)) (SIGNATURE |parts| ((|List| |#2|) |#1|)) (SIGNATURE |count| ((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#2|) |#1|)) (SIGNATURE |every?| ((|Boolean|) (|Mapping| (|Boolean|) |#2|) |#1|)) (SIGNATURE |any?| ((|Boolean|) (|Mapping| (|Boolean|) |#2|) |#1|)) (SIGNATURE |map!| (|#1| (|Mapping| 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(|PositiveInteger|)) NIL)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) NIL) (($ $ $) 75) (($ $ |#1|) NIL) (($ |#1| $) NIL) (($ (|SquareMatrix| |#2| |#1|) $) 19))) +((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) NIL)) (|unit| (((|Union| $ "failed")) NIL (|has| |#1| (|IntegralDomain|)))) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL)) (|structuralConstants| (((|Vector| (|Matrix| |#1|)) (|Vector| $)) NIL) (((|Vector| (|Matrix| |#1|))) 24)) (|someBasis| (((|Vector| $)) 51)) (|sample| (($) NIL T CONST)) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) NIL (|has| |#1| (|IntegralDomain|)))) (|rightUnit| (((|Union| $ "failed")) NIL (|has| |#1| (|IntegralDomain|)))) (|rightTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) NIL) (((|Matrix| |#1|)) NIL)) (|rightTrace| ((|#1| $) NIL)) (|rightRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) NIL) (((|Matrix| |#1|) $) NIL)) (|rightRecip| (((|Union| $ "failed") $) NIL (|has| |#1| (|IntegralDomain|)))) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) NIL (|has| |#1| (|Field|)))) (|rightPower| (($ $ (|PositiveInteger|)) NIL)) (|rightNorm| ((|#1| $) NIL)) (|rightMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) NIL (|has| |#1| (|IntegralDomain|)))) (|rightDiscriminant| ((|#1| (|Vector| $)) NIL) ((|#1|) NIL)) (|rightCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) NIL)) (|rightAlternative?| (((|Boolean|)) 88)) (|represents| (($ (|Vector| |#1|) (|Vector| $)) NIL) (($ (|Vector| |#1|)) NIL)) (|recip| (((|Union| $ "failed") $) 14 (|has| |#1| (|IntegralDomain|)))) (|rank| (((|PositiveInteger|)) 52)) (|powerAssociative?| (((|Boolean|)) NIL)) (|plenaryPower| (($ $ (|PositiveInteger|)) NIL)) (|noncommutativeJordanAlgebra?| (((|Boolean|)) NIL)) (|lieAlgebra?| (((|Boolean|)) NIL)) (|lieAdmissible?| (((|Boolean|)) 90)) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) NIL (|has| |#1| (|IntegralDomain|)))) (|leftUnit| (((|Union| $ "failed")) NIL (|has| |#1| (|IntegralDomain|)))) (|leftTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) NIL) (((|Matrix| |#1|)) NIL)) (|leftTrace| ((|#1| $) NIL)) (|leftRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) NIL) (((|Matrix| |#1|) $) NIL)) (|leftRecip| (((|Union| $ "failed") $) NIL (|has| |#1| (|IntegralDomain|)))) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) NIL (|has| |#1| (|Field|)))) (|leftPower| (($ $ (|PositiveInteger|)) NIL)) (|leftNorm| ((|#1| $) NIL)) (|leftMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) NIL (|has| |#1| (|IntegralDomain|)))) (|leftDiscriminant| ((|#1| (|Vector| $)) NIL) ((|#1|) NIL)) (|leftCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) NIL)) (|leftAlternative?| (((|Boolean|)) 87)) (|latex| (((|String|) $) NIL)) (|jordanAlgebra?| (((|Boolean|)) 96)) (|jordanAdmissible?| (((|Boolean|)) 94)) (|jacobiIdentity?| (((|Boolean|)) 97)) (|hash| (((|SingleInteger|) $) NIL)) (|flexible?| (((|Boolean|)) 89)) (|elt| ((|#1| $ (|Integer|)) 54)) (|coordinates| (((|Vector| |#1|) $ (|Vector| $)) 48) (((|Matrix| |#1|) (|Vector| $) (|Vector| $)) NIL) (((|Vector| |#1|) $) 28) (((|Matrix| |#1|) (|Vector| $)) NIL)) (|convert| (((|Vector| |#1|) $) NIL) (($ (|Vector| |#1|)) NIL)) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|)) (|Vector| $)) NIL) (((|List| (|Polynomial| |#1|))) NIL)) (|commutator| (($ $ $) NIL)) (|commutative?| (((|Boolean|)) 85)) (|coerce| (((|OutputForm|) $) 69) (($ (|Vector| |#1|)) 22)) (|basis| (((|Vector| $)) 45)) (|associatorDependence| (((|List| (|Vector| |#1|))) NIL (|has| |#1| (|IntegralDomain|)))) (|associator| (($ $ $ $) NIL)) (|associative?| (((|Boolean|)) 83)) (|apply| (($ (|Matrix| |#1|) $) 18)) (|antiCommutator| (($ $ $) NIL)) (|antiCommutative?| (((|Boolean|)) 86)) (|antiAssociative?| (((|Boolean|)) 84)) (|alternative?| (((|Boolean|)) 82)) (|Zero| (($) NIL T CONST)) (= (((|Boolean|) $ $) NIL)) (- (($ $) NIL) (($ $ $) NIL)) (+ (($ $ $) NIL)) (** (($ $ (|PositiveInteger|)) NIL)) (* (($ (|PositiveInteger|) $) NIL) (($ (|NonNegativeInteger|) $) NIL) (($ (|Integer|) $) NIL) (($ $ $) 76) (($ $ |#1|) NIL) (($ |#1| $) NIL) (($ (|SquareMatrix| |#2| |#1|) $) 19))) (((|AlgebraGivenByStructuralConstants| |#1| |#2| |#3| |#4|) (|Join| (|FramedNonAssociativeAlgebra| |#1|) (|LeftModule| (|SquareMatrix| |#2| |#1|)) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|Vector| |#1|))))) (|Field|) (|PositiveInteger|) (|List| (|Symbol|)) (|Vector| (|Matrix| |#1|))) (T |AlgebraGivenByStructuralConstants|)) ((|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Vector| *3)) (|ofCategory| *3 (|Field|)) (|ofType| *6 (|Vector| (|Matrix| *3))) (|isDomain| *1 (|AlgebraGivenByStructuralConstants| *3 *4 *5 *6)) (|ofType| *4 (|PositiveInteger|)) (|ofType| *5 (|List| (|Symbol|)))))) (|Join| (|FramedNonAssociativeAlgebra| |#1|) (|LeftModule| (|SquareMatrix| |#2| |#1|)) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|Vector| |#1|))))) @@ -409,6 +409,10 @@ NIL ((|atan| (*1 *1 *1) (|ofCategory| *1 (|ArcTrigonometricFunctionCategory|))) (|asin| (*1 *1 *1) (|ofCategory| *1 (|ArcTrigonometricFunctionCategory|))) (|asec| (*1 *1 *1) (|ofCategory| *1 (|ArcTrigonometricFunctionCategory|))) (|acsc| (*1 *1 *1) (|ofCategory| *1 (|ArcTrigonometricFunctionCategory|))) (|acot| (*1 *1 *1) (|ofCategory| *1 (|ArcTrigonometricFunctionCategory|))) (|acos| (*1 *1 *1) (|ofCategory| *1 (|ArcTrigonometricFunctionCategory|)))) (|Join| (CATEGORY |domain| (SIGNATURE |acos| ($ $)) (SIGNATURE |acot| ($ $)) (SIGNATURE |acsc| ($ $)) (SIGNATURE |asec| ($ $)) (SIGNATURE |asin| ($ $)) (SIGNATURE |atan| ($ $)))) NIL +(((|RightUnitaryAttribute|) (|Category|)) (T |RightUnitaryAttribute|)) +NIL +(|Join| (CATEGORY |package| (ATTRIBUTE |nil|))) +NIL (((|ShallowlyMutableAttribute|) (|Category|)) (T |ShallowlyMutableAttribute|)) NIL (|Join| (CATEGORY |package| (ATTRIBUTE |nil|))) @@ -907,10 +911,10 @@ NIL (((|Dequeue| |#1|) (|Join| (|DequeueAggregate| |#1|) (CATEGORY |domain| (SIGNATURE |dequeue| ($ (|List| |#1|))) (SIGNATURE |dequeue!| (|#1| $)) (SIGNATURE |extract!| (|#1| $)) (SIGNATURE |enqueue!| (|#1| |#1| $)) (SIGNATURE |insert!| ($ |#1| $)) (SIGNATURE |inspect| (|#1| $)) (SIGNATURE |front| (|#1| $)) (SIGNATURE |back| (|#1| $)) (SIGNATURE |rotate!| ($ $)) (SIGNATURE |length| ((|NonNegativeInteger|) $)) (SIGNATURE |less?| ((|Boolean|) $ (|NonNegativeInteger|))) (SIGNATURE |more?| ((|Boolean|) $ (|NonNegativeInteger|))) (SIGNATURE |size?| ((|Boolean|) $ (|NonNegativeInteger|))) (SIGNATURE |bag| ($ (|List| |#1|))) (SIGNATURE |empty?| ((|Boolean|) $)) (SIGNATURE |empty| ($)) (SIGNATURE |sample| ($)) (SIGNATURE |copy| ($ $)) (SIGNATURE |eq?| ((|Boolean|) $ $)) (SIGNATURE |map| ($ (|Mapping| |#1| |#1|) $)) (SIGNATURE |depth| ((|NonNegativeInteger|) $)) (SIGNATURE |dequeue| ($)) (SIGNATURE |height| ((|NonNegativeInteger|) $)) (SIGNATURE |top| (|#1| $)) (SIGNATURE |bottom!| (|#1| $)) 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|noBranch|) (IF (|has| $ (ATTRIBUTE |finiteAggregate|)) (IF (|has| |#1| (|SetCategory|)) (PROGN (SIGNATURE |member?| ((|Boolean|) |#1| $)) (SIGNATURE |count| ((|NonNegativeInteger|) |#1| $))) |noBranch|) |noBranch|))) (|SetCategory|)) (T |Dequeue|)) ((|eq?| (*1 *2 *1 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Dequeue| *3)) (|ofCategory| *3 (|SetCategory|)))) (|copy| (*1 *1 *1) (AND (|isDomain| *1 (|Dequeue| *2)) (|ofCategory| *2 (|SetCategory|)))) (|empty| (*1 *1) (AND (|isDomain| *1 (|Dequeue| *2)) (|ofCategory| *2 (|SetCategory|)))) (|empty?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Dequeue| *3)) (|ofCategory| *3 (|SetCategory|)))) (|less?| (*1 *2 *1 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Dequeue| *4)) (|ofCategory| *4 (|SetCategory|)))) (|more?| (*1 *2 *1 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Dequeue| *4)) (|ofCategory| *4 (|SetCategory|)))) (|size?| (*1 *2 *1 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Dequeue| *4)) (|ofCategory| *4 (|SetCategory|)))) (|sample| (*1 *1) (AND (|isDomain| *1 (|Dequeue| *2)) (|ofCategory| *2 (|SetCategory|)))) (|#| (*1 *2 *1) (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|Dequeue| *3)) (|ofCategory| *3 (|SetCategory|)))) (|map| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| *3 *3)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *1 (|Dequeue| *3)))) (|map!| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| *3 *3)) (|has| $ (ATTRIBUTE |shallowlyMutable|)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *1 (|Dequeue| *3)))) (|any?| (*1 *2 *3 *1) (AND (|isDomain| *3 (|Mapping| (|Boolean|) *4)) (|has| $ (ATTRIBUTE |finiteAggregate|)) (|ofCategory| *4 (|SetCategory|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Dequeue| *4)))) (|every?| (*1 *2 *3 *1) (AND (|isDomain| *3 (|Mapping| (|Boolean|) *4)) (|has| $ (ATTRIBUTE |finiteAggregate|)) (|ofCategory| *4 (|SetCategory|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Dequeue| *4)))) (|count| (*1 *2 *3 *1) (AND (|isDomain| *3 (|Mapping| (|Boolean|) *4)) (|has| $ (ATTRIBUTE |finiteAggregate|)) (|ofCategory| *4 (|SetCategory|)) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|Dequeue| *4)))) (|parts| (*1 *2 *1) (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|isDomain| *2 (|List| *3)) (|isDomain| *1 (|Dequeue| *3)) (|ofCategory| *3 (|SetCategory|)))) (|members| (*1 *2 *1) (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|isDomain| *2 (|List| *3)) (|isDomain| *1 (|Dequeue| *3)) (|ofCategory| *3 (|SetCategory|)))) (|count| (*1 *2 *3 *1) (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|Dequeue| *3)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *3 (|SetCategory|)))) (|member?| (*1 *2 *3 *1) (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Dequeue| *3)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *3 (|SetCategory|)))) (|latex| (*1 *2 *1) (AND (|isDomain| *2 (|String|)) (|isDomain| *1 (|Dequeue| *3)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *3 (|SetCategory|)))) (|hash| (*1 *2 *1) (AND (|isDomain| *2 (|SingleInteger|)) (|isDomain| *1 (|Dequeue| *3)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *3 (|SetCategory|)))) (|coerce| (*1 *2 *1) (AND (|isDomain| *2 (|OutputForm|)) (|isDomain| *1 (|Dequeue| *3)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *3 (|SetCategory|)))) (= (*1 *2 *1 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Dequeue| *3)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *3 (|SetCategory|)))) (~= (*1 *2 *1 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Dequeue| *3)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *3 (|SetCategory|)))) (|bag| (*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *1 (|Dequeue| *3)))) (|extract!| (*1 *2 *1) (AND (|isDomain| *1 (|Dequeue| *2)) (|ofCategory| *2 (|SetCategory|)))) (|insert!| (*1 *1 *2 *1) (AND (|isDomain| *1 (|Dequeue| *2)) (|ofCategory| *2 (|SetCategory|)))) (|inspect| (*1 *2 *1) (AND (|isDomain| *1 (|Dequeue| *2)) (|ofCategory| *2 (|SetCategory|)))) (|push!| (*1 *2 *2 *1) (AND (|isDomain| *1 (|Dequeue| *2)) (|ofCategory| *2 (|SetCategory|)))) (|pop!| (*1 *2 *1) (AND (|isDomain| *1 (|Dequeue| *2)) (|ofCategory| *2 (|SetCategory|)))) (|top| (*1 *2 *1) (AND (|isDomain| *1 (|Dequeue| *2)) (|ofCategory| *2 (|SetCategory|)))) (|depth| (*1 *2 *1) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|Dequeue| *3)) (|ofCategory| *3 (|SetCategory|)))) (|back| (*1 *2 *1) (AND (|isDomain| *1 (|Dequeue| *2)) (|ofCategory| *2 (|SetCategory|)))) (|front| (*1 *2 *1) (AND (|isDomain| *1 (|Dequeue| *2)) (|ofCategory| *2 (|SetCategory|)))) (|length| (*1 *2 *1) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|Dequeue| *3)) (|ofCategory| *3 (|SetCategory|)))) (|rotate!| (*1 *1 *1) (AND (|isDomain| *1 (|Dequeue| *2)) (|ofCategory| *2 (|SetCategory|)))) (|dequeue!| (*1 *2 *1) (AND (|isDomain| *1 (|Dequeue| *2)) (|ofCategory| *2 (|SetCategory|)))) (|enqueue!| (*1 *2 *2 *1) (AND (|isDomain| *1 (|Dequeue| *2)) (|ofCategory| *2 (|SetCategory|)))) (|dequeue| (*1 *1) (AND (|isDomain| *1 (|Dequeue| *2)) (|ofCategory| *2 (|SetCategory|)))) (|dequeue| (*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *1 (|Dequeue| *3)))) (|height| (*1 *2 *1) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|Dequeue| *3)) (|ofCategory| *3 (|SetCategory|)))) (|top!| (*1 *2 *1) (AND (|isDomain| *1 (|Dequeue| *2)) (|ofCategory| *2 (|SetCategory|)))) (|bottom!| (*1 *2 *1) (AND (|isDomain| *1 (|Dequeue| *2)) (|ofCategory| *2 (|SetCategory|)))) (|insertTop!| (*1 *2 *2 *1) (AND (|isDomain| *1 (|Dequeue| *2)) (|ofCategory| *2 (|SetCategory|)))) (|insertBottom!| (*1 *2 *2 *1) (AND (|isDomain| *1 (|Dequeue| *2)) (|ofCategory| *2 (|SetCategory|)))) (|extractTop!| (*1 *2 *1) (AND (|isDomain| *1 (|Dequeue| *2)) (|ofCategory| *2 (|SetCategory|)))) (|extractBottom!| (*1 *2 *1) (AND (|isDomain| *1 (|Dequeue| *2)) (|ofCategory| *2 (|SetCategory|)))) (|reverse!| (*1 *1 *1) (AND (|isDomain| *1 (|Dequeue| *2)) (|ofCategory| *2 (|SetCategory|))))) (|Join| (|DequeueAggregate| |#1|) (CATEGORY |domain| (SIGNATURE |dequeue| ($ (|List| |#1|))) (SIGNATURE |dequeue!| (|#1| $)) (SIGNATURE |extract!| (|#1| $)) (SIGNATURE |enqueue!| (|#1| |#1| $)) (SIGNATURE |insert!| ($ |#1| $)) (SIGNATURE |inspect| (|#1| $)) (SIGNATURE |front| (|#1| $)) (SIGNATURE |back| (|#1| $)) (SIGNATURE |rotate!| ($ $)) (SIGNATURE |length| ((|NonNegativeInteger|) $)) (SIGNATURE |less?| ((|Boolean|) $ (|NonNegativeInteger|))) (SIGNATURE |more?| ((|Boolean|) $ (|NonNegativeInteger|))) (SIGNATURE |size?| ((|Boolean|) $ (|NonNegativeInteger|))) (SIGNATURE |bag| ($ (|List| |#1|))) (SIGNATURE |empty?| ((|Boolean|) $)) (SIGNATURE |empty| ($)) (SIGNATURE |sample| 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$)) (SIGNATURE |cAsec| ($ $)) (SIGNATURE |cAcsc| ($ $)) (SIGNATURE |cSinh| ($ $)) (SIGNATURE |cCosh| ($ $)) (SIGNATURE |cTanh| ($ $)) (SIGNATURE |cCoth| ($ $)) (SIGNATURE |cSech| ($ $)) (SIGNATURE |cCsch| ($ $)) (SIGNATURE |cAsinh| ($ $)) (SIGNATURE |cAcosh| ($ $)) (SIGNATURE |cAtanh| ($ $)) (SIGNATURE |cAcoth| ($ $)) (SIGNATURE |cAsech| ($ $)) (SIGNATURE |cAcsch| ($ $))) |noBranch|))) @@ -3790,9 +3794,9 @@ NIL (|Join| (|Group|) (CATEGORY |domain| (SIGNATURE |cycle| ($ (|List| |t#1|))) (SIGNATURE |cycles| ($ (|List| (|List| |t#1|)))) (SIGNATURE |eval| (|t#1| $ |t#1|)) (SIGNATURE |elt| (|t#1| $ |t#1|)) (SIGNATURE |orbit| ((|Set| |t#1|) $ |t#1|)) (SIGNATURE < ((|Boolean|) $ $)) (IF (|has| |t#1| (|OrderedSet|)) (ATTRIBUTE (|OrderedSet|)) |noBranch|) (IF (|has| |t#1| (|Finite|)) (ATTRIBUTE (|OrderedSet|)) |noBranch|))) (((|BasicType|) . 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*1) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|Permutation| *3)) (|ofCategory| *3 (|SetCategory|)))) (|sign| (*1 *2 *1) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|Permutation| *3)) (|ofCategory| *3 (|SetCategory|)))) (|even?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Permutation| *3)) (|ofCategory| *3 (|SetCategory|)))) (|odd?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Permutation| *3)) (|ofCategory| *3 (|SetCategory|)))) (|sort| (*1 *2 *2) (AND (|isDomain| *2 (|List| (|Permutation| *3))) (|isDomain| *1 (|Permutation| *3)) (|ofCategory| *3 (|SetCategory|)))) (|fixedPoints| (*1 *2 *1) (AND (|isDomain| *2 (|Set| *3)) (|isDomain| *1 (|Permutation| *3)) (|ofCategory| *3 (|Finite|)) (|ofCategory| *3 (|SetCategory|)))) (|coerceImages| (*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *1 (|Permutation| *3))))) @@ -4700,10 +4704,10 @@ NIL (((|SparseMultivariatePolynomial| |#1| |#2|) 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|bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) 102) (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) 101)) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) |#4| (|List| |#4|))) 91)) (|augment| (((|List| $) |#4| $) 114) (((|List| $) |#4| (|List| $)) 113) (((|List| $) (|List| |#4|) $) 112) (((|List| $) (|List| |#4|) (|List| $)) 111)) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#4|) $) 48 (|has| $ (ATTRIBUTE |finiteAggregate|)))) (|algebraicVariables| (((|List| |#3|) $) 74)) (|algebraicCoefficients?| (((|Boolean|) |#4| $) 128)) (|algebraic?| (((|Boolean|) |#3| $) 73)) (= (((|Boolean|) $ $) 6)) (|#| (((|NonNegativeInteger|) $) 45 (|has| $ (ATTRIBUTE |finiteAggregate|))))) (((|SquareFreeNormalizedTriangularSetCategory| |#1| |#2| |#3| |#4|) (|Category|) (|GcdDomain|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|RecursivePolynomialCategory| |t#1| |t#2| |t#3|)) (T |SquareFreeNormalizedTriangularSetCategory|)) NIL @@ -4882,7 +4886,7 @@ NIL (((|SupFractionFactorizer| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |factor| ((|Factored| (|SparseUnivariatePolynomial| (|Fraction| |#4|))) (|SparseUnivariatePolynomial| (|Fraction| |#4|)))) (SIGNATURE |squareFree| ((|Factored| (|SparseUnivariatePolynomial| (|Fraction| |#4|))) (|SparseUnivariatePolynomial| (|Fraction| |#4|))))) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|GcdDomain|) (|PolynomialCategory| |#3| |#1| |#2|)) (T |SupFractionFactorizer|)) ((|squareFree| (*1 *2 *3) (AND (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|GcdDomain|)) (|ofCategory| *7 (|PolynomialCategory| *6 *4 *5)) (|isDomain| *2 (|Factored| (|SparseUnivariatePolynomial| (|Fraction| *7)))) (|isDomain| *1 (|SupFractionFactorizer| *4 *5 *6 *7)) (|isDomain| *3 (|SparseUnivariatePolynomial| (|Fraction| *7))))) (|factor| (*1 *2 *3) (AND (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|GcdDomain|)) (|ofCategory| *7 (|PolynomialCategory| *6 *4 *5)) (|isDomain| *2 (|Factored| (|SparseUnivariatePolynomial| (|Fraction| *7)))) (|isDomain| *1 (|SupFractionFactorizer| *4 *5 *6 *7)) (|isDomain| *3 (|SparseUnivariatePolynomial| (|Fraction| *7)))))) (CATEGORY |package| (SIGNATURE |factor| ((|Factored| (|SparseUnivariatePolynomial| (|Fraction| |#4|))) (|SparseUnivariatePolynomial| (|Fraction| |#4|)))) (SIGNATURE |squareFree| ((|Factored| (|SparseUnivariatePolynomial| (|Fraction| |#4|))) (|SparseUnivariatePolynomial| (|Fraction| |#4|))))) -((~= (((|Boolean|) $ $) NIL)) (|zero?| (((|Boolean|) $) 30)) (|vectorise| (((|Vector| |#1|) $ (|NonNegativeInteger|)) NIL)) (|variables| (((|List| (|SingletonAsOrderedSet|)) $) NIL)) (|unvectorise| (($ (|Vector| |#1|)) NIL)) (|unmakeSUP| (($ (|SparseUnivariatePolynomial| |#1|)) NIL)) (|univariate| (((|SparseUnivariatePolynomial| $) $ 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(|AlgebraicallyClosedField&| 16600 17188 18117 "ACF-" 18122 NIL ACF- (NIL T) |domain| NIL NIL) (|AbelianSemiGroup| 15981 16189 16251 "ABELSG" 16410 T ABELSG (NIL) |category| NIL 16518) (|AbelianSemiGroup&| 15728 15766 15909 "ABELSG-" 15914 NIL ABELSG- (NIL T) |domain| NIL NIL) (|AbelianMonoid| 14733 15060 15116 "ABELMON" 15417 T ABELMON (NIL) |category| NIL 15619) (|AbelianMonoid&| 14172 14295 14545 "ABELMON-" 14550 NIL ABELMON- (NIL T) |domain| NIL NIL) (|AbelianGroup| 13194 13622 13676 "ABELGRP" 13869 T ABELGRP (NIL) |category| NIL 14003) (|AbelianGroup&| 12401 12575 12914 "ABELGRP-" 12919 NIL ABELGRP- (NIL T) |domain| NIL NIL) (|OneDimensionalArrayAggregate| 6156 11366 11466 "A1AGG" 11471 NIL A1AGG (NIL T) |category| NIL 11565) (|OneDimensionalArrayAggregate&| 30 1630 3956 "A1AGG-" 3961 NIL A1AGG- (NIL T T) |domain| NIL NIL)) \ No newline at end of file diff --git a/src/share/algebra/operation.daase b/src/share/algebra/operation.daase index 6d6cba5..f159084 100644 --- a/src/share/algebra/operation.daase +++ b/src/share/algebra/operation.daase @@ -1,3337 +1,3342 @@ -(1577508 . 3621447416) -(((*1 *2 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|IntegerNumberTheoryFunctions|))))) -(((*1 *2 *2 *3 *4) (|partial| AND (|isDomain| *3 (|Mapping| (|Union| (|Record| (|:| |ratpart| *4) (|:| |coeff| *4)) "failed") *4)) (|ofCategory| *4 (|Field|)) (|isDomain| *1 (|TranscendentalIntegration| *4 *2)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *4))))) -(((*1 *1) (|isDomain| *1 (|Void|)))) -(((*1 *2 *1 *3) (AND (|isDomain| *3 (|List| *1)) (|ofCategory| *1 (|RecursivePolynomialCategory| *4 *5 *6)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|Boolean|)))) ((*1 *2 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Boolean|)))) ((*1 *2 *3 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(AND (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *2)) (|ofCategory| *2 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *2 (|Ring|))))) -(((*1 *1 *1) (AND (|ofCategory| *1 (|SExpressionCategory| *2 *3 *4 *5 *6)) (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|)) (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|SetCategory|))))) -(((*1 *2 *3 *4) (AND (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *3 (|PartialDifferentialRing| *5)) (|isDomain| *2 (|Matrix| *3)) (|isDomain| *1 (|MultiVariableCalculusFunctions| *5 *3 *6 *4)) (|ofCategory| *6 (|FiniteLinearAggregate| *3)) (|ofCategory| *4 (|Join| (|FiniteLinearAggregate| *5) (CATEGORY |package| (ATTRIBUTE |finiteAggregate|))))))) -(((*1 *2) (AND (|isDomain| *2 (|PermutationGroup| (|Integer|))) (|isDomain| *1 (|PermutationGroupExamples|))))) -(((*1 *1 *2 *3) (AND (|isDomain| *3 (|String|)) (|ofCategory| *1 (|FileCategory| *2 *4)) (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|)))) ((*1 *1 *2) (AND (|ofCategory| *1 (|FileCategory| *2 *3)) (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *3 (|SetCategory|))))) -(((*1 *2 *1 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|ArrayStack| *3)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *3 (|SetCategory|)))) ((*1 *2 *1 *1) (AND (|ofCategory| *1 (|BasicType|)) (|isDomain| *2 (|Boolean|)))) ((*1 *2 *1 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Dequeue| *3)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *3 (|SetCategory|)))) ((*1 *2 *1 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Heap| *3)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *3 (|OrderedSet|)))) ((*1 *2 *1 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Queue| *3)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *3 (|SetCategory|)))) ((*1 *2 *1 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Stack| *3)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *3 (|SetCategory|))))) -(((*1 *1 *1) (AND (|ofCategory| *1 (|SExpressionCategory| *2 *3 *4 *5 *6)) (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|)) (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|SetCategory|))))) -(((*1 *2 *3) (AND (|isDomain| *3 (|Mapping| *5 *4 *4)) (|ofCategory| *4 (|SetCategory|)) (|ofCategory| *5 (|SetCategory|)) (|isDomain| *2 (|Mapping| *5 *4)) (|isDomain| *1 (|MappingPackage2| *4 *5))))) -(((*1 *2 *2 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|IntegerNumberTheoryFunctions|)))) ((*1 *2 *3) (AND (|isDomain| *2 (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) (|isDomain| *1 (|PolynomialNumberTheoryFunctions|)) (|isDomain| *3 (|Integer|))))) -((|legendre| . 1577235) (|diag| . 1577032) (|car| . 1576783) (~= . 1575958) (|open| . 1575669) (|rubiksGroup| . 1575556) (|hessian| . 1575201) (|cdr| . 1574952) (|cAcos| . 1574792) (|dimensionOfIrreducibleRepresentation| . 1574654) (|var2StepsDefault| . 1574464) (|totalGroebner| . 1574292) (|cap| . 1574125) (|subs1stVar| . 1573867) (|linear| . 1573349) (|numericIfCan| . 1571981) (|internalSubPolSet?| . 1571232) (|maxrow| . 1570938) (|semiResultantEuclidean1| . 1570707) (|removeRedundantFactors| . 1569217) (|polyRing2UPUP| . 1568779) (|jacobiIdentity?| . 1568439) (|mainVariable?| . 1568165) (|comparison| . 1568030) (|mapCoef| . 1567835) (|factor1| . 1567355) (|infieldint| . 1567101) (|length| . 1565581) (|lazyPseudoRemainder| . 1565476) (|discriminant| . 1564099) (|acosIfCan| . 1563958) (|scripts| . 1563602) (|doubleFloatFormat| . 1563521) (|semiDiscriminantEuclidean| . 1563290) (|child?| . 1563132) (|countRealRootsMultiple| . 1562888) (|lcmCoef| . 1562747) (|besselJ| . 1562292) (|tracePowMod| . 1562079) (|degOneCoef| . 1561785) (|rows| . 1561207) (|coerce| . 1520690) (|symmetricRemainder| . 1520629) (|monic?| . 1520229) (|viewThetaDefault| . 1520049) (|rationalPlaces| . 1518798) (|isQuotient| . 1518499) (|encode| . 1518382) (|optAttributes| . 1517878) (|decomposeFunc| . 1517663) (|reducedForm| . 1517562) (|removeZero| . 1517306) (|shiftLeft| . 1517161) (|lfunc| . 1517078) (|iitanh| . 1516882) (|nrows| . 1516229) (|subResultantGcd| . 1515699) (|interpretString| . 1515588) (|frobenius| . 1515408) (|jordanAdmissible?| . 1515068) (|ncols| . 1514415) (|sin?| . 1514292) (|composite| . 1513839) (|listRepresentation| . 1513666) (|viewWriteAvailable| . 1513571) (|integerDecode| . 1513480) (|iiBesselK| . 1513278) (|getBadValues| . 1513158) (|mulmod| . 1513094) (|position| . 1512212) (|spherical| . 1512028) (|twoFactor| . 1511722) (|realSolve| . 1509621) (|linGenPos| . 1509277) (|showFortranOutputStack| . 1509175) (|degreeSubResultant| . 1508967) (|quotient| . 1508508) (|inverseIntegralMatrix| . 1508224) (|call| . 1508143) (|listSD| . 1507957) (|string?| . 1507680) (|ldf2vmf| . 1507528) (|reciprocalPolynomial| . 1507335) (|formula| . 1507237) (|lazyEvaluate| . 1507143) (|collectUpper| . 1506897) (|suchThat| . 1504965) (|multiplyExponents| . 1504487) (|nlde| . 1504260) (|bivariateSLPEBR| . 1503863) (|placesOfDegree| . 1501620) (|base| . 1501177) (|drawComplex| . 1500913) (|maxDegree| . 1500635) (|leadingCoefficientRicDE| . 1500172) (|coleman| . 1500012) (|getGraph| . 1499877) (|iisech| . 1499681) (|factorList| . 1499119) (|repack1| . 1498893) (|sqfree| . 1498576) (|multV| . 1498050) (|solveInField| . 1497113) (|subst| . 1496668) (|minimumExponent| . 1496508) (|component| . 1495990) (|ptFunc| . 1495646) (|df2fi| . 1495506) (|invertible?| . 1494888) (|extendIfCan| . 1494622) (|concat!| . 1494001) (|kovacic| . 1493208) (|trailingCoefficient| . 1493051) (|fortranCharacter| . 