diff --git a/changelog b/changelog index 3bf1d1e..5e82394 100644 --- a/changelog +++ b/changelog @@ -1,3 +1,5 @@ +20141202 tpd src/axiom-website/patches.html 20141202.02.tpd.patch +20141202 tpd src/input/*.input: rewrite ** to ^ 20141202 tpd src/axiom-website/patches.html 20141202.01.tpd.patch 20141202 tpd buglist: bug 7267: src/input/liu ^ is not always ** 20141201 tpd src/axiom-website/patches.html 20141201.01.tpd.patch diff --git a/patch b/patch index a1e9687..6524afe 100644 --- a/patch +++ b/patch @@ -1,10 +1,3 @@ -buglist: bug 7267: src/input/liu ^ is not always ** - -This makes it clear that the exponential operation semantics is different -for the use of ``\verb|^|'' and ``\verb|**|'' in some cases. - -Does exponential operation ``\verb|^|'' and ``\verb|**|'' of a differential -operator, say L, means repeating multiplications of L in Axiom ? If -so, it seems the following code produced an unexpected result: - +src/input/*.input: rewrite ** to ^ +regularize input files to the the ^ notation diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html index f1c4fe5..3b1bce4 100644 --- a/src/axiom-website/patches.html +++ b/src/axiom-website/patches.html @@ -4744,6 +4744,8 @@ buglist: bug 7266: integration failure for 1/(sin(x)^4+1)
readme: update the readme file to remove outdated comments
20141202.01.tpd.patch buglist: bug 7267: src/input/liu ^ is not always **
+20141202.02.tpd.patch +src/input/*.input: rewrite ** to ^
diff --git a/src/input/Makefile.pamphlet b/src/input/Makefile.pamphlet index 435c5e2..32f04ef 100644 --- a/src/input/Makefile.pamphlet +++ b/src/input/Makefile.pamphlet @@ -526,9 +526,12 @@ LISPTANGLE=${OBJ}/${SYS}/bin/lisp all: alltests algebratests: ${OUTS} + @ echo ====================================== + @ echo src/input RUNNING ALGEBRA TESTS + @ echo ====================================== @ echo si13 starting algebra regression testing @ (cd ${MID} ; \ - ${BOOKS}/tanglec ${SRC}/algebra/Makefile.pamphlet algebra.regress \ + ${BOOKS}/tanglec ${BOOKS}/bookvol10.pamphlet algebra.regress \ >Makefile.algebra ; \ ${MAKE} -f Makefile.algebra ) @ echo si14 finished ${INT}/input @@ -553,7 +556,7 @@ regresstests: ${REGRESSTESTS} ${OUTS} @ echo src/input RUNNING REGRESSION TESTS @ echo ====================================== -alltests: regresstests catstests newrichtests richtests algebratests ${OUTS} +alltests: regresstests algebratests catstests newrichtests richtests ${OUTS} @ echo ====================================== @ echo src/input RUNNING ALL TESTS @ echo ====================================== diff --git a/src/input/algbrbf.input.pamphlet b/src/input/algbrbf.input.pamphlet index 54106f0..38312c6 100644 --- a/src/input/algbrbf.input.pamphlet +++ b/src/input/algbrbf.input.pamphlet @@ -110,7 +110,7 @@ c := cos(p/12) --E 11 --S 12 of 13 -16*c**4 - 16*c**2 + 1 +16*c^4 - 16*c^2 + 1 --R --R --R (12) 0.0 diff --git a/src/input/algfacob.input.pamphlet b/src/input/algfacob.input.pamphlet index 1428a8c..1e3058f 100644 --- a/src/input/algfacob.input.pamphlet +++ b/src/input/algfacob.input.pamphlet @@ -28,7 +28,7 @@ --E 1 --S 2 of 37 -x := 2**8 * 78**7 * 111**3 * 74534 +x := 2^8 * 78^7 * 111^3 * 74534 --R --R --R 16 10 7 3 @@ -84,7 +84,7 @@ f := x/y --E 7 --S 8 of 37 -g := (x**9)/y +g := (x^9)/y --R --R --R 134 70 63 27 9 9 @@ -128,7 +128,7 @@ h := (f*g)/(g*nilFactor(2,200)) --E 11 --S 12 of 37 -u := factor (x**4 - y**4) +u := factor (x^4 - y^4) --R --R --R 2 2 @@ -137,7 +137,7 @@ u := factor (x**4 - y**4) --E 12 --S 13 of 37 -v := nilFactor(x-y,2) * nilFactor(x+y,2) * nilFactor(x**2 + y**2,1) +v := nilFactor(x-y,2) * nilFactor(x+y,2) * nilFactor(x^2 + y^2,1) --R --R --R 2 2 2 2 @@ -146,7 +146,7 @@ v := nilFactor(x-y,2) * nilFactor(x+y,2) * nilFactor(x**2 + y**2,1) --E 13 --S 14 of 37 -w := factor(x**2 + 2*x*y + 2*x + 2*y + y**2 + 1) * nilFactor(x-y,2) +w := factor(x^2 + 2*x*y + 2*x + 2*y + y^2 + 1) * nilFactor(x-y,2) --R --R --R 2 2 diff --git a/src/input/allfact.input.pamphlet b/src/input/allfact.input.pamphlet index 8b86206..2694060 100644 --- a/src/input/allfact.input.pamphlet +++ b/src/input/allfact.input.pamphlet @@ -56,7 +56,7 @@ factor m -- factorization of polynomials over finite fields --S 5 of 21 -u:UP(x,PF(19)) :=3*x**4+2*x**2+15*x+18 +u:UP(x,PF(19)) :=3*x^4+2*x^2+15*x+18 --R --R --R 4 2 @@ -75,7 +75,7 @@ factor u -- factorization of polynomials over the integers --S 7 of 21 -v:UP(x,INT):= (4*x**3+2*x**2+1)*(12*x**5-x**3+12) +v:UP(x,INT):= (4*x^3+2*x^2+1)*(12*x^5-x^3+12) --R --R --R 8 7 6 5 3 2 @@ -94,7 +94,7 @@ factor v -- factorization of multivariate polynomial over the integers --S 9 of 21 -w:MPOLY([x,y,z],INT) :=(x**2-y**2-z**2)*(x**2+y**2+z**2)*(z*y+3*z) +w:MPOLY([x,y,z],INT) :=(x^2-y^2-z^2)*(x^2+y^2+z^2)*(z*y+3*z) --R --R --R 4 5 4 3 3 3 2 5 5 @@ -113,7 +113,7 @@ factor w -- factorization of univariate and multivariate over the rational numbers --S 11 of 21 -f:MPOLY([x,y,z],FRAC INT) :=(4/9*x**2-1/16)*(x**3/27+125) +f:MPOLY([x,y,z],FRAC INT) :=(4/9*x^2-1/16)*(x^3/27+125) --R --R --R 4 5 1 3 500 2 125 @@ -134,7 +134,7 @@ factor f -- factorization over rational functions --S 13 of 21 -g:DMP([x,y],FRAC POLY INT):=a**2*x**2/b**2 -c**2*y**2/d**2 +g:DMP([x,y],FRAC POLY INT):=a^2*x^2/b^2 -c^2*y^2/d^2 --R --R --R 2 2 @@ -159,7 +159,7 @@ factor g -- decomposition of a rational function --S 15 of 21 -r:FRAC POLY INT:= (a**3/b**3-c**3/(b+1)**3)*(a*d+a/c) +r:FRAC POLY INT:= (a^3/b^3-c^3/(b+1)^3)*(a*d+a/c) --R --R --R (15) @@ -185,7 +185,7 @@ factorFraction r -- factorization over simple algebraic extensions --S 17 of 21 -aa|aa**2+aa+1 +aa|aa^2+aa+1 --R --R Your statement has resulted in the following assignments and --R declaration: @@ -198,7 +198,7 @@ aa|aa**2+aa+1 --E 17 --S 18 of 21 -p:UP(x,SAEaa) :=(x**3+aa**2*x+1)*(aa*x**2+aa*x+aa)**2 +p:UP(x,SAEaa) :=(x^3+aa^2*x+1)*(aa*x^2+aa*x+aa)^2 --R --R --R (18) @@ -221,7 +221,7 @@ factor(p)$SAEFACT(UP('aa,FRAC INT),SAEaa,UP(x,SAEaa)) -- factorization over algebraic numbers --S 20 of 21 -a:=rootOf(a**2+3)$AN +a:=rootOf(a^2+3)$AN --R --R --R (20) a @@ -229,7 +229,7 @@ a:=rootOf(a**2+3)$AN --E 20 --S 21 of 21 -factor(x**2+x+1,[a]) +factor(x^2+x+1,[a]) --R --R --R - a + 1 a + 1 diff --git a/src/input/arith.input.pamphlet b/src/input/arith.input.pamphlet index 72c1feb..f76fb4f 100644 --- a/src/input/arith.input.pamphlet +++ b/src/input/arith.input.pamphlet @@ -38,7 +38,7 @@ --E 2 --S 3 of 25 -234**108 +234^108 --R --R --R (3) @@ -69,7 +69,7 @@ z := 1/2 --E 5 --S 6 of 25 -v := (z + 1) ** 10 +v := (z + 1)^10 --R --R --R 59049 @@ -87,7 +87,7 @@ v := (z + 1) ** 10 --E 7 --S 8 of 25 -u := (x+1)**6 +u := (x+1)^6 --R --R --R 6 5 4 3 2 diff --git a/src/input/array1.input.pamphlet b/src/input/array1.input.pamphlet index b65d175..465adf0 100644 --- a/src/input/array1.input.pamphlet +++ b/src/input/array1.input.pamphlet @@ -22,7 +22,7 @@ )clear all --S 1 of 9 -oneDimensionalArray [i**2 for i in 1..10] +oneDimensionalArray [i^2 for i in 1..10] --R --R --R (1) [1,4,9,16,25,36,49,64,81,100] @@ -46,7 +46,7 @@ for i in 1..10 repeat a.i := i; a --E 3 --S 4 of 9 -map!(i +-> i ** 2,a); a +map!(i +-> i^2,a); a --R --R --R (4) [1,4,9,16,25,36,49,64,81,100] diff --git a/src/input/as-eg1.input.pamphlet b/src/input/as-eg1.input.pamphlet index 73b9f57..cefbc7a 100644 --- a/src/input/as-eg1.input.pamphlet +++ b/src/input/as-eg1.input.pamphlet @@ -22,9 +22,9 @@ a+a a*a gcd(a-1,a+1) x+a -%**3 +%^3 sin a -%**2+cos(a)**2 +%^2+cos(a)^2 simplify % matrix [[a,a+1],[a-1,a-2]] inverse % diff --git a/src/input/as-eg5.input.pamphlet b/src/input/as-eg5.input.pamphlet index cd59e49..d4ba8c0 100644 --- a/src/input/as-eg5.input.pamphlet +++ b/src/input/as-eg5.input.pamphlet @@ -18,8 +18,8 @@ \getchunk{license} )co pdecomp0.as (u,v):UP(x,FRAC INT) -u:=x**2+x+2 -v:=x**3+2*x**2+x+1 +u:=x^2+x+2 +v:=x^3+2*x^2+x+1 compose(u,v) decompose % diff --git a/src/input/bbtree.input.pamphlet b/src/input/bbtree.input.pamphlet index 1d20add..262f6bd 100644 --- a/src/input/bbtree.input.pamphlet +++ b/src/input/bbtree.input.pamphlet @@ -86,7 +86,7 @@ leaves % --E 8 --S 9 of 10 -squares := [x**2 rem m for x in % for m in lm] +squares := [x^2 rem m for x in % for m in lm] --R --R --R (9) [0,4,4,1] diff --git a/src/input/bern.input.pamphlet b/src/input/bern.input.pamphlet index 7863fdd..108045c 100644 --- a/src/input/bern.input.pamphlet +++ b/src/input/bern.input.pamphlet @@ -11,8 +11,8 @@ \tableofcontents \eject \begin{chunk}{*} -f(t)==cos(t)/(1+sin(t)**2) -g(t)==sin(t)*cos(t)/(1+sin(t)**2) +f(t)==cos(t)/(1+sin(t)^2) +g(t)==sin(t)*cos(t)/(1+sin(t)^2) c(t)==curve(f(t),g(t)) d:=draw(c(t)),t = -%pi..%pi, [title "Lemniscate of Bernoulli"]) close(d) diff --git a/src/input/bernpoly.input.pamphlet b/src/input/bernpoly.input.pamphlet index 2884d70..1e2c33f 100644 --- a/src/input/bernpoly.input.pamphlet +++ b/src/input/bernpoly.input.pamphlet @@ -20,15 +20,15 @@ -- by V. Krylov Macmillan 1962 p13) draw(1,x=0..1) draw(x-(1/2),x=0..1) -draw(x**2-x+(1/6),x=0..1) -draw(x**3-(3/2)*x**2+(1/2)*x,x=0..1) -draw(x**4-2*x**3+x**2-(1/30),x=0..1) -draw(x**5-(5/2)*x**4+(5/3)*x**3-(1/6)*x,x=0..1) -draw(x**6-3*x**5+(5/2)*x**4-(1/2)*x**2+(1/42),x=0..1) -draw(x**7-(7/2)*x**6+(7/2)*x**5-(7/6)*x**3+(1/6)*x,x=0..1) -draw(x**8-4*x**7+(14/3)*x**6-(7/3)*x**4+(2/3)*x**2-(1/30),x=0..1) -draw(x**9-(9/2)*x**8+6*x**7-(21/5)*x**5+2*x**3-(3/10)*x,x=0..1) -draw(x**10-5*x**9+(15/2)*x**8-7*x**6+5*x**4-(3/2)*x**2+(5/66),x=0..1) +draw(x^2-x+(1/6),x=0..1) +draw(x^3-(3/2)*x^2+(1/2)*x,x=0..1) +draw(x^4-2*x^3+x^2-(1/30),x=0..1) +draw(x^5-(5/2)*x^4+(5/3)*x^3-(1/6)*x,x=0..1) +draw(x^6-3*x^5+(5/2)*x^4-(1/2)*x^2+(1/42),x=0..1) +draw(x^7-(7/2)*x^6+(7/2)*x^5-(7/6)*x^3+(1/6)*x,x=0..1) +draw(x^8-4*x^7+(14/3)*x^6-(7/3)*x^4+(2/3)*x^2-(1/30),x=0..1) +draw(x^9-(9/2)*x^8+6*x^7-(21/5)*x^5+2*x^3-(3/10)*x,x=0..1) +draw(x^10-5*x^9+(15/2)*x^8-7*x^6+5*x^4-(3/2)*x^2+(5/66),x=0..1) \end{chunk} \eject \begin{thebibliography}{99} diff --git a/src/input/binary.input.pamphlet b/src/input/binary.input.pamphlet index 7ce04fd..a8d4ea9 100644 --- a/src/input/binary.input.pamphlet +++ b/src/input/binary.input.pamphlet @@ -70,7 +70,7 @@ binary(1/1007) --E 4 --S 5 of 7 -p := binary(1/4)*x**2 + binary(2/3)*x + binary(4/9) +p := binary(1/4)*x^2 + binary(2/3)*x + binary(4/9) --R --R --R 2 __ ______ diff --git a/src/input/bug10312.input.pamphlet b/src/input/bug10312.input.pamphlet index a0b642b..4ffdd0e 100644 --- a/src/input/bug10312.input.pamphlet +++ b/src/input/bug10312.input.pamphlet @@ -32,7 +32,7 @@ p:=(1/2+n)::UTS(FRAC INT, 'n, 0) --E 1 --S 2 of 2 -(p**(-1))$UTS(FRAC INT, 'n, 0) +(p^(-1))$UTS(FRAC INT, 'n, 0) --R --I Compiling function G1473 with type Integer -> Boolean --R diff --git a/src/input/bugs.input.pamphlet b/src/input/bugs.input.pamphlet index 68628be..4b72cab 100644 --- a/src/input/bugs.input.pamphlet +++ b/src/input/bugs.input.pamphlet @@ -29,7 +29,7 @@ )clear all --S 1 of 44 -eq1:= A*x**2 + B*x*y + C*y**2 +D*x + E*y + F +eq1:= A*x^2 + B*x*y + C*y^2 +D*x + E*y + F --R --R --R 2 2 @@ -295,7 +295,7 @@ u f )clear all --S 24 of 44 -groebner [x**2 - y, y**3+1] +groebner [x^2 - y, y^3+1] --R --R --R 2 6 @@ -363,7 +363,7 @@ p(n,x) == if n=0 then 1 else (x+n-1)*p(n-1,x) --E 29 --S 30 of 44 -pp(n,x) == if n=0 then 1 else if n<0 then (-1)**n/p(-n,1-x) else p(n,x) +pp(n,x) == if n=0 then 1 else if n<0 then (-1)^n/p(-n,1-x) else p(n,x) --R --R Type: Void --E 30 @@ -464,7 +464,7 @@ f 3 -- Bombs --S 36 of 44 mp(x,l) == l is [a,:b] => - a*x**(#b)+ mp(x,b) + a*x^(#b)+ mp(x,b) 0 --R --R Type: Void diff --git a/src/input/c05nbf.input.pamphlet b/src/input/c05nbf.input.pamphlet index 2da8d57..d14f542 100644 --- a/src/input/c05nbf.input.pamphlet +++ b/src/input/c05nbf.input.pamphlet @@ -24,15 +24,15 @@ n:=9 lwa:=n*(3*n+13)/2 xtol:SF:=1.0e-9 fi:ASP6(FCN):=retract vector[_ - 3*X[1] - 2*X[1]**2 - 2*X[2] + 1,_ - -X[1] + 3*X[2] - 2*X[2]**2 - 2*X[3] + 1,_ - -X[2] + 3*X[3] - 2*X[3]**2 - 2*X[4] + 1,_ - -X[3] + 3*X[4] - 2*X[4]**2 - 2*X[5] + 1,_ - -X[4] + 3*X[5] - 2*X[5]**2 - 2*X[6] + 1,_ - -X[5] + 3*X[6] - 2*X[6]**2 - 2*X[7] + 1,_ - -X[6] + 3*X[7] - 2*X[7]**2 - 2*X[8] + 1,_ - -X[7] + 3*X[8] - 2*X[8]**2 - 2*X[9] + 1,_ - -X[8] + 3*X[9] - 2*X[9]**2 + 1] + 3*X[1] - 2*X[1]^2 - 2*X[2] + 1,_ + -X[1] + 3*X[2] - 2*X[2]^2 - 2*X[3] + 1,_ + -X[2] + 3*X[3] - 2*X[3]^2 - 2*X[4] + 1,_ + -X[3] + 3*X[4] - 2*X[4]^2 - 2*X[5] + 1,_ + -X[4] + 3*X[5] - 2*X[5]^2 - 2*X[6] + 1,_ + -X[5] + 3*X[6] - 2*X[6]^2 - 2*X[7] + 1,_ + -X[6] + 3*X[7] - 2*X[7]^2 - 2*X[8] + 1,_ + -X[7] + 3*X[8] - 2*X[8]^2 - 2*X[9] + 1,_ + -X[8] + 3*X[9] - 2*X[9]^2 + 1] x:Matrix SF:= [[-1.0 ,-1.0 ,-1.0 ,-1.0 ,-1.0 ,-1.0 ,-1.0 ,-1.0 ,-1.0 ]] result:=c05nbf(n,lwa,x,xtol,-1,fi) diff --git a/src/input/c05pbf.input.pamphlet b/src/input/c05pbf.input.pamphlet index 9562c3e..13f9a62 100644 --- a/src/input/c05pbf.input.pamphlet +++ b/src/input/c05pbf.input.pamphlet @@ -27,15 +27,15 @@ xtol:SF:=1.0e-9 x:Matrix SF:= [[-1.0 ,-1.0 ,-1.0 ,-1.0 ,-1.0 ,-1.0 ,-1.0 ,-1.0 ,-1.0 ]] fcn:ASP35(FCN):=retract vector[_ -3*X[1] - 2*X[1]**2 - 2*X[2] + 1,_ --X[1] + 3*X[2] - 2*X[2]**2 - 2*X[3] + 1,_ --X[2] + 3*X[3] - 2*X[3]**2 - 2*X[4] + 1,_ --X[3] + 3*X[4] - 2*X[4]**2 - 2*X[5] + 1,_ --X[4] + 3*X[5] - 2*X[5]**2 - 2*X[6] + 1,_ --X[5] + 3*X[6] - 2*X[6]**2 - 2*X[7] + 1,_ --X[6] + 3*X[7] - 2*X[7]**2 - 2*X[8] + 1,_ --X[7] + 3*X[8] - 2*X[8]**2 - 2*X[9] + 1,_ --X[8] + 3*X[9] - 2*X[9]**2 + 1] +3*X[1] - 2*X[1]^2 - 2*X[2] + 1,_ +-X[1] + 3*X[2] - 2*X[2]^2 - 2*X[3] + 1,_ +-X[2] + 3*X[3] - 2*X[3]^2 - 2*X[4] + 1,_ +-X[3] + 3*X[4] - 2*X[4]^2 - 2*X[5] + 1,_ +-X[4] + 3*X[5] - 2*X[5]^2 - 2*X[6] + 1,_ +-X[5] + 3*X[6] - 2*X[6]^2 - 2*X[7] + 1,_ +-X[6] + 3*X[7] - 2*X[7]^2 - 2*X[8] + 1,_ +-X[7] + 3*X[8] - 2*X[8]^2 - 2*X[9] + 1,_ +-X[8] + 3*X[9] - 2*X[9]^2 + 1] result:=c05pbf(n,ldfjac,lwa,x,xtol,-1,fcn) \end{chunk} \eject diff --git a/src/input/calculus.input.pamphlet b/src/input/calculus.input.pamphlet index 13cf593..e9deffc 100644 --- a/src/input/calculus.input.pamphlet +++ b/src/input/calculus.input.pamphlet @@ -56,7 +56,7 @@ y := operator y --E 4 --S 5 of 24 -a := f(x z, y z, z**2) + x y(z+1) +a := f(x z, y z, z^2) + x y(z+1) --R --R --R 2 @@ -163,7 +163,7 @@ laplace(2/t * (1 - cos(a*t)), t, s) --E 13 --S 14 of 24 -laplace(exp(-a*t) * sin(b*t) / b**2, t, s) +laplace(exp(-a*t) * sin(b*t) / b^2, t, s) --R --R --R 1 @@ -211,7 +211,7 @@ laplace(a*Ci(b*t) + c*Si(d*t), t, s) --E 17 --S 18 of 24 -laplace(sin(a*t) - a*t*cos(a*t) + exp(t**2), t, s) +laplace(sin(a*t) - a*t*cos(a*t) + exp(t^2), t, s) --R --R --R 2 @@ -257,7 +257,7 @@ differentiate(f, x, 4) --E 21 --S 22 of 24 -g := sin(x**2 + y) +g := sin(x^2 + y) --R --R --R 2 diff --git a/src/input/calculus2.input.pamphlet b/src/input/calculus2.input.pamphlet index bc5d87d..dd8023b 100644 --- a/src/input/calculus2.input.pamphlet +++ b/src/input/calculus2.input.pamphlet @@ -56,7 +56,7 @@ y := operator y --E 4 --S 5 of 112 -a := f(x z, y z, z**2) + x y(z+1) +a := f(x z, y z, z^2) + x y(z+1) --R --R --R 2 @@ -181,7 +181,7 @@ expon := x * base --E 15 --S 16 of 112 -base ** expon +base ^ expon --R --R --R (7) @@ -283,7 +283,7 @@ series(sqrt(tan(a*x)),x = 0) --E 23 --S 24 of 112 -series(sec(x) ** 2,x = %pi/2) +series(sec(x) ^ 2,x = %pi/2) --R --R --R (8) @@ -398,7 +398,7 @@ x := operator 'x --E 30 --S 31 of 112 -eq1 := differentiate(x(t), t) = 1 + x(t)**2 +eq1 := differentiate(x(t), t) = 1 + x(t)^2 --R --R --R , 2 @@ -474,7 +474,7 @@ laplace(2/t * (1 - cos(a*t)), t, s) --E 37 --S 38 of 112 -laplace(exp(-a*t) * sin(b*t) / b**2, t, s) +laplace(exp(-a*t) * sin(b*t) / b^2, t, s) --R --R --R 1 @@ -520,7 +520,7 @@ laplace(a*Ci(b*t) + c*Si(d*t), t, s) --E 41 --S 42 of 112 -laplace(sin(a*t) - a*t*cos(a*t) + exp(t**2), t, s) +laplace(sin(a*t) - a*t*cos(a*t) + exp(t^2), t, s) --R --R --R 2 @@ -592,7 +592,7 @@ y )clear all --S 48 of 112 -f := (x**2+2*x+1) / (x**6+6*x**5+15*x**4+20*x**3+15*x**2+6*x+2) +f := (x^2+2*x+1) / (x^6+6*x^5+15*x^4+20*x^3+15*x^2+6*x+2) --R --R --R 2 @@ -637,7 +637,7 @@ integrate(g, x) --E 51 --S 52 of 112 -integrate(1/(x**2 - 2),x) +integrate(1/(x^2 - 2),x) --R --R --R 2 +-+ @@ -652,7 +652,7 @@ integrate(1/(x**2 - 2),x) --E 52 --S 53 of 112 -integrate(1/(x**2 + 2),x) +integrate(1/(x^2 + 2),x) --R --R --R +-+ @@ -666,7 +666,7 @@ integrate(1/(x**2 + 2),x) --E 53 --S 54 of 112 -h := x**2 / (x**4 - a**2) +h := x^2 / (x^4 - a^2) --R --R --R 2 @@ -818,7 +818,7 @@ differentiate(f, x, 4) --E 62 --S 63 of 112 -g := sin(x**2 + y) +g := sin(x^2 + y) --R --R --R 2 @@ -858,7 +858,7 @@ taylor(n +-> 1/factorial(n),x = 0) --E 66 --S 67 of 112 -taylor(n +-> (-1)**(n-1)/n,x = 1,1..) +taylor(n +-> (-1)^(n-1)/n,x = 1,1..) --R --R --R (2) @@ -873,7 +873,7 @@ taylor(n +-> (-1)**(n-1)/n,x = 1,1..) --E 67 --S 68 of 112 -taylor(n +-> (-1)**(n-1)/n,x = 1,1..7) +taylor(n +-> (-1)^(n-1)/n,x = 1,1..7) --R --R --R (3) @@ -888,7 +888,7 @@ taylor(n +-> (-1)**(n-1)/n,x = 1,1..7) --E 68 --S 69 of 112 -laurent(n +-> (-1)**(n-1)/(n + 2),x = 1,-1..) +laurent(n +-> (-1)^(n-1)/(n + 2),x = 1,-1..) --R --R --R (4) @@ -903,7 +903,7 @@ laurent(n +-> (-1)**(n-1)/(n + 2),x = 1,-1..) --E 69 --S 70 of 112 -puiseux(i +-> (-1)**((i-1)/2)/factorial(i),x = 0,1..,2) +puiseux(i +-> (-1)^((i-1)/2)/factorial(i),x = 0,1..,2) --R --R --R 1 3 1 5 1 7 9 @@ -913,7 +913,7 @@ puiseux(i +-> (-1)**((i-1)/2)/factorial(i),x = 0,1..,2) --E 70 --S 71 of 112 -puiseux(j +-> j**2,x = 8,-4/3..,1/2) +puiseux(j +-> j^2,x = 8,-4/3..,1/2) --R --R --R 4 5 1 @@ -935,7 +935,7 @@ series(n +-> 1/factorial(n),x = 0) --E 72 --S 73 of 112 -series(n +-> (-1)**(n - 1)/(n + 2),x = 1,-1..) +series(n +-> (-1)^(n - 1)/(n + 2),x = 1,-1..) --R --R --R (8) @@ -950,7 +950,7 @@ series(n +-> (-1)**(n - 1)/(n + 2),x = 1,-1..) --E 73 --S 74 of 112 -series(i +-> (-1)**((i - 1)/2)/factorial(i),x = 0,1..,2) +series(i +-> (-1)^((i - 1)/2)/factorial(i),x = 0,1..,2) --R --R --R 1 3 1 5 1 7 9 @@ -971,7 +971,7 @@ x := series x --E 75 --S 76 of 112 -1/(1 - x - x**2) +1/(1 - x - x^2) --R --R --R 2 3 4 5 6 7 8 @@ -1068,7 +1068,7 @@ x := series x --E 83 --S 84 of 112 -rat := x**2 / (1 - 6*x + x**2) +rat := x^2 / (1 - 6*x + x^2) --R --R --R (2) @@ -1107,7 +1107,7 @@ exp(y) --E 87 --S 88 of 112 -tan(y**2) +tan(y^2) --R --R --R 2 1 6 8 @@ -1117,7 +1117,7 @@ tan(y**2) --E 88 --S 89 of 112 -cos(y + y**5) +cos(y + y^5) --R --R --R 1 2 1 4 721 6 8 @@ -1226,7 +1226,7 @@ limit(g,x=0) --E 98 --S 99 of 112 -h := (1 + k/x)**x +h := (1 + k/x)^x --R --R --R x + k x @@ -1248,7 +1248,7 @@ limit(h,x=%plusInfinity) )clear all --S 101 of 112 -reduce(+,[m**4 for m in 1..10]) +reduce(+,[m^4 for m in 1..10]) --R --R --R (1) 25333 @@ -1256,7 +1256,7 @@ reduce(+,[m**4 for m in 1..10]) --E 101 --S 102 of 112 -sum4 := sum(m**4, m = 1..k) +sum4 := sum(m^4, m = 1..k) --R --R --R 5 4 3 diff --git a/src/input/card.input.pamphlet b/src/input/card.input.pamphlet index 3818678..31518f3 100644 --- a/src/input/card.input.pamphlet +++ b/src/input/card.input.pamphlet @@ -126,7 +126,7 @@ countable? A1 --E 13 --S 14 of 20 -[c2**c0, c2**c1, c2**c2, A1**c0, A1**c1, A1**c2] +[c2^c0, c2^c1, c2^c2, A1^c0, A1^c1, A1^c2] --R --R --R (14) [1,2,4,1,Aleph(1),Aleph(1)] @@ -150,7 +150,7 @@ generalizedContinuumHypothesisAssumed true --E 16 --S 17 of 20 -[c0**A0, c1**A0, c2**A0, A0**A0, A0**A1, A1**A0, A1**A1] +[c0^A0, c1^A0, c2^A0, A0^A0, A0^A1, A1^A0, A1^A1] --R --R --R (17) [0,1,Aleph(1),Aleph(1),Aleph(2),Aleph(1),Aleph(2)] @@ -166,7 +166,7 @@ a := Aleph 0 --E 18 --S 19 of 20 -c := 2**a +c := 2^a --R --R --R (19) Aleph(1) @@ -174,7 +174,7 @@ c := 2**a --E 19 --S 20 of 20 -f := 2**c +f := 2^c --R --R --R (20) Aleph(2) diff --git a/src/input/cardinal.input.pamphlet b/src/input/cardinal.input.pamphlet index 011e6e4..3e11611 100644 --- a/src/input/cardinal.input.pamphlet +++ b/src/input/cardinal.input.pamphlet @@ -124,7 +124,7 @@ A1 := Aleph 1 --E 13 --S 14 of 16 -[c2**c0, c2**c1, c2**c2, A1**c0, A1**c1, A1**c2] +[c2^c0, c2^c1, c2^c2, A1^c0, A1^c1, A1^c2] --R --R --R (14) [1,2,4,1,Aleph(1),Aleph(1)] @@ -140,7 +140,7 @@ generalizedContinuumHypothesisAssumed true --E 15 --S 16 of 16 -[c0**A0, c1**A0, c2**A0, A0**A0, A0**A1, A1**A0, A1**A1] +[c0^A0, c1^A0, c2^A0, A0^A0, A0^A1, A1^A0, A1^A1] --R --R --R (16) [0,1,Aleph(1),Aleph(1),Aleph(2),Aleph(1),Aleph(2)] diff --git a/src/input/classtalk.input.pamphlet b/src/input/classtalk.input.pamphlet index 788c9e8..7ddd3fb 100644 --- a/src/input/classtalk.input.pamphlet +++ b/src/input/classtalk.input.pamphlet @@ -144,7 +144,7 @@ b:=[log a, exp a, asin a, acos a, atan a, acot a, sinh a] --E 16 --S 17 of 72 -simplify(sin(x)**2+cos(x)**2) +simplify(sin(x)^2+cos(x)^2) --R --R (17) 1 --R Type: Expression(Integer) diff --git a/src/input/clifford.input.pamphlet b/src/input/clifford.input.pamphlet index c749cc8..f3f2e52 100644 --- a/src/input/clifford.input.pamphlet +++ b/src/input/clifford.input.pamphlet @@ -11,10 +11,10 @@ \tableofcontents \eject \section{Overview} -CliffordAlgebra(n, K, Q) defines a vector space of dimension 2**n -over K, given a quadratic form Q on K**n. +CliffordAlgebra(n, K, Q) defines a vector space of dimension 2^n +over K, given a quadratic form Q on K^n. \begin{verbatim} - If e[i] 1<=i<=n is a basis for K**n then + If e[i] 1<=i<=n is a basis for K^n then 1, e[i] 1<=i<=n, e[i1]*e[i2] 1<=i12 then sp := -sp point [cosTheta*cp, sinTheta*cp, -sp + 1] diff --git a/src/input/constant.input.pamphlet b/src/input/constant.input.pamphlet index 4411da5..d64265e 100644 --- a/src/input/constant.input.pamphlet +++ b/src/input/constant.input.pamphlet @@ -69,7 +69,7 @@ numeric(sqrt(10)) --E 6 --S 7 of 37 -numeric(2**(1/3)) +numeric(2^(1/3)) --R --R --R (7) 1.25992 10498 94873 16476 72106 07278 22835 05702 5 @@ -77,7 +77,7 @@ numeric(2**(1/3)) --E 7 --S 8 of 37 -numeric(3**(1/3)) +numeric(3^(1/3)) --R --R --R (8) 1.44224 95703 07408 38232 16383 10780 10958 83918 7 @@ -85,7 +85,7 @@ numeric(3**(1/3)) --E 8 --S 9 of 37 -numeric(2**(1/4)) +numeric(2^(1/4)) --R --R --R (9) 1.18920 71150 02721 06671 74999 70560 47591 52929 7 @@ -157,7 +157,7 @@ numeric(1/%pi) --E 17 --S 18 of 37 -numeric(%pi**2) +numeric(%pi^2) --R --R --R (18) 9.86960 44010 89358 61883 44909 99876 15113 53136 9 @@ -213,7 +213,7 @@ numeric(1/%e) --E 24 --S 25 of 37 -numeric(%e**2) +numeric(%e^2) --R --R --R (25) 7.38905 60989 30650 22723 04274 60575 00781 31803 1 @@ -277,7 +277,7 @@ gamma:=0.5772156649015328606065120900824024310422 --E 30 --S 31 of 37 -numeric(%e**gamma) +numeric(%e^gamma) --R --R --R (31) 1.78107 24179 90197 98523 65041 03107 17954 91697 2 @@ -285,7 +285,7 @@ numeric(%e**gamma) --E 31 --S 32 of 37 -numeric(%e**(%pi/4)) +numeric(%e^(%pi/4)) --R --R --R (32) 2.19328 00507 38015 45655 97696 59278 73822 34616 4 diff --git a/src/input/contfrac.input.pamphlet b/src/input/contfrac.input.pamphlet index 134effe..2d02025 100644 --- a/src/input/contfrac.input.pamphlet +++ b/src/input/contfrac.input.pamphlet @@ -321,7 +321,7 @@ q : Fraction UnivariatePolynomial('x, Fraction Integer) --E 28 --S 29 of 40 -q := (2*x**2 - x + 1) / (3*x**3 - x + 8) +q := (2*x^2 - x + 1) / (3*x^3 - x + 8) --R --R --R 2 2 1 1 diff --git a/src/input/contfrc.input.pamphlet b/src/input/contfrc.input.pamphlet index 2901711..9bf4fec 100644 --- a/src/input/contfrc.input.pamphlet +++ b/src/input/contfrc.input.pamphlet @@ -159,7 +159,7 @@ exp 1.0 --E 13 --S 14 of 22 -cf := continuedFraction(1,[(2*i+1)**2 for i in 0..],repeating [2]) +cf := continuedFraction(1,[(2*i+1)^2 for i in 0..],repeating [2]) --R --R --R (14) diff --git a/src/input/coordsys.input.pamphlet b/src/input/coordsys.input.pamphlet index ff0c2c5..e53a63f 100644 --- a/src/input/coordsys.input.pamphlet +++ b/src/input/coordsys.input.pamphlet @@ -26,12 +26,12 @@ draw(surface(u*cos(v),u*sin(v),u),u=1..4,v=1..2*%pi,coordinates == _ --conical(a,b) maps a 3D point (lambda,mu,nu) to the rectangular coordinates: --x = lambda*mu*nu/(a*b) ---y = lambda/a*sqrt((mu**2-a**2)*(nu**2-a**2)/(a**2-b**2)) ---z = lambda/b*sqrt((mu**2-b**2)*(nu**2-b**2)/(b**2-a**2)) ---NOTE: There will be a division by zero error if a*b = 0, or a**2-b**2 = 0, --- or if b**2-a**2 = 0. Also, the following relations must be true: --- (mu**2-a**2)*(nu**2-a**2)/(a**2-b**2) > 0 and --- (mu**2-b**2)*(nu**2-b**2)/(b**2-a**2) > 0. +--y = lambda/a*sqrt((mu^2-a^2)*(nu^2-a^2)/(a^2-b^2)) +--z = lambda/b*sqrt((mu^2-b^2)*(nu^2-b^2)/(b^2-a^2)) +--NOTE: There will be a division by zero error if a*b = 0, or a^2-b^2 = 0, +-- or if b^2-a^2 = 0. Also, the following relations must be true: +-- (mu^2-a^2)*(nu^2-a^2)/(a^2-b^2) > 0 and +-- (mu^2-b^2)*(nu^2-b^2)/(b^2-a^2) > 0. j1(t:DFLOAT):DFLOAT == 4 j2(t:DFLOAT):DFLOAT == t diff --git a/src/input/cycles.input.pamphlet b/src/input/cycles.input.pamphlet index 33603f2..1f95ae6 100644 --- a/src/input/cycles.input.pamphlet +++ b/src/input/cycles.input.pamphlet @@ -199,7 +199,7 @@ We can for example represent {\tt complete 2 * complete 2} as the set of objects {\tt a a b b} and {\tt complete 2 * complete 1 * complete 1} as {\tt c c d e}. -The integer {\tt cap(complete 2**2,complete 2*complete 1**2)} +The integer {\tt cap(complete 2^2,complete 2*complete 1^2)} is the number of different sets of four pairs. \begin{verbatim} a a b b a a b b a a b b a a b b @@ -207,7 +207,7 @@ is the number of different sets of four pairs. \end{verbatim} \begin{chunk}{*} --S 10 of 46 -cap(complete 2**2,complete 2*complete 1**2) +cap(complete 2^2,complete 2*complete 1^2) --R --R --R (10) 4 @@ -215,7 +215,7 @@ cap(complete 2**2,complete 2*complete 1**2) --E 10 \end{chunk} -The integer {\tt cap(elementary 2**2,complete 2*complete 1**2)} +The integer {\tt cap(elementary 2^2,complete 2*complete 1^2)} is the number of different sets of four pairs no two pairs being equal. \begin{verbatim} a a b b a a b b @@ -223,7 +223,7 @@ is the number of different sets of four pairs no two pairs being equal. \end{verbatim} \begin{chunk}{*} --S 11 of 46 -cap(elementary 2**2,complete 2*complete 1**2) +cap(elementary 2^2,complete 2*complete 1^2) --R --R --R (11) 2 @@ -237,7 +237,7 @@ actually constructing them. Similarly the number of 6-pairs, first from {\tt a a a b b c}, second from {\tt d d e e f g}. \begin{chunk}{*} --S 12 of 46 -cap(complete 3*complete 2*complete 1,complete 2**2*complete 1**2) +cap(complete 3*complete 2*complete 1,complete 2^2*complete 1^2) --R --R --R (12) 24 @@ -248,7 +248,7 @@ cap(complete 3*complete 2*complete 1,complete 2**2*complete 1**2) Same again, but with no equal pairs \begin{chunk}{*} --S 13 of 46 -cap(elementary 3*elementary 2*elementary 1,complete 2**2*complete 1**2) +cap(elementary 3*elementary 2*elementary 1,complete 2^2*complete 1^2) --R --R --R (13) 8 @@ -256,7 +256,7 @@ cap(elementary 3*elementary 2*elementary 1,complete 2**2*complete 1**2) --E 13 --S 14 of 46 -cap(complete 3*complete 2*complete 1,elementary 2**2*elementary 1**2) +cap(complete 3*complete 2*complete 1,elementary 2^2*elementary 1^2) --R --R --R (14) 8 @@ -269,7 +269,7 @@ The number of 6-triples, first from {\tt a a a b b c}, second from \begin{chunk}{*} --S 15 of 46 eval(cup(complete 3*complete 2*complete 1, _ - cup(complete 2**2*complete 1**2,complete 2**3))) + cup(complete 2^2*complete 1^2,complete 2^3))) --R --R --R (15) 1500 @@ -293,7 +293,7 @@ square:=dihedral 4 The number of different squares with 2 red vertices and 2 blue vertices \begin{chunk}{*} --S 17 of 46 -cap(complete 2**2,square) +cap(complete 2^2,square) --R --R --R (17) 2 @@ -304,7 +304,7 @@ cap(complete 2**2,square) The number of necklaces with 3 red beads,2 blue beads and 2 green beads \begin{chunk}{*} --S 18 of 46 -cap(complete 3*complete 2**2,dihedral 7) +cap(complete 3*complete 2^2,dihedral 7) --R --R --R (18) 18 @@ -332,7 +332,7 @@ macro s == powerSum --E 20 --S 21 of 46 -cube:=(1/24)*(s 1**8+9*s 2**4 + 8*s 3**2*s 1**2+6*s 4**2) +cube:=(1/24)*(s 1^8+9*s 2^4 + 8*s 3^2*s 1^2+6*s 4^2) --R --R --R 1 2 1 2 2 3 4 1 8 @@ -345,7 +345,7 @@ cube:=(1/24)*(s 1**8+9*s 2**4 + 8*s 3**2*s 1**2+6*s 4**2) The number of cubes with 4 red vertices and 4 blue vertices \begin{chunk}{*} --S 22 of 46 -cap(complete 4**2,cube) +cap(complete 4^2,cube) --R --R --R (22) 7 @@ -357,7 +357,7 @@ The number of labeled graphs with degree sequence 2 2 2 1 1 with no loops or multiple edges \begin{chunk}{*} --S 23 of 46 -cap(complete 2**3*complete 1**2,wreath(elementary 4,elementary 2)) +cap(complete 2^3*complete 1^2,wreath(elementary 4,elementary 2)) --R --R --R (23) 7 @@ -368,7 +368,7 @@ cap(complete 2**3*complete 1**2,wreath(elementary 4,elementary 2)) with loops allowed but not multiple edges \begin{chunk}{*} --S 24 of 46 -cap(complete 2**3*complete 1**2,wreath(elementary 4,complete 2)) +cap(complete 2^3*complete 1^2,wreath(elementary 4,complete 2)) --R --R --R (24) 17 @@ -379,7 +379,7 @@ cap(complete 2**3*complete 1**2,wreath(elementary 4,complete 2)) with multiple edges allowed, but not loops \begin{chunk}{*} --S 25 of 46 -cap(complete 2**3*complete 1**2,wreath(complete 4,elementary 2)) +cap(complete 2^3*complete 1^2,wreath(complete 4,elementary 2)) --R --R --R (25) 10 @@ -390,7 +390,7 @@ cap(complete 2**3*complete 1**2,wreath(complete 4,elementary 2)) with both multiple edges and loops allowed \begin{chunk}{*} --S 26 of 46 -cap(complete 2**3*complete 1**2,wreath(complete 4,complete 2)) +cap(complete 2^3*complete 1^2,wreath(complete 4,complete 2)) --R --R --R (26) 23 @@ -428,7 +428,7 @@ Integers:INT->ULS(FRAC INT,'x,0) For the integers 0 1 , or two colors \begin{chunk}{*} --S 30 of 46 -ZeroOrOne n == 1+x**n +ZeroOrOne n == 1+x^n --R --R Type: Void --E @@ -448,7 +448,7 @@ ZeroOrOne 5 For the integers 0,1,2,... \begin{chunk}{*} --S 32 of 46 -Integers n == 1/(1-x**n) +Integers n == 1/(1-x^n) --R --R Type: Void --E 32 @@ -630,11 +630,11 @@ It counts the number of different tableaux of shape 3,2,2,1 filled with objects with an ascending order in the columns and a non-descending order in the rows. -{\tt cap(sf3221,complete 4**2)} is the number filled +{\tt cap(sf3221,complete 4^2)} is the number filled with {\tt a a b b c c d d.} \begin{chunk}{*} --S 44 of 46 -cap(sf3221,complete 2**4) +cap(sf3221,complete 2^4) --R --R --R (44) 3 @@ -649,10 +649,10 @@ The configurations enumerated are c d c d c c d d d \end{verbatim} -{\tt cap(sf3221,powerSum 1**8)} is the number of tableaux filled with 1..8. +{\tt cap(sf3221,powerSum 1^8)} is the number of tableaux filled with 1..8. \begin{chunk}{*} --S 45 of 46 -cap(sf3221,powerSum 1**8) +cap(sf3221,powerSum 1^8) --R --R --R (45) 70 diff --git a/src/input/cycles1.input.pamphlet b/src/input/cycles1.input.pamphlet index 9cac561..293231e 100644 --- a/src/input/cycles1.input.pamphlet +++ b/src/input/cycles1.input.pamphlet @@ -138,7 +138,7 @@ graphs 5 --E 9 --S 10 of 46 -cap(complete 2**2, complete 2*complete 1**2) +cap(complete 2^2, complete 2*complete 1^2) --R --R --R (10) 4 @@ -146,7 +146,7 @@ cap(complete 2**2, complete 2*complete 1**2) --E 10 --S 11 of 46 -cap(elementary 2**2, complete 2*complete 1**2) +cap(elementary 2^2, complete 2*complete 1^2) --R --R --R (11) 2 @@ -154,7 +154,7 @@ cap(elementary 2**2, complete 2*complete 1**2) --E 11 --S 12 of 46 -cap(complete 3*complete 2*complete 1,complete 2**2*complete 1**2) +cap(complete 3*complete 2*complete 1,complete 2^2*complete 1^2) --R --R --R (12) 24 @@ -162,7 +162,7 @@ cap(complete 3*complete 2*complete 1,complete 2**2*complete 1**2) --E 12 --S 13 of 46 -cap(elementary 3*elementary 2*elementary 1,complete 2**2*complete 1**2) +cap(elementary 3*elementary 2*elementary 1,complete 2^2*complete 1^2) --R --R --R (13) 8 @@ -170,7 +170,7 @@ cap(elementary 3*elementary 2*elementary 1,complete 2**2*complete 1**2) --E 13 --S 14 of 46 -cap(complete 3*complete 2*complete 1,elementary 2**2*elementary 1**2) +cap(complete 3*complete 2*complete 1,elementary 2^2*elementary 1^2) --R --R --R (14) 8 @@ -179,7 +179,7 @@ cap(complete 3*complete 2*complete 1,elementary 2**2*elementary 1**2) --S 15 of 46 eval(cup(complete 3*complete 2*complete 1, _ - cup(complete 2**2*complete 1**2,complete 2**3))) + cup(complete 2^2*complete 1^2,complete 2^3))) --R --R --R (15) 1500 @@ -197,7 +197,7 @@ square:=dihedral 4 --E 16 --S 17 of 46 -cap(complete 2**2,square) +cap(complete 2^2,square) --R --R --R (17) 2 @@ -205,7 +205,7 @@ cap(complete 2**2,square) --E 17 --S 18 of 46 -cap(complete 3*complete 2**2,dihedral 7) +cap(complete 3*complete 2^2,dihedral 7) --R --R --R (18) 18 @@ -227,7 +227,7 @@ s(x) == powerSum(x) --E 20 --S 21 of 46 -cube:=(1/24)*(s 1**8+9*s 2**4 + 8*s 3**2*s 1**2+6*s 4**2) +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 -> --R SymmetricPolynomial(Fraction(Integer)) @@ -239,7 +239,7 @@ cube:=(1/24)*(s 1**8+9*s 2**4 + 8*s 3**2*s 1**2+6*s 4**2) --E 21 --S 22 of 46 -cap(complete 4**2,cube) +cap(complete 4^2,cube) --R --R --R (22) 7 @@ -247,7 +247,7 @@ cap(complete 4**2,cube) --E 22 --S 23 of 46 -cap(complete 2**3*complete 1**2,wreath(elementary 4,elementary 2)) +cap(complete 2^3*complete 1^2,wreath(elementary 4,elementary 2)) --R --R --R (23) 7 @@ -255,7 +255,7 @@ cap(complete 2**3*complete 1**2,wreath(elementary 4,elementary 2)) --E 23 --S 24 of 46 -cap(complete 2**3*complete 1**2,wreath(elementary 4,complete 2)) +cap(complete 2^3*complete 1^2,wreath(elementary 4,complete 2)) --R --R --R (24) 17 @@ -263,7 +263,7 @@ cap(complete 2**3*complete 1**2,wreath(elementary 4,complete 2)) --E 24 --S 25 of 46 -cap(complete 2**3*complete 1**2,wreath(complete 4,elementary 2)) +cap(complete 2^3*complete 1^2,wreath(complete 4,elementary 2)) --R --R --R (25) 10 @@ -271,7 +271,7 @@ cap(complete 2**3*complete 1**2,wreath(complete 4,elementary 2)) --E 25 --S 26 of 46 -cap(complete 2**3*complete 1**2,wreath(complete 4,complete 2)) +cap(complete 2^3*complete 1^2,wreath(complete 4,complete 2)) --R --R --R (26) 23 @@ -299,7 +299,7 @@ Integers: INT -> ULS(FRAC INT, 'x, 0) --E 29 --S 30 of 46 -ZeroOrOne n == 1+x**n +ZeroOrOne n == 1+x^n --R --R Type: Void --E 30 @@ -316,7 +316,7 @@ ZeroOrOne 5 --E 31 --S 32 of 46 -Integers n == 1/(1-x**n) +Integers n == 1/(1-x^n) --R --R Type: Void --E 32 @@ -449,7 +449,7 @@ sf3221:= SFunction [3,2,2,1] --E 43 --S 44 of 46 -cap(sf3221,complete 2**4) +cap(sf3221,complete 2^4) --R --R --R (44) 3 @@ -457,7 +457,7 @@ cap(sf3221,complete 2**4) --E 44 --S 45 of 46 -cap(sf3221, powerSum 1**8) +cap(sf3221, powerSum 1^8) --R --R --R (45) 70 diff --git a/src/input/cyfactor.input.pamphlet b/src/input/cyfactor.input.pamphlet index 392ff8b..6690155 100644 --- a/src/input/cyfactor.input.pamphlet +++ b/src/input/cyfactor.input.pamphlet @@ -26,7 +26,7 @@ Special case tests of factoring code for cyclotomic polynomials $\pm x^n-1 (n even)$ \begin{chunk}{*} --S 1 of 10 -factor(x**84 - 1) +factor(x^84 - 1) --R --R --R (1) @@ -51,7 +51,7 @@ factor(x**84 - 1) --E 1 --S 2 of 10 -factor(-(x**68 -1)) +factor(-(x^68 -1)) --R --R --R (2) @@ -83,7 +83,7 @@ factor(-(x**68 -1)) $\pm x^n + 1$ (n odd) \begin{chunk}{*} --S 3 of 10 -factor(x**99 + 1) +factor(x^99 + 1) --R --R --R (3) @@ -107,7 +107,7 @@ factor(x**99 + 1) --E 3 --S 4 of 10 -factor(-(x**77 +1)) +factor(-(x^77 +1)) --R --R --R (4) @@ -133,7 +133,7 @@ factor(-(x**77 +1)) $\pm x^(2^k) + 1$ \begin{chunk}{*} --S 5 of 10 -ind := 2**6 +ind := 2^6 --R --R --R (5) 64 @@ -141,7 +141,7 @@ ind := 2**6 --E 5 --S 6 of 10 -factor(x**ind + 1) +factor(x^ind + 1) --R --R --R 64 @@ -150,7 +150,7 @@ factor(x**ind + 1) --E 6 --S 7 of 10 -ind := 2**7 +ind := 2^7 --R --R --R (7) 128 @@ -158,7 +158,7 @@ ind := 2**7 --E 7 --S 8 of 10 -factor(-(x**ind + 1)) +factor(-(x^ind + 1)) --R --R --R 128 @@ -171,7 +171,7 @@ This takes a lot longer than it should. It will improve when the cyclotomic code improves. \begin{chunk}{*} --S 9 of 10 -factor(x**84 + 1) +factor(x^84 + 1) --R --R --R (9) diff --git a/src/input/d01ajf.input.pamphlet b/src/input/d01ajf.input.pamphlet index 5d56281..e2befb7 100644 --- a/src/input/d01ajf.input.pamphlet +++ b/src/input/d01ajf.input.pamphlet @@ -20,7 +20,7 @@ showArrayValues true showScalarValues true -e:EXPR FLOAT:=(X*sin(30*X)/(sqrt(1-(X/(2*%pi))**2))) +e:EXPR FLOAT:=(X*sin(30*X)/(sqrt(1-(X/(2*%pi))^2))) f:ASP1(F):=retract e a:SF:=0.0 b:SF:=%pi*2 diff --git a/src/input/d01aqf.input.pamphlet b/src/input/d01aqf.input.pamphlet index cb6406e..637b6da 100644 --- a/src/input/d01aqf.input.pamphlet +++ b/src/input/d01aqf.input.pamphlet @@ -20,7 +20,7 @@ showArrayValues true showScalarValues true -e:Expression Float:=(X**2+0.01**2)**-1 +e:Expression Float:=(X^2+0.01^2)^-1 f:ASP1(G):=retract e a:SF:=-1.0 b:SF:=1.0 diff --git a/src/input/d01fcf.input.pamphlet b/src/input/d01fcf.input.pamphlet index 0512eef..97d1e2e 100644 --- a/src/input/d01fcf.input.pamphlet +++ b/src/input/d01fcf.input.pamphlet @@ -20,7 +20,7 @@ showArrayValues true showScalarValues true -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 +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 f:ASP4(FUNCTN):=retract e ndim:=4 a:Matrix SF:=[[0.0,0.0,0.0,0.0]] diff --git a/src/input/d01gbf.input.pamphlet b/src/input/d01gbf.input.pamphlet index 986c6f7..79a94ee 100644 --- a/src/input/d01gbf.input.pamphlet +++ b/src/input/d01gbf.input.pamphlet @@ -21,7 +21,7 @@ showArrayValues true showScalarValues true ndim:=4 -e:=(4.0*X[1]*X[3]*X[3]*exp(2.0*X[1]*X[3])/((1.0+X[2]+X[4])**2)) +e:=(4.0*X[1]*X[3]*X[3]*exp(2.0*X[1]*X[3])/((1.0+X[2]+X[4])^2)) f:ASP4(FUNCTN):=retract e a:Matrix SF:=[[0.0,0.0,0.0,0.0]] b:Matrix SF:=[[1.0,1.0,1.0,1.0]] diff --git a/src/input/d02bbf.input.pamphlet b/src/input/d02bbf.input.pamphlet index 472f9b4..446a63d 100644 --- a/src/input/d02bbf.input.pamphlet +++ b/src/input/d02bbf.input.pamphlet @@ -28,7 +28,7 @@ y:Matrix SF:= [[0.0 ,0.5 ,%pi*0.2 ]] tol:SF:=0.0001 vef:Vector Expression Float:= - [tan(Y[3]) ,-0.032*tan(Y[3])/Y[2] -0.02*Y[2]/cos(Y[3]) ,-0.032/(Y[2]**2) ] + [tan(Y[3]) ,-0.032*tan(Y[3])/Y[2] -0.02*Y[2]/cos(Y[3]) ,-0.032/(Y[2]^2) ] fcn:Asp7(FCN):= retract vef vm:Vector MachineFloat:= [1,2,3,4,5,6,7,8] diff --git a/src/input/d02bhf.input.pamphlet b/src/input/d02bhf.input.pamphlet index 707f811..d340503 100644 --- a/src/input/d02bhf.input.pamphlet +++ b/src/input/d02bhf.input.pamphlet @@ -31,7 +31,7 @@ tol:SF:=0.0001 ef:Expression Float:=1.0*Y[1]::EXPR FLOAT g:Asp9(G):=retract ef vef:Vector Expression Float:= - [tan(Y[3]) ,-0.032*tan(Y[3])/Y[2] -0.02*Y[2]/cos(Y[3]) ,-0.032/(Y[2]**2) ] + [tan(Y[3]) ,-0.032*tan(Y[3])/Y[2] -0.02*Y[2]/cos(Y[3]) ,-0.032/(Y[2]^2) ] fcn:Asp7(FCN):= retract vef result:=d02bhf(xend,n,irelab,hmax,x,y,tol,-1,g,fcn) \end{chunk} diff --git a/src/input/d02cjf.input.pamphlet b/src/input/d02cjf.input.pamphlet index b423d25..e6fce70 100644 --- a/src/input/d02cjf.input.pamphlet +++ b/src/input/d02cjf.input.pamphlet @@ -29,7 +29,7 @@ y:Matrix SF:=[[0.5 ,0.5 ,%pi*0.2 ]] ef:Expression Float:=Y[1]:: EXPR FLOAT g:Asp9(G):=retract ef vef:Vector Expression Float:= - [tan(Y[3]) ,-0.032*tan(Y[3])/Y[2] -0.02*Y[2]/cos(Y[3]) ,-0.032/(Y[2]**2) ] + [tan(Y[3]) ,-0.032*tan(Y[3])/Y[2] -0.02*Y[2]/cos(Y[3]) ,-0.032/(Y[2]^2) ] fcn:Asp7(FCN):= retract vef vm:Vector MachineFloat:= [2,4,6,8] diff --git a/src/input/d02kef.input.pamphlet b/src/input/d02kef.input.pamphlet index 5edb339..e847c7f 100644 --- a/src/input/d02kef.input.pamphlet +++ b/src/input/d02kef.input.pamphlet @@ -21,7 +21,7 @@ showArrayValues true showScalarValues true xpoint:Matrix SF:= - [[0.0 ,0.1 ,4**(1/3) ,30.0 ,30.0 ]] + [[0.0 ,0.1 ,4^(1/3) ,30.0 ,30.0 ]] m:=5 k:=11 tol:SF:=0.0001 diff --git a/src/input/d03faf.input.pamphlet b/src/input/d03faf.input.pamphlet index 094335c..c79c902 100644 --- a/src/input/d03faf.input.pamphlet +++ b/src/input/d03faf.input.pamphlet @@ -61,14 +61,14 @@ foo()== setelt!(f,1,j,k,sin(y(1,j))*cos(z(1,k))) for j in 1..m+1 repeat for i in 1..l+1 repeat - setelt!(f,i,j,1,x(1,i)**4*sin(y(1,j))) + setelt!(f,i,j,1,x(1,i)^4*sin(y(1,j))) for k in 2..n+1 repeat for j in 1..m+1 repeat for i in 2..l repeat - setelt!(f,i,j,k,4*x(1,i)**2*(3-x(1,i)**2)*sin(y(1,j))*cos(z(1,k))) + setelt!(f,i,j,k,4*x(1,i)^2*(3-x(1,i)^2)*sin(y(1,j))*cos(z(1,k))) for j in 1..m+1 repeat for i in 1..l+1 repeat - bdzf(i,j):=-x(1,i)**4*sin(y(1,j)) + bdzf(i,j):=-x(1,i)^4*sin(y(1,j)) foo() result:=d03faf(xs,xf,l,lbdcnd,bdxs,bdxf,ys,yf,m,mbdcnd,bdys,bdyf,_ zs,zf,n,nbdcnd,bdzs,bdzf,lambda,ldimf,mdimf,lwrk,f,ifail) diff --git a/src/input/damped.input.pamphlet b/src/input/damped.input.pamphlet index af65feb..fbf4430 100644 --- a/src/input/damped.input.pamphlet +++ b/src/input/damped.input.pamphlet @@ -20,9 +20,9 @@ -- with driving force A*cos(wt). -- The equation is solved at y(0)=y'(0)=0 for --- (i) an overdamped, forced motion example c**2-4*k*m > 0 --- (ii) critically damped c**2-4*k*m = 0 --- (iii) underdamped c**2-4*k*m < 0 +-- (i) an overdamped, forced motion example c^2-4*k*m > 0 +-- (ii) critically damped c^2-4*k*m = 0 +-- (iii) underdamped c^2-4*k*m < 0 -- The resulting equations are then plotted. @@ -32,14 +32,14 @@ deq := m*D(y x, x, 2) + c*D(y x, x) + k*(y x) = A * cos (w * x) solve(deq, y, x=0, [0,0]) -- takes a few minutes ex:=% -eval(%, [c=6,k=5,m=1,A=6*sqrt(5),w=sqrt(5)]) -- c**2-4*k*m = 16 +eval(%, [c=6,k=5,m=1,A=6*sqrt(5),w=sqrt(5)]) -- c^2-4*k*m = 16 draw(%,x=0..15,title=="Overdamping") -eval(ex, [k=5,m=1,A=6*sqrt(5),w=sqrt(5)]) -- c**2-4*k*m = 0 +eval(ex, [k=5,m=1,A=6*sqrt(5),w=sqrt(5)]) -- c^2-4*k*m = 0 limit(%,c=sqrt(20),"right") -- otherwise division by zero draw(%,x=0..15,title=="Critically Damped") -eval(ex, [c=2,k=5,m=1,A=6*sqrt(5),w=sqrt(5)]) -- c**2-4*k*m = -16 +eval(ex, [c=2,k=5,m=1,A=6*sqrt(5),w=sqrt(5)]) -- c^2-4*k*m = -16 trigs % rule1 := rule sin(-x) == - sin(x) rule2 := rule cos(-x) == cos(x) diff --git a/src/input/danzwill.input.pamphlet b/src/input/danzwill.input.pamphlet index 39bcc49..671e105 100644 --- a/src/input/danzwill.input.pamphlet +++ b/src/input/danzwill.input.pamphlet @@ -53,7 +53,7 @@ i1 := integrate( sin(x), x) --i2 := integrate( sqrt(tan(x)), x) --S 2 of 17 -i3 := integrate( x/(x**3-1),x) +i3 := integrate( x/(x^3-1),x) --R --R --R +-+ @@ -67,7 +67,7 @@ i3 := integrate( x/(x**3-1),x) --E 2 --S 3 of 17 -i4 := integrate( x/sin(x)**2, x) +i4 := integrate( x/sin(x)^2, x) --R --R --R sin(x) 2 @@ -88,7 +88,7 @@ i5 := integrate( log(x)/sqrt(x+1), x) --E 4 --S 5 of 17 -i6 := integrate( exp(-a*x**2), x) +i6 := integrate( exp(-a*x^2), x) --R --R --R x 2 @@ -99,7 +99,7 @@ i6 := integrate( exp(-a*x**2), x) --E 5 --S 6 of 17 -i7 := integrate( x/(log(x))**3, x) +i7 := integrate( x/(log(x))^3, x) --R --R --R 2 2 2 @@ -136,7 +136,7 @@ i9 := integrate( 1/(2+cos(x)),x) --E 8 --S 9 of 17 -i10:= integrate( sin(x)/x**2, x) +i10:= integrate( sin(x)/x^2, x) --R --R --R x @@ -170,7 +170,7 @@ d2:= integrate( sin(x)/x,x=%minusInfinity..%plusInfinity) )set mes test on --S 12 of 17 -d3:= integrate( x**2/(1+x**3),x=0..%plusInfinity) +d3:= integrate( x^2/(1+x^3),x=0..%plusInfinity) --R --R --R (11) + infinity @@ -188,7 +188,7 @@ d4:= integrate( exp(-x)/sqrt(x),x=0..%plusInfinity) --E 13 --S 14 of 17 -d5:= integrate( exp(-x**2)*log(x)**2,x=0..