diff --git a/changelog b/changelog index 88477f9..90b2e1c 100644 --- a/changelog +++ b/changelog @@ -1,3 +1,4 @@ +20080220 tpd src/hyper/bookvol11 add additional hyperdoc page translations 20080219 tpd src/hyper/Makefile handle hyperdoc bitmaps properly 20080219 tpd src/Makefile handle hyperdoc bitmaps properly 20080219 tpd src/hyper/bookvol11 add additional hyperdoc page translations diff --git a/src/hyper/bookvol11.pamphlet b/src/hyper/bookvol11.pamphlet index 9335c11..b9f36fc 100644 --- a/src/hyper/bookvol11.pamphlet +++ b/src/hyper/bookvol11.pamphlet @@ -515,16 +515,21 @@ PAGES=rootpage.xhtml \ dbopdigits.xhtml \ dbopdimension.xhtml \ dbopdivide.xhtml \ + dbopei.xhtml \ dbopeigenmatrix.xhtml \ dbopeigenvalues.xhtml \ dbopeigenvector.xhtml \ dbopeigenvectors.xhtml \ dbopelt.xhtml \ + dbopequalsign.xhtml \ + dbopeulerphi.xhtml \ dbopeval.xhtml \ dbopevenq.xhtml \ dbopexp.xhtml \ + dbopexquo.xhtml \ dbopfactor.xhtml \ dbopfactorfraction.xhtml \ + dbopfibonacci.xhtml \ dbopfiniteq.xhtml \ dbopfirstdenom.xhtml \ dbopfirstnumer.xhtml \ @@ -539,10 +544,12 @@ PAGES=rootpage.xhtml \ dbopintegrate.xhtml \ dbopinverse.xhtml \ dbopinvmod.xhtml \ + dbopjacobi.xhtml \ dboplaurent.xhtml \ dboplcm.xhtml \ dbopleadingcoefficient.xhtml \ dbopleadingmonomial.xhtml \ + dboplegendre.xhtml \ dboplength.xhtml \ dboplimit.xhtml \ dboplog.xhtml \ @@ -556,10 +563,12 @@ PAGES=rootpage.xhtml \ dbopmin.xhtml \ dbopminimumdegree.xhtml \ dbopminus.xhtml \ + dbopmoebiusmu.xhtml \ dbopmonicdivide.xhtml \ dbopmulmod.xhtml \ dbopncols.xhtml \ dbopnew.xhtml \ + dbopnextprime.xhtml \ dbopnorm.xhtml \ dbopnrows.xhtml \ dbopnthfractionalterm.xhtml \ @@ -569,6 +578,7 @@ PAGES=rootpage.xhtml \ dbopnumberoffractionalterms.xhtml \ dbopnumer.xhtml \ dbopnumeric.xhtml \ + dbopoddq.xhtml \ dbopoperator.xhtml \ dboporthonormalbasis.xhtml \ dboppadicfraction.xhtml \ @@ -581,7 +591,10 @@ PAGES=rootpage.xhtml \ dboppolygamma.xhtml \ dboppositiveremainder.xhtml \ dbopprefixragits.xhtml \ + dbopprevprime.xhtml \ dbopprimefactor.xhtml \ + dbopprimeq.xhtml \ + dbopprimes.xhtml \ dboppuiseux.xhtml \ dbopqelt.xhtml \ dbopqseteltbang.xhtml \ @@ -608,7 +621,8 @@ PAGES=rootpage.xhtml \ dbopseteltbang.xhtml \ dbopsetrowbang.xhtml \ dbopsetsubmatrixbang.xhtml \ - dbopsimplify.xhtml\ + dbopsign.xhtml \ + dbopsimplify.xhtml \ dbopsec.xhtml \ dbopsech.xhtml \ dbopseries.xhtml \ @@ -641,6 +655,7 @@ PAGES=rootpage.xhtml \ dbopvertconcat.xhtml \ dbopwholepart.xhtml \ dbopwholeragits.xhtml \ + dbopzeroq.xhtml \ dbopzeroof.xhtml \ dbopzerosof.xhtml \ dbpolynomialinteger.xhtml \ @@ -3673,10 +3688,288 @@ abstract algebra \subsection{basicfunctions.xhtml} <>= <> + <> -basicfunctions not implemented +The size of an integer in Axiom is only limited by the amount of +computer storage you have available. The usual arithmetic operations +are available. +
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+There are a number of ways of working with the sign of an integer. +Let's use this x as an example. +
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+First of all, there is the absolute value function. +
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+The sign operation returns -1 if its +argument is negative, 0 if zero and 1 if positive. +
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+You can determine if an integer is negative in several other ways. +
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+Similarly, you can find out if it is positive. +
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+This is the recommended way of determining whether an integer is zero. +
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+
+Use the zero? operation whenever you are +testing any mathematical object for equality with zero. This is usually +more efficient than using = (think of +matrices; it is easier to tell if a matrix is zero by just checking term +by term than constructing another ``zero'' matrix and comparing the +two matrices term by term) and also avoids the problem that += is usually used for creating equations. +