1493006) (|convert| . 1484432) (|limitedIntegrate| . 1483992) (|SturmHabichtMultiple| . 1483745) (|unitNormalize| . 1483654) (|purelyTranscendental?| . 1483368) (|and| . 1483223) (|flatten| . 1483177) (|integralBasis| . 1481445) (|cycle| . 1481316) (|imagI| . 1481113) (|positiveRemainder| . 1481052) (|replaceVarByZero| . 1480766) (|removeRoughlyRedundantFactorsInPol| . 1480476) (|transcendent?| . 1480358) (|expintfldpoly| . 1480034) (|iiasinh| . 1479838) (|cyclicEqual?| . 1479723) (|fill!| . 1479348) (|fresnelS| . 1478960) (|integrate| . 1466050) (|roughUnitIdeal?| . 1465742) (|solve| . 1448924) (|float?| . 1448647) (|removeFirstZeroes| . 1448547) (|parametrize| . 1445264) (|multiplicity| . 1444307) (|outputArgs| . 1443935) (|repeatUntilLoop| . 1443851) (|getPickedPoints| . 1443735) (|order| . 1439110) (|cAsinh| . 1438950) (|second| . 1438852) (|semiIndiceSubResultantEuclidean| . 1438576) (|makingStats?| . 1438407) (|exprToGenUPS| . 1437528) (|alternatingGroup| . 1437226) (|B1solve| . 1436522) (|birth| . 1436404) (|chartCoord| . 1436311) (|zero?| . 1435595) (|rightOne| . 1435475) (|leftDiscriminant| . 1435059) (|wrregime| . 1434406) (|firstDenom| . 1434275) (|lowerCase?| . 1434195) (|quartic| . 1433668) (|stepBlowUp| . 1432911) (|interpolate| . 1431622) (|iidsum| . 1431424) (|sec2cos| . 1431209) (|say| . 1430985) (|nodes| . 1430864) (|coHeight| . 1430543) (^= . 1430493) (|bipolar| . 1430284) (|mapmult| . 1430150) (|debug| . 1429866) (|permutationRepresentation| . 1429097) (|OMencodingBinary| . 1429047) (|sayLength| . 1428817) (|seriesToOutputForm| . 1428464) (|idealiserMatrix| . 1428154) (|socf2socdf| . 1427961) (|library| . 1427882) (|belong?| . 1426174) (|leftPower| . 1425988) (|selectIntegrationRoutines| . 1425938) (|zeroDimPrime?| . 1425566) (|operation| . 1425068) (|goto| . 1424980) (|exptMod| . 1424602) (|readIfCan!| . 1424329) (|initializeGroupForWordProblem| . 1424056) (|fullParamInit| . 1423366) (|drawCurves| . 1422888) (|graphState| . 1422635) (|bernoulli| . 1422324) (|qShiftAction| . 1422097) (|mainCoefficients| . 1421882) (|nthFlag| . 1421705) (|construct| . 1417385) (|limit| . 1415168) (|swapColumns!| . 1414945) (|leaf?| . 1414513) (|gcdPolynomial| . 1413965) (|numberOfPlacesOfDegree| . 1412556) (|displayKind| . 1412475) (|subresultantSequence| . 1412232) (|rowEch| . 1412090) (|OMputString| . 1411978) (|schwerpunkt| . 1411766) (|OMreceive| . 1411639) (|overlap| . 1411201) (|knownInfBasis| . 1410894) (|LyndonWordsList1| . 1410671) (|cot2trig| . 1410456) (|moebius| . 1410357) (|subset?| . 1410232) (|segment| . 1409938) (|trapezoidalo| . 1409638) (|loopPoints| . 1409421) (|factorOfDegree| . 1408000) (|irreducibleFactor| . 1407878) (|rischNormalize| . 1407417) (|makeSeries| . 1407172) (|nullary?| . 1407088) (|iiGamma| . 1406914) (|selectPolynomials| . 1406497) (|pseudoQuotient| . 1406354) (|closedCurve| . 1405834) (|rowEchWoZeroLines| . 1405719) (|linearAssociatedLog| . 1405341) (|removeIrreducibleRedundantFactors| . 1404972) (|removeSuperfluousQuasiComponents| . 1404285) (|screenResolution3D| . 1404211) (|getOp| . 1403824) (|setParam!| . 1403625) (|paren| . 1403352) (|viewWriteDefault| . 1403162) (|powmod| . 1403098) (|indiceSubResultant| . 1402890) (|possiblyNewVariety?| . 1402535) (|basisOfLeftAnnihilator| . 1402354) (|primitive?| . 1402071) (|horizConcat| . 1401613) (|comment| . 1401445) (|tubePointsDefault| . 1401255) (|eigenMatrix| . 1401062) (|multinomial| . 1400915) (|generalizedEigenvectors| . 1400564) (|mask| . 1400506) (|float| . 1400034) (|mkAnswer| . 1399689) (|leadingSupport| . 1399543) (|baseRDE| . 1399213) (|id| . 1399118) (|sh| . 1398754) (|perfectSquare?| . 1398626) (|ffactor| . 1398319) (|integer| . 1397942) (|whatInfinity| . 1397811) (|besselI| . 1397356) (|selectPDERoutines| . 1397306) (|zerosOf| . 1396228) (|adaptive3D?| . 1396154) (|subMatrix| . 1395344) (|leastMonomial| . 1395157) (|initParLocLeaves| . 1394467) (|clearTheIFTable| . 1394376) (|invmod| . 1394315) (|string| . 1393865) (|stop| . 1393820) (|rightTraceMatrix| . 1393314) (|rootPower| . 1392757) (|OMopenString| . 1392633) (|primitivePart!| . 1392414) (|endSubProgram| . 1392333) (|checkRur| . 1391888) (|useEisensteinCriterion?| . 1391733) (|computeInt| . 1391310) (|lineColorDefault| . 1391136) (|keys| . 1390285) (|setMinPoints3D| . 1390208) (|OMgetString| . 1390124) (|integers| . 1389956) (|commaSeparate| . 1389744) (|basisOfLeftNucleus| . 1389566) (|leftRecip| . 1389343) (|slex| . 1389184) (|uncouplingMatrices| . 1388940) (|has?| . 1388826) (|dnrm2| . 1388648) (|basisOfRightNucloid| . 1388459) (|indexName| . 1388249) (|convertIfCan| . 1388142) (|maxTower| . 1388025) (|critpOrder| . 1387640) (|extractIfCan| . 1387486) (|reduceLineOverLine| . 1387367) (|ScanFloatIgnoreSpaces| . 1387258) (|createThreeSpace| . 1387153) (|mesh?| . 1387032) (|setOfMinN| . 1386848) (|compdegd| . 1386462) (|makeFR| . 1385953) (|key| . 1385690) (|alphabetic?| . 1385610) (|df2st| . 1385241) (|degreePartition| . 1384737) (|zeroDimPrimary?| . 1384365) (|mapMatrixIfCan| . 1383963) (|LyndonWordsList| . 1383764) (|newSubProgram| . 1383655) (|coefChoose| . 1383348) (|squareFreeLexTriangular| . 1382887) (|asechIfCan| . 1382746) (|monicCompleteDecompose| . 1382506) (|edf2fi| . 1382351) (|powerSum| . 1382200) (|sum| . 1379523) (|npcoef| . 1378886) (|Not| . 1378756) (|iFTable| . 1378161) (|symbol| . 1377912) (|insertionSort!| . 1377369) (|orthonormalBasis| . 1377177) (|one| . 1376965) (|probablyZeroDim?| . 1376650) (|entry| . 1375561) (|zero| . 1375169) (|Or| . 1375033) (|complexSolve| . 1373940) (^ . 1373340) (|palgint| . 1372891) (|symbolTable| . 1372748) (|exp| . 1370481) (|pushFortranOutputStack| . 1370242) (|drawToScale| . 1370074) (|powern| . 1369866) (|queue| . 1369753) (|pi| . 1369284) (|leftAlternative?| . 1368944) (|squareFreePart| . 1368109) (|filename| . 1368015) (|sqrt| . 1367349) (|generator| . 1366265) (|rotate!| . 1366010) (|popFortranOutputStack| . 1365920) (|inconsistent?| . 1365162) (|useSingleFactorBound?| . 1365007) (|rowEchLocal| . 1364862) (|outputAsFortran| . 1363990) (|li| . 1363695) (|copyBSD| . 1363571) (|convergents| . 1363427) (|erf| . 1363132) (|color| . 1362945) (|deepExpand| . 1362734) (|edf2ef| . 1362579) (|extendedSubResultantGcd| . 1361959) (|linearDependenceOverZ| . 1361752) (|rule| . 1361090) (|createRandomElement| . 1360923) (|updatD| . 1360557) (|dilog| . 1360262) (|antisymmetric?| . 1359808) (|imagk| . 1359706) (|tab| . 1359544) (|sin| . 1358074) (|iidprod| . 1357876) (|commutator| . 1357773) (|trace2PowMod| . 1357560) (|dn| . 1357385) (|cos| . 1355915) (|ShiftAction| . 1355691) (|ruleset| . 1355335) (|bombieriNorm| . 1354671) (|newtonPolygon| . 1354269) (|tan| . 1352891) (|effective?| . 1352766) (|radix| . 1352613) (|wholeRadix| . 1352490) (|rroot| . 1351967) (|cot| . 1350772) (|lo| . 1350682) (|partialNumerators| . 1350551) (|clearTheSymbolTable| . 1350366) (|semiDegreeSubResultantEuclidean| . 1350090) (|differentiate| . 1345734) (|sec| . 1344539) (|incr| . 1344327) (|quasiMonic?| . 1344112) (|deepestTail| . 1343925) (|cotIfCan| . 1343784) (|csc| . 1342589) (|hi| . 1342499) (|zeroOf| . 1341828) (|copyIto| . 1341692) (|ravel| . 1341496) (|asin| . 1340115) (|exists?| . 1340026) (|allIndices| . 1339870) (|iflist2Result| . 1339602) (|maxMixedDegree| . 1339368) (|vector| . 1339144) (|acos| . 1337763) (|rootSimp| . 1337206) (|rootSplit| . 1336801) (|fortranLogical| . 1336756) (|resultantReduitEuclidean| . 1336470) (|atan| . 1334999) (|constantOperator| . 1334829) (|branchIfCan| . 1333840) (|set| . 1333630) (|csubst| . 1333302) (|possiblyInfinite?| . 1333184) (|acot| . 1331986) (|testModulus| . 1331775) (|sorted?| . 1331448) (|newElement| . 1330867) (|digamma| . 1330424) (|asec| . 1329226) (|trivialIdeal?| . 1328955) (|replace| . 1328840) (|Ei2| . 1328715) (|rotatey| . 1328574) (|acsc| . 1327376) (|bitLength| . 1327294) (|UP2ifCan| . 1326830) (|iisec| . 1326634) (|cSin| . 1326474) (|sinh| . 1325099) (|dihedral| . 1324948) (|e01sff| . 1324728) (|iiBesselY| . 1324526) (|packModulus| . 1324260) (|cosh| . 1322885) (|setCurve| . 1321682) (|ScanFloatIgnoreSpacesIfCan| . 1321563) (|shrinkable| . 1321302) (|lazyGintegrate| . 1321052) (|factorUsingMusser| . 1320628) (|tanh| . 1319253) (|adaptive?| . 1319181) (|mapUnivariate| . 1318520) (|repSq| . 1318330) (|qShiftC| . 1318081) (|square?| . 1317627) (|coth| . 1316435) (|enumerate| . 1316166) (|indicialEquationAtInfinity| . 1315526) (|resetNew| . 1315455) (|suppOfPole| . 1315330) (|genericRightTrace| . 1315018) (|gcdprim| . 1314875) (|sech| . 1313683) (|generate| . 1313201) (|cycleSplit!| . 1313061) (|bumptab1| . 1312890) (|incrementBy| . 1312735) (|associates?| . 1312645) (|lfinfieldint| . 1312273) (|concat| . 1311164) (|removeSinhSq| . 1310949) (|csch| . 1309757) (|shift| . 1309226) (|nodeOf?| . 1308979) (|polyRDE| . 1308516) (|OMputInteger| . 1308403) (|OMlistCDs| . 1308312) (|evalIfCan| . 1304225) (|asinh| . 1303030) (|expand| . 1301138) (|OMputApp| . 1301056) (|coshIfCan| . 1300915) (|makeSUP| . 1300762) (|eyeDistance| . 1300641) (|deriv| . 1300510) (|acosh| . 1299315) (|filterWhile| . 1299061) (|semiResultantEuclidean2| . 1298830) (|linearPolynomials| . 1298459) (|affineRationalPoints| . 1297568) (|OMputAttr| . 1297486) (|balancedBinaryTree| . 1297346) (|atanh| . 1296151) (|filterUntil| . 1295897) (|in?| . 1295275) (|resultantReduit| . 1295077) (|cubicBezier| . 1294918) (|insert!| . 1291948) (|extractPoint| . 1291801) (|acoth| . 1290606) (|select| . 1289788) (|weierstrass| . 1289581) (|showRegion| . 1289459) (|edf2df| . 1289313) (|tubeRadiusDefault| . 1289105) (|asech| . 1287910) (|oddintegers| . 1287742) (|dimensions| . 1287389) (|simpson| . 1287089) (|lists| . 1286863) (|nextPrimitiveNormalPoly| . 1286687) (|cCos| . 1286527) (|lowerCase| . 1286385) (|pseudoDivide| . 1285656) (|postfix| . 1285606) (|linears| . 1285444) (|row| . 1284732) (|semiResultantEuclideannaif| . 1284501) (|mapExpon| . 1284007) (|subQuasiComponent?| . 1282568) (|ptree| . 1282386) (|changeName| . 1282267) (|green| . 1282228) (|generalCoefficient| . 1281830) (|RemainderList| . 1281444) (|symmetric?| . 1280990) (|stirling1| . 1280871) (|generalPosition| . 1280478) (|semicolonSeparate| . 1280385) (|makeRecord| . 1280208) (|prem| . 1279828) (|Musser| . 1279617) (|leader| . 1279370) (|result| . 1279126) (|inspect| . 1278624) (|midpoint| . 1278355) (|leftRegularRepresentation| . 1278035) (|resultant| . 1277152) (|#| . 1275771) (|musserTrials| . 1275445) (|OMgetEndError| . 1275363) (|fixedPoint| . 1275031) (|extractClosed| . 1274885) (|rewriteSetByReducingWithParticularGenerators| . 1274463) (|rischDEsys| . 1273768) (|varList| . 1272393) (|genericRightNorm| . 1272081) (|restorePrecision| . 1271995) (|cyclotomicDecomposition| . 1271829) (|ratPoly| . 1271374) (|maxColIndex| . 1270907) (|prepareDecompose| . 1269880) (|createGenericMatrix| . 1269701) (|multiEuclideanTree| . 1269576) (|completeHensel| . 1269342) (|ramified?| . 1268801) (|desingTree| . 1266832) (|geometric| . 1266690) (|graphCurves| . 1266090) (|integralLastSubResultant| . 1265695) (|setelt!| . 1265355) (|eisensteinIrreducible?| . 1265197) (|mainMonomials| . 1264982) (|mdeg| . 1264756) (|pointSizeDefault| . 1264566) (|putGraph| . 1264403) (|mathieu22| . 1264140) (|quotientByP| . 1264078) (|isMult| . 1263857) (|normalizeIfCan| . 1263467) (|binomThmExpt| . 1263240) (|graphStates| . 1262791) (|blue| . 1262752) (|monomialIntPoly| . 1262494) (|maxLevel| . 1262216) (|computeCycleEntry| . 1262075) (|midpoints| . 1261788) (|setFoundPlacesToEmpty| . 1261620) (|resetVariableOrder| . 1261528) (|minPoly| . 1261070) (|mapGen| . 1260442) (|leftRank| . 1260250) (|patternMatchTimes| . 1259780) (|factorGroebnerBasis| . 1259058) (|setLegalFortranSourceExtensions| . 1258965) (LODO2FUN . 1258651) (|defineProperty| . 1258433) (|principalSubResultantSet| . 1258198) (|complexEigenvalues| . 1257966) (|getShiftRec| . 1257476) (|myDegree| . 1257061) (|findCoef| . 1256930) (|numberOfHues| . 1256849) (|explicitlyEmpty?| . 1256727) (|dot2eps| . 1256624) (|operator| . 1254706) (|retract| . 1245498) (|deleteProperty!| . 1245412) (|expPot| . 1245224) (|specialise| . 1244967) (|divisors| . 1244831) (|sinIfCan| . 1244690) (|realEigenvalues| . 1244485) (|OMlistSymbols| . 1244364) (|viewpoint| . 1242439) (|basisOfInterpolateFormsForFact| . 1241878) (|iicoth| . 1241682) (|neglist| . 1241549) (|hadamard| . 1241386) (|separateDegrees| . 1241131) (|pointColorPalette| . 1240997) (|extractIndex| . 1240840) (|writeLine!| . 1240684) (|transcendentalDecompose| . 1238769) (|returnTypeOf| . 1238602) (|endOfFile?| . 1238523) (|bfEntry| . 1238282) (|vspace| . 1238201) (|curryRight| . 1237958) (|displayAsGF| . 1237825) (|listexp| . 1237492) (|normal?| . 1236966) (|omError| . 1236833) (|elRow1!| . 1236538) (|qsetelt!| . 1236126) (|charthRoot| . 1235874) (|singularPointsWithRestriction| . 1235467) (|cycleEntry| . 1235369) (BY . 1235248) (|unaryFunction| . 1235006) (|noncommutativeJordanAlgebra?| . 1234666) (|fullOutput| . 1231891) (|truncatedmultiplication| . 1231752) (|reducedQPowers| . 1231517) (|rootsOf| . 1230706) (|numeric| . 1229129) (|makeResult| . 1228855) (|leftFactorIfCan| . 1228630) (|Gamma| . 1227906) (|parse| . 1227827) (|normalized?| . 1226807) (|extension| . 1226719) (|radical| . 1226375) (|OMputEndApp| . 1226293) (|element| . 1226010) (|prime| . 1225871) (|nthFactor| . 1225024) (|dark| . 1224948) (|phiCoord| . 1224834) (|symbol?| . 1224445) (|SFunction| . 1224285) (|curve?| . 1224164) (|represents| . 1223035) (|pureLex| . 1222828) (|perfectNthRoot| . 1222496) (|nor| . 1222398) (|OMgetAtp| . 1222316) (|index| . 1221781) (|moduloP| . 1221685) (|perspective| . 1221563) (|option?| . 1221412) (|less?| . 1220196) (|selectSumOfSquaresRoutines| . 1220146) (|innerint| . 1219506) (|point| . 1218490) (|plus| . 1218051) (|ParCond| . 1217543) (|OMgetEndObject| . 1217461) (|cAcot| . 1217301) (|light| . 1217225) (|min| . 1216736) (|positive?| . 1216259) (|characteristicSet| . 1215593) (|showTypeInOutput| . 1215492) (|diophantineSystem| . 1215147) (|maxIndex| . 1214986) (|minrank| . 1214418) (|minset| . 1214064) (|modularFactor| . 1213853) (|cosIfCan| . 1213712) (|stablePol| . 1213561) (|cyclicEntries| . 1213440) (|pointLists| . 1213327) (|readLineIfCan!| . 1213239) (|nthFractionalTerm| . 1213109) (D . 1211554) (|sncndn| . 1211310) (|patternMatch| . 1207185) (|laplace| . 1206799) (|monicRightDivide| . 1206271) (|plus!| . 1206130) (|assoc| . 1205915) (|sqfrFactor| . 1205793) (|uncorrelated?| . 1205203) (|prevPrime| . 1205095) (|lllp| . 1204946) (|isPower| . 1204098) (|yCoordinates| . 1203786) (|resize| . 1203523) (|leftLcm| . 1203229) (|guessRat| . 1196176) (|pseudoRemainder| . 1196070) (|daxpy| . 1195883) (|completeSmith| . 1195548) (|LiePoly| . 1195378) (|stosePrepareSubResAlgo| . 1194964) (|sts2stst| . 1194737) (|simplifyPower| . 1194580) (|splitDenominator| . 1192989) (|numberOfPrimitivePoly| . 1192837) (|null?| . 1192560) (|unitNormal| . 1192416) (|inf| . 1192266) (|hasTopPredicate?| . 1192151) (|leftRankPolynomial| . 1191384) (|numberOfComposites| . 1191252) (|f2df| . 1191127) (|alphanumeric| . 1191079) (|specialTrigs| . 1190793) (|constantCoefficientRicDE| . 1190299) (|stopTable!| . 1189624) (|over| . 1189574) (|space| . 1189287) (|aspFilename| . 1189196) (|listAllMonoExp| . 1188885) (|vectorise| . 1188591) (|zaxpy| . 1188380) (|third| . 1188282) (|totalDifferential| . 1188101) (|internalLastSubResultant| . 1187175) (|position!| . 1187085) (|numberRatPlacesExtDeg| . 1185676) (|prinshINFO| . 1185412) (|quotValuation| . 1185319) (|cyclePartition| . 1185198) (|zCoord| . 1185084) (|sbt| . 1184981) (|height| . 1184047) (|splitConstant| . 1183644) (|integerIfCan| . 1183503) (|foundZeroes| . 1183385) (|adjoint| . 1182350) (|permutations| . 1182206) (|integralBasisAtInfinity| . 1181935) (|brillhartTrials| . 1181617) (|dfRange| . 1181484) (|pushuconst| . 1181113) (|randomR| . 1180390) (|constantRight| . 1180150) (|contract| . 1179368) (|modTree| . 1179243) (|allDegrees| . 1179031) (|first| . 1178063) (|largest| . 1177716) (|oddlambert| . 1177223) (|removeSquaresIfCan| . 1176936) (|curryLeft| . 1176693) (|normal| . 1176559) (|key?| . 1176394) (|mulbyscalar| . 1176230) (|linear?| . 1175672) (|coerceImages| . 1175553) (|toseInvertibleSet| . 1175201) (|changeNameToObjf| . 1175085) (|mapUp!| . 1174803) (|localPointV| . 1174261) (|point?| . 1174140) (|tubePlot| . 1172849) (|addPoint2| . 1172699) (|oneDimensionalArray| . 1172448) (|find| . 1172307) (|cAsech| . 1172147) (|solveLinear| . 1171623) (|zoom| . 1171094) (|factorUsingYun| . 1170670) (|setVariableOrder| . 1170408) (|cAcoth| . 1170248) (|rationalIfCan| . 1168848) (|prologue| . 1168665) (|variationOfParameters| . 1168438) (|vertSplit| . 1167816) (|primextendedint| . 1167324) (|affineAlgSet| . 1166413) (|weakBiRank| . 1166221) (|basisOfNucleus| . 1166043) (|iipolygamma| . 1165841) (|Somos| . 1165569) (|getVariableOrder| . 1165410) (|chebyshevU| . 1165097) (|lastNonNull| . 1164970) (|unit| . 1164636) (|setright!| . 1164492) (|zeroDim?| . 1163952) (|f02aff| . 1163787) (|nextsousResultant2| . 1163615) (|right| . 1163034) (|roughSubIdeal?| . 1162723) (|withPredicates| . 1162600) (|relativeApprox| . 1162040) (|factorPolynomial| . 1161583) (|intermediateResultsIF| . 1161176) (|symmetricPower| . 1160730) (|f02aef| . 1160556) (|components| . 1160435) (|left| . 1159854) (|minPoints| . 1159617) (|alterDrift!| . 1159427) (|companionBlocks| . 1159186) (|crushedSet| . 1158899) (|basisOfCenter| . 1158721) (|kroneckerDelta| . 1158556) (|replaceDiffs| . 1158133) (|guessExpRat| . 1151080) (|f02adf| . 1150909) (|positiveSolve| . 1149421) (|objects| . 1149143) (|pointToCell| . 1148931) (|numFunEvals3D| . 1148857) (|obj| . 1148786) (|iicsc| . 1148590) (|fortranDoubleComplex| . 1148545) (|tanintegrate| . 1148146) (|compiledFunction| . 1147622) (|f02abf| . 1147454) (|infiniteProduct| . 1146568) (|monicLeftDivide| . 1146040) (|zRange| . 1145924) (|setButtonValue| . 1145694) (|pfaffian| . 1145467) (|f02aaf| . 1145302) (|internalInfRittWu?| . 1144553) (|removeSinSq| . 1144338) (|primitiveElement| . 1142398) (|squareMatrix| . 1142243) (|dmp2rfi| . 1141079) (|inGroundField?| . 1140961) (|shiftRoots| . 1140798) (|lfextlimint| . 1140288) (|cLog| . 1140128) (|taylor| . 1136277) (|contractSolve| . 1135621) (|clikeUniv| . 1135403) (|sinhIfCan| . 1135262) (|augment| . 1134071) (|measure| . 1129161) (|balancedFactorisation| . 1128690) (|unravel| . 1128494) (|rightFactorIfCan| . 1128227) (|distinguishedRootsOf| . 1127831) (|laurent| . 1124684) (|match| . 1123342) (|variableOf| . 1123164) (|var1StepsDefault| . 1122974) (|rootNormalize| . 1122614) (|setleaves!| . 1122485) (|iisqrt2| . 1122292) (|showTheIFTable| . 1122232) (|froot| . 1121677) (|puiseux| . 1118501) (|unitsColorDefault| . 1118327) (|showArrayValues| . 1118250) (|delta| . 1118064) (|showAllElements| . 1117920) (|makeFloatFunction| . 1117482) (|graeffe| . 1117289) (|genusTree| . 1116571) (|nextNormalPoly| . 1116395) (|elem?| . 1116276) (|psolve| . 1109608) (|hue| . 1109348) (|tanAn| . 1109168) (|elements| . 1108984) (|coerceP| . 1108778) (|zeta| . 1108695) (|moduleSum| . 1108309) (|primintegrate| . 1107890) (|polynomial| . 1107093) (|romberg| . 1106793) (|lexico| . 1106437) (|move| . 1106168) (|complexForm| . 1105483) (|polygon?| . 1105362) (|quadTransform| . 1104942) (|bipolarCylindrical| . 1104733) (|integralCoordinates| . 1104421) (|primaryDecomp| . 1103869) (|tensorProduct| . 1103354) (|columns| . 1102776) (|stFunc2| . 1102478) (|selectsecond| . 1102354) (|factorSFBRlcUnit| . 1101627) (|integerBound| . 1101408) (|factorial| . 1101060) (|approximants| . 1100916) (|guessRec| . 1093863) (|algebraicCoefficients?| . 1093577) (|signAround| . 1092833) (|push!| . 1092479) (|allRootsOf| . 1091437) (|Ei6| . 1091312) (|stiffnessAndStabilityFactor| . 1091100) (|expenseOfEvaluationIF| . 1090693) (|clip| . 1089351) (|linkToFortran| . 1088504) (UTS2UP . 1088191) (|checkExtraValues| . 1087979) (|rightMinimalPolynomial| . 1087775) (|fractRadix| . 1087649) (|cPower| . 1087486) (|machineFraction| . 1087391) (|makeGraphImage| . 1086789) (|linSolve| . 1086338) (|associator| . 1086276) (|fintegrate| . 1085712) (|indicialEquation| . 1084959) (|numFunEvals| . 1084887) (|evalat| . 1084748) (|cAcsc| . 1084588) (|iitan| . 1084392) (|lambda| . 1084301) (|identification| . 1084040) (|ODESolve| . 1083603) (|returnType!| . 1083060) (|listOfMonoms| . 1082842) (|removeRedundantFactorsInContents| . 1082520) (|normal01| . 1082430) (|aromberg| . 1082127) (|newLine| . 1082046) (|previous| . 1081950) (|cAcosh| . 1081790) (|scale| . 1081308) (|recip| . 1079324) (|numberPlacesDegExtDeg| . 1077906) (|minRowIndex| . 1077439) (|pushdown| . 1076335) (|pseudoRem| . 1076195) (|genus| . 1073733) (|randomLC| . 1073380) (|bringDown| . 1072841) (|sumSquares| . 1072705) (|tomodpa| . 1072513) (|samplePoint| . 1072249) (|nextSublist| . 1071855) (|complexNumericIfCan| . 1068800) (|cAsin| . 1068640) (|dequeue| . 1068243) (|block| . 1068148) (|generalInterpolation| . 1066181) (|rangePascalTriangle| . 1065923) (|revert| . 1065430) (|evalADE| . 1064989) (|join| . 1064858) (|unmakeSUP| . 1064705) (|purelyAlgebraicLeadingMonomial?| . 1064419) (|principal?| . 1064111) (|whileLoop| . 1064027) (|redPol| . 1063757) (|OMgetEndAtp| . 1063675) (|selectNonFiniteRoutines| . 1063625) (|leadingIndex| . 1063152) (|even?| . 1062811) (|po| . 1062655) (|simpsono| . 1062355) (|createIrreduciblePoly| . 1062153) (|modularGcd| . 1061891) (|FormatRoman| . 1061772) (|isOp| . 1061412) (|llprop| . 1061255) (|OMgetEndAttr| . 1061173) (|toseSquareFreePart| . 1060781) (|subs2ndVar| . 1060523) (|headReduce| . 1060080) (|logIfCan| . 1059939) (|rightTrace| . 1059822) (|guessADE| . 1052769) (|inc| . 1052711) (|OMputVariable| . 1052599) (|squareFreePrim| . 1052323) (|binaryFunction| . 1052047) (|factorset| . 1051702) (|zeroSetSplitIntoTriangularSystems| . 1051343) (|univariatePolynomials| . 1050972) (|copyInto!| . 1050800) (|fortranComplex| . 1050755) (|setsubMatrix!| . 1050529) (|outputAsScript| . 1050285) (|rename!| . 1050191) (** . 1044347) (|OMputEndBVar| . 1044265) (|ricDsolve| . 1040806) (|euclideanNormalForm| . 1040524) (|LowTriBddDenomInv| . 1040263) (|remainder!| . 1040102) (|sechIfCan| . 1039961) (|rewriteSetWithReduction| . 1039588) (|OMencodingUnknown| . 1039538) (|prepareSubResAlgo| . 1039134) (|normalForm| . 1038547) (|tanh2trigh| . 1038332) (|Hausdorff| . 1038067) (|fortranDouble| . 1038022) (|DiffC| . 1037776) (|blockConcat| . 1037498) (|listAllMono| . 1037216) (|halfExtendedSubResultantGcd2| . 1036664) (|sub| . 1036614) (|subHeight| . 1036533) (RF2UTS . 1036193) (|numberOfIrreduciblePoly| . 1036041) (|genericRightDiscriminant| . 1035732) (|iiBesselI| . 1035530) (|symbNameV| . 1034996) (|LyndonBasis| . 1034702) (|complexLimit| . 1033733) (|htrigs| . 1033518) (|e01sbf| . 1033259) (|setlast!| . 1033116) (|quasiRegular| . 1032869) (|removeCoshSq| . 1032654) (|critBonD| . 1032288) (|quotVecSpaceBasis| . 1032163) (|internalSubQuasiComponent?| . 1031450) (|getExplanations| . 1031328) (|toseInvertible?| . 1030578) (|pdct| . 1030498) (|viewDeltaYDefault| . 1030318) (|maxShift| . 1030040) (|rationalPower| . 1029822) (|leastPower| . 1029503) (|isTimes| . 1028569) (|zeroSetSplit| . 1024871) (|freeOf?| . 1024460) (|algebraicDecompose| . 1023512) (|atoms| . 1023286) (|mkIntegral| . 1022977) (|finiteSeries2LinSys| . 1022727) (|resultantEuclideannaif| . 1022479) (|palginfieldint| . 1022014) (|OMUnknownSymbol?| . 1021926) (|aQuadratic| . 1021689) (|more?| . 1020633) (|pair?| . 1020356) (|scanOneDimSubspaces| . 1020104) (|foundPlaces| . 1019936) (|irreducibleFactors| . 1019570) (|mapExponents| . 1019100) (|getDomains| . 1018968) (|alphanumeric?| . 1018888) (|canonicalIfCan| . 1018741) (|diff| . 1018329) (|monomial?| . 1017413) (|usingTable?| . 1017244) (|noKaratsuba| . 1017070) (|adjunctionDivisor| . 1015214) (|explogs2trigs| . 1014821) (|morphism| . 1014455) (|hexDigit?| . 1014375) (|guessHolo| . 1010040) (|zeroMatrix| . 1009513) (|width| . 1009210) (|rootOf| . 1007714) (|sparsityIF| . 1007571) (|listOfTerms| . 1006922) (|gbasis| . 1006621) (|iiacos| . 1006425) (|curry| . 1006225) (|e02bcf| . 1006020) (|quadraticForm| . 1005857) (|showTheSymbolTable| . 1005809) (|monicModulo| . 1005517) (|untab| . 1005337) (|updatF| . 1004964) (|octon| . 1004715) (|dictionary| . 1004489) (|palgint0| . 1003474) (|trapezoidal| . 1003174) (|internalAugment| . 1001913) (|csc2sin| . 1001698) (|e02bbf| . 1001496) (|pToHdmp| . 1001273) (|mat| . 1001080) (|numberOfMonomials| . 1000585) (|qinterval| . 1000432) (|e02baf| . 1000256) (|setMinPoints| . 1000181) (|cubic| . 999657) (|aQuartic| . 999414) (|imagE| . 999312) (|leadingTerm| . 999134) (|SturmHabichtSequence| . 998891) (|nilFactor| . 998769) (|rules| . 998413) (|leastAffineMultiple| . 998247) (|clearFortranOutputStack| . 998145) (|external?| . 998063) (|guessPade| . 993728) (|e02akf| . 993517) (|normDeriv2| . 993192) (|complexElementary| . 991919) (|qfactor| . 991549) (|anfactor| . 991128) (|pattern| . 990811) (|e02ajf| . 990594) (|transcendenceDegree| . 990273) (|internalZeroSetSplit| . 989512) (|cycleRagits| . 989389) (|addMatch| . 989217) (|homogenize| . 987412) (|desingTreeWoFullParam| . 986132) (|iicos| . 985936) (|getCode| . 985850) (|e04ycf| . 985634) (|cache| . 985518) (|resultantEuclidean| . 985270) (|sinhcosh| . 985029) (|lcm| . 984714) (|viewSizeDefault| . 984506) (|perfectSqrt| . 984396) (|doubleRank| . 984204) (|setProperties| . 984089) (|lowerPolynomial| . 983760) (|classNumber| . 982472) (|e04ucf| . 981928) (|orbits| . 981797) (|meshPar2Var| . 980766) (|children| . 980486) (|e04naf| . 980077) (|finite?| . 979747) (|roughBasicSet| . 979350) (|nextsubResultant2| . 979117) (|column| . 978644) (|separant| . 978397) (|ScanRoman| . 978278) (|numerators| . 978147) (|safety| . 977913) (|setmult!| . 977384) (|e04mbf| . 977151) (|lighting| . 977024) (|resetBadValues| . 976937) (|lhs| . 976427) (|rquo| . 975519) (|highCommonTerms| . 975315) (|radPoly| . 974973) (|lepol| . 974706) (|center| . 974165) (|nullary| . 