%plusInfinity) +d5:= integrate( exp(-x^2)*log(x)^2,x=0..%plusInfinity) --R --R --R _ 1 1 _ 1 1 2 @@ -200,7 +200,7 @@ d5:= integrate( exp(-x**2)*log(x)**2,x=0..%plusInfinity) --E 14 --S 15 of 17 -d6:= integrate( exp(-x)*log(x)**2*x**3,x=1..%plusInfinity) +d6:= integrate( exp(-x)*log(x)^2*x^3,x=1..%plusInfinity) --R --R --R (14) potentialPole @@ -208,7 +208,7 @@ d6:= integrate( exp(-x)*log(x)**2*x**3,x=1..%plusInfinity) --E 15 --S 16 of 17 -d7:= integrate( exp(-x)*x**(1/3),x=1..%plusInfinity) +d7:= integrate( exp(-x)*x^(1/3),x=1..%plusInfinity) --R --R --R (15) potentialPole @@ -216,7 +216,7 @@ d7:= integrate( exp(-x)*x**(1/3),x=1..%plusInfinity) --E 16 --S 17 of 17 -d8:= integrate( exp(-x)*x**2/(1-exp(-2*x)),x=0..%plusInfinity) +d8:= integrate( exp(-x)*x^2/(1-exp(-2*x)),x=0..%plusInfinity) --R --R --R (16) potentialPole diff --git a/src/input/davenport.input.pamphlet b/src/input/davenport.input.pamphlet index 4fa3849..e5e2360 100644 --- a/src/input/davenport.input.pamphlet +++ b/src/input/davenport.input.pamphlet @@ -72,7 +72,7 @@ quotient(1,1+x,8) --E 3 --S 4 of 12 -quotient(x**2-x+1,x**3-x-6/7,8) +quotient(x^2-x+1,x^3-x-6/7,8) --R --R --R (4) @@ -87,7 +87,7 @@ quotient(x**2-x+1,x**3-x-6/7,8) --E 4 --S 5 of 12 -ext1:=SAE(FRAC INT,UP(a,FRAC INT),a**2+a+1) +ext1:=SAE(FRAC INT,UP(a,FRAC INT),a^2+a+1) --R --R --R (5) @@ -97,7 +97,7 @@ ext1:=SAE(FRAC INT,UP(a,FRAC INT),a**2+a+1) --E 5 --S 6 of 12 -e:ext1:=convert(((3/4)*a**2-a+(7/4))::UP(a,FRAC INT)) +e:ext1:=convert(((3/4)*a^2-a+(7/4))::UP(a,FRAC INT)) --R --R --R 7 @@ -117,7 +117,7 @@ recip(e) --E 7 --S 8 of 12 -e**2 +e^2 --R --R --R 105 33 @@ -127,7 +127,7 @@ e**2 --E 8 --S 9 of 12 -e:=convert((a**2-1)::UP(a,FRAC INT)) +e:=convert((a^2-1)::UP(a,FRAC INT)) --R --R --R (9) - a - 2 @@ -135,7 +135,7 @@ e:=convert((a**2-1)::UP(a,FRAC INT)) --E 9 --S 10 of 12 -p1:UP(x,ext1):=x**4+3*x**3+(2*a+1)*x**2+(3*a+3)*x-1 +p1:UP(x,ext1):=x^4+3*x^3+(2*a+1)*x^2+(3*a+3)*x-1 --R --R --R 4 3 2 @@ -144,7 +144,7 @@ p1:UP(x,ext1):=x**4+3*x**3+(2*a+1)*x**2+(3*a+3)*x-1 --E 10 --S 11 of 12 -p2:UP(x,ext1):=x**2+a+1 +p2:UP(x,ext1):=x^2+a+1 --R --R --R 2 diff --git a/src/input/dbtest.input.pamphlet b/src/input/dbtest.input.pamphlet new file mode 100644 index 0000000..90e29d7 --- /dev/null +++ b/src/input/dbtest.input.pamphlet @@ -0,0 +1,1149 @@ +\documentclass{article} +\setlength{\textwidth}{400pt} +\usepackage{axiom} +\begin{document} +\title{\$SPAD/src/input dbtest.input} +\author{Timothy Daly} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{verbatim} +Building A Query Facility + +We now turn to an entirely different kind of application, +building a query language for a database. + +Here is the practical problem to solve. The hyperdoc facility of +Axiom has a database for all operations and constructors which is +stored on disk and accessed by Hyperdoc. For our purposes here, we +regard each line of this file as having eight fields: +\begin{itemize} +\item class +\item name +\item type +\item nargs +\item exposed +\item kind +\item origin +\item condition +\end{itemize} +Here is an example entry: + +begin{verbatim} + o`determinant`$->R`1`x`d`Matrix(R)`has(R,commutative("*")) +end{verbatim} + +In English, the entry means that the operation +begin{verbatim} + determinant: $ -> R +end{verbatim} +with it 1 argument, is exposed and is exported by the domain +Matrix(R) if R has commutative("*"). + +Our task is to create a little query language that allows us +to get useful information from this database. + +First we design a simple language for accessing information from the +database. We have the following simple model in mind for its design. +Think of the database as a box of index cards. There is only one +search operation---it takes the name of a field and a predicate (a +boolean-valued function) defined on the fields of the index cards. +When applied, the search operation goes through the entire box +selecting only those index cards for which the predicate is true. The +result of a search is a new box of index cards. This process can be +repeated again and again. + +The predicates all have a particularly simple form: +begin{verbatim} + symbol = pattern +end{verbatim} +where symbol designates one of the fields, and pattern is a +``search string''---a string that may contain a ``*'' as a +wildcard. Wildcards match any substring, including the empty string. +Thus the pattern ``*ma*t'' matches ``mat'', ``doormat'' and ``smart''. + +To illustrate how queries are given, we give you a sneak preview +of the facility we are about to create. + +Extract the database of all Axiom operations. +begin{verbatim} + ops := getDatabase("o") +end{verbatim} + +How many exposed three-argument ``map'' operations involving streams? +begin{verbatim} + ops.(name="map").(nargs="3").(type="*Stream*") +end{verbatim} + +As usual, the arguments of elt associate to the left. +The first elt produces the set of all operations with +name {\tt map}. +The second elt produces the set of all map operations +with three arguments. +The third elt produces the set of all three-argument map +operations having a type mentioning Stream. + +Another thing we'd like to do is to extract one field from each of +the index cards in the box and look at the result. +Here is an example of that kind of request. + +What constructors explicitly export a determinant operation? + +elt(elt(elt(elt(ops,name="determinant"),origin),sort),unique) + + +The first elt produces the set of all index cards with +name {\tt determinant}. +The second elt extracts the {\tt origin} component from +each index card. Each origin component +is the name of a constructor which directly +exports the operation represented by the index card. +Extracting a component from each index card produces what we call +a {\it datalist}. +The third elt, {\tt sort}, causes the datalist of +origins to be sorted in alphabetic +order. +The fourth, {\tt unique}, causes duplicates to be removed. + +Before giving you a more extensive demo of this facility, +we now build the necessary domains and packages to implement it. +%We will introduce a few of our minor conveniences. + +\endscroll +\autobuttons +\end{page} + +\begin{patch}{ugDomainsQueryLanguagePagePatch1} +\begin{paste}{ugDomainsQueryLanguagePageFull1} +{ugDomainsQueryLanguagePageEmpty1} +\pastebutton{ugDomainsQueryLanguagePageFull1}{\hidepaste} +\tab{5}\spadcommand{ops := getDatabase("o")\bound{o1 }} +\indentrel{3}begin{verbatim} + (1) 6315 + Type: Database IndexCard +end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugDomainsQueryLanguagePageEmpty1} +\begin{paste}{ugDomainsQueryLanguagePageEmpty1} +{ugDomainsQueryLanguagePagePatch1} +\pastebutton{ugDomainsQueryLanguagePageEmpty1}{\showpaste} +\tab{5}\spadcommand{ops := getDatabase("o")\bound{o1 }} +\end{paste}\end{patch} + +\begin{patch}{ugDomainsQueryLanguagePagePatch2} +\begin{paste}{ugDomainsQueryLanguagePageFull2} +{ugDomainsQueryLanguagePageEmpty2} +\pastebutton{ugDomainsQueryLanguagePageFull2}{\hidepaste} +\tab{5} +\spadcommand{ops.(name="map").(nargs="3").(type="*Stream*") +\bound{o2 }\free{o1 }} +\indentrel{3}begin{verbatim} + (2) 3 + Type: Database IndexCard +end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugDomainsQueryLanguagePageEmpty2} +\begin{paste}{ugDomainsQueryLanguagePageEmpty2} +{ugDomainsQueryLanguagePagePatch2} +\pastebutton{ugDomainsQueryLanguagePageEmpty2}{\showpaste} +\tab{5} +\spadcommand{ops.(name="map").(nargs="3").(type="*Stream*") +\bound{o2 }\free{o1 }} +\end{paste}\end{patch} + +\begin{patch}{ugDomainsQueryLanguagePagePatch3} +\begin{paste}{ugDomainsQueryLanguagePageFull3} +{ugDomainsQueryLanguagePageEmpty3} +\pastebutton{ugDomainsQueryLanguagePageFull3}{\hidepaste} +\tab{5} +\spadcommand{elt(elt(elt(elt(ops,name="determinant"),origin),sort),unique) +\free{o1 }} +\indentrel{3}begin{verbatim} + (3) + ["InnerMatrixLinearAlgebraFunctions", + "MatrixCategory", "MatrixLinearAlgebraFunctions", + "SquareMatrixCategory"] + Type: DataList String +end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugDomainsQueryLanguagePageEmpty3} +\begin{paste}{ugDomainsQueryLanguagePageEmpty3} +{ugDomainsQueryLanguagePagePatch3} +\pastebutton{ugDomainsQueryLanguagePageEmpty3}{\showpaste} +\tab{5} +\spadcommand{elt(elt(elt(elt(ops,name="determinant"),origin),sort),unique) +\free{o1 }} +\end{paste}\end{patch} + +@ +\pagehead{ugDomainsDatabaseConstructorPage}{ug13.ht} +{The Database Constructor} +<>= +\begin{page}{ugDomainsDatabaseConstructorPage} +{13.13.2. The Database Constructor} +\beginscroll + +We work from the top down. First, we define a database, +our box of index cards, as an abstract datatype. +For sake of illustration and generality, +we assume that an index card is some type S, and +that a database is a box of objects of type S. +Here is the Axiom program defining the \pspadtype{Database} +domain. + +\beginImportant + +\noindent +{\tt 1.\ \ \ PI\ ==>\ PositiveInteger}\newline +{\tt 2.\ \ \ Database(S):\ Exports\ ==\ Implementation\ where}\newline +{\tt 3.\ \ \ \ \ S:\ Object\ with\ }\newline +{\tt 4.\ \ \ \ \ \ \ elt:\ (\$,\ Symbol)\ ->\ String}\newline +{\tt 5.\ \ \ \ \ \ \ display:\ \$\ ->\ Void}\newline +{\tt 6.\ \ \ \ \ \ \ fullDisplay:\ \$\ ->\ Void}\newline +{\tt 7.\ \ \ }\newline +{\tt 8.\ \ \ \ \ Exports\ ==\ with}\newline +{\tt 9.\ \ \ \ \ \ \ elt:\ (\$,QueryEquation)\ ->\ \$}\newline +{\tt 10.\ \ \ \ \ \ elt:\ (\$,\ Symbol)\ ->\ DataList\ String}\newline +{\tt 11.\ \ \ \ \ \ "+":\ (\$,\$)\ ->\ \$}\newline +{\tt 12.\ \ \ \ \ \ "-":\ (\$,\$)\ ->\ \$}\newline +{\tt 13.\ \ \ \ \ \ display:\ \$\ ->\ Void}\newline +{\tt 14.\ \ \ \ \ \ fullDisplay:\ \$\ ->\ Void}\newline +{\tt 15.\ \ \ \ \ \ fullDisplay:\ (\$,PI,PI)\ ->\ Void}\newline +{\tt 16.\ \ \ \ \ \ coerce:\ \$\ ->\ OutputForm}\newline +{\tt 17.\ \ \ \ Implementation\ ==\ add}\newline +{\tt 18.\ \ \ \ \ \ \ \ ...}\newline +\endImportant + +The domain constructor takes a parameter S, which +stands for the class of index cards. +We describe an index card later. +Here think of an index card as a string which has +the eight fields mentioned above. + +First, we tell Axiom what operations we are going to require +from index cards. +We need an elt to extract the contents of a field +(such as {\tt name} and {\tt type}) as a string. +For example, c.name returns a string that is the content of the +name field on the index card c. +We need to display an index card in two ways: +\pspadfun{display} shows only the name and type of an +operation; +\pspadfun{fullDisplay} displays all fields. +The display operations return no useful information and thus have +return type Void. + +Next, we tell Axiom what operations the user can apply +to the database. +This part defines our little query language. +The most important operation is +{\frenchspacing\tt db . field = pattern} which +returns a new database, consisting of all index +cards of {\tt db} such that the field part of the index +card is matched by the string pattern called pattern. +The expression {\tt field = pattern} is an object of type +QueryEquation (defined in the next section). + +Another elt is needed to produce a DataList object. +Operation + is to merge two databases together; +- is used to subtract away common entries in a second +database from an initial database. +There are three display functions. +The \pspadfun{fullDisplay} function has two versions: one +that prints all the records, the other that prints only a fixed +number of records. +A coerce to OutputForm creates a display object. + +The {\tt Implementation} part of Database is straightforward. +\beginImportant + +\noindent +{\tt 1.\ \ \ \ \ Implementation\ ==\ add}\newline +{\tt 2.\ \ \ \ \ \ \ s:\ Symbol}\newline +{\tt 3.\ \ \ \ \ \ \ Rep\ :=\ List\ S}\newline +{\tt 4.\ \ \ \ \ \ \ elt(db,equation)\ ==\ ...}\newline +{\tt 5.\ \ \ \ \ \ \ +elt(db,key)\ ==\ [x.key\ for\ x\ in\ db]::DataList(String)}\newline +{\tt 6.\ \ \ \ \ \ \ +display(db)\ ==\ \ for\ x\ in\ db\ repeat\ display\ x}\newline +{\tt 7.\ \ \ \ \ \ \ +fullDisplay(db)\ ==\ for\ x\ in\ db\ repeat\ fullDisplay\ x}\newline +{\tt 8.\ \ \ \ \ \ \ +fullDisplay(db,\ n,\ m)\ ==\ for\ x\ in\ db\ for\ i\ in\ 1..m}\newline +{\tt 9.\ \ \ \ \ \ \ \ \ repeat}\newline +{\tt 10.\ \ \ \ \ \ \ \ \ \ if\ i\ >=\ n\ then\ fullDisplay\ x}\newline +{\tt 11.\ \ \ \ \ \ x+y\ ==\ removeDuplicates!\ merge(x,y)}\newline +{\tt 12.\ \ \ \ \ \ x-y\ ==\ mergeDifference(copy(x::Rep),}\newline +{\tt 13.\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ +y::Rep)\$MergeThing(S)}\newline +{\tt 14.\ \ \ \ \ \ coerce(db):\ OutputForm\ ==\ (\#db)::\ OutputForm} +\newline +\endImportant + +The database is represented by a list of elements of S +(index cards). +We leave the definition of the first elt operation +(on line 4) until the next section. +The second elt collects all the strings with field name +{\it key} into a list. +The display function and first fullDisplay function +simply call the corresponding functions from S. +The second fullDisplay function provides an efficient way of +printing out a portion of a large list. +The + is defined by using the existing +\spadfunFrom{merge}{List} operation defined on lists, then +removing duplicates from the result. +The - operation requires writing a corresponding +subtraction operation. +A package MergeThing (not shown) provides this. + +The coerce function converts the database to an +OutputForm by computing the number of index cards. +This is a good example of the independence of +the representation of an Axiom object from how it presents +itself to the user. We usually do not want to look at a database---but +do care how many ``hits'' we get for a given query. +So we define the output representation of a database to be simply +the number of index cards our query finds. +\endscroll +\autobuttons +\end{page} + +@ +\pagehead{ugDomainsQueryEquationsPage}{ug13.ht}{Query Equations} +<>= +\begin{page}{ugDomainsQueryEquationsPage}{13.13.3. Query Equations} +\beginscroll + +The predicate for our search is given by an object of type +\pspadtype{QueryEquation}. +Axiom does not have such an object yet so we +have to invent it. + +\beginImportant + +\noindent +{\tt 1.\ \ \ QueryEquation():\ Exports\ ==\ Implementation\ where}\newline +{\tt 2.\ \ \ \ \ Exports\ ==\ with}\newline +{\tt 3.\ \ \ \ \ \ \ equation:\ (Symbol,\ String)\ ->\ \$}\newline +{\tt 4.\ \ \ \ \ \ \ variable:\ \$\ ->\ Symbol}\newline +{\tt 5.\ \ \ \ \ \ \ value:\\ \\ \\ \\ \$\ ->\ String}\newline +{\tt 6.\ \ \ }\newline +{\tt 7.\ \ \ \ \ Implementation\ ==\ add}\newline +{\tt 8.\ \ \ \ \ \ \ Rep\ :=\ Record(var:Symbol,\ val:String)}\newline +{\tt 9.\ \ \ \ \ \ \ equation(x,\ s)\ ==\ [x,\ s]}\newline +{\tt 10.\ \ \ \ \ \ variable\ q\ ==\ q.var}\newline +{\tt 11.\ \ \ \ \ \ value\\ \\ \\ \\ q\ ==\ q.val}\newline +\endImportant + +Axiom converts an input expression of the form +{\it a} = {\it b} to equation({\it a, b}}. +Our equations always have a symbol on the left and a string +on the right. +The {\tt Exports} part thus specifies an operation +equation to create a query equation, and +\pspadfun{variable} and \pspadfun{value} to select the left- and +right-hand sides. +The {\tt Implementation} part uses \pspadtype{Record} for a +space-efficient representation of an equation. + +Here is the missing definition for the elt function of +\pspadtype{Database} in the last section: + +\beginImportant + +\noindent +{\tt 1.\ \ \ \ \ \ \ elt(db,eq)\ ==}\newline +{\tt 2.\ \ \ \ \ \ \ \ \ field\\ \ :=\ variable\ eq}\newline +{\tt 3.\ \ \ \ \ \ \ \ \ value\ :=\ value\ eq}\newline +{\tt 4.\ \ \ \ \ \ \ \ \ +[x\ for\ x\ in\ db\ |\ matches?(value,x.field)]}\newline +\endImportant + +Recall that a database is represented by a list. +Line 4 simply runs over that list collecting all elements +such that the pattern (that is, value) +matches the selected field of the element. + +\endscroll +\autobuttons +\end{page} + +@ +\pagehead{ugDomainsDataListsPage}{ug13.ht}{DataLists} +<>= +\begin{page}{ugDomainsDataListsPage}{13.13.4. DataLists} +\beginscroll + +Type \pspadtype{DataList} is a new type invented to hold the result +of selecting one field from each of the index cards in the box. +It is useful to make datalists extensions of lists---lists that +have special elt operations defined on them for +sorting and removing duplicates. + +\beginImportant + +\noindent +{\tt 1.\ \ \ DataList(S:OrderedSet)\ :\ Exports\ ==\ +Implementation\ where}\newline +{\tt 2.\ \ \ \ \ Exports\ ==\ ListAggregate(S)\ with}\newline +{\tt 3.\ \ \ \ \ \ \ elt:\ (\$,"unique")\ ->\ \$}\newline +{\tt 4.\ \ \ \ \ \ \ elt:\ (\$,"sort")\ ->\ \$}\newline +{\tt 5.\ \ \ \ \ \ \ elt:\ (\$,"count")\ ->\ NonNegativeInteger}\newline +{\tt 6.\ \ \ \ \ \ \ coerce:\ List\ S\ ->\ \$}\newline +{\tt 7.\ \ \ }\newline +{\tt 8.\ \ \ \ \ Implementation\ ==\ \ List(S)\ add}\newline +{\tt 9.\ \ \ \ \ \ \ Rep\ :=\ List\ S}\newline +{\tt 10.\ \ \ \ \ \ elt(x,"unique")\ ==\ removeDuplicates(x)}\newline +{\tt 11.\ \ \ \ \ \ elt(x,"sort")\ ==\ sort(x)}\newline +{\tt 12.\ \ \ \ \ \ elt(x,"count")\ ==\ \#x}\newline +{\tt 13.\ \ \ \ \ \ coerce(x:List\ S)\ ==\ x\ ::\ \$}\newline +\endImportant + +The {\tt Exports} part asserts that datalists belong to the +category ListAggregate. +Therefore, you can use all the usual list operations on datalists, +such as \spadfunFrom{first}{List}, \spadfunFrom{rest}{List}, and +\spadfunFrom{concat}{List}. +In addition, datalists have four explicit operations. +Besides the three elt operations, there is a +coerce operation that creates datalists from lists. + +The {\tt Implementation} part needs only to define four functions. +All the rest are obtained from List(S). + +\endscroll +\autobuttons +\end{page} + +@ +\pagehead{ugDomainsDatabasePage}{ug13.ht}{Index Cards} +<>= +\begin{page}{ugDomainsDatabasePage}{13.13.5. Index Cards} +\beginscroll + +An index card comes from a file as one long string. We define +functions that extract substrings from the long string. Each field +has a name that is passed as a second argument to elt. + +\beginImportant + +\noindent +{\tt 1.\ \ \ IndexCard()\ ==\ Implementation\ where}\newline +{\tt 2.\ \ \ \ \ Exports\ ==\ with}\newline +{\tt 3.\ \ \ \ \ \ \ elt:\ (\$,\ Symbol)\ ->\ String}\newline +{\tt 4.\ \ \ \ \ \ \ display:\ \$\ ->\ Void}\newline +{\tt 5.\ \ \ \ \ \ \ fullDisplay:\ \$\ ->\ Void}\newline +{\tt 6.\ \ \ \ \ \ \ coerce:\ String\ ->\ \$}\newline +{\tt 7.\ \ \ \ \ Implementation\ ==\ String\ add\ ...}\newline +\endImportant + +We leave the {\tt Implementation} part to the reader. +All operations involve straightforward string manipulations. + +\endscroll +\autobuttons +\end{page} + +@ +\pagehead{ugDomainsCreatingPage}{ug13.ht}{Creating a Database} +<>= +\begin{page}{ugDomainsCreatingPage}{13.13.6. Creating a Database} +\beginscroll + +We must not forget one important operation: one that builds the +database in the first place! We'll name it \pspadfun{getDatabase} and +put it in a package. This function is implemented by calling the +\Lisp{} function getBrowseDatabase(s) to get appropriate +information from \Browse{}. This operation takes a string indicating +which lines you want from the database: "o" gives you all +operation lines, and "k", all constructor lines. Similarly, +"c", "d", and "p" give you all category, +domain and package lines respectively. + +\beginImportant + +\noindent +{\tt 1.\ \ \ OperationsQuery():\ Exports\ ==\ Implementation\ where} +\newline +{\tt 2.\ \ \ \ \ Exports\ ==\ with}\newline +{\tt 3.\ \ \ \ \ \ \ getDatabase:\ String\ ->\ Database(IndexCard)} +\newline +{\tt 4.\ \ \ }\newline +{\tt 5.\ \ \ \ \ Implementation\ ==\ add}\newline +{\tt 6.\ \ \ \ \ \ \ getDatabase(s)\ ==\ getBrowseDatabase(s)\$Lisp} +\newline +\endImportant + +We do not bother creating a special name for databases of index +cards. +\pspadtype{Database (IndexCard)} will do. +Notice that we used the package \pspadtype{OperationsQuery} to +create, in effect, +a new kind of domain: \pspadtype{Database(IndexCard)}. + +\endscroll +\autobuttons +\end{page} + +@ +\pagehead{ugDomainsPuttingPage}{ug13.ht}{Putting It All Together} +<>= +\begin{page}{ugDomainsPuttingPage}{13.13.7. Putting It All Together} +\beginscroll + +To create the database facility, you put all these constructors +into one file.\footnote{You could use separate files, but we +are putting them all together because, organizationally, that is +the logical thing to do.} +At the top of the file put \spadcmd{)abbrev} commands, giving the +constructor abbreviations you created. + +\beginImportant + +\noindent +{\tt 1.\ \ \ )abbrev\ domain\ \ ICARD\ \ \ IndexCard}\newline +{\tt 2.\ \ \ )abbrev\ domain\ \ QEQUAT\ \ QueryEquation}\newline +{\tt 3.\ \ \ )abbrev\ domain\ \ MTHING\ \ MergeThing}\newline +{\tt 4.\ \ \ )abbrev\ domain\ \ DLIST\ \ \ DataList}\newline +{\tt 5.\ \ \ )abbrev\ domain\ \ DBASE\ \ \ Database}\newline +{\tt 6.\ \ \ )abbrev\ package\ OPQUERY\ OperationsQuery}\newline +\endImportant + +With all this in {\bf alql.spad}, for example, compile it using +begin{verbatim} +)compile alql +end{verbatim} +and then load each of the constructors: +begin{verbatim} +)load ICARD QEQUAT MTHING DLIST DBASE OPQUERY +end{verbatim} +You are ready to try some sample queries. + +\endscroll +\autobuttons +\end{page} + +@ +\pagehead{ugDomainsExamplesPage}{ug13.ht}{Example Queries} +<>= +\begin{page}{ugDomainsExamplesPage}{13.13.8. Example Queries} +\beginscroll + +Our first set of queries give some statistics on constructors in +the current Axiom system. + +\xtc{ +How many constructors does Axiom have? +}{ +\spadpaste{ks := getDatabase "k"\bound{q1}} +} +\xtc{ +Break this down into the number of categories, domains, and packages. +}{ +\spadpaste{[ks.(kind=k) for k in ["c","d","p"]]\bound{q3}\free{q1}} +} +\xtc{ +What are all the domain constructors that take no parameters? +}{ +\spadpaste{elt(ks.(kind="d").(nargs="0"),name)\bound{q4}\free{q1}} +} +\xtc{ +How many constructors have ``Matrix'' in their name? +}{ +\spadpaste{mk := ks.(name="*Matrix*")\bound{q5}\free{q1}} +} +\xtc{ +What are the names of those that are domains? +}{ +\spadpaste{elt(mk.(kind="d"),name)\bound{q6}\free{q5}} +} +\xtc{ +How many operations are there in the library? +}{ +\spadpaste{o := getDatabase "o"\bound{o1}} +} +\xtc{ +Break this down into categories, domains, and packages. +}{ +\spadpaste{[o.(kind=k) for k in ["c","d","p"]]\free{o1}} +} + +The query language is helpful in getting information about a +particular operation you might like to apply. +While this information can be obtained with +\Browse{}, the use of the query database gives you data that you +can manipulate in the workspace. + +\xtc{ +How many operations have ``eigen'' in the name? +}{ +\spadpaste{eigens := o.(name="*eigen*")\bound{eigens}\free{o1}} +} +\xtc{ +What are their names? +}{ +\spadpaste{elt(eigens,name)\free{eigens}} +} +\xtc{ +Where do they come from? +}{ +\spadpaste{elt(elt(elt(eigens,origin),sort),unique) \free{eigens}} +} + +The operations + and - are useful for +constructing small databases and combining them. +However, remember that the only matching you can do is string +matching. +Thus a pattern such as {\tt "*Matrix*"} on the type field +matches +any type containing Matrix, MatrixCategory, SquareMatrix, and so on. + +\xtc{ +How many operations mention ``Matrix'' in their type? +}{ +\spadpaste{tm := o.(type="*Matrix*")\bound{x10}\free{o1}} +} +\xtc{ +How many operations come from constructors with ``Matrix'' in +their name? +}{ +\spadpaste{fm := o.(origin="*Matrix*")\bound{x11}\free{o1}} +} +\xtc{ +How many operations are in fm but not in tm? +}{ +\spadpaste{fm-tm \bound{x12}\free{x10 x11}} +} +\xtc{ +Display the operations that both mention ``Matrix'' in their type +and come from a constructor having ``Matrix'' in their name. +}{ +\spadpaste{fullDisplay(fm-\%) \bound{x13}\free{x12}} +} +\xtc{ +How many operations involve matrices? +}{ +\spadpaste{m := tm+fm \bound{x14}\free{x10 x11}} +} +\xtc{ +Display 4 of them. +}{ +\spadpaste{fullDisplay(m, 202, 205) \free{x14}} +} +\xtc{ +How many distinct names of operations involving matrices are there? +}{ +\spadpaste{elt(elt(elt(m,name),unique),count) \free{x14}} +} + +\endscroll +\autobuttons +\end{page} + +\begin{patch}{ugDomainsExamplesPagePatch1} +\begin{paste}{ugDomainsExamplesPageFull1}{ugDomainsExamplesPageEmpty1} +\pastebutton{ugDomainsExamplesPageFull1}{\hidepaste} +\tab{5}\spadcommand{ks := getDatabase "k"\bound{q1 }} +\indentrel{3}begin{verbatim} + (1) 1067 + Type: Database IndexCard +end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugDomainsExamplesPageEmpty1} +\begin{paste}{ugDomainsExamplesPageEmpty1}{ugDomainsExamplesPagePatch1} +\pastebutton{ugDomainsExamplesPageEmpty1}{\showpaste} +\tab{5}\spadcommand{ks := getDatabase "k"\bound{q1 }} +\end{paste}\end{patch} + +\begin{patch}{ugDomainsExamplesPagePatch2} +\begin{paste}{ugDomainsExamplesPageFull2}{ugDomainsExamplesPageEmpty2} +\pastebutton{ugDomainsExamplesPageFull2}{\hidepaste} +\tab{5}\spadcommand{[ks.(kind=k) for k in ["c","d","p"]]\bound{q3 }\free{q1 }} +\indentrel{3}begin{verbatim} + (2) [205,393,469] + Type: List Database IndexCard +end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugDomainsExamplesPageEmpty2} +\begin{paste}{ugDomainsExamplesPageEmpty2}{ugDomainsExamplesPagePatch2} +\pastebutton{ugDomainsExamplesPageEmpty2}{\showpaste} +\tab{5}\spadcommand{[ks.(kind=k) for k in ["c","d","p"]]\bound{q3 }\free{q1 }} +\end{paste}\end{patch} + +\begin{patch}{ugDomainsExamplesPagePatch3} +\begin{paste}{ugDomainsExamplesPageFull3}{ugDomainsExamplesPageEmpty3} +\pastebutton{ugDomainsExamplesPageFull3}{\hidepaste} +\tab{5}\spadcommand{elt(ks.(kind="d").(nargs="0"),name)\bound{q4 }\free{q1 }} +\indentrel{3}begin{verbatim} + (3) + ["AlgebraicNumber", "AnonymousFunction", "Any", + "AttributeButtons", "BasicFunctions", + "BasicOperator", "BinaryExpansion", "BinaryFile", + "Bits", "Boolean", "CardinalNumber", + "CharacterClass", "Character", "Color", "Commutator", + "DecimalExpansion", "DoubleFloat", "DrawOption", + "Exit", "ExtAlgBasis", "FileName", "Float", + "FortranCode", "FortranScalarType", + "FortranTemplate", "FortranType", "GraphImage", + "HexadecimalExpansion", "IVBaseColor", "IVBasicNode", + "IVCoordinate3", "IVCoordinate4", "IVFaceSet", + "IVField", "IVGroup", "IVIndexedLineSet", + "IVNodeConnection", "IVNodeObject", "IVPointSet", + "IVQuadMesh", "IVSeparator", "IVSimpleInnerNode", + "IVUtilities", "IVValue", "IndexCard", + "InnerAlgebraicNumber", "InputForm", "Integer", + "IntegrationFunctionsTable", "InventorDataSink", + "InventorRenderPackage", "InventorViewPort", + "Library", "MachineComplex", "MachineFloat", + "MachineInteger", + "NagDiscreteFourierTransformInterfacePackage", + "NagEigenInterfacePackage", + "NagOptimisationInterfacePackage", + "NagQuadratureInterfacePackage", "NagResultChecks", + "NagSpecialFunctionsInterfacePackage", + "NonNegativeInteger", "None", + "NumericalIntegrationProblem", "NumericalODEProblem", + "NumericalOptimizationProblem", + "NumericalPDEProblem", "ODEIntensityFunctionsTable", + "OrdSetInts", "OutputForm", "Palette", "Partition", + "Pi", "PlaneAlgebraicCurvePlot", "Plot3D", "Plot", + "PositiveInteger", "QueryEquation", "RenderTools", + "Result", "RomanNumeral", "RoutinesTable", + "SExpression", "ScriptFormulaFormat", + "SingleInteger", "SingletonAsOrderedSet", "String", + "SubSpaceComponentProperty", "Switch", "SymbolTable", + "Symbol", "TexFormat", "TextFile", "TheSymbolTable", + "ThreeDimensionalViewport", "Timer", + "TwoDimensionalViewport", "Void", + "d01TransformFunctionType", "d01ajfAnnaType", + "d01akfAnnaType", "d01alfAnnaType", "d01amfAnnaType", + "d01anfAnnaType", "d01apfAnnaType", "d01aqfAnnaType", + "d01asfAnnaType", "d01fcfAnnaType", "d01gbfAnnaType", + "d02bbfAnnaType", "d02bhfAnnaType", "d02cjfAnnaType", + "d02ejfAnnaType", "d03eefAnnaType", "d03fafAnnaType", + "e04dgfAnnaType", "e04fdfAnnaType", "e04gcfAnnaType", + "e04jafAnnaType", "e04mbfAnnaType", "e04nafAnnaType", + "e04ucfAnnaType"] + Type: DataList String +end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugDomainsExamplesPageEmpty3} +\begin{paste}{ugDomainsExamplesPageEmpty3}{ugDomainsExamplesPagePatch3} +\pastebutton{ugDomainsExamplesPageEmpty3}{\showpaste} +\tab{5}\spadcommand{elt(ks.(kind="d").(nargs="0"),name)\bound{q4 }\free{q1 }} +\end{paste}\end{patch} + +\begin{patch}{ugDomainsExamplesPagePatch4} +\begin{paste}{ugDomainsExamplesPageFull4}{ugDomainsExamplesPageEmpty4} +\pastebutton{ugDomainsExamplesPageFull4}{\hidepaste} +\tab{5}\spadcommand{mk := ks.(name="*Matrix*")\bound{q5 }\free{q1 }} +\indentrel{3}begin{verbatim} + (4) 26 + Type: Database IndexCard +end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugDomainsExamplesPageEmpty4} +\begin{paste}{ugDomainsExamplesPageEmpty4}{ugDomainsExamplesPagePatch4} +\pastebutton{ugDomainsExamplesPageEmpty4}{\showpaste} +\tab{5}\spadcommand{mk := ks.(name="*Matrix*")\bound{q5 }\free{q1 }} +\end{paste}\end{patch} + +\begin{patch}{ugDomainsExamplesPagePatch5} +\begin{paste}{ugDomainsExamplesPageFull5}{ugDomainsExamplesPageEmpty5} +\pastebutton{ugDomainsExamplesPageFull5}{\hidepaste} +\tab{5}\spadcommand{elt(mk.(kind="d"),name)\bound{q6 }\free{q5 }} +\indentrel{3}begin{verbatim} + (5) + ["DenavitHartenbergMatrix", + "DirectProductMatrixModule", "IndexedMatrix", + "LieSquareMatrix", "Matrix", "RectangularMatrix", + "SquareMatrix", "ThreeDimensionalMatrix"] + Type: DataList String +end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugDomainsExamplesPageEmpty5} +\begin{paste}{ugDomainsExamplesPageEmpty5}{ugDomainsExamplesPagePatch5} +\pastebutton{ugDomainsExamplesPageEmpty5}{\showpaste} +\tab{5}\spadcommand{elt(mk.(kind="d"),name)\bound{q6 }\free{q5 }} +\end{paste}\end{patch} + +\begin{patch}{ugDomainsExamplesPagePatch6} +\begin{paste}{ugDomainsExamplesPageFull6}{ugDomainsExamplesPageEmpty6} +\pastebutton{ugDomainsExamplesPageFull6}{\hidepaste} +\tab{5}\spadcommand{o := getDatabase "o"\bound{o1 }} +\indentrel{3}begin{verbatim} + (6) 6315 + Type: Database IndexCard +end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugDomainsExamplesPageEmpty6} +\begin{paste}{ugDomainsExamplesPageEmpty6}{ugDomainsExamplesPagePatch6} +\pastebutton{ugDomainsExamplesPageEmpty6}{\showpaste} +\tab{5}\spadcommand{o := getDatabase "o"\bound{o1 }} +\end{paste}\end{patch} + +\begin{patch}{ugDomainsExamplesPagePatch7} +\begin{paste}{ugDomainsExamplesPageFull7}{ugDomainsExamplesPageEmpty7} +\pastebutton{ugDomainsExamplesPageFull7}{\hidepaste} +\tab{5}\spadcommand{[o.(kind=k) for k in ["c","d","p"]]\free{o1 }} +\indentrel{3}begin{verbatim} + (7) [1646,2040,2629] + Type: List Database IndexCard +end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugDomainsExamplesPageEmpty7} +\begin{paste}{ugDomainsExamplesPageEmpty7}{ugDomainsExamplesPagePatch7} +\pastebutton{ugDomainsExamplesPageEmpty7}{\showpaste} +\tab{5}\spadcommand{[o.(kind=k) for k in ["c","d","p"]]\free{o1 }} +\end{paste}\end{patch} + +\begin{patch}{ugDomainsExamplesPagePatch8} +\begin{paste}{ugDomainsExamplesPageFull8}{ugDomainsExamplesPageEmpty8} +\pastebutton{ugDomainsExamplesPageFull8}{\hidepaste} +\tab{5}\spadcommand{eigens := o.(name="*eigen*")\bound{eigens }\free{o1 }} +\indentrel{3}begin{verbatim} + (8) 4 + Type: Database IndexCard +end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugDomainsExamplesPageEmpty8} +\begin{paste}{ugDomainsExamplesPageEmpty8}{ugDomainsExamplesPagePatch8} +\pastebutton{ugDomainsExamplesPageEmpty8}{\showpaste} +\tab{5}\spadcommand{eigens := o.(name="*eigen*")\bound{eigens }\free{o1 }} +\end{paste}\end{patch} + +\begin{patch}{ugDomainsExamplesPagePatch9} +\begin{paste}{ugDomainsExamplesPageFull9}{ugDomainsExamplesPageEmpty9} +\pastebutton{ugDomainsExamplesPageFull9}{\hidepaste} +\tab{5}\spadcommand{elt(eigens,name)\free{eigens }} +\indentrel{3}begin{verbatim} + (9) + ["eigenMatrix", "eigenvalues", "eigenvector", + "eigenvectors"] + Type: DataList String +end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugDomainsExamplesPageEmpty9} +\begin{paste}{ugDomainsExamplesPageEmpty9}{ugDomainsExamplesPagePatch9} +\pastebutton{ugDomainsExamplesPageEmpty9}{\showpaste} +\tab{5}\spadcommand{elt(eigens,name)\free{eigens }} +\end{paste}\end{patch} + +\begin{patch}{ugDomainsExamplesPagePatch10} +\begin{paste}{ugDomainsExamplesPageFull10}{ugDomainsExamplesPageEmpty10} +\pastebutton{ugDomainsExamplesPageFull10}{\hidepaste} +\tab{5}\spadcommand{elt(elt(elt(eigens,origin),sort),unique)\free{eigens }} +\indentrel{3}begin{verbatim} + (10) ["EigenPackage","RadicalEigenPackage"] + Type: DataList String +end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugDomainsExamplesPageEmpty10} +\begin{paste}{ugDomainsExamplesPageEmpty10}{ugDomainsExamplesPagePatch10} +\pastebutton{ugDomainsExamplesPageEmpty10}{\showpaste} +\tab{5}\spadcommand{elt(elt(elt(eigens,origin),sort),unique)\free{eigens }} +\end{paste}\end{patch} + +\begin{patch}{ugDomainsExamplesPagePatch11} +\begin{paste}{ugDomainsExamplesPageFull11}{ugDomainsExamplesPageEmpty11} +\pastebutton{ugDomainsExamplesPageFull11}{\hidepaste} +\tab{5}\spadcommand{tm := o.(type="*Matrix*")\bound{x10 }\free{o1 }} +\indentrel{3}begin{verbatim} + (11) 353 + Type: Database IndexCard +end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugDomainsExamplesPageEmpty11} +\begin{paste}{ugDomainsExamplesPageEmpty11}{ugDomainsExamplesPagePatch11} +\pastebutton{ugDomainsExamplesPageEmpty11}{\showpaste} +\tab{5}\spadcommand{tm := o.(type="*Matrix*")\bound{x10 }\free{o1 }} +\end{paste}\end{patch} + +\begin{patch}{ugDomainsExamplesPagePatch12} +\begin{paste}{ugDomainsExamplesPageFull12}{ugDomainsExamplesPageEmpty12} +\pastebutton{ugDomainsExamplesPageFull12}{\hidepaste} +\tab{5}\spadcommand{fm := o.(origin="*Matrix*")\bound{x11 }\free{o1 }} +\indentrel{3}begin{verbatim} + (12) 192 + Type: Database IndexCard +end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugDomainsExamplesPageEmpty12} +\begin{paste}{ugDomainsExamplesPageEmpty12}{ugDomainsExamplesPagePatch12} +\pastebutton{ugDomainsExamplesPageEmpty12}{\showpaste} +\tab{5}\spadcommand{fm := o.(origin="*Matrix*")\bound{x11 }\free{o1 }} +\end{paste}\end{patch} + +\begin{patch}{ugDomainsExamplesPagePatch13} +\begin{paste}{ugDomainsExamplesPageFull13}{ugDomainsExamplesPageEmpty13} +\pastebutton{ugDomainsExamplesPageFull13}{\hidepaste} +\tab{5}\spadcommand{fm-tm\bound{x12 }\free{x10 x11 }} +\indentrel{3}begin{verbatim} + (13) 146 + Type: Database IndexCard +end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugDomainsExamplesPageEmpty13} +\begin{paste}{ugDomainsExamplesPageEmpty13}{ugDomainsExamplesPagePatch13} +\pastebutton{ugDomainsExamplesPageEmpty13}{\showpaste} +\tab{5}\spadcommand{fm-tm\bound{x12 }\free{x10 x11 }} +\end{paste}\end{patch} + +\begin{patch}{ugDomainsExamplesPagePatch14} +\begin{paste}{ugDomainsExamplesPageFull14}{ugDomainsExamplesPageEmpty14} +\pastebutton{ugDomainsExamplesPageFull14}{\hidepaste} +\tab{5}\spadcommand{fullDisplay(fm-\%)\bound{x13 }\free{x12 }} +\indentrel{3}begin{verbatim} + ** : (Matrix(R),NonNegativeInteger)->Matrix(R) + from StorageEfficientMatrixOperations(R) (unexposed) + clearDenominator : (Matrix(Q))->Matrix(R) + from MatrixCommonDenominator(R,Q) + coerceP + : (Vector(Matrix(R)))->Vector(Matrix(Polynomial(R))) + from CoerceVectorMatrixPackage(R) (unexposed) + coerce + : + (Vector(Matrix(R)))->Vector(Matrix(Fraction(Polynom + ial(R)))) + from CoerceVectorMatrixPackage(R) (unexposed) + coerce : (_$)->Matrix(R) + from RectangularMatrix(m,n,R) (unexposed) + coerce : (_$)->Matrix(R) + from SquareMatrix(ndim,R) (unexposed) + coerce : (Matrix(MachineFloat))->_$ + from FortranMatrixCategory + commonDenominator : (Matrix(Q))->R + from MatrixCommonDenominator(R,Q) + copy! : (Matrix(R),Matrix(R))->Matrix(R) + from StorageEfficientMatrixOperations(R) (unexposed) + f01brf + : + (Integer,Integer,Integer,Integer,DoubleFloat,Boolea + n,Boolean,List(Boolean),Matrix(DoubleFloat),Matrix( + Integer),Matrix(Integer),Integer)->Result + from NagMatrixOperationsPackage + f01bsf + : + (Integer,Integer,Integer,Matrix(Integer),Matrix(Int + eger),Matrix(Integer),Matrix(Integer),Boolean,Doubl + eFloat,Boolean,Matrix(Integer),Matrix(DoubleFloat), + Integer)->Result + from NagMatrixOperationsPackage + f01maf + : + (Integer,Integer,Integer,Integer,List(Boolean),Matr + ix(DoubleFloat),Matrix(Integer),Matrix(Integer),Dou + bleFloat,DoubleFloat,Integer)->Result + from NagMatrixOperationsPackage + f01mcf + : + (Integer,Matrix(DoubleFloat),Integer,Matrix(Integer + ),Integer)->Result + from NagMatrixOperationsPackage + f01qcf + : + (Integer,Integer,Integer,Matrix(DoubleFloat),Intege + r)->Result + from NagMatrixOperationsPackage + f01qdf + : + (String,String,Integer,Integer,Matrix(DoubleFloat), + Integer,Matrix(DoubleFloat),Integer,Integer,Matrix( + DoubleFloat),Integer)->Result + from NagMatrixOperationsPackage + f01qef + : + (String,Integer,Integer,Integer,Integer,Matrix(Doub + leFloat),Matrix(DoubleFloat),Integer)->Result + from NagMatrixOperationsPackage + f01rcf + : + (Integer,Integer,Integer,Matrix(Complex(DoubleFloat + )),Integer)->Result + from NagMatrixOperationsPackage + f01rdf + : + (String,String,Integer,Integer,Matrix(Complex(Doubl + eFloat)),Integer,Matrix(Complex(DoubleFloat)),Integ + er,Integer,Matrix(Complex(DoubleFloat)),Integer)->R + esult + from NagMatrixOperationsPackage + f01ref + : + (String,Integer,Integer,Integer,Integer,Matrix(Comp + lex(DoubleFloat)),Matrix(Complex(DoubleFloat)),Inte + ger)->Result + from NagMatrixOperationsPackage + hasSolution? : (Matrix(F),Vector(F))->Boolean + from LinearSystemMatrixPackage1(F) + leftScalarTimes! : (Matrix(R),R,Matrix(R))->Matrix(R) + from StorageEfficientMatrixOperations(R) (unexposed) + minus! : (Matrix(R),Matrix(R))->Matrix(R) + from StorageEfficientMatrixOperations(R) (unexposed) + minus! : (Matrix(R),Matrix(R),Matrix(R))->Matrix(R) + from StorageEfficientMatrixOperations(R) (unexposed) + particularSolution + : (Matrix(F),Vector(F))->Union(Vector(F),"failed") + from LinearSystemMatrixPackage1(F) + plus! : (Matrix(R),Matrix(R),Matrix(R))->Matrix(R) + from StorageEfficientMatrixOperations(R) (unexposed) + power! + : + (Matrix(R),Matrix(R),Matrix(R),Matrix(R),NonNegativ + eInteger)->Matrix(R) + from StorageEfficientMatrixOperations(R) (unexposed) + rank : (Matrix(F),Vector(F))->NonNegativeInteger + from LinearSystemMatrixPackage1(F) + rectangularMatrix : (Matrix(R))->_$ + from RectangularMatrix(m,n,R) (unexposed) + retractIfCan + : (Matrix(Expression(Float)))->Union(_$,"failed") + from FortranMatrixFunctionCategory + retractIfCan + : (Matrix(Expression(Integer)))->Union(_$,"failed") + from FortranMatrixFunctionCategory + retractIfCan + : + (Matrix(Fraction(Polynomial(Float))))->Union(_$,"fa + iled") + from FortranMatrixFunctionCategory + retractIfCan + : + (Matrix(Fraction(Polynomial(Integer))))->Union(_$," + failed") + from FortranMatrixFunctionCategory + retractIfCan + : (Matrix(Polynomial(Float)))->Union(_$,"failed") + from FortranMatrixFunctionCategory + retractIfCan + : (Matrix(Polynomial(Integer)))->Union(_$,"failed") + from FortranMatrixFunctionCategory + retract : (Matrix(Expression(Float)))->_$ + from FortranMatrixFunctionCategory + retract : (Matrix(Expression(Integer)))->_$ + from FortranMatrixFunctionCategory + retract : (Matrix(Fraction(Polynomial(Float))))->_$ + from FortranMatrixFunctionCategory + retract : (Matrix(Fraction(Polynomial(Integer))))->_$ + from FortranMatrixFunctionCategory + retract : (Matrix(Polynomial(Float)))->_$ + from FortranMatrixFunctionCategory + retract : (Matrix(Polynomial(Integer)))->_$ + from FortranMatrixFunctionCategory + rightScalarTimes! : (Matrix(R),Matrix(R),R)->Matrix(R) + from StorageEfficientMatrixOperations(R) (unexposed) + solve + : + (Matrix(F),List(Vector(F)))->List(Record(particular + :Union(Vector(F),"failed"),basis:List(Vector(F)))) + from LinearSystemMatrixPackage1(F) + solve + : + (Matrix(F),Vector(F))->Record(particular:Union(Vect + or(F),"failed"),basis:List(Vector(F))) + from LinearSystemMatrixPackage1(F) + splitDenominator + : (Matrix(Q))->Record(num:Matrix(R),den:R) + from MatrixCommonDenominator(R,Q) + squareMatrix : (Matrix(R))->_$ + from SquareMatrix(ndim,R) (unexposed) + times! : (Matrix(R),Matrix(R),Matrix(R))->Matrix(R) + from StorageEfficientMatrixOperations(R) (unexposed) + Type: Void +end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugDomainsExamplesPageEmpty14} +\begin{paste}{ugDomainsExamplesPageEmpty14}{ugDomainsExamplesPagePatch14} +\pastebutton{ugDomainsExamplesPageEmpty14}{\showpaste} +\tab{5}\spadcommand{fullDisplay(fm-\%)\bound{x13 }\free{x12 }} +\end{paste}\end{patch} + +\begin{patch}{ugDomainsExamplesPagePatch15} +\begin{paste}{ugDomainsExamplesPageFull15}{ugDomainsExamplesPageEmpty15} +\pastebutton{ugDomainsExamplesPageFull15}{\hidepaste} +\tab{5}\spadcommand{m := tm+fm\bound{x14 }\free{x10 x11 }} +\indentrel{3}begin{verbatim} + (15) 499 + Type: Database IndexCard +end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugDomainsExamplesPageEmpty15} +\begin{paste}{ugDomainsExamplesPageEmpty15}{ugDomainsExamplesPagePatch15} +\pastebutton{ugDomainsExamplesPageEmpty15}{\showpaste} +\tab{5}\spadcommand{m := tm+fm\bound{x14 }\free{x10 x11 }} +\end{paste}\end{patch} + +\begin{patch}{ugDomainsExamplesPagePatch16} +\begin{paste}{ugDomainsExamplesPageFull16}{ugDomainsExamplesPageEmpty16} +\pastebutton{ugDomainsExamplesPageFull16}{\hidepaste} +\tab{5}\spadcommand{fullDisplay(m, 202, 205)\free{x14 }} +\indentrel{3}begin{verbatim} + elt : (_$,List(Integer),List(Integer))->_$ + from MatrixCategory(R,Row,Col) + elt : (_$,Integer,Integer,R)->R + from RectangularMatrixCategory(m,n,R,Row,Col) + elt + : + (_$,NonNegativeInteger,NonNegativeInteger,NonNegati + veInteger)->R + from ThreeDimensionalMatrix(R) + eval + : + (Matrix(Expression(DoubleFloat)),List(Symbol),Vecto + r(Expression(DoubleFloat)))->Matrix(Expression(Doub + leFloat)) + from d02AgentsPackage + Type: Void +end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugDomainsExamplesPageEmpty16} +\begin{paste}{ugDomainsExamplesPageEmpty16}{ugDomainsExamplesPagePatch16} +\pastebutton{ugDomainsExamplesPageEmpty16}{\showpaste} +\tab{5}\spadcommand{fullDisplay(m, 202, 205)\free{x14 }} +\end{paste}\end{patch} + +\begin{patch}{ugDomainsExamplesPagePatch17} +\begin{paste}{ugDomainsExamplesPageFull17}{ugDomainsExamplesPageEmpty17} +\pastebutton{ugDomainsExamplesPageFull17}{\hidepaste} +\tab{5}\spadcommand{elt(elt(elt(m,name),unique),count)\free{x14 }} +\indentrel{3}begin{verbatim} + (17) 317 + Type: PositiveInteger +end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugDomainsExamplesPageEmpty17} +\begin{paste}{ugDomainsExamplesPageEmpty17}{ugDomainsExamplesPagePatch17} +\pastebutton{ugDomainsExamplesPageEmpty17}{\showpaste} +\tab{5}\spadcommand{elt(elt(elt(m,name),unique),count)\free{x14 }} +\end{paste}\end{patch} +\end{verbatim} + +@ +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} diff --git a/src/input/de2re.input.pamphlet b/src/input/de2re.input.pamphlet index ee1d5dc..615318c 100644 --- a/src/input/de2re.input.pamphlet +++ b/src/input/de2re.input.pamphlet @@ -16,9 +16,9 @@ The function |LinearOrdinaryDifferentialOperator| is undefined dn := D()$L -- 4 well known differential operators exp:= dn - 1 -sincos := dn**2 + 1 -airy := dn**2 - n -hermite := dn**2 - 2*n*dn + 1 +sincos := dn^2 + 1 +airy := dn^2 - n +hermite := dn^2 - 2*n*dn + 1 -- the recurrences satisfied by the coefficients of their series solutions --recurrence(exp, 0) @@ -28,7 +28,7 @@ hermite := dn**2 - 2*n*dn + 1 --recurrence(hermite, 0) -- a non-trivial example from the GFUN tech. rep (Salvy & Zimmermann) -op := (335 * n**2 + 1290) * dn**2 + 1540 * n * dn + 468720 +op := (335 * n^2 + 1290) * dn^2 + 1540 * n * dn + 468720 --recurrence(op, 0) \end{chunk} \begin{chunk}{bugs} diff --git a/src/input/decimal.input.pamphlet b/src/input/decimal.input.pamphlet index cff1dcd..9136db1 100644 --- a/src/input/decimal.input.pamphlet +++ b/src/input/decimal.input.pamphlet @@ -68,7 +68,7 @@ decimal(1/2049) --E 4 --S 5 of 7 -p := decimal(1/4)*x**2 + decimal(2/3)*x + decimal(4/9) +p := decimal(1/4)*x^2 + decimal(2/3)*x + decimal(4/9) --R --R --R 2 _ _ diff --git a/src/input/defintef.input.pamphlet b/src/input/defintef.input.pamphlet index db06ce5..35a530e 100644 --- a/src/input/defintef.input.pamphlet +++ b/src/input/defintef.input.pamphlet @@ -31,7 +31,7 @@ int(sin(x)^3/(sin(x)^3+cos(x)^3),x=0..Pi/2) is one of them. \begin{chunk}{*} --S 1 of 8 -sin(x)**3/(sin(x)**3+cos(x)**3) +sin(x)^3/(sin(x)^3+cos(x)^3) --R --R --R 3 @@ -53,7 +53,7 @@ integrate(%, x = 0..