+This is the recommended way of determining whether an integer is +equal to one. +
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+This syntax is used to test equality using =. +It says that you want a Boolean (true or +false) answer rather than an equation. +
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+The operations odd? and +even? determine whether an integer is odd +or even, respectively. They each return a +Boolean object. +
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+The operation gcd computes the greatest +common divisor of two integers. +
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+The operation lcm computes their least +common multiple. +
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+To determine the maximum of two integers, use max. +
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+To determine the minimum, use min. +
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+The reduce operation is used to extend +binary operations to more than two arguments. For example, you can use +reduce to find the maximum integer in a +list or compute the least common multiple of all integers in the list. +
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+The infix operator "/" is not used to compute the quotient of integers. +Rather, it is used to create rational numbers as described in +Fraction. +
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+The infix operation quo computes the integer +quotient. +
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+The infix operation rem computes the integer +remainder. +
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+One integer is evenly divisible by another if the remainder is zero. +The operation exquo can also be used. +See Unions. for an example. +
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+The operation divide returns a record of +the quotient and remainder and thus is more efficient when both are needed. +
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+Records are discussed in detail in +Records. +
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<> @ \subsection{basiclimit.xhtml} @@ -8441,6 +8734,16 @@ the operations will have extra ones added at some stage. <> @ +\subsection{dbopei.xhtml} +<>= +<> + + +<> + dbopei not implemented +<> +@ + \subsection{dbopeigenmatrix.xhtml} <>= <> @@ -8481,6 +8784,16 @@ the operations will have extra ones added at some stage. <> @ +\subsection{dbopequalsign.xhtml} +<>= +<> + + +<> + dbopequalsign not implemented +<> +@ + \subsection{dbopelt.xhtml} <>= <> @@ -8491,6 +8804,16 @@ the operations will have extra ones added at some stage. <> @ +\subsection{dbopeulerphi.xhtml} +<>= +<> + + +<> + dbopeulerphi not implemented +<> +@ + \subsection{dbopeval.xhtml} <>= <> @@ -8521,6 +8844,16 @@ the operations will have extra ones added at some stage. <> @ +\subsection{dbopexquo.xhtml} +<>= +<> + + +<> + dbopexquo not implemented +<> +@ + \subsection{dbopfactor.xhtml} <>= <> @@ -8541,6 +8874,16 @@ the operations will have extra ones added at some stage. <> @ +\subsection{dbopfibonacci.xhtml} +<>= +<> + + +<> + dbopfibonacci not implemented +<> +@ + \subsection{dbopfiniteq.xhtml} <>= <> @@ -8681,6 +9024,16 @@ the operations will have extra ones added at some stage. <> @ +\subsection{dbopjacobi.xhtml} +<>= +<> + + +<> + dbopjacobi not implemented +<> +@ + \subsection{dboplaurent.xhtml} <>= <> @@ -8721,6 +9074,16 @@ the operations will have extra ones added at some stage. <> @ +\subsection{dboplegendre.xhtml} +<>= +<> + + +<> + dboplegendre not implemented +<> +@ + \subsection{dboplength.xhtml} <>= <> @@ -8851,6 +9214,16 @@ the operations will have extra ones added at some stage. <> @ +\subsection{dbopmoebiusmu.xhtml} +<>= +<> + + +<> + dbopmoebiusmu not implemented +<> +@ + \subsection{dbopmonicdivide.xhtml} <>= <> @@ -8891,6 +9264,16 @@ the operations will have extra ones added at some stage. <> @ +\subsection{dbopnextprime.xhtml} +<>= +<> + + +<> + dbopnextprime not implemented +<> +@ + \subsection{dbopnorm.xhtml} <>= <> @@ -8951,6 +9334,16 @@ the operations will have extra ones added at some stage. <> @ +\subsection{dbopoddq.xhtml} +<>= +<> + + +<> + dbopoddq not implemented +<> +@ + \subsection{dbopoperator.xhtml} <>= <> @@ -9101,6 +9494,16 @@ the operations will have extra ones added at some stage. <> @ +\subsection{dbopprevprime.xhtml} +<>= +<> + + +<> + dbopprevprime not implemented +<> +@ + \subsection{dbopprimefactor.xhtml} <>= <> @@ -9111,6 +9514,26 @@ the operations will have extra ones added at some stage. <> @ +\subsection{dbopprimeq.xhtml} +<>= +<> + + +<> + dbopprimeq not implemented +<> +@ + +\subsection{dbopprimes.xhtml} +<>= +<> + + +<> + dbopprimes not implemented +<> +@ + \subsection{dboppuiseux.xhtml} <>= <> @@ -9381,6 +9804,16 @@ the operations will have extra ones added at some stage. <> @ +\subsection{dbopsign.xhtml} +<>= +<> + + +<> + dbopsign not implemented +<> +@ + \subsection{dbopsimplify.xhtml} <>= <> @@ -9661,6 +10094,16 @@ the operations will have extra ones added at some stage. <> @ +\subsection{dbopzeroq.xhtml} +<>= +<> + + +<> + dbopzeroq not implemented +<> +@ + \subsection{dbopzeroof.xhtml} <>= <> @@ -41462,10 +41905,83 @@ You can also substitute numerical values for some or all of the variables. \subsection{primesandfactorization.xhtml} <>= <> + <> -primesandfactorization not implemented +Use the operation factor to factor integers. +It returns an object of type +Factored Integer. See Factored for a +discussion of the manipulation of factored objects. +
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+The operation prime? returns true or false +depending on whether its argument is a prime. +
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+The operation nextPrime returns the +least prime greater than its argument. +
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+The operation prevPrime returns the +greatest prime less than its argument +
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+To compute all primes between two integers (inclusively), use the +operation primes. +
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+You might sometimes want to see the factorization of an integer when it is +considered a Gaussian integer. See Complex +for more details. +
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+ <> @ @@ -42366,10 +42882,97 @@ Enter the size of the matrix: \subsection{somenumbertheoreticfunctions.xhtml} <>= <> + <> -somenumbertheoreticfunctions not implemented +Axiom provides several number theoretic operations for integers. +More examples are in +IntegerNumberTheoryFunctions. + +The operation fibonacci computes the +Fibonacci numbers. The algorithm has running time O(log(n)^3) for +argument n. +
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+The operation legendre computes the +Legendre symbol for its two integer arguments where the second one is prime. +If you know the second argument to be prime, use +jacobi instead where no check is made. +
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+The operation jacobi computes the Jacobi +symbol for its two integer arguments. By convention, 0 is returned if +the greatest common divisor of the numerator and denominator is not 1. +
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+The operation eulerPhi computes the +values of Euler's phi function where phi(n) equals the number of positive +integers less than or equal to n that are relatively prime to the positive +integer n. +
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+The operation moebiusMu +computes the Moebius mu function. +
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+The Ei function computes the Exponential Integral. +
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+Although they have somewhat limited utility, Axiom provides Roman numerals. +
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<> @