974039) (|fixPredicate| . 973741) (|e04jaf| . 973476) (|polCase| . 973129) (|partialQuotients| . 972998) (|chartV| . 972493) (|toScale| . 972281) (|coord| . 971651) (|e04gcf| . 971392) (|OMsetEncoding| . 971270) (|listVariable| . 970990) (|radicalSolve| . 968725) (|setlocalParam!| . 968187) (|extendedEuclidean| . 967908) (|genericLeftNorm| . 967596) (|generalizedInverse| . 967340) (|e04fdf| . 967081) (|compactFraction| . 966982) (|internal?| . 966836) (|firstSubsetGray| . 966699) (|splitSquarefree| . 966419) (|tan2cot| . 966204) (|startPolynomial| . 965935) (|fullPartialFraction| . 965712) (|systemCommand| . 965599) (|e04dgf| . 965256) (|cothIfCan| . 965115) (|pointPlot| . 964449) (|plenaryPower| . 964303) (|bitCoef| . 964218) (|log10| . 963912) (|f01ref| . 963685) (|singularPoints| . 962072) (|interReduce| . 961785) (|mkPrim| . 961537) (|subResultantGcdEuclidean| . 961295) (|OMconnInDevice| . 961199) (|goodPoint| . 960959) (|localParamV| . 960424) (|f01rdf| . 960188) (|bivariate?| . 959901) (|alphabetic| . 959853) (|antisymmetricTensors| . 959433) (|fixedDivisor| . 959272) (|f01rcf| . 959081) (|slope| . 958135) (|extendedResultant| . 957843) (|qelt| . 957236) (|OMconnOutDevice| . 957140) (|interpolateFormsForFact| . 955130) (|ShiftC| . 954884) (|colorFunction| . 954503) (|cCot| . 954343) (|f01qef| . 954128) (|Beta| . 953481) (|bubbleSort!| . 952938) (|OMgetObject| . 952856) (|poisson| . 952714) (|hypergeometric0F1| . 952495) (|hex| . 952391) (|filterUpTo| . 952260) (|f01qdf| . 952036) (|explimitedint| . 951481) (|allPairsAmong| . 950935) (|palglimint| . 950364) (|cylindrical| . 950180) (|divisor| . 948682) (|leftMinimalPolynomial| . 948478) (|trim| . 948290) (|f01qcf| . 948111) (|routines| . 948064) (|polar| . 947880) (|setCondition!| . 947701) (|f01mcf| . 947483) (|csch2sinh| . 947268) (|tanSum| . 947149) (|selectODEIVPRoutines| . 947099) (|torsion?| . 946254) (|OMopenFile| . 946127) (|physicalLength| . 945844) (|search| . 945697) (|init| . 945466) (|dequeue!| . 945211) (|f01maf| . 944906) (E1 . 944749) (|tValues| . 944650) (|removeRedundantFactorsInPols| . 944328) (|blowUpWithExcpDiv| . 943638) (|setrest!| . 943385) (|f01bsf| . 943083) (|empty| . 942113) (|getMeasure| . 942001) (|replaceKthElement| . 941844) (|datalist| . 941729) (|computePowers| . 941540) (|f01brf| . 941204) (|headRemainder| . 940864) (|listLoops| . 940700) (|modifyPoint| . 940102) (|rationalApproximation| . 939569) (|determinant| . 938582) (|extensionDegree| . 937894) (|hdmpToP| . 937671) (|diffHP| . 924447) (|OMcloseConn| . 924361) (|outputAsTex| . 924117) (|interpolateForms| . 922087) (|leftTrace| . 921970) (|shallowExpand| . 921759) (|singular?| . 921218) (|packExps| . 921011) (|functionIsContinuousAtEndPoints| . 920390) (|bsolve| . 919547) (|weights| . 918957) (|FormatArabic| . 918838) (|smith| . 918590) (|unit?| . 918503) (|multiEuclidean| . 918402) (|copyQuadVar| . 918190) (|normalise| . 918074) (|tryFunctionalDecomposition?| . 917919) (|decompose| . 915059) (|rightRemainder| . 914921) (|setchart!| . 914413) (|ratDsolve| . 912606) (|cross| . 912301) (|central?| . 912120) (|dioSolve| . 911800) (|unrankImproperPartitions0| . 911651) (|fractRagits| . 911526) (|stoseInvertibleSetreg| . 911164) (|triangulate| . 910487) (|Ei4| . 910362) (|negative?| . 909885) (|parametric?| . 909810) (|size?| . 908921) (|hermiteH| . 908766) (|innerEigenvectors| . 908315) (|variablesOf| . 908191) (|generalizedEigenvector| . 907423) (|atanIfCan| . 907282) (|cschIfCan| . 907141) (|makeCell| . 906820) (|vconcat| . 906680) (|pastel| . 906604) (|isPlus| . 905663) (|createNormalElement| . 905532) (|iiBesselJ| . 905330) (|origin| . 905238) (|cyclotomicFactorization| . 905068) (|leftTrim| . 904880) (|basisOfMiddleNucleus| . 904702) (|rightUnits| . 904075) (|evaluate| . 903084) (|gcdBasisAdd| . 902876) (|elliptic| . 902116) (|directSum| . 901748) (|palgLODE| . 901145) (|startTableGcd!| . 900380) (|upperCase!| . 900326) (|distdfact| . 900009) (|startTableInvSet!| . 899244) (|goodnessOfFit| . 898906) (|value| . 898482) (|minPol| . 897822) (|solveLinearPolynomialEquationByRecursion| . 897108) (|upDateBranches| . 895825) (|low| . 895735) (|additive?| . 895582) (|complement| . 895453) (|dim| . 895377) (|outlineRender| . 895255) (|selectfirst| . 895131) (|evaluateInverse| . 894853) (|drawStyle| . 894731) (|powerAssociative?| . 894589) (|lookup| . 894321) (|numberOfVariables| . 893466) (|properties| . 893354) (|getMultiplicationTable| . 892576) (|divergence| . 892251) (|print| . 892065) (|lastSubResultantElseSplit| . 891763) (|wordsForStrongGenerators| . 891610) (|copyDrift| . 891398) (|ef2edf| . 891243) (|palglimint0| . 889984) (|edf2efi| . 889814) (|sup| . 889602) (|localParam| . 889431) (|optional?| . 889316) (|minIndex| . 889155) (|rootKerSimp| . 888519) (|maxrank| . 887951) (|izamax| . 887765) (|factorByRecursion| . 887069) (|subResultantChain| . 886814) (|pade| . 885899) (|OMgetInteger| . 885814) (|diagonal?| . 885360) (|distribute| . 885252) (|dom| . 885174) (|exteriorDifferential| . 885027) (|tubePoints| . 884799) (|iiasech| . 884603) (|hitherPlane| . 884482) (|degreeOfMinimalForm| . 884228) (|OMgetType| . 884144) (|script| . 883780) (|atanhIfCan| . 883639) (|skewSFunction| . 883476) (|setsubmult!| . 882947) (|moebiusMu| . 882848) (|cCosh| . 882688) (|constDsolve| . 882160) (|coordinates| . 880034) (LE . 879816) (|exactQuotient!| . 879365) (|checkForZero| . 878474) (|common| . 878354) (|mergeDifference| . 878234) (|ReduceOrder| . 877817) (|numberOfFactors| . 877440) (|symbolIfCan| . 877318) (|basisOfLeftNucloid| . 877129) (|primPartElseUnitCanonical| . 876905) (|getButtonValue| . 876790) (|declare| . 876672) (|irreducibleRepresentation| . 876143) (|mulbybinomial| . 875821) (|chebyshevT| . 875508) (|moreAlgebraic?| . 874815) (|tube| . 874411) (|limitedint| . 873991) (|mainVariables| . 873720) (|clipBoolean| . 873586) (|scalarTypeOf| . 873452) (|bright| . 873169) (|mainForm| . 873068) (|tab1| . 872891) (|tensorMap| . 872730) (|mr| . 872426) (|bezoutDiscriminant| . 872092) (|OMputEndBind| . 872010) (|coefficientSet| . 871778) (|finiteBound| . 871593) (|iiabs| . 871419) (|contains?| . 871238) (|getGoodPrime| . 870967) (|invertIfCan| . 870659) (|imagJ| . 870456) (|delete!| . 870176) (|LiePolyIfCan| . 869803) (|universe| . 869677) (|backOldPos| . 869315) (|output| . 868793) (|monicDecomposeIfCan| . 868511) (|high| . 868421) (|solveLinearPolynomialEquationByFractions| . 868164) (|yCoord| . 868050) (|fortran| . 867838) (|eigenvectors| . 867451) (|polarCoordinates| . 867203) (|Ei5| . 867078) (|relationsIdeal| . 866679) (|Ci| . 866384) (|denomRicDE| . 866006) (|iteratedInitials| . 865791) (|unvectorise| . 865186) (|OMputError| . 865104) (|createPrimitivePoly| . 864902) (|outputGeneral| . 864723) (|lyndon?| . 864565) (|times!| . 864424) (|viewPhiDefault| . 864244) (|symmetricGroup| . 863942) (|OMParseError?| . 863854) (|integralDerivationMatrix| . 863508) (|projectionSet| . 863267) (|prinpolINFO| . 862975) (|monomials| . 862181) (|supersub| . 862085) (|algebraic?| . 861686) (|findOrderOfDivisor| . 859888) (|ref| . 859806) (|definingInequation| . 859573) (|radicalOfLeftTraceForm| . 859395) (|axServer| . 859232) (|subPolSet?| . 858483) (|rationalFunction| . 858041) (|guessAlg| . 853706) (|resultantnaif| . 853540) (|setnext!| . 853399) (|viewPosDefault| . 853185) (|primlimintfrac| . 852784) (|posExpnPart| . 852684) (|hdmpToDmp| . 852435) (|radicalEigenvectors| . 852137) (|getOrder| . 851958) (|sincos| . 851719) (|setRealSteps| . 851637) (|linearlyDependent?| . 851427) (|exprHasAlgebraicWeight| . 851098) (Y . 850661) (|rotate| . 850414) (|LagrangeInterpolation| . 850219) (|nextPartition| . 849883) (|roman| . 849721) (|setValue!| . 849542) (|iiacsc| . 849346) (|distFact| . 848704) (|var1Steps| . 848476) (|genericRightTraceForm| . 848161) (|normInvertible?| . 847770) (|messagePrint| . 847665) (|univariate?| . 847378) (|root?| . 847232) (|palgextint0| . 846147) (|groebnerFactorize| . 844700) (|exprHasLogarithmicWeights| . 844394) (|euclideanSize| . 844295) (|printStatement| . 844201) (|nextPrimitivePoly| . 844025) (|list?| . 843748) (|pushucoef| . 843331) (|logical?| . 843243) (|palgRDE| . 842749) (|bits| . 842397) (|nthExponent| . 842275) (|bitTruth| . 842162) (|swapRows!| . 841939) (|changeVar| . 841161) (|truncatedmuladd| . 840994) (|characteristic| . 839308) (|packageCall| . 839159) (|primextintfrac| . 838832) (|setAttributeButtonStep| . 838747) (|lyndon| . 838617) (|squareFreePolynomial| . 838160) (|hasHi| . 838043) (|pile| . 837950) (|tan2trig| . 837735) (|critMTonD1| . 837372) (|changeBase| . 837045) (|leadingBasisTerm| . 836783) (|lfextendedint| . 836345) (|reduceRowOnList| . 836192) (|airyAi| . 835749) (|conjugates| . 835633) (|getEq| . 835280) (|harmonic| . 835140) (|lagrange| . 834647) (|rotatez| . 834506) (|redPo| . 834177) (|pmComplexintegrate| . 833598) (|atom?| . 833321) (|stronglyReduce| . 833065) (|divide!| . 832901) (|OMreadStr| . 832792) (|mapDown!| . 832501) (|linearBezier| . 832348) (|partialDenominators| . 832217) (|raisePolynomial| . 831888) (|closeComponent| . 831688) (|OMreadFile| . 831579) (|nextPrime| . 831471) (|symmetricProduct| . 831103) (|ramifMult| . 831010) (|associatedSystem| . 830693) (|clipWithRanges| . 830399) (|systemSizeIF| . 829992) (|quasiMonicPolynomials| . 829621) (|pointColorDefault| . 829447) (|clearDenominator| . 828558) (|laurentRep| . 828381) (|cyclic| . 828230) (|binaryTree| . 828047) (|initializeParamOfPlaces| . 826635) (|inverseIntegralMatrixAtInfinity| . 826351) (|node?| . 826193) (|prime?| . 825457) (|cup| . 825331) (|sdf2lst| . 824902) (|createPrimitiveNormalPoly| . 824700) (|setleft!| . 824556) (|ellipticCylindrical| . 824347) (|rightCharacteristicPolynomial| . 824180) (|rootBound| . 823838) (|infinityNorm| . 823524) (|ignore?| . 823167) (|traceMatrix| . 822543) (|rarrow| . 822493) (|range| . 822281) (|internalIntegrate0| . 821872) (|palgRDE0| . 820773) (|bumptab| . 820553) (|doubleDisc| . 820318) (|leaves| . 820197) (|constantIfCan| . 820026) (|radicalEigenvalues| . 819845) (|complexZeros| . 819144) (|factorAndSplit| . 818985) (|lieAdmissible?| . 818645) (|cSinh| . 818485) (|meshFun2Var| . 818071) (|theCurve| . 816877) (|lexGroebner| . 816705) (GE . 816487) (|removeRoughlyRedundantFactorsInPols| . 815879) (|jordanAlgebra?| . 815539) (|antiCommutative?| . 815199) (|charpol| . 814934) (|maxPoints| . 814697) (|binomial| . 814123) (|pushup| . 813019) (|points| . 812860) (|fglmIfCan| . 812443) (|smaller?| . 812357) (|normalizeAtInfinity| . 812083) (|setFormula!| . 811982) (|unparse| . 811903) (|interpret| . 811708) (|inverseColeman| . 811548) (|palgLODE0| . 810285) (|approxSqrt| . 810185) (|const| . 810019) (|cardinality| . 809880) (|element?| . 809621) (|OMsupportsCD?| . 809508) (|assert| . 809089) (|thetaCoord| . 808975) (|quasiAlgebraicSet| . 808711) (|setAdaptive| . 808636) (|red| . 808597) (|nand| . 808499) (|dcabs1| . 808368) (|cartesian| . 808184) (|functionIsOscillatory| . 807881) (|sturmVariationsOf| . 807619) (|surface| . 807523) (|setClipValue| . 807437) (|fortranInteger| . 807392) (|tex| . 807304) (|nextNormalPrimitivePoly| . 807128) (|iicosh| . 806932) (|write!| . 806798) (|taylorQuoByVar| . 806693) (|imagj| . 806591) (|removeCosSq| . 806376) (|xCoord| . 806262) (|submod| . 806198) (|structuralConstants| . 804982) (|pleskenSplit| . 804498) (|integralMatrix| . 804214) (|ddFact| . 803980) (|deref| . 803898) (|imagK| . 803695) (|conditionP| . 803374) (|purge!| . 803175) (|every?| . 801980) (|bfKeys| . 801890) (|dasum| . 801712) (|projection| . 801614) (|btwFact| . 801233) (|rk4f| . 800946) (|outputFloating| . 800767) (|setFoundZeroes| . 800646) (|exponential| . 800283) (|sizePascalTriangle| . 800154) (|chineseRemainder| . 799235) (|complexEigenvectors| . 798898) (|certainlySubVariety?| . 798580) (|currentSubProgram| . 798499) (|janko2| . 798236) (|evenlambert| . 797743) (|MPtoMPT| . 797494) (|Si| . 797199) (|removeDuplicates!| . 796971) (|pToDmp| . 796759) (|uniform01| . 796669) (|failed?| . 796300) (|sinh2csch| . 796085) (|logGamma| . 795872) (|df2ef| . 795732) (|simpleBounds?| . 795589) (|removeZeroes| . 794290) (|check| . 793534) (|calcRanges| . 793369) (|firstNumer| . 793270) (|viewport2D| . 793214) (|sPol| . 792860) (|mainKernel| . 792760) (|insertTop!| . 792579) (|normalDeriv| . 792269) (|increment| . 792117) (|indicialEquations| . 790324) (|numberOfValuesNeeded| . 789898) (|setPoly| . 789760) (|OMputEndObject| . 789678) (|level| . 789521) (|reseed| . 789407) (|finiteBasis| . 789107) (|tablePow| . 788833) (|magnitude| . 788679) (|quote| . 788592) (|close!| . 788420) (|leftMult| . 788265) (|medialSet| . 787599) (|newton| . 787419) (|iisqrt3| . 787226) (|algSplitSimple| . 786854) (|groebnerIdeal| . 786598) (|eq?| . 785943) (|mesh| . 784655) (|multiServ| . 784544) (|retractable?| . 783733) (|fffg| . 783292) (|expintegrate| . 782859) (|anticoord| . 782563) (|setchildren!| . 782397) (|gradient| . 782042) (|idealSimplify| . 781809) (|maxint| . 781629) (|delete| . 781369) (|accuracyIF| . 780962) (|leftNorm| . 780845) (|maxSubst| . 780573) (|nsqfree| . 780048) (|vertConcat| . 779590) (|applyTransform| . 779283) (|OMputEndAttr| . 779201) (|rightRankPolynomial| . 778434) (|subResultantsChain| . 778230) (|wronskianMatrix| . 777769) (|getMatch| . 777590) (|OMread| . 777473) (|curveColor| . 777316) (|complexExpand| . 776668) (|reopen!| . 776507) (|padecf| . 776202) (|setTower!| . 776088) (|lllip| . 775929) (|split| . 773856) (|maximumExponent| . 773696) (|reindex| . 773488) (|parabolicCylindrical| . 773304) (|numberOfDivisors| . 773205) (|addPointLast| . 773010) (|leftDivide| . 772276) (|definingPolynomial| . 771032) (|dzasum| . 770842) (|quoted?| . 770727) (|bezoutResultant| . 770390) (|rotatex| . 770249) (|setpoint!| . 769741) (|parent| . 769623) (|elColumn2!| . 769325) (|iicsch| . 769129) (|tanQ| . 768758) (= . 767607) (|shanksDiscLogAlgorithm| . 767377) (|substring?| . 767255) (|unprotectedRemoveRedundantFactors| . 766965) (|rename| . 766871) (|translate| . 765848) (|quadraticNorm| . 765534) (|flush| . 765378) (|orderIfNegative| . 765240) (|table| . 764912) (|doubleComplex?| . 764824) (|minPoints3D| . 764750) (|randnum| . 764578) (|rightGcd| . 764440) (|coth2trigh| . 764225) (|chiSquare| . 764081) (< . 763573) (|upperCase?| . 763493) (|associatorDependence| . 763094) (|fullOut| . 761964) (|gderiv| . 761787) (|vectorcombination| . 761614) (|rowEchelon| . 759706) (> . 759573) (|ranges| . 759126) (|d03faf| . 758787) (|mapUnivariateIfCan| . 758426) (|viewZoomDefault| . 758246) (|setfirst!| . 758103) (|aColumn| . 757823) (|coordinate| . 757427) (<= . 757045) (|infClsPt?| . 756952) (|d03eef| . 756575) (|coercePreimagesImages| . 756447) (|sizeLess?| . 756356) (|expandPower| . 756141) (|validExponential| . 755732) (|nary?| . 755648) (>= . 755515) (|next| . 755419) (|integralRepresents| . 755142) (|d03edf| . 754904) (|beauzamyBound| . 754562) (|iExquo| . 754413) (|errorKind| . 754319) (|saturate| . 753829) (|iiAiryAi| . 753655) (|basisOfRightNucleus| . 753477) (|integralAtInfinity?| . 753205) (|setvalue!| . 753067) (|algDsolve| . 752532) (|standardBasisOfCyclicSubmodule| . 752297) (|pushdterm| . 751895) (|functionName| . 751685) (|suffix?| . 751594) (|setPrologue!| . 751405) (|optpair| . 751268) (|Lazard2| . 751057) (|primitiveRowEchelon| . 750727) (|assign| . 746265) (+ . 743570) (|readable?| . 743481) (|prolateSpheroidal| . 743272) (|problemPoints| . 742770) (|roughBase?| . 742462) (|argumentList!| . 742051) (- . 739231) (|rCoord| . 739117) (|subNodeOf?| . 738821) (|OMserve| . 738695) (|yellow| . 738656) (|ode1| . 738428) (/ . 734335) (|char| . 734179) (|realZeros| . 731908) (|antiCommutator| . 731849) (|hspace| . 731768) (|lSpaceBasis| . 731468) (|reverseLex| . 731261) (|makeSketch| . 731060) (|OMclose| . 730978) (|blockSplit| . 729608) (|LyndonCoordinates| . 729314) (|nonLinearPart| . 729199) (|hclf| . 729010) (|complete| . 728438) (|insertRoot!| . 728340) (|quadratic| . 727819) (|modulus| . 726669) (|true| . 726628) (|isExpt| . 725002) (|pole?| . 724683) (|changeMeasure| . 724568) (|pivots| . 724357) (|numberOfNormalPoly| . 724205) (|pascalTriangle| . 724042) (|ratpart| . 723951) (|startTable!| . 723204) (|cSech| . 723044) (|inRadical?| . 722785) (|exponent| . 722001) (|mainVariableOf| . 721886) (|lazyVariations| . 721590) (|localize| . 721001) (|selectAndPolynomials| . 720575) (|setTex!| . 720484) (|tubeRadius| . 720276) (|controlPanel| . 720037) (|localAbs| . 718974) (|mainPrimitivePart| . 718755) (|findCycle| . 718504) (|direction| . 718364) (|newReduc| . 718144) (|lastSubResultant| . 717289) (|setStatus| . 717006) (|generalizedContinuumHypothesisAssumed?| . 716924) (|c05nbf| . 716641) (|prefix?| . 716550) (|equation| . 715815) (|pol| . 715617) (|qnew| . 715015) (|createZechTable| . 714804) (|c05adf| . 714566) (|map| . 689158) (|cAtan| . 688998) (|DiffAction| . 688774) (|univcase| . 688495) (|c06gsf| . 688320) (|numberOfChildren| . 688163) (|redpps| . 687665) (|c06gqf| . 687490) (|completeHermite| . 687179) (|rur| . 685559) (|c06gcf| . 685387) (|guessPRec| . 678334) (|Ei| . 677917) (|c06gbf| . 677745) (|hcrf| . 677556) (|mathieu11| . 677293) (|c06fuf| . 677079) (|cRationalPower| . 676897) (|subSet| . 676748) (|c06frf| . 676537) (|viewDefaults| . 676453) (|nextIrreduciblePoly| . 676277) (|c06fqf| . 676069) (|pquo| . 675689) (|leftUnits| . 675062) (|eval| . 664074) (|c06fpf| . 663866) (|member?| . 662397) (|complexNormalize| . 661124) (|c06ekf| . 660946) (|leftOne| . 660826) (|lifting1| . 660123) (|empty?| . 659027) (|c06ecf| . 658852) (|euclideanGroebner| . 657958) (|OMbindTCP| . 657832) (|setprevious!| . 657691) (|c06ebf| . 657519) (|secIfCan| . 657378) (|content| . 656679) (|symmetricTensors| . 656345) (|c06eaf| . 656173) (|lexTriangular| . 655868) (|pointColor| . 655711) (|droot| . 655486) (|s17def| . 655247) (|fmecg| . 654182) (|partitions| . 653747) (|realElementary| . 653066) (|s17dcf| . 652827) (|slash| . 652777) (|addmod| . 652713) (|consnewpol| . 652213) (|s17akf| . 652054) (|combineFeatureCompatibility| . 651846) (|OMputAtp| . 651764) (|gramschmidt| . 651639) (|s17ajf| . 651480) (|increasePrecision| . 651308) (|shallowCopy| . 651190) (|predicate| . 650989) (|subtractIfCan| . 650912) (|condition| . 650736) (|s17ahf| . 650577) (|dec| . 650519) (|back| . 650264) (|hash| . 649184) (|axes| . 648749) (|choosemon| . 648484) (|s17agf| . 648325) (|typeLists| . 648115) (|divisorAtDesingTree| . 647450) (|iter| . 647263) (|pop!| . 646921) (|s17aff| . 646762) (|quasiRegular?| . 646459) (|iisinh| . 646263) (|dznrm2| . 646073) (|generalTwoFactor| . 645798) (|s17aef| . 645639) (|zag| . 645589) (|exprToXXP| . 645029) (|permanent| . 644809) (|splitLinear| . 644703) (|parabolic| . 644519) (|complexRoots| . 644001) (|s17adf| . 643842) (|symbolTableOf| . 643723) (|close| . 643448) (|optimize| . 642212) (|pomopo!| . 642059) (|movedPoints| . 641821) (|aRow| . 641541) (|s17acf| . 641382) (|OMunhandledSymbol| . 641269) (|lift| . 639368) (|OMputBVar| . 639286) (|sort!| . 638931) (|s15aef| . 638772) (|cot2tan| . 638557) (|setStatus!| . 638350) (|reduce| . 631765) (|permutation| . 631408) (|outputSpacing| . 631296) (|showTheFTable| . 631237) (|s15adf| . 631078) (|multisect| . 630449) (|tableForDiscreteLogarithm| . 630288) (|cyclicSubmodule| . 630042) (|binarySearchTree| . 629919) (|s14baf| . 629754) (|solveLinearlyOverQ| . 629531) (|nonQsign| . 629408) (|algint| . 629025) (|invertibleSet| . 628739) (|display| . 627467) (|s14abf| . 627308) (|asinhIfCan| . 627167) (|printStats!| . 627001) (|flagFactor| . 626821) (|complexIntegrate| . 626102) (|s14aaf| . 625943) (|binaryTournament| . 625820) (|critT| . 625438) (|cExp| . 625278) (|halfExtendedResultant1| . 625037) (|s13adf| . 624878) (|safeFloor| . 624715) (|changeWeightLevel| . 624094) (|readLine!| . 624016) (|acothIfCan| . 623875) (|s13acf| . 623716) (|cTan| . 623556) (|extendedgcd| . 623381) (|RittWuCompare| . 623153) (|SturmHabichtCoefficients| . 622938) (|s13aaf| . 622779) (|swap!| . 622578) (|decimal| . 622478) (|setMaxPoints3D| . 622401) (|delay| . 622152) (|Zero| . 621851) (|regime| . 620934) (LT . 620716) (|s01eaf| . 620545) (|twist| . 620302) (|pointToPlace| . 619841) (|intensity| . 619720) (|LazardQuotient2| . 619448) (|outputForm| . 618505) (|s21bdf| . 618337) (|nullity| . 617161) (|characteristicSerie| . 616387) (|monicRightFactorIfCan| . 616123) (|typeList| . 615881) (|squareFreeBasis| . 615676) (|s21bcf| . 615511) (|rootPoly| . 615110) (|identitySquareMatrix| . 614943) (|normalDenom| . 614721) (|errorInfo| . 614629) (|areEquivalent?| . 613957) (|s21bbf| . 613792) (|simplify| . 613112) (|numberOfFractionalTerms| . 612985) (|sequences| . 612679) (|supRittWu?| . 612461) (|setref| . 612376) (|s21baf| . 612214) (|setRow!| . 611468) (|OMgetSymbol| . 611338) (|rightDivide| . 610828) (|stack| . 610715) (|generalSqFr| . 610440) (|integral| . 609455) (|s20adf| . 609296) (|mainValue| . 609176) (|createPrimitiveElement| . 609121) (|vectoraddmul| . 608951) (|leadingIdeal| . 608723) (|rightPower| . 608537) (|e02agf| . 608263) (|doubleResultant| . 607947) (|dimension| . 606465) (|SturmHabicht| . 606250) (|guessBinRat| . 599197) (|match?| . 599073) (|s20acf| . 598914) (|Ei3| . 598789) (|stopTableGcd!| . 598096) (|sylvesterSequence| . 597904) (|solid| . 597805) (|d01aqf| . 597558) (|genusNeg| . 595709) (|mapdiv| . 595547) (|mpsode| . 595245) (|rightRegularRepresentation| . 594925) (|s19adf| . 594766) (|relerror| . 594687) (|biringToPolyRing| . 594289) (|lyndonIfCan| . 594149) (|or| . 594004) (|lieAlgebra?| . 593664) (|d01apf| . 593411) (|radicalSimplify| . 593073) (|lazyIntegrate| . 592842) (|reduceLODE| . 592429) (|permutationGroup| . 592289) (|s19acf| . 592130) (|constantKernel| . 591969) (|box| . 591786) (|qPot| . 591607) (|minimalForm| . 590683) (|d01anf| . 590433) (|character?| . 590345) (|compose| . 590060) (|merge| . 589109) (|elliptic?| . 588579) (|d01amf| . 588335) (|distance| . 588211) (|extractTop!| . 588036) (|bandedHessian| . 587639) (|d01alf| . 587346) (|chvar| . 586958) (|checkOptions| . 586828) (|addiag| . 586656) (|s19abf| . 586497) (|constantOpIfCan| . 586317) (|projectivePoint| . 585576) (|derivationCoordinates| . 585292) (|insert| . 585047) (|d01akf| . 584803) (|polynomialZeros| . 584535) (|maxDerivative| . 584257) (|copyfirst| . 584096) (|s19aaf| . 583937) (|f2st| . 583817) (|basisOfInterpolateForms| . 583256) (|singularitiesOf| . 582391) (|d01ajf| . 582147) (|log2| . 582024) (|mainSquareFreePart| . 581805) (|stoseInternalLastSubResultant| . 580859) (|s18def| . 580620) (|plot| . 578737) (|removeConjugate| . 578162) (|UnVectorise| . 577994) (|stoseIntegralLastSubResultant| . 577589) (|s18dcf| . 577350) (|algebraicSort| . 576663) (|bivariatePolynomials| . 576292) (|maxPower| . 576020) (|s18aff| . 575861) (|En| . 575673) (|subspace| . 575209) (|inHallBasis?| . 575092) (|localReal?| . 574868) (|s18aef| . 574709) (|module| . 574048) (|recur| . 573689) (|acsch| . 572494) (|denomLODE| . 571671) (|s18adf| . 571512) (|sylvesterMatrix| . 571218) (|stoseInvertibleSetsqfreg| . 570856) (|bandMatrix| . 570294) (|reshape| . 569565) (|s18acf| . 569406) (|guess| . 557907) (|xRange| . 557678) (|lquo| . 556770) (|UpTriBddDenomInv| . 556509) (|f04qaf| . 556192) (|nthExpon| . 555572) (|particularSolution| . 554560) (|digits| . 553939) (|f04mcf| . 553698) (|pow| . 553298) (|compBound| . 553076) (|acoshIfCan| . 552935) (GT . 552717) (|f04mbf| . 552297) (|presub| . 552247) (|Aleph| . 552151) (|rightLcm| . 552013) (|f04maf| . 551763) (|stopMusserTrials| . 551437) (|fortranLinkerArgs| . 551349) (|inrootof| . 551130) (|label| . 551080) (|f04jgf| . 550855) (|eq| . 550575) (|computeBasis| . 550362) (|constantLeft| . 550122) (|f04faf| . 549935) (|printCode| . 549856) (|OMputEndError| . 549774) (|trunc| . 549431) (|f04axf| . 549199) (|heap| . 549088) (~ . 548997) (|coefOfFirstNonZeroTerm| . 548897) (|hasoln| . 548450) (|open?| . 548318) (|f04atf| . 548131) (|commonDenominator| . 547272) (|linearMatrix| . 547072) (|numericalOptimization| . 546482) (|f04asf| . 546298) (|lazyIrreducibleFactors| . 545932) (|triangularSystems| . 545684) (|att2Result| . 544787) (|homogeneous| . 544515) (|partialFraction| . 543872) (|rectangularMatrix| . 543672) (|fracPart| . 543372) (SEGMENT . 543102) (|f04arf| . 542918) (|credPol| . 542648) (|makeCos| . 542440) (|testDim| . 542132) (|headReduced?| . 541112) (|algebraicOf| . 540824) (|shufflein| . 540668) (|f04adf| . 540463) (|basisOfCommutingElements| . 540285) (|solveid| . 540050) (|An| . 539882) (|PDESolve| . 539325) (|tableau| . 539201) (|expressIdealMember| . 539095) (|declare!| . 538336) (|fixedPointExquo| . 538142) (|plotPolar| . 537513) (|cyclicParents| . 537392) (|intersectionDivisor| . 535326) (|digit?| . 535246) (|null| . 535141) (|subCase?| . 534312) (|unexpand| . 533996) (|writeDotGraph| . 533851) (|continue| . 533763) (|aLinear| . 533529) (|middle| . 533336) (|OMwrite| . 532005) (|initial| . 531758) (|option| . 531275) (|multiset| . 530992) (|deleteRoutine!| . 530906) (|ord| . 530826) (|mainMonomial| . 530639) (|new| . 529349) (|cyclicCopy| . 529265) (|topFortranOutputStack| . 529173) (|index?| . 529014) (|f07fef| . 528819) (|factorials| . 528296) (|sech2cosh| . 528081) (|rischDE| . 527349) (|f07fdf| . 527163) (|And| . 527027) (|rightNorm| . 526910) (|setPredicates| . 526787) (|ratDenom| . 525100) (|f07aef| . 524863) (|critM| . 524593) (|iifact| . 524423) (|factors| . 523736) (|f07adf| . 523577) (|makeViewport3D| . 523221) (|BasicMethod| . 523074) (|topPredicate| . 522907) (|removeSuperfluousCases| . 522122) (|leftScalarTimes!| . 521981) (|dihedralGroup| . 521679) (|s17dlf| . 521437) (|excpDivV| . 520932) (|printTypes| . 520747) (|lflimitedint| . 520222) (|s17dhf| . 520018) (|multiple| . 519742) (|arg1| . 519594) (|quoByVar| . 519489) (|divideIfCan| . 519233) (|monomRDEsys| . 518782) (|s17dgf| . 518578) (|optional| . 518302) (|localUnquote| . 517954) (|tower| . 517855) (|tree| . 517191) (|arg2| . 517043) (|colorDef| . 516919) (|f02xef| . 516690) (NOT . 516435) (|extend| . 514196) (|alternating| . 