%pi/2, "noPole") --E 2 --S 3 of 8 -x**2/(1+x**3) +x^2/(1+x^3) --R --R --R 2 @@ -73,7 +73,7 @@ integrate(%, x=0..%plusInfinity) --E 4 --S 5 of 8 -exp(-x**2)*log(x)**2 +exp(-x^2)*log(x)^2 --R --R --R 2 diff --git a/src/input/defintrf.input.pamphlet b/src/input/defintrf.input.pamphlet index ddb71f1..25a825c 100644 --- a/src/input/defintrf.input.pamphlet +++ b/src/input/defintrf.input.pamphlet @@ -27,7 +27,7 @@ Most symbolic indefinite integrals for $f$ will have a pole between 1 and 2. Note that $f$ is positive on $[1..2]$ so we expect the integral to be positive \begin{chunk}{*} --S 1 of 3 -f := (x**4 - 3*x**2 + 6)/(x**6-5*x**4+5*x**2+4) +f := (x^4 - 3*x^2 + 6)/(x^6-5*x^4+5*x^2+4) --R --R --R 4 2 diff --git a/src/input/defs.input.pamphlet b/src/input/defs.input.pamphlet index bec137a..b23aff2 100644 --- a/src/input/defs.input.pamphlet +++ b/src/input/defs.input.pamphlet @@ -20,7 +20,7 @@ fib(1) == 1 fib(n) == fib(n-1) + fib(n-2) otherwise fib(10) fib(100) -[fib(2**i) for i in 1..] +[fib(2^i) for i in 1..] \end{chunk} The when clause is not recognized either in the NAG version or diff --git a/src/input/derham.input.pamphlet b/src/input/derham.input.pamphlet index 652d3b0..9e23907 100644 --- a/src/input/derham.input.pamphlet +++ b/src/input/derham.input.pamphlet @@ -54,7 +54,7 @@ R := Expression coefRing --E 4 --S 5 of 33 -f : R := x**2*y*z-5*x**3*y**2*z**5 +f : R := x^2*y*z-5*x^3*y^2*z^5 --R --R --R 3 2 5 2 @@ -63,7 +63,7 @@ f : R := x**2*y*z-5*x**3*y**2*z**5 --E 5 --S 6 of 33 -g : R := z**2*y*cos(z)-7*sin(x**3*y**2)*z**2 +g : R := z^2*y*cos(z)-7*sin(x^3*y^2)*z^2 --R --R --R 2 3 2 2 @@ -72,7 +72,7 @@ g : R := z**2*y*cos(z)-7*sin(x**3*y**2)*z**2 --E 6 --S 7 of 33 -h : R :=x*y*z-2*x**3*y*z**2 +h : R :=x*y*z-2*x^3*y*z^2 --R --R --R 3 2 diff --git a/src/input/divisor.input.pamphlet b/src/input/divisor.input.pamphlet index 83b0254..7a737e8 100644 --- a/src/input/divisor.input.pamphlet +++ b/src/input/divisor.input.pamphlet @@ -42,7 +42,7 @@ P1 := UP(y, FRAC P0) This is the curve given by $y^2 = x^8 + 1$ (genus = 3) \begin{chunk}{*} --S 3 of 18 -R := RADFF(FRAC INT, P0, P1, 1 + x**8, 2) +R := RADFF(FRAC INT, P0, P1, 1 + x^8, 2) --R --R --R (3) diff --git a/src/input/dmp.input.pamphlet b/src/input/dmp.input.pamphlet index f05f7bc..11f8c76 100644 --- a/src/input/dmp.input.pamphlet +++ b/src/input/dmp.input.pamphlet @@ -30,7 +30,7 @@ --E 1 --S 2 of 8 -d1 := -4*z + 4*y**2*x + 16*x**2 + 1 +d1 := -4*z + 4*y^2*x + 16*x^2 + 1 --R --R --R 2 2 @@ -39,7 +39,7 @@ d1 := -4*z + 4*y**2*x + 16*x**2 + 1 --E 2 --S 3 of 8 -d2 := 2*z*y**2 + 4*x + 1 +d2 := 2*z*y^2 + 4*x + 1 --R --R --R 2 @@ -48,7 +48,7 @@ d2 := 2*z*y**2 + 4*x + 1 --E 3 --S 4 of 8 -d3 := 2*z*x**2 - 2*y**2 - x +d3 := 2*z*x^2 - 2*y^2 - x --R --R --R 2 2 diff --git a/src/input/dpol.input.pamphlet b/src/input/dpol.input.pamphlet index 1f2ef85..2901f9a 100644 --- a/src/input/dpol.input.pamphlet +++ b/src/input/dpol.input.pamphlet @@ -114,7 +114,7 @@ f:=w.4::dpol - w.1 * w.1 * z.3 --E 8 --S 9 of 18 -b:=(z.1::dpol)**3 * (z.2)**2 - w.2 +b:=(z.1::dpol)^3 * (z.2)^2 - w.2 --R --R --R 3 2 diff --git a/src/input/draw.input.pamphlet b/src/input/draw.input.pamphlet index fa47095..e6e4c34 100644 --- a/src/input/draw.input.pamphlet +++ b/src/input/draw.input.pamphlet @@ -55,7 +55,7 @@ draw(cos(x*y),x = -3..3,y = -3..3) colorFunction1(x:DFLOAT,y:DFLOAT):DFLOAT == x draw(cos(x*y),x = -3..3,y = -3..3,colorFunction == colorFunction1) -colorFunction2(x:DFLOAT,y:DFLOAT):DFLOAT == x**2 + y**2 +colorFunction2(x:DFLOAT,y:DFLOAT):DFLOAT == x^2 + y^2 draw(cos(x*y),x = -3..3,y = -3..3,colorFunction == colorFunction2) colorFunction3(x:DFLOAT,y:DFLOAT,z:DFLOAT):DFLOAT == -z diff --git a/src/input/drawalg.input.pamphlet b/src/input/drawalg.input.pamphlet index cc00f56..9ed302b 100644 --- a/src/input/drawalg.input.pamphlet +++ b/src/input/drawalg.input.pamphlet @@ -19,7 +19,7 @@ -- TopLevelDrawFunctionsForAlgebraicCurves example --Plotting Plane Algebraic Curve -draw(y**2 + y - (x**3 - x) = 0, x, y, range == [-2..2,-2..1]) +draw(y^2 + y - (x^3 - x) = 0, x, y, range == [-2..2,-2..1]) \end{chunk} \eject diff --git a/src/input/drawcfn.input.pamphlet b/src/input/drawcfn.input.pamphlet index 7cc01fa..c42442d 100644 --- a/src/input/drawcfn.input.pamphlet +++ b/src/input/drawcfn.input.pamphlet @@ -66,7 +66,7 @@ draw(l,-3..3,-3..3) colorFunction1(x:SF,y:SF):SF == x draw(l,-3..3,-3..3,colorFunction == colorFunction1) -colorFunction2(x:SF,y:SF):SF == x**2 + y**2 +colorFunction2(x:SF,y:SF):SF == x^2 + y^2 draw(l,-3..3,-3..3,colorFunction == colorFunction2) colorFunction3(x:SF,y:SF,z:SF):SF == -z diff --git a/src/input/drawcfun.input.pamphlet b/src/input/drawcfun.input.pamphlet index 78016c0..9ec0796 100644 --- a/src/input/drawcfun.input.pamphlet +++ b/src/input/drawcfun.input.pamphlet @@ -72,7 +72,7 @@ draw(l,-3..3,-3..3) colorFunction1(x:DFLOAT,y:DFLOAT):DFLOAT == x draw(l,-3..3,-3..3,colorFunction == colorFunction1) -colorFunction2(x:DFLOAT,y:DFLOAT):DFLOAT == x**2 + y**2 +colorFunction2(x:DFLOAT,y:DFLOAT):DFLOAT == x^2 + y^2 draw(l,-3..3,-3..3,colorFunction == colorFunction2) colorFunction3(x:DFLOAT,y:DFLOAT,z:DFLOAT):DFLOAT == -z diff --git a/src/input/drawcurv.input.pamphlet b/src/input/drawcurv.input.pamphlet index 4b489c7..56b142b 100644 --- a/src/input/drawcurv.input.pamphlet +++ b/src/input/drawcurv.input.pamphlet @@ -23,21 +23,21 @@ seg1 : SEG FRAC INT := -3/2..3/2 range1 : LIST SEG FRAC INT := [seg1,seg1] -draw(x**2 + y**2 = 1,x,y,range == range1,title == "Unit Circle") +draw(x^2 + y^2 = 1,x,y,range == range1,title == "Unit Circle") -- ditto seg2 : SEG FLOAT := -1.1..1.1 range2 : LIST SEG FLOAT := [seg2,seg2] -draw(x**2 + y**2 = 1,x,y,range == range2,title == "Unit Circle, 2nd Graph") +draw(x^2 + y^2 = 1,x,y,range == range2,title == "Unit Circle, 2nd Graph") -- an ellipse seg3 : SEG FRAC INT := -4..4 range3 : LIST SEG FRAC INT := [seg3,seg3] -draw(x**2/9 + y**2/4 = 1,x,y,range == range3,_ +draw(x^2/9 + y^2/4 = 1,x,y,range == range3,_ toScale == true,title == "Ellipse") -- another ellipse @@ -45,18 +45,18 @@ draw(x**2/9 + y**2/4 = 1,x,y,range == range3,_ seg4 : SEG FRAC INT := -5..5 range4 : LIST SEG FRAC INT := [seg4,seg4] -draw(5*x**2 - 8*x*y + 5*y**2 = 9,x,y,range == range4) +draw(5*x^2 - 8*x*y + 5*y^2 = 9,x,y,range == range4) -- a parabola seg5a : SEG FRAC INT := -3..14 seg5b : SEG FRAC INT := -3..10 range5 : LIST SEG FRAC INT := [seg5a,seg5b] -draw(x**2 - 2*x*y + y**2 - x - 2 = 0,x,y,range == range5) +draw(x^2 - 2*x*y + y^2 - x - 2 = 0,x,y,range == range5) -- a hyperbola -draw(x**2/4 - y**2 = 1,x,y,range == range4) +draw(x^2/4 - y^2 = 1,x,y,range == range4) -- an elliptic curve @@ -64,7 +64,7 @@ seg6a : SEG FRAC INT := -2..2 seg6b : SEG FRAC INT := -2..1 range6 : LIST SEG FRAC INT := [seg6a,seg6b] -draw(y**2 + y = x**3 - x,x,y,range == range6) +draw(y^2 + y = x^3 - x,x,y,range == range6) -- ovals @@ -72,13 +72,13 @@ seg7a : SEG FRAC INT := -8..8 seg7b : SEG FRAC INT := -4..4 range7 : LIST SEG FRAC INT := [seg7a,seg7b] -eq1 := (x**2 + y**2 + 5**2)**2 - (6**4 + 4*5**2*x**2) = 0 +eq1 := (x^2 + y^2 + 5^2)^2 - (6^4 + 4*5^2*x^2) = 0 draw(eq1,x,y,range == range7,title == "Cassinian oval with one loop") seg8a : SEG FRAC INT := -10..10 range8 : LIST SEG FRAC INT := [seg8a,seg7b] -eq2 := (x**2 + y**2 + 7**2)**2 - (6**4 + 4*7**2*x**2) = 0 +eq2 := (x^2 + y^2 + 7^2)^2 - (6^4 + 4*7^2*x^2) = 0 draw(eq2,x,y,range == range8,title == "Cassinian oval with two loops") \end{chunk} \eject diff --git a/src/input/drawcx.input.pamphlet b/src/input/drawcx.input.pamphlet index 410d781..9300489 100644 --- a/src/input/drawcx.input.pamphlet +++ b/src/input/drawcx.input.pamphlet @@ -39,7 +39,7 @@ draw(curve(i1,i2,i3),0..15*%pi,title == "Parametric Curve") --Plotting Three Dimensional Compiled Functions of Two Variables l(x:DFLOAT,y:DFLOAT):DFLOAT == cos(x*y) draw(l,-3..3,-3..3) -colorFxn(x:DFLOAT,y:DFLOAT):DFLOAT == 1/(x**2 + y**2 + 1) +colorFxn(x:DFLOAT,y:DFLOAT):DFLOAT == 1/(x^2 + y^2 + 1) draw(l,-3..3,-3..3, colorFunction == colorFxn) --Plotting Three Dimensional Compiled Parametric Surface Functions @@ -47,7 +47,7 @@ n1(u:DFLOAT,v:DFLOAT):DFLOAT == u*cos(v) n2(u:DFLOAT,v:DFLOAT):DFLOAT == u*sin(v) n3(u:DFLOAT,v:DFLOAT):DFLOAT == v*cos(u) draw(surface(n1,n2,n3),-4..4,0..2*%pi) -colorFxn(x:DFLOAT,y:DFLOAT):DFLOAT == 1/(x**2 + y**2 + 1) +colorFxn(x:DFLOAT,y:DFLOAT):DFLOAT == 1/(x^2 + y^2 + 1) draw(surface(n1,n2,n3),-4..4,0..2*%pi, colorFunction == colorFxn) \end{chunk} diff --git a/src/input/drawex.input.pamphlet b/src/input/drawex.input.pamphlet index 3af5f7e..d0c5f45 100644 --- a/src/input/drawex.input.pamphlet +++ b/src/input/drawex.input.pamphlet @@ -33,13 +33,13 @@ draw(curve(t - 2*sin t,1 - 2*cos t),t = -5..5) draw(surface(5*sin(u)*cos(v),4*sin(u)*sin(v),3*cos(u)),u=0..%pi,v=0..2*%pi) -draw(surface(cos(t)/(1+sin(t)**2),sin(t)*cos(t)*cos(u)/(1+sin(t)**2), - sin(t)*cos(t)*sin(u)/(1+sin(t)**2)),t = -%pi..%pi,u = 0..%pi) +draw(surface(cos(t)/(1+sin(t)^2),sin(t)*cos(t)*cos(u)/(1+sin(t)^2), + sin(t)*cos(t)*sin(u)/(1+sin(t)^2)),t = -%pi..%pi,u = 0..%pi) -- helix draw(curve(4*cos(t),4*sin(t),t),t = -10..10, title == "Helix") -draw(sin(2 * x**2 + 3 * y**2)/(x**2 + y**2),x = -3..3,y = -3..3) +draw(sin(2 * x^2 + 3 * y^2)/(x^2 + y^2),x = -3..3,y = -3..3) draw(curve(9*sin(3*t/4),8*sin(t)),t = -4*%pi..4*%pi, _ title == "Lissajous curve") @@ -47,11 +47,11 @@ draw(curve(9*sin(3*t/4),8*sin(t)),t = -4*%pi..4*%pi, _ draw(curve(-9*sin(4*t/5),8*sin(t)),t = -5*%pi..5*%pi, _ title == "Lissajous curve") -draw(curve(t**2 + 2*t - 1,t**2 + t - 2),t = -4..3) +draw(curve(t^2 + 2*t - 1,t^2 + t - 2),t = -4..3) -draw((x**2 - y**2)/(x**2 + y**2),x = -1..1,y = -1..1) +draw((x^2 - y^2)/(x^2 + y^2),x = -1..1,y = -1..1) -draw(x**2 - y**2,x = -2..2, y = -2..2) +draw(x^2 - y^2,x = -2..2, y = -2..2) draw(sin inv x,x = -1.03..3) @@ -63,16 +63,16 @@ draw(t/100,t = 0..100,coordinates == polar) draw(cos(x*y),x = -3..3, y = -3..3) -draw(curve(3*(t**2-3),t*(t**2-3)),t = -3..3, title == "Tschirnhausen's Cubic") +draw(curve(3*(t^2-3),t*(t^2-3)),t = -3..3, title == "Tschirnhausen's Cubic") draw(curve(sin(t), cos(t), 0), t=0..2*%pi, tubeRadius == 0.5) -draw(curve((t**2-1)/(3*t**2+1),t*(t**2-1)/(3*t**2+1)),t = -3..3, title == _ +draw(curve((t^2-1)/(3*t^2+1),t*(t^2-1)/(3*t^2+1)),t = -3..3, title == _ "Folium of Descartes") draw(curve(t - 2*sin t,1 - 2*cos t),t = -5..5) -draw(curve(cos(t)/(1+sin(t)**2),sin(t)*cos(t)/(1+sin(t)**2)),t = _ +draw(curve(cos(t)/(1+sin(t)^2),sin(t)*cos(t)/(1+sin(t)^2)),t = _ -%pi..%pi, title == "Lemniscate of Bernoulli") \end{chunk} diff --git a/src/input/drawpoly.input.pamphlet b/src/input/drawpoly.input.pamphlet index e135855..50060b3 100644 --- a/src/input/drawpoly.input.pamphlet +++ b/src/input/drawpoly.input.pamphlet @@ -16,14 +16,14 @@ \end{chunk} \begin{chunk}{*} \getchunk{license} -a1**18 - 83.30408576104702*a1**17 + 4016.670203940073*a1**16 + _ - - 167241.63892168205*a1**15 + 5649108.7097550742*a1**14 + _ - - 1.4927698938773671E8*a1**13 + 3.2737267549354239E9*a1**12 + _ - - 6.0880865153029945E10*a1**11 + 8.4818140701374121E11*a1**10 + _ - - 7.1925755048090801E12*a1**9 + 3.6866360833695195E13*a1**8 + _ - - 1.2269584766923825E14*a1**7 + 2.990307540150555E14*a1**6 + _ - - 5.580671179246935E14*a1**5 + 5.4087180857969938E14*a1**4 + _ - 3.5962416171315931E14*a1**3 - 8.254469833838275E14*a1**2 + _ +a1^18 - 83.30408576104702*a1^17 + 4016.670203940073*a1^16 + _ + - 167241.63892168205*a1^15 + 5649108.7097550742*a1^14 + _ + - 1.4927698938773671E8*a1^13 + 3.2737267549354239E9*a1^12 + _ + - 6.0880865153029945E10*a1^11 + 8.4818140701374121E11*a1^10 + _ + - 7.1925755048090801E12*a1^9 + 3.6866360833695195E13*a1^8 + _ + - 1.2269584766923825E14*a1^7 + 2.990307540150555E14*a1^6 + _ + - 5.580671179246935E14*a1^5 + 5.4087180857969938E14*a1^4 + _ + 3.5962416171315931E14*a1^3 - 8.254469833838275E14*a1^2 + _ - 4.3259667313869412E14*a1 - 1.2086386259492219E13 draw(%,a1=-0.028..-0.027) \end{chunk} diff --git a/src/input/drawx.input.pamphlet b/src/input/drawx.input.pamphlet index 067e4de..e5fe38d 100644 --- a/src/input/drawx.input.pamphlet +++ b/src/input/drawx.input.pamphlet @@ -34,13 +34,13 @@ draw(curve(cos(t),sin(t),t),t=0..6,tubeRadius == .35,tubePoints == 8) --Plotting Three Dimensional Functions of Two Variables draw(cos(x*y),x = -3..3, y = -3..3) l(x:DoubleFloat,y:DoubleFloat):DoubleFloat == cos(x*y) -colorFxn(x:DoubleFloat,y:DoubleFloat):DoubleFloat == 1/(x**2 + y**2 + 1) +colorFxn(x:DoubleFloat,y:DoubleFloat):DoubleFloat == 1/(x^2 + y^2 + 1) draw(cos(x*y),x = -3..3, y = -3..3, colorFunction == colorFxn) --Plotting Three Dimensional Parametric Surfaces draw(surface(u*cos(v),u*sin(v),v*cos(u)),u=-4..4,v=0..2*%pi) l(x:DoubleFloat,y:DoubleFloat):DoubleFloat == cos(x*y) -colorFxn(x:DoubleFloat,y:DoubleFloat):DoubleFloat == 1/(x**2 + y**2 + 1) +colorFxn(x:DoubleFloat,y:DoubleFloat):DoubleFloat == 1/(x^2 + y^2 + 1) draw(cos(x*y),x = -3..3, y = -3..3, colorFunction == colorFxn) \end{chunk} diff --git a/src/input/dropt.input.pamphlet b/src/input/dropt.input.pamphlet index 9675779..45f3167 100644 --- a/src/input/dropt.input.pamphlet +++ b/src/input/dropt.input.pamphlet @@ -42,12 +42,12 @@ draw(sin(x),x=-%pi..%pi,curveColor == bright red()) draw(sin(x),x=-%pi..%pi,pointColor == 3.0) draw(sin(x),x=-%pi..%pi,pointColor == dim yellow()) -draw(y**2 + y - (x**3 - x) = 0,x,y,range == [-2..2,-2..1]) -p := ((x**2 + y**2 + 1) - 8*x)**2 - (8*(x**2 + y**2 + 1) - 4*x - 1) +draw(y^2 + y - (x^3 - x) = 0,x,y,range == [-2..2,-2..1]) +p := ((x^2 + y^2 + 1) - 8*x)^2 - (8*(x^2 + y^2 + 1) - 4*x - 1) draw(p = 0,x,y,range == [-1.0..11.0, -7.0..7.0]) seg1 : SEG FRAC INT := -3/2..3/2 range1 : LIST SEG FRAC INT := [seg1,seg1] -draw(x**2 + y**2 = 1,x,y,range == range1) +draw(x^2 + y^2 = 1,x,y,range == range1) f1(t:DFLOAT):DFLOAT == 9*sin(3*t/4) f2(t:DFLOAT):DFLOAT == 8*sin(t) @@ -73,9 +73,9 @@ colorFxn1(x:DFLOAT,y:DFLOAT):DFLOAT == x*sin(x) draw(m,0..2*%pi,0..%pi,colorFunction == colorFxn1,title == _ "color = x*sin(x)",coordinates == spherical) -colorFxn2(x:DFLOAT,y:DFLOAT):DFLOAT == x**2 - y**2 +colorFxn2(x:DFLOAT,y:DFLOAT):DFLOAT == x^2 - y^2 draw(m,0..2*%pi,0..%pi,colorFunction == colorFxn2,title == _ - "color = x**2 - y**2",coordinates == spherical) + "color = x^2 - y^2",coordinates == spherical) colorFxn3(x:DFLOAT,y:DFLOAT,z:DFLOAT):DFLOAT == sin(x*z) + cos(y*z) draw(m,0..2*%pi,0..%pi,colorFunction == colorFxn3,title == _ diff --git a/src/input/e04dgf.input.pamphlet b/src/input/e04dgf.input.pamphlet index 97a5876..aa109f3 100644 --- a/src/input/e04dgf.input.pamphlet +++ b/src/input/e04dgf.input.pamphlet @@ -35,7 +35,7 @@ ve:=0 x:Matrix SF:= [[-1.0 ,1.0 ]] ef:Expression Float:=_ - (exp(X[1])*(4*X[1]**2+2*X[2]**2+4*X[1]*X[2]+2*X[2]+1))::EXPR FLOAT + (exp(X[1])*(4*X[1]^2+2*X[2]^2+4*X[1]*X[2]+2*X[2]+1))::EXPR FLOAT objfun:ASP49(OBJFUN):= retract ef result:=e04dgf(n,es,fu,it,lin,list,ma,op,pr,sta,sto,ve,x,-1,objfun) \end{chunk} diff --git a/src/input/e04fdf.input.pamphlet b/src/input/e04fdf.input.pamphlet index 3b8939e..2baa82f 100644 --- a/src/input/e04fdf.input.pamphlet +++ b/src/input/e04fdf.input.pamphlet @@ -27,21 +27,21 @@ lw:=171 x:Matrix SF:= [[0.5 ,1.0 ,1.5 ]] vef:Vector Expression Float:= vector - [(XC[3]+15*XC[2])**(-1)+XC[1]-0.14 ,_ - 2*(2*XC[3]+14*XC[2])**(-1)+XC[1]-0.18 ,_ - 3*(3*XC[3]+13*XC[2])**(-1)+XC[1]-0.22 ,_ - 4*(4*XC[3]+12*XC[2])**(-1)+XC[1]-0.25 ,_ - 5*(5*XC[3]+11*XC[2])**(-1)+XC[1]-0.29 ,_ - 6*(6*XC[3]+10*XC[2])**(-1)+XC[1]-0.32 ,_ - 7*(7*XC[3]+9*XC[2])**(-1)+XC[1]-0.35 ,_ - 8*(8*XC[3]+8*XC[2])**(-1)+XC[1]-0.39 ,_ - 9*(7*XC[3]+7*XC[2])**(-1)+XC[1]-0.37 ,_ - 10*(6*XC[3]+6*XC[2])**(-1)+XC[1]-0.58 ,_ - 11*(5*XC[3]+5*XC[2])**(-1)+XC[1]-0.73 ,_ - 12*(4*XC[3]+4*XC[2])**(-1)+XC[1]-0.96 ,_ - 13*(3*XC[3]+3*XC[2])**(-1)+XC[1]-1.34 ,_ - 14*(2*XC[3]+2*XC[2])**(-1)+XC[1]-2.1 ,_ - 15*(XC[3]+XC[2])**(-1)+XC[1]-4.39 ] + [(XC[3]+15*XC[2])^(-1)+XC[1]-0.14 ,_ + 2*(2*XC[3]+14*XC[2])^(-1)+XC[1]-0.18 ,_ + 3*(3*XC[3]+13*XC[2])^(-1)+XC[1]-0.22 ,_ + 4*(4*XC[3]+12*XC[2])^(-1)+XC[1]-0.25 ,_ + 5*(5*XC[3]+11*XC[2])^(-1)+XC[1]-0.29 ,_ + 6*(6*XC[3]+10*XC[2])^(-1)+XC[1]-0.32 ,_ + 7*(7*XC[3]+9*XC[2])^(-1)+XC[1]-0.35 ,_ + 8*(8*XC[3]+8*XC[2])^(-1)+XC[1]-0.39 ,_ + 9*(7*XC[3]+7*XC[2])^(-1)+XC[1]-0.37 ,_ + 10*(6*XC[3]+6*XC[2])^(-1)+XC[1]-0.58 ,_ + 11*(5*XC[3]+5*XC[2])^(-1)+XC[1]-0.73 ,_ + 12*(4*XC[3]+4*XC[2])^(-1)+XC[1]-0.96 ,_ + 13*(3*XC[3]+3*XC[2])^(-1)+XC[1]-1.34 ,_ + 14*(2*XC[3]+2*XC[2])^(-1)+XC[1]-2.1 ,_ + 15*(XC[3]+XC[2])^(-1)+XC[1]-4.39 ] lsfun1:ASP50(LSFUN1):= retract vef result:=e04fdf(m,n,liw,lw,x,-1,lsfun1) \end{chunk} diff --git a/src/input/e04gcf.input.pamphlet b/src/input/e04gcf.input.pamphlet index c79858d..18565d9 100644 --- a/src/input/e04gcf.input.pamphlet +++ b/src/input/e04gcf.input.pamphlet @@ -27,21 +27,21 @@ lw:=177 x:Matrix SF:= [[0.5 ,1.0 ,1.5 ]] vef:Vector Expression Float:=vector - [(XC[3]+15*XC[2])**(-1)+XC[1]-0.14 ,_ - 2*(2*XC[3]+14*XC[2])**(-1)+XC[1]-0.18 ,_ - 3*(3*XC[3]+13*XC[2])**(-1)+XC[1]-0.22 ,_ - 4*(4*XC[3]+12*XC[2])**(-1)+XC[1]-0.25 ,_ - 5*(5*XC[3]+11*XC[2])**(-1)+XC[1]-0.29 ,_ - 6*(6*XC[3]+10*XC[2])**(-1)+XC[1]-0.32 ,_ - 7*(7*XC[3]+9*XC[2])**(-1)+XC[1]-0.35 ,_ - 8*(8*XC[3]+8*XC[2])**(-1)+XC[1]-0.39 ,_ - 9*(7*XC[3]+7*XC[2])**(-1)+XC[1]-0.37 ,_ - 10*(6*XC[3]+6*XC[2])**(-1)+XC[1]-0.58 ,_ - 11*(5*XC[3]+5*XC[2])**(-1)+XC[1]-0.73 ,_ - 12*(4*XC[3]+4*XC[2])**(-1)+XC[1]-0.96 ,_ - 13*(3*XC[3]+3*XC[2])**(-1)+XC[1]-1.34 ,_ - 14*(2*XC[3]+2*XC[2])**(-1)+XC[1]-2.1 ,_ - 15*(XC[3]+XC[2])**(-1)+XC[1]-4.39 ] + [(XC[3]+15*XC[2])^(-1)+XC[1]-0.14 ,_ + 2*(2*XC[3]+14*XC[2])^(-1)+XC[1]-0.18 ,_ + 3*(3*XC[3]+13*XC[2])^(-1)+XC[1]-0.22 ,_ + 4*(4*XC[3]+12*XC[2])^(-1)+XC[1]-0.25 ,_ + 5*(5*XC[3]+11*XC[2])^(-1)+XC[1]-0.29 ,_ + 6*(6*XC[3]+10*XC[2])^(-1)+XC[1]-0.32 ,_ + 7*(7*XC[3]+9*XC[2])^(-1)+XC[1]-0.35 ,_ + 8*(8*XC[3]+8*XC[2])^(-1)+XC[1]-0.39 ,_ + 9*(7*XC[3]+7*XC[2])^(-1)+XC[1]-0.37 ,_ + 10*(6*XC[3]+6*XC[2])^(-1)+XC[1]-0.58 ,_ + 11*(5*XC[3]+5*XC[2])^(-1)+XC[1]-0.73 ,_ + 12*(4*XC[3]+4*XC[2])^(-1)+XC[1]-0.96 ,_ + 13*(3*XC[3]+3*XC[2])^(-1)+XC[1]-1.34 ,_ + 14*(2*XC[3]+2*XC[2])^(-1)+XC[1]-2.1 ,_ + 15*(XC[3]+XC[2])^(-1)+XC[1]-4.39 ] lsfun2:Asp19(LSFUN2):= retract vef result:=e04gcf(m,n,liw,lw,x,-1,lsfun2) \end{chunk} diff --git a/src/input/e04jaf.input.pamphlet b/src/input/e04jaf.input.pamphlet index 08f8b73..2479974 100644 --- a/src/input/e04jaf.input.pamphlet +++ b/src/input/e04jaf.input.pamphlet @@ -31,8 +31,8 @@ bu:Matrix SF:= x:Matrix SF:= [[3 ,-1 ,0 ,1 ]] ef:Expression Float:= - ((XC[1]+10*XC[2])**2+5*(XC[3]-XC[4])**2+(XC[2]-2*XC[3])**4+_ - 10*(XC[1]-XC[4])**4)::EXPR FLOAT + ((XC[1]+10*XC[2])^2+5*(XC[3]-XC[4])^2+(XC[2]-2*XC[3])^4+_ + 10*(XC[1]-XC[4])^4)::EXPR FLOAT funct1:Asp24(FUNCT1):=retract ef result:=e04jaf(n,ibound,liw,lw,bl,bu,x,-1,funct1) \end{chunk} diff --git a/src/input/e04ucf.input.pamphlet b/src/input/e04ucf.input.pamphlet index 7d1b849..efdaf6a 100644 --- a/src/input/e04ucf.input.pamphlet +++ b/src/input/e04ucf.input.pamphlet @@ -73,20 +73,20 @@ r:Matrix SF:=new(9,9,0.0) x:Matrix SF:= [[0.1 ,0.125 ,0.666666 ,0.142857 ,0.111111 ,0.2 ,0.25 ,-0.2 ,-0.25 ]] vef:Vector Expression Float:=vector - [X[1]**2 + X[6]**2 ,_ - (X[2] - X[1])**2 + (X[7] - X[6])**2 ,_ - (X[3] - X[1])**2 + X[6]*2 ,_ - (X[1] - X[4])**2 + (X[6] - X[8])**2 ,_ - (X[1] - X[5])**2 + (X[6] - X[9])**2 ,_ - X[2]**2 + X[7]**2 ,_ - (X[3] - X[2])**2 + X[7]**2 ,_ - (X[4] - X[2])**2 + (X[8] - X[7])**2 ,_ - (X[2] - X[5])**2 + (X[7] - X[9])**2 ,_ - (X[4] - X[3])**2 + X[8]**2 ,_ - (X[5] - X[3])**2 + X[9]**2 ,_ - X[4]**2 + X[8]**2 ,_ - (X[4] - X[5])**2 + (X[9] - X[8])**2 ,_ - X[5]**2 + X[9]**2 ] + [X[1]^2 + X[6]^2 ,_ + (X[2] - X[1])^2 + (X[7] - X[6])^2 ,_ + (X[3] - X[1])^2 + X[6]*2 ,_ + (X[1] - X[4])^2 + (X[6] - X[8])^2 ,_ + (X[1] - X[5])^2 + (X[6] - X[9])^2 ,_ + X[2]^2 + X[7]^2 ,_ + (X[3] - X[2])^2 + X[7]^2 ,_ + (X[4] - X[2])^2 + (X[8] - X[7])^2 ,_ + (X[2] - X[5])^2 + (X[7] - X[9])^2 ,_ + (X[4] - X[3])^2 + X[8]^2 ,_ + (X[5] - X[3])^2 + X[9]^2 ,_ + X[4]^2 + X[8]^2 ,_ + (X[4] - X[5])^2 + (X[9] - X[8])^2 ,_ + X[5]^2 + X[9]^2 ] confun:Asp55(CONFUN):= retract vef ef:Expression Float:=(-X[2]*X[6] + X[1]*X[7] - X[3]*X[7] - _ X[5]*X[8] + X[4]*X[9] + X[3]*X[8])::EXPR FLOAT diff --git a/src/input/easter.input.pamphlet b/src/input/easter.input.pamphlet index 54d2c86..33afc73 100644 --- a/src/input/easter.input.pamphlet +++ b/src/input/easter.input.pamphlet @@ -192,7 +192,7 @@ Numbers are nice, but symbols allow for variability---try some high school algebra: rational simplification \begin{chunk}{*} --S 15 of 200 -(x**2 - 4)/(x**2 + 4*x + 4) +(x^2 - 4)/(x^2 + 4*x + 4) --R --R --R x - 2 @@ -205,7 +205,7 @@ algebra: rational simplification This example requires more sophistication \begin{chunk}{*} --S 16 of 200 -(%e**x - 1)/(%e**(x/2) + 1) +(%e^x - 1)/(%e^(x/2) + 1) --R --R --R x @@ -233,7 +233,7 @@ normalize(%) Expand and factor polynomials \begin{chunk}{*} --S 18 of 200 -(x + 1)**20 +(x + 1)^20 --R --R --R (18) @@ -274,7 +274,7 @@ factor(%) --E 20 --S 21 of 200 -x**100 - 1 +x^100 - 1 --R --R --R 100 @@ -302,7 +302,7 @@ factor(%) Factor polynomials over finite fields and field extensions \begin{chunk}{*} --S 23 of 200 -p:= x**4 - 3*x**2 + 1 +p:= x^4 - 3*x^2 + 1 --R --R --R 4 2 @@ -320,7 +320,7 @@ factor(p) --E 24 --S 25 of 200 -phi:= rootOf(phi**2 - phi - 1); +phi:= rootOf(phi^2 - phi - 1); --R --R --R Type: AlgebraicNumber @@ -356,7 +356,7 @@ expand(%) Partial fraction decomposition \begin{chunk}{*} --S 29 of 200 -(x**2 + 2*x + 3)/(x**3 + 4*x**2 + 5*x + 2) +(x^2 + 2*x + 3)/(x^3 + 4*x^2 + 5*x + 2) --R --R --R 2 @@ -450,7 +450,7 @@ r:= 'r; The following expressions are all equal to zero \begin{chunk}{*} --S 37 of 200 -sqrt(997) - (997**3)**(1/6) +sqrt(997) - (997^3)^(1/6) --R --R --R (37) 0 @@ -458,7 +458,7 @@ sqrt(997) - (997**3)**(1/6) --E 37 --S 38 of 200 -sqrt(999983) - (999983**3)**(1/6) +sqrt(999983) - (999983^3)^(1/6) --R --R --R (38) 0 @@ -466,7 +466,7 @@ sqrt(999983) - (999983**3)**(1/6) --E 38 --S 39 of 200 -(2**(1/3) + 4**(1/3))**3 - 6*(2**(1/3) + 4**(1/3)) - 6 +(2^(1/3) + 4^(1/3))^3 - 6*(2^(1/3) + 4^(1/3)) - 6 --R --R --R 3+-+3+-+2 3+-+2 3+-+ 3+-+ @@ -487,7 +487,7 @@ simplify(%) This expression is zero for $x, y > 0$ and $n$ not equal to zero \begin{chunk}{*} --S 41 of 200 -x**(1/n)*y**(1/n) - (x*y)**(1/n) +x^(1/n)*y^(1/n) - (x*y)^(1/n) --R --R --R 1 1 1 @@ -647,8 +647,8 @@ simplify(%) --E 49 --S 50 of 200 -(4*r + 4*sqrt(r) + 1)**(sqrt(r)/(2*sqrt(r) + 1)) _ - * (2*sqrt(r) + 1)**(1/(2*sqrt(r) + 1)) - 2*sqrt(r) - 1 +(4*r + 4*sqrt(r) + 1)^(sqrt(r)/(2*sqrt(r) + 1)) _ + * (2*sqrt(r) + 1)^(1/(2*sqrt(r) + 1)) - 2*sqrt(r) - 1 --R --R --R +-+ @@ -712,7 +712,7 @@ $\sqrt{(x y)}/\sqrt{(x)}$, but no further in general (consider what happens when x, y = -1). \begin{chunk}{*} --S 55 of 200 -sqrt(x*y*abs(z)**2) / (sqrt(x)*abs(z)) +sqrt(x*y*abs(z)^2) / (sqrt(x)*abs(z)) --R --R --R +-----------+ @@ -745,7 +745,7 @@ sqrt(1/z) - 1/sqrt(z) If $z = 3 \pi i$, $\log(\exp(z))$ is not equal to $z$ \begin{chunk}{*} --S 57 of 200 -log(%e**z) +log(%e^z) --R --R --R (57) z @@ -764,7 +764,7 @@ normalize(%) The principal value of this expression is $(10 - 4 \pi) i$ \begin{chunk}{*} --S 59 of 200 -log(%e**(10*%i)) +log(%e^(10*%i)) --R --R --R 10%i @@ -796,7 +796,7 @@ atan(tan(z)) If $z = 2 \pi i$, $\sqrt(\exp(z))$ is not equal to $\exp(z/2)$ \begin{chunk}{*} --S 62 of 200 -sqrt(%e**z) - %e**(z/2) +sqrt(%e^z) - %e^(z/2) --R --R --R z @@ -824,7 +824,7 @@ Manipulate an equation using a natural syntax Solve various nonlinear equations---this cubic polynomial has all real roots \begin{chunk}{*} --S 64 of 200 -radicalSolve(3*x**3 - 18*x**2 + 33*x - 19 = 0, x) +radicalSolve(3*x^3 - 18*x^2 + 33*x - 19 = 0, x) --R --R --R (64) @@ -926,7 +926,7 @@ map(e +-> lhs(e) = rectform(rhs(e)), %) Some simple seeming problems can have messy answers \begin{chunk}{*} --S 66 of 200 -eqn:= x**4 + x**3 + x**2 + x + 1 = 0 +eqn:= x^4 + x^3 + x^2 + x + 1 = 0 --R --R --R 4 3 2 @@ -1375,7 +1375,7 @@ eval(eqn, %.1) --E 68 --S 69 of 200 -%e**(2*x) + 2*%e**x + 1 = z +%e^(2*x) + 2*%e^x + 1 = z --R --R --R 2x x @@ -1396,7 +1396,7 @@ solve(%, x) This equation is already factored and so {\sl should} be easy to solve \begin{chunk}{*} --S 71 of 200 -(x + 1) * (sin(x)**2 + 1)**2 * cos(3*x)**3 = 0 +(x + 1) * (sin(x)^2 + 1)^2 * cos(3*x)^3 = 0 --R --R --R 3 4 3 2 3 @@ -1419,7 +1419,7 @@ The following equations have an infinite number of solutions (let $n$ be an arbitrary integer): $z = 0 [+ n 2 \pi i]$ \begin{chunk}{*} --S 73 of 200 -solve(%e**z = 1, z) +solve(%e^z = 1, z) --R --R --R (73) [z= 0] @@ -1464,7 +1464,7 @@ solve(sin(x) = tan(x), x) This equation has no solutions \begin{chunk}{*} --S 77 of 200 -solve(sqrt(x**2 + 1) = x - 2, x) +solve(sqrt(x^2 + 1) = x - 2, x) --R --R --R (77) [] @@ -1512,7 +1512,7 @@ solve([eq1, eq2, eq3], [x, y, z]) Solve a system of nonlinear equations \begin{chunk}{*} --S 82 of 200 -eq1:= x**2*y + 3*y*z - 4 = 0 +eq1:= x^2*y + 3*y*z - 4 = 0 --R --R --R 2 @@ -1521,7 +1521,7 @@ eq1:= x**2*y + 3*y*z - 4 = 0 --E 82 --S 83 of 200 -eq2:= -3*x**2*z + 2*y**2 + 1 = 0 +eq2:= -3*x^2*z + 2*y^2 + 1 = 0 --R --R --R 2 2 @@ -1530,7 +1530,7 @@ eq2:= -3*x**2*z + 2*y**2 + 1 = 0 --E 83 --S 84 of 200 -eq3:= 2*y*z**2 - z**2 - 1 = 0 +eq3:= 2*y*z^2 - z^2 - 1 = 0 --R --R --R 2 @@ -1608,8 +1608,8 @@ Define a Vandermonde matrix (useful for doing polynomial interpolations) --S 89 of 200 matrix([[1, 1, 1, 1 ], _ [w, x, y, z ], _ - [w**2, x**2, y**2, z**2], _ - [w**3, x**3, y**3, z**3]]) + [w^2, x^2, y^2, z^2], _ + [w^3, x^3, y^3, z^3]]) --R --R --R +1 1 1 1 + @@ -1700,7 +1700,7 @@ m:= 'm; \subsection{Sums: finite and infinite} \begin{chunk}{*} --S 96 of 200 -summation(k**3, k = 1..n) +summation(k^3, k = 1..n) --R --R --R n @@ -1712,7 +1712,7 @@ summation(k**3, k = 1..n) --E 96 --S 97 of 200 -sum(k**3, k = 1..n) +sum(k^3, k = 1..n) --R --R --R 4 3 2 @@ -1723,7 +1723,7 @@ sum(k**3, k = 1..n) --E 97 --S 98 of 200 -limit(sum(1/k**2 + 1/k**3, k = 1..n), n = %plusInfinity) +limit(sum(1/k^2 + 1/k^3, k = 1..n), n = %plusInfinity) --R --R --R (98) "failed" @@ -1749,7 +1749,7 @@ product(k, k = 1..n) \subsection{Limits --- start with a famous example} \begin{chunk}{*} --S 100 of 200 -limit((1 + 1/n)**n, n = %plusInfinity) +limit((1 + 1/n)^n, n = %plusInfinity) --R --R --R (100) %e @@ -1757,7 +1757,7 @@ limit((1 + 1/n)**n, n = %plusInfinity) --E 100 --S 101 of 200 -limit((1 - cos(x))/x**2, x = 0) +limit((1 - cos(x))/x^2, x = 0) --R --R --R 1 @@ -1800,7 +1800,7 @@ D(y(x(t)), t, 2) \subsection{Indefinite Integrals} \begin{chunk}{*} --S 105 of 200 -1/(x**3 + 2) +1/(x^3 + 2) --R --R --R 1 @@ -1978,7 +1978,7 @@ integrate(1/x, x = -1..1) --E 117 --S 118 of 200 -integrate(1/x**2, x = -1..1) +integrate(1/x^2, x = -1..1) --R --R --RDaly Bug @@ -2054,7 +2054,7 @@ integrate(sqrt(x + 1/x - 2), x = 0..2, "noPole") \subsection{Contour integrals} \begin{chunk}{*} --S 125 of 200 -integrate(cos(x)/(x**2 + a**2), x = %minusInfinity..%plusInfinity) +integrate(cos(x)/(x^2 + a^2), x = %minusInfinity..%plusInfinity) --R --R --R (123) potentialPole @@ -2062,7 +2062,7 @@ integrate(cos(x)/(x**2 + a**2), x = %minusInfinity..%plusInfinity) --E 125 --S 126 of 200 -integrate(cos(x)/(x**2 + a**2), x = %minusInfinity..%plusInfinity, "noPole") +integrate(cos(x)/(x^2 + a^2), x = %minusInfinity..%plusInfinity, "noPole") --R --R --R (124) "failed" @@ -2073,7 +2073,7 @@ integrate(cos(x)/(x**2 + a**2), x = %minusInfinity..%plusInfinity, "noPole") \subsection{Integrand with a branch point} \begin{chunk}{*} --S 127 of 200 -integrate(t**(a - 1)/(1 + t), t = 0..%plusInfinity) +integrate(t^(a - 1)/(1 + t), t = 0..%plusInfinity) --R --R --R (125) potentialPole @@ -2081,7 +2081,7 @@ integrate(t**(a - 1)/(1 + t), t = 0..%plusInfinity) --E 127 --S 128 of 200 -integrate(t**(a - 1)/(1 + t), t = 0..%plusInfinity, "noPole") +integrate(t^(a - 1)/(1 + t), t = 0..%plusInfinity, "noPole") --R --R --R (126) "failed" @@ -2108,7 +2108,7 @@ integrate(integrate(integrate(1, z = 0..c*(1 - x/a - y/b)), _ Taylor series---this first example comes from special relativity \begin{chunk}{*} --S 130 of 200 -1/sqrt(1 - (v/c)**2) +1/sqrt(1 - (v/c)^2) --R --R --R 1 @@ -2134,7 +2134,7 @@ series(%, v = 0) --E 131 --S 132 of 200 -1/%**2 +1/%^2 --R --R --R 1 2 8 @@ -2194,7 +2194,7 @@ Look at the Taylor series around $x = 1$ )set streams calculate 1 --S 137 of 200 -log(x)**a*exp(-b*x) +log(x)^a*exp(-b*x) --R --R --R - b x a @@ -2442,7 +2442,7 @@ y:= operator('y); --E 158 --S 159 of 200 -x**2 * D(y(x), x) + 3*x*y(x) = sin(x)/x +x^2 * D(y(x), x) + 3*x*y(x) = sin(x)/x --R --R --R 2 , sin(x) @@ -2466,7 +2466,7 @@ solve(%, y, x) \subsection{Nonlinear ODE} \begin{chunk}{*} --S 161 of 200 -D(y(x), x, 2) + y(x)*D(y(x), x)**3 = 0 +D(y(x), x, 2) + y(x)*D(y(x), x)^3 = 0 --R --R --R ,, , 3 @@ -2517,7 +2517,7 @@ This problem has nontrivial solutions $y(x) = A \sin([\pi/2 + n \pi] x)$ for $n$ an arbitrary integer. \begin{chunk}{*} --S 165 of 200 -solve(D(y(x), x, 2) + k**2*y(x) = 0, y, x) +solve(D(y(x), x, 2) + k^2*y(x) = 0, y, x) --R --R --R (157) [particular= 0,basis= [cos(k x),sin(k x)]] @@ -2673,7 +2673,7 @@ subst(L(subst(g(y), y = x)), x = y) --E 179 --S 180 of 200 -subst(L(subst(A * sin(z**2), z = x)), x = z) +subst(L(subst(A * sin(z^2), z = x)), x = z) --R --R --R 2 2 2 @@ -2685,9 +2685,9 @@ subst(L(subst(A * sin(z**2), z = x)), x = z) \subsection{Truncated Taylor series operator} \begin{chunk}{*} --S 181 of 200 -T:= (f, xx, a) +-> subst((DD**0)(f(x)), x = a)/factorial(0) * (xx - a)**0 + _ - subst((DD**1)(f(x)), x = a)/factorial(1) * (xx - a)**1 + _ - subst((DD**2)(f(x)), x = a)/factorial(2) * (xx - a)**2 +T:= (f, xx, a) +-> subst((DD^0)(f(x)), x = a)/factorial(0) * (xx - a)^0 + _ + subst((DD^1)(f(x)), x = a)/factorial(1) * (xx - a)^1 + _ + subst((DD^2)(f(x)), x = a)/factorial(2) * (xx - a)^2 --R --R --R (173) @@ -2761,7 +2761,7 @@ T(Sin, z, c) Write a simple program to compute Legendre polynomials \begin{chunk}{*} --S 187 of 200 -p(n, x) == 1/(2**n*factorial(n)) * D((x**2 - 1)**n, x, n) +p(n, x) == 1/(2^n*factorial(n)) * D((x^2 - 1)^n, x, n) --R --R Type: Void --E 187 @@ -2876,7 +2876,7 @@ a:= operator('a) --E 194 --S 195 of 200 -sum(a(i)*x**i, i = 1..5) +sum(a(i)*x^i, i = 1..5) --R --R --R 5 4 3 2 diff --git a/src/input/eigen.input.pamphlet b/src/input/eigen.input.pamphlet index 443ce63..c466ba8 100644 --- a/src/input/eigen.input.pamphlet +++ b/src/input/eigen.input.pamphlet @@ -59,7 +59,7 @@ characteristicPolynomial(m,x) \subsection{For matrix of polynomials} \begin{chunk}{*} --S 4 of 36 -p:=matrix([[x+1,2-x*y,x**2+1],[2-x,y+2*x,x**2-2],[y**2,x-2,4-x*y]]) +p:=matrix([[x+1,2-x*y,x^2+1],[2-x,y+2*x,x^2-2],[y^2,x-2,4-x*y]]) --R --R --R + 2 + @@ -226,7 +226,7 @@ eigenvectors m --E 14 --S 15 of 36 -q:=matrix [[x**2-y**2,(x-y)*(2*x+3*y)],[x+y,2*x+3*y]] +q:=matrix [[x^2-y^2,(x-y)*(2*x+3*y)],[x+y,2*x+3*y]] --R --R --R + 2 2 2 2+ @@ -342,7 +342,7 @@ generalizedEigenvector(ll.1,p)$EP(INT) These functions return respectively the complete set of generalized eigenvectors or the generalized eigenvectors associated to a particular eigenvalue alpha, -i.e. a basis of the nullSpace((p-alpha*I)**k) where k is the algebraic +i.e. a basis of the nullSpace((p-alpha*I)^k) where k is the algebraic multiplicity of alpha. In the case of symbolic eigenvalues it is possible to convert the symbolic diff --git a/src/input/elemfun.input.pamphlet b/src/input/elemfun.input.pamphlet index 70b63db..1500cad 100644 --- a/src/input/elemfun.input.pamphlet +++ b/src/input/elemfun.input.pamphlet @@ -76,7 +76,7 @@ simplify % The same goes with the usual relations \begin{chunk}{*} --S 7 of 28 -sin(3)**2 + cos(3)**2 +sin(3)^2 + cos(3)^2 --R --R --R 2 2 @@ -166,7 +166,7 @@ Given such a trig expression not involving any variables, we can get a numeric approximation \begin{chunk}{*} --S 17 of 28 -t := sin(7)**2 - sec(7)/(1 - cot(7) + csc(7)**3) +t := sin(7)^2 - sec(7)/(1 - cot(7) + csc(7)^3) --R --R --R 3 2 @@ -230,7 +230,7 @@ If we do have an expression involving variables, we can use eval to give them values \begin{chunk}{*} --S 22 of 28 -u := exp(sin(x-1)**2 - cos(x-1)/sec(x-1)) +u := exp(sin(x-1)^2 - cos(x-1)/sec(x-1)) --R --R --R 2 @@ -255,7 +255,7 @@ eval(u,x=1) Here is another technique using rewrite rules \begin{chunk}{*} --S 24 of 28 -v(x) == exp(sin(x-1)**2 - cos(x-1)/sec(x-1)) +v(x) == exp(sin(x-1)^2 - cos(x-1)/sec(x-1)) --R --R Type: Void --E 24 diff --git a/src/input/elfuts.input.pamphlet b/src/input/elfuts.input.pamphlet index de84dcd..4f1251f 100644 --- a/src/input/elfuts.input.pamphlet +++ b/src/input/elfuts.input.pamphlet @@ -144,7 +144,7 @@ dnn:=dn(yy,k::QF UP(k,RN)) --E 10 --S 11 of 40 -snn**2+cnn**2 +snn^2+cnn^2 --R --R --R 11 @@ -153,7 +153,7 @@ snn**2+cnn**2 --E 11 --S 12 of 40 -ksquared:=(k::UP(k,RN))**2 +ksquared:=(k::UP(k,RN))^2 --R --R --R 2 @@ -162,7 +162,7 @@ ksquared:=(k::UP(k,RN))**2 --E 12 --S 13 of 40 -dnn**2+ksquared*snn**2 +dnn^2+ksquared*snn^2 --R --R --R 11 @@ -171,7 +171,7 @@ dnn**2+ksquared*snn**2 --E 13 --S 14 of 40 -(differentiate snn)**2 +(differentiate snn)^2 --R --R --R (14) @@ -190,7 +190,7 @@ dnn**2+ksquared*snn**2 --E 14 --S 15 of 40 -(1-snn**2)*(1-ksquared*snn**2) +(1-snn^2)*(1-ksquared*snn^2) --R --R --R (15) @@ -209,7 +209,7 @@ dnn**2+ksquared*snn**2 --E 15 --S 16 of 40 -(differentiate cnn)**2 +(differentiate cnn)^2 --R --R --R (16) @@ -228,7 +228,7 @@ dnn**2+ksquared*snn**2 --E 16 --S 17 of 40 -(1-cnn**2)*(1-ksquared+ksquared*cnn**2) +(1-cnn^2)*(1-ksquared+ksquared*cnn^2) --R --R --R (17) @@ -247,7 +247,7 @@ dnn**2+ksquared*snn**2 --E 17 --S 18 of 40 -(differentiate dnn)**2 +(differentiate dnn)^2 --R --R --R (18) @@ -266,7 +266,7 @@ dnn**2+ksquared*snn**2 --E 18 --S 19 of 40 -(1-dnn**2)*(dnn**2-1+ksquared) +(1-dnn^2)*(dnn^2-1+ksquared) --R --R --R (19) @@ -285,7 +285,7 @@ dnn**2+ksquared*snn**2 --E 19 --S 20 of 40 -kkk:=integrate(1/((1-yy**2)*(1-ksquared*yy**2))**(1/2)) +kkk:=integrate(1/((1-yy^2)*(1-ksquared*yy^2))^(1/2)) --R --R --R (20) @@ -358,10 +358,10 @@ snn \end{chunk} Theta-functions expanded as power series \begin{chunk}{*} -q0=*/[1-q**2*n for n in 1..] -q1=*/[1+q**2*n for n in 1..] -q2=*/[1+q**(2*n-1) for n in 1..] -q3=*/[1-q**(2*n-1) for n in 1..] +q0=*/[1-q^2*n for n in 1..] +q1=*/[1+q^2*n for n in 1..] +q2=*/[1+q^(2*n-1) for n in 1..] +q3=*/[1-q^(2*n-1) for n in 1..] \begin{chunk}{*} --S 23 of 40 eprod x==exp evenlambert log x @@ -433,7 +433,7 @@ q1*q2*q3 --E 30 --S 31 of 40 -q2**8-q3**8 +q2^8-q3^8 --R --R --R 3 5 7 9 11 @@ -442,7 +442,7 @@ q2**8-q3**8 --E 31 --S 32 of 40 -16*qq*q1**8 +16*qq*q1^8 --R --R --R 3 5 7 9 11 @@ -450,11 +450,11 @@ q2**8-q3**8 --R Type: UnivariateTaylorSeries(Fraction(Integer),q,0) --E 32 ---(q1**2/q2**2)**2 ---(q3**2/q2**2)**2 +--(q1^2/q2^2)^2 +--(q3^2/q2^2)^2 --S 33 of 40 -q0**3 +q0^3 --R --R --R 2 6 11 @@ -463,7 +463,7 @@ q0**3 --E 33 --S 34 of 40 -q1**2*q0 +q1^2*q0 --R --R --R 2 6 11 @@ -472,7 +472,7 @@ q1**2*q0 --E 34 --S 35 of 40 -q2**2*q0 +q2^2*q0 --R --R --R 4 9 11 @@ -481,7 +481,7 @@ q2**2*q0 --E 35 --S 36 of 40 -q3**2*q0 +q3^2*q0 --R --R --R 4 9 11 @@ -529,7 +529,7 @@ eprod(1-qqq)*oprod(1-a*qqq)*oprod(1-qqq/a) --E 39 --S 40 of 40 -sq:=ksquared*snn**2 +sq:=ksquared*snn^2 --R --R --R (40) diff --git a/src/input/elt.input.pamphlet b/src/input/elt.input.pamphlet index a86777f..af2fcfe 100644 --- a/src/input/elt.input.pamphlet +++ b/src/input/elt.input.pamphlet @@ -43,7 +43,7 @@ u(3..5) := false; u )clear all --S 3 of 4 -u:Any := [1, 7.2, 3/2, x**2, "wally"] +u:Any := [1, 7.2, 3/2, x^2, "wally"] --R --R --R 3 2 diff --git a/src/input/eq.input.pamphlet b/src/input/eq.input.pamphlet index b719659..a3b48ac 100644 --- a/src/input/eq.input.pamphlet +++ b/src/input/eq.input.pamphlet @@ -82,7 +82,7 @@ eq1 * eq2 --E 7 --S 8 of 12 -eq1**2 +eq1^2 --R --R --R 2 2 diff --git a/src/input/equation.input.pamphlet b/src/input/equation.input.pamphlet index 3f73d54..4829fc8 100644 --- a/src/input/equation.input.pamphlet +++ b/src/input/equation.input.pamphlet @@ -50,7 +50,7 @@ is 0 and we have an IntegralDomain. \begin{chunk}{*} --S 1 of 12 -eq1 := (-6*x**3+13*x**2+4)=(-x**4+12*x) +eq1 := (-6*x^3+13*x^2+4)=(-x^4+12*x) --R --R --R 3 2 4 @@ -59,7 +59,7 @@ eq1 := (-6*x**3+13*x**2+4)=(-x**4+12*x) --E 1 --S 2 of 12 -eq2 := x**4+13*x**2-12*x = 6*x**3-4 +eq2 := x^4+13*x^2-12*x = 6*x^3-4 --R --R --R 4 2 3 @@ -68,7 +68,7 @@ eq2 := x**4+13*x**2-12*x = 6*x**3-4 --E 2 --S 3 of 12 -eq := eq1*y**2+eq2 +eq := eq1*y^2+eq2 --R --R --R 3 2 2 4 2 4 2 3 @@ -95,7 +95,7 @@ swap % --E 5 --S 6 of 12 -%-6*x**3 +%-6*x^3 --R --R --R 4 2 3 2 2 4 3 2 diff --git a/src/input/equation2.input.pamphlet b/src/input/equation2.input.pamphlet index f144282..edb08b1 100644 --- a/src/input/equation2.input.pamphlet +++ b/src/input/equation2.input.pamphlet @@ -22,7 +22,7 @@ )clear all --S 1 of 27 -solve([3*x**3 + y + 1,y - 1],[x,y]) +solve([3*x^3 + y + 1,y - 1],[x,y]) --R --R --R 3 @@ -31,7 +31,7 @@ solve([3*x**3 + y + 1,y - 1],[x,y]) --E 1 --S 2 of 27 -solve([x**3 + x - y**2 + 4,x*y + 2],[x,y],"sym") +solve([x^3 + x - y^2 + 4,x*y + 2],[x,y],"sym") --R --R There are 6 exposed and 1 unexposed library operations named solve --R having 3 argument(s) but none was determined to be applicable. @@ -53,7 +53,7 @@ solve([x**3 + x - y**2 + 4,x*y + 2],[x,y],"sym") --E 2 --S 3 of 27 -solve([x = y**2-19,y = z**2+x+3,z = 3*x],[x,y,z]) +solve([x = y^2-19,y = z^2+x+3,z = 3*x],[x,y,z]) --R --R --R 2 @@ -72,7 +72,7 @@ solve([3*x + 2*y - z,x - 1/2*y + 1/3*z,4/5*x - 2/3*y - z]) --E 4 --S 5 of 27 -solve([x**2*y - 1,x*y**2 - 2],[x,y],.01) +solve([x^2*y - 1,x*y^2 - 2],[x,y],.01) --R --R There are 6 exposed and 1 unexposed library operations named solve --R having 3 argument(s) but none was determined to be applicable. @@ -94,7 +94,7 @@ solve([x**2*y - 1,x*y**2 - 2],[x,y],.01) --E 5 --S 6 of 27 -solve([x**2/a = 1,a**2 - a*x = 0],[x,a],.001) +solve([x^2/a = 1,a^2 - a*x = 0],[x,a],.001) --R --R There are 6 exposed and 1 unexposed library operations named solve --R having 3 argument(s) but none was determined to be applicable. @@ -116,7 +116,7 @@ solve([x**2/a = 1,a**2 - a*x = 0],[x,a],.001) --E 6 --S 7 of 27 -solve([x**2/a + a + y**3 - 1,a*y + a + 1],[x,y]) +solve([x^2/a + a + y^3 - 1,a*y + a + 1],[x,y]) --R --R --R 2 2 4 3 2 - a - 1 @@ -128,7 +128,7 @@ solve([x**2/a + a + y**3 - 1,a*y + a + 1],[x,y]) )clear all --S 8 of 27 -solve(x**3 + 1 = 0,x) +solve(x^3 + 1 = 0,x) --R --R --R 2 @@ -137,7 +137,7 @@ solve(x**3 + 1 = 0,x) --E 8 --S 9 of 27 -solve(x**3*y + x*y + 1,x,"sym") +solve(x^3*y + x*y + 1,x,"sym") --R --R There are 6 exposed and 1 unexposed library operations named solve --R having 3 argument(s) but none was determined to be applicable. @@ -169,7 +169,7 @@ solve(3*x + 1/4*y = 1,x) --E 10 --S 11 of 27 -solve(x**4 - 10*x**3 + 35*x**2 - 50*x + 25,x,1/1000) +solve(x^4 - 10*x^3 + 35*x^2 - 50*x + 25,x,1/1000) --R --R There are 6 exposed and 1 unexposed library operations named solve --R having 3 argument(s) but none was determined to be applicable. @@ -191,7 +191,7 @@ solve(x**4 - 10*x**3 + 35*x**2 - 50*x + 25,x,1/1000) --E 11 --S 12 of 27 -solve(x**4 - 10*x**3 + 35*x**2 - 50*x + 25,x,"sym") +solve(x^4 - 10*x^3 + 35*x^2 - 50*x + 25,x,"sym") --R --R There are 6 exposed and 1 unexposed library operations named solve --R having 3 argument(s) but none was determined to be applicable. @@ -213,7 +213,7 @@ solve(x**4 - 10*x**3 + 35*x**2 - 50*x + 25,x,"sym") --E 12 --S 13 of 27 -solve(x**3 - sqrt(2)) +solve(x^3 - sqrt(2)) --R --R --R 3 +-+ @@ -222,7 +222,7 @@ solve(x**3 - sqrt(2)) --E 13 --S 14 of 27 -solve(x**3/a + x/a + 1,x) +solve(x^3/a + x/a + 1,x) --R --R --R 3 @@ -233,7 +233,7 @@ solve(x**3/a + x/a + 1,x) )clear all --S 15 of 27 -solve(1/x**3 + 1/x**2 + 1/x = 0,x,"sym") +solve(1/x^3 + 1/x^2 + 1/x = 0,x,"sym") --R --R There are 6 exposed and 1 unexposed library operations named solve --R having 3 argument(s) but none was determined to be applicable. @@ -255,7 +255,7 @@ solve(1/x**3 + 1/x**2 + 1/x = 0,x,"sym") --E 15 --S 16 of 27 -solve(x**3 + 1 = 0,x) +solve(x^3 + 1 = 0,x) --R --R --R 2 @@ -264,7 +264,7 @@ solve(x**3 + 1 = 0,x) --E 16 --S 17 of 27 -solve(x**3*y + x*y + 1,x,"sym") +solve(x^3*y + x*y + 1,x,"sym") --R --R There are 6 exposed and 1 unexposed library operations named solve --R having 3 argument(s) but none was determined to be applicable. @@ -296,7 +296,7 @@ solve(3*x + 1/4*y = 1,x) --E 18 --S 19 of 27 -solve(x**4 - 10*x**3 + 35*x**2 - 50*x + 25,x,1/1000) +solve(x^4 - 10*x^3 + 35*x^2 - 50*x + 25,x,1/1000) --R --R There are 6 exposed and 1 unexposed library operations named solve --R having 3 argument(s) but none was determined to be applicable. @@ -318,7 +318,7 @@ solve(x**4 - 10*x**3 + 35*x**2 - 50*x + 25,x,1/1000) --E 19 --S 20 of 27 -solve(x**4 - 10*x**3 + 35*x**2 - 50*x + 25,x,"sym") +solve(x^4 - 10*x^3 + 35*x^2 - 50*x + 25,x,"sym") --R --R There are 6 exposed and 1 unexposed library operations named solve --R having 3 argument(s) but none was determined to be applicable. @@ -340,7 +340,7 @@ solve(x**4 - 10*x**3 + 35*x**2 - 50*x + 25,x,"sym") --E 20 --S 21 of 27 -solve(x**3 - sqrt(2)) +solve(x^3 - sqrt(2)) --R --R --R 3 +-+ @@ -349,7 +349,7 @@ solve(x**3 - sqrt(2)) --E 21 --S 22 of 27 -solve(x**3/a + x/a + 1,x) +solve(x^3/a + x/a + 1,x) --R --R --R 3 @@ -358,7 +358,7 @@ solve(x**3/a + x/a + 1,x) --E 22 --S 23 of 27 -solve(1/x**3 + 1/x**2 + 1/x = 0,x,"sym") +solve(1/x^3 + 1/x^2 + 1/x = 0,x,"sym") --R --R There are 6 exposed and 1 unexposed library operations named solve --R having 3 argument(s) but none was determined to be applicable. diff --git a/src/input/eval.input.pamphlet b/src/input/eval.input.pamphlet index 1aa6127..da05c3c 100644 --- a/src/input/eval.input.pamphlet +++ b/src/input/eval.input.pamphlet @@ -38,7 +38,7 @@ f := operator 'f --E 1 --S 2 of 23 -a := f(x**2) +a := f(x^2) --R --R --R 2 diff --git a/src/input/exampleagcode.input.pamphlet b/src/input/exampleagcode.input.pamphlet index f765867..6ca150b 100644 --- a/src/input/exampleagcode.input.pamphlet +++ b/src/input/exampleagcode.input.pamphlet @@ -120,7 +120,7 @@ P1:= PAFFFF(K1,[X,Y,Z],BLQT) --E 3 --S 4 of 19 -C1:R1:=X**5 + Y**2*Z**3+Y*Z**4 +C1:R1:=X^5 + Y^2*Z^3+Y*Z^4 --R --R --R 5 2 3 4 @@ -173,7 +173,7 @@ definingPolynomial(a) --E 8 --S 9 of 19 -a**3 + a**2 + 1 +a^3 + a^2 + 1 --R --R --R (9) 0 diff --git a/src/input/exdiff.input.pamphlet b/src/input/exdiff.input.pamphlet index 52eff66..df1411b 100644 --- a/src/input/exdiff.input.pamphlet +++ b/src/input/exdiff.input.pamphlet @@ -22,7 +22,7 @@ )clear all --S 1 of 10 -differentiate(sin(x) * exp(x**2),x) +differentiate(sin(x) * exp(x^2),x) --R --R --R 2 2 @@ -35,7 +35,7 @@ differentiate(sin(x) * exp(x**2),x) )clear all --S 2 of 10 -differentiate(sin(x) * tan(y)/(x**2 + y**2),x) +differentiate(sin(x) * tan(y)/(x^2 + y^2),x) --R --R --R 2 2 @@ -47,7 +47,7 @@ differentiate(sin(x) * tan(y)/(x**2 + y**2),x) --E 2 --S 3 of 10 -differentiate(sin(x) * tan(y)/(x**2 + y**2),y) +differentiate(sin(x) * tan(y)/(x^2 + y^2),y) --R --R --R 2 2 2 2 2 @@ -62,7 +62,7 @@ differentiate(sin(x) * tan(y)/(x**2 + y**2),y) )clear all --S 4 of 10 -differentiate(sin(x)/(x**2 + y**2),[x,y]) +differentiate(sin(x)/(x^2 + y^2),[x,y]) --R --R --R 3 2 @@ -74,7 +74,7 @@ differentiate(sin(x)/(x**2 + y**2),[x,y]) --E 4 --S 5 of 10 -differentiate(sin(x)/(x**2 + y**2),[x,y,y]) +differentiate(sin(x)/(x^2 + y^2),[x,y,y]) --R --R --R 2 3 4 2 2 4 @@ -90,7 +90,7 @@ differentiate(sin(x)/(x**2 + y**2),[x,y,y]) )clear all --S 6 of 10 -differentiate(cos(z)/(x**2 + y**3),[x,y,z],[1,2,3]) +differentiate(cos(z)/(x^2 + y^3),[x,y,z],[1,2,3]) --R --R --R 4 3 @@ -105,7 +105,7 @@ differentiate(cos(z)/(x**2 + y**3),[x,y,z],[1,2,3]) )clear all --S 7 of 10 -differentiate(exp(x**2),x,4) +differentiate(exp(x^2),x,4) --R --R --R 2 @@ -118,7 +118,7 @@ differentiate(exp(x**2),x,4) )clear all --S 8 of 10 -f := integrate(sqrt(1 + t**3),t) +f := integrate(sqrt(1 + t^3),t) --R --R --R t +-------+ @@ -139,7 +139,7 @@ differentiate(f,t) --E 9 --S 10 of 10 -differentiate(f * t**2,t) +differentiate(f * t^2,t) --R --R --R t +-------+ +------+ diff --git a/src/input/exint.input.pamphlet b/src/input/exint.input.pamphlet index 91a20b5..f4085ce 100644 --- a/src/input/exint.input.pamphlet +++ b/src/input/exint.input.pamphlet @@ -22,7 +22,7 @@ )clear all --S 1 of 10 -integrate(1/(x**2 + a),x) +integrate(1/(x^2 + a),x) --R --R --R 2 +---+ @@ -39,7 +39,7 @@ integrate(1/(x**2 + a),x) )clear all --S 2 of 10 -integrate((x**2+2*x+1)/((x+1)**6+1),x) +integrate((x^2+2*x+1)/((x+1)^6+1),x) --R --R --R 3 2 @@ -66,7 +66,7 @@ integrate(tan(atan(x)/3),x) )clear all --S 4 of 10 -complexIntegrate(1/(x**2 + a),x) +complexIntegrate(1/(x^2 + a),x) --R --R --R +---+ +---+ +---+ +---+ @@ -94,7 +94,7 @@ integrate(log(1 + sqrt(a*x + b)) / x,x) )clear all --S 6 of 10 -integrate(x**3 / (a+b*x)**(1/3),x) +integrate(x^3 / (a+b*x)^(1/3),x) --R --R --R 3 3 2 2 2 3 3+-------+2 @@ -106,7 +106,7 @@ integrate(x**3 / (a+b*x)**(1/3),x) --E 6 --S 7 of 10 -integrate(1 / (x**3 * (a+b*x)**(1/3)),x) +integrate(1 / (x^3 * (a+b*x)^(1/3)),x) --R --R --R (2) @@ -129,7 +129,7 @@ integrate(1 / (x**3 * (a+b*x)**(1/3)),x) )clear all --S 8 of 10 -integrate((x + 1) / (x * (x + log x)**(3/2)),x) +integrate((x + 1) / (x * (x + log x)^(3/2)),x) --R --R --R +----------+ @@ -142,7 +142,7 @@ integrate((x + 1) / (x * (x + log x)**(3/2)),x) )clear all --S 9 of 10 -integrate(exp(-x**2) * erf(x) / (erf(x)**3 - erf(x)**2 - erf(x) + 1),x) +integrate(exp(-x^2) * erf(x) / (erf(x)^3 - erf(x)^2 - erf(x) + 1),x) --R --R --R +---+ erf(x) - 1 +---+ diff --git a/src/input/exlap.input.pamphlet b/src/input/exlap.input.pamphlet index 9d28435..0ffb1cf 100644 --- a/src/input/exlap.input.pamphlet +++ b/src/input/exlap.input.pamphlet @@ -83,7 +83,7 @@ laplace(sin(a*t) * cosh(a*t) - cos(a*t) * sinh(a*t), t, s) )clear all --S 6 of 6 -laplace(t**4 * exp(-a*t) / factorial(4), t, s) +laplace(t^4 * exp(-a*t) / factorial(4), t, s) --R --R --R 1 diff --git a/src/input/exlimit.input.pamphlet b/src/input/exlimit.input.pamphlet index 5a9deca..26202b2 100644 --- a/src/input/exlimit.input.pamphlet +++ b/src/input/exlimit.input.pamphlet @@ -22,7 +22,7 @@ )clear all --S 1 of 13 -limit((x**2 - 3*x + 2)/(x**2 - 1),x = 1) +limit((x^2 - 3*x + 2)/(x^2 - 1),x = 1) --R --R --R 1 @@ -78,7 +78,7 @@ limit(x * log(x),x = 0) )clear all --S 7 of 13 -limit(sqrt(y**2)/y,y = 0) +limit(sqrt(y^2)/y,y = 0) --R --R --R (1) [leftHandLimit= - 1,rightHandLimit= 1] @@ -99,7 +99,7 @@ limit(sqrt(1 - cos(t))/t,t = 0) )clear all --S 9 of 13 -limit(sqrt(3*x**2 + 1)/(5*x),x = %plusInfinity) +limit(sqrt(3*x^2 + 1)/(5*x),x = %plusInfinity) --R --R --R +-+ @@ -110,7 +110,7 @@ limit(sqrt(3*x**2 + 1)/(5*x),x = %plusInfinity) --E 9 --S 10 of 13 -limit(sqrt(3*x**2 + 1)/(5*x),x = %minusInfinity) +limit(sqrt(3*x^2 + 1)/(5*x),x = %minusInfinity) --R --R --R +-+ diff --git a/src/input/expexpan.input.pamphlet b/src/input/expexpan.input.pamphlet index 3338da1..4353392 100644 --- a/src/input/expexpan.input.pamphlet +++ b/src/input/expexpan.input.pamphlet @@ -32,7 +32,7 @@ xxp f == exprToXXP(f,true)$FS2EXPXP(INT,EXPR INT,x,0) --E 1 --S 2 of 18 -f1 := (a**2 + 1) * exp(1/x**3 + 2/x**2) - exp(b) * exp(1/x**3 + 3/x**2) +f1 := (a^2 + 1) * exp(1/x^3 + 2/x^2) - exp(b) * exp(1/x^3 + 3/x^2) --R --R --R 3x + 1 2x + 1 @@ -65,7 +65,7 @@ limitPlus x1 -- %minusInfinity --E 4 --S 5 of 18 -f2 := (a**2 + 1) * exp(1/x**3 + 2/x**2) - exp(b) * exp(-1/x**3 + 3/x**2) +f2 := (a^2 + 1) * exp(1/x^3 + 2/x^2) - exp(b) * exp(-1/x^3 + 3/x^2) --R --R --R 3x - 1 2x + 1 @@ -95,7 +95,7 @@ limitPlus x2 -- %plusInfinity --E 7 --S 8 of 18 -f3 := (a**2 + 1) * exp(1/x**3) - exp(b) * exp(c/x**2) +f3 := (a^2 + 1) * exp(1/x^3) - exp(b) * exp(c/x^2) --R --R --R c 1 @@ -125,7 +125,7 @@ limitPlus x3 -- %plusInfinity --E 10 --S 11 of 18 -f4 := (a**2 + 1) * exp(-1/x**3) - exp(b) * exp(c/x**2) +f4 := (a^2 + 1) * exp(-1/x^3) - exp(b) * exp(c/x^2) --R --R --R c 1 @@ -155,7 +155,7 @@ limitPlus x4 -- "failed" --E 13 --S 14 of 18 -p5 := tan(x) * exp(1/x**2) - tan(x) * exp(1/x**2 - 1/x) + sin(x) * exp(1/x) +p5 := tan(x) * exp(1/x^2) - tan(x) * exp(1/x^2 - 1/x) + sin(x) * exp(1/x) --R --R --R 1 - x + 1 @@ -167,7 +167,7 @@ p5 := tan(x) * exp(1/x**2) - tan(x) * exp(1/x**2 - 1/x) + sin(x) * exp(1/x) --E 14 --S 15 of 18 -q5 := -4 * exp(-1/x**2 - 1/x) + sin(x) * exp(-1/x**2 + 1/x) +q5 := -4 * exp(-1/x^2 - 1/x) + sin(x) * exp(-1/x^2 + 1/x) --R --R --R x - 1 - x - 1 diff --git a/src/input/explim.input.pamphlet b/src/input/explim.input.pamphlet index a7a7cdb..fa53d2a 100644 --- a/src/input/explim.input.pamphlet +++ b/src/input/explim.input.pamphlet @@ -36,7 +36,7 @@ limit(x/exp(x),x = %plusInfinity) -- 0 --E 1 --S 2 of 12 -limit(x**10000/exp(x),x = %plusInfinity) -- 0 +limit(x^10000/exp(x),x = %plusInfinity) -- 0 --R --R --R (2) 0 @@ -44,7 +44,7 @@ limit(x**10000/exp(x),x = %plusInfinity) -- 0 --E 2 --S 3 of 12 -limit(x**(10**20)/exp(x),x = %plusInfinity) -- 0 +limit(x^(10^20)/exp(x),x = %plusInfinity) -- 0 --R --R --R (3) 0 @@ -52,7 +52,7 @@ limit(x**(10**20)/exp(x),x = %plusInfinity) -- 0 --E 3 --S 4 of 12 -limit(x**h/exp(x),x = %plusInfinity) -- 0 +limit(x^h/exp(x),x = %plusInfinity) -- 0 --R --R --R (4) 0 @@ -68,7 +68,7 @@ limit(x/exp(x),x = %minusInfinity) -- %minusInfinity --E 5 --S 6 of 12 -limit(x**10000/exp(x),x = %minusInfinity) -- %plusInfinity +limit(x^10000/exp(x),x = %minusInfinity) -- %plusInfinity --R --R --R (6) + infinity @@ -76,7 +76,7 @@ limit(x**10000/exp(x),x = %minusInfinity) -- %plusInfinity --E 6 --S 7 of 12 -limit(x**(10**20)/exp(x),x = %minusInfinity) -- %plusInfinity +limit(x^(10^20)/exp(x),x = %minusInfinity) -- %plusInfinity --R --R --R (7) + infinity @@ -84,7 +84,7 @@ limit(x**(10**20)/exp(x),x = %minusInfinity) -- %plusInfinity --E 7 --S 8 of 12 -limit(x**h/exp(x),x = %minusInfinity) -- "failed" +limit(x^h/exp(x),x = %minusInfinity) -- "failed" --R --R --R (8) "failed" @@ -120,7 +120,7 @@ limit(exp(-x) * exp(x),x = %plusInfinity) -- 1 --E 11 --S 12 of 12 -limit((x + 1)**(x + 1)/x**x - x**x/(x - 1)**(x - 1),x = %plusInfinity) -- %e +limit((x + 1)^(x + 1)/x^x - x^x/(x - 1)^(x - 1),x = %plusInfinity) -- %e --R --R --R (12) %e diff --git a/src/input/explot2d.input.pamphlet b/src/input/explot2d.input.pamphlet index d5a4e69..c08dd67 100644 --- a/src/input/explot2d.input.pamphlet +++ b/src/input/explot2d.input.pamphlet @@ -20,7 +20,7 @@ draw(sin(4*t/7),t = 0..14*%pi,coordinates == polar) -- Input for page ExPlot2DAlgebraic )clear all -draw(solution(y**2 + y - (x**3 - x) = 0),x,y,clip == (-2..2,-2..1)) +draw(solution(y^2 + y - (x^3 - x) = 0),x,y,clip == (-2..2,-2..1)) -- Input for page ExPlot2DFunctions )clear all diff --git a/src/input/explot3d.input.pamphlet b/src/input/explot3d.input.pamphlet index 3f6b6d8..87a5002 100644 --- a/src/input/explot3d.input.pamphlet +++ b/src/input/explot3d.input.pamphlet @@ -16,7 +16,7 @@ )clear all draw(curve(cos(t),sin(t),t),t=0..6) -draw(curve(t,t**2,t**3),t=-3..3) +draw(curve(t,t^2,t^3),t=-3..3) -- Input for page ExPlot3DParametricSurface )clear all diff --git a/src/input/expr.input.pamphlet b/src/input/expr.input.pamphlet index 80e6ae5..0814522 100644 --- a/src/input/expr.input.pamphlet +++ b/src/input/expr.input.pamphlet @@ -46,7 +46,7 @@ g := foo x --E 3 --S 4 of 29 -eval(g, x = x**2 + 1) +eval(g, x = x^2 + 1) --R --R --R 2 @@ -102,7 +102,7 @@ eval(f, [x = y, y = x]) The multivariate chain rule \begin{chunk}{*} --S 9 of 29 -ff := eval(f, [x = x**2 * foo y, y = x + y]) +ff := eval(f, [x = x^2 * foo y, y = x + y]) --R --R --R 2 @@ -250,7 +250,7 @@ derivative(bar, [bar1, bar2]$(LIST(LIST(EXPR INT) -> EXPR INT))) Some structural testing \begin{chunk}{*} --S 23 of 29 -h := inv(x + f + g**2) +h := inv(x + f + g^2) --R --R --R 1 @@ -270,7 +270,7 @@ isPower h --E 24 --S 25 of 29 -y * g**2 * h +y * g^2 * h --R --R --R 2 @@ -302,7 +302,7 @@ isPlus(denom(h)::EXPR(INT)) --E 27 --S 28 of 29 -isExpt(inv(g**2), "foo") +isExpt(inv(g^2), "foo") --R --R --R (27) [var= foo(x),exponent= - 2] @@ -310,7 +310,7 @@ isExpt(inv(g**2), "foo") --E 28 --S 29 of 29 -isExpt(inv(g**2), "bar") +isExpt(inv(g^2), "bar") --R --R --R (28) "failed" diff --git a/src/input/expr1.input.pamphlet b/src/input/expr1.input.pamphlet index b05a48f..50ba204 100644 --- a/src/input/expr1.input.pamphlet +++ b/src/input/expr1.input.pamphlet @@ -22,7 +22,7 @@ )clear all --S 1 of 23 -sin(x) + 3*cos(x)**2 +sin(x) + 3*cos(x)^2 --R --R --R 2 @@ -39,7 +39,7 @@ tan(x) - 3.45*x --E 2 --S 3 of 23 -(tan sqrt 7 - sin sqrt 11)**2 / (4 - cos(x - y)) +(tan sqrt 7 - sin sqrt 11)^2 / (4 - cos(x - y)) --R --R --R +-+ 2 +--+ +-+ +--+ 2 @@ -95,7 +95,7 @@ height mainKernel sin(x + 4) --E 8 --S 9 of 23 -e := (sin(x) - 4)**2 / ( 1 - 2*y*sqrt(- y) ) +e := (sin(x) - 4)^2 / ( 1 - 2*y*sqrt(- y) ) --R --R --R 2 @@ -175,7 +175,7 @@ numeric(tan 3.8) --E 15 --S 16 of 23 -e2 := cos(x**2 - y + 3) +e2 := cos(x^2 - y + 3) --R --R --R 2 @@ -230,7 +230,7 @@ cos(%pi / 4) --E 21 --S 22 of 23 -tan(x)**6 + 3*tan(x)**4 + 3*tan(x)**2 + 1 +tan(x)^6 + 3*tan(x)^4 + 3*tan(x)^2 + 1 --R --R --R 6 4 2 diff --git a/src/input/exprode.input.pamphlet b/src/input/exprode.input.pamphlet index 024227f..eb5e96e 100644 --- a/src/input/exprode.input.pamphlet +++ b/src/input/exprode.input.pamphlet @@ -126,7 +126,7 @@ x := operator 'x --E 7 --S 8 of 13 -eq1 := differentiate(x t, t) = 1 + x(t)**2 +eq1 := differentiate(x t, t) = 1 + x(t)^2 --R --R --R , 2 diff --git a/src/input/exprpoly.input.pamphlet b/src/input/exprpoly.input.pamphlet index 16eda49..12945c6 100644 --- a/src/input/exprpoly.input.pamphlet +++ b/src/input/exprpoly.input.pamphlet @@ -29,7 +29,7 @@ polynomial types and back. Start with a simple expression involving variables \begin{chunk}{*} --S 1 of 20 -a := sin(i)*x**2 - y*x*sin(j) +a := sin(i)*x^2 - y*x*sin(j) --R --R --R 2 @@ -159,7 +159,7 @@ We needn't have had such a complicated expression. The following is really just a multivariate polynomial. \begin{chunk}{*} --S 14 of 20 -b : EXPR INT := (x - 2*y + 3*z)**3 +b : EXPR INT := (x - 2*y + 3*z)^3 --R --R --R (14) diff --git a/src/input/exseries.input.pamphlet b/src/input/exseries.input.pamphlet index b107e60..1bc435a 100644 --- a/src/input/exseries.input.pamphlet +++ b/src/input/exseries.input.pamphlet @@ -143,7 +143,7 @@ f := series(1/(1-x),x = 0) --E 8 --S 9 of 9 -f ** 2 +f ^ 2 --R --R --R (2) diff --git a/src/input/exsum.input.pamphlet b/src/input/exsum.input.pamphlet index c47b5a8..f7bcdd1 100644 --- a/src/input/exsum.input.pamphlet +++ b/src/input/exsum.input.pamphlet @@ -22,7 +22,7 @@ )clear all --S 1 of 13 -sum(k * x**k,k = 1..n) +sum(k * x^k,k = 1..n) --R --R --R 2 n @@ -48,7 +48,7 @@ limit( sum(1/(k * (k + 2)),k = 1..n) ,n = %plusInfinity) )clear all --S 3 of 13 -s := sum(k**2,k = a..b) +s := sum(k^2,k = a..b) --R --R --R 3 2 3 2 @@ -67,7 +67,7 @@ eval(s,[a,b],[1,25]) --E 4 --S 5 of 13 -reduce(+,[i**2 for i in 1..25]) +reduce(+,[i^2 for i in 1..25]) --R --R --R (3) 5525 @@ -77,7 +77,7 @@ reduce(+,[i**2 for i in 1..25]) )clear all --S 6 of 13 -sum(3*k**2/(c**2 + 1) + 12*k/d,k = (3*a)..(4*b)) +sum(3*k^2/(c^2 + 1) + 12*k/d,k = (3*a)..(4*b)) --R --R --R (1) @@ -123,7 +123,7 @@ reduce(+,[1.0/factorial(n) for n in 0..20]) )clear all --S 10 of 13 -[n**2 for n in 5..20] +[n^2 for n in 5..20] --R --R --R (1) [25,36,49,64,81,100,121,144,169,196,225,256,289,324,361,400] @@ -131,7 +131,7 @@ reduce(+,[1.0/factorial(n) for n in 0..20]) --E 10 --S 11 of 13 -reduce(+,[n**2 for n in 5..20]) +reduce(+,[n^2 for n in 5..20]) --R --R --R (2) 2840 @@ -141,7 +141,7 @@ reduce(+,[n**2 for n in 5..20]) )clear all --S 12 of 13 -sum(k**3,k = 1..n) +sum(k^3,k = 1..n) --R --R --R 4 3 2 @@ -152,7 +152,7 @@ sum(k**3,k = 1..n) --E 12 --S 13 of 13 -sum(k,k = 1..n) ** 2 +sum(k,k = 1..n) ^ 2 --R --R --R 4 3 2 diff --git a/src/input/f04qaf.input.pamphlet b/src/input/f04qaf.input.pamphlet index 2745f3e..e98f251 100644 --- a/src/input/f04qaf.input.pamphlet +++ b/src/input/f04qaf.input.pamphlet @@ -23,7 +23,7 @@ showScalarValues true n := 12 m := 13 h:SF := 0.1 -b :Matrix SF:= -h**2 * [[0],[0],[0],[1],[1],[0],[0],[1],[1],[0],[0],[0],[-h**-3]] +b :Matrix SF:= -h^2 * [[0],[0],[0],[1],[1],[0],[0],[1],[1],[0],[0],[0],[-h^-3]] 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],_ diff --git a/src/input/ffdemo.input.pamphlet b/src/input/ffdemo.input.pamphlet index 9d2877a..fc29e89 100644 --- a/src/input/ffdemo.input.pamphlet +++ b/src/input/ffdemo.input.pamphlet @@ -110,7 +110,7 @@ a/b --E 9 --S 10 of 350 -a**1234 +a^1234 --R --R --R (10) 2068 @@ -118,7 +118,7 @@ a**1234 --E 10 --S 11 of 350 -a**(-1) +a^(-1) --R --R --R (11) 2407 @@ -172,7 +172,7 @@ discreteLog(a) The next one should equal 0 \begin{chunk}{*} --S 17 of 350 -g**% - a +g^% - a --R --R --R (17) 0 @@ -397,7 +397,7 @@ a/b --E 39 --S 40 of 350 -a**1234 +a^1234 --R --R --R 5 4 3 @@ -406,7 +406,7 @@ a**1234 --E 40 --S 41 of 350 -a**(-1) +a^(-1) --R --R --R (41) %A + 6 @@ -460,7 +460,7 @@ discreteLog(a) The next one should equal 0 \begin{chunk}{*} --S 47 of 350 -g**% - a +g^% - a --R --R --R (47) 0 @@ -678,7 +678,7 @@ a/b --E 66 --S 67 of 350 -a**1234 +a^1234 --R --R --R 5 4 3 2 @@ -688,7 +688,7 @@ a**1234 --E 67 --S 68 of 350 -a**(-1) +a^(-1) --R --R --R 5 4 3 2 @@ -746,7 +746,7 @@ discreteLog(a) The next one should equal 0 \begin{chunk}{*} --S 74 of 350 -g**% - a +g^% - a --R --R --R (74) 0 @@ -998,7 +998,7 @@ a/b --E 96 --S 97 of 350 -a**1234 +a^1234 --R --R --R 222 @@ -1007,7 +1007,7 @@ a**1234 --E 97 --S 98 of 350 -a**(-1) +a^(-1) --R --R --R 417 @@ -1064,7 +1064,7 @@ discreteLog(a) The next one should equal 0 \begin{chunk}{*} --S 104 of 350 -g**% - a +g^% - a --R --R --R (104) 0 @@ -1332,7 +1332,7 @@ a/b --E 129 --S 130 of 350 -a**1234 +a^1234 --R --R --R 2 @@ -1341,7 +1341,7 @@ a**1234 --E 130 --S 131 of 350 -a**(-1) +a^(-1) --R --R --R 2 @@ -1396,7 +1396,7 @@ discreteLog(a) The next one should equal 0 \begin{chunk}{*} --S 137 of 350 -g**% - a +g^% - a --R --R --R (137) 0 @@ -1621,7 +1621,7 @@ a/b --E 158 --S 159 of 350 -a**1234 +a^1234 --R --R --R q 2 q @@ -1630,7 +1630,7 @@ a**1234 --E 159 --S 160 of 350 -a**(-1) +a^(-1) --R --R --R q 2 q @@ -1685,7 +1685,7 @@ discreteLog(a) The next one should equal 0 \begin{chunk}{*} --S 166 of 350 -g**% - a +g^% - a --R --R --R (166) 0 @@ -1913,7 +1913,7 @@ a/b --E 187 --S 188 of 350 -a**1234 +a^1234 --R --R --R 5 2 7 @@ -1922,7 +1922,7 @@ a**1234 --E 188 --S 189 of 350 -a**(-1) +a^(-1) --R --R --R 4 2 1 4 @@ -1977,7 +1977,7 @@ discreteLog(a) The next one should equal 0 \begin{chunk}{*} --S 195 of 350 -g**% - a +g^% - a --R --R --R (195) 0 @@ -2209,7 +2209,7 @@ a/b --E 216 --S 217 of 350 -a**1234 +a^1234 --R --R --R q @@ -2218,7 +2218,7 @@ a**1234 --E 217 --S 218 of 350 -a**(-1) +a^(-1) --R --R --R q @@ -2274,7 +2274,7 @@ discreteLog(a) The next one should equal 0 \begin{chunk}{*} --S 224 of 350 -g**% - a +g^% - a --R --R --R (224) 0 @@ -2508,7 +2508,7 @@ a/b --E 245 --S 246 of 350 -a**1234 +a^1234 --R --R --R q q q @@ -2517,7 +2517,7 @@ a**1234 --E 246 --S 247 of 350 -a**(-1) +a^(-1) --R --R --R q @@ -2573,7 +2573,7 @@ discreteLog(a) The next one should equal 0 \begin{chunk}{*} --S 253 of 350 -g**% - a +g^% - a --R --R --R (253) 0 @@ -2809,7 +2809,7 @@ a/b --E 274 --S 275 of 350 -a**1234 +a^1234 --R --R --R q 4 @@ -2818,7 +2818,7 @@ a**1234 --E 275 --S 276 of 350 -a**(-1) +a^(-1) --R --R --R 6 q 2 @@ -2874,7 +2874,7 @@ discreteLog(a) The next one should equal 0 \begin{chunk}{*} --S 282 of 350 -g**% - a +g^% - a --R --R --R (282) 0 @@ -3503,7 +3503,7 @@ discreteLog(ac) \subsection{Exponentiation} \begin{chunk}{*} --S 345 of 350 -ap**1234567 +ap^1234567 --R --R --R 4 2 @@ -3512,7 +3512,7 @@ ap**1234567 --E 345 --S 346 of 350 -an**1234567 +an^1234567 --R --R --R 4 2 @@ -3522,7 +3522,7 @@ an**1234567 --E 346 --S 347 of 350 -ac**1234567 +ac^1234567 --R --R --R 16 diff --git a/src/input/ffieldbug.input.pamphlet b/src/input/ffieldbug.input.pamphlet index e0d1e47..2ef6834 100644 --- a/src/input/ffieldbug.input.pamphlet +++ b/src/input/ffieldbug.input.pamphlet @@ -26,7 +26,7 @@ gf2 := PrimeField 2 --E 1 --S 2 of 29 -gf16 := FiniteFieldExtensionByPolynomial(gf2,x**4+x+1) +gf16 := FiniteFieldExtensionByPolynomial(gf2,x^4+x+1) --R --R --R (2) FiniteFieldExtensionByPolynomial(PrimeField(2),?^4+?+1) @@ -42,7 +42,7 @@ a:=primitiveElement()$gf16 --E 3 --S 4 of 29 -p:POLY gf16:=a*x**3 +p:POLY gf16:=a*x^3 --R --R --R 3 @@ -51,7 +51,7 @@ p:POLY gf16:=a*x**3 --E 4 --S 5 of 29 -q:POLY gf16:=a*x**2+1 +q:POLY gf16:=a*x^2+1 --R --R --R 2 @@ -98,7 +98,7 @@ a:=primitiveElement()$gf16 --E 9 --S 10 of 29 -p:POLY gf16:=a*x**3 +p:POLY gf16:=a*x^3 --R --R --R 3 @@ -107,7 +107,7 @@ p:POLY gf16:=a*x**3 --E 10 --S 11 of 29 -q:POLY gf16:=a*x**2+1 +q:POLY gf16:=a*x^2+1 --R --R --R 2 @@ -154,7 +154,7 @@ a:=primitiveElement()$gf16 --E 15 --S 16 of 29 -p:POLY gf16:=a*x**3 +p:POLY gf16:=a*x^3 --R --R --R 3 @@ -163,7 +163,7 @@ p:POLY gf16:=a*x**3 --E 16 --S 17 of 29 -q:POLY gf16:=a*x**2+1 +q:POLY gf16:=a*x^2+1 --R --R --R 2 @@ -211,7 +211,7 @@ gf2:=PrimeField 2 --E 19 --S 20 of 29 -gf16:=FiniteFieldExtensionByPolynomial(gf2,x**4+x+1) +gf16:=FiniteFieldExtensionByPolynomial(gf2,x^4+x+1) --R --R --R (2) FiniteFieldExtensionByPolynomial(PrimeField(2),?^4+?+1) diff --git a/src/input/ffx72.input.pamphlet b/src/input/ffx72.input.pamphlet index 5329a68..655ade5 100644 --- a/src/input/ffx72.input.pamphlet +++ b/src/input/ffx72.input.pamphlet @@ -40,7 +40,7 @@ gf72 := FF(7, 2) $x^2+1$ is irreducible over PF 7 \begin{chunk}{*} --S 2 of 13 -u: UP(x,PF 7) := x**2 + 1 +u: UP(x,PF 7) := x^2 + 1 --R --R --R 2 @@ -79,7 +79,7 @@ factor u2 \end{chunk} The following is the irreducible polynomial used in the representation -of GF(7**2) over PF 7. It will be the same every time this field is +of GF(7^2) over PF 7. It will be the same every time this field is used. \begin{chunk}{*} --S 6 of 13 diff --git a/src/input/fixed.input.pamphlet b/src/input/fixed.input.pamphlet index 34816b6..a5619e1 100644 --- a/src/input/fixed.input.pamphlet +++ b/src/input/fixed.input.pamphlet @@ -122,7 +122,7 @@ as a constant )clear all --S 7 of 267 -f:=(a-b-c-d)**2::EXPR INT +f:=(a-b-c-d)^2::EXPR INT --R --R 2 2 2 2 --R (1) d + (2c + 2b - 2a)d + c + (2b - 2a)c + b - 2a b + a @@ -148,7 +148,7 @@ degree t1 bmt/10/26/92 wrong answer I believe this problem simplifies to -{\tt lfintegrate(sqrt(u**3+u**2),u)} which returns the +{\tt lfintegrate(sqrt(u^3+u^2),u)} which returns the wrong answer due to some confusion in prootintegrate in {\tt INTPAF}. I think the confusion happens with the use of radPoly and rootPoly. The answer is computed with respect to the result returned by rootPoly @@ -176,7 +176,7 @@ gives: Cannot convert kernel to gaussian function )clear all --S 11 of 267 -integrate(exp(x**2),x) +integrate(exp(x^2),x) --R --R x 2 --I ++ %K @@ -202,7 +202,7 @@ Do you agree, thus max/ empty list would return 0. )clear all --S 12 of 267 -f:=log(1-(b*x/(a+c*x**2)))/x +f:=log(1-(b*x/(a+c*x^2)))/x --R --R 2 --R c x - b x + a @@ -384,7 +384,7 @@ m*m --E 25 --S 26 of 267 -m**2 +m^2 --R --R + + 2 ++ --R |+2a + 1 2b + 2 + |2b + 2a + 4 b + 3b + 2a || @@ -400,7 +400,7 @@ m**2 --E 26 --S 27 of 267 -m**3 +m^3 --R --R +matrix1 matrix2+ --R (9) | | @@ -527,7 +527,7 @@ Johannes \begin{chunk}{*} )clear all --S 31 of 267 -eq1 := (-6*x**3+13*x**2+4)=(-x**4+12*x) +eq1 := (-6*x^3+13*x^2+4)=(-x^4+12*x) --R --R 3 2 4 --R (1) - 6x + 13x + 4= - x + 12x @@ -535,7 +535,7 @@ eq1 := (-6*x**3+13*x**2+4)=(-x**4+12*x) --E 31 --S 32 of 267 -eq2 := x**4+13*x**2-12*x = 6*x**3-4 +eq2 := x^4+13*x^2-12*x = 6*x^3-4 --R --R 4 2 3 --R (2) x + 13x - 12x= 6x - 4 @@ -543,7 +543,7 @@ eq2 := x**4+13*x**2-12*x = 6*x**3-4 --E 32 --S 33 of 267 -eq := eq1*y**2+eq2 +eq := eq1*y^2+eq2 --R --R 3 2 2 4 2 4 2 3 --R (3) (- 6x + 13x + 4)y + x + 13x - 12x= (- x + 12x)y + 6x - 4 @@ -567,7 +567,7 @@ t2:=t1 + 4 --E 35 --S 36 of 267 -t3:=t2-6*x**3 +t3:=t2-6*x^3 --R --R 4 2 3 2 2 4 3 2 --R (6) (- x + 12x)y = (- 6x + 13x + 4)y + x - 6x + 13x - 12x + 4 @@ -657,7 +657,7 @@ properly declared despite the error message. --Tim --E 43 --S 44 of 267 -p1:=3*x**4+11*x**2-4 +p1:=3*x^4+11*x^2-4 --R --R 4 2 --R (2) 3x + 11x - 4 @@ -665,7 +665,7 @@ p1:=3*x**4+11*x**2-4 --E 44 --S 45 of 267 -p2:=9*x**4+9*x**2-4 +p2:=9*x^4+9*x^2-4 --R --R 4 2 --R (3) 9x + 9x - 4 @@ -701,7 +701,7 @@ dewar/10/02/92 actually, this was never wrong )clear all --S 49 of 267 -numeric(%e ** %pi) +numeric(%e ^ %pi) --R --R (1) 23.1406926327 79269006 --R Type: Float @@ -825,7 +825,7 @@ y:=operator 'y --E 60 --S 61 of 267 -deq:=D(y(x),x)+x**2=(y x)/x-(y x)**2 +deq:=D(y(x),x)+x^2=(y x)/x-(y x)^2 --R --R 2 --R , 2 - x y(x) + y(x) @@ -840,7 +840,7 @@ bmt/10/08/92 laplace )clear all --S 62 of 267 -laplace(exp(-x**3)*x**7,x,s) +laplace(exp(-x^3)*x^7,x,s) --R --R 3 --R 7 - x @@ -865,7 +865,7 @@ y:=operator 'y --E 63 --S 64 of 267 -x**2 * D(y x, x) + 2*x*(y x) - (y x)**3 = 0 +x^2 * D(y x, x) + 2*x*(y x) - (y x)^3 = 0 --R --R 2 , 3 --R (2) x y (x) - y(x) + 2x y(x)= 0 @@ -901,7 +901,7 @@ Is wrong (missing factor of 3). \begin{chunk}{*} --S 67 of 267 -factor(p)**2 +factor(p)^2 --R --R 2 --R (2) 9(x + 1) @@ -985,7 +985,7 @@ bmt/10/08/92 factoring over SAEs )clear all --S 76 of 267 -a | a**2+1 +a | a^2+1 --R Your statement has resulted in the following assignments and --R declaration: --R @@ -1122,7 +1122,7 @@ Has an extra factor of 2. )clear all --S 85 of 267 -squareFree((2*x*y+1)*(x*y+1)**2) +squareFree((2*x*y+1)*(x*y+1)^2) --R --R 2 --R (1) (x y + 1) (2x y + 1) @@ -2136,7 +2136,7 @@ evaluate(dx,p+-> differentiate(p,'x)) --E 98 --S 99 of 267 -E n == (1-x**2)*dx**2-2*x*dx+n*(n+1) +E n == (1-x^2)*dx^2-2*x*dx+n*(n+1) --R Type: Void --E 99 @@ -2177,7 +2177,7 @@ bmt/10/12/92 EFSTRUC recursion problem )clear all --S 102 of 267 -bug:=(1+x**(1/4))**(1/3)/(x**(1/2)) +bug:=(1+x^(1/4))^(1/3)/(x^(1/2)) --R --R +--------+ --R 3|4+-+ @@ -2253,19 +2253,19 @@ themos/11/05/92 fortran output bug )clear all -- REAL T7,T6,T5,T4,T3,T2,T1 -- T1=x*x --- T2=2.*y**5 +-- T2=2.*y^5 -- T3=4.*T1 --- T4=y**3 +-- T4=y^3 -- T5=2.*T7 --- T6=x**3 --- T7=x**4 +-- T6=x^3 +-- T7=x^4 -- R46=((T2+(T3+8.*x+8.)*T4+(T5+8.*T6+(-40.*T1))*y)*SIN(x)+(-T2+(-T3+ --- &16.*x)*T4+(-T5+16.*T6)*y)*COS(x))/(y**8+4.*T1*y**6+6.*T7*y**4+4.*x --- &**6*y*y+x**8) +-- &16.*x)*T4+(-T5+16.*T6)*y)*COS(x))/(y^8+4.*T1*y^6+6.*T7*y^4+4.*x +-- &^6*y*y+x^8) -- T7 is referenced before it is defined --S 107 of 267 -a1:=sin(x)/(x**2+y**2) +a1:=sin(x)/(x^2+y^2) --R --R sin(x) --R (1) ------- @@ -2349,7 +2349,7 @@ gbp := groebner lip --E 113 --S 114 of 267 -normalForm(x1**2+x2**2+x3**2,gbp) +normalForm(x1^2+x2^2+x3^2,gbp) --R --R 2 --R (5) e3 - 2e2 @@ -2382,7 +2382,7 @@ gb := groebner li --E 117 --S 118 of 267 -p:dmp:=(x1**2+x2**2+x3**2) +p:dmp:=(x1^2+x2^2+x3^2) --R --R 2 2 2 --R (9) x1 + x2 + x3 @@ -2398,7 +2398,7 @@ normalForm(p,gb) --E 119 --S 120 of 267 -normalForm(x1**2+x2**2+x3**2,gb) +normalForm(x1^2+x2^2+x3^2,gb) --R --R 2 2 2 --R (11) 2x2 + (2x1 - 2e1)x2 + 2x1 - 2e1 x1 + e1 @@ -2453,7 +2453,7 @@ used to give error: )clear all --S 122 of 267 -integrate(((-x-1)*log((x**2+x))**2+2*log(x))/(x+1),x) +integrate(((-x-1)*log((x^2+x))^2+2*log(x))/(x+1),x) --R --R x 2 2 --I ++ (- %K - 1)log(%K + %K) + 2log(%K) @@ -2605,7 +2605,7 @@ retract back from the algebraic extension. )clear all --S 133 of 267 -pol:DMP([x,y,z],PF(2)):=x**2*y**2+x**2*y*z+x**2*z**2+x*y*z**2+y**3*z+y*z**3 +pol:DMP([x,y,z],PF(2)):=x^2*y^2+x^2*y*z+x^2*z^2+x*y*z^2+y^3*z+y*z^3 --R --R 2 2 2 2 2 2 3 3 --R (1) x y + x y z + x z + x y z + y z + y z @@ -2638,7 +2638,7 @@ up := UP('w,FRAC INT) --E 135 --S 136 of 267 -p : up := w**4 + w**3 + w**2 + w + 1 +p : up := w^4 + w^3 + w^2 + w + 1 --R --R 4 3 2 --R (2) w + w + w + w + 1 @@ -2655,7 +2655,7 @@ sae := SAE(FRAC INT,up,p) --E 137 --S 138 of 267 -q : UP('x,sae) := x**5 - 1 +q : UP('x,sae) := x^5 - 1 --R --R 5 --R (4) x - 1 @@ -2663,7 +2663,7 @@ q : UP('x,sae) := x**5 - 1 --E 138 \end{chunk} -Used to report: x**5-1 +Used to report: x^5-1 \begin{chunk}{*} --S 139 of 267 factor q @@ -2750,7 +2750,7 @@ t1:=factor(-12) --E 145 --S 146 of 267 -t1**2 +t1^2 --R --R 4 2 --R (2) 2 3 @@ -2921,7 +2921,7 @@ exp(log(-1)) --E 154 --S 155 of 267 -sum((-1)**k * (k+m),k=0..n) +sum((-1)^k * (k+m),k=0..n) --R --R n --R (2n + 2m + 1)(- 1) + 2m - 1 @@ -2952,7 +2952,7 @@ bronstei@inf.ethz.ch/10/4/93 (Manuel Bronstein) )clear all --S 157 of 267 -integrate(1/(x**2 + %i*a),x) +integrate(1/(x^2 + %i*a),x) --R --R +--+ +--+ +--+ +--+ --R |%i |%i |%i |%i @@ -2969,7 +2969,7 @@ bmt@spadserv.watson.ibm.com/9/28/93 (Barry Trager) )clear all --S 158 of 267 -limit(1/2**n,n=%plusInfinity) +limit(1/2^n,n=%plusInfinity) --R --R (1) 0 --R Type: Union(OrderedCompletion(Expression(Integer)),...) @@ -2988,7 +2988,7 @@ As a result, integrals involving sqrt(-2) etc... are now treated correctly )clear all --S 159 of 267 -x := sqrt(-3) + sqrt 2 + sqrt(- exp a) + log(-a**2-1) +x := sqrt(-3) + sqrt 2 + sqrt(- exp a) + log(-a^2-1) --R --R +-----+ --R | a 2 +-+ +---+ @@ -3024,8 +3024,8 @@ imag x bronstei@inf.ethz.ch/9/22/93 (Manuel Bronstein) \begin{verbatim} haha := rule x*x == z - haha(a*a + b*b + c**2) --> 3z - haha(a*a + b*b + c**2 + d*d) --> z + haha(a*a + b*b + c^2) --> 3z + haha(a*a + b*b + c^2 + d*d) --> z \end{verbatim} The bug is that the last line returns z instead of 4z. @@ -3033,7 +3033,7 @@ The bug is that the last line returns z instead of 4z. Sorry guys, this is not a bug: haha is so general a rule that it matches the integer 4 (as 2 squared), so the rewrite chain for the last example is: \begin{verbatim} - a*a + b*b + c**2 + d*d ---> z + z + z + z = 4 * z ---> z * z ---> z + a*a + b*b + c^2 + d*d ---> z + z + z + z = 4 * z ---> z * z ---> z \end{verbatim} Here is a console showing what exactly happens: \begin{chunk}{*} @@ -3080,7 +3080,7 @@ To see the whole rewrite chain: \begin{chunk}{*} --S 168 of 267 -t1:=a*a + b*b + c**2 + d*d +t1:=a*a + b*b + c^2 + d*d --R --R 2 2 2 2 --R (6) d + c + b + a @@ -3194,7 +3194,7 @@ The technical problem is that ``generalized'' power series may have )clear all --S 177 of 267 -t1:=series(x**x,x=0) +t1:=series(x^x,x=0) --R --R (1) --R 2 3 4 5 @@ -3271,7 +3271,7 @@ should be able to truncate a series to an EXPR. I thought I had you on this one! The signature is there (in pscat.spad): \begin{verbatim} if Coef has coerce: Symbol -> Coef then - if Coef has "**":(Coef,Expon) -> Coef then + if Coef has "^":(Coef,Expon) -> Coef then approximate: ($,Expon) -> Coef ++ \spad{approximate(f)} returns a truncated power series with the ++ series variable viewed as an element of the coefficient domain. @@ -3333,7 +3333,7 @@ approximate(t2,3) --E 182 --S 183 of 267 -t3:=series(cos(x**(2/3) + a),x=0) +t3:=series(cos(x^(2/3) + a),x=0) --R --R (5) --R 2 4 8 10 11 @@ -3418,8 +3418,8 @@ As a side-effect, this fixes the problem with numeric\hfill\\ bronstei@inf.ethz.ch/9/22/93 (manuel bronstein) Here is a (rather major) bug fix to ffactor in FSUPFACT.nrlib. It causes -a large family of integrals to return 0, because ffactor(?**2+expr) returned -?**2 when expr involved a parameter. This is fixed now. +a large family of integrals to return 0, because ffactor(?^2+expr) returned +?^2 when expr involved a parameter. This is fixed now. jhd@maths.bath.ac.uk/8/15/93 James Davenport @@ -3462,7 +3462,7 @@ is still fairly ugly. )clear all --S 190 of 267 -integrate(1/(x*(log(x)**2+a**2-1)),x) +integrate(1/(x*(log(x)^2+a^2-1)),x) --R --R (1) --R +--------+ +------+ @@ -3482,12 +3482,12 @@ integrate(1/(x*(log(x)**2+a**2-1)),x) bronstei@inf.ethz.ch/8/9/93 (manuel bronstein) Here is efstruc.spad with a change to normalize so that -this now returns 2**(1/4) ** 2 + 2**(1/4) +this now returns 2^(1/4) ^ 2 + 2^(1/4) \begin{chunk}{*} )clear all --S 191 of 267 -normalize(2**(1/2) + 2**(1/4)) +normalize(2^(1/2) + 2^(1/4)) --R --R 4+-+2 4+-+ --R (1) \|2 + \|2 @@ -3505,7 +3505,7 @@ Isn't this a bug? )clear all --S 912 of 267 -integrate(%e**x,x=0..1) +integrate(%e^x,x=0..1) --R --R (1) %e - 1 --R Type: Union(f1: OrderedCompletion(Expression(Integer)),...) @@ -3522,12 +3522,12 @@ integrate(log(x),x=1..2) bronstei@inf.ethz.ch/8/5/93 (manuel bronstein) -This will return 2**(5/6). +This will return 2^(5/6). \begin{chunk}{*} )clear all --S 194 of 267 -simplify(2**(1/3)*2**(1/2)) -- +simplify(2^(1/3)*2^(1/2)) -- --R --R 6+-+5 --R (1) \|2 @@ -3575,7 +3575,7 @@ bronstei@inf.ethz.ch/8/4/93 (manuel bronstein) )clear all --S 197 of 267 -a := 2**(1/6) +a := 2^(1/6) --R --R 6+-+ --R (1) \|2 @@ -3583,7 +3583,7 @@ a := 2**(1/6) --E 197 --S 198 of 267 -[a**n for n in 2..13] +[a^n for n in 2..13] --R --R 6+-+2 6+-+3 6+-+4 6+-+5 6+-+ 6+-+2 6+-+3 6+-+4 6+-+5 6+-+ --R (2) [\|2 ,\|2 ,\|2 ,\|2 ,2,2\|2 ,2\|2 ,2\|2 ,2\|2 ,2\|2 ,4,4\|2 ] @@ -3597,7 +3597,7 @@ bronstei@inf.ethz.ch/8/4/93 (manuel bronstein) )clear all --S 199 of 267 -int:=sqrt(a*(1-u**2)/(1+u**2))/u +int:=sqrt(a*(1-u^2)/(1+u^2))/u --R --R +----------+ --R | 2 @@ -3678,7 +3678,7 @@ integrate(eval(int,a=sqrt(-1)),u) Dies after a long time with an elt index error \begin{chunk}{*} --S 202 of 267 -integrate(eval(int,a=1)*(-1)**(1/4),u) +integrate(eval(int,a=1)*(-1)^(1/4),u) --R --R (4) --R +--------+ @@ -3721,7 +3721,7 @@ bronstei@inf.ethz.ch/8/4/93 (manuel bronstein) )clear all --S 203 of 267 -t1:=sqrt((1-x**2)*(1-k**2*x**2)) +t1:=sqrt((1-x^2)*(1-k^2*x^2)) --R --R +-----------------------+ --R | 2 4 2 2 @@ -3746,7 +3746,7 @@ bronstei@inf.ethz.ch/7/26/93 (manuel bronstein) )clear all --S 205 of 267 -t1:=last zerosOf((2+y)**8-3,y) +t1:=last zerosOf((2+y)^8-3,y) --R --R +-------------+ --R | +-------+ @@ -3899,7 +3899,7 @@ b := x::EXPR COMPLEX INT --E 218 --S 219 of 267 -zeroOf(a**4+1,x) +zeroOf(a^4+1,x) --R --R +---+ --R \|- 1 + 1 @@ -3910,7 +3910,7 @@ zeroOf(a**4+1,x) --E 219 --S 220 of 267 -zeroOf(b**4+1,x) +zeroOf(b^4+1,x) --R --R 1 + %i --R (4) ------ @@ -3927,7 +3927,7 @@ Now returns 0 (was crashing before) )clear all --S 221 of 267 -normalize(0**a) +normalize(0^a) --R --R (1) 0 --R Type: Expression(Integer) @@ -5762,7 +5762,7 @@ bronstei@inf.ethz.ch/11/24/93 Manuel Bronstein copper@yktvmv/12/1/93 Don Coppersmith -Attached is the list of integers n such that 2**512-n is prime +Attached is the list of integers n such that 2^512-n is prime and n is between 0 and 5000: \begin{verbatim} 4893,4653,4475,4005,3893,3669,3459,3143,2967, @@ -5774,7 +5774,7 @@ It was gotten from Axiom by issuing the commands )clear all --S 241 of 267 -qrimes : Stream Integer := generate(nextPrime,2**512-5000) +qrimes : Stream Integer := generate(nextPrime,2^512-5000) --R --R (1) --R [ @@ -5832,7 +5832,7 @@ qrimes : Stream Integer := generate(nextPrime,2**512-5000) --E 241 --S 242 of 267 -rrimes := [ 2**512-p for p in qrimes while p < 2**512 ] +rrimes := [ 2^512-p for p in qrimes while p < 2^512 ] --R --R (2) [5000,4893,4653,4475,4005,3893,3669,3459,3143,2967,...] --R Type: Stream(Integer) @@ -6033,7 +6033,7 @@ n : PositiveInteger := 15 --E 257 --S 258 of 267 -E := SimpleAlgebraicExtension(K, PolK, X**n + X**(n-3) -1) +E := SimpleAlgebraicExtension(K, PolK, X^n + X^(n-3) -1) --R --R (5) --R SimpleAlgebraicExtension(Fraction(Integer),UnivariatePolynomial(X,Fraction(In @@ -6060,7 +6060,7 @@ minimalPolynomial(y)$E \begin{verbatim} Internal Error The function minimalPolynomial with signature SimpleAlgebraicExtension( -Fraction Integer,UnivariatePolynomial(X,Fraction Integer),X**15+X**12-1) +Fraction Integer,UnivariatePolynomial(X,Fraction Integer),X^15+X^12-1) UnivariatePolynomial(X,Fraction Integer) is missing from domain SimpleAlgebraicExtension(Fraction (Integer)) (UnivariatePolynomial X (Fraction (Integer)))((15 1 . 1) (12 1 . 1) (0 -1 . 1)) @@ -6074,7 +6074,7 @@ I'm trying to define the following rule )clear all --S 261 of 267 -tr := rule cos(x)**(n | integer? n and even? n)==(1-sin(x)**2)**(n/2) +tr := rule cos(x)^(n | integer? n and even? n)==(1-sin(x)^2)^(n/2) --R --R n --R - @@ -6163,7 +6163,7 @@ from bob sutor: The pade operation requires a taylor series as its third object while ``series'' returns a UnivariatePuiseuxSeries. If you set \begin{verbatim} - y := taylor(1+x)**(1/5) + y := taylor(1+x)^(1/5) \end{verbatim} then things work. You can also do \begin{verbatim} @@ -6271,7 +6271,7 @@ Used to give a lisp error )clear all --S 266 of 267 -x**10+1::Polynomial PrimeField 2 +x^10+1::Polynomial PrimeField 2 --R --R 10 --R (1) x + 1 @@ -6284,7 +6284,7 @@ themos@num-alg-grp.co.uk/03/11/94 Themos Tsikas )clear all --S 267 of 267 -f(x)==x**2 +f(x)==x^2 --R Type: Void --E 267 diff --git a/src/input/float.input.pamphlet b/src/input/float.input.pamphlet index c0a6499..23bedc8 100644 --- a/src/input/float.input.pamphlet +++ b/src/input/float.input.pamphlet @@ -114,7 +114,7 @@ c := cos(p/12) -- we have enough precision to get 0 in following --S 12 of 13 -16*c**4 - 16*c**2 + 1 +16*c^4 - 16*c^2 + 1 --R --R --R (12) 0.0 diff --git a/src/input/float1.input.pamphlet b/src/input/float1.input.pamphlet index 7a75037..1999198 100644 --- a/src/input/float1.input.pamphlet +++ b/src/input/float1.input.pamphlet @@ -39,7 +39,7 @@ --E 2 --S 3 of 37 -sqrt(1.2 + 2.3 / 3.4 ** 4.5) +sqrt(1.2 + 2.3 / 3.4 ^ 4.5) --R --R --R (3) 1.0996972790 671286226 @@ -215,7 +215,7 @@ outputSpacing 5; x --E 22 --S 23 of 37 -y := x/10**10 +y := x/10^10 --R --R --R (3) 0.44721 35954 99957 93928 E -10 diff --git a/src/input/float2.input.pamphlet b/src/input/float2.input.pamphlet index f859f9a..26a953a 100644 --- a/src/input/float2.input.pamphlet +++ b/src/input/float2.input.pamphlet @@ -86,7 +86,7 @@ atanh tanh f --E 8 --S 9 of 41 -sqrt(f**2) +sqrt(f^2) --R --R --R (9) 0.6666666666 6666666667 @@ -142,7 +142,7 @@ exp log f --E 15 --S 16 of 41 -sqrt(f**2) +sqrt(f^2) --R --R --R (16) 14.2857142857 14285714 @@ -150,7 +150,7 @@ sqrt(f**2) --E 16 --S 17 of 41 -sin(f)**2+cos(f)**2 +sin(f)^2+cos(f)^2 --R --R --R (17) 1.0 @@ -158,7 +158,7 @@ sin(f)**2+cos(f)**2 --E 17 --S 18 of 41 -sinh(f)**2-cosh(f)**2 +sinh(f)^2-cosh(f)^2 --R --R --R (18) - 1.0 diff --git a/src/input/folium.input.pamphlet b/src/input/folium.input.pamphlet index 3f50141..ee7a2f9 100644 --- a/src/input/folium.input.pamphlet +++ b/src/input/folium.input.pamphlet @@ -11,7 +11,7 @@ \tableofcontents \eject \begin{chunk}{*} -draw(curve((t**2-1)/(3*t**2+1),t*(t**2-1)/(3*t**2+1)),_ +draw(curve((t^2-1)/(3*t^2+1),t*(t^2-1)/(3*t^2+1)),_ t = -3..3, [title "Folium of Descartes"]) \end{chunk} \eject diff --git a/src/input/fparfrac.input.pamphlet b/src/input/fparfrac.input.pamphlet index 67533ff..b0b8fa2 100644 --- a/src/input/fparfrac.input.pamphlet +++ b/src/input/fparfrac.input.pamphlet @@ -53,7 +53,7 @@ Fx := FRAC Px Here is a simple-looking function \begin{chunk}{*} --S 4 of 18 -f:Fx := 36 / (x**5-2*x**4-2*x**3+4*x**2+x-2) +f:Fx := 36 / (x^5-2*x^4-2*x^3+4*x^2+x-2) --R --R --R 36 @@ -144,7 +144,7 @@ g5::Fx - f5 Here are more complicated examples: \begin{chunk}{*} --S 10 of 18 -f:Fx := (x**5 * (x-1)) / ((x**2 + x + 1)**2 * (x-2)**3) +f:Fx := (x^5 * (x-1)) / ((x^2 + x + 1)^2 * (x-2)^3) --R --R --R 6 5 @@ -187,7 +187,7 @@ g::Fx - f --E 12 --S 13 of 18 -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) +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 --R 7 5 3 @@ -221,9 +221,9 @@ g::Fx - f --E 15 --S 16 of 18 -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) +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 --R (16) diff --git a/src/input/fparfrc.input.pamphlet b/src/input/fparfrc.input.pamphlet index ed0f84f..7c8db26 100644 --- a/src/input/fparfrc.input.pamphlet +++ b/src/input/fparfrc.input.pamphlet @@ -30,7 +30,7 @@ Fx := FRAC UP(x, FRAC INT) --E 1 --S 2 of 16 -f : Fx := 36 / (x**5-2*x**4-2*x**3+4*x**2+x-2) +f : Fx := 36 / (x^5-2*x^4-2*x^3+4*x^2+x-2) --R --R --R 36 @@ -106,7 +106,7 @@ g5::Fx - f5 --E 7 --S 8 of 16 -f : Fx := (x**5 * (x-1)) / ((x**2 + x + 1)**2 * (x-2)**3) +f : Fx := (x^5 * (x-1)) / ((x^2 + x + 1)^2 * (x-2)^3) --R --R --R 6 5 @@ -149,7 +149,7 @@ g :: Fx - f --E 10 --S 11 of 16 -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) +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 --R 7 5 3 @@ -183,10 +183,10 @@ g :: Fx - f --E 13 --S 14 of 16 -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) +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 --R (14) diff --git a/src/input/fr.input.pamphlet b/src/input/fr.input.pamphlet index a89fe63..a51bdbd 100644 --- a/src/input/fr.input.pamphlet +++ b/src/input/fr.input.pamphlet @@ -31,7 +31,7 @@ Automatic coercion of integers to factored integers \begin{chunk}{*} --S 2 of 55 -x := 2**8 * 78**7 * 111**3 * 74534 +x := 2^8 * 78^7 * 111^3 * 74534 --R --R --R 16 10 7 3 @@ -40,7 +40,7 @@ x := 2**8 * 78**7 * 111**3 * 74534 --E 2 --S 3 of 55 -y := 2**4 * 45**3 * 162**6 * 774325 +y := 2^4 * 45^3 * 162^6 * 774325 --R --R --R 10 30 5 @@ -209,7 +209,7 @@ f := x/y --E 18 --S 19 of 55 -g := (x ** 9) / y +g := (x ^ 9) / y --R --R --R 134 60 63 27 9 9 @@ -271,7 +271,7 @@ Manipulation of factored polynomials Coercion to FR POLY INT involves factoring \begin{chunk}{*} --S 24 of 55 -u := (x**4 - y**4) :: POLY INT +u := (x^4 - y^4) :: POLY INT --R --R --R 2 2 @@ -283,7 +283,7 @@ u := (x**4 - y**4) :: POLY INT PrimeFactor creates factors that are asserted to be prime \begin{chunk}{*} --S 25 of 55 -v := primeFactor(x-y,2) * primeFactor(x+y,2) * primeFactor(x**2 + y**2,1) +v := primeFactor(x-y,2) * primeFactor(x+y,2) * primeFactor(x^2 + y^2,1) --R --R --R 2 2 2 2 @@ -292,7 +292,7 @@ v := primeFactor(x-y,2) * primeFactor(x+y,2) * primeFactor(x**2 + y**2,1) --E 25 --S 26 of 55 -w := factor(x**2 + 2*x*y + 2*x + 2*y + y**2 + 1) * primeFactor(x-y,2) +w := factor(x^2 + 2*x*y + 2*x + 2*y + y^2 + 1) * primeFactor(x-y,2) --R --R --R 2 2 diff --git a/src/input/fr1.input.pamphlet b/src/input/fr1.input.pamphlet index be447a2..99e8d4d 100644 --- a/src/input/fr1.input.pamphlet +++ b/src/input/fr1.input.pamphlet @@ -154,7 +154,7 @@ f * g --E 15 --S 16 of 38 -f**500 +f^500 --R --R --R 2000 1000 500 1500 diff --git a/src/input/frac.input.pamphlet b/src/input/frac.input.pamphlet index 9f3669c..d9e513e 100644 --- a/src/input/frac.input.pamphlet +++ b/src/input/frac.input.pamphlet @@ -42,7 +42,7 @@ b := 23/24 --E 2 --S 3 of 12 -3 - a*b**2 + a + b/a +3 - a*b^2 + a + b/a --R --R --R 313271 @@ -68,7 +68,7 @@ denom(b) --E 5 --S 6 of 12 -r := (x**2 + 2*x + 1)/(x**2 - 2*x + 1) +r := (x^2 + 2*x + 1)/(x^2 - 2*x + 1) --R --R --R 2 diff --git a/src/input/function.input.pamphlet b/src/input/function.input.pamphlet index a9331aa..dc49e0a 100644 --- a/src/input/function.input.pamphlet +++ b/src/input/function.input.pamphlet @@ -65,7 +65,7 @@ Input for page AlgebraicFunctionPage )clear all --S 6 of 33 -f := sqrt(1 + x ** (1/3)) +f := sqrt(1 + x ^ (1/3)) --R --R +--------+ --R |3+-+ @@ -74,7 +74,7 @@ f := sqrt(1 + x ** (1/3)) --E 6 --S 7 of 33 -y := rootOf(y**3 + y**2 - x*y + x**3 - 1, y) +y := rootOf(y^3 + y^2 - x*y + x^3 - 1, y) --R --R (2) y --R Type: Expression(Integer) @@ -92,7 +92,7 @@ differentiate(y, x) --E 8 --S 9 of 33 -(y + 1) ** 3 +(y + 1) ^ 3 --R --R 2 3 --R (4) 2y + (x + 3)y - x + 2 @@ -156,7 +156,7 @@ Input for page FunctionSimplificationPage )clear all --S 15 of 33 -f := cos(x)/sec(x) * log(sin(x)**2/(cos(x)**2+sin(x)**2)) +f := cos(x)/sec(x) * log(sin(x)^2/(cos(x)^2+sin(x)^2)) --R --R 2 --R sin(x) @@ -202,7 +202,7 @@ expandLog h --E 18 --S 19 of 33 -f1 := sqrt((x+1)**3) +f1 := sqrt((x+1)^3) --R --R +-----------------+ --R | 3 2 @@ -318,7 +318,7 @@ groupSqrt a --E 29 --S 30 of 33 -a := (sqrt(x) + sqrt(y))**4 +a := (sqrt(x) + sqrt(y))^4 --R --R +-+ +-+ 2 2 --R (4) (4y + 4x)\|x \|y + y + 6x y + x diff --git a/src/input/galois.input.pamphlet