514045) (|setexcpDiv!| . 513537) (|f02wef| . 513320) (|not| . 513137) (OR . 512919) (|isList| . 512782) (|atrapezoidal| . 512479) (|numericalIntegration| . 511854) (|f02fjf| . 511067) (AND . 510849) (|quotedOperators| . 510503) (|explicitEntries?| . 510381) (|bracket| . 510244) (|f02bjf| . 510004) (|update| . 509841) (|makeViewport2D| . 509646) (|showAll?| . 509508) (|OMencodingXML| . 509458) (|f02bbf| . 509249) (|applyQuote| . 508595) (|product| . 507502) (|rewriteIdealWithHeadRemainder| . 507191) (|modularGcdPrimitive| . 506929) (|crest| . 506708) (|OMconnectTCP| . 506552) (|f02axf| . 506375) (|doublyTransitive?| . 506221) (|separate| . 505535) (|rightAlternative?| . 505195) (|printInfo| . 502290) (|nextItem| . 502230) (|f02awf| . 502059) (|leftCharacteristicPolynomial| . 501892) (|getRef| . 501723) (|upperCase| . 501581) (|infix| . 501435) (|f02akf| . 501258) (|genericLeftDiscriminant| . 500949) (|squareFree| . 498436) (|numerator| . 498059) (|series| . 492191) (|top| . 491849) (|f02ajf| . 491678) (|useEisensteinCriterion| . 491520) (|setSingularPoints| . 490271) (|trigs2explogs| . 489828) (|objectOf| . 489751) (|f02agf| . 489580) (|build| . 489101) (|superscript| . 489009) (|numberOfComputedEntries| . 488876) (|reduceByQuasiMonic| . 488620) (|countRealRoots| . 488408) (|biRank| . 488216) (|bat| . 488045) (|standardDotHeader| . 487961) (|innerSolve| . 487642) (|partition| . 487440) (|gcd| . 485020) (* . 476441) (|characteristicPolynomial| . 474496) (|itsALeaf!| . 474328) (|yRange| . 474099) (|aCubic| . 473859) (|noLinearFactor?| . 473708) (|ramifiedAtInfinity?| . 473439) (|critMonD1| . 473073) (|summation| . 472462) (|cyclic?| . 472232) (|vark| . 471998) (|OMputFloat| . 471881) (|rst| . 471787) (|front| . 471532) (|remainder| . 471173) (|false| . 471132) (|figureUnits| . 470978) (|shiftHP| . 457754) (|cAsec| . 457594) (|denominator| . 457207) (|listYoungTableaus| . 457044) (|iiexp| . 456848) (|definingField| . 456657) (|hasSolution?| . 456068) (|xor| . 455920) (|stoseInvertible?reg| . 455509) (|groebner?| . 455253) (|coerceS| . 455032) (|numberOfImproperPartitions| . 454923) (|OMgetError| . 454841) (|one?| . 454426) (|setColumn!| . 454190) (|lazyPseudoDivide| . 453283) (|nthr| . 452751) (|simplifyExp| . 452536) (|simplifyLog| . 452321) (|PollardSmallFactor| . 452196) (|separateFactors| . 451645) (|cycleLength| . 451508) (|mainCharacterization| . 451244) (|findTerm| . 451046) (|triangular?| . 450738) (|externalList| . 450648) (|scalarMatrix| . 450216) (|divide| . 449257) (|lambert| . 448764) (|increase| . 448540) (|extendedint| . 448194) (|eigenvector| . 447877) (|iiatanh| . 447681) (|varselect| . 447475) (|integralMatrixAtInfinity| . 447191) (|clearTheFTable| . 447101) (|finiteSeries2Vector| . 446881) (|sort| . 446157) (|pack!| . 446021) (|seed| . 445935) (|dmpToHdmp| . 445686) (|generic?| . 445571) (|overbar| . 445524) (|selectOptimizationRoutines| . 445474) (|scripted?| . 445397) (|epilogue| . 445214) (|tanhIfCan| . 445073) (|nullSpace| . 443366) (|pointDominateBy| . 441612) (|karatsubaOnce| . 441438) (|homogeneous?| . 441120) (|groebgen| . 440788) (|mightHaveRoots| . 440564) (|representationType| . 440438) (|tail| . 440063) (|createHN| . 439850) (|jacobian| . 439284) (|discriminantSet| . 439043) (|symmetricSquare| . 438898) (|chainSubResultants| . 438704) (|cn| . 438529) (|wreath| . 438403) (|rowEchelonLocal| . 438255) (|functionIsFracPolynomial?| . 437937) (|ceiling| . 437737) (|Is| . 436520) (|addMatchRestricted| . 436345) (|setImagSteps| . 436263) (|parts| . 435117) (|fullInfClsPt| . 434669) (|rdHack1| . 434436) (|distinguishedCommonRootsOf| . 434198) (|rightQuotient| . 434060) (|regularRepresentation| . 433654) (|commutativeEquality| . 433471) (|redmat| . 433093) (|unrankImproperPartitions1| . 432944) (|pointData| . 432788) (|dot| . 432277) (|bat1| . 432100) (|iiBeta| . 431898) (|cyclicGroup| . 431596) (|useSingleFactorBound| . 431438) (|dAndcExp| . 431211) (|leftExtendedGcd| . 430991) (|supDimElseRittWu?| . 430298) (|drotg| . 430151) (|palgintegrate| . 429655) (|OMgetBVar| . 429573) (|lazyResidueClass| . 429047) (|traverse| . 428878) (|taylorIfCan| . 428692) (|subresultantVector| . 428492) (|variableName| . 428282) (|evalRec| . 427841) (|notelem| . 427675) (|debug3D| . 427598) (|generalLambert| . 426969) (|diagonalMatrix| . 425696) (|gethi| . 425210) (|cond| . 425042) (|frst| . 424948) (|lex| . 424817) (|qroot| . 424253) (|preprocess| . 423398) (|copyslice| . 423234) (|rightZero| . 423118) (|rightDiscriminant| . 422702) (|split!| . 422531) (|complex?| . 422443) (|rspace| . 422359) (|indices| . 422203) (|type| . 422064) (|expenseOfEvaluation| . 421714) (|expandLog| . 421499) (|numberOfCycles| . 421369) (|sturmSequence| . 421180) (|setAdaptive3D| . 421103) (|generalInfiniteProduct| . 420099) (|dscal| . 419918) (|evenInfiniteProduct| . 419032) (|fullDesTree| . 418584) (|depth| . 417963) (|approximate| . 416832) (|leftGcd| . 416538) (|create| . 414933) (|branchPointAtInfinity?| . 414664) (|shellSort| . 414406) (|badValues| . 414220) (|comp| . 413964) (|nthRoot| . 413590) (|horizSplit| . 412726) (|degree| . 407923) (|mkcomm| . 407795) (|exp1| . 407714) (|repeating?| . 407542) (|printInfo!| . 407343) (|count| . 404878) (|hMonic| . 404639) (|quatern| . 404526) (|suppOfZero| . 404401) (|solveLinearPolynomialEquation| . 403413) (|userOrdered?| . 403282) (|argscript| . 403190) (|OMReadError?| . 403102) (|setClosed| . 402967) (|cycleElt| . 402819) (|processTemplate| . 402645) (|univariatePolynomial| . 401769) (|alterQuadVar!| . 401576) (|goppaCode| . 400276) (|linearAssociatedExp| . 400089) (|satisfy?| . 399482) (|factorSquareFreePolynomial| . 399293) (|sampleDotGraph| . 399209) (|extractBottom!| . 399034) (|cylindricalDecomposition| . 398590) (|henselFact| . 398017) (|remove!| . 396767) (|OMgetEndBind| . 396685) (|mul| . 396549) (|differentialVariables| . 396274) (|repeating| . 396167) (|reorder| . 395527) (|operators| . 395424) (|eulerE| . 395209) (|implies| . 395162) (|divOfPole| . 395065) (|leftRemainder| . 394771) (|getZechTable| . 394150) (|makeEq| . 393833) (|mapSolve| . 393449) (|showIntensityFunctions| . 392874) (|inR?| . 392759) (|OMUnknownCD?| . 392671) (|torsionIfCan| . 391694) (|minimize| . 391413) (|decrease| . 391189) (|invertibleElseSplit?| . 390881) (|message| . 390801) (|setMaxPoints| . 390726) (|pdf2df| . 390580) (|linearPart| . 390465) (|horizJoin| . 390334) (|getCurve| . 390230) (|maxRowIndex| . 389763) (|property| . 389642) (|minimalPolynomial| . 388887) (|linearDependence| . 388665) (|algebraicVariables| . 388384) (|GospersMethod| . 387910) (|lfintegrate| . 387507) (|legendreP| . 387297) (|exactQuotient| . 386846) (|setLabelValue| . 386758) (|excepCoord| . 386665) (|countable?| . 386580) (|reduction| . 386030) (|units| . 385403) (|iCompose| . 385295) (|symmetricDifference| . 385198) (|modifyPointData| . 384855) (|OMsend| . 384700) (|expint| . 384319) (|exquo| . 382819) (|localParamOfSimplePt| . 382297) (|fractionFreeGauss!| . 381999) (|nextLatticePermutation| . 381850) (|splitNodeOf!| . 381342) (|div| . 381292) (|entry?| . 381058) (|youngGroup| . 380762) (|invmultisect| . 380133) (|singRicDE| . 379040) (|getSmgl| . 378933) (|makeVariable| . 378147) (|code| . 376904) (|collectUnder| . 376658) (GF2FG . 376265) (|integral?| . 375449) (|rightExactQuotient| . 375301) (|failed| . 374994) (|rational| . 373674) (|bag| . 373004) (|intChoose| . 372411) (|lintgcd| . 372240) (|arity| . 372135) (|rational?| . 370325) (|schema| . 370111) (|squareFreeFactors| . 369792) (|polyPart| . 369601) (|escape| . 369558) (|rk4| . 368981) (|chiSquare1| . 368849) (|imaginary| . 368751) (|factorsOfCyclicGroupSize| . 368598) (|clipParametric| . 368020) (|dotview| . 367914) (|initials| . 367633) (|checkPrecision| . 367544) (|ZetaFunction| . 364634) (|clearCache| . 364521) (|matrixDimensions| . 364369) (|iiasin| . 364173) (|hasPredicate?| . 364058) (|setOrder| . 363740) (|divOfZero| . 363643) (|round| . 363588) (|copies| . 363473) (|OMgetApp| . 363391) (|prefixRagits| . 363268) (|swap| . 362968) (|inverseLaplace| . 362537) (|mainContent| . 362318) (|antiAssociative?| . 361978) (|irreducible?| . 361369) (|charClass| . 361192) (|rank| . 358713) (|groebSolve| . 358348) (|commutative?| . 358008) (|safetyMargin| . 357666) (|stoseInvertibleSet| . 357304) (|sumOfKthPowerDivisors| . 357163) (|removeRoughlyRedundantFactorsInContents| . 356841) (|definingEquations| . 356580) (|fortranLiteralLine| . 356470) (|exponential1| . 356380) (|rootRadius| . 355994) (|ldf2lst| . 355571) (|screenResolution| . 355334) (|roughEqualIdeals?| . 355023) (|sn| . 354848) (|exprHasWeightCosWXorSinWX| . 354478) (|singularAtInfinity?| . 354209) (|iiacot| . 354013) (|genericRightMinimalPolynomial| . 353670) (|lastNonNul| . 353543) (|separe| . 353358) (|physicalLength!| . 353100) (|generators| . 352707) (|placesAbove| . 351359) (|reducedSystem| . 350962) (|conditions| . 350758) (|leftQuotient| . 350464) (|derivative| . 349905) (|mathieu23| . 349642) (|idamax| . 349502) (|df2mf| . 349370) (|singleFactorBound| . 348647) (|resultantSet| . 348406) (|fTable| . 347287) (|fortranReal| . 347242) (|getMultiplicationMatrix| . 346585) (|flexible?| . 346245) (|intersect| . 344449) (|reducedDiscriminant| . 344164) (|paraboloidal| . 343980) (|duplicates?| . 343853) (|realEigenvectors| . 343555) (|printHeader| . 343261) (|summary| . 343169) (|enqueue!| . 342905) (|iprint| . 342790) (|stopTableInvSet!| . 342097) (|hasDimension?| . 341775) (|denominators| . 341644) (|composites| . 341523) (|show| . 341364) (|radicalRoots| . 340800) (|oddInfiniteProduct| . 339914) (|indiceSubResultantEuclidean| . 339621) (|computeCycleLength| . 339444) (|stiffnessAndStabilityOfODEIF| . 338968) (|genericLeftMinimalPolynomial| . 338625) (|selectOrPolynomials| . 338199) (|e02aef| . 338000) (|ode| . 337735) (|stFuncN| . 337436) (|exponentialOrder| . 337213) (|appendPoint| . 337090) (|rangeIsFinite| . 336531) (|mirror| . 335887) (|dmpToP| . 335675) (|exprToUPS| . 334796) (|dflist| . 334575) (|writeObj| . 334422) (|zeroSquareMatrix| . 334255) (|totolex| . 333973) (|constant| . 333007) (|c02agf| . 332804) (|rightFactorCandidate| . 332608) (|idealiser| . 331988) (|returns| . 331352) (|cTanh| . 331192) (|c02aff| . 330989) (|cscIfCan| . 330848) (|bumprow| . 330559) (|replaceVarByOne| . 330273) (|mindegTerm| . 330075) (|equality| . 329940) (|rationalPoint?| . 329338) (|totalDegree| . 328625) (|someBasis| . 328481) (|bit?| . 328386) (|e02adf| . 328210) (|OMputObject| . 328128) (|iiperm| . 327930) (|flexibleArray| . 327669) (|algintegrate| . 327173) (|c05pbf| . 326886) (|principalIdeal| . 326720) (|shade| . 326531) (|toroidal| . 326322) (|showAttributes| . 325223) (|ran| . 324966) (|zeroDimensional?| . 324513) (|eulerPhi| . 324414) (|groebner| . 322663) (|explicitlyFinite?| . 322545) (|read!| . 322414) (|icamax| . 322268) (|createLowComplexityNormalBasis| . 321984) (|monomialIntegrate| . 321630) (|primPartElseUnitCanonical!| . 321406) (|qqq| . 321143) (|credits| . 321051) (|minGbasis| . 320784) (|compile| . 320663) (|quadratic?| . 320529) (|fortranCompilerName| . 320441) (|OMgetEndBVar| . 320359) (|terms| . 319743) (|tanIfCan| . 319602) (|extract!| . 319100) (|gcdcofact| . 318957) (|columnSpace| . 318702) (|opeval| . 318424) (|abelianGroup| . 318263) (|minimumDegree| . 317371) (|e01sef| . 317151) (|xn| . 316944) (|isamax| . 316810) (|e01saf| . 316634) (|quasiComponent| . 316303) (|startStats!| . 316107) (|initiallyReduce| . 315664) (|outputList| . 315550) (|subNode?| . 315294) (|solid?| . 315198) (|e01daf| . 315019) (|OMencodingSGML| . 314969) (|extDegree| . 314844) (|infix?| . 314763) (|setScreenResolution3D| . 314686) (|diagonals| . 314564) (|taylorRep| . 314388) (|iilog| . 314192) (|branchPoint?| . 313651) (|double?| . 313563) (|totalfract| . 313127) (|factorSquareFreeByRecursion| . 312431) (|e01bhf| . 312217) (|axesColorDefault| . 312043) (|hexDigit| . 311995) (|nthCoef| . 311806) (|se2rfi| . 311397) (|bandedJacobian| . 310997) (|addBadValue| . 310725) (|e01bgf| . 310543) (|random| . 309290) (|resetAttributeButtons| . 309209) (|getlo| . 308723) (|pmintegrate| . 307592) (|lazyPremWithDefault| . 307014) (|minus!| . 306738) (|mindeg| . 306450) (|e01bff| . 306268) (|sumOfSquares| . 306152) (|constantToUnaryFunction| . 305999) (|e01bef| . 305826) (|deepestInitial| . 305639) (|merge!| . 305168) (|closed?| . 304943) (|listBranches| . 304682) (|semiSubResultantGcdEuclidean2| . 304457) (|isobaric?| . 304182) (|cAtanh| . 304022) (|e01baf| . 303843) (|root| . 303594) (|hermite| . 303188) (|last| . 302600) (|meatAxe| . 301518) (|cos2sec| . 301303) (|forLoop| . 301022) (|e02zaf| . 300837) (|infLex?| . 300532) (|showTheRoutinesTable| . 300485) (|rhs| . 299975) (|infRittWu?| . 298730) (|One| . 298285) (|extractProperty| . 298121) (|bottom!| . 297946) (|makeSin| . 297738) (|guessHP| . 290271) (|mainVariable| . 289508) (|shuffle| . 289352) (|e02gaf| . 289144) (|pointInIdeal?| . 288766) (|affineAlgSetLocal| . 288249) (|arrayStack| . 288131) (|iiAiryBi| . 287957) (|e02dff| . 287766) (|dominantTerm| . 287092) (|curve| . 286383) (|leviCivitaSymbol| . 286218) (|factorSqFree| . 285633) (|Yun| . 285422) (|cycles| . 285284) (|e02def| . 285102) (|primes| . 284963) (|boundOfCauchy| . 284768) (|supp| . 284643) (|ddot| . 284459) (|adaptive| . 284082) (|stoseInvertible?sqfreg| . 283671) (|e02ddf| . 283406) (|deepCopy| . 283288) (|shiftInfoRec| . 282718) (|palgextint| . 282234) (|iiatan| . 282038) (|createNormalPoly| . 281836) (|cCsch| . 281676) (|actualExtensionV| . 281171) (|identityMatrix| . 281003) (|e02dcf| . 280696) (|cAcsch| . 280536) (|nonSingularModel| . 279828) (|fortranLiteral| . 279718) (|fprindINFO| . 279318) (|solve1| . 279052) (|e02daf| . 278781) (|superHeight| . 278700) (|sin2csc| . 278485) (|gcdBasis| . 278280) (|e02bef| . 277988) (|univariateSolve| . 275747) (|mathieu12| . 275484) (|besselK| . 275029) (|purelyAlgebraic?| . 274463) (|sortedPurge!| . 274264) (|newtonPolySlope| . 273812) (|style| . 273602) (|sortConstraints| . 273269) (|e02bdf| . 273102) (|dimensionsOf| . 272668) (|reset| . 271785) (|nextColeman| . 271625) (|applyRules| . 270865) (|totalLex| . 270658) (|normalizedAssociate| . 270344) (|laguerre| . 270183) (|write| . 269538) (|outerProduct| . 269389) (|mix| . 269067) (|minusInfinity| . 268878) (|lBasis| . 266534) (|basicSet| . 265679) (|save| . 265634) (|leftUnit| . 265473) (|rightScalarTimes!| . 265332) (|coefficient| . 262309) (|enterPointData| . 262136) (|plusInfinity| . 261947) (|initTable!| . 261781) (|iomode| . 261623) (|basisOfRightAnnihilator| . 261442) (|ocf2ocdf| . 261273) (|matrixGcd| . 260921) (|subMultV| . 260395) (|firstExponent| . 260140) (|useNagFunctions| . 259718) (|d| . 259551) (|mantissa| . 259379) (|OMputSymbol| . 259264) (|semiResultantReduitEuclidean| . 258995) (|floor| . 258795) (|refine| . 257023) (|writable?| . 256934) (|conical| . 256722) (|lazyPquo| . 256342) (|wordInStrongGenerators| . 256160) (|getDatabase| . 255951) (|leftExactQuotient| . 255637) (|fresnelC| . 255249) (|introduce!| . 255139) (|monomial2series| . 254929) (|numberOfOperations| . 254641) (|setlocalPoint!| . 254096) (|airyBi| . 253653) (|addPoint| . 253058) (|number?| . 252904) (|HenselLift| . 252599) (|leadingExponent| . 252126) (|clipPointsDefault| . 251958) (|basis| . 250328) (|fortranTypeOf| . 250212) (|complexNumeric| . 246525) (|status| . 246053) (|createLowComplexityTable| . 245803) (|max| . 245236) (|jacobi| . 245134) (|minordet| . 244400) (|rightMult| . 244245) (|kernels| . 244146) (|duplicates| . 243959) (|genusTreeNeg| . 243209) (|presuper| . 243159) (|laplacian| . 242834) (|exprex| . 242613) (|generic| . 240927) (|univariate| . 237980) (|sign| . 235562) (|genericLeftTraceForm| . 235247) (|rightRecip| . 235024) (|OMputBind| . 234942) (|d01gbf| . 234644) (|polygon| . 234124) (|OMgetBind| . 234042) (|affineSingularPoints| . 232682) (|factor| . 220853) (|polyRingToBlUpRing| . 220455) (|ksec| . 220216) (|d01gaf| . 220045) (|badNum| . 219519) (|Lazard| . 219311) (|tanNa| . 219189) (|padicFraction| . 219090) (|rk4a| . 218797) (|imag| . 218057) (|e| . 217871) (|divisorCascade| . 217289) (|d01fcf| . 216994) (|wholePart| . 216570) (|sample| . 215841) (|options| . 215420) (|prefix| . 215324) (|directProduct| . 215195) (|halfExtendedSubResultantGcd1| . 214643) (|digit| . 214595) (|identity| . 214457) (|linearlyDependentOverZ?| . 214271) (|clipSurface| . 214149) (|gcdPrimitive| . 213345) (|d01bbf| . 213179) (|destruct| . 212694) (|rewriteIdealWithQuasiMonicGenerators| . 212318) (|elementary| . 212167) (|iisin| . 211971) (|negAndPosEdge| . 211677) (|corrPoly| . 211117) (|rk4qc| . 210331) (|d01asf| . 210084) (|monomial| . 207187) (|orbit| . 206043) (|Ei1| . 205918) (|graphs| . 205641) (|leftTraceMatrix| . 205135) (|maxPoints3D| . 205061) (|pointValue| . 204814) (|multivariate| . 203145) (|lazyPrem| . 202765) (|brillhartIrreducible?| . 202463) (|internalIntegrate| . 201739) (|d02raf| . 201303) (|asinIfCan| . 201162) (|rightTrim| . 200974) (|retractToGrn| . 200806) (|conjugate| . 199776) (|generateIrredPoly| . 199578) (|cCsc| . 199418) (|argument| . 199062) (|collect| . 198722) (|transform| . 198458) (|statusIto| . 198301) (|d02kef| . 197461) (|completeEval| . 197070) (|getAncestors| . 196938) (|subscriptedVariables| . 196832) (|finiteSeries2LinSysWOVectorise| . 196582) (|mvar| . 196155) (|makeTerm| . 196000) (|infinite?| . 195752) (|d02gbf| . 195346) (|inv| . 194140) (|apply| . 193397) (|oblateSpheroidal| . 193188) (|degreeSubResultantEuclidean| . 192895) (|select!| . 192563) (|d02gaf| . 192241) (|stoseSquareFreePart| . 191839) (|Vectorise| . 191671) (|ground?| . 191085) (|ground| . 190850) (|safeCeiling| . 190687) (|lifting| . 190106) (|makeUnit| . 189957) (|d02ejf| . 189379) (|cycleTail| . 189281) (|brace| . 188937) (|univariatePolynomialsGcds| . 188271) (|pdf2ef| . 188116) (|associative?| . 187776) (|d02cjf| . 187284) (|leadingMonomial| . 186192) (|coerceListOfPairs| . 186064) (|acschIfCan| . 185923) (|cons| . 185764) (|mathieu24| . 185501) (|prinb| . 185209) (|multMonom| . 184730) (|d02bhf| . 184345) (|leadingCoefficient| . 182321) (|setEmpty!| . 182145) (|head| . 181705) (|copy| . 180609) (|setGcdMode| . 180422) (|dswap| . 180210) (|virtualDegree| . 179932) (|makeMulti| . 179714) (|cosh2sech| . 179499) (|d02bbf| . 179109) (|primitiveMonomials| . 178903) (|pr2dmp| . 178552) (|iipow| . 178354) (|inBetweenExcpDiv| . 177692) (|e02ahf| . 177478) (|asimpson| . 177175) (|showClipRegion| . 177053) (|trueEqual| . 176959) (|reductum| . 174924) (|double| . 174738) (|OMgetVariable| . 174654) (|leftZero| . 174538) (|OMputEndAtp| . 174456) (|minColIndex| . 173989) (|factorsOfDegree| . 173730) (|stoseInvertible?| . 172960) (|vedf2vef| . 172783) (|acotIfCan| . 172642) (|HermiteIntegrate| . 171885) (F2FG . 171523) (|graphImage| . 171479) (|remove| . 170513) (|isAbsolutelyIrreducible?| . 170105) (|list| . 169691) (|stoseLastSubResultant| . 169286) (|linearAssociatedOrder| . 169102) (|makeop| . 168796) (|updateStatus!| . 168620) (|weighted| . 168410) (|lprop| . 168262) (|tRange| . 168081) (|besselY| . 167626) (|primitivePart| . 166459) (|elt| . 157239) (|trace| . 156422) (|factorSquareFree| . 154458) (|fillPascalTriangle| . 154343) (|patternVariable| . 154192) (|nil| . 154118) (|multiple?| . 154003) (|setelt| . 151601) (|gcdcofactprim| . 151458) (|prindINFO| . 151061) (|overset?| . 150648) (|factorCantorZassenhaus| . 150148) (|expextendedint| . 149642) (|normalizedDivide| . 149092) (|diagonal| . 148888) (|karatsuba| . 148669) (|expt| . 148483) (|innerSolve1| . 147952) (|listOfLists| . 147359) (|removeDuplicates| . 147199) (|iiacosh| . 147003) (|stronglyReduced?| . 146441) (|coerceL| . 146220) (|lp| . 146089) (|unitVector| . 145362) (|elRow2!| . 145064) (|rest| . 144288) (|maxdeg| . 143997) (|bernoulliB| . 143782) (|triangSolve| . 142700) (|transCoord| . 142607) (|reverse| . 142205) (|exQuo| . 141238) (|Frobenius| . 140649) (|mapBivariate| . 140286) (|setsymbName!| . 139749) (|translateToOrigin| . 138621) (|setDifference| . 138507) (|copy!| . 138369) (F . 138222) (|rightExtendedGcd| . 138002) (|viewDeltaXDefault| . 137822) (|create3Space| . 137608) (|ridHack1| . 137502) (|createMultiplicationTable| . 137248) (|setIntersection| . 137134) (|mainDefiningPolynomial| . 137014) (|euler| . 136744) (|firstUncouplingMatrix| . 136481) (|integer?| . 135982) (|monicDivide| . 135559) (|union| . 134963) (|Nul| . 134870) (|reduceRow| . 134748) (|wholeRagits| . 134625) (|iroot| . 134389) (|tryFunctionalDecomposition| . 134231) (|setUnion| . 134117) (|setErrorBound| . 133924) (|stFunc1| . 133643) (|hconcat| . 133503) (|abs| . 132573) (|size| . 130634) (|makeprod| . 130507) (|trigs| . 129899) (|lastSubResultantEuclidean| . 129648) (|primeFrobenius| . 129473) (|substitute| . 129368) (|log| . 127034) (|ideal| . 126132) (|extendedIntegrate| . 125751) (|clearTable!| . 125585) (|iibinom| . 125387) (|variable| . 124696) (|input| . 124444) (|extract| . 124282) (|drawComplexVectorField| . 124049) (|getStream| . 123871) (|selectFiniteRoutines| . 123821) (|test| . 123777) (|insertMatch| . 123605) (|laurentIfCan| . 123418) (|overlabel| . 123368) (|mergeFactors| . 123225) (|subscript| . 123133) (|LazardQuotient| . 122864) (|autoReduced?| . 122525) (|subsInVar| . 122236) (|real| . 121296) (|completeEchelonBasis| . 121130) (|squareTop| . 120941) (|OMmakeConn| . 120846) (|createNormalPrimitivePoly| . 120644) (|complex| . 120540) (|stripCommentsAndBlanks| . 120453) (|ParCondList| . 119852) (UP2UTS . 119581) (|gnuDraw| . 118722) (|elimZeroCols!| . 118569) (|iiacoth| . 118373) (|iiacsch| . 118177) (|expIfCan| . 118036) (|predicates| . 117916) (|entries| . 116644) (|drift| . 116515) (|allSimpleCells| . 116036) (|name| . 115393) (|cfirst| . 115172) (|continuedFraction| . 114243) (|numer| . 112980) (|realRoots| . 112516) (|listConjugateBases| . 112011) (|algebraicSet| . 111607) (|LPolynomial| . 108727) (|previousTower| . 108644) (|denom| . 107401) (|normFactors| . 107058) (|node| . 106952) (|makeYoungTableau| . 106795) (F2EXPRR . 106605) (|uniform| . 106171) (|kernel| . 105654) (|append| . 105574) (|discriminantEuclidean| . 105326) (|closedCurve?| . 105205) (|norm| . 101692) (|tanh2coth| . 101477) (|coth2tanh| . 101262) (|draw| . 93232) (|function| . 92523) (|deleteRow!| . 92339) (|unary?| . 92255) (|imagi| . 92153) (|collectQuasiMonic| . 91900) (|pivot| . 91680) (|makeObject| . 87209) (|scaleRoots| . 87046) (|setProperty| . 86932) (|putColorInfo| . 86779) (|blowUp| . 86087) (|acscIfCan| . 85946) (|coef| . 85346) (|associatedEquations| . 84945) (|curveV| . 84347) (|multiplicative?| . 84194) (|prod| . 84050) (|cyclotomic| . 83578) (|enterInCache| . 83304) (|monom| . 82853) (|eigenvalues| . 82597) (|leftFactor| . 82430) (|cSec| . 82270) (|infinity| . 82079) (|KrullNumber| . 81224) (|cCoth| . 81064) (|localIntegralBasis| . 79605) (|child| . 79445) (|discreteLog| . 79222) (|wordInGenerators| . 79040) (|normalize| . 77941) (|zeroVector| . 77774) (|meshPar1Var| . 77444) (|consRow!| . 77205) (|setcurve!| . 76604) (|transpose| . 75752) (|rationalPoints| . 73437) (|sizeMultiplication| . 72528) (|fullDisplay| . 71921) (|precision| . 71510) (|dcopy| . 71358) (|pointV| . 70853) (|map!| . 69638) (|alternative?| . 69298) (|viewport3D| . 69240) (|generalizedContinuumHypothesisAssumed| . 69155) (|setTopPredicate| . 69002) (|bezoutMatrix| . 68708) (|reduceBasisAtInfinity| . 68434) (|difference| . 68243) (|fixedPoints| . 68096) (|ScanArabic| . 67977) (|real?| . 67228) (|functionNames| . 67138) (|intcompBasis| . 66876) (|rootProduct| . 66319) (|rightUnit| . 66158) (|argumentListOf| . 66035) (|is?| . 64931) (FG2F . 64569) (|OMgetEndApp| . 64487) (|newTypeLists| . 64401) (|fi2df| . 64261) (|monomRDE| . 63860) (|variables| . 61644) (|appendRow!| . 61405) (|OMgetAttr| . 61323) (|expandTrigProducts| . 60922) (|recoverAfterFail| . 60795) (|inverse| . 59066) (|seriesSolve| . 54996) (|times| . 54748) (|drot| . 54524) (|absolutelyIrreducible?| . 53934) (|intPatternMatch| . 53260) (|karatsubaDivide| . 53047) (|outputFixed| . 52868) (|constant?| . 52453) (|expr| . 52204) (|stirling2| . 52085) (|lazyPseudoQuotient| . 51980) (|latex| . 51177) (|divideIfCan!| . 50833) (|primlimitedint| . 50292) (|asecIfCan| . 50151) (|truncate| . 49793) (|iiasec| . 49597) (|baseRDEsys| . 49288) (|ipow| . 49090) (|odd?| . 48749) (|basisOfCentroid| . 48560) (|directory| . 48472) (|decreasePrecision| . 48300) (|complementaryBasis| . 48026) (|any?| . 46831) (|lowerCase!| . 46777) (|makeCrit| . 46318) (|region| . 46159) (|toseLastSubResultant| . 45764) (|reverse!| . 45305) (|numberOfComponents| . 44564) (|weight| . 43660) (|iicot| . 43464) (|measure2Result| . 43018) (|title| . 42572) (|super| . 42522) (|initiallyReduced?| . 41502) (|members| . 40470) (|outputMeasure| . 40350) (|infieldIntegrate| . 40091) (|insertBottom!| . 39910) (|subTriSet?| . 39217) (|setEpilogue!| . 39028) (|rewriteIdealWithRemainder| . 38717) (|int| . 38067) (|op| . 37911) (|any| . 37805) (|setPosition| . 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(|Integer|))) (|ofCategory| *6 (|Ring|)) (|isDomain| *2 (|OutputForm|)) (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *6))))) +(((*1 *1 *2 *3) (AND (|isDomain| *3 (|Integer|)) (|isDomain| *1 (|Factored| *2)) (|ofCategory| *2 (|IntegralDomain|))))) +(((*1 *2 *3 *4) (AND (|isDomain| *2 (|Record| (|:| |part1| *3) (|:| |part2| *4))) (|isDomain| *1 (|MakeRecord| *3 *4)) (|ofCategory| *3 (|Type|)) (|ofCategory| *4 (|Type|))))) +(((*1 *2 *1) (AND (|ofCategory| *1 (|IndexedAggregate| *3 *2)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *2 (|Type|)))) ((*1 *2 *1) (AND (|isDomain| *1 (|Magma| *2)) (|ofCategory| *2 (|OrderedSet|)))) ((*1 *2 *1) (AND (|isDomain| *1 (|OrderedFreeMonoid| *2)) (|ofCategory| *2 (|OrderedSet|)))) ((*1 *2 *1) (AND (|isDomain| *2 (|LyndonWord| *3)) (|isDomain| *1 (|PoincareBirkhoffWittLyndonBasis| *3)) (|ofCategory| *3 (|OrderedSet|)))) ((*1 *2 *1) (|partial| AND (|ofCategory| *1 (|TriangularSetCategory| *3 *4 *5 *2)) (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *2 (|RecursivePolynomialCategory| *3 *4 *5)))) ((*1 *1 *1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|ofCategory| *1 (|UnaryRecursiveAggregate| *3)) (|ofCategory| *3 (|Type|)))) ((*1 *2 *1) (AND (|ofCategory| *1 (|UnaryRecursiveAggregate| *2)) (|ofCategory| *2 (|Type|))))) +(((*1 *1 *2) (AND (|isDomain| *2 (|Color|)) (|isDomain| *1 (|Palette|))))) +((|dark| . 