b/src/input/galois.input.pamphlet index 1e1904a..edb2996 100644 --- a/src/input/galois.input.pamphlet +++ b/src/input/galois.input.pamphlet @@ -22,7 +22,7 @@ )clear all --S 1 of 28 -p := x**5 - 5*x + 12 +p := x^5 - 5*x + 12 --R --R --R 5 @@ -44,7 +44,7 @@ q := resultant(eval(p,x,y),-eval(p,x,y-x),y) --E 2 --S 3 of 28 -q1 := exquo(q, x**5) +q1 := exquo(q, x^5) --R --R --R (3) diff --git a/src/input/genups.input.pamphlet b/src/input/genups.input.pamphlet index 349380a..57461bc 100644 --- a/src/input/genups.input.pamphlet +++ b/src/input/genups.input.pamphlet @@ -37,7 +37,7 @@ taylor(n +-> 1/factorial(n),x = 0) -- expansion of exp(x) at x = 0 --E 1 --S 2 of 40 -taylor(n +-> (-1)**(n-1)/n,x = 1,1..) -- expansion of log(x) at x = 1 +taylor(n +-> (-1)^(n-1)/n,x = 1,1..) -- expansion of log(x) at x = 1 --R --R --R (2) @@ -52,7 +52,7 @@ taylor(n +-> (-1)**(n-1)/n,x = 1,1..) -- expansion of log(x) at x = 1 --E 2 --S 3 of 40 -taylor(n +-> (-1)**(n-1)/n,x = 1,1..6) -- truncated expansion of log(x) +taylor(n +-> (-1)^(n-1)/n,x = 1,1..6) -- truncated expansion of log(x) --R --R --R (3) @@ -63,7 +63,7 @@ taylor(n +-> (-1)**(n-1)/n,x = 1,1..6) -- truncated expansion of log(x) --E 3 --S 4 of 40 -laurent(m +-> m**2,x = 7,-2..) -- infinite Laurent expansion +laurent(m +-> m^2,x = 7,-2..) -- infinite Laurent expansion --R --R --R (4) @@ -76,7 +76,7 @@ laurent(m +-> m**2,x = 7,-2..) -- infinite Laurent expansion --E 4 --S 5 of 40 -laurent(m +-> m**2,x = 7,-2..5) -- finite Laurent expansion +laurent(m +-> m^2,x = 7,-2..5) -- finite Laurent expansion --R --R --R (5) @@ -89,7 +89,7 @@ laurent(m +-> m**2,x = 7,-2..5) -- finite Laurent expansion --E 5 --S 6 of 40 -puiseux(i +-> (-1)**((i-1)/2)/factorial(i),x = 0,1..,2) -- sin(x) at x = 0 +puiseux(i +-> (-1)^((i-1)/2)/factorial(i),x = 0,1..,2) -- sin(x) at x = 0 --R --R --R 1 3 1 5 1 7 1 9 1 11 12 @@ -99,7 +99,7 @@ puiseux(i +-> (-1)**((i-1)/2)/factorial(i),x = 0,1..,2) -- sin(x) at x = 0 --E 6 --S 7 of 40 -puiseux(i +-> (-1)**(i/2)/factorial(i),x = 0,0..,2) -- cos(x) at x = 0 +puiseux(i +-> (-1)^(i/2)/factorial(i),x = 0,0..,2) -- cos(x) at x = 0 --R --R --R 1 2 1 4 1 6 1 8 1 10 11 @@ -108,10 +108,10 @@ puiseux(i +-> (-1)**(i/2)/factorial(i),x = 0,0..,2) -- cos(x) at x = 0 --R Type: UnivariatePuiseuxSeries(Expression(Integer),x,0) --E 7 --- puiseux(i +-> (-1)**((i-1)/2)/factorial(i),x = 0,1..9,2) -- truncated sin(x) +-- puiseux(i +-> (-1)^((i-1)/2)/factorial(i),x = 0,1..9,2) -- truncated sin(x) -- interpretor needs help here --S 8 of 40 -puiseux(i +-> (-1)**((i-1)/2)/factorial(i),x = 0,1..9/1,2) -- truncated sin(x) +puiseux(i +-> (-1)^((i-1)/2)/factorial(i),x = 0,1..9/1,2) -- truncated sin(x) --R --R --R 1 3 1 5 1 7 1 9 @@ -164,7 +164,7 @@ taylor(1/factorial(n),n,x = 0) -- expansion of exp(x) at x = 0 --E 11 --S 12 of 40 -taylor((-1)**(n-1)/n,n,x = 1,1..) -- expansion of log(x) at x = 1 +taylor((-1)^(n-1)/n,n,x = 1,1..) -- expansion of log(x) at x = 1 --R --R --R (12) @@ -179,7 +179,7 @@ taylor((-1)**(n-1)/n,n,x = 1,1..) -- expansion of log(x) at x = 1 --E 12 --S 13 of 40 -taylor((-1)**(n-1)/n,n,x = 1,1..6) -- truncated expansion of log(x) +taylor((-1)^(n-1)/n,n,x = 1,1..6) -- truncated expansion of log(x) --R --R --R (13) @@ -190,7 +190,7 @@ taylor((-1)**(n-1)/n,n,x = 1,1..6) -- truncated expansion of log(x) --E 13 --S 14 of 40 -laurent(m**2,m,x = 7,-2..) -- infinite Laurent expansion +laurent(m^2,m,x = 7,-2..) -- infinite Laurent expansion --R --R --R (14) @@ -203,7 +203,7 @@ laurent(m**2,m,x = 7,-2..) -- infinite Laurent expansion --E 14 --S 15 of 40 -laurent(m**2,m,x = 7,-2..5) -- finite Laurent expansion +laurent(m^2,m,x = 7,-2..5) -- finite Laurent expansion --R --R --R (15) @@ -216,7 +216,7 @@ laurent(m**2,m,x = 7,-2..5) -- finite Laurent expansion --E 15 --S 16 of 40 -puiseux((-1)**((i-1)/2)/factorial(i),i,x = 0,1..,2) -- sin(x) at x = 0 +puiseux((-1)^((i-1)/2)/factorial(i),i,x = 0,1..,2) -- sin(x) at x = 0 --R --R --R 1 3 1 5 1 7 1 9 1 11 12 @@ -226,7 +226,7 @@ puiseux((-1)**((i-1)/2)/factorial(i),i,x = 0,1..,2) -- sin(x) at x = 0 --E 16 --S 17 of 40 -puiseux((-1)**(i/2)/factorial(i),i,x = 0,0..,2) -- cos(x) at x = 0 +puiseux((-1)^(i/2)/factorial(i),i,x = 0,0..,2) -- cos(x) at x = 0 --R --R --R 1 2 1 4 1 6 1 8 1 10 11 @@ -235,10 +235,10 @@ puiseux((-1)**(i/2)/factorial(i),i,x = 0,0..,2) -- cos(x) at x = 0 --R Type: UnivariatePuiseuxSeries(Expression(Integer),x,0) --E 17 --- puiseux((-1)**((i-1)/2)/factorial(i),i,x = 0,1..9,2) -- truncated sin(x) +-- puiseux((-1)^((i-1)/2)/factorial(i),i,x = 0,1..9,2) -- truncated sin(x) -- interpretor needs help here --S 18 of 40 -puiseux((-1)**((i-1)/2)/factorial(i),i,x = 0,1..9/1,2) -- truncated sin(x) +puiseux((-1)^((i-1)/2)/factorial(i),i,x = 0,1..9/1,2) -- truncated sin(x) --R --R --R 1 3 1 5 1 7 1 9 @@ -292,7 +292,7 @@ series(n +-> 1/factorial(n),x = 0) -- expansion of exp(x) at x = 0 --E 21 --S 22 of 40 -series(n +-> (-1)**(n-1)/n,x = 1,1..) -- expansion of log(x) at x = 1 +series(n +-> (-1)^(n-1)/n,x = 1,1..) -- expansion of log(x) at x = 1 --R --R --R (22) @@ -310,7 +310,7 @@ series(n +-> (-1)**(n-1)/n,x = 1,1..) -- expansion of log(x) at x = 1 --E 22 --S 23 of 40 -series(n +-> (-1)**(n-1)/n,x = 1,1..6) -- truncated expansion of log(x) +series(n +-> (-1)^(n-1)/n,x = 1,1..6) -- truncated expansion of log(x) --R --R --R (23) @@ -321,7 +321,7 @@ series(n +-> (-1)**(n-1)/n,x = 1,1..6) -- truncated expansion of log(x) --E 23 --S 24 of 40 -series(m +-> m**2,x = 7,-2..) -- infinite Laurent expansion +series(m +-> m^2,x = 7,-2..) -- infinite Laurent expansion --R --R --R (24) @@ -334,7 +334,7 @@ series(m +-> m**2,x = 7,-2..) -- infinite Laurent expansion --E 24 --S 25 of 40 -series(m +-> m**2,x = 7,-2..5) -- finite Laurent expansion +series(m +-> m^2,x = 7,-2..5) -- finite Laurent expansion --R --R --R (25) @@ -347,7 +347,7 @@ series(m +-> m**2,x = 7,-2..5) -- finite Laurent expansion --E 25 --S 26 of 40 -series(i +-> (-1)**((i-1)/2)/factorial(i),x = 0,1..,2) -- sin(x) at x = 0 +series(i +-> (-1)^((i-1)/2)/factorial(i),x = 0,1..,2) -- sin(x) at x = 0 --R --R --R 1 3 1 5 1 7 1 9 1 11 12 @@ -357,7 +357,7 @@ series(i +-> (-1)**((i-1)/2)/factorial(i),x = 0,1..,2) -- sin(x) at x = 0 --E 26 --S 27 of 40 -series(i +-> (-1)**(i/2)/factorial(i),x = 0,0..,2) -- cos(x) at x = 0 +series(i +-> (-1)^(i/2)/factorial(i),x = 0,0..,2) -- cos(x) at x = 0 --R --R --R 1 2 1 4 1 6 1 8 1 10 11 @@ -366,10 +366,10 @@ series(i +-> (-1)**(i/2)/factorial(i),x = 0,0..,2) -- cos(x) at x = 0 --R Type: UnivariatePuiseuxSeries(Expression(Integer),x,0) --E 27 --- series(i +-> (-1)**((i-1)/2)/factorial(i),x = 0,1..9,2) -- truncated sin(x) +-- series(i +-> (-1)^((i-1)/2)/factorial(i),x = 0,1..9,2) -- truncated sin(x) -- interpretor needs help here --S 28 of 40 -series(i +-> (-1)**((i-1)/2)/factorial(i),x = 0,1..9/1,2) -- truncated sin(x) +series(i +-> (-1)^((i-1)/2)/factorial(i),x = 0,1..9/1,2) -- truncated sin(x) --R --R --R 1 3 1 5 1 7 1 9 @@ -422,7 +422,7 @@ series(1/factorial(n),n,x = 0) -- expansion of exp(x) at x = 0 --E 31 --S 32 of 40 -series((-1)**(n-1)/n,n,x = 1,1..) -- expansion of log(x) at x = 1 +series((-1)^(n-1)/n,n,x = 1,1..) -- expansion of log(x) at x = 1 --R --R --R (32) @@ -440,7 +440,7 @@ series((-1)**(n-1)/n,n,x = 1,1..) -- expansion of log(x) at x = 1 --E 32 --S 33 of 40 -series((-1)**(n-1)/n,n,x = 1,1..6) -- truncated expansion of log(x) +series((-1)^(n-1)/n,n,x = 1,1..6) -- truncated expansion of log(x) --R --R --R (33) @@ -451,7 +451,7 @@ series((-1)**(n-1)/n,n,x = 1,1..6) -- truncated expansion of log(x) --E 33 --S 34 of 40 -series(m**2,m,x = 7,-2..) -- infinite Laurent expansion +series(m^2,m,x = 7,-2..) -- infinite Laurent expansion --R --R --R (34) @@ -464,7 +464,7 @@ series(m**2,m,x = 7,-2..) -- infinite Laurent expansion --E 34 --S 35 of 40 -series(m**2,m,x = 7,-2..5) -- finite Laurent expansion +series(m^2,m,x = 7,-2..5) -- finite Laurent expansion --R --R --R (35) @@ -477,7 +477,7 @@ series(m**2,m,x = 7,-2..5) -- finite Laurent expansion --E 35 --S 36 of 40 -series((-1)**((i-1)/2)/factorial(i),i,x = 0,1..,2) -- sin(x) at x = 0 +series((-1)^((i-1)/2)/factorial(i),i,x = 0,1..,2) -- sin(x) at x = 0 --R --R --R 1 3 1 5 1 7 1 9 1 11 12 @@ -487,7 +487,7 @@ series((-1)**((i-1)/2)/factorial(i),i,x = 0,1..,2) -- sin(x) at x = 0 --E 36 --S 37 of 40 -series((-1)**(i/2)/factorial(i),i,x = 0,0..,2) -- cos(x) at x = 0 +series((-1)^(i/2)/factorial(i),i,x = 0,0..,2) -- cos(x) at x = 0 --R --R --R 1 2 1 4 1 6 1 8 1 10 11 @@ -496,10 +496,10 @@ series((-1)**(i/2)/factorial(i),i,x = 0,0..,2) -- cos(x) at x = 0 --R Type: UnivariatePuiseuxSeries(Expression(Integer),x,0) --E 37 --- series((-1)**((i-1)/2)/factorial(i),i,x = 0,1..9,2) -- truncated sin(x) +-- series((-1)^((i-1)/2)/factorial(i),i,x = 0,1..9,2) -- truncated sin(x) -- interpretor needs help here --S 38 of 40 -series((-1)**((i-1)/2)/factorial(i),i,x = 0,1..9/1,2) -- truncated sin(x) +series((-1)^((i-1)/2)/factorial(i),i,x = 0,1..9/1,2) -- truncated sin(x) --R --R --R 1 3 1 5 1 7 1 9 diff --git a/src/input/gnarly1.input.pamphlet b/src/input/gnarly1.input.pamphlet index 0c78961..2ed0fbd 100644 --- a/src/input/gnarly1.input.pamphlet +++ b/src/input/gnarly1.input.pamphlet @@ -11,8 +11,8 @@ \tableofcontents \eject \begin{chunk}{*} -draw(surface(cos(t)/(1+sin(t)**2),sin(t)*cos(t)*cos(u)/(1+sin(t)**2), - sin(t)*cos(t)*sin(u)/(1+sin(t)**2)),t = -%pi..%pi,u = 0..%pi) +draw(surface(cos(t)/(1+sin(t)^2),sin(t)*cos(t)*cos(u)/(1+sin(t)^2), + sin(t)*cos(t)*sin(u)/(1+sin(t)^2)),t = -%pi..%pi,u = 0..%pi) \end{chunk} \eject \begin{thebibliography}{99} diff --git a/src/input/graphics.input.pamphlet b/src/input/graphics.input.pamphlet index 33b2925..f4ba30d 100644 --- a/src/input/graphics.input.pamphlet +++ b/src/input/graphics.input.pamphlet @@ -31,10 +31,10 @@ write(v,"saddle","pixmap") )clear all draw(x * y = 1, x, y, range == [-3..3, -3..3]) -draw(y**2 + y = x**3 - x, x, y, range == [-2..2, -2..1]) -p := ((x**2 + y**2 + 1) - 8*x)**2 - (8*(x**2 + y**2 + 1) - 4*x - 1) +draw(y^2 + y = x^3 - x, x, y, range == [-2..2, -2..1]) +p := ((x^2 + y^2 + 1) - 8*x)^2 - (8*(x^2 + y^2 + 1) - 4*x - 1) draw(p = 0, x, y, range == [-1..11, -7..7], title == "Cartesian Ovals") -q := (x**2 + y**2 + 7**2)**2 - (6**4 + 4*7**2*x**2) +q := (x^2 + y^2 + 7^2)^2 - (6^4 + 4*7^2*x^2) draw(q = 0, x, y, range == [-10..10, -4..4], title == _ "Cassinian oval with two loops") All @@ -60,7 +60,7 @@ All -- Input for page ParametricCurveGraphicsExamplePage )clear all -draw(curve(cos(t/(1+sin(t)**2)), sin(t)*cos(t)/(1+sin(t)**2)), t = -%pi..%pi) +draw(curve(cos(t/(1+sin(t)^2)), sin(t)*cos(t)/(1+sin(t)^2)), t = -%pi..%pi) draw(curve(9*sin(3*t/4), 8*sin(t)), t = -4*%pi..4*%pi) draw(curve(sin(t)*sin(2*t)*sin(3*t), sin(4*t)*sin(5*t)*sin(6*t)),t = 0..2*%pi) draw(curve(cos(4*t)*cos(7*t), cos(4*t)*sin(7*t)), t = 0..2*%pi) @@ -94,7 +94,7 @@ draw(sin tan x - tan sin x,x = 0..6) draw(curve(sin(t)*sin(2*t), sin(3*t)*sin(4*t)), t = 0..2*%pi) draw(curve(sin(t)*sin(2*t), sin(3*t)*sin(4*t), sin(5*t)*sin(6*t)), t = 0..2*%pi) draw(sin(17*t), t = 0..2*%pi, coordinates == polar) -draw(y**2 + y = x**3 - x, x, y,range == [-2..2,-2..1]) +draw(y^2 + y = x^3 - x, x, y,range == [-2..2,-2..1]) All \end{chunk} \eject diff --git a/src/input/graphviz.input.pamphlet b/src/input/graphviz.input.pamphlet index 890d13c..7ff4ace 100644 --- a/src/input/graphviz.input.pamphlet +++ b/src/input/graphviz.input.pamphlet @@ -22,7 +22,7 @@ )set message auto off )clear all ---S 1 of 6 +--S 1 of 5 header:=standardDotHeader() --R --R @@ -32,7 +32,7 @@ header:=standardDotHeader() --R Type: List(String) --E 1 ---S 2 of 6 +--S 2 of 5 graph:=sampleDotGraph() --R --R @@ -52,23 +52,19 @@ graph:=sampleDotGraph() --R Type: List(String) --E 2 ---S 3 of 6 +--S 3 of 5 writeDotGraph(header,graph,"NeuralNet") --R --R Type: Void --E 3 ---S 4 of 6 +--S 4 of 5 dot2eps "NeuralNet" --R --R Type: Void --E 4 ---S 5 of 6 --- dotview("evince","NeuralNet") ---S 5 - ---S 6 of 6 +--S 5 of 5 )show Graphviz --R --R Graphviz is a package constructor @@ -82,7 +78,11 @@ dot2eps "NeuralNet" --R standardDotHeader : () -> List(String) --R writeDotGraph : (List(String),List(String),String) -> Void --R ---E 6 +--E 5 + +--S 6 of 6 +-- dotview("evince","NeuralNet") +--S 5 )spool )lisp (bye) diff --git a/src/input/groeb.input.pamphlet b/src/input/groeb.input.pamphlet index 4ba10f6..e1c37ef 100644 --- a/src/input/groeb.input.pamphlet +++ b/src/input/groeb.input.pamphlet @@ -35,7 +35,7 @@ s2:DMP([w,p,z,t,s,b],FRAC(INT)):= 35*p + 40*z + 25*t - 27*s --E 2 --S 3 of 12 -s3:DMP([w,p,z,t,s,b],FRAC(INT)):= 15*w + 25*p*s + 30*z - 18*t - 165*b**2 +s3:DMP([w,p,z,t,s,b],FRAC(INT)):= 15*w + 25*p*s + 30*z - 18*t - 165*b^2 --R --R --R 2 @@ -52,7 +52,7 @@ s4:DMP([w,p,z,t,s,b],FRAC(INT)):= -9*w + 15*p*t + 20*z*s --E 4 --S 5 of 12 -s5:DMP([w,p,z,t,s,b],FRAC(INT)):= w*p + 2*z*t - 11*b**3 +s5:DMP([w,p,z,t,s,b],FRAC(INT)):= w*p + 2*z*t - 11*b^3 --R --R --R 3 @@ -61,7 +61,7 @@ s5:DMP([w,p,z,t,s,b],FRAC(INT)):= w*p + 2*z*t - 11*b**3 --E 5 --S 6 of 12 -s6:DMP([w,p,z,t,s,b],FRAC(INT)):= 99*w - 11*b*s + 3*b**2 +s6:DMP([w,p,z,t,s,b],FRAC(INT)):= 99*w - 11*b*s + 3*b^2 --R --R --R 2 @@ -70,7 +70,7 @@ s6:DMP([w,p,z,t,s,b],FRAC(INT)):= 99*w - 11*b*s + 3*b**2 --E 6 --S 7 of 12 -s7:DMP([w,p,z,t,s,b],FRAC(INT)):= b**2 + 33/50*b + 2673/10000 +s7:DMP([w,p,z,t,s,b],FRAC(INT)):= b^2 + 33/50*b + 2673/10000 --R --R --R 2 33 2673 diff --git a/src/input/grpthry.input.pamphlet b/src/input/grpthry.input.pamphlet index 39c5457..5e1684e 100644 --- a/src/input/grpthry.input.pamphlet +++ b/src/input/grpthry.input.pamphlet @@ -1638,7 +1638,7 @@ px * pz --E 27 --S 28 of 55 -py ** 3 +py ^ 3 --R --R --R (5) (3 9 7 5) diff --git a/src/input/help.input.pamphlet b/src/input/help.input.pamphlet index 8d4463f..066a15e 100644 --- a/src/input/help.input.pamphlet +++ b/src/input/help.input.pamphlet @@ -22,7 +22,7 @@ )clear all --S 1 of 2 -a:= x**2 + 1 +a:= x^2 + 1 --R --R --R 2 @@ -31,7 +31,7 @@ a:= x**2 + 1 --E 1 --S 2 of 2 -(a - 2)**2 +(a - 2)^2 --R --R --R 4 2 diff --git a/src/input/hexadec.input.pamphlet b/src/input/hexadec.input.pamphlet index aed12d5..02cdeb5 100644 --- a/src/input/hexadec.input.pamphlet +++ b/src/input/hexadec.input.pamphlet @@ -63,7 +63,7 @@ hex(1/1007) --E 4 --S 5 of 7 -p := hex(1/4)*x**2 + hex(2/3)*x + hex(4/9) +p := hex(1/4)*x^2 + hex(2/3)*x + hex(4/9) --R --R --R 2 _ ___ diff --git a/src/input/i2e.input.pamphlet b/src/input/i2e.input.pamphlet index 7c3e900..1744446 100644 --- a/src/input/i2e.input.pamphlet +++ b/src/input/i2e.input.pamphlet @@ -2,7 +2,7 @@ \usepackage{axiom} \setlength{\textwidth}{400pt} \begin{document} -\title{\$SPAD/src/input algaggr.input} +\title{\$SPAD/src/input i2e.input} \author{Ralf Hemmecke} \maketitle \begin{abstract} @@ -32,28 +32,28 @@ ex:=sin(cos(x+2)+3)+exp(x+2)+sqrt(x) --S 2 of 6 exi:=ex::InputForm --R ---R (2) (+ (sin (+ (cos (+ x 2)) 3)) (+ (** x (/ 1 2)) (exp (+ x 2)))) +--R (2) (+ (sin (+ (cos (+ x 2)) 3)) (+ (^ x (/ 1 2)) (exp (+ x 2)))) --R Type: InputForm --E 2 --S 3 of 6 d1:=destruct exi --R ---R (3) [+,(sin (+ (cos (+ x 2)) 3)),(+ (** x (/ 1 2)) (exp (+ x 2)))] +--R (3) [+,(sin (+ (cos (+ x 2)) 3)),(+ (^ x (/ 1 2)) (exp (+ x 2)))] --R Type: List(InputForm) --E 3 --S 4 of 6 l2:=[first d1, first rest d1, first rest destruct first rest rest d1] --R ---R (4) [+,(sin (+ (cos (+ x 2)) 3)),(** x (/ 1 2))] +--R (4) [+,(sin (+ (cos (+ x 2)) 3)),(^ x (/ 1 2))] --R Type: List(InputForm) --E 4 --S 5 of 6 inf:=convert l2 --R ---R (5) (+ (sin (+ (cos (+ x 2)) 3)) (** x (/ 1 2))) +--R (5) (+ (sin (+ (cos (+ x 2)) 3)) (^ x (/ 1 2))) --R Type: InputForm --E 5 diff --git a/src/input/ideal.input.pamphlet b/src/input/ideal.input.pamphlet index c73cf09..53b13f5 100644 --- a/src/input/ideal.input.pamphlet +++ b/src/input/ideal.input.pamphlet @@ -28,7 +28,7 @@ --E 1 --S 2 of 18 -m := [x**2+y**2-1] +m := [x^2+y^2-1] --R --R --R 2 2 @@ -37,7 +37,7 @@ m := [x**2+y**2-1] --E 2 --S 3 of 18 -n := [x**2-y**2] +n := [x^2-y^2] --R --R --R 2 2 @@ -86,7 +86,7 @@ dimension ideal m --E 8 --S 9 of 18 -f := x**2-1 +f := x^2-1 --R --R --R 2 @@ -95,7 +95,7 @@ f := x**2-1 --E 9 --S 10 of 18 -g := x*(x**2-1) +g := x*(x^2-1) --R --R --R 3 @@ -119,7 +119,7 @@ l: List DMP([x,y,z],FRAC INT) --E 12 --S 13 of 18 -l:=[x**2+2*y**2,x*z**2-y*z,z**2-4] +l:=[x^2+2*y^2,x*z^2-y*z,z^2-4] --R --R --R 2 2 2 2 diff --git a/src/input/ifact.input.pamphlet b/src/input/ifact.input.pamphlet index 6e3dc1a..329593f 100644 --- a/src/input/ifact.input.pamphlet +++ b/src/input/ifact.input.pamphlet @@ -25,7 +25,7 @@ Some integer factorizations \begin{chunk}{*} --S 1 of 7 -factor(3**17-1) +factor(3^17-1) --R --R --R (1) 2 1871 34511 @@ -33,7 +33,7 @@ factor(3**17-1) --E 1 --S 2 of 7 -factor(3**23-1) +factor(3^23-1) --R --R --R (2) 2 47 1001523179 @@ -41,7 +41,7 @@ factor(3**23-1) --E 2 --S 3 of 7 -factor(3**31-1) +factor(3^31-1) --R --R --R (3) 2 683 102673 4404047 @@ -49,7 +49,7 @@ factor(3**31-1) --E 3 --S 4 of 7 -factor(3**41-1) +factor(3^41-1) --R --R --R (4) 2 83 2526913 86950696619 @@ -57,7 +57,7 @@ factor(3**41-1) --E 4 --S 5 of 7 -factor(3**53-1) +factor(3^53-1) --R --R --R (5) 2 107 24169 3747607031112307667 diff --git a/src/input/ifthenelse.input.pamphlet b/src/input/ifthenelse.input.pamphlet index 3d1c511..2adff07 100644 --- a/src/input/ifthenelse.input.pamphlet +++ b/src/input/ifthenelse.input.pamphlet @@ -180,7 +180,7 @@ a:= exp(j+1/j) else j:=cos(i*0.5*pi()) - log(abs(j)**5+1) + log(abs(j)^5+1) --R --R --R (8) 0.1353352832 3661269189 diff --git a/src/input/images2.input.pamphlet b/src/input/images2.input.pamphlet index 394e9a2..09f198a 100644 --- a/src/input/images2.input.pamphlet +++ b/src/input/images2.input.pamphlet @@ -21,13 +21,13 @@ )r newton )r cdraw --- create a Newton's iteration function for the equation x**3 = 2. -f := newtonStep(x**3 - 2) +-- create a Newton's iteration function for the equation x^3 = 2. +f := newtonStep(x^3 - 2) setClipValue(4) -drawComplexVectorField(f**3, -3..3, -3..3) -drawComplex(f**3, -3..3, -3..3) -drawComplex(f**4, -3..3, -3..3) +drawComplexVectorField(f^3, -3..3, -3..3) +drawComplex(f^3, -3..3, -3..3) +drawComplex(f^4, -3..3, -3..3) \end{chunk} \eject diff --git a/src/input/images2a.input.pamphlet b/src/input/images2a.input.pamphlet index 08bdcaf..66a1964 100644 --- a/src/input/images2a.input.pamphlet +++ b/src/input/images2a.input.pamphlet @@ -193,13 +193,13 @@ clipFun(x:DoubleFloat):DoubleFloat == min(max(x, -clipValue), clipValue) --- create a Newton's iteration function for the equation x**3 = 2. -f := newtonStep(x**3 - 2) +-- create a Newton's iteration function for the equation x^3 = 2. +f := newtonStep(x^3 - 2) setClipValue(4) -drawComplexVectorField(f**3, -3..3, -3..3) -drawComplex(f**3, -3..3, -3..3) -drawComplex(f**4, -3..3, -3..3) +drawComplexVectorField(f^3, -3..3, -3..3) +drawComplex(f^3, -3..3, -3..3) +drawComplex(f^4, -3..3, -3..3) \end{chunk} \eject diff --git a/src/input/images7a.input.pamphlet b/src/input/images7a.input.pamphlet index 11aef83..b7a8e09 100644 --- a/src/input/images7a.input.pamphlet +++ b/src/input/images7a.input.pamphlet @@ -104,7 +104,7 @@ riemannTransform(z) == r := sqrt norm z cosTheta := (real z)/r sinTheta := (imag z)/r - cp := 4*r/(4+r**2) + cp := 4*r/(4+r^2) sp := sqrt(1-cp*cp) if r>2 then sp := -sp point [cosTheta*cp, sinTheta*cp, -sp + 1] diff --git a/src/input/images8.input.pamphlet b/src/input/images8.input.pamphlet index 01ddcbe..16bac7e 100644 --- a/src/input/images8.input.pamphlet +++ b/src/input/images8.input.pamphlet @@ -36,12 +36,12 @@ drawRings 2 drawScherk(3,3) --- Ribbon Plot of [x**i for i in 1..5] +-- Ribbon Plot of [x^i for i in 1..5] )r ribbons )set message test off -drawRibbons([x**i for i in 1..5], x=-1..1, y=0..2) +drawRibbons([x^i for i in 1..5], x=-1..1, y=0..2) )set message test on \end{chunk} \eject diff --git a/src/input/images8a.input.pamphlet b/src/input/images8a.input.pamphlet index 1627ec3..f4702a3 100644 --- a/src/input/images8a.input.pamphlet +++ b/src/input/images8a.input.pamphlet @@ -143,7 +143,7 @@ drawPyramid 4 torusRot: DHMATRIX(DoubleFloat) -- Draw Antoine's Rings with n levels of recursive subdivision. --- The number of subrings is 10**n. +-- The number of subrings is 10^n. drawRings(n) == s := create3Space()$ThreeSpace DoubleFloat -- create an identity transformation @@ -240,7 +240,7 @@ drawOneScherk(s) == drawScherk(3,3) --- Ribbon Plot of [x**i for i in 1..5] +-- Ribbon Plot of [x^i for i in 1..5] drawRibbons(flist, xrange, yrange) == sp := createThreeSpace() @@ -261,7 +261,7 @@ drawRibbons(flist, xrange, yrange) == )set message test off -drawRibbons([x**i for i in 1..5], x=-1..1, y=0..2) +drawRibbons([x^i for i in 1..5], x=-1..1, y=0..2) )set message test on \end{chunk} \eject diff --git a/src/input/infprod.input.pamphlet b/src/input/infprod.input.pamphlet index e3642ab..466cc45 100644 --- a/src/input/infprod.input.pamphlet +++ b/src/input/infprod.input.pamphlet @@ -62,7 +62,7 @@ infiniteProduct g Ramanujan's tau function \begin{chunk}{*} --S 4 of 11 -h := infiniteProduct(f ** 24) +h := infiniteProduct(f ^ 24) --R --R --R (4) diff --git a/src/input/int.input.pamphlet b/src/input/int.input.pamphlet index f11cf15..57bf4f4 100644 --- a/src/input/int.input.pamphlet +++ b/src/input/int.input.pamphlet @@ -21,7 +21,7 @@ )set message auto off )clear all --S 1 of 47 -2**(5678 - 4856 + 2 * 17) +2^(5678 - 4856 + 2 * 17) --R --R --R (1) diff --git a/src/input/intaf.input.pamphlet b/src/input/intaf.input.pamphlet index 2a5c743..31a6311 100644 --- a/src/input/intaf.input.pamphlet +++ b/src/input/intaf.input.pamphlet @@ -22,7 +22,7 @@ )clear all --S 1 of 20 -x**2 / sqrt(a + b*x**3) +x^2 / sqrt(a + b*x^3) --R --R --R 2 @@ -47,7 +47,7 @@ integrate(%,x) --E 2 --S 3 of 20 -x**3 * sqrt(a + b*x**4) +x^3 * sqrt(a + b*x^4) --R --R --R +--------+ @@ -69,7 +69,7 @@ integrate(%,x) --E 4 --S 5 of 20 -1/sqrt(1+x**3) +1/sqrt(1+x^3) --R --R --R 1 @@ -94,7 +94,7 @@ integrate(%,x) --E 6 --S 7 of 20 -sqrt(1+x**3) +sqrt(1+x^3) --R --R --R +------+ @@ -115,7 +115,7 @@ integrate(%,x) --E 8 --S 9 of 20 -1/(x * sqrt(1 + x**3)) +1/(x * sqrt(1 + x^3)) --R --R --R 1 @@ -139,7 +139,7 @@ integrate(%,x) --E 10 --S 11 of 20 -x**3/sqrt(1+x**8) +x^3/sqrt(1+x^8) --R --R --R 3 @@ -164,7 +164,7 @@ integrate(%,x) --E 12 --S 13 of 20 -x/sqrt(1-x**4) +x/sqrt(1-x^4) --R --R --R x @@ -189,7 +189,7 @@ integrate(%,x) --E 14 --S 15 of 20 -(x+1)/((x-2) * sqrt(1 + x**3)) +(x+1)/((x-2) * sqrt(1 + x^3)) --R --R --R x + 1 @@ -216,7 +216,7 @@ integrate(%,x) --E 16 --S 17 of 20 -x**6/sqrt((x**7+1)*(x**7+2)) +x^6/sqrt((x^7+1)*(x^7+2)) --R --R --R 6 diff --git a/src/input/intdeq.input.pamphlet b/src/input/intdeq.input.pamphlet index ff675db..51a6ecb 100644 --- a/src/input/intdeq.input.pamphlet +++ b/src/input/intdeq.input.pamphlet @@ -29,7 +29,7 @@ y := operator y --E 1 --S 2 of 7 -deq := differentiate(y x, x, 2) + 2*w[0]*differentiate(y x, x) + w[0]**2*y x +deq := differentiate(y x, x, 2) + 2*w[0]*differentiate(y x, x) + w[0]^2*y x --R --R --R ,, , 2 diff --git a/src/input/intef.input.pamphlet b/src/input/intef.input.pamphlet index f4e6aba..c7474d5 100644 --- a/src/input/intef.input.pamphlet +++ b/src/input/intef.input.pamphlet @@ -22,7 +22,7 @@ )clear all --S 1 of 16 -(a*x+b) / (b**2 * x * log(x)**2 + 2*a*b*x**2*log(x) + a**2*x**3 + x) +(a*x+b) / (b^2 * x * log(x)^2 + 2*a*b*x^2*log(x) + a^2*x^3 + x) --R --R --R a x + b @@ -41,7 +41,7 @@ integrate(%,x) --E 2 --S 3 of 16 -((exp(x)-x**2+2*x)/(x**2*(exp(x)+x)**2))*exp((x**2-1)/x+1/(exp(x)+x)) +((exp(x)-x^2+2*x)/(x^2*(exp(x)+x)^2))*exp((x^2-1)/x+1/(exp(x)+x)) --R --R --R 2 x 3 @@ -113,7 +113,7 @@ integrate(%,x) --E 8 --S 9 of 16 -(2 * log(x)**2 - log x - x**2) / (log(x)**3 - x**2 * log x) +(2 * log(x)^2 - log x - x^2) / (log(x)^3 - x^2 * log x) --R --R --R 2 2 diff --git a/src/input/intef2.input.pamphlet b/src/input/intef2.input.pamphlet index 126aca3..a60c833 100644 --- a/src/input/intef2.input.pamphlet +++ b/src/input/intef2.input.pamphlet @@ -21,7 +21,7 @@ )set message auto off )clear all --S 1 of 10 -(a*x+b) / (b**2 * x * log(x)**2 + 2*a*b*x**2*log(x) + a**2*x**3 + x) +(a*x+b) / (b^2 * x * log(x)^2 + 2*a*b*x^2*log(x) + a^2*x^3 + x) --R --R --R a x + b @@ -40,7 +40,7 @@ integrate(%,x) --E 2 --S 3 of 10 -((exp(x)-x**2+2*x)/(x**2*(exp(x)+x)**2))*exp((x**2-1)/x+1/(exp(x)+x)) +((exp(x)-x^2+2*x)/(x^2*(exp(x)+x)^2))*exp((x^2-1)/x+1/(exp(x)+x)) --R --R --R 2 x 3 diff --git a/src/input/intg0.input.pamphlet b/src/input/intg0.input.pamphlet index 1677ee0..680e1cf 100644 --- a/src/input/intg0.input.pamphlet +++ b/src/input/intg0.input.pamphlet @@ -66,7 +66,7 @@ integrate(t1,x) --E 4 --S 5 of 25 -z := sqrt(a**2 - x**2) +z := sqrt(a^2 - x^2) --R --R --R +---------+ @@ -100,7 +100,7 @@ integrate(t2,x) --E 7 --S 8 of 25 -t3:=x**2 * z +t3:=x^2 * z --R --R --R +---------+ @@ -135,7 +135,7 @@ integrate(t3,x) --E 9 --S 10 of 25 -t4:=x**3 / (a+b*x)**(1/3) +t4:=x^3 / (a+b*x)^(1/3) --R --R --R 3 @@ -159,7 +159,7 @@ integrate(t4,x) --E 11 --S 12 of 25 -t5:=1 / (x**3 * (a+b*x)**(1/3)) +t5:=1 / (x^3 * (a+b*x)^(1/3)) --R --R --R 1 @@ -194,7 +194,7 @@ integrate(t5,x) Examples of transcendentals over a curve of genus 0 \begin{chunk}{*} --S 14 of 25 -t6:=x / (y + y**2) + log(y + 1) +t6:=x / (y + y^2) + log(y + 1) --R --R --R +-------+ +-------+ diff --git a/src/input/intlf.input.pamphlet b/src/input/intlf.input.pamphlet index 49f409e..6f6e440 100644 --- a/src/input/intlf.input.pamphlet +++ b/src/input/intlf.input.pamphlet @@ -21,7 +21,7 @@ )set message auto off )clear all --S 1 of 2 -exp(-x**2) * erf(x) / (erf(x)**3 - erf(x)**2 - erf(x) + 1) +exp(-x^2) * erf(x) / (erf(x)^3 - erf(x)^2 - erf(x) + 1) --R --R --R 2 diff --git a/src/input/intmix.input.pamphlet b/src/input/intmix.input.pamphlet index f1a1576..b65bf75 100644 --- a/src/input/intmix.input.pamphlet +++ b/src/input/intmix.input.pamphlet @@ -22,7 +22,7 @@ )clear all --S 1 of 6 -(x + 1) / (x * (x + log x)**(3/2)) - 1/(x * log(x)**2) +(x + 1) / (x * (x + log x)^(3/2)) - 1/(x * log(x)^2) --R --R --R +----------+ 2 @@ -49,7 +49,7 @@ integrate(%, x) This one requires solving a risch d.e. over an elliptic curve \begin{chunk}{*} --S 3 of 6 -((5*x**4+2*x-2)/x**2 * (1+1/sqrt(x**3+1))+x/sqrt(x**3+1)) * exp(x*sqrt(x**3+1)) +((5*x^4+2*x-2)/x^2 * (1+1/sqrt(x^3+1))+x/sqrt(x^3+1)) * exp(x*sqrt(x^3+1)) --R --R --R +------+ @@ -80,7 +80,7 @@ integrate(%, x) This one does not have an elementary integral \begin{chunk}{*} --S 5 of 6 -log(1 + exp x)**(1/3) / (1 + log(1 + exp x)) +log(1 + exp x)^(1/3) / (1 + log(1 + exp x)) --R --R --R +------------+ diff --git a/src/input/intmix2.input.pamphlet b/src/input/intmix2.input.pamphlet index a5c26a8..abab3d2 100644 --- a/src/input/intmix2.input.pamphlet +++ b/src/input/intmix2.input.pamphlet @@ -21,7 +21,7 @@ )set message auto off )clear all --S 1 of 4 -(x + 1) / (x * (x + log x)**(3/2)) +(x + 1) / (x * (x + log x)^(3/2)) --R --R --R x + 1 @@ -46,7 +46,7 @@ integrate(%, x) This one does not have an elementary integral \begin{chunk}{*} --S 3 of 4 -log(1 + exp x)**(1/3) / (1 + log(1 + exp x)) +log(1 + exp x)^(1/3) / (1 + log(1 + exp x)) --R --R --R +------------+ diff --git a/src/input/intrf.input.pamphlet b/src/input/intrf.input.pamphlet index f0b5fc1..ba3bdb7 100644 --- a/src/input/intrf.input.pamphlet +++ b/src/input/intrf.input.pamphlet @@ -50,7 +50,7 @@ integrate(%,x) We need not factor the denominator \begin{chunk}{*} --S 3 of 14 -(x+1)**2/((x+1)**6+1) +(x+1)^2/((x+1)^6+1) --R --R --R 2 @@ -73,7 +73,7 @@ integrate(%,x) --E 4 --S 5 of 14 -(2*x**2+4)**4/(x**2-2)**5 +(2*x^2+4)^4/(x^2-2)^5 --R --R --R 8 6 4 2 @@ -104,7 +104,7 @@ integrate(%,x) --E 6 --S 7 of 14 -x**5/(x**4+x**2+1)**2 +x^5/(x^4+x^2+1)^2 --R --R --R 5 @@ -130,7 +130,7 @@ integrate(%,x) --E 8 --S 9 of 14 -1/(x**2 + a) +1/(x^2 + a) --R --R --R 1 @@ -156,7 +156,7 @@ integrate(%,x) --E 10 --S 11 of 14 -x**2/(x**4-a**2) +x^2/(x^4-a^2) --R --R --R 2 @@ -192,7 +192,7 @@ integrate(%,x) --E 12 --S 13 of 14 -x/(1-x**3) +x/(1-x^3) --R --R --R x diff --git a/src/input/kamke0.input.pamphlet b/src/input/kamke0.input.pamphlet index 2c03218..b7913aa 100644 --- a/src/input/kamke0.input.pamphlet +++ b/src/input/kamke0.input.pamphlet @@ -43,7 +43,7 @@ g := operator 'g --E 3 --S 4 of 134 -ode1 := D(y(x),x) - (a4*x**4+a3*x**3+a2*x**2+a1*x+a0)**(-1/2) +ode1 := D(y(x),x) - (a4*x^4+a3*x^3+a2*x^2+a1*x+a0)^(-1/2) --R --R --R +---------------------------------+ @@ -146,7 +146,7 @@ ode3expr:=D(yx,x) + a*yx - b*sin(c*x) --E 13 --S 14 of 134 -ode4 := D(y(x),x) + 2*x*y(x) - x*exp(-x**2) +ode4 := D(y(x),x) + 2*x*y(x) - x*exp(-x^2) --R --R 2 --R , - x @@ -178,7 +178,7 @@ yx:=ode4a.particular --E 16 --S 17 of 134 -ode4expr:=D(yx,x) + 2*x*yx - x*exp(-x**2) +ode4expr:=D(yx,x) + 2*x*yx - x*exp(-x^2) --R --R (17) 0 --R Type: Expression(Integer) @@ -414,7 +414,7 @@ ode11a:=solve(ode11,y,x) --E 41 --S 42 of 134 -ode12 := D(y(x),x) + y(x)**2 - 1 +ode12 := D(y(x),x) + y(x)^2 - 1 --R --R , 2 --R (40) y (x) + y(x) - 1 @@ -432,7 +432,7 @@ yx:=solve(ode12,y,x) --E 43 --S 44 of 134 -ode12expr:=D(yx,x) + yx**2 - 1 +ode12expr:=D(yx,x) + yx^2 - 1 --R --R (42) --R , 2 2 @@ -451,7 +451,7 @@ ode12expr:=D(yx,x) + yx**2 - 1 --E 44 --S 45 of 134 -ode13 := D(y(x),x) + y(x)**2 - a*x - b +ode13 := D(y(x),x) + y(x)^2 - a*x - b --R --R , 2 --R (43) y (x) + y(x) - a x - b @@ -467,7 +467,7 @@ ode13a:=solve(ode13,y,x) --E 46 --S 47 of 134 -ode14 := D(y(x),x) + y(x)**2 + a*x**m +ode14 := D(y(x),x) + y(x)^2 + a*x^m --R --R --R , m 2 @@ -484,7 +484,7 @@ ode14a:=solve(ode14,y,x) --E 48 --S 49 of 134 -ode15 := D(y(x),x) + y(x)**2 - 2*x**2*y(x) + x**4 -2*x-1 +ode15 := D(y(x),x) + y(x)^2 - 2*x^2*y(x) + x^4 -2*x-1 --R --R --R , 2 2 4 @@ -505,7 +505,7 @@ yx:=solve(ode15,y,x) --E 50 --S 51 of 134 -ode15expr:=D(yx,x) + yx**2 - 2*x**2*yx + x**4 -2*x-1 +ode15expr:=D(yx,x) + yx^2 - 2*x^2*yx + x^4 -2*x-1 --R --R (49) --R 2x , @@ -533,7 +533,7 @@ ode15expr:=D(yx,x) + yx**2 - 2*x**2*yx + x**4 -2*x-1 --E 51 --S 52 of 134 -ode16 := D(y(x),x) + y(x)**2 +(x*y(x)-1)*f(x) +ode16 := D(y(x),x) + y(x)^2 +(x*y(x)-1)*f(x) --R --R , 2 --R (50) y (x) + y(x) + x f(x)y(x) - f(x) @@ -549,7 +549,7 @@ ode16a:=solve(ode16,y,x) --E 53 --S 54 of 134 -ode17 := D(y(x),x) - y(x)**2 -3*y(x) + 4 +ode17 := D(y(x),x) - y(x)^2 -3*y(x) + 4 --R --R --R , 2 @@ -569,7 +569,7 @@ yx:=solve(ode17,y,x) --E 55 --S 56 of 134 -ode17expr:=D(yx,x) - yx**2 -3*yx + 4 +ode17expr:=D(yx,x) - yx^2 -3*yx + 4 --R --R (54) --R , 2 2 @@ -598,7 +598,7 @@ ode17expr:=D(yx,x) - yx**2 -3*yx + 4 --E 56 --S 57 of 134 -ode18 := D(y(x),x) - y(x)**2 - x*y(x) - x + 1 +ode18 := D(y(x),x) - y(x)^2 - x*y(x) - x + 1 --R --R --R , 2 @@ -631,7 +631,7 @@ yx:=solve(ode18,y,x) --E 58 --S 59 of 134 -ode18expr:=D(yx,x) - yx**2 - x*yx - x + 1 +ode18expr:=D(yx,x) - yx^2 - x*yx - x + 1 --R (57) --R 2 2 --R - x + 4x @@ -687,7 +687,7 @@ ode18expr:=D(yx,x) - yx**2 - x*yx - x + 1 --E 59 --S 60 of 134 -ode19 := D(y(x),x) - (y(x) + x)**2 +ode19 := D(y(x),x) - (y(x) + x)^2 --R --R --R , 2 2 @@ -710,7 +710,7 @@ yx:=solve(ode19,y,x) --E 61 --S 62 of 134 -ode19expr := D(yx,x) - (yx + x)**2 +ode19expr := D(yx,x) - (yx + x)^2 --R --R (60) --R +---+ @@ -745,7 +745,7 @@ ode19expr := D(yx,x) - (yx + x)**2 --E 62 --S 63 of 134 -ode20 := D(y(x),x) - y(x)**2 +(x**2 + 1)*y(x) - 2*x +ode20 := D(y(x),x) - y(x)^2 +(x^2 + 1)*y(x) - 2*x --R --R --R , 2 2 @@ -777,7 +777,7 @@ yx:=solve(ode20,y,x) --E 64 --S 65 of 134 -ode20expr:=D(yx,x) - yx**2 +(x**2 + 1)*yx - 2*x +ode20expr:=D(yx,x) - yx^2 +(x^2 + 1)*yx - 2*x --R --R (63) --R 3 2 @@ -847,7 +847,7 @@ ode20expr:=D(yx,x) - yx**2 +(x**2 + 1)*yx - 2*x --E 65 --S 66 of 134 -ode21 := D(y(x),x) - y(x)**2 +y(x)*sin(x) - cos(x) +ode21 := D(y(x),x) - y(x)^2 +y(x)*sin(x) - cos(x) --R --R --R , 2 @@ -865,7 +865,7 @@ ode21a:=solve(ode21,y,x) --E 67 --S 68 of 134 -ode22 := D(y(x),x) - y(x)**2 -y(x)*sin(2*x) - cos(2*x) +ode22 := D(y(x),x) - y(x)^2 -y(x)*sin(2*x) - cos(2*x) --R --R --R , 2 @@ -883,7 +883,7 @@ ode22a:=solve(ode22,y,x) --E 69 --S 70 of 134 -ode23 := D(y(x),x) + a*y(x)**2 - b +ode23 := D(y(x),x) + a*y(x)^2 - b --R --R --R , 2 @@ -908,7 +908,7 @@ yx:=solve(ode23,y,x) --E 71 --S 72 of 134 -ode23expr := D(yx,x) + a*yx**2 - b +ode23expr := D(yx,x) + a*yx^2 - b --R --R (70) --R 2 +---+ 2 @@ -932,7 +932,7 @@ ode23expr := D(yx,x) + a*yx**2 - b --E 72 --S 73 of 134 -ode24 := D(y(x),x) + a*y(x)**2 - b*x**nu +ode24 := D(y(x),x) + a*y(x)^2 - b*x^nu --R --R --R , nu 2 @@ -950,7 +950,7 @@ ode24a:=solve(ode24,y,x) --E 74 --S 75 of 134 -ode25 := D(y(x),x) + a*y(x)**2 - b*x**(2*nu) - c*x**(nu-1) +ode25 := D(y(x),x) + a*y(x)^2 - b*x^(2*nu) - c*x^(nu-1) --R --R --R , 2nu nu - 1 2 @@ -1100,7 +1100,7 @@ ode27a:=solve(ode27,y,x) --E 81 --S 82 of 134 -ode28 := D(y(x),x) + x*y(x)**2 -x**3*y(x) - 2*x +ode28 := D(y(x),x) + x*y(x)^2 -x^3*y(x) - 2*x --R --R --R , 2 3 @@ -1133,7 +1133,7 @@ ode28a:=solve(ode28,y,x) --E 83 --S 84 of 134 -ode29 := D(y(x),x) - x*y(x)**2 - 3*x*y(x) +ode29 := D(y(x),x) - x*y(x)^2 - 3*x*y(x) --R --R --R , 2 @@ -1154,7 +1154,7 @@ yx:=solve(ode29,y,x) --E 85 --S 86 of 134 -ode29expr := D(yx,x) - x*yx**2 - 3*x*yx +ode29expr := D(yx,x) - x*yx^2 - 3*x*yx --R --R (84) --R , 2 2 @@ -1184,7 +1184,7 @@ ode29expr := D(yx,x) - x*yx**2 - 3*x*yx --E 86 --S 87 of 134 -ode30 := D(y(x),x) + x**(-a-1)*y(x)**2 - x**a +ode30 := D(y(x),x) + x^(-a-1)*y(x)^2 - x^a --R --R --R , a 2 - a - 1 @@ -1202,7 +1202,7 @@ ode30a:=solve(ode30,y,x) --E 88 --S 89 of 134 -ode31 := D(y(x),x) - a*x**n*(y(x)**2+1) +ode31 := D(y(x),x) - a*x^n*(y(x)^2+1) --R --R --R , 2 n @@ -1223,7 +1223,7 @@ yx:=solve(ode31,y,x) --E 90 --S 91 of 134 -ode31expr := D(yx,x) - a*x**n*(yx**2+1) +ode31expr := D(yx,x) - a*x^n*(yx^2+1) --R --R (89) --R 2 , 3 2 2 3 2 n n log(x) 2 @@ -1251,7 +1251,7 @@ ode31expr := D(yx,x) - a*x**n*(yx**2+1) --E 91 --S 92 of 134 -ode32 := D(y(x),x) + y(x)**2*sin(x) - 2*sin(x)/cos(x)**2 +ode32 := D(y(x),x) + y(x)^2*sin(x) - 2*sin(x)/cos(x)^2 --R --R --R 2 , 2 2 @@ -1272,7 +1272,7 @@ yx:=solve(ode32,y,x) --E 93 --S 94 of 134 -ode33 := D(y(x),x) - y(x)**2*D(f(x),x)/g(x) + D(g(x),x)/f(x) +ode33 := D(y(x),x) - y(x)^2*D(f(x),x)/g(x) + D(g(x),x)/f(x) --R --R , , 2 , --R f(x)g(x)y (x) + g(x)g (x) - f(x)y(x) f (x) @@ -1290,7 +1290,7 @@ ode33a:=solve(ode33,y,x) --E 95 --S 96 of 134 -ode34 := D(y(x),x) + f(x)*y(x)**2 + g(x)*y(x) +ode34 := D(y(x),x) + f(x)*y(x)^2 + g(x)*y(x) --R --R , 2 --R (94) y (x) + f(x)y(x) + g(x)y(x) @@ -1310,7 +1310,7 @@ ode34a:=solve(ode34,y,x) --E 97 --S 98 of 134 -ode35 := D(y(x),x) + f(x)*(y(x)**2 + 2*a*y(x) +b) +ode35 := D(y(x),x) + f(x)*(y(x)^2 + 2*a*y(x) +b) --R --R , 2 --R (95) y (x) + f(x)y(x) + 2a f(x)y(x) + b f(x) @@ -1341,7 +1341,7 @@ yx:=solve(ode35,y,x) --E 99 --S 100 of 134 -ode35expr := D(yx,x) + f(x)*(yx**2 + 2*a*yx +b) +ode35expr := D(yx,x) + f(x)*(yx^2 + 2*a*yx +b) --R --R (97) --R 2 2 3 2 2 @@ -1400,7 +1400,7 @@ ode35expr := D(yx,x) + f(x)*(yx**2 + 2*a*yx +b) --R / --R 2 --R y(x) + 2a y(x) + b ---R ** +--R ^ --R 2 --R + --R 3 2 2 4 2 3 @@ -1433,7 +1433,7 @@ ode35expr := D(yx,x) + f(x)*(yx**2 + 2*a*yx +b) --E 100 --S 101 of 134 -ode36 := D(y(x),x) + y(x)**3 + a*x*y(x)**2 +ode36 := D(y(x),x) + y(x)^3 + a*x*y(x)^2 --R --R --R , 3 2 @@ -1451,7 +1451,7 @@ ode36a:=solve(ode36,y,x) --E 102 --S 103 of 134 -ode37 := D(y(x),x) - y(x)**3 - a*exp(x)*y(x)**2 +ode37 := D(y(x),x) - y(x)^3 - a*exp(x)*y(x)^2 --R --R , 2 x 3 --R (100) y (x) - a y(x) %e - y(x) @@ -1467,7 +1467,7 @@ ode37a:=solve(ode37,y,x) --E 104 --S 105 of 134 -ode38 := D(y(x),x) - a*y(x)**3 - b*x**(3/2) +ode38 := D(y(x),x) - a*y(x)^3 - b*x^(3/2) --R --R , +-+ 3 --R (102) y (x) - b x\|x - a y(x) @@ -1483,7 +1483,7 @@ ode38a:=solve(ode38,y,x) --E 106 --S 107 of 134 -ode39 := D(y(x),x) - a3*y(x)**3 - a2*y(x)**2 - a1*y(x) - a0 +ode39 := D(y(x),x) - a3*y(x)^3 - a2*y(x)^2 - a1*y(x) - a0 --R --R , 3 2 --R (104) y (x) - a3 y(x) - a2 y(x) - a1 y(x) - a0 @@ -1662,7 +1662,7 @@ yx:=solve(ode39,y,x) --E 108 --S 109 of 134 -ode40 := D(y(x),x) + 3*a*y(x)**3 + 6*a*x*y(x)**2 +ode40 := D(y(x),x) + 3*a*y(x)^3 + 6*a*x*y(x)^2 --R --R , 3 2 --R (106) y (x) + 3a y(x) + 6a x y(x) @@ -1678,7 +1678,7 @@ ode40a:=solve(ode40,y,x) --E 110 --S 111 of 134 -ode41 := D(y(x),x) + a*x*y(x)**3 + b*y(x)**2 +ode41 := D(y(x),x) + a*x*y(x)^3 + b*y(x)^2 --R --R , 3 2 --R (108) y (x) + a x y(x) + b y(x) @@ -1694,7 +1694,7 @@ ode41a:=solve(ode41,y,x) --E 112 --S 113 of 134 -ode42 := D(y(x),x) - x*(x+2)*y(x)**3 - (x+3)*y(x)**2 +ode42 := D(y(x),x) - x*(x+2)*y(x)^3 - (x+3)*y(x)^2 --R --R , 2 3 2 --R (110) y (x) + (- x - 2x)y(x) + (- x - 3)y(x) @@ -1710,7 +1710,7 @@ ode42a:=solve(ode42,y,x) --E 114 --S 115 of 134 -ode43 := D(y(x),x) + (3*a*x**2 + 4*a**2*x + b)*y(x)**3 + 3*x*y(x)**2 +ode43 := D(y(x),x) + (3*a*x^2 + 4*a^2*x + b)*y(x)^3 + 3*x*y(x)^2 --R --R , 2 2 3 2 --R (112) y (x) + (3a x + 4a x + b)y(x) + 3x y(x) @@ -1726,7 +1726,7 @@ ode43a:=solve(ode43,y,x) --E 116 --S 117 of 134 -ode44 := D(y(x),x) + 2*a*x**3*y(x)**3 + 2*x*y(x) +ode44 := D(y(x),x) + 2*a*x^3*y(x)^3 + 2*x*y(x) --R --R , 3 3 --R (114) y (x) + 2a x y(x) + 2x y(x) @@ -1747,7 +1747,7 @@ yx:=solve(ode44,y,x) --E 118 --S 119 of 134 -ode44expr := D(yx,x) + 2*a*x**3*yx**3 + 2*x*yx +ode44expr := D(yx,x) + 2*a*x^3*yx^3 + 2*x*yx --R --R (116) --R 2 2 2 2 @@ -1768,7 +1768,7 @@ ode44expr := D(yx,x) + 2*a*x**3*yx**3 + 2*x*yx --E 119 --S 120 of 134 -ode45 := D(y(x),x) + 2*(a**2*x**3 - b**2*x)*y(x)**3 + 3*b*y(x)**2 +ode45 := D(y(x),x) + 2*(a^2*x^3 - b^2*x)*y(x)^3 + 3*b*y(x)^2 --R --R , 2 3 2 3 2 --R (117) y (x) + (2a x - 2b x)y(x) + 3b y(x) @@ -1784,8 +1784,8 @@ ode45a:=solve(ode45,y,x) --E 121 --S 122 of 134 -ode46 := D(y(x),x) - x**a*y(x)**3 + 3*y(x)**2 - x**(-a)*y(x) _ - -x**(-2*a) + a*x**(-a-1) +ode46 := D(y(x),x) - x^a*y(x)^3 + 3*y(x)^2 - x^(-a)*y(x) _ + -x^(-2*a) + a*x^(-a-1) --R --R , 3 a - a - a - 1 - 2a 2 --R (119) y (x) - y(x) x - y(x)x + a x - x + 3y(x) @@ -1801,7 +1801,7 @@ ode46a:=solve(ode46,y,x) --E 123 --S 124 of 134 -ode47 := D(y(x),x) - a*(x**n - x)*y(x)**3 - y(x)**2 +ode47 := D(y(x),x) - a*(x^n - x)*y(x)^3 - y(x)^2 --R --R , 3 n 3 2 --R (121) y (x) - a y(x) x + a x y(x) - y(x) @@ -1817,7 +1817,7 @@ ode47a:=solve(ode47,y,x) --E 125 --S 126 of 134 -ode48 := D(y(x),x) - (a*x**n + b*x)*y(x)**3 - c*y(x)**2 +ode48 := D(y(x),x) - (a*x^n + b*x)*y(x)^3 - c*y(x)^2 --R --R , 3 n 3 2 --R (123) y (x) - a y(x) x - b x y(x) - c y(x) @@ -1833,7 +1833,7 @@ ode48a:=solve(ode48,y,x) --E 127 --S 128 of 134 -ode49 := D(y(x),x) + a*diff(phi(x),x)*y(x)**3 + 6*a*phi(x)*y(x)**2 + _ +ode49 := D(y(x),x) + a*diff(phi(x),x)*y(x)^3 + 6*a*phi(x)*y(x)^2 + _ (2*a+1)*y(x)*diff(phi(x),x,x)/diff(phi(x),x) +2*(a+1) --R --R There are no library operations named phi @@ -1879,7 +1879,7 @@ f0 := operator 'f0 --E 132 --S 133 of 134 -ode50 := D(y(x),x) - f3(x)*y(x)**3 - f2(x)*y(x)**2 - f1(x)*y(x) - f0(x) +ode50 := D(y(x),x) - f3(x)*y(x)^3 - f2(x)*y(x)^2 - f1(x)*y(x) - f0(x) --R --R , 3 2 --R (129) y (x) - f3(x)y(x) - f2(x)y(x) - f1(x)y(x) - f0(x) diff --git a/src/input/kamke1.input.pamphlet b/src/input/kamke1.input.pamphlet index db98425..c9fe836 100644 --- a/src/input/kamke1.input.pamphlet +++ b/src/input/kamke1.input.pamphlet @@ -87,7 +87,7 @@ ode51a:=solve(ode51,y,x) --E 6 --S 7 of 120 -ode52 := D(y(x),x) - a*y(x)**n - b*x**(n/(1-n)) +ode52 := D(y(x),x) - a*y(x)^n - b*x^(n/(1-n)) --R --R n --R - ----- @@ -105,7 +105,7 @@ ode52a:=solve(ode52,y,x) --E 8 --S 9 of 120 -ode53 := D(y(x),x) - f(x)**(1-n)*D(g(x),x)*y(x)**n/(a*g(x)+b)**n _ +ode53 := D(y(x),x) - f(x)^(1-n)*D(g(x),x)*y(x)^n/(a*g(x)+b)^n _ - D(f(x),x)*y(x)/f(x) - f(x)*D(g(x),x) --R --R (9) @@ -130,7 +130,7 @@ ode53a:=solve(ode53,y,x) --E 10 --S 11 of 120 -ode54 := D(y(x),x) - a**n*f(x)**(1-n)*D(g(x),x)*y(x)**n - _ +ode54 := D(y(x),x) - a^n*f(x)^(1-n)*D(g(x),x)*y(x)^n - _ D(f(x),x)*y(x)/f(x) - f(x)*D(g(x),x) --R --R , n - n + 1 n 2 , , @@ -149,7 +149,7 @@ ode54a:=solve(ode54,y,x) --E 12 --S 13 of 120 -ode55 := D(y(x),x) - f(x)*y(x)**n - g(x)*y(x) - h(x) +ode55 := D(y(x),x) - f(x)*y(x)^n - g(x)*y(x) - h(x) --R --R , n --R (13) y (x) - f(x)y(x) - g(x)y(x) - h(x) @@ -165,7 +165,7 @@ ode55a:=solve(ode55,y,x) --E 14 --S 15 of 120 -ode56 := D(y(x),x) - f(x)*y(x)**a - g(x)*y(x)**b +ode56 := D(y(x),x) - f(x)*y(x)^a - g(x)*y(x)^b --R --R , b a --R (15) y (x) - g(x)y(x) - f(x)y(x) @@ -235,11 +235,11 @@ ode58a:=solve(ode58,y,x) --E 21 -- this never finishes --- ode59 := D(y(x),x) - a*sqrt(y(x)**2+1) - b +-- ode59 := D(y(x),x) - a*sqrt(y(x)^2+1) - b -- --S 22 of 120 -ode60 := D(y(x),x) - sqrt(y(x)**2-1)/sqrt(x**2-1) +ode60 := D(y(x),x) - sqrt(y(x)^2-1)/sqrt(x^2-1) --R --R +------+ +---------+ --R | 2 , | 2 @@ -260,7 +260,7 @@ ode60a:=solve(ode60,y,x) --E 23 --S 24 of 120 -ode61 := D(y(x),x) - sqrt(x**2-1)/sqrt(y(x)**2-1) +ode61 := D(y(x),x) - sqrt(x^2-1)/sqrt(y(x)^2-1) --R --R +---------+ +------+ --R | 2 , | 2 @@ -326,7 +326,7 @@ yx:=solve(ode61,y,x) --E 25 --S 26 of 120 -ode61expr := D(yx,x) - sqrt(x**2-1)/sqrt(yx**2-1) +ode61expr := D(yx,x) - sqrt(x^2-1)/sqrt(yx^2-1) --R --R (26) --R 4 2 5 4 2 3 @@ -964,8 +964,8 @@ ode61expr := D(yx,x) - sqrt(x**2-1)/sqrt(yx**2-1) --E 26 --S 27 of 120 -ode62 := D(y(x),x) - (y(x)-x**2*sqrt(x**2-y(x)**2))/_ - (x*y(x)*sqrt(x**2-y(x)**2)+x) +ode62 := D(y(x),x) - (y(x)-x^2*sqrt(x^2-y(x)^2))/_ + (x*y(x)*sqrt(x^2-y(x)^2)+x) --R --R +------------+ +------------+ --R | 2 2 , 2 | 2 2 @@ -986,7 +986,7 @@ ode62a:=solve(ode62,y,x) --E 28 --S 29 of 120 -ode63 := D(y(x),x) - (1+ y(x)**2)/(abs(y(x)+sqrt(1+y(x)))*sqrt(1+x)**3) +ode63 := D(y(x),x) - (1+ y(x)^2)/(abs(y(x)+sqrt(1+y(x)))*sqrt(1+x)^3) --R --R +-----+ , +--------+ 2 --R (x + 1)\|x + 1 y (x)abs(\|y(x) + 1 + y(x)) - y(x) - 1 @@ -1005,7 +1005,7 @@ ode63a:=solve(ode63,y,x) --E 30 --S 31 of 120 -ode64 := D(y(x),x) - sqrt((a*y(x)**2+b*y(x)+c)/(a*x**2+b*x+c)) +ode64 := D(y(x),x) - sqrt((a*y(x)^2+b*y(x)+c)/(a*x^2+b*x+c)) --R --R +--------------------+ --R | 2 @@ -1116,11 +1116,11 @@ The results of this substitution are too long to include. It should be zero but Axiom cannot simplify it. \begin{chunk}{*} --S 33 of 120 -ode64expr := D(yx,x) - sqrt((a*yx**2+b*yx+c)/(a*x**2+b*x+c)); +ode64expr := D(yx,x) - sqrt((a*yx^2+b*yx+c)/(a*x^2+b*x+c)); --E 33 --S 34 of 120 -ode65 := D(y(x),x) - sqrt((y(x)**3+1)/(x**3+1)) +ode65 := D(y(x),x) - sqrt((y(x)^3+1)/(x^3+1)) --R --R +---------+ --R | 3 @@ -1175,7 +1175,7 @@ ode66a:=solve(ode66,y,x) --E 37 --S 38 of 120 -ode67 := D(y(x),x) - sqrt(1-y(x)**4)/sqrt(1-x**4) +ode67 := D(y(x),x) - sqrt(1-y(x)^4)/sqrt(1-x^4) --R --R +--------+ +-----------+ --R | 4 , | 4 @@ -1196,7 +1196,7 @@ ode67a:=solve(ode67,y,x) --E 39 --S 40 of 120 -ode68 := D(y(x),x) - sqrt((a*y(x)**4+b*y(x)**2+1)/(a*x**4+b*x**2+1)) +ode68 := D(y(x),x) - sqrt((a*y(x)^4+b*y(x)^2+1)/(a*x^4+b*x^2+1)) --R --R +---------------------+ --R | 4 2 @@ -1226,8 +1226,8 @@ ode68a:=solve(ode68,y,x) --E 41 --S 42 of 120 -ode69 := D(y(x),x) - sqrt((b4*y(x)**4+b3*y(x)**3+b2*y(x)**2+b1*y(x)+b0)*_ - (a4*x**4+a3*x**3+a2*x**2+a1*x+a0)) +ode69 := D(y(x),x) - sqrt((b4*y(x)^4+b3*y(x)^3+b2*y(x)^2+b1*y(x)+b0)*_ + (a4*x^4+a3*x^3+a2*x^2+a1*x+a0)) --R --R --R (42) @@ -1266,8 +1266,8 @@ ode69a:=solve(ode69,y,x) --E 43 --S 44 of 120 -ode70 := D(y(x),x) - sqrt((a4*x**4+a3*x**3+a2*x**2+a1*x+a0)/_ - (b4*y(x)**4+b3*y(x)**3+b2*y(x)**2+b1*y(x)+b0)) +ode70 := D(y(x),x) - sqrt((a4*x^4+a3*x^3+a2*x^2+a1*x+a0)/_ + (b4*y(x)^4+b3*y(x)^3+b2*y(x)^2+b1*y(x)+b0)) --R --R +---------------------------------------------+ --R | 4 3 2 @@ -1290,8 +1290,8 @@ ode70a:=solve(ode70,y,x) --E 45 --S 46 of 120 -ode71 := D(y(x),x) - sqrt((b4*y(x)**4+b3*y(x)**3+b2*y(x)**2+b1*y(x)+b0)/_ - (a4*x**4+a3*x**3+a2*x**2+a1*x+a0)) +ode71 := D(y(x),x) - sqrt((b4*y(x)^4+b3*y(x)^3+b2*y(x)^2+b1*y(x)+b0)/_ + (a4*x^4+a3*x^3+a2*x^2+a1*x+a0)) --R --R +---------------------------------------------+ --R | 4 3 2 @@ -1342,8 +1342,8 @@ R2:=operator 'R2 --E 49 --S 50 of 120 -ode72 := D(y(x),x) - R1(x,sqrt(a4*x**4+a3*x**3+a2*x**2+a1*x+a0))*_ - R2(y(x),sqrt(b4*y(x)**4+b3*y(x)**3+b2*y(x)**2+b1*y(x)+b0)) +ode72 := D(y(x),x) - R1(x,sqrt(a4*x^4+a3*x^3+a2*x^2+a1*x+a0))*_ + R2(y(x),sqrt(b4*y(x)^4+b3*y(x)^3+b2*y(x)^2+b1*y(x)+b0)) --R --R (48) --R - @@ -1372,8 +1372,8 @@ ode72a:=solve(ode72,y,x) --E 51 --S 52 of 120 -ode73 := D(y(x),x) - ((a3*x**3+a2*x**2+a1*x+a0)/_ - (a3*y(x)**3+a2*y(x)**2+a1*y(x)+a0))**(2/3) +ode73 := D(y(x),x) - ((a3*x^3+a2*x^2+a1*x+a0)/_ + (a3*y(x)^3+a2*y(x)^2+a1*y(x)+a0))^(2/3) --R --R +----------------------------------+2 --R | 3 2 @@ -1600,7 +1600,7 @@ ode81a:=solve(ode81,y,x) --E 69 --S 70 of 120 -ode82 := D(y(x),x) - a*(1+tan(y(x))**2) + tan(y(x))*tan(x) +ode82 := D(y(x),x) - a*(1+tan(y(x))^2) + tan(y(x))*tan(x) --R --R , 2 --R (67) y (x) - a tan(y(x)) + tan(x)tan(y(x)) - a @@ -1648,7 +1648,7 @@ ode84a:=solve(ode84,y,x) --E 75 --S 76 of 120 -ode85 := D(y(x),x) - x**(a-1)*y(x)**(1-b)*f(x**a/a + y(x)**b/b) +ode85 := D(y(x),x) - x^(a-1)*y(x)^(1-b)*f(x^a/a + y(x)^b/b) --R --R b a --R a - 1 - b + 1 a y(x) + b x , @@ -1665,7 +1665,7 @@ ode85a:=solve(ode85,y,x) --E 77 --S 78 of 120 -ode86 := D(y(x),x) - (y(x)-x*f(x**2+a*y(x)**2))/(x+a*y(x)*f(x**2+a*y(x)**2)) +ode86 := D(y(x),x) - (y(x)-x*f(x^2+a*y(x)^2))/(x+a*y(x)*f(x^2+a*y(x)^2)) --R --R 2 2 , 2 2 --R (a y(x)f(a y(x) + x ) + x)y (x) + x f(a y(x) + x ) - y(x) @@ -1684,8 +1684,8 @@ ode86a:=solve(ode86,y,x) --E 79 --S 80 of 120 -ode87 := D(y(x),x) - (y(x)*a*f(x**c*y(x))+c*x**a*y(x)**b)/_ - (x*b*f(x**c*y(x))-x**a*y(x)**b) +ode87 := D(y(x),x) - (y(x)*a*f(x^c*y(x))+c*x^a*y(x)^b)/_ + (x*b*f(x^c*y(x))-x^a*y(x)^b) --R --R a b c , a b c --R (x y(x) - b x f(y(x)x ))y (x) + c x y(x) + a y(x)f(y(x)x ) @@ -1704,7 +1704,7 @@ ode87a:=solve(ode87,y,x) --E 81 --S 82 of 120 -ode88 := 2*D(y(x),x) - 3*y(x)**2 - 4*a*y(x) - b - c*exp(-2*a*x) +ode88 := 2*D(y(x),x) - 3*y(x)^2 - 4*a*y(x) - b - c*exp(-2*a*x) --R --R , - 2a x 2 --R (79) 2y (x) - c %e - 3y(x) - 4a y(x) - b @@ -1720,7 +1720,7 @@ ode88a:=solve(ode88,y,x) --E 83 --S 84 of 120 -ode89 := x*D(y(x),x) - sqrt(a**2 - x**2) +ode89 := x*D(y(x),x) - sqrt(a^2 - x^2) --R --R +---------+ --R , | 2 2 @@ -1761,7 +1761,7 @@ yx:=ode89a.particular --E 86 --S 87 of 120 -ode89expr := x*D(yx,x) - sqrt(a**2 - x**2) +ode89expr := x*D(yx,x) - sqrt(a^2 - x^2) --R --R (84) 0 --R Type: Expression(Integer) @@ -1834,7 +1834,7 @@ ode91expr := x*D(yx,x) - yx - x/log(x) --E 95 --S 96 of 120 -ode92 := x*D(y(x),x) - y(x) - x**2*sin(x) +ode92 := x*D(y(x),x) - y(x) - x^2*sin(x) --R --R , 2 --R (93) xy (x) - x sin(x) - y(x) @@ -1857,7 +1857,7 @@ yx:=ode92a.particular --E 98 --S 99 of 120 -ode92expr := x*D(yx,x) - yx - x**2*sin(x) +ode92expr := x*D(yx,x) - yx - x^2*sin(x) --R --R (96) 0 --R Type: Expression(Integer) @@ -1897,7 +1897,7 @@ ode93 := x*D(yx,x) - yx - x*cos(log(log(x)))/log(x) --E 103 --S 104 of 120 -ode94 := x*D(y(x),x) +a*y(x) + b*x**n +ode94 := x*D(y(x),x) +a*y(x) + b*x^n --R --R , n --R (101) xy (x) + b x + a y(x) @@ -1926,7 +1926,7 @@ yx:=ode94a.particular --E 106 --S 107 of 120 -ode94expr := x*D(yx,x) +a*yx + b*x**n +ode94expr := x*D(yx,x) +a*yx + b*x^n --R --R n log(x) n --R (104) - b %e + b x @@ -1949,7 +1949,7 @@ exprule ode94expr --E 109 --S 110 of 120 -ode95 := x*D(y(x),x) + y(x)**2 + x**2 +ode95 := x*D(y(x),x) + y(x)^2 + x^2 --R --R , 2 2 --R (107) xy (x) + y(x) + x @@ -1966,7 +1966,7 @@ ode95a:=solve(ode95,y,x) --E 111 --S 112 of 120 -ode96 := x*D(y(x),x) - y(x)**2 + 1 +ode96 := x*D(y(x),x) - y(x)^2 + 1 --R --R --R , 2 @@ -1986,7 +1986,7 @@ yx:=solve(ode96,y,x) --E 113 --S 114 of 120 -ode96expr := x*D(yx,x) - yx**2 + 1 +ode96expr := x*D(yx,x) - yx^2 + 1 --R --R (111) --R 2 , 2 2 +--------+ +--------+ 2 @@ -1999,7 +1999,7 @@ ode96expr := x*D(yx,x) - yx**2 + 1 --E 114 --S 115 of 120 -ode98 := x*D(y(x),x) + a*y(x)**2 - b*y(x) + c*x**(2*b) +ode98 := x*D(y(x),x) + a*y(x)^2 - b*y(x) + c*x^(2*b) --R --R --R , 2b 2 @@ -2016,7 +2016,7 @@ ode98a:=solve(ode98,y,x) --E 116 --S 117 of 120 -ode99 := x*D(y(x),x) + a*y(x)**2 - b*y(x) - c*x**beta +ode99 := x*D(y(x),x) + a*y(x)^2 - b*y(x) - c*x^beta --R --R --R , beta 2 @@ -2034,7 +2034,7 @@ ode99a:=solve(ode99,y,x) --E 118 --S 119 of 120 -ode100 := x*D(y(x),x) + x*y(x)**2 + a +ode100 := x*D(y(x),x) + x*y(x)^2 + a --R --R --R , 2 diff --git a/src/input/kamke2.input.pamphlet b/src/input/kamke2.input.pamphlet index cf319aa..0930ad6 100644 --- a/src/input/kamke2.input.pamphlet +++ b/src/input/kamke2.input.pamphlet @@ -43,7 +43,7 @@ g:=operator 'g ------------------------------------------------------------------- --S 4 of 126 -ode101 := x*D(y(x),x) + x*y(x)**2 - y(x) +ode101 := x*D(y(x),x) + x*y(x)^2 - y(x) --R --R , 2 --R (4) xy (x) + x y(x) - y(x) @@ -74,7 +74,7 @@ yx:=solve(ode101,y,x) --E 5 --S 6 of 126 -ode101expr := x*D(yx,x) + x*yx**2 - yx +ode101expr := x*D(yx,x) + x*yx^2 - yx --R --R 2 , 5 2 2 4 3 --R 4x y (x) + (x + 2x )y(x) - 4x y(x) + 4x @@ -87,7 +87,7 @@ ode101expr := x*D(yx,x) + x*yx**2 - yx ------------------------------------------------------------------- --S 7 of 126 -ode102 := x*D(y(x),x) + x*y(x)**2 - y(x) - a*x**3 +ode102 := x*D(y(x),x) + x*y(x)^2 - y(x) - a*x^3 --R --R , 2 3 --R (7) xy (x) + x y(x) - y(x) - a x @@ -120,7 +120,7 @@ yx:=solve(ode102,y,x) --E 8 --S 9 of 126 -ode102expr := x*D(yx,x) + x*yx**2 - yx - a*x**3 +ode102expr := x*D(yx,x) + x*yx^2 - yx - a*x^3 --R --R (9) --R 2 2 3 2 3 +-+ @@ -222,7 +222,7 @@ ode102expr := x*D(yx,x) + x*yx**2 - yx - a*x**3 ------------------------------------------------------------------- --S 10 of 126 -ode103 := x*D(y(x),x) + x*y(x)**2 - (2*x**2+1)*y(x) - x**3 +ode103 := x*D(y(x),x) + x*y(x)^2 - (2*x^2+1)*y(x) - x^3 --R --R , 2 2 3 --R (10) xy (x) + x y(x) + (- 2x - 1)y(x) - x @@ -257,7 +257,7 @@ yx:=solve(ode103,y,x) --E 11 --S 12 of 126 -ode103expr := x*D(yx,x) + x*yx**2 - (2*x**2+1)*yx - x**3 +ode103expr := x*D(yx,x) + x*yx^2 - (2*x^2+1)*yx - x^3 --R --R (12) --R 2 +-+ @@ -311,7 +311,7 @@ ode103expr := x*D(yx,x) + x*yx**2 - (2*x**2+1)*yx - x**3 ------------------------------------------------------------------- --S 13 of 126 -ode106 := x*D(y(x),x) + x**a*y(x)**2 + (a-b)*y(x)/2 + x**b +ode106 := x*D(y(x),x) + x^a*y(x)^2 + (a-b)*y(x)/2 + x^b --R --R , b 2 a --R 2xy (x) + 2x + 2y(x) x + (- b + a)y(x) @@ -347,7 +347,7 @@ yx:=solve(ode106,y,x) ------------------------------------------------------------------- --S 15 of 126 -ode107 := x*D(y(x),x) + a*x**alpha*y(x)**2 + b*y(x) - c*x**beta +ode107 := x*D(y(x),x) + a*x^alpha*y(x)^2 + b*y(x) - c*x^beta --R --R , beta 2 alpha --R (15) xy (x) - c x + a y(x) x + b y(x) @@ -367,7 +367,7 @@ yx:=solve(ode107,y,x) ------------------------------------------------------------------- --S 17 of 126 -ode108 := x*D(y(x),x) - y(x)**2*log(x) + y(x) +ode108 := x*D(y(x),x) - y(x)^2*log(x) + y(x) --R --R , 2 --R (17) xy (x) - y(x) log(x) + y(x) @@ -397,7 +397,7 @@ yx:=solve(ode108,y,x) --E 18 --S 19 of 126 -ode108expr := x*D(yx,x) - yx**2*log(x) + yx +ode108expr := x*D(yx,x) - yx^2*log(x) + yx --R --R (19) --R 2 , 2 3 2 2 @@ -462,7 +462,7 @@ ode109expr := x*D(yx,x) - yx*(2*yx*log(x)-1) ------------------------------------------------------------------- --S 23 of 126 -ode110 := x*D(y(x),x) + f(x)*(y(x)**2-x**2) +ode110 := x*D(y(x),x) + f(x)*(y(x)^2-x^2) --R --R , 2 2 --R (23) xy (x) + f(x)y(x) - x f(x) @@ -482,7 +482,7 @@ yx:=solve(ode110,y,x) ------------------------------------------------------------------- --S 25 of 126 -ode111 := x*D(y(x),x) + y(x)**3 + 3*x*y(x)**2 +ode111 := x*D(y(x),x) + y(x)^3 + 3*x*y(x)^2 --R --R , 3 2 --R (25) xy (x) + y(x) + 3x y(x) @@ -505,7 +505,7 @@ yx:=solve(ode111,y,x) ------------------------------------------------------------------- --S 27 of 126 -ode112 := x*D(y(x),x) - sqrt(y(x)**2 + x**2) - y(x) +ode112 := x*D(y(x),x) - sqrt(y(x)^2 + x^2) - y(x) --R --R +----------+ --R , | 2 2 @@ -532,7 +532,7 @@ yx:=solve(ode112,y,x) ------------------------------------------------------------------- --S 29 of 126 -ode113 := x*D(y(x),x) + a*sqrt(y(x)**2 + x**2) - y(x) +ode113 := x*D(y(x),x) + a*sqrt(y(x)^2 + x^2) - y(x) --R --R +----------+ --R , | 2 2 @@ -564,7 +564,7 @@ yx:=solve(ode113,y,x) ------------------------------------------------------------------- --S 31 of 126 -ode114 := x*D(y(x),x) - x*sqrt(y(x)**2 + x**2) - y(x) +ode114 := x*D(y(x),x) - x*sqrt(y(x)^2 + x^2) - y(x) --R --R +----------+ --R , | 2 2 @@ -591,7 +591,7 @@ yx:=solve(ode114,y,x) ------------------------------------------------------------------- --S 33 of 126 -ode115 := x*D(y(x),x) - x*(y(x)-x)*sqrt(y(x)**2 + x**2) - y(x) +ode115 := x*D(y(x),x) - x*(y(x)-x)*sqrt(y(x)^2 + x^2) - y(x) --R --R +----------+ --R , 2 | 2 2 @@ -618,7 +618,7 @@ yx:=solve(ode115,y,x) ------------------------------------------------------------------- --S 35 of 126 -ode116 := x*D(y(x),x) - x*sqrt((y(x)**2 - x**2)*(y(x)**2-4*x**2)) - y(x) +ode116 := x*D(y(x),x) - x*sqrt((y(x)^2 - x^2)*(y(x)^2-4*x^2)) - y(x) --R --R +----------------------+ --R , | 4 2 2 4 @@ -759,7 +759,7 @@ yx:=solve(ode119,y,x) ------------------------------------------------------------------- --S 44 of 126 -ode120 := x*D(y(x),x) - y(x)*(x*log(x**2/y(x))+2) +ode120 := x*D(y(x),x) - y(x)*(x*log(x^2/y(x))+2) --R --R 2 --R , x @@ -812,7 +812,7 @@ yx:=solve(ode121,y,x) ------------------------------------------------------------------- --S 48 of 126 -ode122 := x*D(y(x),x) + (sin(y(x))-3*x**2*cos(y(x)))*cos(y(x)) +ode122 := x*D(y(x),x) + (sin(y(x))-3*x^2*cos(y(x)))*cos(y(x)) --R --R , 2 2 --R (48) xy (x) + cos(y(x))sin(y(x)) - 3x cos(y(x)) @@ -963,7 +963,7 @@ yx:=solve(ode126,y,x) ------------------------------------------------------------------- --S 58 of 126 -ode127 := x*D(y(x),x) - y(x)*f(x**a*y(x)**b) +ode127 := x*D(y(x),x) - y(x)*f(x^a*y(x)^b) --R --R a b , --R (58) - y(x)f(x y(x) ) + xy (x) @@ -988,7 +988,7 @@ yx:=solve(ode127,y,x) ------------------------------------------------------------------- --S 60 of 126 -ode128 := x*D(y(x),x) + a*y(x) - f(x)*g(x**a*y(x)) +ode128 := x*D(y(x),x) + a*y(x) - f(x)*g(x^a*y(x)) --R --R , a --R (60) xy (x) - f(x)g(y(x)x ) + a y(x) @@ -1054,7 +1054,7 @@ yx:=solve(ode129,y,x) ------------------------------------------------------------------- --S 64 of 126 -ode130 := 2*x*D(y(x),x) - y(x) -2*x**3 +ode130 := 2*x*D(y(x),x) - y(x) -2*x^3 --R --R , 3 --R (64) 2xy (x) - y(x) - 2x @@ -1096,7 +1096,7 @@ yx:=ode130a.particular --E 66 --S 67 of 126 -ode130expr := 2*x*D(yx,x) - yx -2*x**3 +ode130expr := 2*x*D(yx,x) - yx -2*x^3 --R --R (67) 0 --R Type: Expression(Integer) @@ -1149,7 +1149,7 @@ ode131expr := (2*x+1)*D(yx,x) - 4*exp(-yx) + 2 ------------------------------------------------------------------- --S 71 of 126 -ode132 := 3*x*D(y(x),x) - 3*x*log(x)*y(x)**4 - y(x) +ode132 := 3*x*D(y(x),x) - 3*x*log(x)*y(x)^4 - y(x) --R --R , 4 --R (71) 3xy (x) - 3x y(x) log(x) - y(x) @@ -1200,7 +1200,7 @@ yx:=solve(ode132,y,x) --E 72 --S 73 of 126 -ode132expr := 3*x*D(yx,x) - 3*x*log(x)*yx**4 - yx +ode132expr := 3*x*D(yx,x) - 3*x*log(x)*yx^4 - yx --R --R (73) --R 2 8 , 9 12 5 @@ -1234,7 +1234,7 @@ ode132expr := 3*x*D(yx,x) - 3*x*log(x)*yx**4 - yx ------------------------------------------------------------------- --S 74 of 126 -ode133 := x**2*D(y(x),x) + y(x) - x +ode133 := x^2*D(y(x),x) + y(x) - x --R --R 2 , --R (74) x y (x) + y(x) - x @@ -1272,7 +1272,7 @@ yx:=solve(ode133,y,x) ------------------------------------------------------------------- --S 76 of 126 -ode134 := x**2*D(y(x),x) - y(x) + x**2*exp(x-1/x) +ode134 := x^2*D(y(x),x) - y(x) + x^2*exp(x-1/x) --R --R 2 --R x - 1 @@ -1322,7 +1322,7 @@ yx:=ode134a.particular --E 78 --S 79 of 126 -ode134expr := x**2*D(yx,x) - yx + x**2*exp(x-1/x) +ode134expr := x^2*D(yx,x) - yx + x^2*exp(x-1/x) --R --R (79) 0 --R Type: Expression(Integer) @@ -1330,7 +1330,7 @@ ode134expr := x**2*D(yx,x) - yx + x**2*exp(x-1/x) ------------------------------------------------------------------- --S 80 of 126 -ode135 := x**2*D(y(x),x) - (x-1)*y(x) +ode135 := x^2*D(y(x),x) - (x-1)*y(x) --R --R 2 , --R (80) x y (x) + (- x + 1)y(x) @@ -1368,7 +1368,7 @@ yx:=ode135a.particular --E 82 --S 83 of 126 -ode135expr := x**2*D(yx,x) - (x-1)*yx +ode135expr := x^2*D(yx,x) - (x-1)*yx --R --R (83) 0 --R Type: Expression(Integer) @@ -1376,7 +1376,7 @@ ode135expr := x**2*D(yx,x) - (x-1)*yx ------------------------------------------------------------------- --S 84 of 126 -ode136 := x**2*D(y(x),x) + y(x)**2 + x*y(x) + x**2 +ode136 := x^2*D(y(x),x) + y(x)^2 + x*y(x) + x^2 --R --R 2 , 2 2 --R (84) x y (x) + y(x) + x y(x) + x @@ -1406,7 +1406,7 @@ yx:=solve(ode136,y,x) --E 85 --S 86 of 126 -ode136expr := x**2*D(yx,x) + yx**2 + x*yx + x**2 +ode136expr := x^2*D(yx,x) + yx^2 + x*yx + x^2 --R --R (86) --R 3 , 2 2 2 @@ -1426,7 +1426,7 @@ ode136expr := x**2*D(yx,x) + yx**2 + x*yx + x**2 ------------------------------------------------------------------- --S 87 of 126 -ode137 := x**2*D(y(x),x) - y(x)**2 - x*y(x) +ode137 := x^2*D(y(x),x) - y(x)^2 - x*y(x) --R --R 2 , 2 --R (87) x y (x) - y(x) - x y(x) @@ -1456,7 +1456,7 @@ yx:=solve(ode137,y,x) --E 88 --S 89 of 126 -ode137expr := x**2*D(yx,x) - yx**2 - x*yx +ode137expr := x^2*D(yx,x) - yx^2 - x*yx --R --R 3 , 2 2 2 2 2 --R - x y (x) - y(x) log(x) + (- x y(x) - 2x y(x))log(x) + x y(x) - x @@ -1469,7 +1469,7 @@ ode137expr := x**2*D(yx,x) - yx**2 - x*yx ------------------------------------------------------------------- --S 90 of 126 -ode138 := x**2*D(y(x),x) - y(x)**2 - x*y(x) - x**2 +ode138 := x^2*D(y(x),x) - y(x)^2 - x*y(x) - x^2 --R --R 2 , 2 2 --R (90) x y (x) - y(x) - x y(x) - x @@ -1503,7 +1503,7 @@ yx:=solve(ode138,y,x) --E 91 --S 92 of 126 -ode138expr := x**2*D(yx,x) - yx**2 - x*yx - x**2 +ode138expr := x^2*D(yx,x) - yx^2 - x*yx - x^2 --R --R (92) --R 3 +---+ 3 4 +---+ 4 @@ -1554,7 +1554,7 @@ ode138expr := x**2*D(yx,x) - yx**2 - x*yx - x**2 ------------------------------------------------------------------- --S 93 of 126 -ode139 := x**2*(D(y(x),x)+y(x)**2) + a*x**k - b*(b-1) +ode139 := x^2*(D(y(x),x)+y(x)^2) + a*x^k - b*(b-1) --R --R 2 , k 2 2 2 --R (93) x y (x) + a x + x y(x) - b + b @@ -1579,7 +1579,7 @@ yx:=solve(ode139,y,x) ------------------------------------------------------------------- --S 95 of 126 -ode140 := x**2*(D(y(x),x)+y(x)**2) + 4*x*y(x) + 2 +ode140 := x^2*(D(y(x),x)+y(x)^2) + 4*x*y(x) + 2 --R --R 2 , 2 2 --R (95) x y (x) + x y(x) + 4x y(x) + 2 @@ -1610,7 +1610,7 @@ yx:=solve(ode140,y,x) --E 96 --S 97 of 126 -ode140expr := x**2*(D(yx,x)+yx**2) + 4*x*yx + 2 +ode140expr := x^2*(D(yx,x)+yx^2) + 4*x*yx + 2 --R --R (97) --R 4 , 4 3 2 2 3 2 2 @@ -1624,7 +1624,7 @@ ode140expr := x**2*(D(yx,x)+yx**2) + 4*x*yx + 2 ------------------------------------------------------------------- --S 98 of 126 -ode141 := x**2*(D(y(x),x)+y(x)**2) + a*x*y(x) + b +ode141 := x^2*(D(y(x),x)+y(x)^2) + a*x*y(x) + b --R --R 2 , 2 2 --R (98) x y (x) + x y(x) + a x y(x) + b @@ -1663,7 +1663,7 @@ yx:=solve(ode141,y,x) --E 99 --S 100 of 126 -ode141expr := x**2*(D(yx,x)+yx**2) + a*x*yx + b +ode141expr := x^2*(D(yx,x)+yx^2) + a*x*yx + b --R --R (100) --R 2 4 3 2 3 @@ -1824,7 +1824,7 @@ ode141expr := x**2*(D(yx,x)+yx**2) + a*x*yx + b ------------------------------------------------------------------- --S 101 of 126 -ode142 := x**2*(D(y(x),x)-y(x)**2) - a*x**2*y(x) + a*x + 2 +ode142 := x^2*(D(y(x),x)-y(x)^2) - a*x^2*y(x) + a*x + 2 --R --R 2 , 2 2 2 --R (101) x y (x) - x y(x) - a x y(x) + a x + 2 @@ -1848,7 +1848,7 @@ yx:=solve(ode142,y,x) --E 102 --S 103 of 126 -ode142expr := x**2*(D(yx,x)-yx**2) - a*x**2*yx + a*x + 2 +ode142expr := x^2*(D(yx,x)-yx^2) - a*x^2*yx + a*x + 2 --R --R (103) --R 6 6 - a x , @@ -1883,7 +1883,7 @@ ode142expr := x**2*(D(yx,x)-yx**2) - a*x**2*yx + a*x + 2 ------------------------------------------------------------------- --S 104 of 126 -ode143 := x**2*(D(y(x),x)+a*y(x)**2) - b +ode143 := x^2*(D(y(x),x)+a*y(x)^2) - b --R --R 2 , 2 2 --R (104) x y (x) + a x y(x) - b @@ -1924,7 +1924,7 @@ yx:=solve(ode143,y,x) --E 105 --S 106 of 126 -ode143expr := x**2*(D(yx,x)+a*yx**2) - b +ode143expr := x^2*(D(yx,x)+a*yx^2) - b --R --R (106) --R +--------+ @@ -1963,7 +1963,7 @@ ode143expr := x**2*(D(yx,x)+a*yx**2) - b ------------------------------------------------------------------- --S 107 of 126 -ode144 := x**2*(D(y(x),x)+a*y(x)**2) + b*x**alpha + c +ode144 := x^2*(D(y(x),x)+a*y(x)^2) + b*x^alpha + c --R --R 2 , alpha 2 2 --R (107) x y (x) + b x + a x y(x) + c @@ -1983,7 +1983,7 @@ yx:=solve(ode144,y,x) ------------------------------------------------------------------- --S 109 of 126 -ode145 := x**2*D(y(x),x) + a*y(x)**3 - a*x**2*y(x)**2 +ode145 := x^2*D(y(x),x) + a*y(x)^3 - a*x^2*y(x)^2 --R --R 2 , 3 2 2 --R (109) x y (x) + a y(x) - a x y(x) @@ -2005,7 +2005,7 @@ yx:=solve(ode145,y,x) ------------------------------------------------------------------- --S 111 of 126 -ode146 := x**2*D(y(x),x) + x*y(x)**3 + a*y(x)**2 +ode146 := x^2*D(y(x),x) + x*y(x)^3 + a*y(x)^2 --R --R 2 , 3 2 --R (111) x y (x) + x y(x) + a y(x) @@ -2027,7 +2027,7 @@ yx:=solve(ode146,y,x) ------------------------------------------------------------------- --S 113 of 126 -ode147 := x**2*D(y(x),x) + a*x**2*y(x)**3 + b*y(x)**2 +ode147 := x^2*D(y(x),x) + a*x^2*y(x)^3 + b*y(x)^2 --R --R 2 , 2 3 2 --R (113) x y (x) + a x y(x) + b y(x) @@ -2048,7 +2048,7 @@ yx:=solve(ode147,y,x) ------------------------------------------------------------------- --S 115 of 126 -ode148 := (x**2+1)*D(y(x),x) + x*y(x) - 1 +ode148 := (x^2+1)*D(y(x),x) + x*y(x) - 1 --R --R 2 , --R (115) (x + 1)y (x) + x y(x) - 1 @@ -2095,7 +2095,7 @@ yx:=ode148a.particular --E 117 --S 118 of 126 -ode148expr := (x**2+1)*D(yx,x) + x*yx - 1 +ode148expr := (x^2+1)*D(yx,x) + x*yx - 1 --R --R (118) 0 --R Type: Expression(Integer) @@ -2103,7 +2103,7 @@ ode148expr := (x**2+1)*D(yx,x) + x*yx - 1 ------------------------------------------------------------------- --S 119 of 126 -ode149 := (x**2+1)*D(y(x),x) + x*y(x) - x*(x**2+1) +ode149 := (x^2+1)*D(y(x),x) + x*y(x) - x*(x^2+1) --R --R 2 , 3 --R (119) (x + 1)y (x) + x y(x) - x - x @@ -2147,7 +2147,7 @@ yx:=ode149a.particular --E 121 --S 122 of 126 -ode149expr := (x**2+1)*D(yx,x) + x*yx - x*(x**2+1) +ode149expr := (x^2+1)*D(yx,x) + x*yx - x*(x^2+1) --R --R (122) 0 --R Type: Expression(Integer) @@ -2155,7 +2155,7 @@ ode149expr := (x**2+1)*D(yx,x) + x*yx - x*(x**2+1) ------------------------------------------------------------------- --S 123 of 126 -ode150 := (x**2+1)*D(y(x),x) + 2*x*y(x) - 2*x**2 +ode150 := (x^2+1)*D(y(x),x) + 2*x*y(x) - 2*x^2 --R --R 2 , 2 --R (123) (x + 1)y (x) + 2x y(x) - 2x @@ -2199,7 +2199,7 @@ yx:=ode150a.particular --E 125 --S 126 of 126 -ode150expr := (x**2+1)*D(yx,x) + 2*x*yx - 2*x**2 +ode150expr := (x^2+1)*D(yx,x) + 2*x*yx - 2*x^2 --R --R (126) 0 --R Type: Expression(Integer) diff --git a/src/input/kamke3.input.pamphlet b/src/input/kamke3.input.pamphlet index 7834508..697b94a 100644 --- a/src/input/kamke3.input.pamphlet +++ b/src/input/kamke3.input.pamphlet @@ -29,7 +29,7 @@ y:=operator 'y --E 1 --S 2 of 139 -ode151 := (x**2+1)*D(y(x),x) + (y(x)**2+1)*(2*x*y(x) - 1) +ode151 := (x^2+1)*D(y(x),x) + (y(x)^2+1)*(2*x*y(x) - 1) --R --R --R 2 , 3 2 @@ -47,7 +47,7 @@ ode151a:=solve(ode151,y,x) --E 3 --S 4 of 139 -ode152 := (x**2+1)*D(y(x),x) + x*sin(y(x))*cos(y(x)) - x*(x**2+1)*cos(y(x))**2 +ode152 := (x^2+1)*D(y(x),x) + x*sin(y(x))*cos(y(x)) - x*(x^2+1)*cos(y(x))^2 --R --R --R 2 , 3 2 @@ -65,7 +65,7 @@ ode152a:=solve(ode152,y,x) --E 5 --S 6 of 139 -ode153 := (x**2-1)*D(y(x),x) - x*y(x) + a +ode153 := (x^2-1)*D(y(x),x) - x*y(x) + a --R --R --R 2 , @@ -93,7 +93,7 @@ yx:=ode153a.particular --E 8 --S 9 of 139 -ode153expr := (x**2-1)*D(yx,x) - x*yx + a +ode153expr := (x^2-1)*D(yx,x) - x*yx + a --R --R --R (9) 0 @@ -101,7 +101,7 @@ ode153expr := (x**2-1)*D(yx,x) - x*yx + a --E 9 --S 10 of 139 -ode154 := (x**2-1)*D(y(x),x) + 2*x*y(x) - cos(x) +ode154 := (x^2-1)*D(y(x),x) + 2*x*y(x) - cos(x) --R --R --R 2 , @@ -133,7 +133,7 @@ yx:=ode154a.particular --E 12 --S 13 of 139 -ode154expr := (x**2-1)*D(yx,x) + 2*x*yx - cos(x) +ode154expr := (x^2-1)*D(yx,x) + 2*x*yx - cos(x) --R --R --R (13) 0 @@ -141,7 +141,7 @@ ode154expr := (x**2-1)*D(yx,x) + 2*x*yx - cos(x) --E 13 --S 14 of 139 -ode155 := (x**2-1)*D(y(x),x) + y(x)**2 - 2*x*y(x) + 1 +ode155 := (x^2-1)*D(y(x),x) + y(x)^2 - 2*x*y(x) + 1 --R --R --R 2 , 2 @@ -161,7 +161,7 @@ yx:=solve(ode155,y,x) --E 15 --S 16 of 139 -ode155expr := (x**2-1)*D(yx,x) + yx**2 - 2*x*yx + 1 +ode155expr := (x^2-1)*D(yx,x) + yx^2 - 2*x*yx + 1 --R --R --R (16) @@ -188,7 +188,7 @@ ode155expr := (x**2-1)*D(yx,x) + yx**2 - 2*x*yx + 1 --E 16 --S 17 of 139 -ode156 := (x**2-1)*D(y(x),x) - y(x)*(y(x)-x) +ode156 := (x^2-1)*D(y(x),x) - y(x)*(y(x)-x) --R --R --R 2 , 2 @@ -210,7 +210,7 @@ yx:=solve(ode156,y,x) --E 18 --S 19 of 139 -ode156expr := (x**2-1)*D(yx,x) - yx*(yx-x) +ode156expr := (x^2-1)*D(yx,x) - yx*(yx-x) --R --R --R (19) @@ -229,7 +229,7 @@ ode156expr := (x**2-1)*D(yx,x) - yx*(yx-x) --E 19 --S 20 of 139 -ode157 := (x**2-1)*D(y(x),x) + a*(y(x)**2-2*x*y(x)+1) +ode157 := (x^2-1)*D(y(x),x) + a*(y(x)^2-2*x*y(x)+1) --R --R --R 2 , 2 @@ -247,7 +247,7 @@ ode157a:=solve(ode157,y,x) --E 21 --S 22 of 139 -ode158 := (x**2-1)*D(y(x),x) + a*x*y(x)**2 + x*y(x) +ode158 := (x^2-1)*D(y(x),x) + a*x*y(x)^2 + x*y(x) --R --R --R 2 , 2 @@ -269,7 +269,7 @@ yx:=solve(ode158,y,x) --E 23 --S 24 of 139 -ode158expr := (x**2-1)*D(yx,x) + a*x*yx**2 + x*yx +ode158expr := (x^2-1)*D(yx,x) + a*x*yx^2 + x*yx --R --R --R (24) @@ -289,7 +289,7 @@ ode158expr := (x**2-1)*D(yx,x) + a*x*yx**2 + x*yx --E 24 --S 25 of 139 -ode159 := (x**2-1)*D(y(x),x) - 2*x*y(x)*log(y(x)) +ode159 := (x^2-1)*D(y(x),x) - 2*x*y(x)*log(y(x)) --R --R --R 2 , @@ -310,7 +310,7 @@ yx:=solve(ode159,y,x) --E 26 --S 27 of 139 -ode159expr := (x**2-1)*D(yx,x) - 2*x*yx*log(yx) +ode159expr := (x^2-1)*D(yx,x) - 2*x*yx*log(yx) --R --R --R (27) @@ -328,7 +328,7 @@ ode159expr := (x**2-1)*D(yx,x) - 2*x*yx*log(yx) --E 27 --S 28 of 139 -ode160 := (x**2-4)*D(y(x),x) + (x+2)*y(x)**2 - 4*y(x) +ode160 := (x^2-4)*D(y(x),x) + (x+2)*y(x)^2 - 4*y(x) --R --R --R 2 , 2 @@ -348,7 +348,7 @@ yx:=solve(ode160,y,x) --E 29 --S 30 of 139 -ode160expr := (x**2-4)*D(yx,x) + (x+2)*yx**2 - 4*yx +ode160expr := (x^2-4)*D(yx,x) + (x+2)*yx^2 - 4*yx --R --R --R (30) @@ -365,7 +365,7 @@ ode160expr := (x**2-4)*D(yx,x) + (x+2)*yx**2 - 4*yx --E 30 --S 31 of 139 -ode161 := (x**2-5*x+6)*D(y(x),x) + 3*x*y(x) - 8*y(x) + x**2 +ode161 := (x^2-5*x+6)*D(y(x),x) + 3*x*y(x) - 8*y(x) + x^2 --R --R --R 2 , 2 @@ -399,7 +399,7 @@ yx:=ode161a.particular --E 33 --S 34 of 139 -ode161expr := (x**2-5*x+6)*D(yx,x) + 3*x*yx - 8*yx + x**2 +ode161expr := (x^2-5*x+6)*D(yx,x) + 3*x*yx - 8*yx + x^2 --R --R --R (34) 0 @@ -407,7 +407,7 @@ ode161expr := (x**2-5*x+6)*D(yx,x) + 3*x*yx - 8*yx + x**2 --E 34 --S 35 of 139 -ode162 := (x-a)*(x-b)*D(y(x),x) + y(x)**2 + k*(y(x)+x-a)*(y(x)+x-b) +ode162 := (x-a)*(x-b)*D(y(x),x) + y(x)^2 + k*(y(x)+x-a)*(y(x)+x-b) --R --R --R (35) @@ -431,7 +431,7 @@ ode162a:=solve(ode162,y,x) \end{verbatim} \begin{chunk}{*} --S 36 of 139 -ode163 := 2*x**2*D(y(x),x) - 2*y(x)**2 - x*y(x) + 2*a**2*x +ode163 := 2*x^2*D(y(x),x) - 2*y(x)^2 - x*y(x) + 2*a^2*x --R --R --R 2 , 2 2 @@ -456,7 +456,7 @@ yx:=solve(ode163,y,x) --E 37 --S 38 of 139 -ode163expr := 2*x**2*D(yx,x) - 2*yx**2 - x*yx + 2*a**2*x +ode163expr := 2*x^2*D(yx,x) - 2*yx^2 - x*yx + 2*a^2*x --R --R --R (38) @@ -515,7 +515,7 @@ ode163expr := 2*x**2*D(yx,x) - 2*yx**2 - x*yx + 2*a**2*x --E 38 --S 39 of 139 -ode164 := 2*x**2*D(y(x),x) - 2*y(x)**2 - 3*x*y(x) + 2*a**2*x +ode164 := 2*x^2*D(y(x),x) - 2*y(x)^2 - 3*x*y(x) + 2*a^2*x --R --R --R 2 , 2 2 @@ -540,7 +540,7 @@ yx:=solve(ode164,y,x) --E 40 --S 41 of 139 -ode164expr := 2*x**2*D(yx,x) - 2*yx**2 - 3*x*yx + 2*a**2*x +ode164expr := 2*x^2*D(yx,x) - 2*yx^2 - 3*x*yx + 2*a^2*x --R --R --R (41) @@ -656,7 +656,7 @@ ode164expr := 2*x**2*D(yx,x) - 2*yx**2 - 3*x*yx + 2*a**2*x --E 41 --S 42 of 139 -ode165 := x*(2*x-1)*D(y(x),x) + y(x)**2 - (4*x+1)*y(x) + 4*x +ode165 := x*(2*x-1)*D(y(x),x) + y(x)^2 - (4*x+1)*y(x) + 4*x --R --R --R 2 , 2 @@ -677,7 +677,7 @@ yx:=solve(ode165,y,x) --E 43 --S 44 of 139 -ode165expr := x*(2*x-1)*D(yx,x) + yx**2 - (4*x+1)*yx + 4*x +ode165expr := x*(2*x-1)*D(yx,x) + yx^2 - (4*x+1)*yx + 4*x --R --R --R (44) @@ -694,7 +694,7 @@ ode165expr := x*(2*x-1)*D(yx,x) + yx**2 - (4*x+1)*yx + 4*x --E 44 --S 45 of 139 -ode166 := 2*x*(x-1)*D(y(x),x) + (x-1)*y(x)**2 - x +ode166 := 2*x*(x-1)*D(y(x),x) + (x-1)*y(x)^2 - x --R --R --R 2 , 2 @@ -712,7 +712,7 @@ ode166a:=solve(ode166,y,x) --E 46 --S 47 of 139 -ode167 := 3*x**2*D(y(x),x) - 7*y(x)**2 - 3*x*y(x) - x**2 +ode167 := 3*x^2*D(y(x),x) - 7*y(x)^2 - 3*x*y(x) - x^2 --R --R --R 2 , 2 2 @@ -737,7 +737,7 @@ yx:=solve(ode167,y,x) --E 48 --S 49 of 139 -ode167expr := 3*x**2*D(yx,x) - 7*yx**2 - 3*x*yx - x**2 +ode167expr := 3*x^2*D(yx,x) - 7*yx^2 - 3*x*yx - x^2 --R --R --R (49) @@ -808,7 +808,7 @@ ode167expr := 3*x**2*D(yx,x) - 7*yx**2 - 3*x*yx - x**2 --E 49 --S 50 of 139 -ode168 := 3*(x**2-4)*D(y(x),x) + y(x)**2 - x*y(x) - 3 +ode168 := 3*(x^2-4)*D(y(x),x) + y(x)^2 - x*y(x) - 3 --R --R --R 2 , 2 @@ -826,7 +826,7 @@ ode168a:=solve(ode168,y,x) --E 51 --S 52 of 139 -ode169 := (a*x+b)**2*D(y(x),x) + (a*x+b)*y(x)**3 + c*y(x)**2 +ode169 := (a*x+b)^2*D(y(x),x) + (a*x+b)*y(x)^3 + c*y(x)^2 --R --R --R 2 2 2 , 3 2 @@ -844,7 +844,7 @@ ode169a:=solve(ode169,y,x) --E 53 --S 54 of 139 -ode170 := x**3*D(y(x),x) - y(x)**2 - x**4 +ode170 := x^3*D(y(x),x) - y(x)^2 - x^4 --R --R --R 3 , 2 4 @@ -866,7 +866,7 @@ yx:=solve(ode170,y,x) --E 55 --S 56 of 139 -ode170expr := x**3*D(yx,x) - yx**2 - x**4 +ode170expr := x^3*D(yx,x) - yx^2 - x^4 --R --R --R (56) @@ -883,7 +883,7 @@ ode170expr := x**3*D(yx,x) - yx**2 - x**4 --E 56 --S 57 of 139 -ode171 := x**3*D(y(x),x) - y(x)**2 - x**2*y(x) +ode171 := x^3*D(y(x),x) - y(x)^2 - x^2*y(x) --R --R --R 3 , 2 2 @@ -904,7 +904,7 @@ yx:=solve(ode171,y,x) --E 58 --S 59 of 139 -ode171expr := x**3*D(yx,x) - yx**2 - x**2*yx +ode171expr := x^3*D(yx,x) - yx^2 - x^2*yx --R --R --R 6 , 3 2 2 4 @@ -917,7 +917,7 @@ ode171expr := x**3*D(yx,x) - yx**2 - x**2*yx --E 59 --S 60 of 139 -ode172 := x**3*D(y(x),x) - x**4*y(x)**2 + x**2*y(x) + 20 +ode172 := x^3*D(y(x),x) - x^4*y(x)^2 + x^2*y(x) + 20 --R --R --R 3 , 4 2 2 @@ -939,7 +939,7 @@ yx:=solve(ode172,y,x) --E 61 --S 62 of 139 -ode172expr := x**3*D(yx,x) - x**4*yx**2 + x**2*yx + 20 +ode172expr := x^3*D(yx,x) - x^4*yx^2 + x^2*yx + 20 --R --R --R (62) @@ -979,7 +979,7 @@ ode172expr := x**3*D(yx,x) - x**4*yx**2 + x**2*yx + 20 --E 62 --S 63 of 139 -ode173 := x**3*D(y(x),x) - x**6*y(x)**2 - (2*x-3)*x**2*y(x) + 3 +ode173 := x^3*D(y(x),x) - x^6*y(x)^2 - (2*x-3)*x^2*y(x) + 3 --R --R --R 3 , 6 2 3 2 @@ -1001,7 +1001,7 @@ yx:=solve(ode173,y,x) --E 64 --S 65 of 139 -ode173expr := x**3*D(yx,x) - x**6*yx**2 - (2*x-3)*x**2*yx + 3 +ode173expr := x^3*D(yx,x) - x^6*yx^2 - (2*x-3)*x^2*yx + 3 --R --R --R (65) @@ -1021,7 +1021,7 @@ ode173expr := x**3*D(yx,x) - x**6*yx**2 - (2*x-3)*x**2*yx + 3 --E 65 --S 66 of 139 -ode174 := x*(x**2+1)*D(y(x),x) + x**2*y(x) +ode174 := x*(x^2+1)*D(y(x),x) + x^2*y(x) --R --R --R 3 , 2 @@ -1051,7 +1051,7 @@ yx:=ode174a.particular --E 68 --S 69 of 139 -ode174expr := x*(x**2+1)*D(yx,x) + x**2*yx +ode174expr := x*(x^2+1)*D(yx,x) + x^2*yx --R --R --R (69) 0 @@ -1059,7 +1059,7 @@ ode174expr := x*(x**2+1)*D(yx,x) + x**2*yx --E 69 --S 70 of 139 -ode175 := x*(x**2-1)*D(y(x),x) - (2*x**2-1)*y(x) + a*x**3 +ode175 := x*(x^2-1)*D(y(x),x) - (2*x^2-1)*y(x) + a*x^3 --R --R --R 3 , 2 3 @@ -1087,7 +1087,7 @@ yx:=ode175a.particular --E 72 --S 73 of 139 -ode175expr := x*(x**2-1)*D(yx,x) - (2*x**2-1)*yx + a*x**3 +ode175expr := x*(x^2-1)*D(yx,x) - (2*x^2-1)*yx + a*x^3 --R --R --R (73) 0 @@ -1095,7 +1095,7 @@ ode175expr := x*(x**2-1)*D(yx,x) - (2*x**2-1)*yx + a*x**3 --E 73 --S 74 of 139 -ode176 := x*(x**2-1)*D(y(x),x) + (x**2-1)*y(x)**2 - x**2 +ode176 := x*(x^2-1)*D(y(x),x) + (x^2-1)*y(x)^2 - x^2 --R --R --R 3 , 2 2 2 @@ -1113,7 +1113,7 @@ ode176a:=solve(ode176,y,x) --E 75 --S 76 of 139 -ode177 := x**2*(x-1)*D(y(x),x) - y(x)**2 - x*(x-2)*y(x) +ode177 := x^2*(x-1)*D(y(x),x) - y(x)^2 - x*(x-2)*y(x) --R --R --R 3 2 , 2 2 @@ -1134,7 +1134,7 @@ yx:=solve(ode177,y,x) --E 77 --S 78 of 139 -ode177expr := x**2*(x-1)*D(yx,x) - yx**2 - x*(x-2)*yx +ode177expr := x^2*(x-1)*D(yx,x) - yx^2 - x*(x-2)*yx --R --R --R 6 5 4 , 3 2 2 2 4 @@ -1147,8 +1147,8 @@ ode177expr := x**2*(x-1)*D(yx,x) - yx**2 - x*(x-2)*yx --E 78 --S 79 of 139 -ode178 := 2*x*(x**2-1)*D(y(x),x) + 2*(x**2-1)*y(x)**2 _ - - (3*x**2-5)*y(x) + x**2 - 3 +ode178 := 2*x*(x^2-1)*D(y(x),x) + 2*(x^2-1)*y(x)^2 _ + - (3*x^2-5)*y(x) + x^2 - 3 --R --R --R 3 , 2 2 2 2 @@ -1175,8 +1175,8 @@ yx:=solve(ode178,y,x) --E 80 --S 81 of 139 -ode178expr := 2*x*(x**2-1)*D(yx,x) + 2*(x**2-1)*yx**2 _ - - (3*x**2-5)*yx + x**2 - 3 +ode178expr := 2*x*(x^2-1)*D(yx,x) + 2*(x^2-1)*yx^2 _ + - (3*x^2-5)*yx + x^2 - 3 --R --R --R (81) @@ -1223,7 +1223,7 @@ ode178expr := 2*x*(x**2-1)*D(yx,x) + 2*(x**2-1)*yx**2 _ --E 81 --S 82 of 139 -ode179 := 3*x*(x**2-1)*D(y(x),x) + x*y(x)**2 - (x**2+1)*y(x) - 3*x +ode179 := 3*x*(x^2-1)*D(y(x),x) + x*y(x)^2 - (x^2+1)*y(x) - 3*x --R --R --R 3 , 2 2 @@ -1241,7 +1241,7 @@ ode179a:=solve(ode179,y,x) --E 83 --S 84 of 139 -ode180 := (a*x**2+b*x+c)*(x*D(y(x),x)-y(x)) - y(x)**2 + x**2 +ode180 := (a*x^2+b*x+c)*(x*D(y(x),x)-y(x)) - y(x)^2 + x^2 --R --R --R 3 2 , 2 2 2 @@ -1255,7 +1255,7 @@ yx:=solve(ode180,y,x) --E 85 --S 86 of 139 -ode180expr := (a*x**2+b*x+c)*(x*D(yx,x)-yx) - yx**2 + x**2 +ode180expr := (a*x^2+b*x+c)*(x*D(yx,x)-yx) - yx^2 + x^2 --R --R --R (86) @@ -1339,7 +1339,7 @@ ode180expr := (a*x**2+b*x+c)*(x*D(yx,x)-yx) - yx**2 + x**2 --E 86 --S 87 of 139 -ode181 := x**4*(D(y(x),x)+y(x)**2) + a +ode181 := x^4*(D(y(x),x)+y(x)^2) + a --R --R --R 4 , 4 2 @@ -1366,7 +1366,7 @@ yx:=solve(ode181,y,x) --E 88 --S 89 of 139 -ode181expr := x**4*(D(yx,x)+yx**2) + a +ode181expr := x^4*(D(yx,x)+yx^2) + a --R --R --R (89) @@ -1407,7 +1407,7 @@ ode181expr := x**4*(D(yx,x)+yx**2) + a --E 89 --S 90 of 139 -ode182 := x*(x**3-1)*D(y(x),x) - 2*x*y(x)**2 + y(x) + x**2 +ode182 := x*(x^3-1)*D(y(x),x) - 2*x*y(x)^2 + y(x) + x^2 --R --R --R 4 , 2 2 @@ -1424,7 +1424,7 @@ This never completes \begin{chunk}{*} --S 91 of 139 -ode183 := (2*x**4-x)*D(y(x),x) - 2*(x**3-1)*y(x) +ode183 := (2*x^4-x)*D(y(x),x) - 2*(x^3-1)*y(x) --R --R --R 4 , 3 @@ -1455,7 +1455,7 @@ yx:=ode183a.particular --E 93 --S 94 of 139 -ode183expr := (2*x**4-x)*D(yx,x) - 2*(x**3-1)*yx +ode183expr := (2*x^4-x)*D(yx,x) - 2*(x^3-1)*yx --R --R --R (94) 0 @@ -1463,7 +1463,7 @@ ode183expr := (2*x**4-x)*D(yx,x) - 2*(x**3-1)*yx --E 94 --S 95 of 139 -ode184 := (a*x**2+b*x+c)**2*(D(y(x),x)+y(x)**2) + A +ode184 := (a*x^2+b*x+c)^2*(D(y(x),x)+y(x)^2) + A --R --R --R (95) @@ -1484,7 +1484,7 @@ This never completes \begin{chunk}{*} --S 96 of 139 -ode185 := x**7*D(y(x),x) + 2*(x**2+1)*y(x)**3 + 5*x**3*y(x)**2 +ode185 := x^7*D(y(x),x) + 2*(x^2+1)*y(x)^3 + 5*x^3*y(x)^2 --R --R --R 7 , 2 3 3 2 @@ -1502,7 +1502,7 @@ ode185a:=solve(ode185,y,x) --E 97 --S 98 of 139 -ode186 := x**n*D(y(x),x) + y(x)**2 -(n-1)*x**(n-1)*y(x) + x**(2*n-2) +ode186 := x^n*D(y(x),x) + y(x)^2 -(n-1)*x^(n-1)*y(x) + x^(2*n-2) --R --R --R n , 2n - 2 n - 1 2 @@ -1520,7 +1520,7 @@ ode186a:=solve(ode186,y,x) --E 99 --S 100 of 139 -ode187 := x**n*D(y(x),x) - a*y(x)**2 - b*x**(2*n-2) +ode187 := x^n*D(y(x),x) - a*y(x)^2 - b*x^(2*n-2) --R --R --R n , 2n - 2 2 @@ -1538,7 +1538,7 @@ ode187a:=solve(ode187,y,x) --E 101 --S 102 of 139 -ode188 := x**(2*n+1)*D(y(x),x) - a*y(x)**3 - b*x**3*n +ode188 := x^(2*n+1)*D(y(x),x) - a*y(x)^3 - b*x^3*n --R --R --R 2n + 1 , 3 3 @@ -1556,7 +1556,7 @@ ode188a:=solve(ode188,y,x) --E 103 --S 104 of 139 -ode189 := x**(m*(n-1)+n)*D(y(x),x) - a*y(x)**n - b*x**(n*(m+1)) +ode189 := x^(m*(n-1)+n)*D(y(x),x) - a*y(x)^n - b*x^(n*(m+1)) --R --R --R (m + 1)n - m , n (m + 1)n @@ -1574,7 +1574,7 @@ ode189a:=solve(ode189,y,x) --E 105 --S 106 of 139 -ode190 := sqrt(x**2-1)*D(y(x),x) - sqrt(y(x)**2-1) +ode190 := sqrt(x^2-1)*D(y(x),x) - sqrt(y(x)^2-1) --R --R --R +------+ +---------+ @@ -1593,7 +1593,7 @@ ode190a:=solve(ode190,y,x) --E 107 --S 108 of 139 -ode191 := sqrt(1-x**2)*D(y(x),x) - y(x)*sqrt(y(x)**2-1) +ode191 := sqrt(1-x^2)*D(y(x),x) - y(x)*sqrt(y(x)^2-1) --R --R --R +--------+ +---------+ @@ -1612,7 +1612,7 @@ ode191a:=solve(ode191,y,x) --E 109 --S 110 of 139 -ode192 := sqrt(x**2+a**2)*D(y(x),x) + y(x) - sqrt(x**2+a**2) + x +ode192 := sqrt(x^2+a^2)*D(y(x),x) + y(x) - sqrt(x^2+a^2) + x --R --R --R +-------+ +-------+ @@ -1644,7 +1644,7 @@ yx:=ode192a.particular --E 112 --S 113 of 139 -ode192expr := sqrt(x**2+a**2)*D(yx,x) + yx - sqrt(x**2+a**2) + x +ode192expr := sqrt(x^2+a^2)*D(yx,x) + yx - sqrt(x^2+a^2) + x --R --R --R (113) 0 @@ -1686,8 +1686,8 @@ ode193expr := x*D(yx,x)*log(x) + yx - a*x*(log(x)+1) --E 117 --S 118 of 139 -ode194 := x*D(y(x),x)*log(x) - y(x)**2*log(x) - _ - (2*log(x)**2+1)*y(x) - log(x)**3 +ode194 := x*D(y(x),x)*log(x) - y(x)^2*log(x) - _ + (2*log(x)^2+1)*y(x) - log(x)^3 --R --R --R , 3 2 2 @@ -1705,7 +1705,7 @@ ode194a:=solve(ode194,y,x) --E 119 --S 120 of 139 -ode195 := sin(x)*D(y(x),x) - y(x)**2*sin(x)**2 + (cos(x) - 3*sin(x))*y(x) + 4 +ode195 := sin(x)*D(y(x),x) - y(x)^2*sin(x)^2 + (cos(x) - 3*sin(x))*y(x) + 4 --R --R --R , 2 2 @@ -1726,7 +1726,7 @@ yx:=solve(ode195,y,x) --E 121 --S 122 of 139 -ode195expr:=sin(x)*D(yx,x) - yx**2*sin(x)**2 + (cos(x) - 3*sin(x))*yx + 4 +ode195expr:=sin(x)*D(yx,x) - yx^2*sin(x)^2 + (cos(x) - 3*sin(x))*yx + 4 --R --R --R (122) @@ -1835,7 +1835,7 @@ ode196expr := cos(x)*D(yx,x) + yx + (1 + sin(x))*cos(x) --E 126 --S 127 of 139 -ode197 := cos(x)*D(y(x),x) - y(x)**4 - y(x)*sin(x) +ode197 := cos(x)*D(y(x),x) - y(x)^4 - y(x)*sin(x) --R --R --R , 4 @@ -1857,7 +1857,7 @@ yx:=solve(ode197,y,x) --E 128 --S 129 of 139 -ode197expr := cos(x)*D(yx,x) - yx**4 - yx*sin(x) +ode197expr := cos(x)*D(yx,x) - yx^4 - yx*sin(x) --R --R --R (129) @@ -1892,7 +1892,7 @@ ode197expr := cos(x)*D(yx,x) - yx**4 - yx*sin(x) --E 129 --S 130 of 139 -ode198 := sin(x)*cos(x)*D(y(x),x) - y(x) - sin(x)**3 +ode198 := sin(x)*cos(x)*D(y(x),x) - y(x) - sin(x)^3 --R --R --R , 3 @@ -1920,7 +1920,7 @@ yx:=ode198a.particular --E 132 --S 133 of 139 -ode198expr := sin(x)*cos(x)*D(yx,x) - yx - sin(x)**3 +ode198expr := sin(x)*cos(x)*D(yx,x) - yx - sin(x)^3 --R --R --R 3 2 @@ -1947,7 +1947,7 @@ ode199a:=solve(ode199,y,x) --E 135 --S 136 of 139 -ode200 := (a*sin(x)**2+b)*D(y(x),x) + a*y(x)*sin(2*x) + A*x*(a*sin(x)**2+c) +ode200 := (a*sin(x)^2+b)*D(y(x),x) + a*y(x)*sin(2*x) + A*x*(a*sin(x)^2+c) --R --R --R 2 , 2 @@ -1986,7 +1986,7 @@ yx:=ode200a.particular --E 138 --S 139 of 139 -ode200expr := (a*sin(x)**2+b)*D(yx,x) + a*yx*sin(2*x) + A*x*(a*sin(x)**2+c) +ode200expr := (a*sin(x)^2+b)*D(yx,x) + a*yx*sin(2*x) + A*x*(a*sin(x)^2+c) --R --R --R (139) diff --git a/src/input/kamke4.input.pamphlet b/src/input/kamke4.input.pamphlet index 1fe0f82..1cd0200 100644 --- a/src/input/kamke4.input.pamphlet +++ b/src/input/kamke4.input.pamphlet @@ -84,7 +84,7 @@ h:=operator 'h --E 8 --S 9 of 127 -ode201 := 2*f(x)*D(y(x),x)+2*f(x)*y(x)**2-D(f(x),x)*y(x)-2*f(x)**2 +ode201 := 2*f(x)*D(y(x),x)+2*f(x)*y(x)^2-D(f(x),x)*y(x)-2*f(x)^2 --R --R --R , , 2 2 @@ -120,7 +120,7 @@ solve(ode202,y,x) --E 12 --S 13 of 127 -ode203 := y(x)*D(y(x),x)+y(x)+x**3 +ode203 := y(x)*D(y(x),x)+y(x)+x^3 --R --R --R , 3 @@ -156,7 +156,7 @@ solve(ode204,y,x) --E 16 --S 17 of 127 -ode205 := y(x)*D(y(x),x)+a*y(x)+(a**2-1)/(4)*x+b*x**n +ode205 := y(x)*D(y(x),x)+a*y(x)+(a^2-1)/(4)*x+b*x^n --R --R --R , n 2 @@ -194,7 +194,7 @@ solve(ode206,y,x) --E 20 --S 21 of 127 -ode207 := y(x)*D(y(x),x)+y(x)**2+4*x*(x+1) +ode207 := y(x)*D(y(x),x)+y(x)^2+4*x*(x+1) --R --R --R , 2 2 @@ -215,7 +215,7 @@ yx:=solve(ode207,y,x) --E 22 --S 23 of 127 -ode207expr := yx*D(yx,x)+yx**2+4*x*(x+1) +ode207expr := yx*D(yx,x)+yx^2+4*x*(x+1) --R --R --R (23) @@ -231,7 +231,7 @@ ode207expr := yx*D(yx,x)+yx**2+4*x*(x+1) --E 23 --S 24 of 127 -ode208 := y(x)*D(y(x),x)+a*y(x)**2-b*cos(x+c) +ode208 := y(x)*D(y(x),x)+a*y(x)^2-b*cos(x+c) --R --R --R , 2 @@ -253,7 +253,7 @@ yx:=solve(ode208,y,x) --E 25 --S 26 of 127 -ode208expr := yx*D(yx,x)+a*yx**2-b*cos(x+c) +ode208expr := yx*D(yx,x)+a*yx^2-b*cos(x+c) --R --R --R (26) @@ -291,7 +291,7 @@ ode208expr := yx*D(yx,x)+a*yx**2-b*cos(x+c) --E 26 --S 27 of 127 -ode209 := y(x)*D(y(x),x)-sqrt(a*y(x)**2+b) +ode209 := y(x)*D(y(x),x)-sqrt(a*y(x)^2+b) --R --R --R +-----------+ @@ -316,7 +316,7 @@ yx:=solve(ode209,y,x) --E 28 --S 29 of 127 -ode209expr := yx*D(yx,x)-sqrt(a*yx**2+b) +ode209expr := yx*D(yx,x)-sqrt(a*yx^2+b) --R --R --R (29) @@ -361,7 +361,7 @@ ode209expr := yx*D(yx,x)-sqrt(a*yx**2+b) --E 29 --S 30 of 127 -ode210 := y(x)*D(y(x),x)+x*y(x)**2-4*x +ode210 := y(x)*D(y(x),x)+x*y(x)^2-4*x --R --R --R , 2 @@ -383,7 +383,7 @@ yx:=solve(ode210,y,x) --E 31 --S 32 of 127 -ode210expr := yx*D(yx,x)+x*yx**2-4*x +ode210expr := yx*D(yx,x)+x*yx^2-4*x --R --R --R (32) @@ -417,7 +417,7 @@ solve(ode211,y,x) --E 34 --S 35 of 127 -ode212 := y(x)*D(y(x),x)+f(x**2+y(x)**2)*g(x)+x +ode212 := y(x)*D(y(x),x)+f(x^2+y(x)^2)*g(x)+x --R --R --R , 2 2 @@ -507,7 +507,7 @@ solve(ode216,y,x) --E 44 --S 45 of 127 -ode217 := (y(x)-x**2)*D(y(x),x)-x +ode217 := (y(x)-x^2)*D(y(x),x)-x --R --R --R 2 , @@ -528,7 +528,7 @@ yx:=solve(ode217,y,x) --E 46 --S 47 of 127 -ode217expr := (yx-x**2)*D(yx,x)-x +ode217expr := (yx-x^2)*D(yx,x)-x --R --R --R (47) @@ -550,7 +550,7 @@ ode217expr := (yx-x**2)*D(yx,x)-x --E 47 --S 48 of 127 -ode218 := (y(x)-x**2)*D(y(x),x)+4*x*y(x) +ode218 := (y(x)-x^2)*D(y(x),x)+4*x*y(x) --R --R --R 2 , @@ -572,7 +572,7 @@ yx:=solve(ode218,y,x) --E 49 --S 50 of 127 -ode218expr := (yx-x**2)*D(yx,x)+4*x*yx +ode218expr := (yx-x^2)*D(yx,x)+4*x*yx --R --R --R (50) @@ -589,7 +589,7 @@ ode218expr := (yx-x**2)*D(yx,x)+4*x*yx --E 50 --S 51 of 127 -ode219 := (y(x)+g(x))*D(y(x),x)-f2(x)*y(x)**2-f1(x)*y(x)-f0(x) +ode219 := (y(x)+g(x))*D(y(x),x)-f2(x)*y(x)^2-f1(x)*y(x)-f0(x) --R --R --R , 2 @@ -607,7 +607,7 @@ solve(ode219,y,x) --E 52 --S 53 of 127 -ode220 := 2*y(x)*D(y(x),x)-x*y(x)**2-x**3 +ode220 := 2*y(x)*D(y(x),x)-x*y(x)^2-x^3 --R --R --R , 2 3 @@ -629,7 +629,7 @@ yx:=solve(ode220,y,x) --E 54 --S 55 of 127 -ode220expr := 2*yx*D(yx,x)-x*yx**2-x**3 +ode220expr := 2*yx*D(yx,x)-x*yx^2-x^3 --R --R --R (55) @@ -876,7 +876,7 @@ ode229expr := (12*yx-5*x-8)*D(yx,x)-5*yx+2*x+3 --E 76 --S 77 of 127 -ode230 := a*y(x)*D(y(x),x)+b*y(x)**2+f(x) +ode230 := a*y(x)*D(y(x),x)+b*y(x)^2+f(x) --R --R --R , 2 @@ -916,7 +916,7 @@ solve(ode231,y,x) --E 80 --S 81 of 127 -ode232 := x*y(x)*D(y(x),x)+y(x)**2+x**2 +ode232 := x*y(x)*D(y(x),x)+y(x)^2+x^2 --R --R --R , 2 2 @@ -937,7 +937,7 @@ yx:=solve(ode232,y,x) --E 82 --S 83 of 127 -ode232expr := x*yx*D(yx,x)+yx**2+x**2 +ode232expr := x*yx*D(yx,x)+yx^2+x^2 --R --R --R 5 3 7 , 4 4 6 2 8 2 @@ -949,7 +949,7 @@ ode232expr := x*yx*D(yx,x)+yx**2+x**2 --E 83 --S 84 of 127 -ode233 := x*y(x)*D(y(x),x)-y(x)**2+a*x**3*cos(x) +ode233 := x*y(x)*D(y(x),x)-y(x)^2+a*x^3*cos(x) --R --R --R , 3 2 @@ -971,7 +971,7 @@ yx:=solve(ode233,y,x) --E 85 --S 86 of 127 -ode233expr := x*yx*D(yx,x)-yx**2+a*x**3*cos(x) +ode233expr := x*yx*D(yx,x)-yx^2+a*x^3*cos(x) --R --R --R (86) @@ -988,7 +988,7 @@ ode233expr := x*yx*D(yx,x)-yx**2+a*x**3*cos(x) --E 86 --S 87 of 127 -ode234 := x*y(x)*D(y(x),x)-y(x)**2+x*y(x)+x**3-2*x**2 +ode234 := x*y(x)*D(y(x),x)-y(x)^2+x*y(x)+x^3-2*x^2 --R --R --R , 2 3 2 @@ -1062,7 +1062,7 @@ ode235expr := (x*yx+a)*D(yx,x)+b*yx --E 91 --S 92 of 127 -ode236 := x*(y(x)+4)*D(y(x),x)-y(x)**2-2*y(x)-2*x +ode236 := x*(y(x)+4)*D(y(x),x)-y(x)^2-2*y(x)-2*x --R --R --R , 2 @@ -1116,7 +1116,7 @@ solve(ode238,y,x) --E 97 --S 98 of 127 -ode239 := (x*y(x)-x**2)*D(y(x),x)+y(x)**2-3*x*y(x)-2*x**2 +ode239 := (x*y(x)-x^2)*D(y(x),x)+y(x)^2-3*x*y(x)-2*x^2 --R --R --R 2 , 2 2 @@ -1137,7 +1137,7 @@ yx:=solve(ode239,y,x) --E 99 --S 100 of 127 -ode239expr := (x*yx-x**2)*D(yx,x)+yx**2-3*x*yx-2*x**2 +ode239expr := (x*yx-x^2)*D(yx,x)+yx^2-3*x*yx-2*x^2 --R --R --R (100) @@ -1153,7 +1153,7 @@ ode239expr := (x*yx-x**2)*D(yx,x)+yx**2-3*x*yx-2*x**2 --E 100 --S 101 of 127 -ode240 := 2*x*y(x)*D(y(x),x)-y(x)**2+a*x +ode240 := 2*x*y(x)*D(y(x),x)-y(x)^2+a*x --R --R --R , 2 @@ -1174,7 +1174,7 @@ yx:=solve(ode240,y,x) --E 102 --S 103 of 127 -ode240expr := 2*x*yx*D(yx,x)-yx**2+a*x +ode240expr := 2*x*yx*D(yx,x)-yx^2+a*x --R --R --R (103) @@ -1191,7 +1191,7 @@ ode240expr := 2*x*yx*D(yx,x)-yx**2+a*x --E 103 --S 104 of 127 -ode241 := 2*x*y(x)*D(y(x),x)-y(x)**2+a*x**2 +ode241 := 2*x*y(x)*D(y(x),x)-y(x)^2+a*x^2 --R --R --R , 2 2 @@ -1212,7 +1212,7 @@ yx:=solve(ode241,y,x) --E 105 --S 106 of 127 -ode241expr := 2*x*yx*D(yx,x)-yx**2+a*x**2 +ode241expr := 2*x*yx*D(yx,x)-yx^2+a*x^2 --R --R --R 3 3 , 4 2 2 2 4 @@ -1225,7 +1225,7 @@ ode241expr := 2*x*yx*D(yx,x)-yx**2+a*x**2 --E 106 --S 107 of 127 -ode242 := 2*x*y(x)*D(y(x),x)+2*y(x)**2+1 +ode242 := 2*x*y(x)*D(y(x),x)+2*y(x)^2+1 --R --R --R , 2 @@ -1246,7 +1246,7 @@ yx:=solve(ode242,y,x) --E 108 --S 109 of 127 -ode242expr := 2*x*yx*D(yx,x)+2*yx**2+1 +ode242expr := 2*x*yx*D(yx,x)+2*yx^2+1 --R --R --R 5 3 5 , 4 4 4 2 4 @@ -1294,7 +1294,7 @@ solve(ode244,y,x) --E 113 --S 114 of 127 -ode245 := (2*x*y(x)+4*x**3)*D(y(x),x)+y(x)**2+112*x**2*y(x) +ode245 := (2*x*y(x)+4*x^3)*D(y(x),x)+y(x)^2+112*x^2*y(x) --R --R --R 3 , 2 2 @@ -1312,7 +1312,7 @@ solve(ode245,y,x) --E 115 --S 116 of 127 -ode246 := x*(3*y(x)+2*x)*D(y(x),x)+3*(y(x)+x)**2 +ode246 := x*(3*y(x)+2*x)*D(y(x),x)+3*(y(x)+x)^2 --R --R --R 2 , 2 2 @@ -1333,7 +1333,7 @@ yx:=solve(ode246,y,x) --E 117 --S 118 of 127 -ode246expr := x*(3*yx+2*x)*D(yx,x)+3*(yx+x)**2 +ode246expr := x*(3*yx+2*x)*D(yx,x)+3*(yx+x)^2 --R --R --R (118) @@ -1352,7 +1352,7 @@ ode246expr := x*(3*yx+2*x)*D(yx,x)+3*(yx+x)**2 --E 118 --S 119 of 127 -ode247 := (3*x+2)*(y(x)-2*x-1)*D(y(x),x)-y(x)**2+x*y(x)-7*x**2-9*x-3 +ode247 := (3*x+2)*(y(x)-2*x-1)*D(y(x),x)-y(x)^2+x*y(x)-7*x^2-9*x-3 --R --R --R 2 , 2 2 @@ -1370,7 +1370,7 @@ solve(ode247,y,x) --E 120 --S 121 of 127 -ode248 := (6*x*y(x)+x**2+3)*D(y(x),x)+3*y(x)**2+2*x*y(x)+2*x +ode248 := (6*x*y(x)+x^2+3)*D(y(x),x)+3*y(x)^2+2*x*y(x)+2*x --R --R --R 2 , 2 @@ -1389,7 +1389,7 @@ yx:=solve(ode248,y,x) --E 122 --S 123 of 127 -ode248expr := (6*x*yx+x**2+3)*D(yx,x)+3*yx**2+2*x*yx+2*x +ode248expr := (6*x*yx+x^2+3)*D(yx,x)+3*yx^2+2*x*yx+2*x --R --R --R (123) @@ -1412,7 +1412,7 @@ ode248expr := (6*x*yx+x**2+3)*D(yx,x)+3*yx**2+2*x*yx+2*x --E 123 --S 124 of 127 -ode249 := (a*x*y(x)+b*x**n)*D(y(x),x)+alpha*y(x)**3+beta*y(x)**2 +ode249 := (a*x*y(x)+b*x^n)*D(y(x),x)+alpha*y(x)^3+beta*y(x)^2 --R --R --R n , 3 2 @@ -1430,7 +1430,7 @@ solve(ode249,y,x) --E 125 --S 126 of 127 -ode250 := (B*x*y(x)+A*x**2+a*x+b*y(x)+c)*D(y(x),x)-B*g(x)**2+_ +ode250 := (B*x*y(x)+A*x^2+a*x+b*y(x)+c)*D(y(x),x)-B*g(x)^2+_ A*x*y(x)+alpha*x+beta*y(x)+gamma --R --R diff --git a/src/input/kamke5.input.pamphlet b/src/input/kamke5.input.pamphlet index c6aa5e9..3136845 100644 --- a/src/input/kamke5.input.pamphlet +++ b/src/input/kamke5.input.pamphlet @@ -101,7 +101,7 @@ h:=operator 'h --E 10 --S 11 of 130 -ode251 := (x**2*y(x)-1)*D(y(x),x)+x*y(x)**2-1 +ode251 := (x^2*y(x)-1)*D(y(x),x)+x*y(x)^2-1 --R --R --R 2 , 2 @@ -122,7 +122,7 @@ yx:=solve(ode251,y,x) --E 12 --S 13 of 130 -ode251expr := (x**2*yx-1)*D(yx,x)+x*yx**2-1 +ode251expr := (x^2*yx-1)*D(yx,x)+x*yx^2-1 --R --R --R (13) @@ -138,7 +138,7 @@ ode251expr := (x**2*yx-1)*D(yx,x)+x*yx**2-1 --E 13 --S 14 of 130 -ode252 := (x**2*y(x)-1)*D(y(x),x)-(x*y(x)**2-1) +ode252 := (x^2*y(x)-1)*D(y(x),x)-(x*y(x)^2-1) --R --R --R 2 , 2 @@ -156,7 +156,7 @@ solve(ode252,y,x) --E 15 --S 16 of 130 -ode253 := (x**2*y(x)-1)*D(y(x),x)+8*(x*y(x)**2-1) +ode253 := (x^2*y(x)-1)*D(y(x),x)+8*(x*y(x)^2-1) --R --R --R 2 , 2 @@ -174,7 +174,7 @@ solve(ode253,y,x) --E 17 --S 18 of 130 -ode254 := x*(x*y(x)-2)*D(y(x),x)+x**2*y(x)**3+x*y(x)**2-2*y(x) +ode254 := x*(x*y(x)-2)*D(y(x),x)+x^2*y(x)^3+x*y(x)^2-2*y(x) --R --R --R 2 , 2 3 2 @@ -192,7 +192,7 @@ solve(ode254,y,x) --E 19 --S 20 of 130 -ode255 := x*(x*y(x)-3)*D(y(x),x)+x*y(x)**2-y(x) +ode255 := x*(x*y(x)-3)*D(y(x),x)+x*y(x)^2-y(x) --R --R --R 2 , 2 @@ -210,7 +210,7 @@ solve(ode255,y,x) --E 21 --S 22 of 130 -ode256 := x**2*(y(x)-1)*D(y(x),x)+(x-1)*y(x) +ode256 := x^2*(y(x)-1)*D(y(x),x)+(x-1)*y(x) --R --R --R 2 2 , @@ -228,7 +228,7 @@ solve(ode256,y,x) --E 23 --S 24 of 130 -ode257 := x*(x*y(x)+x**4-1)*D(y(x),x)-y(x)*(x*y(x)-x**4-1) +ode257 := x*(x*y(x)+x^4-1)*D(y(x),x)-y(x)*(x*y(x)-x^4-1) --R --R --R 2 5 , 2 4 @@ -246,7 +246,7 @@ solve(ode257,y,x) --E 25 --S 26 of 130 -ode258 := 2*x**2*y(x)*D(y(x),x)+y(x)**2-2*x**3-x**2 +ode258 := 2*x^2*y(x)*D(y(x),x)+y(x)^2-2*x^3-x^2 --R --R --R 2 , 2 3 2 @@ -267,7 +267,7 @@ yx:=solve(ode258,y,x) --E 27 --S 28 of 130 -ode258expr := 2*x**2*yx*D(yx,x)+yx**2-2*x**3-x**2 +ode258expr := 2*x^2*yx*D(yx,x)+yx^2-2*x^3-x^2 --R --R --R (28) @@ -285,7 +285,7 @@ ode258expr := 2*x**2*yx*D(yx,x)+yx**2-2*x**3-x**2 --E 28 --S 29 of 130 -ode259 := 2*x**2*y(x)*D(y(x),x)-y(x)**2-x**2*exp(x-1/x) +ode259 := 2*x^2*y(x)*D(y(x),x)-y(x)^2-x^2*exp(x-1/x) --R --R --R 2 @@ -310,7 +310,7 @@ yx:=solve(ode259,y,x) --E 30 --S 31 of 130 -ode259expr := 2*x**2*yx*D(yx,x)-yx**2-x**2*exp(x-1/x) +ode259expr := 2*x^2*yx*D(yx,x)-yx^2-x^2*exp(x-1/x) --R --R --R (31) @@ -335,7 +335,7 @@ ode259expr := 2*x**2*yx*D(yx,x)-yx**2-x**2*exp(x-1/x) --E 31 --S 32 of 130 -ode260 := (2*x**2*y(x)+x)*D(y(x),x)-x**2*y(x)**3+2*x*y(x)**2+y(x) +ode260 := (2*x^2*y(x)+x)*D(y(x),x)-x^2*y(x)^3+2*x*y(x)^2+y(x) --R --R --R 2 , 2 3 2 @@ -353,7 +353,7 @@ solve(ode260,y,x) --E 33 --S 34 of 130 -ode261 := (2*x**2*y(x)-x)*D(y(x),x)-2*x*y(x)**2-y(x) +ode261 := (2*x^2*y(x)-x)*D(y(x),x)-2*x*y(x)^2-y(x) --R --R --R 2 , 2 @@ -371,7 +371,7 @@ solve(ode261,y,x) --E 35 --S 36 of 130 -ode262 := (2*x**2*y(x)-x**3)*D(y(x),x)+y(x)**3-4*x*y(x)**2+2*x**3 +ode262 := (2*x^2*y(x)-x^3)*D(y(x),x)+y(x)^3-4*x*y(x)^2+2*x^3 --R --R --R 2 3 , 3 2 3 @@ -389,7 +389,7 @@ solve(ode262,y,x) --E 37 --S 38 of 130 -ode263 := 2*x**3+y(x)*D(y(x),x)+3*x**2*y(x)**2+7 +ode263 := 2*x^3+y(x)*D(y(x),x)+3*x^2*y(x)^2+7 --R --R --R , 2 2 3 @@ -410,7 +410,7 @@ solve(ode263,y,x) --E 39 --S 40 of 130 -ode264 := 2*x*(x**3*y(x)+1)*D(y(x),x)+(3*x**3*y(x)-1)*y(x) +ode264 := 2*x*(x^3*y(x)+1)*D(y(x),x)+(3*x^3*y(x)-1)*y(x) --R --R --R 4 , 3 2 @@ -428,8 +428,8 @@ solve(ode264,y,x) --E 41 --S 42 of 130 -ode265 := (x**(n*(n+1))*y(x)-1)*D(y(x),x)+2*(n+1)**2*x**(n-1)_ - *(x**(n**2)*y(x)**2-1) +ode265 := (x^(n*(n+1))*y(x)-1)*D(y(x),x)+2*(n+1)^2*x^(n-1)_ + *(x^(n^2)*y(x)^2-1) --R --R --R (42) @@ -452,7 +452,7 @@ solve(ode265,y,x) --E 43 --S 44 of 130 -ode266 := (y(x)-x)*sqrt(x**2+1)*D(y(x),x)-a*sqrt((y(x)**2+1)**3) +ode266 := (y(x)-x)*sqrt(x^2+1)*D(y(x),x)-a*sqrt((y(x)^2+1)^3) --R --R --R +------+ +---------------------------+ @@ -471,7 +471,7 @@ solve(ode266,y,x) --E 45 --S 46 of 130 -ode267 := y(x)*D(y(x),x)*sin(x)**2+y(x)**2*cos(x)*sin(x)-1 +ode267 := y(x)*D(y(x),x)*sin(x)^2+y(x)^2*cos(x)*sin(x)-1 --R --R --R 2 , 2 @@ -492,7 +492,7 @@ yx:=solve(ode267,y,x) --E 47 --S 48 of 130 -ode267expr := yx*D(yx,x)*sin(x)**2+yx**2*cos(x)*sin(x)-1 +ode267expr := yx*D(yx,x)*sin(x)^2+yx^2*cos(x)*sin(x)-1 --R --R --R (48) @@ -508,7 +508,7 @@ ode267expr := yx*D(yx,x)*sin(x)**2+yx**2*cos(x)*sin(x)-1 --E 48 --S 49 of 130 -ode268 := f(x)*y(x)*D(y(x),x)+g(x)*y(x)**2+h(x) +ode268 := f(x)*y(x)*D(y(x),x)+g(x)*y(x)^2+h(x) --R --R --R , 2 @@ -530,7 +530,7 @@ solve(ode268,y,x) --S 51 of 130 ode269 := (g1(x)*y(x)+g0(x))*D(y(x),x)-f1(x)*y(x)-_ - f2(x)*y(x)**2-f3(x)*y(x)**3-f0(x) + f2(x)*y(x)^2-f3(x)*y(x)^3-f0(x) --R --R --R (50) @@ -549,7 +549,7 @@ solve(ode269,y,x) --E 52 --S 53 of 130 -ode270 := (y(x)**2-x)*D(y(x),x)-y(x)+x**2 +ode270 := (y(x)^2-x)*D(y(x),x)-y(x)+x^2 --R --R --R 2 , 2 @@ -570,7 +570,7 @@ yx:=solve(ode270,y,x) --E 54 --S 55 of 130 -ode270expr := (yx**2-x)*D(yx,x)-yx+x**2 +ode270expr := (yx^2-x)*D(yx,x)-yx+x^2 --R --R --R (54) @@ -595,7 +595,7 @@ ode270expr := (yx**2-x)*D(yx,x)-yx+x**2 --E 55 --S 56 of 130 -ode271 := (y(x)**2+x**2)*D(y(x),x)+2*x*(y(x)+2*x) +ode271 := (y(x)^2+x^2)*D(y(x),x)+2*x*(y(x)+2*x) --R --R --R 2 2 , 2 @@ -616,7 +616,7 @@ yx:=solve(ode271,y,x) --E 57 --S 58 of 130 -ode271expr := (yx**2+x**2)*D(yx,x)+2*x*(yx+2*x) +ode271expr := (yx^2+x^2)*D(yx,x)+2*x*(yx+2*x) --R --R --R (57) @@ -641,7 +641,7 @@ ode271expr := (yx**2+x**2)*D(yx,x)+2*x*(yx+2*x) --E 58 --S 59 of 130 -ode272 := (y(x)**2+x**2)*D(y(x),x)-y(x)**2 +ode272 := (y(x)^2+x^2)*D(y(x),x)-y(x)^2 --R --R --R 2 2 , 2 @@ -659,7 +659,7 @@ solve(ode272,y,x) --E 60 --S 61 of 130 -ode273 := (y(x)**2+x**2+a)*D(y(x),x)+2*x*y(x) +ode273 := (y(x)^2+x^2+a)*D(y(x),x)+2*x*y(x) --R --R --R 2 2 , @@ -680,7 +680,7 @@ yx:=solve(ode273,y,x) --E 62 --S 63 of 130 -ode273expr := (yx**2+x**2+a)*D(yx,x)+2*x*yx +ode273expr := (yx^2+x^2+a)*D(yx,x)+2*x*yx --R --R --R (62) @@ -705,7 +705,7 @@ ode273expr := (yx**2+x**2+a)*D(yx,x)+2*x*yx --E 63 --S 64 of 130 -ode274 := (y(x)**2+x**2+a)*D(y(x),x)+2*x*y(x)+x**2+b +ode274 := (y(x)^2+x^2+a)*D(y(x),x)+2*x*y(x)+x^2+b --R --R --R 2 2 , 2 @@ -726,7 +726,7 @@ yx:=solve(ode274,y,x) --E 65 --S 66 of 130 -ode274expr := (yx**2+x**2+a)*D(yx,x)+2*x*yx+x**2+b +ode274expr := (yx^2+x^2+a)*D(yx,x)+2*x*yx+x^2+b --R --R --R (65) @@ -772,7 +772,7 @@ ode274expr := (yx**2+x**2+a)*D(yx,x)+2*x*yx+x**2+b --E 66 --S 67 of 130 -ode275 := (y(x)**2+x**2+x)*D(y(x),x)-y(x) +ode275 := (y(x)^2+x^2+x)*D(y(x),x)-y(x) --R --R --R 2 2 , @@ -790,7 +790,7 @@ solve(ode275,y,x) --E 68 --S 69 of 130 -ode276 := (y(x)**2-x**2)*D(y(x),x)+2*x*y(x) +ode276 := (y(x)^2-x^2)*D(y(x),x)+2*x*y(x) --R --R --R 2 2 , @@ -811,7 +811,7 @@ yx:=solve(ode276,y,x) --E 70 --S 71 of 130 -ode276expr := (yx**2-x**2)*D(yx,x)+2*x*yx +ode276expr := (yx^2-x^2)*D(yx,x)+2*x*yx --R --R --R 6 6 , 5 3 3 5 @@ -824,7 +824,7 @@ ode276expr := (yx**2-x**2)*D(yx,x)+2*x*yx --E 71 --S 72 of 130 -ode277 := (y(x)**2+x**4)*D(y(x),x)-4*x**3*y(x) +ode277 := (y(x)^2+x^4)*D(y(x),x)-4*x^3*y(x) --R --R --R 2 4 , 3 @@ -845,7 +845,7 @@ yx:=solve(ode277,y,x) --E 73 --S 74 of 130 -ode277expr := (yx**2+x**4)*D(yx,x)-4*x**3*yx +ode277expr := (yx^2+x^4)*D(yx,x)-4*x^3*yx --R --R --R 6 12 , 3 5 7 3 11 @@ -858,7 +858,7 @@ ode277expr := (yx**2+x**4)*D(yx,x)-4*x**3*yx --E 74 --S 75 of 130 -ode278 := (y(x)**2+4*sin(x))*D(y(x),x)-cos(x) +ode278 := (y(x)^2+4*sin(x))*D(y(x),x)-cos(x) --R --R --R 2 , @@ -879,7 +879,7 @@ yx:=solve(ode278,y,x) --E 76 --S 77 of 130 -ode278expr := (yx**2+4*sin(x))*D(yx,x)-cos(x) +ode278expr := (yx^2+4*sin(x))*D(yx,x)-cos(x) --R --R --R (76) @@ -919,7 +919,7 @@ ode278expr := (yx**2+4*sin(x))*D(yx,x)-cos(x) --E 77 --S 78 of 130 -ode279 := (y(x)**2+2*y(x)+x)*D(y(x),x)+(y(x)+x)**2*y(x)**2+y(x)*(y(x)+1) +ode279 := (y(x)^2+2*y(x)+x)*D(y(x),x)+(y(x)+x)^2*y(x)^2+y(x)*(y(x)+1) --R --R --R 2 , 4 3 2 2 @@ -937,7 +937,7 @@ solve(ode279,y,x) --E 79 --S 80 of 130 -ode280 := (y(x)+x)**2*D(y(x),x)-a**2 +ode280 := (y(x)+x)^2*D(y(x),x)-a^2 --R --R --R 2 2 , 2 @@ -955,8 +955,8 @@ solve(ode280,y,x) --E 81 --S 82 of 130 -ode281 := (y(x)**2+2*x*y(x)-x**2)*D(y(x),x)-_ - y(x)**2+2*x*y(x)+x**2 +ode281 := (y(x)^2+2*x*y(x)-x^2)*D(y(x),x)-_ + y(x)^2+2*x*y(x)+x^2 --R --R --R 2 2 , 2 2 @@ -974,7 +974,7 @@ solve(ode281,y,x) --E 83 --S 84 of 130 -ode282 := (y(x)+3*x-1)**2*D(y(x),x)-(2*y(x)-1)*(4*y(x)+6*x-3) +ode282 := (y(x)+3*x-1)^2*D(y(x),x)-(2*y(x)-1)*(4*y(x)+6*x-3) --R --R --R (83) @@ -995,7 +995,7 @@ solve(ode282,y,x) --E 85 --S 86 of 130 -ode283 := 3*(y(x)**2-x**2)*D(y(x),x)+2*y(x)**3-6*x*(x+1)*y(x)-3*exp(x) +ode283 := 3*(y(x)^2-x^2)*D(y(x),x)+2*y(x)^3-6*x*(x+1)*y(x)-3*exp(x) --R --R --R 2 2 , x 3 2 @@ -1014,7 +1014,7 @@ yx:=solve(ode283,y,x) --E 87 --S 88 of 130 -ode283expr := 3*(yx**2-x**2)*D(yx,x)+2*yx**3-6*x*(x+1)*yx-3*exp(x) +ode283expr := 3*(yx^2-x^2)*D(yx,x)+2*yx^3-6*x*(x+1)*yx-3*exp(x) --R --R --R (87) @@ -1052,7 +1052,7 @@ ode283expr := 3*(yx**2-x**2)*D(yx,x)+2*yx**3-6*x*(x+1)*yx-3*exp(x) --E 88 --S 89 of 130 -ode284 := (4*y(x)**2+x**2)*D(y(x),x)-x*y(x) +ode284 := (4*y(x)^2+x^2)*D(y(x),x)-x*y(x) --R --R --R 2 2 , @@ -1074,7 +1074,7 @@ yx:=solve(ode284,y,x) --E 90 --S 91 of 130 -ode284expr := (4*yx**2+x**2)*D(yx,x)-x*yx +ode284expr := (4*yx^2+x^2)*D(yx,x)-x*yx --R --R --R (90) @@ -1103,7 +1103,7 @@ ode284expr := (4*yx**2+x**2)*D(yx,x)-x*yx --E 91 --S 92 of 130 -ode285 := (4*y(x)**2+2*x*y(x)+3*x**2)*D(y(x),x)+y(x)**2+6*x*y(x)+2*x**2 +ode285 := (4*y(x)^2+2*x*y(x)+3*x^2)*D(y(x),x)+y(x)^2+6*x*y(x)+2*x^2 --R --R --R 2 2 , 2 2 @@ -1124,7 +1124,7 @@ yx:=solve(ode285,y,x) --E 93 --S 94 of 130 -ode285expr := (4*yx**2+2*x*yx+3*x**2)*D(yx,x)+yx**2+6*x*yx+2*x**2 +ode285expr := (4*yx^2+2*x*yx+3*x^2)*D(yx,x)+yx^2+6*x*yx+2*x^2 --R --R --R (93) @@ -1161,7 +1161,7 @@ ode285expr := (4*yx**2+2*x*yx+3*x**2)*D(yx,x)+yx**2+6*x*yx+2*x**2 --E 94 --S 95 of 130 -ode286 := (2*y(x)-3*x+1)**2*D(y(x),x)-(3*y(x)-2*x-4)**2 +ode286 := (2*y(x)-3*x+1)^2*D(y(x),x)-(3*y(x)-2*x-4)^2 --R --R --R (94) @@ -1183,7 +1183,7 @@ solve(ode286,y,x) --E 96 --S 97 of 130 -ode287 := (2*y(x)-4*x+1)**2*D(y(x),x)-(y(x)-2*x)**2 +ode287 := (2*y(x)-4*x+1)^2*D(y(x),x)-(y(x)-2*x)^2 --R --R --R (96) @@ -1202,7 +1202,7 @@ solve(ode287,y,x) --E 98 --S 99 of 130 -ode288 := (6*y(x)**2-3*x**2*y(x)+1)*D(y(x),x)-3*x*y(x)**2+x +ode288 := (6*y(x)^2-3*x^2*y(x)+1)*D(y(x),x)-3*x*y(x)^2+x --R --R --R 2 2 , 2 @@ -1223,7 +1223,7 @@ yx:=solve(ode288,y,x) --E 100 --S 101 of 130 -ode288expr := (6*yx**2-3*x**2*yx+1)*D(yx,x)-3*x*yx**2+x +ode288expr := (6*yx^2-3*x^2*yx+1)*D(yx,x)-3*x*yx^2+x --R --R --R (100) @@ -1248,7 +1248,7 @@ ode288expr := (6*yx**2-3*x**2*yx+1)*D(yx,x)-3*x*yx**2+x --E 101 --S 102 of 130 -ode289 := (6*y(x)-x)**2*D(y(x),x)-6*y(x)**2+2*x*y(x)+a +ode289 := (6*y(x)-x)^2*D(y(x),x)-6*y(x)^2+2*x*y(x)+a --R --R --R 2 2 , 2 @@ -1267,7 +1267,7 @@ yx:=solve(ode289,y,x) --E 103 --S 104 of 130 -ode289expr := (6*yx-x)**2*D(yx,x)-6*yx**2+2*x*yx+a +ode289expr := (6*yx-x)^2*D(yx,x)-6*yx^2+2*x*yx+a --R --R --R (103) @@ -1308,7 +1308,7 @@ ode289expr := (6*yx-x)**2*D(yx,x)-6*yx**2+2*x*yx+a --E 104 --S 105 of 130 -ode290 := (a*y(x)**2+2*b*x*y(x)+c*x**2)*D(y(x),x)+b*y(x)**2+2*c*x*y(x)+d*x**2 +ode290 := (a*y(x)^2+2*b*x*y(x)+c*x^2)*D(y(x),x)+b*y(x)^2+2*c*x*y(x)+d*x^2 --R --R --R 2 2 , 2 2 @@ -1329,7 +1329,7 @@ yx:=solve(ode290,y,x) --E 106 --S 107 of 130 -ode290expr:=(a*yx**2+2*b*x*yx+c*x**2)*D(yx,x)+b*yx**2+2*c*x*yx+d*x**2 +ode290expr:=(a*yx^2+2*b*x*yx+c*x^2)*D(yx,x)+b*yx^2+2*c*x*yx+d*x^2 --R --R --R (106) @@ -1384,8 +1384,8 @@ ode290expr:=(a*yx**2+2*b*x*yx+c*x**2)*D(yx,x)+b*yx**2+2*c*x*yx+d*x**2 --E 107 --S 108 of 130 -ode291 := (b*(beta*y(x)+alpha*x)**2-beta*(b*y(x)+a*x))*D(y(x),x)+_ - a*(beta*y(x)+alpha*x)**2-alpha*(b*y(x)+a*x) +ode291 := (b*(beta*y(x)+alpha*x)^2-beta*(b*y(x)+a*x))*D(y(x),x)+_ + a*(beta*y(x)+alpha*x)^2-alpha*(b*y(x)+a*x) --R --R --R (107) @@ -1410,7 +1410,7 @@ solve(ode291,y,x) --E 109 --S 110 of 130 -ode292 := (a*y(x)+b*x+c)**2*D(y(x),x)+(alpha*y(x)+beta*x+gamma)**2 +ode292 := (a*y(x)+b*x+c)^2*D(y(x),x)+(alpha*y(x)+beta*x+gamma)^2 --R --R --R (109) @@ -1432,7 +1432,7 @@ solve(ode292,y,x) --E 111 --S 112 of 130 -ode293 := x*(y(x)**2-3*x)*D(y(x),x)+2*y(x)**3-5*x*y(x) +ode293 := x*(y(x)^2-3*x)*D(y(x),x)+2*y(x)^3-5*x*y(x) --R --R --R 2 2 , 3 @@ -1450,7 +1450,7 @@ solve(ode293,y,x) --E 113 --S 114 of 130 -ode294 := x*(y(x)**2+x**2-a)*D(y(x),x)-y(x)*(y(x)**2+x**2+a) +ode294 := x*(y(x)^2+x^2-a)*D(y(x),x)-y(x)*(y(x)^2+x^2+a) --R --R --R 2 3 , 3 2 @@ -1468,7 +1468,7 @@ solve(ode294,y,x) --E 115 --S 116 of 130 -ode295 := x*(y(x)**2+x*y(x)-x**2)*D(y(x),x)-y(x)**3+x*y(x)**2+x**2*y(x) +ode295 := x*(y(x)^2+x*y(x)-x^2)*D(y(x),x)-y(x)^3+x*y(x)^2+x^2*y(x) --R --R --R 2 2 3 , 3 2 2 @@ -1486,7 +1486,7 @@ solve(ode295,y,x) --E 117 --S 118 of 130 -ode296 := x*(y(x)**2+x**2*y(x)+x**2)*D(y(x),x)-2*y(x)**3-2*x**2*y(x)**2+x**4 +ode296 := x*(y(x)^2+x^2*y(x)+x^2)*D(y(x),x)-2*y(x)^3-2*x^2*y(x)^2+x^4 --R --R --R 2 3 3 , 3 2 2 4 @@ -1504,7 +1504,7 @@ solve(ode296,y,x) --E 119 --S 120 of 130 -ode297 := 2*x*(y(x)**2+5*x**2)*D(y(x),x)+y(x)**3-x**2*y(x) +ode297 := 2*x*(y(x)^2+5*x^2)*D(y(x),x)+y(x)^3-x^2*y(x) --R --R --R 2 3 , 3 2 @@ -1522,7 +1522,7 @@ solve(ode297,y,x) --E 121 --S 122 of 130 -ode298 := 3*x*y(x)**2*D(y(x),x)+y(x)**3-2*x +ode298 := 3*x*y(x)^2*D(y(x),x)+y(x)^3-2*x --R --R --R 2 , 3 @@ -1541,7 +1541,7 @@ yx:=solve(ode298,y,x) --E 123 --S 124 of 130 -ode298expr := 3*x*yx**2*D(yx,x)+yx**3-2*x +ode298expr := 3*x*yx^2*D(yx,x)+yx^3-2*x --R --R --R (123) @@ -1555,7 +1555,7 @@ ode298expr := 3*x*yx**2*D(yx,x)+yx**3-2*x --E 124 --S 125 of 130 -ode299 := (3*x*y(x)**2-x**2)*D(y(x),x)+y(x)**3-2*x*y(x) +ode299 := (3*x*y(x)^2-x^2)*D(y(x),x)+y(x)^3-2*x*y(x) --R --R --R 2 2 , 3 @@ -1574,7 +1574,7 @@ yx:=solve(ode299,y,x) --E 126 --S 127 of 130 -ode299expr := (3*x*yx**2-x**2)*D(yx,x)+yx**3-2*x*yx +ode299expr := (3*x*yx^2-x^2)*D(yx,x)+yx^3-2*x*yx --R --R --R (126) @@ -1588,7 +1588,7 @@ ode299expr := (3*x*yx**2-x**2)*D(yx,x)+yx**3-2*x*yx --E 127 --S 128 of 130 -ode300 := 6*x*y(x)**2*D(y(x),x)+2*y(x)**3+x +ode300 := 6*x*y(x)^2*D(y(x),x)+2*y(x)^3+x --R --R --R 2 , 3 @@ -1609,7 +1609,7 @@ yx:=solve(ode300,y,x) --E 129 --S 130 of 130 -ode300expr := 6*x*yx**2*D(yx,x)+2*yx**3+x +ode300expr := 6*x*yx^2*D(yx,x)+2*yx^3+x --R --R --R (129) diff --git a/src/input/kamke6.input.pamphlet b/src/input/kamke6.input.pamphlet index a16be4c..07479a2 100644 --- a/src/input/kamke6.input.pamphlet +++ b/src/input/kamke6.input.pamphlet @@ -45,7 +45,7 @@ g:=operator 'g --E 3 --S 4 of 120 -ode301 := (6*x*y(x)**2+x**2)*D(y(x),x)-y(x)*(3*y(x)**2-x) +ode301 := (6*x*y(x)^2+x^2)*D(y(x),x)-y(x)*(3*y(x)^2-x) --R --R --R 2 2 , 3 @@ -63,7 +63,7 @@ solve(ode301,y,x) --E 5 --S 6 of 120 -ode302 := (x**2*y(x)**2+x)*D(y(x),x)+y(x) +ode302 := (x^2*y(x)^2+x)*D(y(x),x)+y(x) --R --R --R 2 2 , @@ -81,7 +81,7 @@ solve(ode302,y,x) --E 7 --S 8 of 120 -ode303 := (x*y(x)-1)**2*x*D(y(x),x)+(x**2*y(x)**2+1)*y(x) +ode303 := (x*y(x)-1)^2*x*D(y(x),x)+(x^2*y(x)^2+1)*y(x) --R --R --R 3 2 2 , 2 3 @@ -99,7 +99,7 @@ solve(ode303,y,x) --E 9 --S 10 of 120 -ode304 := (10*x**3*y(x)**2+x**2*y(x)+2*x)*D(y(x),x)+5*x**2*y(x)**3+x*y(x)**2 +ode304 := (10*x^3*y(x)^2+x^2*y(x)+2*x)*D(y(x),x)+5*x^2*y(x)^3+x*y(x)^2 --R --R --R 3 2 2 , 2 3 2 @@ -117,7 +117,7 @@ solve(ode304,y,x) --E 11 --S 12 of 120 -ode305 := (y(x)**3-3*x)*D(y(x),x)-3*y(x)+x**2 +ode305 := (y(x)^3-3*x)*D(y(x),x)-3*y(x)+x^2 --R --R --R 3 , 2 @@ -138,7 +138,7 @@ yx:=solve(ode305,y,x) --E 13 --S 14 of 120 -ode305expr := (yx**3-3*x)*D(yx,x)-3*yx+x**2 +ode305expr := (yx^3-3*x)*D(yx,x)-3*yx+x^2 --R --R --R (14) @@ -175,7 +175,7 @@ ode305expr := (yx**3-3*x)*D(yx,x)-3*yx+x**2 --E 14 --S 15 of 120 -ode306 := (y(x)**3-x**3)*D(y(x),x)-x**2*y(x) +ode306 := (y(x)^3-x^3)*D(y(x),x)-x^2*y(x) --R --R --R 3 3 , 2 @@ -196,7 +196,7 @@ yx:=solve(ode306,y,x) --E 16 --S 17 of 120 -ode306expr := (yx**3-x**3)*D(yx,x)-x**2*yx +ode306expr := (yx^3-x^3)*D(yx,x)-x^2*yx --R --R --R (17) @@ -218,7 +218,7 @@ ode306expr := (yx**3-x**3)*D(yx,x)-x**2*yx --E 17 --S 18 of 120 -ode307 := (y(x)**2+x**2+a)*y(x)*D(y(x),x)+(y(x)**2+x**2-a)*x +ode307 := (y(x)^2+x^2+a)*y(x)*D(y(x),x)+(y(x)^2+x^2-a)*x --R --R --R 3 2 , 2 3 @@ -239,7 +239,7 @@ yx:=solve(ode307,y,x) --E 19 --S 20 of 120 -ode307expr := (yx**2+x**2+a)*yx*D(yx,x)+(yx**2+x**2-a)*x +ode307expr := (yx^2+x^2+a)*yx*D(yx,x)+(yx^2+x^2-a)*x --R --R --R (20) @@ -302,7 +302,7 @@ ode307expr := (yx**2+x**2+a)*yx*D(yx,x)+(yx**2+x**2-a)*x --E 20 --S 21 of 120 -ode308 := 2*y(x)**3*D(y(x),x)+x*y(x)**2 +ode308 := 2*y(x)^3*D(y(x),x)+x*y(x)^2 --R --R --R 3 , 2 @@ -323,7 +323,7 @@ yx:=solve(ode308,y,x) --E 22 --S 23 of 120 -ode308expr := 2*yx**3*D(yx,x)+x*yx**2 +ode308expr := 2*yx^3*D(yx,x)+x*yx^2 --R --R --R (23) @@ -339,7 +339,7 @@ ode308expr := 2*yx**3*D(yx,x)+x*yx**2 --E 23 --S 24 of 120 -ode309 := (2*y(x)**3+y(x))*D(y(x),x)-2*x**3-x +ode309 := (2*y(x)^3+y(x))*D(y(x),x)-2*x^3-x --R --R --R 3 , 3 @@ -360,7 +360,7 @@ yx:=solve(ode309,y,x) --E 25 --S 26 of 120 -ode309expr := (2*yx**3+yx)*D(yx,x)-2*x**3-x +ode309expr := (2*yx^3+yx)*D(yx,x)-2*x^3-x --R --R --R (26) @@ -400,7 +400,7 @@ ode309expr := (2*yx**3+yx)*D(yx,x)-2*x**3-x --E 26 --S 27 of 120 -ode310 := (2*y(x)**3+5*x**2*y(x))*D(y(x),x)+5*x*y(x)**2+x**3 +ode310 := (2*y(x)^3+5*x^2*y(x))*D(y(x),x)+5*x*y(x)^2+x^3 --R --R --R 3 2 , 2 3 @@ -421,7 +421,7 @@ yx:=solve(ode310,y,x) --E 28 --S 29 of 120 -ode310expr := (2*yx**3+5*x**2*yx)*D(yx,x)+5*x*yx**2+x**3 +ode310expr := (2*yx^3+5*x^2*yx)*D(yx,x)+5*x*yx^2+x^3 --R --R --R (29) @@ -452,8 +452,8 @@ ode310expr := (2*yx**3+5*x**2*yx)*D(yx,x)+5*x*yx**2+x**3 --E 29 --S 30 of 120 -ode311 := (20*y(x)**3-3*x*y(x)**2+6*x**2*y(x)+3*x**3)*D(y(x),x)-_ - y(x)**3+6*x*y(x)**2+9*x**2*y(x)+4*x**3 +ode311 := (20*y(x)^3-3*x*y(x)^2+6*x^2*y(x)+3*x^3)*D(y(x),x)-_ + y(x)^3+6*x*y(x)^2+9*x^2*y(x)+4*x^3 --R --R --R (30) @@ -473,8 +473,8 @@ yx:=solve(ode311,y,x) --E 31 --S 32 of 120 -ode311expr := (20*yx**3-3*x*yx**2+6*x**2*yx+3*x**3)*D(yx,x)-_ - yx**3+6*x*yx**2+9*x**2*yx+4*x**3 +ode311expr := (20*yx^3-3*x*yx^2+6*x^2*yx+3*x^3)*D(yx,x)-_ + yx^3+6*x*yx^2+9*x^2*yx+4*x^3 --R --R --R (32) @@ -533,7 +533,7 @@ ode311expr := (20*yx**3-3*x*yx**2+6*x**2*yx+3*x**3)*D(yx,x)-_ --E 32 --S 33 of 120 -ode312 := (y(x)**2/b+x**2/a)*(y(x)*D(y(x),x)+x)+((a-b)/(a+b))*_ +ode312 := (y(x)^2/b+x^2/a)*(y(x)*D(y(x),x)+x)+((a-b)/(a+b))*_ (y(x)*D(y(x),x)-x) --R --R @@ -559,8 +559,8 @@ solve(ode312,y,x) --E 34 --S 35 of 120 -ode313 := (2*a*y(x)**3+3*a*x*y(x)**2-b*x**3+c*x**2)*D(y(x),x)-_ - a*y(x)**3+c*y(x)**2+3*b*x**2*y(x)+2*b*x**3 +ode313 := (2*a*y(x)^3+3*a*x*y(x)^2-b*x^3+c*x^2)*D(y(x),x)-_ + a*y(x)^3+c*y(x)^2+3*b*x^2*y(x)+2*b*x^3 --R --R --R (35) @@ -582,7 +582,7 @@ solve(ode313,y,x) --E 36 --S 37 of 120 -ode314 := x*y(x)**3*D(y(x),x)+y(x)**4-x*sin(x) +ode314 := x*y(x)^3*D(y(x),x)+y(x)^4-x*sin(x) --R --R --R 3 , 4 @@ -603,7 +603,7 @@ yx:=solve(ode314,y,x) --E 38 --S 39 of 120 -ode314expr := x*yx**3*D(yx,x)+yx**4-x*sin(x) +ode314expr := x*yx^3*D(yx,x)+yx^4-x*sin(x) --R --R --R (39) @@ -760,7 +760,7 @@ ode314expr := x*yx**3*D(yx,x)+yx**4-x*sin(x) --E 39 --S 40 of 120 -ode315 := (2*x*y(x)**3-x**4)*D(y(x),x)-y(x)**4+2*x**3*y(x) +ode315 := (2*x*y(x)^3-x^4)*D(y(x),x)-y(x)^4+2*x^3*y(x) --R --R --R 3 4 , 4 3 @@ -778,7 +778,7 @@ solve(ode315,y,x) --E 41 --S 42 of 120 -ode316 := (2*x*y(x)**3+y(x))*D(y(x),x)+2*y(x)**2 +ode316 := (2*x*y(x)^3+y(x))*D(y(x),x)+2*y(x)^2 --R --R --R 3 , 2 @@ -803,7 +803,7 @@ yx:=solve(ode316,y,x) --E 43 --S 44 of 120 -ode316expr := (2*x*yx**3+yx)*D(yx,x)+2*yx**2 +ode316expr := (2*x*yx^3+yx)*D(yx,x)+2*yx^2 --R --R --R (44) @@ -858,7 +858,7 @@ ode316expr := (2*x*yx**3+yx)*D(yx,x)+2*yx**2 --E 44 --S 45 of 120 -ode317 := (2*x*y(x)**3+x*y(x)+x**2)*D(y(x),x)+y(x)**2-x*y(x) +ode317 := (2*x*y(x)^3+x*y(x)+x^2)*D(y(x),x)+y(x)^2-x*y(x) --R --R --R 3 2 , 2 @@ -876,7 +876,7 @@ solve(ode317,y,x) --E 46 --S 47 of 120 -ode318 := (3*x*y(x)**3-4*x*y(x)+y(x))*D(y(x),x)+y(x)**2*(y(x)**2-2) +ode318 := (3*x*y(x)^3-4*x*y(x)+y(x))*D(y(x),x)+y(x)^2*(y(x)^2-2) --R --R --R 3 , 4 2 @@ -903,7 +903,7 @@ yx:=solve(ode318,y,x) --E 48 --S 49 of 120 -ode318expr := (3*x*yx**3-4*x*yx+yx)*D(yx,x)+yx**2*(yx**2-2) +ode318expr := (3*x*yx^3-4*x*yx+yx)*D(yx,x)+yx^2*(yx^2-2) --R --R --R (49) @@ -929,7 +929,7 @@ ode318expr := (3*x*yx**3-4*x*yx+yx)*D(yx,x)+yx**2*(yx**2-2) --E 49 --S 50 of 120 -ode319 := (7*x*y(x)**3+y(x)-5*x)*D(y(x),x)+y(x)**4-5*y(x) +ode319 := (7*x*y(x)^3+y(x)-5*x)*D(y(x),x)+y(x)^4-5*y(x) --R --R --R 3 , 4 @@ -950,7 +950,7 @@ yx:=solve(ode319,y,x) --E 51 --S 52 of 120 -ode319expr := (7*x*yx**3+yx-5*x)*D(yx,x)+yx**4-5*yx +ode319expr := (7*x*yx^3+yx-5*x)*D(yx,x)+yx^4-5*yx --R --R --R (52) @@ -1052,7 +1052,7 @@ ode319expr := (7*x*yx**3+yx-5*x)*D(yx,x)+yx**4-5*yx --E 52 --S 53 of 120 -ode320 := (x**2*y(x)**3+x*y(x))*D(y(x),x)-1 +ode320 := (x^2*y(x)^3+x*y(x))*D(y(x),x)-1 --R --R --R 2 3 , @@ -1070,7 +1070,7 @@ solve(ode320,y,x) --E 54 --S 55 of 120 -ode321 := (2*x**2*y(x)**3+x**2*y(x)**2-2*x)*D(y(x),x)-2*y(x)-1 +ode321 := (2*x^2*y(x)^3+x^2*y(x)^2-2*x)*D(y(x),x)-2*y(x)-1 --R --R --R 2 3 2 2 , @@ -1088,7 +1088,7 @@ solve(ode321,y,x) --E 56 --S 57 of 120 -ode322 := (10*x**2*y(x)**3-3*y(x)**2-2)*D(y(x),x)+5*x*y(x)**4+x +ode322 := (10*x^2*y(x)^3-3*y(x)^2-2)*D(y(x),x)+5*x*y(x)^4+x --R --R --R 2 3 2 , 4 @@ -1109,7 +1109,7 @@ yx:=solve(ode322,y,x) --E 58 --S 59 of 120 -ode322expr := (10*x**2*yx**3-3*yx**2-2)*D(yx,x)+5*x*yx**4+x +ode322expr := (10*x^2*yx^3-3*yx^2-2)*D(yx,x)+5*x*yx^4+x --R --R --R (59) @@ -1164,7 +1164,7 @@ ode322expr := (10*x**2*yx**3-3*yx**2-2)*D(yx,x)+5*x*yx**4+x --E 59 --S 60 of 120 -ode323 := (a*x*y(x)**3+c)*x*D(y(x),x)+(b*x**3*y(x)+c)*y(x) +ode323 := (a*x*y(x)^3+c)*x*D(y(x),x)+(b*x^3*y(x)+c)*y(x) --R --R --R 2 3 , 3 2 @@ -1182,7 +1182,7 @@ solve(ode323,y,x) --E 61 --S 62 of 120 -ode324 := (2*x**3*y(x)**3-x)*D(y(x),x)+2*x**3*y(x)**3-y(x) +ode324 := (2*x^3*y(x)^3-x)*D(y(x),x)+2*x^3*y(x)^3-y(x) --R --R --R 3 3 , 3 3 @@ -1200,7 +1200,7 @@ solve(ode324,y,x) --E 63 --S 64 of 120 -ode325 := y(x)*(y(x)**3-2*x**3)*D(y(x),x)+(2*y(x)**3-x**3)*x +ode325 := y(x)*(y(x)^3-2*x^3)*D(y(x),x)+(2*y(x)^3-x^3)*x --R --R --R 4 3 , 3 4 @@ -1218,7 +1218,7 @@ solve(ode325,y,x) --E 65 --S 66 of 120 -ode326 := y(x)*((a*y(x)+b*x)**3+b*x**3)*D(y(x),x)+x*((a*y(x)+b*x)**3+a*y(x)**3) +ode326 := y(x)*((a*y(x)+b*x)^3+b*x^3)*D(y(x),x)+x*((a*y(x)+b*x)^3+a*y(x)^3) --R --R --R (66) @@ -1240,7 +1240,7 @@ solve(ode326,y,x) --E 67 --S 68 of 120 -ode327 := (x*y(x)**4+2*x**2*y(x)**3+2*y(x)+x)*D(y(x),x)+y(x)**5+y(x) +ode327 := (x*y(x)^4+2*x^2*y(x)^3+2*y(x)+x)*D(y(x),x)+y(x)^5+y(x) --R --R --R 4 2 3 , 5 @@ -1258,7 +1258,7 @@ solve(ode327,y,x) --E 69 --S 70 of 120 -ode328 := a*x**2*y(x)**n*D(y(x),x)-2*x*D(y(x),x)+y(x) +ode328 := a*x^2*y(x)^n*D(y(x),x)-2*x*D(y(x),x)+y(x) --R --R --R 2 n , @@ -1276,7 +1276,7 @@ solve(ode328,y,x) --E 71 --S 72 of 120 -ode329 := y(x)**m*x**n*(a*x*D(y(x),x)+b*y(x))+alpha*x*D(y(x),x)+beta*y(x) +ode329 := y(x)^m*x^n*(a*x*D(y(x),x)+b*y(x))+alpha*x*D(y(x),x)+beta*y(x) --R --R --R n m , n m @@ -1317,14 +1317,14 @@ solve(ode330,y,x) \end{chunk} I have no idea what to do with this \begin{verbatim} - ode331 := D(y(x),x)*convert([sum(f[nu](x)*y(x)**nu,'nu'=1..p)],`+`)-_ - convert([sum(g[nu](x)*y(x)**nu,'nu'=1..q)],`+`) + ode331 := D(y(x),x)*convert([sum(f[nu](x)*y(x)^nu,'nu'=1..p)],`+`)-_ + convert([sum(g[nu](x)*y(x)^nu,'nu'=1..q)],`+`) \end{verbatim} \begin{chunk}{*} --R --S 76 of 120 -ode333 := (2*x**(5/2)*y(x)**(3/2)+x**2*y(x)-x)*D(y(x),x)-_ - x**(3/2)*y(x)**(5/2)+x*y(x)**2-y(x) +ode333 := (2*x^(5/2)*y(x)^(3/2)+x^2*y(x)-x)*D(y(x),x)-_ + x^(3/2)*y(x)^(5/2)+x*y(x)^2-y(x) --R --R --R (75) @@ -1361,7 +1361,7 @@ solve(ode334,y,x) --E 79 --S 80 of 120 -ode335 := sqrt(y(x)**2-1)*D(y(x),x)-sqrt(x**2-1) +ode335 := sqrt(y(x)^2-1)*D(y(x),x)-sqrt(x^2-1) --R --R --R +---------+ +------+ @@ -1425,7 +1425,7 @@ yx:=solve(ode335,y,x) --E 81 --S 82 of 120 -ode335expr := sqrt(yx**2-1)*D(yx,x)-sqrt(x**2-1) +ode335expr := sqrt(yx^2-1)*D(yx,x)-sqrt(x^2-1) --R --R --R (81) @@ -1822,7 +1822,7 @@ ode335expr := sqrt(yx**2-1)*D(yx,x)-sqrt(x**2-1) --E 82 --S 83 of 120 -ode336 := (sqrt(y(x)**2+1)+a*x)*D(y(x),x)+sqrt(x**2+1)+a*y(x) +ode336 := (sqrt(y(x)^2+1)+a*x)*D(y(x),x)+sqrt(x^2+1)+a*y(x) --R --R --R +---------+ +------+ @@ -1889,7 +1889,7 @@ yx:=solve(ode336,y,x) --E 84 --S 85 of 120 -ode336expr := (sqrt(yx**2+1)+a*x)*D(yx,x)+sqrt(x**2+1)+a*yx +ode336expr := (sqrt(yx^2+1)+a*x)*D(yx,x)+sqrt(x^2+1)+a*yx --R --R --R (84) @@ -2974,7 +2974,7 @@ ode336expr := (sqrt(yx**2+1)+a*x)*D(yx,x)+sqrt(x**2+1)+a*yx --E 85 --S 86 of 120 -ode337 := (sqrt(y(x)**2+x**2)+x)*D(y(x),x)-y(x) +ode337 := (sqrt(y(x)^2+x^2)+x)*D(y(x),x)-y(x) --R --R --R +----------+ @@ -2993,9 +2993,9 @@ solve(ode337,y,x) --E 87 --S 88 of 120 -ode338 := (y(x)*sqrt(y(x)**2+x**2)+(y(x)**2-x**2)*sin(alpha)-_ - 2*x*y(x)*cos(alpha))*D(y(x),x)+x*sqrt(y(x)**2+x**2)+_ - 2*x*y(x)*sin(alpha)+(y(x)**2-x**2)*cos(alpha) +ode338 := (y(x)*sqrt(y(x)^2+x^2)+(y(x)^2-x^2)*sin(alpha)-_ + 2*x*y(x)*cos(alpha))*D(y(x),x)+x*sqrt(y(x)^2+x^2)+_ + 2*x*y(x)*sin(alpha)+(y(x)^2-x^2)*cos(alpha) --R --R --R (87) @@ -3019,8 +3019,8 @@ solve(ode338,y,x) --E 89 --S 90 of 120 -ode339 := (x*sqrt(x**2+y(x)**2+1)-y(x)*(x**2+y(x)**2))*D(y(x),x)-_ - y(x)*sqrt(x**2+y(x)**2+1)-x*(x**2+y(x)**2) +ode339 := (x*sqrt(x^2+y(x)^2+1)-y(x)*(x^2+y(x)^2))*D(y(x),x)-_ + y(x)*sqrt(x^2+y(x)^2+1)-x*(x^2+y(x)^2) --R --R --R (89) @@ -3043,9 +3043,9 @@ solve(ode339,y,x) --E 91 --S 92 of 120 -ode340 := (e1*(x+a)/((x+a)**2+y(x)**2)**(3/2)+e2*(x-a)/_ - ((x-a)**2+y(x)**2)**(3/2))*D(y(x),x)-y(x)*_ - (e1/((x+a)**2+y(x)**2)**(3/2)+e2/((x-a)**2+y(x)**2)**(3/2)) +ode340 := (e1*(x+a)/((x+a)^2+y(x)^2)^(3/2)+e2*(x-a)/_ + ((x-a)^2+y(x)^2)^(3/2))*D(y(x),x)-y(x)*_ + (e1/((x+a)^2+y(x)^2)^(3/2)+e2/((x-a)^2+y(x)^2)^(3/2)) --R --R --R (91) @@ -3268,7 +3268,7 @@ ode344expr := (log(yx)+2*x-1)*D(yx,x)-2*yx --E 105 --S 106 of 120 -ode345 := x*(2*x**2*y(x)*log(y(x))+1)*D(y(x),x)-2*y(x) +ode345 := x*(2*x^2*y(x)*log(y(x))+1)*D(y(x),x)-2*y(x) --R --R --R 3 , @@ -3290,7 +3290,7 @@ yx:=solve(ode345,y,x) --E 107 --S 108 of 120 -ode345expr := x*(2*x**2*yx*log(yx)+1)*D(yx,x)-2*yx +ode345expr := x*(2*x^2*yx*log(yx)+1)*D(yx,x)-2*yx --R --R --R (107) @@ -3632,7 +3632,7 @@ solve(ode349,y,x) --E 118 --S 119 of 120 -ode350 := D(y(x),x)*cos(y(x))-cos(x)*sin(y(x))**2-sin(y(x)) +ode350 := D(y(x),x)*cos(y(x))-cos(x)*sin(y(x))^2-sin(y(x)) --R --R --R , 2 diff --git a/src/input/kamke7.input.pamphlet b/src/input/kamke7.input.pamphlet index 05f62f9..bab39ad 100644 --- a/src/input/kamke7.input.pamphlet +++ b/src/input/kamke7.input.pamphlet @@ -298,7 +298,7 @@ ode355expr := (x*cos(yx)+cos(x))*D(yx,x)-yx*sin(x)+sin(yx) --E 22 --S 23 of 97 -ode356 := (x**2*cos(y(x))+2*y(x)*sin(x))*D(y(x),x)+2*x*sin(y(x))+y(x)**2*cos(x) +ode356 := (x^2*cos(y(x))+2*y(x)*sin(x))*D(y(x),x)+2*x*sin(y(x))+y(x)^2*cos(x) --R --R --R 2 , 2 @@ -317,7 +317,7 @@ yx:=solve(ode356,y,x) --E 24 --S 25 of 97 -ode356expr:=(x**2*cos(yx)+2*yx*sin(x))*D(yx,x)+2*x*sin(yx)+yx**2*cos(x) +ode356expr:=(x^2*cos(yx)+2*yx*sin(x))*D(yx,x)+2*x*sin(yx)+yx^2*cos(x) --R --R --R (25) @@ -503,7 +503,7 @@ ode361expr:=(x*sin(x*yx)+cos(x+yx)-sin(yx))*D(yx,x)+_ --E 31 --S 32 of 97 -ode363 := (x*D(y(x),x)-y(x))*cos(y(x)/x)**2+x +ode363 := (x*D(y(x),x)-y(x))*cos(y(x)/x)^2+x --R --R --R y(x) 2 , y(x) 2 @@ -525,7 +525,7 @@ yx:=solve(ode363,y,x) --E 33 --S 34 of 97 -ode363expr := (x*D(yx,x)-yx)*cos(yx/x)**2+x +ode363expr := (x*D(yx,x)-yx)*cos(yx/x)^2+x --R --R --R (34) @@ -640,7 +640,7 @@ ode434expr := D(yx,x)-1 --E 41 --S 42 of 97 -ode683 := (D(y(x),x) = y(x)*(-1+log(x*(x+1))*y(x)*x**4-log(x*(x+1))*x**3)/x) +ode683 := (D(y(x),x) = y(x)*(-1+log(x*(x+1))*y(x)*x^4-log(x*(x+1))*x^3)/x) --R --R --R 4 2 3 2 @@ -665,7 +665,7 @@ solve(ode683,y,x) --E 43 --S 44 of 97 -ode703 := (D(y(x),x) = y(x)*(1-x+y(x)*x**2*log(x)+y(x)*x**3-x*log(x)-x**2)/_ +ode703 := (D(y(x),x) = y(x)*(1-x+y(x)*x^2*log(x)+y(x)*x^3-x*log(x)-x^2)/_ (x-1)/x) --R --R @@ -689,8 +689,8 @@ solve(ode703,y,x) --E 45 --S 46 of 97 -ode714 := (D(y(x),x) = -y(x)*(-log(1/x)+exp(x)+y(x)*x**2*log(x)+_ - y(x)*x**3-x*log(x)-x**2)/(-log(1/x)+exp(x))/x) +ode714 := (D(y(x),x) = -y(x)*(-log(1/x)+exp(x)+y(x)*x^2*log(x)+_ + y(x)*x^3-x*log(x)-x^2)/(-log(1/x)+exp(x))/x) --R --R --R (46) @@ -752,7 +752,7 @@ solve(ode714,y,x) --E 47 --S 48 of 97 -ode719 := (D(y(x),x) = y(x)*(-exp(x)+log(2*x)*x**2*y(x)-log(2*x)*x)/x/exp(x)) +ode719 := (D(y(x),x) = y(x)*(-exp(x)+log(2*x)*x^2*y(x)-log(2*x)*x)/x/exp(x)) --R --R --R 2 2 x @@ -779,7 +779,7 @@ solve(ode719,y,x) --E 49 --S 50 of 97 -ode736 := (D(y(x),x) = (2*x**2+2*x+x**4-2*y(x)*x**2-1+y(x)**2)/(x+1)) +ode736 := (D(y(x),x) = (2*x^2+2*x+x^4-2*y(x)*x^2-1+y(x)^2)/(x+1)) --R --R --R 2 2 4 2 @@ -833,7 +833,7 @@ solve(ode765,y,x) --S 54 of 97 ode766 := (D(y(x),x) = y(x)*(-log(x)-x*log((x-1)*(1+x)/x)+_ - log((x-1)*(1+x)/x)*x**2*y(x))/x/log(x)) + log((x-1)*(1+x)/x)*x^2*y(x))/x/log(x)) --R --R --R 2 @@ -885,8 +885,8 @@ solve(ode766,y,x) --E 55 --S 56 of 97 -ode776 := (D(y(x),x) = y(x)*(-log(1/x)-log((x**2+1)/x)*x+_ - log((x**2+1)/x)*x**2*y(x))/x/log(1/x)) +ode776 := (D(y(x),x) = y(x)*(-log(1/x)-log((x^2+1)/x)*x+_ + log((x^2+1)/x)*x^2*y(x))/x/log(1/x)) --R --R --R 2 @@ -919,9 +919,9 @@ solve(ode776,y,x) --E 57 --S 58 of 97 -ode872 := (D(y(x),x) = 1/5*(-30*y(x)*x**3+12*x**6+70*x**(7/2)-30*x**3-_ - 25*y(x)*x**(1/2)+50*x-25*x**(1/2)-25)/_ - (-5*y(x)+2*x**3+10*x**(1/2)-5)/x) +ode872 := (D(y(x),x) = 1/5*(-30*y(x)*x^3+12*x^6+70*x^(7/2)-30*x^3-_ + 25*y(x)*x^(1/2)+50*x-25*x^(1/2)-25)/_ + (-5*y(x)+2*x^3+10*x^(1/2)-5)/x) --R --R --R 3 +-+ 3 6 3 @@ -948,7 +948,7 @@ solve(ode872,y,x) --E 59 --S 60 of 97 -ode555 := sqrt(D(y(x),x)**2+1)+x*D(y(x),x)-y(x) +ode555 := sqrt(D(y(x),x)^2+1)+x*D(y(x),x)-y(x) --R --R --R +----------+ @@ -973,7 +973,7 @@ solve(ode555,y,x) --E 61 --S 62 of 97 -ode557 := x*(sqrt(D(y(x),x)**2+1)+D(y(x),x))-y(x) +ode557 := x*(sqrt(D(y(x),x)^2+1)+D(y(x),x))-y(x) --R --R --R +----------+ @@ -998,7 +998,7 @@ solve(ode557,y,x) --E 63 --S 64 of 97 -ode558 := a*x*sqrt(D(y(x),x)**2+1)+x*D(y(x),x)-y(x) +ode558 := a*x*sqrt(D(y(x),x)^2+1)+x*D(y(x),x)-y(x) --R --R --R +----------+ @@ -1023,7 +1023,7 @@ solve(ode558,y,x) --E 65 --S 66 of 97 -ode562 := a*(D(y(x),x)**3+1)**(1/3)+b*x*D(y(x),x)-y(x) +ode562 := a*(D(y(x),x)^3+1)^(1/3)+b*x*D(y(x),x)-y(x) --R --R --R +----------+ @@ -1093,7 +1093,7 @@ solve(ode564,y,x) --E 71 --S 72 of 97 -ode571 := a*x**n*f(D(y(x),x))+x*D(y(x),x)-y(x) +ode571 := a*x^n*f(D(y(x),x))+x*D(y(x),x)-y(x) --R --R --R n , , @@ -1116,7 +1116,7 @@ solve(ode571,y,x) --E 73 --S 74 of 97 -ode573 := f(x*D(y(x),x)**2)+2*x*D(y(x),x)-y(x) +ode573 := f(x*D(y(x),x)^2)+2*x*D(y(x),x)-y(x) --R --R --R , 2 , @@ -1139,7 +1139,7 @@ solve(ode573,y,x) --E 75 --S 76 of 97 -ode683 := (D(y(x),x) = y(x)*(-1+log(x*(x+1))*y(x)*x**4-log(x*(x+1))*x**3)/x) +ode683 := (D(y(x),x) = y(x)*(-1+log(x*(x+1))*y(x)*x^4-log(x*(x+1))*x^3)/x) --R --R --R 4 2 3 2 @@ -1164,7 +1164,7 @@ solve(ode683,y,x) --E 77 --S 78 of 97 -ode703 := (D(y(x),x) = y(x)*(1-x+y(x)*x**2*log(x)+y(x)*x**3-x*log(x)-x**2)/_ +ode703 := (D(y(x),x) = y(x)*(1-x+y(x)*x^2*log(x)+y(x)*x^3-x*log(x)-x^2)/_ (x-1)/x) --R --R @@ -1188,8 +1188,8 @@ solve(ode703,y,x) --E 79 --S 80 of 97 -ode714 := (D(y(x),x) = -y(x)*(-log(1/x)+exp(x)+y(x)*x**2*log(x)+_ - y(x)*x**3-x*log(x)-x**2)/(-log(1/x)+exp(x))/x) +ode714 := (D(y(x),x) = -y(x)*(-log(1/x)+exp(x)+y(x)*x^2*log(x)+_ + y(x)*x^3-x*log(x)-x^2)/(-log(1/x)+exp(x))/x) --R --R --R (80) @@ -1251,7 +1251,7 @@ solve(ode714,y,x) --E 81 --S 82 of 97 -ode719 := (D(y(x),x) = y(x)*(-exp(x)+log(2*x)*x**2*y(x)-log(2*x)*x)/x/exp(x)) +ode719 := (D(y(x),x) = y(x)*(-exp(x)+log(2*x)*x^2*y(x)-log(2*x)*x)/x/exp(x)) --R --R --R 2 2 x @@ -1278,7 +1278,7 @@ solve(ode719,y,x) --E 83 --S 84 of 97 -ode736 := (D(y(x),x) = (2*x**2+2*x+x**4-2*y(x)*x**2-1+y(x)**2)/(x+1)) +ode736 := (D(y(x),x) = (2*x^2+2*x+x^4-2*y(x)*x^2-1+y(x)^2)/(x+1)) --R --R --R 2 2 4 2 @@ -1332,7 +1332,7 @@ solve(ode765,y,x) --S 88 of 97 ode766 := (D(y(x),x) = y(x)*(-log(x)-x*log((x-1)*(1+x)/x)+_ - log((x-1)*(1+x)/x)*x**2*y(x))/x/log(x)) + log((x-1)*(1+x)/x)*x^2*y(x))/x/log(x)) --R --R --R 2 @@ -1384,8 +1384,8 @@ solve(ode766,y,x) --E 89 --S 90 of 97 -ode776 := (D(y(x),x) = y(x)*(-log(1/x)-log((x**2+1)/x)*x+_ - log((x**2+1)/x)*x**2*y(x))/x/log(1/x)) +ode776 := (D(y(x),x) = y(x)*(-log(1/x)-log((x^2+1)/x)*x+_ + log((x^2+1)/x)*x^2*y(x))/x/log(1/x)) --R --R --R 2 @@ -1418,9 +1418,9 @@ solve(ode776,y,x) --E 91 --S 92 of 97 -ode872 := (D(y(x),x) = 1/5*(-30*y(x)*x**3+12*x**6+70*x**(7/2)-30*x**3-_ - 25*y(x)*x**(1/2)+50*x-25*x**(1/2)-25)/(-5*y(x)+2*x**3+_ - 10*x**(1/2)-5)/x) +ode872 := (D(y(x),x) = 1/5*(-30*y(x)*x^3+12*x^6+70*x^(7/2)-30*x^3-_ + 25*y(x)*x^(1/2)+50*x-25*x^(1/2)-25)/(-5*y(x)+2*x^3+_ + 10*x^(1/2)-5)/x) --R --R --R 3 +-+ 3 6 3 @@ -1447,12 +1447,12 @@ solve(ode872,y,x) --E 93 --S 94 of 97 -ode956 := (D(y(x),x) = 1/(1+log(x))*y(x)*(-1-x**(2/(1+log(x)))*_ - exp(2/(1+log(x))*log(x)**2)*x**2-x**(2/(1+log(x)))*_ - exp(2/(1+log(x))*log(x)**2)*x**2*log(x)+x**(2/(1+log(x)))*_ - exp(2/(1+log(x))*log(x)**2)*x**2*y(x)+2*x**(2/(1+log(x)))*_ - exp(2/(1+log(x))*log(x)**2)*x**2*y(x)*log(x)+x**(2/(1+log(x)))*_ - exp(2/(1+log(x))*log(x)**2)*x**2*y(x)*log(x)**2)/x) +ode956 := (D(y(x),x) = 1/(1+log(x))*y(x)*(-1-x^(2/(1+log(x)))*_ + exp(2/(1+log(x))*log(x)^2)*x^2-x^(2/(1+log(x)))*_ + exp(2/(1+log(x))*log(x)^2)*x^2*log(x)+x^(2/(1+log(x)))*_ + exp(2/(1+log(x))*log(x)^2)*x^2*y(x)+2*x^(2/(1+log(x)))*_ + exp(2/(1+log(x))*log(x)^2)*x^2*y(x)*log(x)+x^(2/(1+log(x)))*_ + exp(2/(1+log(x))*log(x)^2)*x^2*y(x)*log(x)^2)/x) --R --R --R (94) @@ -1489,12 +1489,12 @@ solve(ode956,y,x) --E 95 --S 96 of 97 -ode957 := (D(y(x),x) = 1/(1+log(x))*y(x)*(-1-x**3*x**(2/(1+log(x)))*_ - exp(2/(1+log(x))*log(x)**2)-x**3*x**(2/(1+log(x)))*_ - exp(2/(1+log(x))*log(x)**2)*log(x)+x**3*x**(2/(1+log(x)))*_ - exp(2/(1+log(x))*log(x)**2)*y(x)+2*x**3*x**(2/(1+log(x)))*_ - exp(2/(1+log(x))*log(x)**2)*y(x)*log(x)+x**3*x**(2/(1+log(x)))*_ - exp(2/(1+log(x))*log(x)**2)*y(x)*log(x)**2)/x) +ode957 := (D(y(x),x) = 1/(1+log(x))*y(x)*(-1-x^3*x^(2/(1+log(x)))*_ + exp(2/(1+log(x))*log(x)^2)-x^3*x^(2/(1+log(x)))*_ + exp(2/(1+log(x))*log(x)^2)*log(x)+x^3*x^(2/(1+log(x)))*_ + exp(2/(1+log(x))*log(x)^2)*y(x)+2*x^3*x^(2/(1+log(x)))*_ + exp(2/(1+log(x))*log(x)^2)*y(x)*log(x)+x^3*x^(2/(1+log(x)))*_ + exp(2/(1+log(x))*log(x)^2)*y(x)*log(x)^2)/x) --R --R --R (96) diff --git a/src/input/kernel.input.pamphlet b/src/input/kernel.input.pamphlet index b8f0f4f..3266624 100644 --- a/src/input/kernel.input.pamphlet +++ b/src/input/kernel.input.pamphlet @@ -53,7 +53,7 @@ kernels % --E 4 --S 5 of 19 -sin(x)**2 + sin(x) + cos(x) +sin(x)^2 + sin(x) + cos(x) --R --R --R 2 diff --git a/src/input/kovacic.input.pamphlet b/src/input/kovacic.input.pamphlet index f8541d0..e233796 100644 --- a/src/input/kovacic.input.pamphlet +++ b/src/input/kovacic.input.pamphlet @@ -39,7 +39,7 @@ were rational functions). Here is an example of an equation that we can solve in 1.5 and not in 1.0: \begin{chunk}{*} --S 2 of 3 -eq := 2*x**3 * differentiate(y x,x,2) + 3*x**2 * differentiate(y x,x) - 2 * y x +eq := 2*x^3 * differentiate(y x,x,2) + 3*x^2 * differentiate(y x,x) - 2 * y x --R --R --R 3 ,, 2 , diff --git a/src/input/laplace.input.pamphlet b/src/input/laplace.input.pamphlet index 6f56836..216ed3a 100644 --- a/src/input/laplace.input.pamphlet +++ b/src/input/laplace.input.pamphlet @@ -25,7 +25,7 @@ Some laplace transforms \begin{chunk}{*} --S 1 of 27 -f n == t**(n-1)*exp(-a*t)/factorial(n-1) +f n == t^(n-1)*exp(-a*t)/factorial(n-1) --R --R Type: Void --E 1 @@ -98,7 +98,7 @@ laplace(%, t, s) --E 7 --S 8 of 27 -(cosh(a*t) - cos(a*t))/(2*a**2) +(cosh(a*t) - cos(a*t))/(2*a^2) --R --R --R cosh(a t) - cos(a t) @@ -120,7 +120,7 @@ laplace(%, t, s) --E 9 --S 10 of 27 -exp(-a*t) * sin(b*t) / b**2 +exp(-a*t) * sin(b*t) / b^2 --R --R --R - a t @@ -290,7 +290,7 @@ laplace(%, t, s) We keep unknown transforms as formal transform in the answer \begin{chunk}{*} --S 26 of 27 -sin(a*t) - a*t*cos(a*t) + exp(t**2) +sin(a*t) - a*t*cos(a*t) + exp(t^2) --R --R --R 2 diff --git a/src/input/lib.input.pamphlet b/src/input/lib.input.pamphlet index a6d7ddb..9c95f99 100644 --- a/src/input/lib.input.pamphlet +++ b/src/input/lib.input.pamphlet @@ -16,8 +16,8 @@ )clear all stuff := library "/tmp/Neat.stuff" -stuff.int := 32**2 -stuff."poly" := x**2 + 1 +stuff.int := 32^2 +stuff."poly" := x^2 + 1 stuff.str := "Hello" keys stuff stuff.poly diff --git a/src/input/linalg.input.pamphlet b/src/input/linalg.input.pamphlet index 4fda6c2..9d80b1f 100644 --- a/src/input/linalg.input.pamphlet +++ b/src/input/linalg.input.pamphlet @@ -133,7 +133,7 @@ vars : LIST POLY INT := [x,y,z,u] --E 12 --S 13 of 82 -for i in 1..4 repeat for j in 1..3 repeat m5(i,j + 1) := (vars.i)**j +for i in 1..4 repeat for j in 1..3 repeat m5(i,j + 1) := (vars.i)^j --R Type: Void --E 13 @@ -268,7 +268,7 @@ m9 : SQMATRIX(2,INT) := matrix([[1,1],[0,1]]) --E 25 --S 26 of 82 -m8 ** 2 +m8 ^ 2 --R --R +5 8 + --R (25) | | @@ -277,7 +277,7 @@ m8 ** 2 --E 26 --S 27 of 82 -m9 ** 3 +m9 ^ 3 --R --R +1 3+ --R (26) | | @@ -338,7 +338,7 @@ mm * mm --E 31 --S 32 of 82 -p : POLY SQMATRIX(2,INT) := m8 * x**2 + m9 * x + m8 * m9 +p : POLY SQMATRIX(2,INT) := m8 * x^2 + m9 * x + m8 * m9 --R --R +1 2+ 2 +1 1+ +1 3+ --R (31) | |x + | |x + | | diff --git a/src/input/lode.input.pamphlet b/src/input/lode.input.pamphlet index eb53ea0..8480c14 100644 --- a/src/input/lode.input.pamphlet +++ b/src/input/lode.input.pamphlet @@ -95,8 +95,8 @@ solve(deq = sin x, y, x) Some inhomogenuous equations with rational coefficients \begin{chunk}{*} --S 7 of 15 -deq := x**3 * differentiate(y x, x, 3) + x**2 * differentiate(y x, x, 2) - _ -2 * x * differentiate(y x, x) + 2 * y x = 2 * x**4 +deq := x^3 * differentiate(y x, x, 3) + x^2 * differentiate(y x, x, 2) - _ +2 * x * differentiate(y x, x) + 2 * y x = 2 * x^4 --R --R --R 3 ,,, 2 ,, , 4 @@ -135,9 +135,9 @@ solve(deq, y, x = 1, [b, 0, a]) Third order equation with nontrivial singularities \begin{chunk}{*} --S 10 of 15 -deq := (x**9 + x**3) * differentiate(y x, x, 3) + _ -18 * x**8 * differentiate(y x, x,2) - 90 * x * differentiate(y x, x) - _ -30 * (11*x**6-3) * y x +deq := (x^9 + x^3) * differentiate(y x, x, 3) + _ +18 * x^8 * differentiate(y x, x,2) - 90 * x * differentiate(y x, x) - _ +30 * (11*x^6-3) * y x --R --R --R 9 3 ,,, 8 ,, , 6 @@ -164,7 +164,7 @@ Third order equation on a curve of genus 0 \begin{chunk}{*} --S 12 of 15 deq := (2*x+2)* differentiate(y x, x, 3) + 3* differentiate(y x, x, 2) + _ -(2*x**2+2*x)* differentiate(y x,x) - sqrt(x+1) * y x = 2 * x**2 + x - 1 +(2*x^2+2*x)* differentiate(y x,x) - sqrt(x+1) * y x = 2 * x^2 + x - 1 --R --R --R (12) @@ -187,7 +187,7 @@ solve(deq, y, x).particular This equation is irreducible over the rational functions \begin{chunk}{*} --S 14 of 15 -deq := 2*x**3*differentiate(y x,x,2) + 3*x**2*differentiate(y x,x) - 2*y x +deq := 2*x^3*differentiate(y x,x,2) + 3*x^2*differentiate(y x,x) - 2*y x --R --R --R 3 ,, 2 , diff --git a/src/input/lodesys.input.pamphlet b/src/input/lodesys.input.pamphlet index aa4e309..c78d919 100644 --- a/src/input/lodesys.input.pamphlet +++ b/src/input/lodesys.input.pamphlet @@ -55,7 +55,7 @@ M := matrix [[ 1+4*t, -5*t, 7*t, -8*t, 8*t, -6*t],_ The original system in Barkatou's AAECC paper is $t^2 dy/dt = M*y$ \begin{chunk}{*} --S 2 of 13 -sol := solve(inv(t**2) * M, t) +sol := solve(inv(t^2) * M, t) --R --R --R (2) @@ -82,7 +82,7 @@ sol := solve(inv(t**2) * M, t) Verify the solutions \begin{chunk}{*} --S 3 of 13 -[t**2 * map(h +-> D(h, t), v) - M * v for v in sol] +[t^2 * map(h +-> D(h, t), v) - M * v for v in sol] --R --R --R (3) @@ -153,7 +153,7 @@ v := vector [1, (-29*t + 19)/5, -1, t + 1, - 2*t + 3, -1] Get a particular solution to $t^2 dy/dt = M y + v$ \begin{chunk}{*} --S 9 of 13 -solp := solve(inv(t**2) * M, inv(t**2) * v, t).particular +solp := solve(inv(t^2) * M, inv(t^2) * v, t).particular --R --R --R 19 @@ -166,7 +166,7 @@ solp := solve(inv(t**2) * M, inv(t**2) * v, t).particular Verify the particular solution \begin{chunk}{*} --S 10 of 13 -t**2 * map(h +-> D(h, t), solp) - M * solp - v +t^2 * map(h +-> D(h, t), solp) - M * solp - v --R --R --R (10) [0,0,0,0,0,0] diff --git a/src/input/lodo.input.pamphlet b/src/input/lodo.input.pamphlet index c83683a..0db65ae 100644 --- a/src/input/lodo.input.pamphlet +++ b/src/input/lodo.input.pamphlet @@ -71,7 +71,7 @@ a := Dx + 1 --E 4 --S 5 of 55 -b := a + 1/2*Dx**2 - 1/2 +b := a + 1/2*Dx^2 - 1/2 --R --R --R 1 2 1 @@ -84,7 +84,7 @@ b := a + 1/2*Dx**2 - 1/2 Something to work on \begin{chunk}{*} --S 6 of 55 -p: UP(x,RN) := 4*x**2 + 2/3 +p: UP(x,RN) := 4*x^2 + 2/3 --R --R --R 2 2 @@ -124,7 +124,7 @@ Exponentiation follows from multiplication \begin{chunk}{*} --S 9 of 55 -c := (1/9)*b*(a + b)**2 +c := (1/9)*b*(a + b)^2 --R --R --R 1 6 5 5 13 4 19 3 79 2 7 1 @@ -137,7 +137,7 @@ c := (1/9)*b*(a + b)**2 General application of operator expressions \begin{chunk}{*} --S 10 of 55 -(a**2 - 3/4*b + c) (p + 1) +(a^2 - 3/4*b + c) (p + 1) --R --R --R 2 44 541 @@ -174,7 +174,7 @@ Dx := D() --E 13 --S 14 of 55 -b := 3*x**2*Dx**2 + 2*Dx + 1/x +b := 3*x^2*Dx^2 + 2*Dx + 1/x --R --R --R 2 2 1 @@ -194,7 +194,7 @@ a := b*(5*x*Dx + 7) --E 15 --S 16 of 55 -p: RFZ := x**2 + 1/x**2 +p: RFZ := x^2 + 1/x^2 --R --R --R 4 @@ -338,8 +338,8 @@ rightRemainder(f, b) \begin{verbatim} Problem: find the first few coefficients of exp(x)/x^i in Dop phi where - Dop := D**3 + G/x**2 * D + H/x**3 - 1 - phi := sum(s[i]*exp(x)/x**i, i = 0..) + Dop := D^3 + G/x^2 * D + H/x^3 - 1 + phi := sum(s[i]*exp(x)/x^i, i = 0..) \end{verbatim} \begin{chunk}{*} )clear all @@ -358,7 +358,7 @@ Dx := D() --E 29 --S 30 of 55 -Dop:= Dx**3 + G/x**2*Dx + H/x**3 - 1 +Dop:= Dx^3 + G/x^2*Dx + H/x^3 - 1 --R --R --R 3 @@ -376,7 +376,7 @@ n == 3 --E 31 --S 32 of 55 -phi == reduce(+,[subscript(s,[i])*exp(x)/x**i for i in 0..n]) +phi == reduce(+,[subscript(s,[i])*exp(x)/x^i for i in 0..n]) --R --R Type: Void --E 32 @@ -388,7 +388,7 @@ phi1 == Dop(phi) / exp x --E 33 --S 34 of 55 -phi2 == phi1 *x**(n+3) +phi2 == phi1 *x^(n+3) --R --R Type: Void --E 34 @@ -644,7 +644,7 @@ Modo := LODO2(SQMATRIX(3,PZ), Vect); --E 45 --S 46 of 55 -p := directProduct([3*x**2 + 1, 2*x, 7*x**3 + 2*x]::(VECTOR(PZ)))@Vect +p := directProduct([3*x^2 + 1, 2*x, 7*x^3 + 2*x]::(VECTOR(PZ)))@Vect --R --R --R 2 3 @@ -653,7 +653,7 @@ p := directProduct([3*x**2 + 1, 2*x, 7*x**3 + 2*x]::(VECTOR(PZ)))@Vect --E 46 --S 47 of 55 -m := [[x**2, 1, 0], [1, x**4, 0], [0, 0, 4*x**2]]::(SQMATRIX(3,PZ)) +m := [[x^2, 1, 0], [1, x^4, 0], [0, 0, 4*x^2]]::(SQMATRIX(3,PZ)) --R --R --R + 2 + diff --git a/src/input/lodo1.input.pamphlet b/src/input/lodo1.input.pamphlet index 88991bd..9f3c6a0 100644 --- a/src/input/lodo1.input.pamphlet +++ b/src/input/lodo1.input.pamphlet @@ -45,7 +45,7 @@ Dx : LODO1 RFZ := D() --E 3 --S 4 of 20 -b : LODO1 RFZ := 3*x**2*Dx**2 + 2*Dx + 1/x +b : LODO1 RFZ := 3*x^2*Dx^2 + 2*Dx + 1/x --R --R --R 2 2 1 @@ -65,7 +65,7 @@ a : LODO1 RFZ := b*(5*x*Dx + 7) --E 5 --S 6 of 20 -p := x**2 + 1/x**2 +p := x^2 + 1/x^2 --R --R --R 4 diff --git a/src/input/lodo2.input.pamphlet b/src/input/lodo2.input.pamphlet index b004d2c..e7f88bd 100644 --- a/src/input/lodo2.input.pamphlet +++ b/src/input/lodo2.input.pamphlet @@ -61,7 +61,7 @@ a := Dx + 1 --E 5 --S 6 of 26 -b := a + 1/2*Dx**2 - 1/2 +b := a + 1/2*Dx^2 - 1/2 --R --R --R 1 2 1 @@ -71,7 +71,7 @@ b := a + 1/2*Dx**2 - 1/2 --E 6 --S 7 of 26 -p := 4*x**2 + 2/3 +p := 4*x^2 + 2/3 --R --R --R 2 2 @@ -101,7 +101,7 @@ a p --E 9 --S 10 of 26 -c := (1/9)*b*(a + b)**2 +c := (1/9)*b*(a + b)^2 --R --R --R 1 6 5 5 13 4 19 3 79 2 7 1 @@ -111,7 +111,7 @@ c := (1/9)*b*(a + b)**2 --E 10 --S 11 of 26 -(a**2 - 3/4*b + c) (p + 1) +(a^2 - 3/4*b + c) (p + 1) --R --R --R 2 44 541 @@ -161,7 +161,7 @@ Modo := LODO2(Mat, Vect); --E 16 --S 17 of 26 -m:Mat := matrix [[x**2,1,0],[1,x**4,0],[0,0,4*x**2]] +m:Mat := matrix [[x^2,1,0],[1,x^4,0],[0,0,4*x^2]] --R --R --R + 2 + @@ -176,7 +176,7 @@ m:Mat := matrix [[x**2,1,0],[1,x**4,0],[0,0,4*x**2]] --E 17 --S 18 of 26 -p:Vect := directProduct [3*x**2+1,2*x,7*x**3+2*x] +p:Vect := directProduct [3*x^2+1,2*x,7*x^3+2*x] --R --R --R 2 3 diff --git a/src/input/lodo3.input.pamphlet b/src/input/lodo3.input.pamphlet index fd06eaa..4484f61 100644 --- a/src/input/lodo3.input.pamphlet +++ b/src/input/lodo3.input.pamphlet @@ -35,7 +35,7 @@ Dx := D() --E 2 --S 3 of 16 -Dop:= Dx**3 + G/x**2*Dx + H/x**3 - 1 +Dop:= Dx^3 + G/x^2*Dx + H/x^3 - 1 --R --R --R 3 @@ -53,7 +53,7 @@ n == 3 --E 4 --S 5 of 16 -phi == reduce(+,[subscript(s,[i])*exp(x)/x**i for i in 0..n]) +phi == reduce(+,[subscript(s,[i])*exp(x)/x^i for i in 0..n]) --R --R Type: Void --E 5 @@ -65,7 +65,7 @@ phi1 == Dop(phi) / exp x --E 6 --S 7 of 16 -phi2 == phi1 *x**(n+3) +phi2 == phi1 *x^(n+3) --R --R Type: Void --E 7 diff --git a/src/input/lodof.input.pamphlet b/src/input/lodof.input.pamphlet index 6635d80..bef41a9 100644 --- a/src/input/lodof.input.pamphlet +++ b/src/input/lodof.input.pamphlet @@ -73,7 +73,7 @@ t := t::P::Q Reducible order 2 operator (1-1) \begin{chunk}{*} --S 7 of 16 -op := d**2 + t * d + 1 +op := d^2 + t * d + 1 --R --R --R 2 @@ -93,7 +93,7 @@ factor op Irreducible order 2 operator \begin{chunk}{*} --S 9 of 16 -op := 2*t**3 * d**2 + 3*t**2 * d - 2 +op := 2*t^3 * d^2 + 3*t^2 * d - 2 --R --R --R 3 2 2 @@ -114,7 +114,7 @@ factor op Reducible order 3 operator (1-2) \begin{chunk}{*} --S 11 of 16 -op := 2*t**3 * d**3 - (2*t**4 - 9*t**2) * d**2 - (3*t**3 - 6*t + 2) * d + 2*t +op := 2*t^3 * d^3 - (2*t^4 - 9*t^2) * d^2 - (3*t^3 - 6*t + 2) * d + 2*t --R --R --R 3 3 4 2 2 3 @@ -135,7 +135,7 @@ factor op Reducible order 3 operator (1-1-1) \begin{chunk}{*} --S 13 of 16 -op := (t**9 + t**3) * d**3 + 18 * t**8 * d**2 - 90 * t * d - 30 * (11*t**6-3) +op := (t^9 + t^3) * d^3 + 18 * t^8 * d^2 - 90 * t * d - 30 * (11*t^6-3) --R --R --R 9 3 3 8 2 6 @@ -165,7 +165,7 @@ factor op Irreducible order 3 operator \begin{chunk}{*} --S 15 of 16 -op := d**3 + 2 * d**2 + 5 / t * d + 7 / t**2 +op := d^3 + 2 * d^2 + 5 / t * d + 7 / t^2 --R --R --R 3 2 5 7 diff --git a/src/input/loop.input.pamphlet b/src/input/loop.input.pamphlet index b973b4e..ff4790c 100644 --- a/src/input/loop.input.pamphlet +++ b/src/input/loop.input.pamphlet @@ -15,7 +15,7 @@ -- Input for page BasicLoops )clear all -p := 2**(2**3) + 1 +p := 2^(2^3) + 1 repeat if prime?