1579383) (|first| . 1578415) (|makeRecord| . 1578238) (|irreducibleFactor| . 1578116) (|seriesToOutputForm| . 1577763) (|simpsono| . 1577463) (|orbits| . 1577332) (+ . 1574637) (|getButtonValue| . 1574522) (|resultantEuclideannaif| . 1574274) (|Aleph| . 1574178) (|intPatternMatch| . 1573504) (|numberOfComposites| . 1573372) (- . 1570552) (|returns| . 1569916) (|pastel| . 1569840) (|shufflein| . 1569684) (|subsInVar| . 1569395) (|purelyAlgebraicLeadingMonomial?| . 1569109) (/ . 1565016) (|corrPoly| . 1564456) (|roughBase?| . 1564148) (|degreeSubResultantEuclidean| . 1563855) (|phiCoord| . 1563741) (|lquo| . 1562833) (|f2df| . 1562708) (|maxDerivative| . 1562430) (|meshPar2Var| . 1561399) (|initializeGroupForWordProblem| . 1561126) (|qqq| . 1560863) (|isMult| . 1560642) (|idealiserMatrix| . 1560332) (|irreducibleRepresentation| . 1559803) (|eyeDistance| . 1559682) (|subQuasiComponent?| . 1558243) (|right| . 1557662) (|curryLeft| . 1557419) (|intersect| . 1555623) (|completeEchelonBasis| . 1555457) (|vectorise| . 1555163) (|removeSinhSq| . 1554948) (|left| . 1554367) (|genusTreeNeg| . 1553617) (|createIrreduciblePoly| . 1553415) (|remainder!| . 1553254) (|palginfieldint| . 1552789) (|fullParamInit| . 1552099) (|basisOfCommutingElements| . 1551921) (|isPlus| . 1550980) (|rightLcm| . 1550842) (|changeName| . 1550723) (|argumentList!| . 1550312) (|apply| . 1549569) (|cTanh| . 1549409) (|rischNormalize| . 1548948) (|taylor| . 1545097) (|table| . 1544769) (|copyfirst| . 1544608) (|rk4qc| . 1543822) (|select!| . 1543490) (|laurent| . 1540343) (|normalizeIfCan| . 1539953) (|brace| . 1539609) (|deriv| . 1539478) (|minGbasis| . 1539211) (|puiseux| . 1536035) (|reducedDiscriminant| . 1535750) (|cons| . 1535591) (|zaxpy| . 1535380) (|karatsubaDivide| . 1535167) (|library| . 1535088) (|e01sbf| . 1534829) (|presuper| . 1534779) (|copy| . 1533683) (|modularGcd| . 1533421) (|normal| . 1533287) (|polynomial| . 1532490) (|OMUnknownSymbol?| . 1532402) (|affineRationalPoints| . 1531511) (|putColorInfo| . 1531358) (|sechIfCan| . 1531217) (|functionName| . 1531007) (|createNormalElement| . 1530876) (|blowUp| . 1530184) (|stopMusserTrials| . 1529858) (|green| . 1529819) (|sort| . 1529095) (|rCoord| . 1528981) (|acscIfCan| . 1528840) (|orbit| . 1527696) (|quadratic?| . 1527562) (|f2st| . 1527442) (|cup| . 1527316) (|cscIfCan| . 1527175) (|solveid| . 1526940) (|paraboloidal| . 1526756) (|list| . 1526342) (|associatedEquations| . 1525941) (|drawCurves| . 1525463) (|outputFixed| . 1525284) (|binomThmExpt| . 1525057) (|sdf2lst| . 1524628) (|semiResultantEuclidean2| . 1524397) (|makeSeries| . 1524152) (|laplacian| . 1523827) (|totalDifferential| . 1523646) (|curveV| . 1523048) (|stoseSquareFreePart| . 1522646) (|segment| . 1522352) (|mapCoef| . 1522157) (|nil| . 1522083) (|aQuadratic| . 1521846) (|createPrimitiveNormalPoly| . 1521644) (|FormatRoman| . 1521525) (|key?| . 1521360) (|guess| . 1509861) (|Ei1| . 1509736) (|iiBesselJ| . 1509534) (|multiplicative?| . 1509381) (|leftGcd| . 1509087) (|rewriteSetWithReduction| . 1508714) (|nullary?| . 1508630) (|subNodeOf?| . 1508334) (|setleft!| . 1508190) (|fortranLinkerArgs| . 1508102) (|structuralConstants| . 1506886) (|removeDuplicates| . 1506726) (|generalCoefficient| . 1506328) (|basisOfInterpolateForms| . 1505767) (|prod| . 1505623) (|bumprow| . 1505334) (|viewDefaults| . 1505250) (|ellipticCylindrical| . 1505041) (|duplicates?| . 1504914) (|factor1| . 1504434) (|rest| . 1503658) (|An| . 1503490) (|graphState| . 1503237) (|op| . 1503081) (|reverse| . 1502679) (|Vectorise| . 1502511) (|graphStates| . 1502062) (|cyclotomic| . 1501590) (|linearPolynomials| . 1501219) (|create| . 1499614) (|pleskenSplit| . 1499130) (|rightCharacteristicPolynomial| . 1498963) (|setDifference| . 1498849) (|exprex| . 1498628) (|fortranCompilerName| . 1498540) (|internalLastSubResultant| . 1497614) (|label| . 1497564) (|nextIrreduciblePoly| . 1497388) (|setIntersection| . 1497274) (|more?| . 1496218) (|enterInCache| . 1495944) (|isOp| . 1495584) (|constant?| . 1495169) (|twoFactor| . 1494863) (|heap| . 1494752) (|inrootof| . 1494533) (|origin| . 1494441) (|branchPointAtInfinity?| . 1494172) (|rootBound| . 1493830) (|mulbyscalar| . 1493666) (|minset| . 1493312) (|balancedBinaryTree| . 1493172) (|singularitiesOf| . 1492307) (|setUnion| . 1492193) (|eigenvalues| . 1491937) (|infieldint| . 1491683) (|OMencodingUnknown| . 1491633) (|numFunEvals| . 1491561) (|color| . 1491374) (|blue| . 1491335) (|stirling2| . 1491216) (|size| . 1489277) (|infinityNorm| . 1488963) (|replaceVarByOne| . 1488677) (|integralMatrix| . 1488393) (|insertTop!| . 1488212) (|assoc| . 1487997) (|iiGamma| . 1487823) (|substitute| . 1487718) (|realEigenvectors| . 1487420) (|OMserve| . 1487294) (|bernoulli| . 1486983) (|pquo| . 1486603) (|iisinh| . 1486407) (|shellSort| . 1486149) (|generic| . 1484463) (|leftFactor| . 1484296) (|lift| . 1482395) (|graphs| . 1482118) (|PDESolve| . 1481561) (|sPol| . 1481207) (|position!| . 1481117) (|yellow| . 1481078) (|pair?| . 1480801) (|safeCeiling| . 1480638) (|reduce| . 1474053) (|lazyPseudoRemainder| . 1473948) (|testModulus| . 1473737) (|commutator| . 1473634) (|cyclotomicFactorization| . 1473464) (|ignore?| . 1473107) (|ddFact| . 1472873) (|llprop| . 1472716) (|OMgetEndBVar| . 1472634) (|quasiRegular?| . 1472331) (|qShiftAction| . 1472104) (|log2| . 1471981) (|leftUnits| . 1471354) (|cSec| . 1471194) (|script| . 1470830) (|RemainderList| . 1470444) (|solve| . 1453626) (|traceMatrix| . 1453002) (|monomialIntPoly| . 1452744) (|leftTraceMatrix| . 1452238) (|badValues| . 1452052) (|linear?| . 1451494) (|realSolve| . 1449393) (|printHeader| . 1449099) (|discriminant| . 1447722) (|ode1| . 1447494) (|eq| . 1447214) (|prepareSubResAlgo| . 1446810) (|modularFactor| . 1446599) (|lifting| . 1446018) (|sign| . 1443600) (|OMputAttr| . 1443518) (|KrullNumber| . 1442663) (|deref| . 1442581) (|evalat| . 1442442) (|lazyPseudoQuotient| . 1442337) (|scanOneDimSubspaces| . 1442085) (|rarrow| . 1442035) (|mindegTerm| . 1441837) (|member?| . 1440368) (|mainKernel| . 1440268) (|basisOfMiddleNucleus| . 1440090) (|dom| . 1440012) (|acosIfCan| . 1439871) (|realZeros| . 1437600) (|numberRatPlacesExtDeg| . 1436191) (|expressIdealMember| . 1436085) (|sorted?| . 1435758) (|range| . 1435546) (|mainSquareFreePart| . 1435327) (|nthRoot| . 1434953) (|fortran| . 1434741) (|OMgetEndAttr| . 1434659) (|terms| . 1434043) (|cAcsc| . 1433883) (|cubicBezier| . 1433724) (|maxLevel| . 1433446) (|cCoth| . 1433286) (|imagK| . 1433083) (|selectPolynomials| . 1432666) (|linGenPos| . 1432322) (|equality| . 1432187) (|delete| . 1431927) (|enqueue!| . 1431663) (|antiCommutator| . 1431604) (|complexNormalize| . 1430331) (|symmetric?| . 1429877) (|float?| . 1429600) (|doubleFloatFormat| . 1429519) (|genericLeftTraceForm| . 1429204) (|computeBasis| . 1428991) (|localIntegralBasis| . 1427532) (|coerceImages| . 1427413) (|leftRemainder| . 1427119) (|internalIntegrate0| . 1426710) (|foundPlaces| . 1426542) (|prinshINFO| . 1426278) (|horizSplit| . 1425414) (|normalForm| . 1424827) (|cosIfCan| . 1424686) (|stirling1| . 1424567) (|rightUnits| . 1423940) (|conditionP| . 1423619) (|hspace| . 1423538) (|mainCoefficients| . 1423323) (|top| . 1422981) (|iitan| . 1422785) (|leftOne| . 1422665) (|stoseInternalLastSubResultant| . 1421719) (|lSpaceBasis| . 1421419) (|maxPoints3D| . 1421345) (|makeUnit| . 1421196) (|normalDeriv| . 1420886) (|rank| . 1418407) (|computeCycleEntry| . 1418266) (|semiDiscriminantEuclidean| . 1418035) (|child| . 1417875) (|fixedPoints| . 1417728) (|fixedPointExquo| . 1417534) (|inverseIntegralMatrix| . 1417250) (|palgRDE0| . 1416151) (|iprint| . 1416036) (|degree| . 1411222) (|toseSquareFreePart| . 1410830) (|tanIfCan| . 1410689) (|getZechTable| . 1410068) (|quotValuation| . 1409975) (|rightRecip| . 1409752) (|discreteLog| . 1409529) (|purge!| . 1409330) (|pseudoQuotient| . 1409187) (|showFortranOutputStack| . 1409085) (|rationalPoint?| . 1408483) (|irreducibleFactors| . 1408117) (|lifting1| . 1407414) (|bumptab| . 1407194) (|latex| . 1406391) (|removeFirstZeroes| . 1406291) (|mkcomm| . 1406163) (|evaluate| . 1405172) (|constantLeft| . 1404932) (|reverseLex| . 1404725) (|toseInvertibleSet| . 1404373) (|newElement| . 1403792) (|makeSketch| . 1403591) (|removeConjugate| . 1403016) (|nthFlag| . 1402839) (|child?| . 1402681) (|tanh2trigh| . 1402466) (|stablePol| . 1402315) (|conditions| . 1402111) (|changeNameToObjf| . 1401995) (|midpoints| . 1401708) (|in?| . 1401086) (|wordInGenerators| . 1400904) (|every?| . 1399709) (|exprToXXP| . 1399149) (|generalPosition| . 1398756) (|stopTableInvSet!| . 1398063) (|doubleDisc| . 1397828) (|pointValue| . 1397581) (|empty?| . 1396485) (|makeEq| . 1396168) (|exp1| . 1396087) (|OMputBind| . 1396005) (|normalize| . 1394906) (|ScanArabic| . 1394787) (|plotPolar| . 1394158) (|generalTwoFactor| . 1393883) (|mapExponents| . 1393413) (|countRealRootsMultiple| . 1393169) (|leaves| . 1393048) (|subs2ndVar| . 1392790) (|extract!| . 1392288) (|digamma| . 1391845) (|bfKeys| . 1391755) (|gcdBasisAdd| . 1391547) (|printCode| . 1391468) (|OMclose| . 1391386) (|closedCurve| . 1390866) (|parametrize| . 1387583) (|zeroVector| . 1387416) (|UnVectorise| . 1387248) (|euclideanGroebner| . 1386354) (|limit| . 1384137) (|cycleTail| . 1384039) (|degreeSubResultant| . 1383831) (|divideIfCan!| . 1383487) (|setFoundPlacesToEmpty| . 1383319) (|constantIfCan| . 1383148) (|real?| . 1382399) (|lcmCoef| . 1382258) (|cyclicEntries| . 1382137) (|blockSplit| . 1380767) (|hasDimension?| . 1380445) (|Hausdorff| . 1380180) (|lazyPrem| . 1379800) (|repeating?| . 1379628) (|identification| . 1379367) (|constant| . 1378401) (|polygon| . 1377881) (|mapUp!| . 1377599) (|LyndonCoordinates| . 1377305) (|dasum| . 1377127) (|quotient| . 1376668) (|getDomains| . 1376536) (|gcdcofact| . 1376393) (|meshPar1Var| . 1376063) (|OMbindTCP| . 1375937) (|tex| . 1375849) (|increment| . 1375697) (|elliptic| . 1374937) (|radicalEigenvalues| . 1374756) (|cyclicParents| . 1374635) (|besselJ| . 1374180) (|zag| . 1374130) (|alphanumeric?| . 1374050) (|complexZeros| . 1373349) (|rowEchWoZeroLines| . 1373234) (|printInfo!| . 1373035) (|trivialIdeal?| . 1372764) (|stoseIntegralLastSubResultant| . 1372359) (|projection| . 1372261) (|consRow!| . 1372022) (|semicolonSeparate| . 1371929) (|multiplicity| . 1370972) (|infinity| . 1370781) (|denominators| . 1370650) (|setprevious!| . 1370509) (|nonLinearPart| . 1370394) (|univariatePolynomialsGcds| . 1369728) (|mapSolve| . 1369344) (|resetVariableOrder| . 1369252) (|tracePowMod| . 1369039) (|setcurve!| . 1368438) (|primlimitedint| . 1367897) (|pointLists| . 1367784) (|OMgetBind| . 1367702) (|factorAndSplit| . 1367543) (|hMonic| . 1367304) (|ODESolve| . 1366867) (|directSum| . 1366499) (|hclf| . 1366310) (|btwFact| . 1365929) (|indicialEquations| . 1364136) (|minPoly| . 1363678) (|lieAdmissible?| . 1363338) (|minimumExponent| . 1363178) (|outputArgs| . 1362806) (|composites| . 1362685) (|transpose| . 1361833) (|secIfCan| . 1361692) (|showIntensityFunctions| . 1361117) (|affineSingularPoints| . 1359757) (|complete| . 1359185) (|degOneCoef| . 1358891) (|replace| . 1358776) (|canonicalIfCan| . 1358629) (|unrankImproperPartitions1| . 1358480) (|quatern| . 1358367) (|readLineIfCan!| . 1358279) (|palgLODE| . 1357676) (|insertRoot!| . 1357578) (|suppOfZero| . 1357453) (|returnType!| . 1356910) (|mapGen| . 1356282) (|rationalPoints| . 1353967) (|rk4f| . 1353680) (|splitLinear| . 1353574) (|radicalRoots| . 1353010) (|inBetweenExcpDiv| . 1352348) (|cSinh| . 1352188) (|content| . 1351489) (|repeatUntilLoop| . 1351405) (|polyRingToBlUpRing| . 1351007) (|pointData| . 1350851) (|taylorRep| . 1350675) (|component| . 1350157) (|numberOfValuesNeeded| . 1349731) (|diff| . 1349319) (|weight| . 1348415) (|sizeMultiplication| . 1347506) (|symmetricRemainder| . 1347445) (|listOfMonoms| . 1347227) (|set| . 1347017) (|startTableGcd!| . 1346252) (|primextendedint| . 1345760) (|meshFun2Var| . 1345346) (|outputFloating| . 1345167) (|inR?| . 1345052) (|leftRank| . 1344860) (|quadratic| . 1344339) (|removeCoshSq| . 1344124) (|ptFunc| . 1343780) (|listSD| . 1343594) (|assert| . 1343175) (|oddInfiniteProduct| . 1342289) (|dot| . 1341534) (|setPredicates| . 1341411) (|symmetricTensors| . 1341077) (|nthFractionalTerm| . 1340947) (|ksec| . 1340708) (|affineAlgSet| . 1339797) (|fullDisplay| . 1339190) (|solveLinearPolynomialEquation| . 1338202) (|sncndn| . 1337958) (|dequeue| . 1337561) (|iilog| . 1337365) (|monomial?| . 1336449) (|parametersOf| . 1336359) (|theCurve| . 1335165) (|monic?| . 1334765) (|setPoly| . 1334627) (|property| . 1334506) (|df2fi| . 1334366) (|upperCase!| . 1334312) (|asimpson| . 1334009) (|modulus| . 1332859) (|definingInequation| . 1332626) (|OMUnknownCD?| . 1332538) (|arrayStack| . 1332420) (|lcm| . 1332105) (|concat| . 1330996) (|badNum| . 1330470) (|iicot| . 1330274) (|bat1| . 1330097) (|setFoundZeroes| . 1329976) (|getPickedPoints| . 1329860) (|dcopy| . 1329708) (|critBonD| . 1329342) (|patternMatchTimes| . 1328872) (|lexTriangular| . 1328567) (|slope| . 1327621) (|units| . 1326994) (|string?| . 1326717) (|ratDenom| . 1325030) (|indiceSubResultantEuclidean| . 1324737) (|unitVector| . 1324010) (|lexGroebner| . 1323838) (|userOrdered?| . 1323707) (|removeRedundantFactorsInContents| . 1323385) (|branchPoint?| . 1322844) (|usingTable?| . 1322675) (|scan| . 1320681) (|isExpt| . 1319055) (|viewThetaDefault| . 1318875) (|ldf2vmf| . 1318723) (|radicalOfLeftTraceForm| . 1318545) (|distdfact| . 1318228) (|iiBeta| . 1318026) (|showClipRegion| . 1317904) (|pointColor| . 1317747) (|complexRoots| . 1317229) (|computeCycleLength| . 1317052) (|measure2Result| . 1316606) (|code| . 1315363) (|iiAiryBi| . 1315189) (|pointV| . 1314684) (|bitLength| . 1314602) (|exponential| . 1314239) (|unit?| . 1314152) (|factorGroebnerBasis| . 1313430) (|kmax| . 1313224) (|quotVecSpaceBasis| . 1313099) (|conjugates| . 1312983) (|removeRoughlyRedundantFactorsInPols| . 1312375) (|rationalPlaces| . 1311124) (|order| . 1306499) (|critM| . 1306229) (|elRow2!| . 1305931) (|Lazard| . 1305723) (|separateFactors| . 1305172) (|pole?| . 1304853) (|invertible?| . 1304235) (|torsionIfCan| . 1303258) (|multiEuclidean| . 1303157) (|double?| . 1303069) (|extendedResultant| . 1302777) (|noKaratsuba| . 1302603) (|cyclicGroup| . 1302301) (NOT . 1302046) (|argscript| . 1301954) (|patternMatch| . 1297829) (|droot| . 1297604) (|axServer| . 1297441) (|trueEqual| . 1297347) (|startTableInvSet!| . 1296582) (|map!| . 1295367) (OR . 1295149) (|getEq| . 1294796) (|normal01| . 1294706) (|reciprocalPolynomial| . 1294513) (|stiffnessAndStabilityOfODEIF| . 1294037) (|jordanAlgebra?| . 1293697) (|sizePascalTriangle| . 1293568) (AND . 1293350) (|super| . 1293300) (|separate| . 1292614) (|cycleLength| . 1292477) (|encode| . 1292360) (|setLegalFortranSourceExtensions| . 1292267) (|minimize| . 1291986) (|changeMeasure| . 1291871) (|internalSubQuasiComponent?| . 1291158) (|qelt| . 1290551) (|copyQuadVar| . 1290339) (|dnrm2| . 1290161) (|iifact| . 1289991) (|useSingleFactorBound| . 1289833) (|tanNa| . 1289711) (|harmonic| . 1289571) (|dominantTerm| . 1288897) (|extendIfCan| . 1288631) (|symbolTableOf| . 1288512) (|say| . 1288288) (|alternative?| . 1287948) (|cAsinh| . 1287788) (|totalfract| . 1287352) (|adjunctionDivisor| . 1285496) (|maxdeg| . 1285205) (|OMReadError?| . 1285117) (|Zero| . 1284816) (|mainCharacterization| . 1284552) (|zRange| . 1284436) (|debug| . 1284152) (|optAttributes| . 1283648) (|antiCommutative?| . 1283308) (|goodnessOfFit| . 1282970) (|UP2ifCan| . 1282506) (|OMgetVariable| . 1282422) (|setScreenResolution| . 1282347) (|normalise| . 1282231) (|retractable?| . 1281420) (|leader| . 1281173) (|genericLeftMinimalPolynomial| . 1280830) (|chineseRemainder| . 1279911) (|laplace| . 1279525) (|pivots| . 1279314) (|initiallyReduced?| . 1278294) (|subPolSet?| . 1277545) (|lagrange| . 1277052) (|solveLinearlyOverQ| . 1276829) (|rightAlternative?| . 1276489) (|dAndcExp| . 1276262) (LODO2FUN . 1275948) (|findTerm| . 1275750) (|getExplanations| . 1275628) (|fmecg| . 1274563) (|aromberg| . 1274260) (|basisOfRightNucloid| . 1274071) (|decrease| . 1273847) (|bernoulliB| . 1273632) (|padicFraction| . 1273533) (|factors| . 1272846) (|viewport3D| . 1272788) (|concat!| . 1272167) (|tryFunctionalDecomposition?| . 1272012) (|setButtonValue| . 1271782) (|partialNumerators| . 1271651) (|rotatez| . 1271510) (|charpol| . 1271245) (|explogs2trigs| . 1270852) (|curve| . 1270143) (|factorSquareFreeByRecursion| . 1269447) (|setClosed| . 1269312) (|iisec| . 1269116) (|fffg| . 1268675) (|leftZero| . 1268559) (|pomopo!| . 1268406) (|numberOfNormalPoly| . 1268254) (|minPol| . 1267594) (|OMconnOutDevice| . 1267498) (* . 1258919) (|triangular?| . 1258611) (|rem| . 1258452) (|nonQsign| . 1258329) (|domainOf| . 1258252) (|morphism| . 1257886) (|cycleElt| . 1257738) (|redPo| . 1257409) (|leftExtendedGcd| . 1257189) (|members| . 1256157) (|powers| . 1256022) (|semiIndiceSubResultantEuclidean| . 1255746) (|indexName| . 1255536) (|generalizedContinuumHypothesisAssumed| . 1255451) (|lazyEvaluate| . 1255357) (|pfaffian| . 1255130) (|defineProperty| . 1254912) (|complexEigenvectors| . 1254575) (|toseInvertible?| . 1253825) (|rationalFunction| . 1253383) (|decompose| . 1250523) (|quo| . 1250364) (|convertIfCan| . 1250257) (|newLine| . 1250176) (|getOp| . 1249789) (|selectOrPolynomials| . 1249363) (|maxPoints| . 1249126) (|makeViewport3D| . 1248770) (|partitions| . 1248335) (|monicRightDivide| . 1247807) (|expintegrate| . 1247374) (|pascalTriangle| . 1247211) (|algint| . 1246828) (|trailingCoefficient| . 1246671) (|rk4a| . 1246378) (|nextItem| . 1246318) (|axesColorDefault| . 1246144) (|or| . 1245999) (|externalList| . 1245909) (|/\\| . 1245812) (|leviCivitaSymbol| . 1245647) (|pmComplexintegrate| . 1245068) (|OMputEndAtp| . 1244986) (|solveLinearPolynomialEquationByRecursion| . 1244272) (|retract| . 1235064) (|supDimElseRittWu?| . 1234371) (|decomposeFunc| . 1234156) (|cSin| . 1233996) (|\\/| . 1233899) (|principalSubResultantSet| . 1233664) (|reducedForm| . 1233563) (|outputMeasure| . 1233443) (|rightRemainder| . 1233305) (|setTopPredicate| . 1233152) (|triangSolve| . 1232070) (|movedPoints| . 1231832) (|internalInfRittWu?| . 1231083) (|realElementary| . 1230402) (|setParam!| . 1230203) (|binomial| . 1229629) (|pdct| . 1229549) (|interpolateFormsForFact| . 1227539) (|collectUpper| . 1227293) (|anticoord| . 1226997) (|guessAlg| . 1222662) (|BasicMethod| . 1222515) (|ratpart| . 1222424) (|scalarMatrix| . 1221992) (|makingStats?| . 1221823) (|certainlySubVariety?| . 1221505) (|invertibleSet| . 1221219) (~= . 1220394) (|drotg| . 1220247) (|hexDigit| . 1220199) (|leftCharacteristicPolynomial| . 1220032) (|processTemplate| . 1219858) (|setchart!| . 1219350) (|invertibleElseSplit?| . 1219042) (|maxTower| . 1218925) (|bezoutMatrix| . 1218631) (|transCoord| . 1218538) (|fortranCharacter| . 1218493) (|minColIndex| . 1218026) (|plus!| . 1217885) (|atom?| . 1217608) (|removeSinSq| . 1217393) (|previous| . 1217297) (|factorSqFree| . 1216712) (|infieldIntegrate| . 1216453) (|pushup| . 1215349) (|clearTheSymbolTable| . 1215164) (|paren| . 1214891) (|setchildren!| . 1214725) (|dihedral| . 1214574) (|ShiftC| . 1214328) (|startTable!| . 1213581) (|viewDeltaYDefault| . 1213401) (|limitedIntegrate| . 1212961) (|divide| . 1212002) (|asinhIfCan| . 1211861) (|exprToGenUPS| . 1210982) (|palgintegrate| . 1210486) (|logpart| . 1210222) (|topPredicate| . 1210055) (|slash| . 1210005) (|ratDsolve| . 1208198) (|critpOrder| . 1207813) (|nthCoef| . 1207624) (|reduceBasisAtInfinity| . 1207350) (|aRow| . 1207070) (|resultantnaif| . 1206904) (|currentSubProgram| . 1206823) (|stronglyReduce| . 1206567) (|primitiveElement| . 1204627) (|factorsOfDegree| . 1204368) (|entry| . 1203279) (|cSech| . 1203119) (|getRef| . 1202950) (|viewWriteDefault| . 1202760) (|semiDegreeSubResultantEuclidean| . 1202484) (|message| . 1202404) (|gradient| . 1202049) (|true| . 1202008) (|insertBottom!| . 1201827) (|colorFunction| . 1201446) (LE . 1201228) (|lambert| . 1200735) (|points| . 1200576) (|removeZero| . 1200320) (|multiplyExponents| . 1199842) (|printStats!| . 1199676) (|e| . 1199490) (|Yun| . 1199279) (|sqfrFactor| . 1199157) (|maxShift| . 1198879) (|OMgetBVar| . 1198797) (|symbolTable| . 1198654) (|univariatePolynomial| . 1197778) (|cross| . 1197473) (|reduction| . 1196923) (|pushFortranOutputStack| . 1196684) (|inRadical?| . 1196425) (|addmod| . 1196361) (|cAcosh| . 1196201) (|removeSuperfluousCases| . 1195416) (|exQuo| . 1194449) (|divide!| . 1194285) (|extractIfCan| . 1194131) (|increase| . 1193907) (|filename| . 1193813) (|difference| . 1193622) (|padicallyExpand| . 1193470) (|se2rfi| . 1193061) (|janko2| . 1192798) (|e01sff| . 1192578) (|squareMatrix| . 1192423) (|setnext!| . 1192282) (|popFortranOutputStack| . 1192192) (|powmod| . 1192128) (|fglmIfCan| . 1191711) (|stoseInvertible?| . 1190941) (|quasiMonic?| . 1190726) (|OMunhandledSymbol| . 1190613) (|idealSimplify| . 1190380) (|central?| . 1190199) (|upperCase| . 1190057) (|alterQuadVar!| . 1189864) (|subTriSet?| . 1189171) (|outputAsFortran| . 1188299) (|alternatingGroup| . 1187997) (|flagFactor| . 1187817) (|cCot| . 1187657) (|leftScalarTimes!| . 1187516) (|OMreadStr| . 1187407) (|SturmHabichtMultiple| . 1187160) (|setMaxPoints| . 1187085) (|iCompose| . 1186977) (|extendedint| . 1186631) (|bandedJacobian| . 1186231) (|height| . 1185297) (|cycles| . 1185159) (|shiftLeft| . 1185014) (|nlde| . 1184787) (|reduceLineOverLine| . 1184668) (|vedf2vef| . 1184491) (|unitNormalize| . 1184400) (|indiceSubResultant| . 1184192) (|Frobenius| . 1183603) (|uncorrelated?| . 1183013) (|dmp2rfi| . 1181849) (|mapDown!| . 1181558) (|lfunc| . 1181475) (|setEpilogue!| . 1181286) (|connect| . 1181127) (|scale| . 1180645) (|maxint| . 1180465) (|plot| . 1178582) (|dioSolve| . 1178262) (|viewPosDefault| . 1178048) (|dihedralGroup| . 1177746) (|evenlambert| . 1177253) (|pdf2df| . 1177107) (|complexIntegrate| . 1176388) (|eigenvector| . 1176071) (|consnewpol| . 1175571) (|addBadValue| . 1175299) (|infix| . 1175153) (|iiBesselY| . 1174951) (|symmetricDifference| . 1174854) (|module| . 1174193) (|subspace| . 1173729) (|mapBivariate| . 1173366) (|acotIfCan| . 1173225) (|OMputBVar| . 1173143) (|possiblyNewVariety?| . 1172788) (|ScanFloatIgnoreSpaces| . 1172679) (|linearBezier| . 1172526) (|rewriteIdealWithRemainder| . 1172215) (|Beta| . 1171568) (|prevPrime| . 1171460) (|inGroundField?| . 1171342) (|excpDivV| . 1170837) (|unrankImproperPartitions0| . 1170688) (|shiftRight| . 1170543) (|B1solve| . 1169839) (|accuracyIF| . 1169432) (|basisOfLeftAnnihilator| . 1169251) (|resetAttributeButtons| . 1169170) (|primlimintfrac| . 1168769) (|bivariateSLPEBR| . 1168372) (|binaryTournament| . 1168249) (|condition| . 1168073) (|iiatanh| . 1167877) (|HermiteIntegrate| . 1167120) (|genericLeftDiscriminant| . 1166811) (|recip| . 1164827) (|modifyPointData| . 1164484) (|construct| . 1160164) (|partialDenominators| . 1160033) (|int| . 1159383) (|recolor| . 1159118) (|linearPart| . 1159003) (|createThreeSpace| . 1158898) (|setsymbName!| . 1158361) (|printTypes| . 1158176) (|packModulus| . 1157910) (|fractRagits| . 1157785) (|shiftRoots| . 1157622) (|getlo| . 1157136) (|bubbleSort!| . 1156593) (|primitive?| . 1156310) (|leftNorm| . 1156193) (F2FG . 1155831) (|posExpnPart| . 1155731) (|varselect| . 1155525) (|critT| . 1155143) (|key| . 1154880) (|setPosition| . 1154757) (|squareFree| . 1152244) (|raisePolynomial| . 1151915) (|OMsend| . 1151760) (|curveColorPalette| . 1151626) (|lflimitedint| . 1151101) (^= . 1151051) (|stoseInvertibleSetreg| . 1150689) (|mesh?| . 1150568) (GE . 1150350) (|pmintegrate| . 1149219) (|OMgetObject| . 1149137) (|integralMatrixAtInfinity| . 1148853) (|lfextlimint| . 1148343) (|comment| . 1148175) (|graphImage| . 1148131) (|translateToOrigin| . 1147003) (|horizConcat| . 1146545) (|maxSubst| . 1146273) (|float| . 1145801) (|sumOfDivisors| . 1145702) (|hdmpToDmp| . 1145453) (|triangulate| . 1144776) (|cExp| . 1144616) (|id| . 1144521) (|quoByVar| . 1144416) (|numerator| . 1144039) (|closeComponent| . 1143839) (|expint| . 1143458) (|integer| . 1143081) (|lazyPremWithDefault| . 1142503) (|quadraticBezier| . 1142347) (|clearTheFTable| . 1142257) (|setOfMinN| . 1142073) (|isAbsolutelyIrreducible?| . 1141665) (|copy!| . 1141527) (|tubePointsDefault| . 1141337) (|cLog| . 1141177) (|tableau| . 1141053) (|solveRetract| . 1140721) (|poisson| . 1140579) (|Ei4| . 1140454) (|nsqfree| . 1139929) (|string| . 1139479) (|symbol| . 1139230) (|divideIfCan| . 1138974) (|radicalEigenvectors| . 1138676) (|OMreadFile| . 1138567) (|halfExtendedResultant1| . 1138326) (|minus!| . 1138050) (|series| . 1131942) (|finiteSeries2Vector| . 1131722) (|localParamOfSimplePt| . 1131200) (|multiset| . 1130917) (|one| . 1130705) (|stoseLastSubResultant| . 1130300) (|hypergeometric0F1| . 1130081) (|eigenMatrix| . 1129888) (|compdegd| . 1129502) (|zero| . 1129110) (|polygamma| . 1128577) (|rightExtendedGcd| . 1128357) (|negative?| . 1127880) (|contractSolve| . 1127224) (^ . 1126624) (|linearAssociatedOrder| . 1126440) (|genericLeftTrace| . 1126128) (|nextPrime| . 1126020) (|vertConcat| . 1125562) (|exp| . 1123295) (|monomRDEsys| . 1122844) (|getOrder| . 1122665) (|multinomial| . 1122518) (|safeFloor| . 1122355) (|pi| . 1121886) (|mindeg| . 1121598) (|useEisensteinCriterion| . 1121440) (|pack!| . 1121304) (|makeFR| . 1120795) (|sqrt| . 1120129) (|setlocalParam!| . 1119591) (|hex| . 1119487) (|symmetricProduct| . 1119119) (|fractionFreeGauss!| . 1118821) (|divideExponents| . 1118666) (|viewDeltaXDefault| . 1118486) (|parametric?| . 1118411) (|primes| . 1118272) (|li| . 1117977) (|localUnquote| . 1117629) (|limitPlus| . 1116789) (|generalizedEigenvectors| . 1116438) (|clikeUniv| . 1116220) (|erf| . 1115925) (|top!| . 1115750) (|sincos| . 1115511) (|seed| . 1115425) (|applyTransform| . 1115118) (|sumOfSquares| . 1115002) (|setSingularPoints| . 1113753) (|ramifMult| . 1113660) (|changeWeightLevel| . 1113039) (|tree| . 1112375) (|makeop| . 1112069) (|approxNthRoot| . 1111927) (|size?| . 1111038) (|alphabetic?| . 1110958) (|dilog| . 1110663) (|extendedEuclidean| . 1110384) (|create3Space| . 1110170) (|mask| . 1110112) (|nextLatticePermutation| . 1109963) (|sin| . 1108493) (|tower| . 1108394) (|filterUpTo| . 1108263) (|dmpToHdmp| . 1108014) (|boundOfCauchy| . 1107819) (|cos| . 1106349) (|constantToUnaryFunction| . 1106196) (|setRealSteps| . 1106114) (|weakBiRank| . 1105922) (|sinhIfCan| . 1105781) (|genericLeftNorm| . 1105469) (|tan| . 1104091) (|center| . 1103550) (|trigs2explogs| . 1103107) (|associatedSystem| . 1102790) (|OMputEndAttr| . 1102708) (|product| . 1101615) (|cot| . 1100420) (|updateStatus!| . 1100244) (|explimitedint| . 1099689) (|hermiteH| . 1099534) (|readLine!| . 1099456) (|sec| . 1098261) (|diagonalProduct| . 1097753) (|factorFraction| . 1097536) (|mkAnswer| . 1097191) (|supp| . 1097066) (|char| . 1096910) (|csc| . 1095715) (|hyperelliptic| . 1095161) (|linearlyDependent?| . 1094951) (|generic?| . 1094836) (|splitNodeOf!| . 1094328) (|asin| . 1092947) (|colorDef| . 1092823) (|objectOf| . 1092746) (|basisOfNucleus| . 1092568) (|df2st| . 1092199) (|allPairsAmong| . 1091653) (|acos| . 1090272) (|deepestInitial| . 1090085) (|d| . 1089918) (|clipWithRanges| . 1089624) (|augment| . 1088433) (|atan| . 1086962) (|weighted| . 1086752) (|removeConstantTerm| . 1086548) (|innerEigenvectors| . 1086097) (|ddot| . 1085913) (|exprHasAlgebraicWeight| . 1085584) (|acot| . 1084386) (|generalizedInverse| . 1084130) (|leadingSupport| . 1083984) (|search| . 1083837) (|rightRankPolynomial| . 1083070) (|partition| . 1082868) (|asec| . 1081670) (|compactFraction| . 1081571) (|build| . 1081092) (|overbar| . 1081045) (|acothIfCan| . 1080904) (|acsc| . 1079706) (|extend| . 1077467) (|palglimint| . 1076896) (|iipolygamma| . 1076694) (|entry?| . 1076460) (|numer| . 1075197) (|sinh| . 1073822) (|merge!| . 1073351) (|BumInSepFFE| . 1072988) (|variablesOf| . 1072864) (|degreePartition| . 1072360) (|denom| . 1071117) (|cosh| . 1069742) (|lprop| . 1069594) (|rotate| . 1069347) (|systemSizeIF| . 1068940) (|balancedFactorisation| . 1068469) (|kernel| . 1067952) (|tanh| . 1066577) (|incrementKthElement| . 1066423) (|superscript| . 1066331) (|baseRDE| . 1066001) (|subResultantsChain| . 1065797) (|draw| . 1057767) (|coth| . 1056575) (|alternating| . 1056424) (|cylindrical| . 1056240) (|selectOptimizationRoutines| . 1056190) (|cTan| . 1056030) (|makeObject| . 1051559) (|sech| . 1050367) (|internal?| . 1050221) (|exponents| . 1050130) (|Somos| . 1049858) (|adaptive| . 1049481) (|coef| . 1048881) (|csch| . 1047689) (|closed?| . 1047464) (|LagrangeInterpolation| . 1047269) (|generalizedEigenvector| . 1046501) (|youngGroup| . 1046205) (|monom| . 1045754) (|zeroDimPrimary?| . 1045382) (|asinh| . 1044187) (|tRange| . 1044006) (|numberOfComputedEntries| . 1043873) (|quasiMonicPolynomials| . 1043502) (|e02bcf| . 1043297) (|totalDegree| . 1042584) (|unravel| . 1042388) (|acosh| . 1041193) (|cosSinInfo| . 1041059) (|leftMinimalPolynomial| . 1040855) (|sh| . 1040491) (|e02bbf| . 1040289) (|resultantReduit| . 1040091) (|quickSort| . 1039833) (|atanh| . 1038638) (|setexcpDiv!| . 1038130) (|e02baf| . 1037954) (|scripted?| . 1037877) (|wronskianMatrix| . 1037416) (|cyclePartition| . 1037295) (|iidigamma| . 1037121) (|acoth| . 1035926) (|e02akf| . 1035715) (|nextPartition| . 1035379) (|getVariableOrder| . 1035220) (|extendedgcd| . 1035045) (|homogeneous| . 1034773) (|headReduce| . 1034330) (|mapMatrixIfCan| . 1033928) (|asech| . 1032733) (|listBranches| . 1032472) (|reduceByQuasiMonic| . 1032216) (|atanIfCan| . 1032075) (|e02ajf| . 1031858) (|brillhartIrreducible?| . 1031556) (|e04ycf| . 1031340) (|besselY| . 1030885) (|trim| . 1030697) (|pointColorDefault| . 1030523) (|invmultisect| . 1029894) (|OMputEndError| . 1029812) (|firstSubsetGray| . 1029675) (|perfectSquare?| . 1029547) (|rdregime| . 1028925) (|e04ucf| . 1028381) (|stoseInvertible?sqfreg| . 1027970) (|someBasis| . 1027826) (|e04naf| . 1027417) (|roman| . 1027255) (|epilogue| . 1027072) (|rightFactorIfCan| . 1026805) (|systemCommand| . 1026692) (|swapColumns!| . 1026469) (|e04mbf| . 1026236) (|countRealRoots| . 1026024) (|chebyshevU| . 1025711) (|getMatch| . 1025532) (|vector| . 1025308) (|functionNames| . 1025218) (|e04jaf| . 1024953) (|new| . 1023663) (|routines| . 1023616) (|cschIfCan| . 1023475) (|RittWuCompare| . 1023247) (|zCoord| . 1023133) (|LyndonWordsList| . 1022934) (|internalDecompose| . 1019959) (|clearDenominator| . 1019070) (|e04gcf| . 1018811) (|logIfCan| . 1018670) (|ffactor| . 1018363) (|setValue!| . 1018184) (|e04fdf| . 1017925) (|singRicDE| . 1016832) (|bit?| . 1016737) (|biRank| . 1016545) (|declare| . 1016427) (|e04dgf| . 1016084) (|tanhIfCan| . 1015943) (|deepCopy| . 1015825) (|npcoef| . 1015188) (|internalIntegrate| . 1014464) (|polar| . 1014280) (|f01ref| . 1014053) (|isQuotient| . 1013754) (|lastNonNull| . 1013627) (|distinguishedRootsOf| . 1013231) (|trunc| . 1012888) (|f01rdf| . 1012652) (|laurentRep| . 1012475) (|OMread| . 1012358) (|intcompBasis| . 1012096) (|f01rcf| . 1011905) (|whatInfinity| . 1011774) (|SturmHabichtCoefficients| . 1011559) (|leaf?| . 1011127) (|getSmgl| . 1011020) (|nullSpace| . 1009313) (|f01qef| . 1009098) (|insert!| . 1006128) (|unit| . 1005794) (|f01qdf| . 1005570) (|shiftInfoRec| . 1005000) (|sbt| . 1004897) (|cyclic| . 1004746) (|f01qcf| . 1004567) (|newSubProgram| . 1004458) (|rightTrace| . 1004341) (|f01mcf| . 1004123) (|besselI| . 1003668) (|match| . 1002326) (|queue| . 1002213) (|rootProduct| . 1001656) (|curveColor| . 1001499) (|pointDominateBy| . 999745) (|f01maf| . 999440) (|coefOfFirstNonZeroTerm| . 999340) (|swap!| . 999139) (|f01bsf| . 998837) (|OMputObject| . 998755) (|leftTrim| . 998567) (|makeVariable| . 997781) (|f01brf| . 997445) (|asinIfCan| . 997304) (|false| . 997263) (|palgextint| . 996779) (|gcdPolynomial| . 996231) (|coefChoose| . 995924) (|extractPoint| . 995777) (|variableOf| . 995599) (|splitConstant| . 995196) (|complexExpand| . 994548) (|guessADE| . 987495) (|decimal| . 987395) (|iiperm| . 987197) (|rightUnit| . 987036) (|hasoln| . 986589) (|retractToGrn| . 986421) (|bright| . 986138) (LT . 985920) (|numberOfPlacesOfDegree| . 984511) (|weierstrass| . 984304) (|integerIfCan| . 984163) (|inc| . 984105) (|displayKind| . 984024) (|errorInfo| . 983932) (|flexibleArray| . 983671) (|factorsOfCyclicGroupSize| . 983518) (|open?| . 983386) (|useSingleFactorBound?| . 983231) (|cond| . 983063) (|argumentListOf| . 982940) (|sortedPurge!| . 982741) (|conjugate| . 981711) (|createMultiplicationMatrix| . 981477) (|depth| . 980856) (|showRegion| . 980734) (|elements| . 980550) (|count| . 978085) (|foundZeroes| . 977967) (|newtonPolySlope| . 977515) (|OMputVariable| . 977403) (|parent| . 977285) (|integralRepresents| . 977008) (|edf2df| . 976862) (|areEquivalent?| . 976190) (|reduceLODE| . 975777) (|algintegrate| . 975281) (|clipParametric| . 974703) (|cyclotomicDecomposition| . 974537) (|generateIrredPoly| . 974339) (|coerceP| . 974133) (|singularAtInfinity?| . 973864) (|commonDenominator| . 973005) (|rowEchLocal| . 972860) (|leftExactQuotient| . 972546) (|is?| . 971442) (|polyRicDE| . 970463) (|cPower| . 970300) (|subresultantSequence| . 970057) (|elColumn2!| . 969759) (|beauzamyBound| . 969417) (|adjoint| . 968382) (|simplify| . 967702) (|permutationGroup| . 967562) (|squareFreePrim| . 967286) (|elt| . 958066) (|copyBSD| . 957942) (|ratPoly| . 957487) (|linearMatrix| . 957287) (|setelt| . 954885) (|iiacot| . 954689) (|dotview| . 954583) (|failed| . 954276) (|cCsc| . 954116) (|style| . 953906) (|fresnelC| . 953518) (FG2F . 953156) (|moduleSum| . 952770) (|machineFraction| . 952675) (|rowEch| . 952533) (|setFieldInfo| . 952291) (|iExquo| . 952142) (|principalIdeal| . 951976) (|iicsch| . 951780) (|constantKernel| . 951619) (|tubeRadiusDefault| . 951411) (|numberOfFractionalTerms| . 951284) (|genericRightMinimalPolynomial| . 950941) (|symbol?| . 950552) (|permutations| . 950408) (F . 950261) (|convergents| . 950117) (GT . 949899) (|maxColIndex| . 949432) (|interpret| . 949237) (|children| . 948957) (|binaryFunction| . 948681) (|initials| . 948400) (|introduce!| . 948290) (|mulbybinomial| . 947968) (|integralBasisAtInfinity| . 947697) (|sortConstraints| . 947364) (|errorKind| . 947270) (|SFunction| . 947110) (|argument| . 946754) (|rightRank| . 946562) (|box| . 946379) (|squareTop| . 946190) (|numericalOptimization| . 945600) (|primintegrate| . 945181) (|prepareDecompose| . 944154) (|finite?| . 943824) (|OMputString| . 943712) (|tanQ| . 943341) (|lastNonNul| . 943214) (|chebyshevT| . 942901) (|shade| . 942712) (|sequences| . 942406) (|monomial2series| . 942196) (|OMmakeConn| . 942101) (|lazyResidueClass| . 941575) (|oddintegers| . 941407) (|deepExpand| . 941196) (|saturate| . 940706) (|smaller?| . 940620) (|curve?| . 940499) (|OMgetEndApp| . 940417) (|ZetaFunction| . 937507) (|qPot| . 937328) (|exponent| . 936544) (|roughBasicSet| . 936147) (|factorset| . 935802) (|brillhartTrials| . 935484) (|dimensionsOf| . 935050) (|createGenericMatrix| . 934871) (|moreAlgebraic?| . 934178) (|level| . 934021) (|taylorIfCan| . 933835) (|romberg| . 933535) (|separe| . 933350) (|mainVariableOf| . 933235) (|createNormalPrimitivePoly| . 933033) (|toroidal| . 932824) (|setDegree!| . 932617) (|numberOfOperations| . 932329) (|normalizeAtInfinity| . 932055) (|represents| . 930926) (|lazyIrreducibleFactors| . 930560) (|shanksDiscLogAlgorithm| . 930330) (|iiAiryAi| . 930156) (|schwerpunkt| . 929944) (|nextsubResultant2| . 929711) (|subresultantVector| . 929511) (|setFormula!| . 929410) (|supRittWu?| . 929192) (|minimalForm| . 928268) (|deepestTail| . 928081) (|tube| . 927677) (|collect| . 927337) (~ . 927246) (|edf2ef| . 927091) (|multiEuclideanTree| . 926966) (|lazyVariations| . 926670) (|stripCommentsAndBlanks| . 926583) (|dimensions| . 926230) (|goppaCode| . 924930) (|matrixDimensions| . 924778) (|physicalLength!| . 924520) (|variableName| . 924310) (|pureLex| . 924103) (|newTypeLists| . 924017) (|combineFeatureCompatibility| . 923809) (|nextColeman| . 923649) (|setlocalPoint!| . 923104) (|unparse| . 923025) (|column| . 922552) (|zeroSetSplitIntoTriangularSystems| . 922193) (|iitanh| . 921997) (|lexico| . 921641) (|basisOfRightNucleus| . 921463) (|dfRange| . 921330) (|limitedint| . 920910) (|selectAndPolynomials| . 920484) (|MPtoMPT| . 920235) (|multiplyCoefficients| . 919787) (|character?| . 919699) (|ran| . 919442) (|perfectNthRoot| . 919110) (|evalRec| . 918669) (|linearAssociatedExp| . 918482) (|call| . 918401) (|unprotectedRemoveRedundantFactors| . 918111) (|completeHensel| . 917877) (|inverseColeman| . 917717) (|ParCondList| . 917116) (|triangularSystems| . 916868) (|purelyTranscendental?| . 916582) (|setref| . 916497) (|generators| . 916104) (|separant| . 915857) (|transform| . 915593) (|setTex!| . 915502) (|cotIfCan| . 915361) (|birth| . 915243) (|applyRules| . 914483) (|airyBi| . 914040) (|notelem| . 913874) (|mainVariables| . 913603) (|OMreceive| . 913476) (|zeroOf| . 912805) (|placesOfDegree| . 910562) (|nor| . 910464) (|iiasin| . 910268) (|integralAtInfinity?| . 909996) (|tubeRadius| . 909788) (|simpson| . 909488) (EQ . 909270) (|Si| . 908975) (|lllp| . 908826) (|extendedSubResultantGcd| . 908206) (|compose| . 907921) (|fi2df| . 907781) (UP2UTS . 907510) (|palgLODE0| . 906247) (|OMputAtp| . 906165) (|numberPlacesDegExtDeg| . 904747) (|move| . 904478) (|ramified?| . 903937) (|ScanRoman| . 903818) (|debug3D| . 903741) (|univariatePolynomials| . 903370) (|satisfy?| . 902763) (|chartCoord| . 902670) (|ode2| . 902436) (|placesAbove| . 901088) (|clipBoolean| . 900954) (|att2Result| . 900057) (|approxSqrt| . 899957) (|integralBasis| . 898225) (|isPower| . 897377) (|setRow!| . 896631) (|addPoint| . 896036) (|nextPrimitiveNormalPoly| . 895860) (|gnuDraw| . 895001) (|controlPanel| . 894762) (|subResultantGcd| . 894232) (|base| . 893789) (|rename| . 893695) (|setvalue!| . 893557) (|zeroDimensional?| . 893104) (|OMgetAtp| . 893022) (|generalLambert| . 892393) (|copyIto| . 892257) (|horizJoin| . 892126) (|substring?| . 892004) (|totalLex| . 891797) (|merge| . 890846) (|numerators| . 890715) (|localAbs| . 889652) (|pushuconst| . 889281) (|removeDuplicates!| . 889053) (|setCurve| . 887850) (|hasPredicate?| . 887735) (|reducedSystem| . 887338) (|scalarTypeOf| . 887204) (|const| . 887038) (|overlap| . 886600) (|gramschmidt| . 886475) (|minRowIndex| . 886008) (|linearDependenceOverZ| . 885801) (|desingTree| . 883832) (|diagonalMatrix| . 882559) (|elimZeroCols!| . 882406) (|statusIto| . 882249) (|cycle| . 882120) (|drawComplex| . 881856) (|complexForm| . 881171) (|number?| . 881017) (|cardinality| . 880878) (|moduloP| . 880782) (|monomRDE| . 880381) (|factorSquareFreePolynomial| . 880192) (|yCoordinates| . 879880) (|nthRootIfCan| . 879697) (|algDsolve| . 879162) (|copyInto!| . 878990) (|safety| . 878756) (|mainPrimitivePart| . 878537) (|interpretString| . 878426) (|ScanFloatIgnoreSpacesIfCan| . 878307) (|knownInfBasis| . 878000) (|quadraticNorm| . 877686) (|elliptic?| . 877156) (|innerint| . 876516) (|mainForm| . 876415) (|gethi| . 875929) (|double| . 875743) (|zero?| . 875027) (|OMgetSymbol| . 874897) (|geometric| . 874755) (|iiacoth| . 874559) (|completeEval| . 874168) (|element?| . 873909) (|exists?| . 873820) (|getCurve| . 873716) (|normalizedAssociate| . 873402) (|leftQuotient| . 873108) (|eulerPhi| . 873009) (|perspective| . 872887) (|findCycle| . 872636) (|increasePrecision| . 872464) (|pushdown| . 871360) (|setOrder| . 871042) (|HenselLift| . 870737) (|setmult!| . 870208) (|frst| . 870114) (|partialFraction| . 869471) (|pToDmp| . 869259) (|rightOne| . 869139) (|createRandomElement| . 868972) (|standardBasisOfCyclicSubmodule| . 868737) (|cCos| . 868577) (|tab1| . 868400) (|OMsupportsCD?| . 868287) (|sampleDotGraph| . 868203) (|maxDegree| . 867925) (|polygon?| . 867804) (|distance| . 867680) (|option?| . 867529) (|direction| . 867389) (|appendRow!| . 867150) (|imagI| . 866947) (|shrinkable| . 866686) (|derivative| . 866127) (|showScalarValues| . 866050) (|iiacsch| . 865854) (|legendre| . 865581) (|sum| . 862904) (|randomR| . 862181) (|frobenius| . 862001) (|pseudoRem| . 861861) (|quadTransform| . 861441) (|graphCurves| . 860841) (|fortranComplex| . 860796) (|lighting| . 860669) (|lex| . 860538) (|plus| . 860099) (|maxRowIndex| . 859632) (|getAncestors| . 859500) (|flush| . 859344) (|leadingExponent| . 858871) (|extractBottom!| . 858696) (|tensorMap| . 858535) (|newReduc| . 858315) (|eval| . 847327) (|resize| . 847064) (|operation| . 846566) (|rightDivide| . 846056) (|rationalPower| . 845838) (|groebner| . 844087) (|expIfCan| . 843946) (|thetaCoord| . 843832) (|jordanAdmissible?| . 843492) (|leftDiscriminant| . 843076) (|divOfZero| . 842979) (|pushdterm| . 842577) (|diag| . 842374) (|less?| . 841158) (|rectangularMatrix| . 840958) (|uniform01| . 840868) (|minimalPolynomial| . 840113) (|updatD| . 839747) (|extractTop!| . 839572) (|LyndonWordsList1| . 839349) (|resetBadValues| . 839262) (|qroot| . 838698) (|shallowCopy| . 838580) (|leadingCoefficientRicDE| . 838117) (|laguerre| . 837956) (|integralLastSubResultant| . 837561) (|constantRight| . 837321) (|mr| . 837017) (|quasiAlgebraicSet| . 836753) (|positiveRemainder| . 836692) (|leftLcm| . 836398) (|c05nbf| . 836115) (|desingTreeAtPoint| . 835451) (|mathieu23| . 835188) (|lastSubResultant| . 834333) (|predicates| . 834213) (|lowerCase| . 834071) (|allIndices| . 833915) (|lazyGintegrate| . 833665) (|c05adf| . 833427) (|orderIfNegative| . 833289) (|clipPointsDefault| . 833121) (|open| . 832832) (|selectSumOfSquaresRoutines| . 832782) (|OMgetAttr| . 832700) (|ParCond| . 832192) (|genus| . 829730) (|c06gsf| . 829555) (|generalSqFr| . 829280) (|leastPower| . 828961) (|setsubMatrix!| . 828735) (|lhs| . 828225) (|preprocess| . 827370) (|cylindricalDecomposition| . 826926) (|factorUsingMusser| . 826502) (|c06gqf| . 826327) (|mix| . 826005) (|setPrologue!| . 825816) (|bezoutDiscriminant| . 825482) (|subscriptedVariables| . 825376) (|setAdaptive| . 825301) (|iflist2Result| . 825033) (|linearDependence| . 824811) (|c06gcf| . 824639) (|round| . 824584) (|bandedHessian| . 824187) (|fracPart| . 823887) (|entries| . 822615) (|setStatus| . 822332) (|failed?| . 821963) (|wrregime| . 821310) (|c06gbf| . 821138) (|antisymmetric?| . 820684) (|idamax| . 820544) (|contract| . 819762) (|rquo| . 818854) (|rubiksGroup| . 818741) (|predicate| . 818540) (|coleman| . 818380) (|c06fuf| . 818166) (|bipolarCylindrical| . 817957) (|setelt!| . 817617) (|OMputEndBind| . 817535) (|copyslice| . 817371) (|explicitlyFinite?| . 817253) (|replaceVarByZero| . 816967) (|guessRat| . 809914) (|c06frf| . 809703) (|extractSplittingLeaf| . 809517) (|basis| . 807887) (|red| . 807848) (|drift| . 807719) (|cot2trig| . 807504) (|sin?| . 807381) (|randomLC| . 807028) (|c06fqf| . 806820) (|doubleComplex?| . 806732) (|isTimes| . 805798) (|generalizedContinuumHypothesisAssumed?| . 805716) (|highCommonTerms| . 805512) (|pseudoDivide| . 804783) (|OMgetEndObject| . 804701) (|bringDown| . 804162) (|match?| . 804038) (|c06fpf| . 803830) (|integral| . 802845) (|optpair| . 802708) (|coefficientSet| . 802476) (|rightZero| . 802360) (|subtractIfCan| . 802283) (|adaptive?| . 802211) (|c06ekf| . 802033) (|copies| . 801918) (|chvar| . 801530) (|allSimpleCells| . 801051) (|hessian| . 800696) (|maxMixedDegree| . 800462) (|firstDenom| . 800331) (|c06ecf| . 800156) (|imagk| . 800054) (|df2mf| . 799922) (|radPoly| . 799580) (|nand| . 799482) (|sinh2csch| . 799267) (|algebraicVariables| . 798986) (|eisensteinIrreducible?| . 798828) (|c06ebf| . 798656) (|lBasis| . 796312) (|optimize| . 795076) (|ruleset| . 794720) (|finiteBound| . 794535) (|pol| . 794337) (|removeRoughlyRedundantFactorsInPol| . 794047) (|c06eaf| . 793875) (|reducedContinuedFraction| . 793741) (|fortranTypeOf| . 793625) (|ravel| . 793429) (|cfirst| . 793208) (|rightDiscriminant| . 792792) (|henselFact| . 792219) (|s17def| . 791980) (|integralCoordinates| . 791668) (|zeroSetSplit| . 787970) (|lepol| . 787703) (|cAcos| . 787543) (|composite| . 787090) (|singleFactorBound| . 786367) (|s17dcf| . 786128) (|minPoints3D| . 786054) (|close| . 785779) (|iiabs| . 785605) (|dcabs1| . 785474) (|cAcot| . 785314) (|s17akf| . 785155) (|mainValue| . 785035) (|Lazard2| . 784824) (|continuedFraction| . 783895) (|qnew| . 783293) (|rootSplit| . 782888) (|s17ajf| . 782729) (|OMgetApp| . 782647) (|checkOptions| . 782517) (|fortranDouble| . 782472) (|nullary| . 782346) (|dimensionOfIrreducibleRepresentation| . 782208) (|rootSimp| . 781651) (|insert| . 781406) (|s17ahf| . 781247) (|basicSet| . 780392) (|mainMonomials| . 780177) (|pdf2ef| . 780022) (|contains?| . 779841) (|split!| . 779670) (|logGamma| . 779457) (|s17agf| . 779298) (|tab| . 779136) (|createLowComplexityTable| . 778886) (|linearAssociatedLog| . 778508) (|realRoots| . 778044) (|cartesian| . 777860) (|dec| . 777802) (|s17aff| . 777643) (|primaryDecomp| . 777091) (|freeOf?| . 776680) (|intersectionDivisor| . 774614) (|getGoodPrime| . 774343) (|createZechTable| . 774132) (|listRepresentation| . 773959) (|complex?| . 773871) (|s17aef| . 773712) (|rowEchWoZeroLinesWOVectorise| . 773597) (|primitiveRowEchelon| . 773267) (|localPointV| . 772725) (|fixPredicate| . 772427) (|precision| . 772016) (|transcendent?| . 771898) (|s17adf| . 771739) (|randnum| . 771567) (|addiag| . 771395) (|listConjugateBases| . 770890) (|columnSpace| . 770635) (|var2StepsDefault| . 770445) (|remove!| . 769195) (|s17acf| . 769036) (|createPrimitiveElement| . 768981) (|resultantSet| . 768740) (|polCase| . 768393) (|prem| . 768013) (|functionIsOscillatory| . 767710) (|light| . 767634) (|iidprod| . 767436) (|s15aef| . 767277) (|cAtan| . 767117) (|mdeg| . 766891) (|invertIfCan| . 766583) (|asecIfCan| . 766442) (|isList| . 766305) (|showTypeInOutput| . 766204) (|DiffC| . 765958) (|s15adf| . 765799) (|prefixRagits| . 765676) (|max| . 765109) (|nextSubsetGray| . 764969) (|algebraicSet| . 764565) (|rspace| . 764481) (|df2ef| . 764341) (|partialQuotients| . 764210) (|s14baf| . 764045) (|leftUnit| . 763884) (|algebraicDecompose| . 762936) (|Musser| . 762725) (|semiSubResultantGcdEuclidean2| . 762500) (|totalGroebner| . 762328) (|expintfldpoly| . 762004) (|reshape| . 761275) (|associative?| . 760935) (|s14abf| . 760776) (|binary| . 760586) (|assign| . 756124) (|primitivePart| . 754957) (|imagJ| . 754754) (|sturmVariationsOf| . 754492) (|back| . 754237) (|constantOpIfCan| . 754057) (|s14aaf| . 753898) (|tensorProduct| . 753383) (|DiffAction| . 753159) (|subCase?| . 752330) (|LPolynomial| . 749450) (|splitSquarefree| . 749170) (|OMgetEndBind| . 749088) (|cap| . 748921) (|directory| . 748833) (|s13adf| . 748674) (|rightGcd| . 748536) (|fTable| . 747417) (|chartV| . 746912) (|opeval| . 746634) (|denomRicDE| . 746256) (|viewWriteAvailable| . 746161) (|isobaric?| . 745886) (|s13acf| . 745727) (|vectoraddmul| . 745557) (|pointSizeDefault| . 745367) (|delete!| . 745087) (|removeIrreducibleRedundantFactors| . 744718) (|indices| . 744562) (|positive?| . 744085) (|trace2PowMod| . 743872) (|s13aaf| . 743713) (|jacobi| . 743611) (|atrapezoidal| . 743308) (|truncate| . 742950) (|previousTower| . 742867) (|surface| . 742771) (|dznrm2| . 742581) (|toScale| . 742369) (|s01eaf| . 742198) (|swap| . 741898) (|atoms| . 741672) (|conditionsForIdempotents| . 740448) (|point?| . 740327) (|univcase| . 740048) (|integerDecode| . 739957) (|expenseOfEvaluation| . 739607) (|s21bdf| . 739439) (|rightScalarTimes!| . 739298) (|readable?| . 739209) (|blockConcat| . 738931) (|LiePolyIfCan| . 738558) (|factorSquareFree| . 736594) (|simpleBounds?| . 736451) (|any| . 736345) (|iiasec| . 736149) (|s21bcf| . 735984) (|fortranCarriageReturn| . 735904) (|projectivePoint| . 735163) (|normFactors| . 734820) (|tan2cot| . 734605) (|subs1stVar| . 734347) (|iiasinh| . 734151) (|setClipValue| . 734065) (|fortranReal| . 734020) (|s21bbf| . 733855) (|columns| . 733277) (|coord| . 732647) (|ptree| . 732465) (|unexpand| . 732149) (|iteratedInitials| . 731934) (|axes| . 731499) (|universe| . 731373) (|s21baf| . 731211) (|coth2trigh| . 730996) (|putGraph| . 730833) (|numericalIntegration| . 730208) (|abelianGroup| . 730047) (|numberOfChildren| . 729890) (|fortranLogical| . 729845) (|node| . 729739) (|s20adf| . 729580) (|leadingIdeal| . 729352) (|minordet| . 728618) (|startPolynomial| . 728349) (|inspect| . 727847) (|numericIfCan| . 726479) (|mul| . 726343) (SEGMENT . 726073) (|mkIntegral| . 725764) (|e02agf| . 725490) (|dn| . 725315) (|cAtanh| . 725155) (|OMsetEncoding| . 725033) (|removeSuperfluousQuasiComponents| . 724346) (|expandLog| . 724131) (|characteristicSet| . 723465) (|setright!| . 723321) (|makeCell| . 723000) (|s20acf| . 722841) (|inverseLaplace| . 722410) (|fortranInteger| . 722365) (|backOldPos| . 722003) (|coerceListOfPairs| . 721875) (|fillPascalTriangle| . 721760) (|makeGraphImage| . 721158) (|binaryTree| . 720975) (|prolateSpheroidal| . 720766) (|d01aqf| . 720519) (|coefficient| . 717496) (|tubePlot| . 716205) (|critB| . 715929) (|makeYoungTableau| . 715772) (|redpps| . 715274) (|constantOperator| . 715104) (|selectPDERoutines| . 715054) (|perfectNthPower?| . 714884) (|s19adf| . 714725) (|derivationCoordinates| . 714441) (|unvectorise| . 713836) (|listAllMono| . 713554) (|listVariable| . 713274) (|numberOfCycles| . 713144) (|differentialVariables| . 712869) (|karatsubaOnce| . 712695) (|getMultiplicationMatrix| . 712038) (|d01apf| . 711785) (|stFunc2| . 711487) (|writeDotGraph| . 711342) (|quotedOperators| . 710996) (|monicDecomposeIfCan| . 710714) (|internalSubPolSet?| . 709965) (|iiBesselK| . 709763) (|zeroDim?| . 709223) (|affinePoint| . 709100) (|s19acf| . 708941) (|chiSquare| . 708797) (|mathieu22| . 708534) (F2EXPRR . 708344) (|baseRDEsys| . 708035) (|nextNormalPrimitivePoly| . 707859) (|removeZeroes| . 706560) (|initializeParamOfPlaces| . 705148) (|rightMult| . 704993) (|d01anf| . 704743) (|rightPower| . 704557) (|root| . 704308) (|minimumDegree| . 703416) (|radicalSolve| . 701151) (|completeHermite| . 700840) (|choosemon| . 700575) (|homogeneous?| . 700257) (|d01amf| . 700013) (|finiteSeries2LinSys| . 699763) (|patternVariable| . 699612) (|midpoint| . 699343) (|high| . 699253) (|sturmSequence| . 699064) (|cyclicEqual?| . 698949) (|zerosOf| . 697871) (|d01alf| . 697578) (|fullPartialFraction| . 697355) (|vconcat| . 697215) (|screenResolution3D| . 697141) (|uniform| . 696707) (|maxrow| . 696413) (|resultantReduitEuclidean| . 696127) (|nextsousResultant2| . 695955) (|s19abf| . 695796) (|iicosh| . 695600) (|problemPoints| . 695098) (|solveLinearPolynomialEquationByFractions| . 694841) (|acschIfCan| . 694700) (|OMputError| . 694618) (|spherical| . 694434) (|inverseIntegralMatrixAtInfinity| . 694150) (|d01akf| . 693906) (|polynomialZeros| . 693638) (|explicitEntries?| . 693516) (|addPoint2| . 693366) (|discriminantEuclidean| . 693118) (|rur| . 691498) (|linSolve| . 691047) (|groebgen| . 690715) (|s19aaf| . 690556) (|flexible?| . 690216) (|halfExtendedResultant2| . 689975) (|halfExtendedSubResultantGcd2| . 689423) (|yCoord| . 689309) (|setAdaptive3D| . 689232) (|parabolic| . 689048) (|adaptive3D?| . 688974) (|d01ajf| . 688730) (|oneDimensionalArray| . 688479) (|quotientByP| . 688417) (|hermite| . 688011) (|closedCurve?| . 687890) (|semiResultantEuclidean1| . 687659) (|fill!| . 687284) (|roughSubIdeal?| . 686973) (|eigenvectors| . 686586) (|s18def| . 686347) (|write!| . 686213) (|duplicates| . 686026) (|multiple?| . 685911) (|aLinear| . 685677) (|check| . 684921) (|void| . 684883) (|node?| . 684725) (|s18dcf| . 684486) (|leftRegularRepresentation| . 684166) (|guessPRec| . 677113) (|norm| . 673600) (|cothIfCan| . 673459) (|typeLists| . 673249) (|subMatrix| . 672439) (|s18aff| . 672280) (|polarCoordinates| . 672032) (|createPrimitivePoly| . 671830) (|xn| . 671623) (|removeRedundantFactors| . 670133) (|getBadValues| . 670013) (|mightHaveRoots| . 669789) (|s18aef| . 669630) (|bracket| . 669493) (|mathieu24| . 669230) (|tanh2coth| . 669015) (|translate| . 667992) (|generalInfiniteProduct| . 666988) (|repeating| . 666881) (|withPredicates| . 666758) (|interval| . 666270) (|s18adf| . 666111) (|ipow| . 665913) (|Ei5| . 665788) (|gcdcofactprim| . 665645) (|taylorQuoByVar| . 665540) (|differentiate| . 661184) (|diophantineSystem| . 660839) (|prime?| . 660103) (|s18acf| . 659944) (|Ei| . 659527) (|lists| . 659301) (|sub| . 659251) (|coth2tanh| . 659036) (|meatAxe| . 657954) (|associator| . 657892) (|representationType| . 657766) (|f04qaf| . 657449) (|polyRing2UPUP| . 657011) (|isamax| . 656877) (|relationsIdeal| . 656478) (|pointPlot| . 655812) (|divisorAtDesingTree| . 655147) (|leastMonomial| . 654960) (|f04mcf| . 654719) (|dscal| . 654538) (|find| . 654397) (|deleteRow!| . 654213) (|strongGenerators| . 654073) (|reorder| . 653433) (|relativeApprox| . 652873) (|f04mbf| . 652453) (|outputGeneral| . 652274) (|Ci| . 651979) (|imagj| . 651877) (|middle| . 651684) (|calcRanges| . 651519) (|length| . 649999) (|initParLocLeaves| . 649309) (|unary?| . 649225) (|f04maf| . 648975) (|hexDigit?| . 648895) (|prinb| . 648603) (|mulmod| . 648539) (|hcrf| . 648350) (|makeViewport2D| . 648155) (|scripts| . 647799) (|tail| . 647424) (|digit?| . 647344) (|f04jgf| . 647119) (|ode| . 646854) (|jacobiIdentity?| . 646514) (|imagi| . 646412) (|resultant| . 645529) (|prindINFO| . 645132) (|fresnelS| . 644744) (|factorPolynomial| . 644287) (|divisorCascade| . 643705) (|f04faf| . 643518) (|#| . 642137) (|cos2sec| . 641922) (|odd?| . 641581) (|collectQuasiMonic| . 641328) (|evenInfiniteProduct| . 640442) (|branchIfCan| . 639453) (|createHN| . 639240) (|f04axf| . 639008) (|upDateBranches| . 637725) (|plenaryPower| . 637579) (|subHeight| . 637498) (|pivot| . 637278) (|removeCosSq| . 637063) (|maxIndex| . 636902) (|clearTheIFTable| . 636811) (|basisOfCentroid| . 636622) (|f04atf| . 636435) (|complexEigenvalues| . 636203) (|intermediateResultsIF| . 635796) (|scaleRoots| . 635633) (|blankSeparate| . 635540) (|mathieu11| . 635277) (|fintegrate| . 634713) (|printInfo| . 631808) (|f04asf| . 631624) (|stFuncN| . 631325) (|setProperty| . 631211) (|lyndon?| . 631053) (|OMwrite| . 629722) (|fullDesTree| . 629274) (|Ei2| . 629149) (|invmod| . 629088) (|wholePart| . 628664) (|implies| . 628617) (|var2Steps| . 628389) (|musserTrials| . 628063) (|mainVariable?| . 627789) (|rotatey| . 627648) (|jacobian| . 627082) (|f04arf| . 626898) (|guessHolo| . 622563) (|forLoop| . 622282) (|quasiComponent| . 621951) (|xCoord| . 621837) (|operators| . 621734) (|symmetricPower| . 621288) (|low| . 621198) (|multMonom| . 620719) (|cRationalPower| . 620537) (|showAll?| . 620399) (|firstNumer| . 620300) (|discriminantSet| . 620059) (|f04adf| . 619854) (|exponentialOrder| . 619631) (|comparison| . 619496) (|cAsech| . 619336) (|bitCoef| . 619251) (|iter| . 619064) (|stop| . 619019) (|getShiftRec| . 618529) (|One| . 618084) (|overset?| . 617671) (RF2UTS . 617331) (|approximate| . 616200) (|integrate| . 603290) (|components| . 603169) (|sample| . 602440) (|decreasePrecision| . 602268) (|submod| . 602204) (|times!| . 602063) (|csubst| . 601735) (|rightTraceMatrix| . 601229) (|zeroMatrix| . 600702) (|result| . 600458) (|OMencodingXML| . 600408) (|deleteRoutine!| . 600322) (|subSet| . 600173) (|minrank| . 599605) (|symmetricSquare| . 599460) (|continue| . 599372) (|additive?| . 599219) (|startStats!| . 599023) (|factorCantorZassenhaus| . 598523) (|indicialEquation| . 597770) (|minPoints| . 597533) (|appendPoint| . 597410) (|OMgetEndError| . 597328) (|infLex?| . 597023) (|divOfPole| . 596926) (|rootPower| . 596369) (|myDegree| . 595954) (|setEmpty!| . 595778) (|log10| . 595472) (|eulerE| . 595257) (|chainSubResultants| . 595063) (|f07fef| . 594868) (|prefix| . 594772) (|solveLinear| . 594248) (|lazy?| . 594126) (|pop!| . 593784) (|alterDrift!| . 593594) (|f07fdf| . 593408) (|width| . 593105) (|numberOfIrreduciblePoly| . 592953) (|viewPhiDefault| . 592773) (|viewport2D| . 592717) (|cn| . 592542) (|f07aef| . 592305) (|complement| . 592176) (|ord| . 592096) (|expextendedint| . 591590) (|possiblyInfinite?| . 591472) (|OMopenString| . 591348) (|f07adf| . 591189) (|rangeIsFinite| . 590630) (|complementaryBasis| . 590356) (|rewriteIdealWithHeadRemainder| . 590045) (|roughUnitIdeal?| . 589737) (|companionBlocks| . 589496) (|findCoef| . 589365) (|update| . 589202) (|fixedPoint| . 588870) (|singularPoints| . 587257) (|wreath| . 587131) (|s17dlf| . 586889) (|rootOf| . 585393) (|initiallyReduce| . 584950) (|showTheRoutinesTable| . 584903) (|primitivePart!| . 584684) (|s17dhf| . 584480) (|halfExtendedSubResultantGcd1| . 583928) (|head| . 583488) (|symFunc| . 583182) (|crushedSet| . 582895) (|s17dgf| . 582691) (|dim| . 582432) (|zoom| . 581903) (|symmetricGroup| . 581601) (|OMputEndObject| . 581519) (|f02xef| . 581290) (|numberOfHues| . 581209) (|genericRightDiscriminant| . 580900) (|modularGcdPrimitive| . 580638) (|rowEchelonLocal| . 580490) (|f02wef| . 580273) (|mirror| . 579629) (|factorUsingYun| . 579205) (|normalizedDivide| . 578655) (|endSubProgram| . 578574) (|operator| . 576656) (|f02fjf| . 575869) (|digit| . 575821) (|mainMonomial| . 575634) (|rhs| . 575124) (|basisOfCenter| . 574946) (|f02bjf| . 574706) (|sparsityIF| . 574563) (|input| . 574311) (|outputList| . 574197) (|interReduce| . 573910) (|reseed| . 573796) (|f02bbf| . 573587) (|outlineRender| . 573465) (|third| . 573367) (|test| . 573323) (|extractClosed| . 573177) (|semiSubResultantGcdEuclidean1| . 572952) (|functionIsFracPolynomial?| . 572634) (|kovacic| . 571841) (|f02axf| . 571664) (|explicitlyEmpty?| . 571542) (|setGcdMode| . 571355) (|OMParseError?| . 571267) (|checkRur| . 570822) (|f02awf| . 570651) (|identity| . 570513) (|any?| . 569318) (|integralDerivationMatrix| . 568972) (|kroneckerDelta| . 568807) (|f02akf| . 568630) (|listOfTerms| . 567981) (|iiBesselI| . 567779) (|mkPrim| . 567531) (|finiteBasis| . 567231) (|f02ajf| . 567060) (|selectfirst| . 566936) (|dswap| . 566724) (|crest| . 566503) (|useEisensteinCriterion?| . 566348) (|f02agf| . 566177) (|dot2eps| . 566074) (|cyclicCopy| . 565990) (|infRittWu?| . 564745) (|ceiling| . 564545) (|linearlyDependentOverZ?| . 564359) (|lowerCase!| . 564305) (|diagonal| . 564101) (|replaceDiffs| . 563678) (|f02aff| . 563513) (|gbasis| . 563212) (|subNode?| . 562956) (|changeThreshhold| . 562841) (|tablePow| . 562567) (|f02aef| . 562393) (|evaluateInverse| . 562115) (|rewriteSetByReducingWithParticularGenerators| . 561693) (|projectionSet| . 561452) (|computeInt| . 561029) (|f02adf| . 560858) (|deleteProperty!| . 560772) (|setVariableOrder| . 560510) (|power!| . 560324) (|Is| . 559107) (|f02abf| . 558939) (|clipSurface| . 558817) (|symbNameV| . 558283) (|OMconnectTCP| . 558127) (|guessExpRat| . 551074) (|f02aaf| . 550909) (|iiacos| . 550713) (|topFortranOutputStack| . 550621) (|extractProperty| . 550457) (|magnitude| . 550303) (|measure| . 545393) (|drawStyle| . 545271) (|solid?| . 545175) (|karatsuba| . 544956) (|lineColorDefault| . 544782) (|expPot| . 544594) (|makeCrit| . 544135) (|subResultantGcdEuclidean| . 543893) (|addMatchRestricted| . 543718) (|gcdPrimitive| . 542914) (|virtualDegree| . 542636) (|doublyTransitive?| . 542482) (|positiveSolve| . 540994) (|curry| . 540794) (|cAcoth| . 540634) (|bottom!| . 540459) (|quote| . 540372) (|powerAssociative?| . 540230) (|remove| . 539264) (|LyndonBasis| . 538970) (|rootOfIrreduciblePoly| . 538558) (|setImagSteps| . 538476) (|specialise| . 538219) (|index?| . 538060) (|expt| . 537874) (|keys| . 537023) (|rewriteIdealWithQuasiMonicGenerators| . 536647) (|makeMulti| . 536429) (|OMconnInDevice| . 536333) (|objects| . 536055) (|quadraticForm| . 535892) (|OMencodingSGML| . 535842) (|prinpolINFO| . 535550) (|close!| . 535378) (|lookup| . 535110) (|region| . 534951) (|goodPoint| . 534711) (|setMinPoints3D| . 534634) (|divisors| . 534498) (|rationalIfCan| . 533098) (|makeSin| . 532890) (|fullInfClsPt| . 532442) (|elementary| . 532291) (|complexLimit| . 531322) (|innerSolve1| . 530791) (|pointToCell| . 530579) (|reset| . 529696) (|showTheSymbolTable| . 529648) (|factorials| . 529125) (|polyred| . 528909) (|leftMult| . 528754) (|write| . 528109) (|numberOfVariables| . 527254) (|toseLastSubResultant| . 526859) (|monomials| . 526065) (|sort!| . 525710) (|save| . 525665) (|sinIfCan| . 525524) (|extDegree| . 525399) (|guessHP| . 517932) (|OMgetString| . 517848) (|iisin| . 517652) (|cosh2sech| . 517437) (|localParamV| . 516902) (|rdHack1| . 516669) (|monicModulo| . 516377) (|prologue| . 516194) (|coefficients| . 515111) (|numFunEvals3D| . 515037) (|options| . 514616) (|getMultiplicationTable| . 513838) (|union| . 513242) (|htrigs| . 513027) (|listOfLists| . 512434) (|traverse| . 512265) (|medialSet| . 511599) (|realEigenvalues| . 511394) (|sech2cosh| . 511179) (|supersub| . 511083) (|cot2tan| . 510868) (|untab| . 510688) (|log| . 508354) (|reverse!| . 507895) (|iiacosh| . 507699) (|integers| . 507531) (|divergence| . 507206) (|setScreenResolution3D| . 507129) (|toint| . 507011) (|distinguishedCommonRootsOf| . 506773) (|OMlistSymbols| . 506652) (|pr2dmp| . 506301) (|mainVariable| . 505538) (|obj| . 505467) (|updatF| . 505094) (|variationOfParameters| . 504867) (|bivariate?| . 504580) (|newton| . 504400) (|lastSubResultantElseSplit| . 504098) (|setlast!| . 503955) (|power| . 503793) (|comp| . 503537) (|setStatus!| . 503330) (|viewpoint| . 501405) (|rischDE| . 500673) (|algebraic?| . 500274) (|commaSeparate| . 500062) (|octon| . 499813) (|iipow| . 499615) (|alphabetic| . 499567) (|rightQuotient| . 499429) (|wordsForStrongGenerators| . 499276) (|diagonals| . 499154) (|shuffle| . 498998) (|iicsc| . 498802) (|basisOfInterpolateFormsForFact| . 498241) (|vertSplit| . 497619) (|stronglyReduced?| . 497057) (|iisqrt3| . 496864) (|palgint0| . 495849) (|numberOfComponents| . 495108) (|primeFactor| . 494986) (|outputSpacing| . 494874) (|copyDrift| . 494662) (|quasiRegular| . 494415) (|findOrderOfDivisor| . 492617) (|basisOfLeftNucleus| . 492439) (|localize| . 491850) (|iicoth| . 491654) (|rightNorm| . 491537) (|normalElement| . 491225) (|append| . 491145) (|regularRepresentation| . 490739) (|hash| . 489659) (|trapezoidal| . 489359) (|pointInIdeal?| . 488981) (|fortranDoubleComplex| . 488936) (|equation| . 488201) (|ef2edf| . 488046) (|coerceL| . 487825) (|algSplitSimple| . 487453) (|map| . 462045) (|neglist| . 461912) (|clearCache| . 461799) (|antisymmetricTensors| . 461379) (|showTheFTable| . 461320) (|internalAugment| . 460059) (|ref| . 459977) (|name| . 459334) (|commutativeEquality| . 459151) (|palglimint0| . 457892) (|affineAlgSetLocal| . 457375) (|leftRecip| . 457152) (|checkPrecision| . 457063) (|hadamard| . 456900) (|fixedDivisor| . 456739) (|tanintegrate| . 456340) (|print| . 456154) (|csc2sin| . 455939) (|lp| . 455808) (|groebnerIdeal| . 455552) (|delta| . 455366) (|edf2efi| . 455196) (BY . 455075) (|multisect| . 454446) (|separateDegrees| . 454191) (|value| . 453767) (|slex| . 453608) (|zeta| . 453525) (|pToHdmp| . 453302) (|properties| . 453190) (|redmat| . 452812) (|sup| . 452600) (|compiledFunction| . 452076) (|pointColorPalette| . 451942) (|eq?| . 451287) (|ridHack1| . 451181) (|tableForDiscreteLogarithm| . 451020) (|mat| . 450827) (|uncouplingMatrices| . 450583) (|lambda| . 450492) (|pattern| . 450175) (|localParam| . 450004) (|infiniteProduct| . 449118) (|output| . 448596) (|createMultiplicationTable| . 448342) (|iiacsc| . 448146) (|mesh| . 446858) (|extractIndex| . 446701) (|bat| . 446530) (|cyclicSubmodule| . 446284) (|numberOfMonomials| . 445789) (|setCondition!| . 445610) (|has?| . 445496) (|declare!| . 444737) (|summary| . 444645) (|optional?| . 444530) (|distFact| . 443888) (|monicLeftDivide| . 443360) (|show| . 443201) (|mainDefiningPolynomial| . 443081) (|standardDotHeader| . 442997) (|multiServ| . 442886) (|writeLine!| . 442730) (|csch2sinh| . 442515) (|binarySearchTree| . 442392) (|qinterval| . 442239) (|var1Steps| . 442011) (Y . 441574) (|minIndex| . 441413) (|innerSolve| . 441094) (|euler| . 440824) (|showAttributes| . 439725) (|genericRightTraceForm| . 439410) (|arg1| . 439262) (|permanent| . 439042) (|transcendentalDecompose| . 437127) (|dictionary| . 436901) (|tanSum| . 436782) (|arg2| . 436634) (|retractIfCan| . 428938) (|compile| . 428817) (|setMinPoints| . 428742) (|characteristicPolynomial| . 426797) (|rootKerSimp| . 426161) (|selectODEIVPRoutines| . 426111) (|permutation| . 425754) (|firstUncouplingMatrix| . 425491) (|normInvertible?| . 425100) (|e02aef| . 424901) (|returnTypeOf| . 424734) (|itsALeaf!| . 424566) (|cubic| . 424042) (|torsion?| . 423197) (|iiatan| . 423001) (|c02agf| . 422798) (|maxrank| . 422230) (|messagePrint| . 422125) (|collectUnder| . 421879) (|c02aff| . 421676) (|integer?| . 421177) (|yRange| . 420948) (|squareFreeLexTriangular| . 420487) (|e02adf| . 420311) (|endOfFile?| . 420232) (|OMopenFile| . 420105) (|credits| . 420013) (|var1StepsDefault| . 419823) (|c05pbf| . 419536) (|cache| . 419420) (|aQuartic| . 419177) (|car| . 418928) (|univariate?| . 418641) (|reopen!| . 418480) (|izamax| . 418294) (|cdr| . 418045) (|aCubic| . 417805) (|setMaxPoints3D| . 417728) (|bfEntry| . 417487) (|physicalLength| . 417204) (|createNormalPoly| . 417002) (|monicDivide| . 416579) (|root?| . 416433) (|ShiftAction| . 416209) (GF2FG . 415816) (|e01sef| . 415596) (|imagE| . 415494) (|noLinearFactor?| . 415343) (|e01saf| . 415167) (|asechIfCan| . 415026) (|mainContent| . 414807) (|random| . 413554) (|factorByRecursion| . 412858) (|dequeue!| . 412603) (|rootNormalize| . 412243) (|e01daf| . 412064) (|enterPointData| . 411891) (|Nul| . 411798) (|stack| . 411685) (|divisor| . 410187) (|palgextint0| . 409102) (|rules| . 408746) (|e01bhf| . 408532) (|padecf| . 408227) (|rombergo| . 407927) (|vspace| . 407846) (|ramifiedAtInfinity?| . 407577) (|e01bgf| . 407395) (|complexNumeric| . 403708) (|delay| . 403459) (|infix?| . 403378) (|selectsecond| . 403254) (|leadingTerm| . 403076) (|upperCase?| . 402996) (E1 . 402839) (|outerProduct| . 402690) (|kernels| . 402591) (|integral?| . 401775) (|e01bff| . 401593) (|subResultantChain| . 401338) (|doubleResultant| . 401022) (|groebnerFactorize| . 399575) (|cCsch| . 399415) (|univariate| . 396468) (|e01bef| . 396295) (|datalist| . 396180) (|antiAssociative?| . 395840) (|critMonD1| . 395474) (|monicCompleteDecompose| . 395234) (|rightTrim| . 395046) (|factor| . 383217) (|e01baf| . 383038) (|setleaves!| . 382909) (|tValues| . 382810) (|bombieriNorm| . 382146) (|imag| . 381406) (|e02zaf| . 381221) (|exprHasLogarithmicWeights| . 380915) (|directProduct| . 380786) (|e02gaf| . 380578) (|setTower!| . 380464) (|initTable!| . 380298) (|summation| . 379687) (|e02dff| . 379496) (|regime| . 378579) (|destruct| . 378094) (|factorSFBRlcUnit| . 377367) (|edf2fi| . 377212) (|removeRedundantFactorsInPols| . 376890) (|e02def| . 376708) (|monomial| . 373811) (|conjug| . 373531) (|proj| . 373342) (|euclideanSize| . 373243) (|rightExactQuotient| . 373095) (|multivariate| . 371426) (|e02ddf| . 371161) (|cyclic?| . 370931) (|associatorDependence| . 370532) (|actualExtensionV| . 370027) (|e02dcf| . 369720) (|blowUpWithExcpDiv| . 369030) (|iisqrt2| . 368837) (|e02daf| . 368566) (|inv| . 367360) (|last| . 366772) (|parts| . 365626) (|dimension| . 364144) (|reduceRow| . 364022) (|powerSum| . 363871) (|printStatement| . 363777) (|irreducible?| . 363168) (|ground?| . 362582) (|e02bef| . 362290) (|curryRight| . 362047) (|option| . 361564) (|next| . 361468) (|iomode| . 361310) (|vark| . 361076) (|ground| . 360841) (|lllip| . 360682) (|e02bdf| . 360515) (|SturmHabichtSequence| . 360272) (|twist| . 360029) (|setrest!| . 359776) (|newtonPolygon| . 359374) (|leadingMonomial| . 358282) (|minusInfinity| . 358093) (|pade| . 357178) (|integerBound| . 356959) (|nextPrimitivePoly| . 356783) (|rational| . 355463) (|leadingCoefficient| . 353439) (|suffix?| . 353348) (|plusInfinity| . 353159) (|displayAsGF| . 353026) (|And| . 352890) (|OMputFloat| . 352773) (|identityMatrix| . 352605) (|primitiveMonomials| . 352399) (|reduced?| . 351608) (|wholeRagits| . 351485) (|empty| . 350515) (|showTheIFTable| . 350455) (|reductum| . 348420) (|lieDerivative| . 348162) (|nilFactor| . 348040) (|type| . 347901) (|list?| . 347624) (|split| . 345551) (** . 339707) (|fullOut| . 338577) (|OMgetInteger| . 338492) (|rst| . 338398) (|pointToPlace| . 337937) (|SturmHabicht| . 337722) (|iroot| . 337486) (|getMeasure| . 337374) (|cAcsch| . 337214) (|basisOfRightAnnihilator| . 337033) (|listexp| . 336700) (|multiple| . 336424) (|pushucoef| . 336007) (|bag| . 335337) (|charClass| . 335160) (|leastAffineMultiple| . 334994) (|optional| . 334718) (|front| . 334463) (|iFTable| . 333868) (|effective?| . 333743) (|shift| . 333212) (|diagonal?| . 332758) (|replaceKthElement| . 332601) (|factorial| . 332253) (|froot| . 331698) (|d01gbf| . 331400) (|tryFunctionalDecomposition| . 331242) (|logical?| . 331154) (|primintfldpoly| . 330885) (|and| . 330740) (|printingInfo?| . 330571) (|d01gaf| . 330400) (|normal?| . 329874) (|remainder| . 329515) (|interiorProduct| . 329257) (|maximumExponent| . 329097) (|d01fcf| . 328802) (|clearFortranOutputStack| . 328700) (|applyQuote| . 328046) (|variable| . 327355) (|computePowers| . 327166) (|d01bbf| . 327000) (|intensity| . 326879) (|gderiv| . 326702) (|distribute| . 326594) (|nonSingularModel| . 325886) (|second| . 325788) (|palgRDE| . 325294) (|guessBinRat| . 318241) (|prefix?| . 318150) (|d01asf| . 317903) (|setErrorBound| . 317710) (|figureUnits| . 317556) (|intChoose| . 316963) (|ocf2ocdf| . 316794) (|omError| . 316661) (|real| . 315721) (|headRemainder| . 315381) (|groebSolve| . 315016) (|insertionSort!| . 314473) (|d02raf| . 314037) (|external?| . 313955) (|complex| . 313851) (|nthExponent| . 313729) (|unitCanonical| . 313676) (|d02kef| . 312836) (|radix| . 312683) (|exteriorDifferential| . 312536) (|shiftHP| . 299312) (|trace| . 298495) (|approximants| . 298351) (|unitsColorDefault| . 298177) (|d02gbf| . 297771) (|elRow1!| . 297476) (|listLoops| . 297312) (|reindex| . 297104) (|fibonacci| . 297005) (|d02gaf| . 296683) (|stFunc1| . 296402) (|bitTruth| . 296289) (|hodgeStar| . 296079) (|fortranLiteral| . 295969) (|d02ejf| . 295391) (|guessPade| . 291056) (|cAsec| . 290896) (|d02cjf| . 290404) (|LazardQuotient2| . 290132) (|not| . 289949) (|vectorcombination| . 289776) (|tubePoints| . 289548) (|null| . 289443) (|Ei3| . 289318) (|modifyPoint| . 288720) (|initial| . 288473) (|lintgcd| . 288302) (|d02bhf| . 287917) (|qsetelt!| . 287505) (|getGraph| . 287370) (|swapRows!| . 287147) (|commutative?| . 286807) (|orthonormalBasis| . 286615) (|d02bbf| . 286225) (|hconcat| . 286085) (|pseudoRemainder| . 285979) (|denominator| . 285592) (|matrixGcd| . 285240) (|showArrayValues| . 285163) (|e02ahf| . 284949) (|daxpy| . 284762) (|normDeriv2| . 284437) (|rationalApproximation| . 283904) (|radicalEigenvector| . 283666) (|wholeRadix| . 283543) (|lowerCase?| . 283463) (|iiasech| . 283267) (|changeVar| . 282489) (|parabolicCylindrical| . 282305) (|guessRec| . 275252) (|iisech| . 275056) (|abs| . 274126) (|listYoungTableaus| . 273963) (|outputForm| . 273020) (|rowEchelon| . 271112) (|GospersMethod| . 270638) (|charthRoot| . 270386) (|arity| . 270281) (|determinant| . 269294) (|d03faf| . 268955) (|init| . 268724) (|stopTableGcd!| . 268031) (|mapUnivariate| . 267370) (|complexElementary| . 266097) (|truncatedmuladd| . 265930) (|safetyMargin| . 265588) (|fprindINFO| . 265188) (|d03eef| . 264811) (|sumSquares| . 264675) (|hitherPlane| . 264554) (|iiexp| . 264358) (|subMultV| . 263832) (|probablyZeroDim?| . 263517) (|d03edf| . 263279) (|factorList| . 262717) (|makeprod| . 262590) (|extensionDegree| . 261902) (|showAllElements| . 261758) (|rroot| . 261235) (|repSq| . 261045) (|singularPointsWithRestriction| . 260638) (D . 259083) (|characteristic| . 257397) (|semiLastSubResultantEuclidean| . 257163) (|algebraicCoefficients?| . 256877) (|qfactor| . 256507) (|algebraicSort| . 255820) (|variables| . 253604) (|definingField| . 253413) (|numberOfDivisors| . 253314) (|ranges| . 252867) (|lfintegrate| . 252464) (|degreeOfMinimalForm| . 252210) (|times| . 251962) (|hdmpToP| . 251739) (|nullity| . 250563) (|sylvesterSequence| . 250371) (|quartic| . 249844) (|trigs| . 249236) (|function| . 248527) (|packageCall| . 248378) (|complexSolve| . 247285) (|stoseInvertibleSet| . 246923) (|tomodpa| . 246731) (|cycleEntry| . 246633) (|hasSolution?| . 246044) (|rational?| . 244234) (|firstExponent| . 243979) (|anfactor| . 243558) (|completeSmith| . 243223) (|diffHP| . 229999) (|solve1| . 229733) (|signAround| . 228989) (|stepBlowUp| . 228232) (|OMgetType| . 228148) (|primextintfrac| . 227821) (|heapSort| . 227563) (|mapUnivariateIfCan| . 227202) (|qShiftC| . 226953) (|unaryFunction| . 226711) (|xor| . 226563) (|makeFloatFunction| . 226125) (|solid| . 226026) (|lastSubResultantEuclidean| . 225775) (|bivariatePolynomials| . 225404) (|title| . 224958) (|OMcloseConn| . 224872) (|addPointLast| . 224677) (|sumOfKthPowerDivisors| . 224536) (|LiePoly| . 224366) (|transcendenceDegree| . 224045) (|Not| . 223915) (|setAttributeButtonStep| . 223830) (|characteristicSerie| . 223056) (|useNagFunctions| . 222634) (|repack1| . 222408) (|atanhIfCan| . 222267) (|stoseInvertible?reg| . 221856) (|palgint| . 221407) (|push!| . 221053) (|noncommutativeJordanAlgebra?| . 220713) (|legendreP| . 220503) (|gcd| . 218083) (|t| . 217939) (|outputAsTex| . 217695) (|schema| . 217481) (|viewZoomDefault| . 217301) (|primeFrobenius| . 217126) (|samplePoint| . 216862) (|lyndon| . 216732) (|superHeight| . 216651) (|genusNeg| . 214802) (|maxPower| . 214530) (|internalZeroSetSplit| . 213769) (|Or| . 213633) (|groebner?| . 213377) (|graeffe| . 213184) (|removeRoughlyRedundantFactorsInContents| . 212862) (|skewSFunction| . 212699) (|square?| . 212245) (|interpolateForms| . 210215) (|fractionPart| . 209601) (|mantissa| . 209429) (|ideal| . 208527) (|sqfree| . 208210) (|squareFreePolynomial| . 207753) (|leftDivide| . 207019) (|allRootsOf| . 205977) (|fullOutput| . 203202) (|interpolate| . 201913) (|coerceS| . 201692) (|monicRightFactorIfCan| . 201428) (|mapdiv| . 201266) (|cycleRagits| . 201143) (|exactQuotient| . 200692) (|leftTrace| . 200575) (|drawToScale| . 200407) (|setfirst!| . 200264) (|setsubmult!| . 199735) (|stosePrepareSubResAlgo| . 199321) (|hasHi| . 199204) (|squareFreeFactors| . 198885) (|definingEquations| . 198624) (|extendedIntegrate| . 198243) (|nextSublist| . 197849) (|numberOfImproperPartitions| . 197740) (|sin2csc| . 197525) (|OMputSymbol| . 197410) (|iidsum| . 197212) (|truncatedmultiplication| . 197073) (|shallowExpand| . 196862) (|genusTree| . 196144) (|Ei6| . 196019) (|En| . 195831) (|addMatch| . 195659) (|pile| . 195566) (|matrixConcat3D| . 195431) (|aColumn| . 195151) (|setLabelValue| . 195063) (|moebiusMu| . 194964) (|rule| . 194302) (|OMgetError| . 194220) (|definingPolynomial| . 192976) (|mpsode| . 192674) (|reducedQPowers| . 192439) (|multV| . 191913) (|matrix| . 190896) (|singular?| . 190355) (|principal?| . 190047) (|typeList| . 189805) (|fortranLiteralLine| . 189695) (|enumerate| . 189426) (|clearTable!| . 189260) (|gcdBasis| . 189055) (|tan2trig| . 188840) (|semiResultantReduitEuclidean| . 188571) (|exquo| . 187071) (|homogenize| . 185266) (|UpTriBddDenomInv| . 185005) (|sts2stst| . 184778) (|stiffnessAndStabilityFactor| . 184566) (|one?| . 184151) (|polyPart| . 183960) (|div| . 183910) (|socf2socdf| . 183717) (|cCosh| . 183557) (|complexNumericIfCan| . 180502) (|packExps| . 180295) (|rootsOf| . 179484) (|powern| . 179276) (|coordinate| . 178880) (|dmpToP| . 178668) (|excepCoord| . 178575) (|critMTonD1| . 178212) (|display| . 176940) (|iibinom| . 176742) (|nextNormalPoly| . 176566) (|rightRegularRepresentation| . 176246) (|nodeOf?| . 175999) (|simplifyPower| . 175842) (|setColumn!| . 175606) (|expr| . 175357) (|alphanumeric| . 175309) (|selectMultiDimensionalRoutines| . 175259) (|exponential1| . 175169) (|inHallBasis?| . 175052) (|desingTreeWoFullParam| . 173772) (|functionIsContinuousAtEndPoints| . 173151) (|dzasum| . 172961) (|whileLoop| . 172877) (|floor| . 172677) (|constDsolve| . 172149) (|indicialEquationAtInfinity| . 171509) (|squareFreeBasis| . 171304) (|changeBase| . 170977) (|expenseOfEvaluationIF| . 170570) (|nthExpon| . 169950) (|expandTrigProducts| . 169549) (|extract| . 169387) (|sec2cos| . 169172) (|infClsPt?| . 169079) (|lazyPseudoDivide| . 168172) (|escape| . 168129) (|exprToUPS| . 167250) (|solveInField| . 166313) (|outputAsScript| . 166069) (|makeResult| . 165795) (|linear| . 165277) (|modTree| . 165152) (|bsolve| . 164309) (|iicos| . 164113) (|leftAlternative?| . 163773) (|relerror| . 163694) (|belong?| . 161986) (|cAsin| . 161826) (|countable?| . 161741) (|leadingBasisTerm| . 161479) (|rootRadius| . 161093) (|univariateSolve| . 158852) (|read!| . 158721) (|polyRDE| . 158258) (|coordinates| . 156132) (|drawComplexVectorField| . 155899) (|nthr| . 155367) (|specialTrigs| . 155081) (|elem?| . 154962) (|refine| . 153190) (|localReal?| . 152966) (|credPol| . 152696) (|weights| . 152106) (|clip| . 150764) (|subst| . 150319) (|OMgetFloat| . 150230) (|redPol| . 149960) (|finiteSeries2LinSysWOVectorise| . 149710) (|leftFactorIfCan| . 149485) (|getCode| . 149399) (|lfextendedint| . 148961) (|block| . 148866) (|quoted?| . 148751) (|coercePreimagesImages| . 148623) (|particularSolution| . 147611) (|moebius| . 147512) (|biringToPolyRing| . 147114) (|simplifyExp| . 146899) (|rootPoly| . 146498) (|dflist| . 146277) (|postfix| . 146227) (|nodes| . 146106) (|exactQuotient!| . 145655) (|ldf2lst| . 145232) (|FormatArabic| . 145113) (|coerce| . 104596) (|getStream| . 104418) (|rk4| . 103841) (|leftPower| . 103655) (|recoverAfterFail| . 103528) (|resetNew| . 103457) (|rows| . 102879) (|writable?| . 102790) (|reduceRowOnList| . 102637) (|OMputInteger| . 102524) (|mathieu12| . 102261) (|rename!| . 102167) (|Gamma| . 101443) (|splitDenominator| . 99852) (|icamax| . 99706) (|simplifyLog| . 99491) (|linkToFortran| . 98644) (|squareFreePart| . 97809) (|recur| . 97450) (|constantCoefficientRicDE| . 96956) (|resultantEuclidean| . 96708) (|checkForZero| . 95817) (|smith| . 95569) (|sizeLess?| . 95478) (|psolve| . 88810) (|makeCos| . 88602) (|OMgetEndAtp| . 88520) (|coHeight| . 88199) (|nrows| . 87546) (|suppOfPole| . 87421) (|airyAi| . 86978) (|allDegrees| . 86766) (|laguerreL| . 86456) (|lyndonIfCan| . 86316) (|digits| . 85695) (|parse| . 85616) (|ncols| . 84963) (|bezoutResultant| . 84626) (|PollardSmallFactor| . 84501) (|writeObj| . 84348) (|numberOfPrimitivePoly| . 84196) (|rischDEsys| . 83501) (|linears| . 83339) (|selectFiniteRoutines| . 83289) (|identitySquareMatrix| . 83122) (|position| . 82240) (|generalInterpolation| . 80273) (|screenResolution| . 80036) (|subset?| . 79911) (|selectIntegrationRoutines| . 79861) (|sinhcosh| . 79620) (|conical| . 79408) (|common| . 79288) (|besselK| . 78833) (|mvar| . 78406) (|OMlistCDs| . 78315) (|acsch| . 77120) (|bipolar| . 76911) (|error| . 76433) (UTS2UP . 76120) (|chiSquare1| . 75988) (|inverse| . 74259) (|stopTable!| . 73584) (|insertMatch| . 73412) (|genericRightTrace| . 73100) (|OMputEndBVar| . 73018) (|rotate!| . 72763) (|expandPower| . 72548) (|selectNonFiniteRoutines| . 72498) (|normalized?| . 71478) (|formula| . 71380) (|reportInstantiations| . 71257) (|createLowComplexityNormalBasis| . 70973) (|lieAlgebra?| . 70633) (|hue| . 70373) (|pow| . 69973) (|null?| . 69696) (|viewSizeDefault| . 69488) (|zeroSquareMatrix| . 69321) (|rangePascalTriangle| . 69063) (|OMsupportsSymbol?| . 68947) (|varList| . 67572) (|testDim| . 67264) (|mergeDifference| . 67144) (|rotatex| . 67003) (|extension| . 66915) (|zeroDimPrime?| . 66543) (|roughEqualIdeals?| . 66232) (|makeTerm| . 66077) (|denomLODE| . 65254) (|normalDenom| . 65032) (|trapezoidalo| . 64732) (|lazyPquo| . 64352) (|suchThat| . 62420) (|evalIfCan| . 58333) (|mapmult| . 58199) (|laurentIfCan| . 58012) (|numeric| . 56435) (|imaginary| . 56337) (|checkExtraValues| . 56125) (|gcdprim| . 55982) (|perfectSqrt| . 55872) (|over| . 55822) (|seriesSolve| . 51752) (|radical| . 51408) (|validExponential| . 50999) (|generator| . 49915) (|leadingIndex| . 49442) (|purelyAlgebraic?| . 48876) (|unitNormal| . 48732) (|row| . 48020) (|ReduceOrder| . 47603) (|compBound| . 47381) (|convert| . 38807) (|OMputEndApp| . 38725) (|inconsistent?| . 37967) (|radicalSimplify| . 37629) (|largest| . 37282) (|revert| . 36789) (|sylvesterMatrix| . 36495) (|flatten| . 36449) (|lo| . 36359) (|sn| . 36184) (|genericPosition| . 35766) (|goto| . 35678) (|ricDsolve| . 32219) (|overlabel| . 32169) (|index| . 31634) (|doubleRank| . 31442) (|incr| . 31230) (|drot| . 31006) (|tanAn| . 30826) (|genericRightNorm| . 30514) (|totolex| . 30232) (|inf| . 30082) (|bits| . 29730) (|point| . 28714) (|numberOfFactors| . 28337) (|hi| . 28247) (|setpoint!| . 27739) (|monomialIntegrate| . 27385) (|wordInStrongGenerators| . 27203) (|OMputApp| . 27121) (|permutationRepresentation| . 26352) (|min| . 25863) (|space| . 25576) (|rightMinimalPolynomial| . 25372) (|mergeFactors| . 25229) (|headReduced?| . 24209) (|cycleSplit!| . 24069) (|nary?| . 23985) (|element| . 23702) (|infinite?| . 23454) (|even?| . 23113) (|evalADE| . 22672) (|setProperties| . 22557) (|exptMod| . 22179) (|lazyIntegrate| . 21948) (|loopPoints| . 21731) (|stoseInvertibleSetsqfreg| . 21369) (|exprHasWeightCosWXorSinWX| . 20999) (|symbolIfCan| . 20877) (|semiResultantEuclideannaif| . 20646) (|acoshIfCan| . 20505) (|join| . 20374) (|generate| . 19892) (|aspFilename| . 19801) (|restorePrecision| . 19715) (|oddlambert| . 19222) (|OMencodingBinary| . 19172) (|subscript| . 19080) (|incrementBy| . 18925) (|euclideanNormalForm| . 18643) (|getDatabase| . 18434) (|prime| . 18295) (|rightFactorCandidate| . 18099) (|bumptab1| . 17928) (|expand| . 16036) (|oblateSpheroidal| . 15827) (|lowerPolynomial| . 15498) (|fractRadix| . 15372) (|coshIfCan| . 15231) (|hasTopPredicate?| . 15116) (= . 13965) (|filterWhile| . 13711) (|basisOfLeftNucloid| . 13522) (|absolutelyIrreducible?| . 12932) (|po| . 12776) (|bandMatrix| . 12214) (|filterUntil| . 11960) (|sayLength| . 11730) (|idealiser| . 11110) (|nthFactor| . 10263) (|algebraicOf| . 9975) (< . 9467) (|select| . 8649) (|factorOfDegree| . 7228) (|leftRankPolynomial| . 6461) (|presub| . 6411) (|LazardQuotient| . 6142) (> . 6009) (|associates?| . 5919) (|negAndPosEdge| . 5625) (|primPartElseUnitCanonical!| . 5401) (|classNumber| . 4113) (<= . 3731) (|mapExpon| . 3237) (|primPartElseUnitCanonical| . 3013) (|readIfCan!| . 2740) (|unmakeSUP| . 2587) (>= . 2454) (|xRange| . 2225) (|makeSUP| . 2072) (|autoReduced?| . 1733) (|removeSquaresIfCan| . 1446) (|lfinfieldint| . 1074) (|status| . 602) (|LowTriBddDenomInv| . 341) (|listAllMonoExp| . 30)) \ No newline at end of file diff --git a/src/share/algebra/users.daase/index.kaf b/src/share/algebra/users.daase/index.kaf index e8692fc..085da5f 100644 --- a/src/share/algebra/users.daase/index.kaf +++ b/src/share/algebra/users.daase/index.kaf @@ -1,4 +1,4 @@ -237944 (|ProjectiveAlgebraicSetPackage|) +238015 (|ProjectiveAlgebraicSetPackage|) (|ProjectiveAlgebraicSetPackage|) (|AffinePlaneOverPseudoAlgebraicClosureOfFiniteField| |BlowUpPackage| |DesingTreePackage| |InfClsPt| |InfinitlyClosePoint| |InfinitlyClosePointOverPseudoAlgebraicClosureOfFiniteField|) (|AffinePlane|) @@ -65,7 +65,7 @@ (|CartesianTensorFunctions2|) (|CylindricalAlgebraicDecompositionPackage|) (|AlgebraicFunctionField| |AlgebraicIntegration| |PureAlgebraicIntegration| |RadicalFunctionField|) -(|AxiomServer| |Character| |CharacterClass| |Float| |FortranTemplate| |HTMLFormat| |IndexedBits| |IndexedString| |LieExponentials| |MathMLFormat| |NumberFormats| |OutputForm| |RadixExpansion| |RecursivePolynomialCategory&| |ScriptFormulaFormat| |String| |StringAggregate&| |Symbol| |TemplateUtilities| |TexFormat| |Tree|) +(|AxiomServer| |Character| |CharacterClass| |Float| |FortranTemplate| |HTMLFormat| |HexadecimalExpansion| |IndexedBits| |IndexedString| |LieExponentials| |MathMLFormat| |NumberFormats| |OutputForm| |RadixExpansion| |RecursivePolynomialCategory&| |ScriptFormulaFormat| |String| |StringAggregate&| |Symbol| |TemplateUtilities| |TexFormat| |Tree|) (|Character| |IndexedString| |MathMLFormat| |String| |StringAggregate&|) (|MonogenicAlgebra&|) (|PAdicWildFunctionFieldIntegralBasis|) @@ -329,7 +329,7 @@ (|MappingPackage1|) (|MappingPackage2|) (|MappingPackage3|) -(|AlgebraGivenByStructuralConstants| |AlgebraPackage| |AlgebraicFunctionField| |AlgebraicHermiteIntegration| |AlgebraicNumber| |AnnaNumericalOptimizationPackage| |AnnaPartialDifferentialEquationPackage| |Asp19| |Asp20| |Asp27| |Asp28| |Asp30| |Asp31| |Asp34| |Asp35| |Asp41| |Asp42| |Asp55| |Asp74| |Asp77| |Asp80| |AssociatedEquations| |AssociatedJordanAlgebra| |AssociatedLieAlgebra| |BalancedPAdicRational| |BinaryExpansion| |CharacteristicPolynomialPackage| |ChineseRemainderToolsForIntegralBases| |CliffordAlgebra| |CoerceVectorMatrixPackage| |Complex| |ComplexCategory&| |ComplexDoubleFloatVector| |CycleIndicators| |DecimalExpansion| |DenavitHartenbergMatrix| |DifferentialSparseMultivariatePolynomial| |DirectProduct| |DirectProductCategory&| |DirectProductMatrixModule| |DirectProductModule| |DistributedMultivariatePolynomial| |DoubleFloatVector| |EigenPackage| |ElementaryFunctionLODESolver| |ElementaryFunctionODESolver| |ExpertSystemToolsPackage| |ExpertSystemToolsPackage2| |ExponentialExpansion| |Expression| |FiniteAlgebraicExtensionField&| |FiniteField| |FiniteFieldCategory&| |FiniteFieldCyclicGroup| |FiniteFieldCyclicGroupExtension| |FiniteFieldCyclicGroupExtensionByPolynomial| |FiniteFieldExtension| |FiniteFieldExtensionByPolynomial| |FiniteFieldFunctions| |FiniteFieldHomomorphisms| |FiniteFieldNormalBasis| |FiniteFieldNormalBasisExtension| |FiniteFieldNormalBasisExtensionByPolynomial| |FiniteFieldPolynomialPackage| |FiniteRankAlgebra&| |FiniteRankNonAssociativeAlgebra&| |FortranCode| |Fraction| |FractionFreeFastGaussian| |FractionFreeFastGaussianFractions| |FractionalIdeal| |FramedAlgebra&| |FramedModule| |FramedNonAssociativeAlgebra&| |FullyLinearlyExplicitRingOver&| |FunctionFieldCategory&| |FunctionFieldIntegralBasis| |GeneralDistributedMultivariatePolynomial| |GenericNonAssociativeAlgebra| |GosperSummationMethod| |Guess| |HexadecimalExpansion| |HomogeneousDirectProduct| |HomogeneousDistributedMultivariatePolynomial| |IndexedVector| |InnerAlgebraicNumber| |InnerFiniteField| |InnerNormalBasisFieldFunctions| |InnerNumericEigenPackage| |InnerPrimeField| |Integer| |IntegralBasisPolynomialTools| |IntegralBasisTools| |InterpolateFormsPackage| |IrrRepSymNatPackage| |LieSquareMatrix| |LinGroebnerPackage| |LinearDependence| |LinearOrdinaryDifferentialOperatorsOps| |LinearSystemFromPowerSeriesPackage| |LinearSystemMatrixPackage1| |LinearSystemPolynomialPackage| |LinesOpPack| |MachineComplex| |MachineInteger| |Matrix| |MatrixCommonDenominator| |MatrixLinearAlgebraFunctions| |ModMonic| |ModularHermitianRowReduction| |MonogenicAlgebra&| |MultiVariableCalculusFunctions| |MultivariatePolynomial| |MyExpression| |MyUnivariatePolynomial| |NAGLinkSupportPackage| |NagEigenPackage| |NagFittingPackage| |NagIntegrationPackage| |NagInterpolationPackage| |NagLapack| |NagLinearEquationSolvingPackage| |NagMatrixOperationsPackage| |NagOptimisationPackage| |NagOrdinaryDifferentialEquationsPackage| |NagPartialDifferentialEquationsPackage| |NagPolynomialRootsPackage| |NagRootFindingPackage| |NagSeriesSummationPackage| |NewSparseMultivariatePolynomial| |NewSparseUnivariatePolynomial| |NumberFieldIntegralBasis| |NumericComplexEigenPackage| |NumericRealEigenPackage| |ODETools| |OrderedDirectProduct| |OrderlyDifferentialPolynomial| |PAdicRational| |PAdicRationalConstructor| |PAdicWildFunctionFieldIntegralBasis| |PackageForAlgebraicFunctionField| |PackageForAlgebraicFunctionFieldOverFiniteField| |ParametricLinearEquations| |Point| |Polynomial| |PolynomialCategory&| |PolynomialFactorizationExplicit&| |PrecomputedAssociatedEquations| |PrimeField| |PseudoAlgebraicClosureOfFiniteField| |PseudoLinearNormalForm| |PureAlgebraicLODE| |Quaternion| |QuotientFieldCategory&| |RadicalEigenPackage| |RadicalFunctionField| |RadixExpansion| |RationalInterpolation| |RationalLODE| |RectangularMatrix| |RectangularMatrixCategoryFunctions2| |ReduceLODE| |RepresentationPackage1| |RepresentationPackage2| |RomanNumeral| |SequentialDifferentialPolynomial| |SimpleAlgebraicExtension| |SingleInteger| |SmithNormalForm| |SparseEchelonMatrix| |SparseMultivariatePolynomial| |SparseUnivariateLaurentSeries| |SparseUnivariatePolynomial| |SparseUnivariatePolynomialExpressions| |SplitHomogeneousDirectProduct| |SquareMatrix| |SquareMatrixCategory&| |StorageEfficientMatrixOperations| |StructuralConstantsPackage| |SymmetricGroupCombinatoricFunctions| |SystemODESolver| |TransSolvePackageService| |TranscendentalIntegration| |TranscendentalRischDESystem| |UnivariateLaurentSeries| |UnivariateLaurentSeriesConstructor| |UnivariatePolynomial| |Vector| |VectorCategory&| |WildFunctionFieldIntegralBasis| |d01alfAnnaType| |d01fcfAnnaType| |d01gbfAnnaType| |d02AgentsPackage| |d02bbfAnnaType| |d02bhfAnnaType| |d02cjfAnnaType| |d02ejfAnnaType| |d03eefAnnaType| |e04AgentsPackage| |e04dgfAnnaType| |e04fdfAnnaType| |e04gcfAnnaType| |e04jafAnnaType| |e04mbfAnnaType| |e04nafAnnaType| |e04ucfAnnaType|) +(|AlgebraGivenByStructuralConstants| |AlgebraPackage| |AlgebraicFunctionField| |AlgebraicHermiteIntegration| |AlgebraicNumber| |AnnaNumericalOptimizationPackage| |AnnaPartialDifferentialEquationPackage| |Asp19| |Asp20| |Asp27| |Asp28| |Asp30| |Asp31| |Asp34| |Asp35| |Asp41| |Asp42| |Asp55| |Asp74| |Asp77| |Asp80| |AssociatedEquations| |AssociatedJordanAlgebra| |AssociatedLieAlgebra| |BalancedPAdicRational| |BinaryExpansion| |CharacteristicPolynomialPackage| |ChineseRemainderToolsForIntegralBases| |CliffordAlgebra| |CoerceVectorMatrixPackage| |Complex| |ComplexCategory&| |ComplexDoubleFloatVector| |CycleIndicators| |DeRhamComplex| |DecimalExpansion| |DenavitHartenbergMatrix| |DifferentialSparseMultivariatePolynomial| |DirectProduct| |DirectProductCategory&| |DirectProductMatrixModule| |DirectProductModule| |DistributedMultivariatePolynomial| |DoubleFloatVector| |EigenPackage| |ElementaryFunctionLODESolver| |ElementaryFunctionODESolver| |ExpertSystemToolsPackage| |ExpertSystemToolsPackage2| |ExponentialExpansion| |Expression| |FiniteAlgebraicExtensionField&| |FiniteField| |FiniteFieldCategory&| |FiniteFieldCyclicGroup| |FiniteFieldCyclicGroupExtension| |FiniteFieldCyclicGroupExtensionByPolynomial| |FiniteFieldExtension| |FiniteFieldExtensionByPolynomial| |FiniteFieldFunctions| |FiniteFieldHomomorphisms| |FiniteFieldNormalBasis| |FiniteFieldNormalBasisExtension| |FiniteFieldNormalBasisExtensionByPolynomial| |FiniteFieldPolynomialPackage| |FiniteRankAlgebra&| |FiniteRankNonAssociativeAlgebra&| |FortranCode| |Fraction| |FractionFreeFastGaussian| |FractionFreeFastGaussianFractions| |FractionalIdeal| |FramedAlgebra&| |FramedModule| |FramedNonAssociativeAlgebra&| |FullyLinearlyExplicitRingOver&| |FunctionFieldCategory&| |FunctionFieldIntegralBasis| |GeneralDistributedMultivariatePolynomial| |GenericNonAssociativeAlgebra| |GosperSummationMethod| |Guess| |HexadecimalExpansion| |HomogeneousDirectProduct| |HomogeneousDistributedMultivariatePolynomial| |IndexedVector| |InnerAlgebraicNumber| |InnerFiniteField| |InnerNormalBasisFieldFunctions| |InnerNumericEigenPackage| |InnerPrimeField| |Integer| |IntegralBasisPolynomialTools| |IntegralBasisTools| |InterpolateFormsPackage| |IrrRepSymNatPackage| |LieSquareMatrix| |LinGroebnerPackage| |LinearDependence| |LinearOrdinaryDifferentialOperatorsOps| |LinearSystemFromPowerSeriesPackage| |LinearSystemMatrixPackage1| |LinearSystemPolynomialPackage| |LinesOpPack| |MachineComplex| |MachineInteger| |Matrix| |MatrixCommonDenominator| |MatrixLinearAlgebraFunctions| |ModMonic| |ModularHermitianRowReduction| |MonogenicAlgebra&| |MultiVariableCalculusFunctions| |MultivariatePolynomial| |MyExpression| |MyUnivariatePolynomial| |NAGLinkSupportPackage| |NagEigenPackage| |NagFittingPackage| |NagIntegrationPackage| |NagInterpolationPackage| |NagLapack| |NagLinearEquationSolvingPackage| |NagMatrixOperationsPackage| |NagOptimisationPackage| |NagOrdinaryDifferentialEquationsPackage| |NagPartialDifferentialEquationsPackage| |NagPolynomialRootsPackage| |NagRootFindingPackage| |NagSeriesSummationPackage| |NewSparseMultivariatePolynomial| |NewSparseUnivariatePolynomial| |NumberFieldIntegralBasis| |NumericComplexEigenPackage| |NumericRealEigenPackage| |ODETools| |OrderedDirectProduct| |OrderlyDifferentialPolynomial| |PAdicRational| |PAdicRationalConstructor| |PAdicWildFunctionFieldIntegralBasis| |PackageForAlgebraicFunctionField| |PackageForAlgebraicFunctionFieldOverFiniteField| |ParametricLinearEquations| |Point| |Polynomial| |PolynomialCategory&| |PolynomialFactorizationExplicit&| |PrecomputedAssociatedEquations| |PrimeField| |PseudoAlgebraicClosureOfFiniteField| |PseudoLinearNormalForm| |PureAlgebraicLODE| |Quaternion| |QuotientFieldCategory&| |RadicalEigenPackage| |RadicalFunctionField| |RadixExpansion| |RationalInterpolation| |RationalLODE| |RectangularMatrix| |RectangularMatrixCategoryFunctions2| |ReduceLODE| |RepresentationPackage1| |RepresentationPackage2| |RomanNumeral| |SequentialDifferentialPolynomial| |SimpleAlgebraicExtension| |SingleInteger| |SmithNormalForm| |SparseEchelonMatrix| |SparseMultivariatePolynomial| |SparseUnivariateLaurentSeries| |SparseUnivariatePolynomial| |SparseUnivariatePolynomialExpressions| |SplitHomogeneousDirectProduct| |SquareMatrix| |SquareMatrixCategory&| |StorageEfficientMatrixOperations| |StructuralConstantsPackage| |SymmetricGroupCombinatoricFunctions| |SystemODESolver| |TransSolvePackageService| |TranscendentalIntegration| |TranscendentalRischDESystem| |UnivariateLaurentSeries| |UnivariateLaurentSeriesConstructor| |UnivariatePolynomial| |Vector| |VectorCategory&| |WildFunctionFieldIntegralBasis| |d01alfAnnaType| |d01fcfAnnaType| |d01gbfAnnaType| |d02AgentsPackage| |d02bbfAnnaType| |d02bhfAnnaType| |d02cjfAnnaType| |d02ejfAnnaType| |d03eefAnnaType| |e04AgentsPackage| |e04dgfAnnaType| |e04fdfAnnaType| |e04gcfAnnaType| |e04jafAnnaType| |e04mbfAnnaType| |e04nafAnnaType| |e04ucfAnnaType|) (|AlgebraicHermiteIntegration| |Asp19| |Asp20| |Asp31| |Asp35| |Asp41| |Asp42| |Asp74| |Asp77| |Asp80| |CoerceVectorMatrixPackage| |ComplexCategory&| |FractionalIdeal| |FramedAlgebra&| |FunctionFieldCategory&| |InnerMatrixQuotientFieldFunctions| |LinearDependence| |MatrixCommonDenominator| |MatrixLinearAlgebraFunctions| |ReduceLODE| |SimpleAlgebraicExtension| |SmithNormalForm|) (|AlgebraicFunctionField| |FractionalIdeal| |FramedModule| |FunctionFieldCategory&| |QuotientFieldCategory&|) (|IndexedMatrix| |Matrix|) @@ -550,7 +550,7 @@ (|SquareFreeRegularTriangularSet|) (|LexTriangularPackage| |RationalUnivariateRepresentationPackage| |ZeroDimensionalSolvePackage|) (|LazardSetSolvingPackage| |NormalizationPackage| |SquareFreeRegularSetDecompositionPackage| |SquareFreeRegularTriangularSet|) -(|AlgebraGivenByStructuralConstants| |CartesianTensor| |GenericNonAssociativeAlgebra| |LieSquareMatrix| |Permanent| |QuadraticForm|) +(|AlgebraGivenByStructuralConstants| |CartesianTensor| |DeRhamComplex| |GenericNonAssociativeAlgebra| |LieSquareMatrix| |Permanent| |QuadraticForm|) (|FortranOutputStackPackage| |Queue|) (|Matrix|) (|BalancedPAdicInteger| |BasicFunctions| |ContinuedFraction| |CycleIndicators| |DirichletRing| |ElementaryFunctionsUnivariateLaurentSeries| |EllipticFunctionsUnivariateTaylorSeries| |ExpertSystemContinuityPackage| |ExpertSystemToolsPackage| |ExponentialOfUnivariatePuiseuxSeries| |FractionFreeFastGaussian| |FractionFreeFastGaussianFractions| |GeneralUnivariatePowerSeries| |GenerateUnivariatePowerSeries| |Guess| |InfiniteProductCharacteristicZero| |InfiniteProductFiniteField| |InfiniteProductPrimeField| |InfiniteTuple| |InfiniteTupleFunctions2| |InfiniteTupleFunctions3| |InnerPAdicInteger| |InnerSparseUnivariatePowerSeries| |InnerTaylorSeries| |LinearSystemFromPowerSeriesPackage| |NeitherSparseOrDensePowerSeries| |NumericContinuedFraction| |PAdicInteger| |PAdicRationalConstructor| |PadeApproximants| |ParadoxicalCombinatorsForStreams| |PartitionsAndPermutations| |RadixExpansion| |SparseMultivariateTaylorSeries| |SparseUnivariateLaurentSeries| |SparseUnivariatePuiseuxSeries| |SparseUnivariateTaylorSeries| |Stream| |StreamFunctions1| |StreamFunctions2| |StreamFunctions3| |StreamInfiniteProduct| |StreamTaylorSeriesOperations| |StreamTensor| |StreamTranscendentalFunctions| |StreamTranscendentalFunctionsNonCommutative| |TableauxBumpers| |TaylorSolve| |UnivariateFormalPowerSeries| |UnivariateFormalPowerSeriesFunctions| |UnivariateLaurentSeries| |UnivariateLaurentSeriesConstructor| |UnivariatePuiseuxSeries| |UnivariatePuiseuxSeriesConstructor| |UnivariatePuiseuxSeriesWithExponentialSingularity| |UnivariateTaylorSeries| |UnivariateTaylorSeriesCZero| |UnivariateTaylorSeriesCategory&| |UnivariateTaylorSeriesFunctions2| |UnivariateTaylorSeriesODESolver| |UniversalSegment| |UniversalSegmentFunctions2| |WeierstrassPreparation| |d01AgentsPackage| |d01ajfAnnaType| |d01akfAnnaType| |d01alfAnnaType| |d01amfAnnaType| |d01aqfAnnaType| |e04gcfAnnaType|) @@ -631,7 +631,7 @@ (|GenerateUnivariatePowerSeries|) (|FunctionSpace&| |Polynomial| |UserDefinedVariableOrdering|) (|GeneralUnivariatePowerSeries| |MyUnivariatePolynomial| |PolynomialToUnivariatePolynomial| |SparseUnivariateLaurentSeries| |SparseUnivariatePuiseuxSeries| |SparseUnivariateTaylorSeries| |UnivariateFormalPowerSeries| |UnivariateLaurentSeries| |UnivariatePolynomial| |UnivariatePuiseuxSeries| |UnivariateSkewPolynomial| |UnivariateTaylorSeries| |UnivariateTaylorSeriesCZero|) -(|AffineAlgebraicSetComputeWithGroebnerBasis| |AffineAlgebraicSetComputeWithResultant| |AlgebraGivenByStructuralConstants| |AlgebraPackage| |AlgebraicFunctionField| |AlgebraicHermiteIntegration| |AlgebraicIntegrate| |AlgebraicNumber| |AnnaOrdinaryDifferentialEquationPackage| |Asp10| |Asp19| |Asp20| |Asp28| |Asp31| |Asp35| |Asp41| |Asp42| |Asp49| |Asp50| |Asp55| |Asp6| |Asp7| |Asp73| |Asp78| |Asp8| |Asp80| |AssociatedEquations| |AssociatedJordanAlgebra| |AssociatedLieAlgebra| |BalancedPAdicRational| |BinaryExpansion| |BlowUpPackage| |CartesianTensor| |CliffordAlgebra| |CoerceVectorMatrixPackage| |Complex| |ComplexCategory&| |ComplexIntegerSolveLinearPolynomialEquation| |DecimalExpansion| |DenavitHartenbergMatrix| |DesingTreePackage| |DifferentialSparseMultivariatePolynomial| |DiophantineSolutionPackage| |DirectProduct| |DirectProductCategory&| |DirectProductFunctions2| |DirectProductMatrixModule| |DirectProductModule| |DistributedMultivariatePolynomial| |EigenPackage| |ElementaryFunctionLODESolver| |ElementaryFunctionODESolver| |ElementaryFunctionStructurePackage| |ExpertSystemContinuityPackage| |ExpertSystemToolsPackage| |ExponentialExpansion| |Expression| |FiniteAlgebraicExtensionField&| |FiniteDivisor| |FiniteField| |FiniteFieldCategory&| |FiniteFieldCyclicGroup| |FiniteFieldCyclicGroupExtension| |FiniteFieldCyclicGroupExtensionByPolynomial| |FiniteFieldExtension| |FiniteFieldExtensionByPolynomial| |FiniteFieldFunctions| |FiniteFieldHomomorphisms| |FiniteFieldNormalBasis| |FiniteFieldNormalBasisExtension| |FiniteFieldNormalBasisExtensionByPolynomial| |FiniteFieldPolynomialPackage| |FiniteFieldPolynomialPackage2| |FiniteFieldSolveLinearPolynomialEquation| |FiniteRankAlgebra&| |FiniteRankNonAssociativeAlgebra&| |FortranCode| |Fraction| |FractionFreeFastGaussian| |FractionFreeFastGaussianFractions| |FractionalIdeal| |FractionalIdealFunctions2| |FramedAlgebra&| |FramedModule| |FramedNonAssociativeAlgebra&| |FramedNonAssociativeAlgebraFunctions2| |FreeNilpotentLie| |FullyLinearlyExplicitRingOver&| |FunctionFieldCategory&| |GaloisGroupPolynomialUtilities| |GenExEuclid| |GeneralDistributedMultivariatePolynomial| |GenericNonAssociativeAlgebra| |GosperSummationMethod| |GrayCode| |Guess| |HallBasis| |HexadecimalExpansion| |HomogeneousDirectProduct| |HomogeneousDistributedMultivariatePolynomial| |HyperellipticFiniteDivisor| |InfinitlyClosePoint| |InnerAlgebraicNumber| |InnerFiniteField| |InnerNormalBasisFieldFunctions| |InnerNumericEigenPackage| |InnerPrimeField| |Integer| |IntegerLinearDependence| |IntegerPrimesPackage| |IntegerSolveLinearPolynomialEquation| |IntegralBasisTools| |IntegrationResultToFunction| |InterpolateFormsPackage| |IrrRepSymNatPackage| |LieSquareMatrix| |LinGroebnerPackage| |LinearDependence| |LinearOrdinaryDifferentialOperatorsOps| |LinearSystemMatrixPackage1| |LinearSystemPolynomialPackage| |LinesOpPack| |MachineComplex| |MachineInteger| |Matrix| |MatrixLinearAlgebraFunctions| |ModMonic| |ModularHermitianRowReduction| |MonogenicAlgebra&| |MultiVariableCalculusFunctions| |MultivariateLifting| |MultivariatePolynomial| |MyExpression| |MyUnivariatePolynomial| |NPCoef| |NewSparseMultivariatePolynomial| |NewSparseUnivariatePolynomial| |NumberFieldIntegralBasis| |NumericalOrdinaryDifferentialEquations| |NumericalQuadrature| |ODETools| |OrderedDirectProduct| |OrderingFunctions| |OrderlyDifferentialPolynomial| |PAdicRational| |PAdicRationalConstructor| |PAdicWildFunctionFieldIntegralBasis| |PackageForPoly| |ParametricLinearEquations| |Permanent| |Permutation| |PermutationGroup| |Point| |PointsOfFiniteOrder| |PointsOfFiniteOrderRational| |PolToPol| |Polynomial| |PolynomialCategory&| |PolynomialFactorizationExplicit&| |PolynomialIdeals| |PrimeField| |PseudoAlgebraicClosureOfAlgExtOfRationalNumber| |PseudoAlgebraicClosureOfFiniteField| |PseudoAlgebraicClosureOfRationalNumber| |PseudoLinearNormalForm| |PseudoRemainderSequence| |PureAlgebraicLODE| |Quaternion| |QuotientFieldCategory&| |RadicalEigenPackage| |RadicalFunctionField| |RadixExpansion| |RandomDistributions| |RationalInterpolation| |RationalLODE| |RealZeroPackage| |RectangularMatrix| |ReduceLODE| |RepresentationPackage1| |RepresentationPackage2| |RomanNumeral| |SequentialDifferentialPolynomial| |SetOfMIntegersInOneToN| |SimpleAlgebraicExtension| |SingleInteger| |SparseEchelonMatrix| |SparseMultivariatePolynomial| |SparseUnivariateLaurentSeries| |SparseUnivariatePolynomial| |SparseUnivariatePolynomialExpressions| |SplitHomogeneousDirectProduct| |SquareMatrix| |SquareMatrixCategory&| |StructuralConstantsPackage| |SymmetricFunctions| |SymmetricGroupCombinatoricFunctions| |SystemODESolver| |SystemSolvePackage| |TangentExpansions| |ThreeDimensionalMatrix| |TransSolvePackageService| |TranscendentalRischDESystem| |TwoDimensionalViewport| |UTSodetools| |UnivariateLaurentSeries| |UnivariateLaurentSeriesConstructor| |UnivariatePolynomial| |UnivariatePolynomialCategory&| |VectorFunctions2| |WildFunctionFieldIntegralBasis| |d02AgentsPackage| |d02bbfAnnaType| |d02bhfAnnaType| |d02cjfAnnaType| |d02ejfAnnaType| |d03eefAnnaType| |e04AgentsPackage| |e04fdfAnnaType| |e04gcfAnnaType| |e04ucfAnnaType|) +(|AffineAlgebraicSetComputeWithGroebnerBasis| |AffineAlgebraicSetComputeWithResultant| |AlgebraGivenByStructuralConstants| |AlgebraPackage| |AlgebraicFunctionField| |AlgebraicHermiteIntegration| |AlgebraicIntegrate| |AlgebraicNumber| |AnnaOrdinaryDifferentialEquationPackage| |Asp10| |Asp19| |Asp20| |Asp28| |Asp31| |Asp35| |Asp41| |Asp42| |Asp49| |Asp50| |Asp55| |Asp6| |Asp7| |Asp73| |Asp78| |Asp8| |Asp80| |AssociatedEquations| |AssociatedJordanAlgebra| |AssociatedLieAlgebra| |BalancedPAdicRational| |BinaryExpansion| |BlowUpPackage| |CartesianTensor| |CliffordAlgebra| |CoerceVectorMatrixPackage| |Complex| |ComplexCategory&| |ComplexIntegerSolveLinearPolynomialEquation| |DeRhamComplex| |DecimalExpansion| |DenavitHartenbergMatrix| |DesingTreePackage| |DifferentialSparseMultivariatePolynomial| |DiophantineSolutionPackage| |DirectProduct| |DirectProductCategory&| |DirectProductFunctions2| |DirectProductMatrixModule| |DirectProductModule| |DistributedMultivariatePolynomial| |EigenPackage| |ElementaryFunctionLODESolver| 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end of file -- 1.7.5.4