(p := p + 1) then leave p repeat if prime?(p := p + 1) then leave p @@ -38,20 +38,20 @@ for i in 1.. for j in 11.. | even? j while i < 6 repeat print [i,j] )clear all i := 2 -repeat (print (i := 2**i; if i > 10 then leave)) -for j in 1..5 repeat print (i := j**i) -while i < 1000 repeat print (i := 2**i) -for i in 1.. while i < 1000 repeat print [j,": ",i := 2**i] -for j in 1..4 repeat for i in 2..4 repeat print [i,"**",j," = ",i**j] +repeat (print (i := 2^i; if i > 10 then leave)) +for j in 1..5 repeat print (i := j^i) +while i < 1000 repeat print (i := 2^i) +for i in 1.. while i < 1000 repeat print [j,": ",i := 2^i] +for j in 1..4 repeat for i in 2..4 repeat print [i,"^",j," = ",i^j] -- Input for page ForLoops )clear all -for i in 0..10 repeat print (i**3) -for i in 0..10 by 2 repeat print (i**3) -for i in 10..0 by -2 repeat print (i**3) -for i in 0..10 | even? i repeat print (i**3) -for i in 0.. by 2 repeat (i**3) +for i in 0..10 repeat print (i^3) +for i in 0..10 by 2 repeat print (i^3) +for i in 10..0 by -2 repeat print (i^3) +for i in 0..10 | even? i repeat print (i^3) +for i in 0.. by 2 repeat (i^3) \end{chunk} \eject \begin{thebibliography}{99} diff --git a/src/input/lump.input.pamphlet b/src/input/lump.input.pamphlet index 4a72a68..335f9b7 100644 --- a/src/input/lump.input.pamphlet +++ b/src/input/lump.input.pamphlet @@ -11,7 +11,7 @@ \tableofcontents \eject \begin{chunk}{*} -draw(sin(2 * x**2 + 3 * y**2)/(x**2 + y**2),x = -3..3,y = -3..3) +draw(sin(2 * x^2 + 3 * y^2)/(x^2 + y^2),x = -3..3,y = -3..3) \end{chunk} \eject \begin{thebibliography}{99} diff --git a/src/input/lupfact.input.pamphlet b/src/input/lupfact.input.pamphlet index 8e09163..7f54af6 100644 --- a/src/input/lupfact.input.pamphlet +++ b/src/input/lupfact.input.pamphlet @@ -181,8 +181,8 @@ lupFactor m == messagePrint("Matrix must be square")$OUTFORM "failed" ilog := intLog2(2) - not(r = 2 ** ilog) => - m := embedMatrix(m,r,(n := 2 ** (ilog + 1))) + not(r = 2 ^ ilog) => + m := embedMatrix(m,r,(n := 2 ^ (ilog + 1))) l := lupFactorEngine(m,n,n) [subMatrix(l.1,1,r,1,r),subMatrix(l.2,1,r,1,r), subMatrix(l.3,1,r,1,r)] diff --git a/src/input/macbug.input.pamphlet b/src/input/macbug.input.pamphlet index 1b54a18..56a377a 100644 --- a/src/input/macbug.input.pamphlet +++ b/src/input/macbug.input.pamphlet @@ -26,7 +26,7 @@ Macros can be parameterized and so can be used for many different kinds of objects. \begin{chunk}{*} --S 1 of 5 -macro ff(x) == x**2 + 1 +macro ff(x) == x^2 + 1 --R --R Type: Void --E 1 diff --git a/src/input/marcbench.input.pamphlet b/src/input/marcbench.input.pamphlet index 8d8d146..c470cf4 100644 --- a/src/input/marcbench.input.pamphlet +++ b/src/input/marcbench.input.pamphlet @@ -115,14 +115,14 @@ LP := List(P); x: P := 'x; y: P := 'y; z: P := 'z; -f1 := 7*y**4 - 20*x**2 ; -f2:= (2160*x**2 + 1512*x +315)*z**4-4000*x**2-2800*x-490 ; -f3 := (67200000*x**5 + 94080000*x**4 + 40924800*x**3 + 2634240*x**2-_ - 2300844*x-432180)*y**3 + ((40320000*x**6 + 28800000*x**5 + _ - 21168000*x**3 + 4939200*x**2 + 347508*x)*z)*y**2 + _ - ((-23520000*x**4-41395200*x**3-26726560*x**2-7727104*x-_ - 852355)*z**2)*y + (-10080000*x**4-28224000*x**3-15288000*x**2-_ - 1978032*x-180075)*z**3 ; +f1 := 7*y^4 - 20*x^2 ; +f2:= (2160*x^2 + 1512*x +315)*z^4-4000*x^2-2800*x-490 ; +f3 := (67200000*x^5 + 94080000*x^4 + 40924800*x^3 + 2634240*x^2-_ + 2300844*x-432180)*y^3 + ((40320000*x^6 + 28800000*x^5 + _ + 21168000*x^3 + 4939200*x^2 + 347508*x)*z)*y^2 + _ + ((-23520000*x^4-41395200*x^3-26726560*x^2-7727104*x-_ + 852355)*z^2)*y + (-10080000*x^4-28224000*x^3-15288000*x^2-_ + 1978032*x-180075)*z^3 ; lp := [f1,f2,f3]; @@ -195,13 +195,13 @@ u: P := 'u; v: P := 'v; w: P := 'w; f0 := b1 + y + z - t - w; -f1 := 2*z*u + 2*y*v + 2*t*w - 2*w**2 - w - 1 ; -f2 := 3*z*u**2 + 3*y*v**2 - 3*t*w**2 + 3*w**3 + 3*w**2 - t + 4*w ; -f3 := 6*x*z*v - 6*t*w**2 + 6*w**3 - 3*t*w + 6*w**2 - t + 4*w ; -f4 := 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 ; -f5 := 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 ; -f6 := 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; -f7 := -24*t*w**3 + 24*w**4 - 24*t*w**2 + 36*w**3 - 8*t*w + 26*w**2 + 7*w + 1 ; +f1 := 2*z*u + 2*y*v + 2*t*w - 2*w^2 - w - 1 ; +f2 := 3*z*u^2 + 3*y*v^2 - 3*t*w^2 + 3*w^3 + 3*w^2 - t + 4*w ; +f3 := 6*x*z*v - 6*t*w^2 + 6*w^3 - 3*t*w + 6*w^2 - t + 4*w ; +f4 := 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 ; +f5 := 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 ; +f6 := 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; +f7 := -24*t*w^3 + 24*w^4 - 24*t*w^2 + 36*w^3 - 8*t*w + 26*w^2 + 7*w + 1 ; lp := [f0,f1,f2,f3,f4,f5,f6,f7]; T := REGSET(R,E,V,P); @@ -244,11 +244,11 @@ C3: P := `C3; C2: P := `C2; f1 := B1+B2+B3+B4-1 ; f2 := 2*B2*C2 + 2*B3*C3 + 2*B4*C4 - 1 ; -f3 := 3*B2*C2**2 +3*B3*C3**2 +3*B4*C4**2 -1 ; +f3 := 3*B2*C2^2 +3*B3*C3^2 +3*B4*C4^2 -1 ; f4 := 6*B3*A32*C2 +6*B4*A42*C2 +6*B4*A43*C3 -1 ; -f5 := 4*B2*C2**3 +4*B3*C3**3 +4*B4*C4**3 -1 ; +f5 := 4*B2*C2^3 +4*B3*C3^3 +4*B4*C4^3 -1 ; f6 := 8*B3*C3*A32*C2 +8*B4*C4*A42*C2 +8*B4*C4*A43*C3 -1 ; -f7 := 12*B3*A32*C2**2 +12*B4*A42*C2**2 +12*B4*A43*C3**2 -1 ; +f7 := 12*B3*A32*C2^2 +12*B4*A42*C2^2 +12*B4*A43*C3^2 -1 ; f8 := 24*B4*A43*A32*C2 -1 ; f9 := -A21+C2 ; f10 := -A31-A32+C3 ; @@ -395,10 +395,10 @@ y: P := 'y; u: P := 'u; v: P := 'v; w: P := 'w; -p1 := (x - u) ** 2 + (y - v) ** 2 - 1 ; -p2 := v ** 2 - u ** 3 ; -p3 := 2 * v * (x - u) + 3 * u ** 2 * (y - v) ; -f1 := (3 * w * u ** 2 - 1) ; +p1 := (x - u) ^ 2 + (y - v) ^ 2 - 1 ; +p2 := v ^ 2 - u ^ 3 ; +p3 := 2 * v * (x - u) + 3 * u ^ 2 * (y - v) ; +f1 := (3 * w * u ^ 2 - 1) ; f2 := (2 * w * v - 1) ; p4 := f1 * f2 ; lp := [p1,p2,p3,p4] ; diff --git a/src/input/matbug.input.pamphlet b/src/input/matbug.input.pamphlet index a5178dc..caf89cd 100644 --- a/src/input/matbug.input.pamphlet +++ b/src/input/matbug.input.pamphlet @@ -104,7 +104,7 @@ m*m --E 7 --S 8 of 12 -m**2 +m^2 --R --R --R + + 2 ++ @@ -121,7 +121,7 @@ m**2 --E 8 --S 9 of 12 -m**3 +m^3 --R --R --R +matrix1 matrix2+ diff --git a/src/input/mathml.input.pamphlet b/src/input/mathml.input.pamphlet index dbe0640..d647d34 100644 --- a/src/input/mathml.input.pamphlet +++ b/src/input/mathml.input.pamphlet @@ -18,7 +18,7 @@ )clear all --S 1 of 21 -(x+y)**2 +(x+y)^2 --R --R --R 2 2 @@ -39,7 +39,7 @@ coerce(%)$MMLFORM --E 2 --S 3 of 21 -(x+y)**2 +(x+y)^2 --R --R --R 2 2 @@ -59,7 +59,7 @@ display(coerce(%)$MMLFORM)$MMLFORM )set output mathml on --S 5 of 21 -(x+y)**2 +(x+y)^2 --R --R --R 2 2 @@ -72,7 +72,7 @@ display(coerce(%)$MMLFORM)$MMLFORM --E 5 --S 6 of 21 -integrate(x**x,x) +integrate(x^x,x) --R --R --R x @@ -87,7 +87,7 @@ integrate(x**x,x) --E 6 --S 7 of 21 -integral(x**x,x) +integral(x^x,x) --R --R --R x @@ -102,7 +102,7 @@ integral(x**x,x) --E 7 --S 8 of 21 -(5+sqrt 63 + sqrt 847)**(1/3) +(5+sqrt 63 + sqrt 847)^(1/3) --R --R --R +----------+ diff --git a/src/input/matrix.input.pamphlet b/src/input/matrix.input.pamphlet index 552221a..5d78a79 100644 --- a/src/input/matrix.input.pamphlet +++ b/src/input/matrix.input.pamphlet @@ -151,7 +151,7 @@ mat1 * mat1inv Vandermonde determinant \begin{chunk}{*} --S 7 of 42 -mat2 : MATRIX INT := matrix [[j**i for i in 0..4] for j in 1..5] +mat2 : MATRIX INT := matrix [[j^i for i in 0..4] for j in 1..5] --R --R --R +1 1 1 1 1 + @@ -203,7 +203,7 @@ Same computation, different indexing \begin{chunk}{*} --S 11 of 42 mat3 : IMATRIX(INT,13,-7) := _ - matrix [[j**i for i in 0..4] for j in 1..5] + matrix [[j^i for i in 0..4] for j in 1..5] --R --R --R +1 1 1 1 1 + @@ -254,7 +254,7 @@ minordet mat3 Same computation, work over the rationals \begin{chunk}{*} --S 15 of 42 -mat4 : MATRIX FRAC INT := matrix [[j**i for i in 0..4] for j in 1..5] +mat4 : MATRIX FRAC INT := matrix [[j^i for i in 0..4] for j in 1..5] --R --R --R +1 1 1 1 1 + @@ -306,7 +306,7 @@ Same computation, different indexing \begin{chunk}{*} --S 19 of 42 mat5 : IMATRIX(FRAC INT,-113,37) := _ - matrix [[j**i for i in 0..4] for j in 1..5] + matrix [[j^i for i in 0..4] for j in 1..5] --R --R --R +1 1 1 1 1 + diff --git a/src/input/matrix1.input.pamphlet b/src/input/matrix1.input.pamphlet index 98187c5..0bffa83 100644 --- a/src/input/matrix1.input.pamphlet +++ b/src/input/matrix1.input.pamphlet @@ -71,7 +71,7 @@ matrix [[1,2,3,4],[0,9,8,7]] --E 5 --S 6 of 38 -dm := diagonalMatrix [1,x**2,x**3,x**4,x**5] +dm := diagonalMatrix [1,x^2,x^3,x^4,x^5] --R --R --R +1 0 0 0 0 + @@ -146,7 +146,7 @@ cdm := copy(dm) --E 9 --S 10 of 38 -setelt(dm,4,1,1-x**7) +setelt(dm,4,1,1-x^7) --R --R --R 7 diff --git a/src/input/matrix22.input.pamphlet b/src/input/matrix22.input.pamphlet index 0f58160..5475be8 100644 --- a/src/input/matrix22.input.pamphlet +++ b/src/input/matrix22.input.pamphlet @@ -47,7 +47,7 @@ determinant m --S 3 of 8 n:SQMATRIX(2,SQMATRIX(2,INT)) := - squareMatrix matrix [[m,m**2],[m**3,m**4]] + squareMatrix matrix [[m,m^2],[m^3,m^4]] --R --R --R ++ 0 1+ +- 1 0 ++ @@ -91,7 +91,7 @@ Another level of matrix \begin{chunk}{*} --S 5 of 8 o:SQMATRIX(2,SQMATRIX(2,SQMATRIX(2,INT))) := - squareMatrix matrix [[n,n**2],[n**3,n**4]] + squareMatrix matrix [[n,n^2],[n^3,n^4]] --R --R --R +++ 0 1+ +- 1 0 ++ ++- 1 1 + +- 1 - 1+++ @@ -113,7 +113,7 @@ o:SQMATRIX(2,SQMATRIX(2,SQMATRIX(2,INT))) := --E 5 --S 6 of 8 -o ** 2 +o ^ 2 --R --R --R +++- 1 - 3+ +3 - 1+ + + +2 - 4+ + 4 2+ ++ diff --git a/src/input/matrox.input.pamphlet b/src/input/matrox.input.pamphlet index a30ab8a..4284787 100644 --- a/src/input/matrox.input.pamphlet +++ b/src/input/matrox.input.pamphlet @@ -78,7 +78,7 @@ move(wiggle,876,200) --)r lumpy --lumpy:=% -lumpy:=sin(2*x**2 + 3 * y**2)/(x**2 + y**2) +lumpy:=sin(2*x^2 + 3 * y^2)/(x^2 + y^2) resize(lumpy,300,330) move(lumpy,600,688) diff --git a/src/input/mfinfact.input.pamphlet b/src/input/mfinfact.input.pamphlet index 867710a..9845141 100644 --- a/src/input/mfinfact.input.pamphlet +++ b/src/input/mfinfact.input.pamphlet @@ -101,7 +101,7 @@ factor p --E 2 --S 3 of 13 -p:POLY PF 7:=(x+3*y+z)*(w*x+y)*(x*y+w**3) +p:POLY PF 7:=(x+3*y+z)*(w*x+y)*(x*y+w^3) --R --R --R (3) @@ -123,7 +123,7 @@ factor p --E 4 --S 5 of 13 -pp:=p**2 +pp:=p^2 --R --R --R (5) @@ -170,7 +170,7 @@ gcd(p,differentiate(p,x)) --E 6 --S 7 of 13 -p23:POLY PF 23:=(x+3*y+z)*(w*x+y)*(x*y+w**3) +p23:POLY PF 23:=(x+3*y+z)*(w*x+y)*(x*y+w^3) --R --R --R (7) @@ -192,7 +192,7 @@ factor(p23) --E 8 --S 9 of 13 -q: POLY PF 2 := y**4 + y**3 + x**4 + x**2 +q: POLY PF 2 := y^4 + y^3 + x^4 + x^2 --R --R --R 4 3 4 2 @@ -219,7 +219,7 @@ factor(q*(q+1)) --E 11 --S 12 of 13 -q:=x**2*y**2+z +q:=x^2*y^2+z --R --R --R 2 2 diff --git a/src/input/mkfunc.input.pamphlet b/src/input/mkfunc.input.pamphlet index bc0d164..fa2fa01 100644 --- a/src/input/mkfunc.input.pamphlet +++ b/src/input/mkfunc.input.pamphlet @@ -21,7 +21,7 @@ )set message auto off )clear all --S 1 of 9 -expr := (x - exp x + 1)**2 * (sin(x**2) * x + 1)**3 +expr := (x - exp x + 1)^2 * (sin(x^2) * x + 1)^3 --R --R --R (1) @@ -56,7 +56,7 @@ tbl := [f(0.1 * i - 1) for i in 0..20]; --E 3 --S 4 of 9 -e := (x - y + 1)**2 * (x**2 * y + 1)**2 +e := (x - y + 1)^2 * (x^2 * y + 1)^2 --R --R --R (4) diff --git a/src/input/mountain.input.pamphlet b/src/input/mountain.input.pamphlet index a71d2bd..d130940 100644 --- a/src/input/mountain.input.pamphlet +++ b/src/input/mountain.input.pamphlet @@ -31,7 +31,7 @@ sf f == f::DFLOAT Nrand := 4 -Arand := 2**26 - 1 +Arand := 2^26 - 1 GaussAdd := sqrt(sf(3.0) * Nrand) GaussFac := sf(2.0) * GaussAdd/((sf Nrand) * (sf Arand)) @@ -55,7 +55,7 @@ f4(delta,x0,x1,x2,x3) == (x0+x1+x2+x3)/sfFour + delta*Gauss() -- perform midpoint subdivision MidPointFM(maxLevel, sigma, H) == - N := 2**maxLevel + N := 2^maxLevel delta := sigma arraySize := (N+1) X:IARRAY2(DFLOAT,0,0) := new(arraySize, arraySize, sf 0.0) @@ -66,7 +66,7 @@ MidPointFM(maxLevel, sigma, H) == D := N d := N quo 2 for stage in 1..maxLevel repeat - delta := delta*(sfHalf**(sfHalf*H)) + delta := delta*(sfHalf^(sfHalf*H)) for x in d..(N-d) by D repeat for y in d..(N-d) by D repeat setelt(X, x, y, f4(delta, elt(X,x+d,y+d), elt(X,x+d,y-d), @@ -74,7 +74,7 @@ MidPointFM(maxLevel, sigma, H) == for x in 0..N by D repeat for y in 0..N by D repeat setelt(X, x, y, elt(X,x,y) + delta*Gauss()) - delta := delta*(sfHalf**(sfHalf*H)) + delta := delta*(sfHalf^(sfHalf*H)) for x in d..(N-d) by D repeat setelt(X,x,0, f3(delta, elt(X,x+d,0), elt(X,x-d,0), elt(X,x,d))) setelt(X,x,N, f3(delta, elt(X,x+d,N), elt(X,x-d,N), elt(X,x,N-d))) @@ -112,13 +112,13 @@ tableVal(x: DFLOAT, y:DFLOAT):DFLOAT == val -- draw a mountain with maxLevel subdivisions with Haussdorf dimension H --- the number of subdivisions of the mountain is 2**maxLevel, so you +-- the number of subdivisions of the mountain is 2^maxLevel, so you -- probably should keep maxLevel <= 8. Also 0 < H <= 1. The closer -- H is to one, the smoother the mountain will be. drawMountain(maxLevel, H) == free table, xIndex, yIndex, rowSize table := MidPointFM(maxLevel, Sigma, H) - N := 2**maxLevel + N := 2^maxLevel xIndex := 0 yIndex := 0 rowSize := N diff --git a/src/input/mpoly.input.pamphlet b/src/input/mpoly.input.pamphlet index aac5522..52b9e78 100644 --- a/src/input/mpoly.input.pamphlet +++ b/src/input/mpoly.input.pamphlet @@ -21,7 +21,7 @@ )set message auto off )clear all --S 1 of 10 -m : MPOLY([x,y],INT) := (x**2 - x*y**3 +3*y)**2 +m : MPOLY([x,y],INT) := (x^2 - x*y^3 +3*y)^2 --R --R --R 4 3 3 6 2 4 2 @@ -45,7 +45,7 @@ p : MPOLY([x,y],POLY INT) --E 3 --S 4 of 10 -p := (a**2*x - b*y**2 + 1)**2 +p := (a^2*x - b*y^2 + 1)^2 --R --R --R 4 2 2 2 2 2 4 2 @@ -78,7 +78,7 @@ q : UP(x, FRAC MPOLY([y,z],INT)) --E 7 --S 8 of 10 -q := (x**2 - x*(z+1)/y +2)**2 +q := (x^2 - x*(z+1)/y +2)^2 --R --R --R 2 2 diff --git a/src/input/mult2d.input.pamphlet b/src/input/mult2d.input.pamphlet index 05109ca..446060a 100644 --- a/src/input/mult2d.input.pamphlet +++ b/src/input/mult2d.input.pamphlet @@ -18,7 +18,7 @@ \getchunk{license} )clear all ---draws x**i for i in 1..5, x=-1..1 +--draws x^i for i in 1..5, x=-1..1 makePoint(x:SF,y:SF):(Point SF) == point([x,y])$(Point SF) @@ -47,7 +47,7 @@ makeListFuns(fl:List(Expression Integer),_ lfuns := cons(ff, lfuns) lfuns -drawFuns(makeListFuns([x**i for i in 1..5], x=-1..1), x=-1..1) +drawFuns(makeListFuns([x^i for i in 1..5], x=-1..1), x=-1..1) drawFuns(makeListFuns([sin(x*i) for i in 1..5], x=-1..1), x=-1..1) drawFuns(makeListFuns([sec x, sin x, cos x, tan x], x=-1..1), x=-1..1) \end{chunk} diff --git a/src/input/multfact.input.pamphlet b/src/input/multfact.input.pamphlet index f472248..ad41a44 100644 --- a/src/input/multfact.input.pamphlet +++ b/src/input/multfact.input.pamphlet @@ -21,7 +21,7 @@ )set message auto off )clear all --S 1 of 5 -a := rootOf(a**2+a+1) +a := rootOf(a^2+a+1) --R --R --R (1) a @@ -29,7 +29,7 @@ a := rootOf(a**2+a+1) --E 1 --S 2 of 5 -p := y*z**2 + a*z*x**2 + a*a*x*y**2 +p := y*z^2 + a*z*x^2 + a*a*x*y^2 --R --R --R 2 2 2 @@ -47,7 +47,7 @@ factor(p,[a]) --E 3 --S 4 of 5 -b:=rootOf(b**2+1) +b:=rootOf(b^2+1) --R --R --R (4) b @@ -55,7 +55,7 @@ b:=rootOf(b**2+1) --E 4 --S 5 of 5 -factor(x**2*y**2+u**2*v**2,[b]) +factor(x^2*y^2+u^2*v^2,[b]) --R --R --R (5) (x y - b u v)(x y + b u v) diff --git a/src/input/newlodo.input.pamphlet b/src/input/newlodo.input.pamphlet index dd10a38..2fa41d5 100644 --- a/src/input/newlodo.input.pamphlet +++ b/src/input/newlodo.input.pamphlet @@ -62,7 +62,7 @@ a := Dx + 1 --E 4 --S 5 of 55 -b := a + 1/2*Dx**2 - 1/2 +b := a + 1/2*Dx^2 - 1/2 --R --R --R 1 2 1 @@ -72,7 +72,7 @@ b := a + 1/2*Dx**2 - 1/2 --E 5 --S 6 of 55 -p: UP(x,RN) := 4*x**2 + 2/3 -- something to work on +p: UP(x,RN) := 4*x^2 + 2/3 -- something to work on --R --R --R 2 2 @@ -102,7 +102,7 @@ a p -- application of an operator to a polynomial --E 8 --S 9 of 55 -c := (1/9)*b*(a + b)**2 -- exponentiation follows from multiplication +c := (1/9)*b*(a + b)^2 -- exponentiation follows from multiplication --R --R --R 1 6 5 5 13 4 19 3 79 2 7 1 @@ -112,7 +112,7 @@ c := (1/9)*b*(a + b)**2 -- exponentiation follows from multiplication --E 9 --S 10 of 55 -(a**2 - 3/4*b + c) (p + 1) -- general application of operator expressions +(a^2 - 3/4*b + c) (p + 1) -- general application of operator expressions --R --R --R 2 44 541 @@ -149,7 +149,7 @@ Dx := D() --E 13 --S 14 of 55 -b := 3*x**2*Dx**2 + 2*Dx + 1/x +b := 3*x^2*Dx^2 + 2*Dx + 1/x --R --R --R 2 2 1 @@ -169,7 +169,7 @@ a := b*(5*x*Dx + 7) --E 15 --S 16 of 55 -p: RFZ := x**2 + 1/x**2 +p: RFZ := x^2 + 1/x^2 --R --R --R 4 @@ -298,8 +298,8 @@ rightRemainder(f, b) -- the remainder is non-zero Problem: find the first few coefficients of $\exp(x)/x^i$ in Dop phi where \begin{verbatim} - Dop := D**3 + G/x**2 * D + H/x**3 - 1 - phi := sum(s[i]*exp(x)/x**i, i = 0..) + Dop := D^3 + G/x^2 * D + H/x^3 - 1 + phi := sum(s[i]*exp(x)/x^i, i = 0..) \end{verbatim} \begin{chunk}{*} @@ -319,7 +319,7 @@ Dx := D() --E 29 --S 30 of 55 -Dop:= Dx**3 + G/x**2*Dx + H/x**3 - 1 +Dop:= Dx^3 + G/x^2*Dx + H/x^3 - 1 --R --R --R 3 @@ -337,7 +337,7 @@ n == 3 --E 31 --S 32 of 55 -phi == reduce(+,[subscript(s,[i])*exp(x)/x**i for i in 0..n]) +phi == reduce(+,[subscript(s,[i])*exp(x)/x^i for i in 0..n]) --R --R Type: Void --E 32 @@ -349,7 +349,7 @@ phi1 == Dop(phi) / exp x --E 33 --S 34 of 55 -phi2 == phi1 *x**(n+3) +phi2 == phi1 *x^(n+3) --R --R Type: Void --E 34 @@ -605,7 +605,7 @@ Modo := LODO2(SQMATRIX(3,PZ), Vect); --E 45 --S 46 of 55 -p := directProduct([3*x**2 + 1, 2*x, 7*x**3 + 2*x]::(VECTOR(PZ)))@Vect +p := directProduct([3*x^2 + 1, 2*x, 7*x^3 + 2*x]::(VECTOR(PZ)))@Vect --R --R --R 2 3 @@ -614,7 +614,7 @@ p := directProduct([3*x**2 + 1, 2*x, 7*x**3 + 2*x]::(VECTOR(PZ)))@Vect --E 46 --S 47 of 55 -m := [[x**2, 1, 0], [1, x**4, 0], [0, 0, 4*x**2]]::(SQMATRIX(3,PZ)) +m := [[x^2, 1, 0], [1, x^4, 0], [0, 0, 4*x^2]]::(SQMATRIX(3,PZ)) --R --R --R + 2 + diff --git a/src/input/newtonlisp.input.pamphlet b/src/input/newtonlisp.input.pamphlet index 77b65e3..3861669 100644 --- a/src/input/newtonlisp.input.pamphlet +++ b/src/input/newtonlisp.input.pamphlet @@ -193,7 +193,7 @@ newtonUsingLisp(f:Expression Float,x:Symbol,x0:DFLOAT):DFLOAT == --E 8 --S 9 of 14 -newtonUsingLisp(x**2-2.0,x,2.0::SF)-sqrt(2.0::SF) +newtonUsingLisp(x^2-2.0,x,2.0::SF)-sqrt(2.0::SF) --R --R Compiling function compiledDF with type (Expression(Float),Symbol) --R -> Symbol diff --git a/src/input/nlode.input.pamphlet b/src/input/nlode.input.pamphlet index e7ef0c3..839be4c 100644 --- a/src/input/nlode.input.pamphlet +++ b/src/input/nlode.input.pamphlet @@ -144,7 +144,7 @@ Bernoulli equation: the result is a first integral when equated to any constant, but it can be explicitly solved for y(x) \begin{chunk}{*} --S 11 of 16 -deq := x**2 * differentiate(y x, x) + 2 * x * y x - y(x)**3 +deq := x^2 * differentiate(y x, x) + 2 * x * y x - y(x)^3 --R --R --R 2 , 3 @@ -170,7 +170,7 @@ Riccati equation: the result is a first integral when equated to any constant, but it can be explicitly solved for y(x) \begin{chunk}{*} --S 13 of 16 -deq := differentiate(y x,x) = 1 + x**2 - 2 * x * y x + y(x)**2 +deq := differentiate(y x,x) = 1 + x^2 - 2 * x * y x + y(x)^2 --R --R --R , 2 2 @@ -195,7 +195,7 @@ Riccati equation: the result is a first integral when equated to any constant, but it can be explicitly solved for y(x) \begin{chunk}{*} --S 15 of 16 -deq := x**2 * differentiate(y x,x) = -1 - x * y x + x**2 * y(x)**2 +deq := x^2 * differentiate(y x,x) = -1 - x * y x + x^2 * y(x)^2 --R --R --R 2 , 2 2 diff --git a/src/input/noonburg.input.pamphlet b/src/input/noonburg.input.pamphlet index 277abc4..c23a97c 100644 --- a/src/input/noonburg.input.pamphlet +++ b/src/input/noonburg.input.pamphlet @@ -41,7 +41,7 @@ dmp0 := DMP([x,y,z,c],RN) --E 2 --S 3 of 6 -px : dmp0 := 1-c*x +x*(y**2 + z**2) +px : dmp0 := 1-c*x +x*(y^2 + z^2) --R --R --R 2 2 @@ -50,7 +50,7 @@ px : dmp0 := 1-c*x +x*(y**2 + z**2) --E 3 --S 4 of 6 -py : dmp0 := 1-c*y +y*(z**2 + x**2) +py : dmp0 := 1-c*y +y*(z^2 + x^2) --R --R --R 2 2 @@ -59,7 +59,7 @@ py : dmp0 := 1-c*y +y*(z**2 + x**2) --E 4 --S 5 of 6 -pz : dmp0 := 1-c*z +z*(x**2 + y**2) +pz : dmp0 := 1-c*z +z*(x^2 + y^2) --R --R --R 2 2 diff --git a/src/input/numbers.input.pamphlet b/src/input/numbers.input.pamphlet index 03418a6..03d6eeb 100644 --- a/src/input/numbers.input.pamphlet +++ b/src/input/numbers.input.pamphlet @@ -35,7 +35,7 @@ x := factorial(200) --E 1 --S 2 of 76 -y := 2**90 - 1 +y := 2^90 - 1 --R --R --R (2) 1237940039285380274899124223 @@ -161,7 +161,7 @@ sin(%pi/6.) --E 13 --S 14 of 76 -f := (x**2 + 1)/(x - 1) +f := (x^2 + 1)/(x - 1) --R --R --R 2 @@ -172,7 +172,7 @@ f := (x**2 + 1)/(x - 1) --E 14 --S 15 of 76 -g := (x**2 - 3*x + 2)/(x + 2) +g := (x^2 - 3*x + 2)/(x + 2) --R --R --R 2 @@ -328,7 +328,7 @@ reduce(+,allElts) --E 29 --S 30 of 76 -u:UP(x, F7) := x**2 + 1 +u:UP(x, F7) := x^2 + 1 --R --R --R 2 @@ -370,7 +370,7 @@ f: NNI -> INT --E 34 --S 35 of 76 -f(n) == 2**n - 1 +f(n) == 2^n - 1 --R --R Type: Void --E 35 @@ -438,7 +438,7 @@ nums := [x for x in numbers | not prime? x] )clear all --S 43 of 76 -numbers := [n**2 - n + 41 for n in 0..40] +numbers := [n^2 - n + 41 for n in 0..40] --R --R --R (1) @@ -496,7 +496,7 @@ x : UTS(ROMAN,'x,0) := x --E 48 --S 49 of 76 -recip(1 - x - x**2) +recip(1 - x - x^2) --R --R --R (5) @@ -582,7 +582,7 @@ f: NNI -> INT --E 55 --S 56 of 76 -f(n) == 2**(2**n) + 1 +f(n) == 2^(2^n) + 1 --R --R Type: Void --E 56 @@ -677,7 +677,7 @@ numeric(1/3) )clear all --S 66 of 76 -61657 ** 10 / 999983 ** 12 +61657 ^ 10 / 999983 ^ 12 --R --R --R (1) diff --git a/src/input/numericgamma.input.pamphlet b/src/input/numericgamma.input.pamphlet index 469c4a7..237e41d 100644 --- a/src/input/numericgamma.input.pamphlet +++ b/src/input/numericgamma.input.pamphlet @@ -229,7 +229,7 @@ SpecialFunctionExtended: Exports == Implementation where NGamma(a:DoubleFloat,x:DoubleFloat):DoubleFloat == if x < 0 or a < 0 then error "Invalid arguments" if x = 0 then return Gamma(a) - EPS := (10.0::DoubleFloat**(-digits()$DoubleFloat))$DoubleFloat + EPS := (10.0::DoubleFloat^(-digits()$DoubleFloat))$DoubleFloat b:DoubleFloat:=x+1-a -- Set up for evaluating continued fractions c:DoubleFloat:=1/FPMIN -- by modified Lentz's method d:DoubleFloat:=1/b -- with b_0 = 0 diff --git a/src/input/odpol.input.pamphlet b/src/input/odpol.input.pamphlet index 9cc56c3..c3b9fa0 100644 --- a/src/input/odpol.input.pamphlet +++ b/src/input/odpol.input.pamphlet @@ -81,7 +81,7 @@ f:= w.4 - w.1 * w.1 * z.3 --E 7 --S 8 of 36 -g:=(z.1)**3 * (z.2)**2 - w.2 +g:=(z.1)^3 * (z.2)^2 - w.2 --R --R --R 3 2 diff --git a/src/input/op1.input.pamphlet b/src/input/op1.input.pamphlet index c125a41..f58f8a4 100644 --- a/src/input/op1.input.pamphlet +++ b/src/input/op1.input.pamphlet @@ -71,7 +71,7 @@ rho := t * s --E 6 --S 7 of 21 -z := rho**4 - 1 +z := rho^4 - 1 --R --R --R +0 1+ +0 1+ +0 1+ +0 1+ @@ -121,7 +121,7 @@ rho rho m --E 11 --S 12 of 21 -(rho**3) m +(rho^3) m --R --R --R +2 4+ @@ -176,7 +176,7 @@ evaluate(dx, p +-> D(p, 'x)) --E 17 --S 18 of 21 -E n == (1 - x**2) * dx**2 - 2 * x * dx + n*(n+1) +E n == (1 - x^2) * dx^2 - 2 * x * dx + n*(n+1) --R --R Type: Void --E 18 diff --git a/src/input/opalg.input.pamphlet b/src/input/opalg.input.pamphlet index bc34e16..68487b6 100644 --- a/src/input/opalg.input.pamphlet +++ b/src/input/opalg.input.pamphlet @@ -72,7 +72,7 @@ evaluate(dx, p +-> differentiate(p, 'x))$OP(POLY FRAC INT) This is the differential equation satisfied by the nth Legendre poly: \begin{chunk}{*} --S 5 of 9 -E n == (1 - x**2) * dx**2 - 2 * x * dx + n*(n+1) +E n == (1 - x^2) * dx^2 - 2 * x * dx + n*(n+1) --R --R Type: Void --E 5 diff --git a/src/input/operator.input.pamphlet b/src/input/operator.input.pamphlet index 8821c16..7648d71 100644 --- a/src/input/operator.input.pamphlet +++ b/src/input/operator.input.pamphlet @@ -46,7 +46,7 @@ evaluate(dx, p +-> differentiate(p, 'x))$OP(POLY FRAC INT) --E 3 --S 4 of 6 -E n == (1 - x**2) * dx**2 - 2 * x * dx + n*(n+1) +E n == (1 - x^2) * dx^2 - 2 * x * dx + n*(n+1) --R --R Type: Void --E 4 diff --git a/src/input/paff.input.pamphlet b/src/input/paff.input.pamphlet index 019b8c7..5fa1427 100644 --- a/src/input/paff.input.pamphlet +++ b/src/input/paff.input.pamphlet @@ -278,11 +278,11 @@ LinSer := LinearSystemFromPowerSeriesPackage(K,PCS) --E 23 --S 24 of 26 -f:PolyRing:= x**28*z**8 + 4*x**26*z**10 + 6*x**24*z**12 + 4*x**22*z**14 + _ - 4*x**21*y**9*z**6 + x**20*z**16 + 12*x**19*y**9*z**8 + _ - 12*x**17*y**9*z**10 + 4*x**15*y**9*z**12 + 6*x**14*y**18*z**4 + _ - 12*x**12*y**18*z**6 + 6*x**10*y**18*z**8 + 4*x**7*y**27*z*z + _ - 4*x**5*y**27*z**4 + y**36 + (-2*y**20*z**16) +f:PolyRing:= x^28*z^8 + 4*x^26*z^10 + 6*x^24*z^12 + 4*x^22*z^14 + _ + 4*x^21*y^9*z^6 + x^20*z^16 + 12*x^19*y^9*z^8 + _ + 12*x^17*y^9*z^10 + 4*x^15*y^9*z^12 + 6*x^14*y^18*z^4 + _ + 12*x^12*y^18*z^6 + 6*x^10*y^18*z^8 + 4*x^7*y^27*z*z + _ + 4*x^5*y^27*z^4 + y^36 + (-2*y^20*z^16) --R --R --R (24) diff --git a/src/input/paffexample.input.pamphlet b/src/input/paffexample.input.pamphlet index 8849473..5dd8930 100644 --- a/src/input/paffexample.input.pamphlet +++ b/src/input/paffexample.input.pamphlet @@ -68,7 +68,7 @@ P:=PAFF(K,[X,Y,Z],BLQT) -- We defined now the polynomial of the curve. --S 4 of 20 -C:R:=X**5 + Y**2*Z**3+Y*Z**4 +C:R:=X^5 + Y^2*Z^3+Y*Z^4 --R --R --R 5 2 3 4 diff --git a/src/input/palette.input.pamphlet b/src/input/palette.input.pamphlet index bbba3db..faed6ae 100644 --- a/src/input/palette.input.pamphlet +++ b/src/input/palette.input.pamphlet @@ -24,7 +24,7 @@ bright blue() pastel blue() light blue() -draw(x**2,x=-1..1,curveColor == hue dark blue()) +draw(x^2,x=-1..1,curveColor == hue dark blue()) shade bright blue() diff --git a/src/input/parabola.input.pamphlet b/src/input/parabola.input.pamphlet index 2793ce8..408fd37 100644 --- a/src/input/parabola.input.pamphlet +++ b/src/input/parabola.input.pamphlet @@ -21,7 +21,7 @@ )set message auto off )clear all --S 1 of 1 -draw(curve(t**2 + 2*t - 1,t**2 + t - 2),t = -4..3) +draw(curve(t^2 + 2*t - 1,t^2 + t - 2),t = -4..3) --R --R Compiling function %B with type DoubleFloat -> DoubleFloat --R Compiling function %D with type DoubleFloat -> DoubleFloat diff --git a/src/input/pasta.input.pamphlet b/src/input/pasta.input.pamphlet index d559d69..ca6ce2f 100644 --- a/src/input/pasta.input.pamphlet +++ b/src/input/pasta.input.pamphlet @@ -2000,7 +2000,7 @@ X(i,j) == 5*cos(i*%pi/50)+0.5*cos(i*%pi/50)*(1+sin(j*%pi/100)) + _ --S 202 of 676 Y(i,j) == 5*sin(i*%pi/50)+0.5*sin(i*%pi/50)*(1+sin(j*%pi/100)) + _ - 0.5*cos(i**%pi/25)*(1+sin(j*%pi/5)) + 0.5*cos(i^%pi/25)*(1+sin(j*%pi/5)) --R Type: Void --E 202 diff --git a/src/input/pat.input.pamphlet b/src/input/pat.input.pamphlet index d65aace..a1924f0 100644 --- a/src/input/pat.input.pamphlet +++ b/src/input/pat.input.pamphlet @@ -96,7 +96,7 @@ powerOf(x,x) == 1 --E 10 --S 11 of 21 -powerOf(x,x**n) == n +powerOf(x,x^n) == n --R --R Type: Void --E 11 @@ -108,7 +108,7 @@ powerOf(x,y) == 0 otherwise --E 12 --S 13 of 21 -powerOf(x,x**n%) == n% +powerOf(x,x^n%) == n% --R --R Type: Void --E 13 diff --git a/src/input/patmatch.input.pamphlet b/src/input/patmatch.input.pamphlet index f1d971b..b95ccd4 100644 --- a/src/input/patmatch.input.pamphlet +++ b/src/input/patmatch.input.pamphlet @@ -21,7 +21,7 @@ )set message auto off )clear all --S 1 of 22 -p := 3 * n ** 2 + 1 +p := 3 * n ^ 2 + 1 --R --R --R 2 @@ -30,7 +30,7 @@ p := 3 * n ** 2 + 1 --E 1 --S 2 of 22 -q := 3 * n% ** 2 + 1 +q := 3 * n% ^ 2 + 1 --R --R --R 2 @@ -166,10 +166,10 @@ a := rational a -- Is([ab, 1, 2, a], [pq, qq, p]) -- Is([ab, 1, 2, 3, a], [pq, qq, p]) -- creating streams using pattern matching --- want the streams of all primes of the form m**2+1 +-- want the streams of all primes of the form m^2+1 --S 17 of 22 -bar?(n:INT):BOOLEAN == prime? n and is?(n, m**2 + 1) +bar?(n:INT):BOOLEAN == prime? n and is?(n, m^2 + 1) --R --R Function declaration bar? : Integer -> Boolean has been added to --R workspace. @@ -186,7 +186,7 @@ myprimes := [i for i in 1.. | bar? i] --E 18 --S 19 of 22 -p := x**2 + 3*x + 1 +p := x^2 + 3*x + 1 --R --R --R 2 @@ -195,7 +195,7 @@ p := x**2 + 3*x + 1 --E 19 --S 20 of 22 -Is(p, n * y**2 + (2*n+1)*y + 1) +Is(p, n * y^2 + (2*n+1)*y + 1) --R --R --R (20) [] @@ -203,7 +203,7 @@ Is(p, n * y**2 + (2*n+1)*y + 1) --E 20 --S 21 of 22 -Is(p, n% * y**2 + (2*n%+1)*y + 1) +Is(p, n% * y^2 + (2*n%+1)*y + 1) --R --R --R (21) [] @@ -211,7 +211,7 @@ Is(p, n% * y**2 + (2*n%+1)*y + 1) --E 21 --S 22 of 22 -Is(3*x**2 + 9*x + 1, n * y**2 + n**2 * y + 1) +Is(3*x^2 + 9*x + 1, n * y^2 + n^2 * y + 1) --R --R --R (22) [n= x,y= 3] diff --git a/src/input/perm.input.pamphlet b/src/input/perm.input.pamphlet index c4bd940..bee365d 100644 --- a/src/input/perm.input.pamphlet +++ b/src/input/perm.input.pamphlet @@ -104,7 +104,7 @@ pw*pk --E 7 --S 8 of 51 -px**3 +px^3 --R --R --R (8) (2 22 18 8 14 5 4)(6 20 13 21 16 17 10)(7 11 19 12 23 9 15) @@ -545,7 +545,7 @@ r : PERM INT := cycles [[21,23,25,27],[22,24,26,28],[13,37,67,43],[15,31,61,45], Some calculation in Rubik's group: \begin{chunk}{*} --S 47 of 51 -(f**2*r**2)**3 +(f^2*r^2)^3 --R --R --R (46) (12 16)(24 28)(32 42)(38 44) diff --git a/src/input/pinch.input.pamphlet b/src/input/pinch.input.pamphlet index ec39cb5..aadd517 100644 --- a/src/input/pinch.input.pamphlet +++ b/src/input/pinch.input.pamphlet @@ -11,7 +11,7 @@ \tableofcontents \eject \begin{chunk}{*} -draw((x**2 - y**2)/(x**2 + y**2),x = -1..1,y = -1..1) +draw((x^2 - y^2)/(x^2 + y^2),x = -1..1,y = -1..1) \end{chunk} \eject \begin{thebibliography}{99} diff --git a/src/input/plotlist.input.pamphlet b/src/input/plotlist.input.pamphlet index 39520c0..afa4d66 100644 --- a/src/input/plotlist.input.pamphlet +++ b/src/input/plotlist.input.pamphlet @@ -18,7 +18,7 @@ )clear all \getchunk{license} ---draws x**i for i in 1..5, x=-1..1 +--draws x^i for i in 1..5, x=-1..1 makePoint(x:DoubleFloat,y:DoubleFloat):(Point DoubleFloat) == point(l :List DoubleFloat := [x,y])$(Point DoubleFloat) @@ -51,7 +51,7 @@ makeListFuns(fl:List(Expression Integer),_ lfuns := cons(ff, lfuns) lfuns -drawFuns(makeListFuns([x**i for i in 1..5], x=-1..1), x=-1..1) +drawFuns(makeListFuns([x^i for i in 1..5], x=-1..1), x=-1..1) \end{chunk} \eject diff --git a/src/input/poly.input.pamphlet b/src/input/poly.input.pamphlet index 04fedd5..2ae1175 100644 --- a/src/input/poly.input.pamphlet +++ b/src/input/poly.input.pamphlet @@ -21,7 +21,7 @@ )set message auto off )clear all --S 1 of 54 -a := rootOf(a**4+1,a) +a := rootOf(a^4+1,a) --R --R --R (1) a @@ -38,7 +38,7 @@ definingPolynomial a --E 2 --S 3 of 54 -b := rootOf(b**2-a-1,b) +b := rootOf(b^2-a-1,b) --R --R --R (3) b @@ -54,7 +54,7 @@ a + b --E 4 --S 5 of 54 -% ** 5 +% ^ 5 --R --R --R 3 2 3 2 @@ -63,7 +63,7 @@ a + b --E 5 --S 6 of 54 -rootOf(c**2+c+1,c) +rootOf(c^2+c+1,c) --R --R --R (6) c @@ -71,7 +71,7 @@ rootOf(c**2+c+1,c) --E 6 --S 7 of 54 -zeroOf(d**2+d+1,d) +zeroOf(d^2+d+1,d) --R --R --R +---+ @@ -82,7 +82,7 @@ zeroOf(d**2+d+1,d) --E 7 --S 8 of 54 -rootOf(e**5-2,e) +rootOf(e^5-2,e) --R --R --R (8) e @@ -90,7 +90,7 @@ rootOf(e**5-2,e) --E 8 --S 9 of 54 -zeroOf(f**5-2,f) +zeroOf(f^5-2,f) --R --R --R 5+-+ @@ -101,7 +101,7 @@ zeroOf(f**5-2,f) )clear all --S 10 of 54 -p := 3*x**8 + 2*x**7 + 6*x**2 + 7*x + 2 +p := 3*x^8 + 2*x^7 + 6*x^2 + 7*x + 2 --R --R --R 8 7 2 @@ -110,7 +110,7 @@ p := 3*x**8 + 2*x**7 + 6*x**2 + 7*x + 2 --E 10 --S 11 of 54 -q := 2*x**13 + 9*x**7 + 2*x**6 + 10*x + 5 +q := 2*x^13 + 9*x^7 + 2*x^6 + 10*x + 5 --R --R --R 13 7 6 @@ -138,7 +138,7 @@ resultant(p,q,x) )clear all --S 14 of 54 -p := x**2 + y**2 +p := x^2 + y^2 --R --R --R 2 2 @@ -165,7 +165,7 @@ eval(p,[x = a + b,y = c + d]) --E 16 --S 17 of 54 -q := x**3 + 5*x - y**4 +q := x^3 + 5*x - y^4 --R --R --R 4 3 @@ -202,7 +202,7 @@ eval(px, x = cos(2.0)) )clear all --S 21 of 54 -factor(x**3 - 3*x + 2) +factor(x^3 - 3*x + 2) --R --R --R 2 @@ -211,7 +211,7 @@ factor(x**3 - 3*x + 2) --E 21 --S 22 of 54 -factor(x**2/4 + x*y + y**2) +factor(x^2/4 + x*y + y^2) --R --R --R 1 2 @@ -221,7 +221,7 @@ factor(x**2/4 + x*y + y**2) --E 22 --S 23 of 54 -p := x**3 + x*y + 2*x**2*y**2 + 2*y**3 + 3*x**2*z + 6*x*y**2*z +p := x^3 + x*y + 2*x^2*y^2 + 2*y^3 + 3*x^2*z + 6*x*y^2*z --R --R --R 2 2 3 2 2 3 @@ -259,7 +259,7 @@ nthFactor(factors,2) )clear all --S 27 of 54 -p := a*x**2 + b*x*y + c*y**2 +p := a*x^2 + b*x*y + c*y^2 --R --R --R 2 2 @@ -268,7 +268,7 @@ p := a*x**2 + b*x*y + c*y**2 --E 27 --S 28 of 54 -q := 13*x**2 + 3*z +q := 13*x^2 + 3*z --R --R --R 2 @@ -295,7 +295,7 @@ p - 3*q --E 30 --S 31 of 54 -p**2 + p*q +p^2 + p*q --R --R --R (5) @@ -308,7 +308,7 @@ p**2 + p*q --E 31 --S 32 of 54 -r := (p + q)**2 +r := (p + q)^2 --R --R --R (6) @@ -406,7 +406,7 @@ coefficient(c,x,2) --E 42 --S 43 of 54 -coefficient(q**2, [x,z], [2,1]) +coefficient(q^2, [x,z], [2,1]) --R --R --R (17) 78 @@ -426,7 +426,7 @@ coefficient(r, [x,y], [2,2]) )clear all --S 45 of 54 -l := rootsOf(x**4+1,x) +l := rootsOf(x^4+1,x) --R --R --R (1) [%x0,%x0 %x1,- %x0,- %x0 %x1] @@ -434,7 +434,7 @@ l := rootsOf(x**4+1,x) --E 45 --S 46 of 54 -x0**5 +x0^5 --R --R --R 5 @@ -491,7 +491,7 @@ x0 * x1 * x2 * x3 --E 52 --S 53 of 54 -zerosOf(y**4+1,y) +zerosOf(y^4+1,y) --R --R --R +---+ +---+ +---+ +---+ diff --git a/src/input/poly1.input.pamphlet b/src/input/poly1.input.pamphlet index 2330824..8d8be6e 100644 --- a/src/input/poly1.input.pamphlet +++ b/src/input/poly1.input.pamphlet @@ -37,7 +37,7 @@ z - 2.3 --E 2 --S 3 of 46 -y**2 - z + 3/4 +y^2 - z + 3/4 --R --R --R 2 3 @@ -47,7 +47,7 @@ y**2 - z + 3/4 --E 3 --S 4 of 46 -y **2 + x*y + y +y ^2 + x*y + y --R --R --R 2 @@ -65,7 +65,7 @@ y **2 + x*y + y --E 5 --S 6 of 46 -p := (y-1)**2 * x * z +p := (y-1)^2 * x * z --R --R --R 2 @@ -90,7 +90,7 @@ factor(q) --E 8 --S 9 of 46 -p - q**2 +p - q^2 --R --R --R (9) @@ -301,7 +301,7 @@ eval(p,x,1) --E 33 --S 34 of 46 -eval(p,x,y**2 - 1) +eval(p,x,y^2 - 1) --R --R --R 4 3 @@ -382,7 +382,7 @@ p/q --E 42 --S 43 of 46 -(2/3) * x**2 - y + 4/5 +(2/3) * x^2 - y + 4/5 --R --R --R 2 2 4 diff --git a/src/input/polycoer.input.pamphlet b/src/input/polycoer.input.pamphlet index b29a0e7..38543f2 100644 --- a/src/input/polycoer.input.pamphlet +++ b/src/input/polycoer.input.pamphlet @@ -32,7 +32,7 @@ u : UP(x,COMPLEX INT) --E 1 --S 2 of 41 -u := (2+3*%i)*x**5 - 7*x**4 +x**2 + 89 +u := (2+3*%i)*x^5 - 7*x^4 +x^2 + 89 --R --R --R 5 4 2 @@ -56,7 +56,7 @@ m := u --E 4 --S 5 of 41 -m := m*y - z**2 +m := m*y - z^2 --R --R --R 5 4 2 2 @@ -167,7 +167,7 @@ f := u --E 19 --S 20 of 41 -u := x**2*y**9 - x**2*y**2 +u := x^2*y^9 - x^2*y^2 --R --R --R 2 9 2 2 @@ -215,7 +215,7 @@ f := u --E 25 --S 26 of 41 -u := x**2*y - z*x**2 + y*z - x**3*y*z + 3 +u := x^2*y - z*x^2 + y*z - x^3*y*z + 3 --R --R --R 3 2 2 @@ -224,7 +224,7 @@ u := x**2*y - z*x**2 + y*z - x**3*y*z + 3 --E 26 --S 27 of 41 -f := x**2*y - z*x**2 + y*z - x**3*y*z + 3 +f := x^2*y - z*x^2 + y*z - x^3*y*z + 3 --R --R --R 3 2 @@ -256,7 +256,7 @@ f : UP(w,DMP([y,z],INT)) --E 30 --S 31 of 41 -u := y**2 - w**5*y**2 - z*w + 3 +u := y^2 - w^5*y^2 - z*w + 3 --R --R --R 2 5 2 @@ -265,7 +265,7 @@ u := y**2 - w**5*y**2 - z*w + 3 --E 31 --S 32 of 41 -f := y**2 - w**5*y**2 - z*w + 3 +f := y^2 - w^5*y^2 - z*w + 3 --R --R --R 2 5 2 diff --git a/src/input/psgenfcn.input.pamphlet b/src/input/psgenfcn.input.pamphlet index b348911..62458f3 100644 --- a/src/input/psgenfcn.input.pamphlet +++ b/src/input/psgenfcn.input.pamphlet @@ -71,7 +71,7 @@ eulerPolynomial(n) == --E 4 --S 5 of 19 -f1 := taylor(t/(1 - t - t**2)) +f1 := taylor(t/(1 - t - t^2)) --R --R --R 2 3 4 5 6 7 8 9 10 11 @@ -223,7 +223,7 @@ h1 := taylor(2*exp(t/2)/(exp(t) + 1)) --E 14 --S 15 of 19 -h2 := taylor(n +-> euler(n)/(2**n * factorial(n)),t = 0) +h2 := taylor(n +-> euler(n)/(2^n * factorial(n)),t = 0) --R --R --R 1 2 5 4 61 6 277 8 50521 10 11 diff --git a/src/input/quat.input.pamphlet b/src/input/quat.input.pamphlet index 9c8a801..581c1c3 100644 --- a/src/input/quat.input.pamphlet +++ b/src/input/quat.input.pamphlet @@ -93,7 +93,7 @@ inv q In addition to the normal arithmetic (ring) operations. \begin{chunk}{*} --S 7 of 25 -q**6 +q^6 --R --R --R 2029490709319345 48251690851 144755072553 48251690851 diff --git a/src/input/quat1.input.pamphlet b/src/input/quat1.input.pamphlet index 94a3462..6989794 100644 --- a/src/input/quat1.input.pamphlet +++ b/src/input/quat1.input.pamphlet @@ -51,7 +51,7 @@ inv q --E 3 --S 4 of 11 -q**6 +q^6 --R --R --R 2029490709319345 48251690851 144755072553 48251690851 diff --git a/src/input/r20abugs.input.pamphlet b/src/input/r20abugs.input.pamphlet index 4606219..ae7731d 100644 --- a/src/input/r20abugs.input.pamphlet +++ b/src/input/r20abugs.input.pamphlet @@ -175,7 +175,7 @@ X : PolR := monomial(1, 1) --E 15 --S 16 of 34 -a : PolR := 2 * X**2 +a : PolR := 2 * X^2 --R --R --R 2 @@ -184,7 +184,7 @@ a : PolR := 2 * X**2 --E 16 --S 17 of 34 -b : PolR := X**2 + 2*X + 1 +b : PolR := X^2 + 2*X + 1 --R --R --R 2 diff --git a/src/input/r20bugs.input.pamphlet b/src/input/r20bugs.input.pamphlet index c5d746d..2d5970c 100644 --- a/src/input/r20bugs.input.pamphlet +++ b/src/input/r20bugs.input.pamphlet @@ -37,7 +37,7 @@ x := operator 'x --E 1 --S 2 of 27 -sum( (x i - mu)**2, i=1..N ) +sum( (x i - mu)^2, i=1..N ) --R --R --R N @@ -200,7 +200,7 @@ positiveRemainder(-1::SINT,-5::SINT) -- Type: List(List(Complex(Float))) --S 17 of 27 ok to fail. it seems there are 2 answers (see above) -complexRoots([u**2-v+1,v**2-4],[u,v],0.01) +complexRoots([u^2-v+1,v^2-4],[u,v],0.01) --R --R --R (1) @@ -209,7 +209,7 @@ complexRoots([u**2-v+1,v**2-4],[u,v],0.01) --E 17 --S 18 of 27 -complexRoots([u**2-v+1,v**2-4],[v,u],0.01) +complexRoots([u^2-v+1,v^2-4],[v,u],0.01) --R --R --R (2) [[- 2.0,- 1.73046875 %i],[- 2.0,1.73046875 %i],[2.0,- 1.0],[2.0,1.0]] diff --git a/src/input/r21bugs.input.pamphlet b/src/input/r21bugs.input.pamphlet index a5d34d8..9bf60fb 100644 --- a/src/input/r21bugs.input.pamphlet +++ b/src/input/r21bugs.input.pamphlet @@ -101,7 +101,7 @@ Q:=FRAC R --E 8 --S 9 of 95 -F:=X**4+X*Z**3 +F:=X^4+X*Z^3 --R --R --R 3 4 @@ -110,7 +110,7 @@ F:=X**4+X*Z**3 --E 9 --S 10 of 95 -G:=X**4+X**2*Y**2+Z**4 +G:=X^4+X^2*Y^2+Z^4 --R --R --R 4 2 2 4 @@ -144,7 +144,7 @@ squareFree ((c^15*e^8+c^23*d^4)::POLY PF 2) )clear completely --S 13 of 95 -FiniteFieldExtensionByPolynomial(FF(3,3),1+2*x**2+x**3) +FiniteFieldExtensionByPolynomial(FF(3,3),1+2*x^2+x^3) --R --R --R (1) FiniteFieldExtensionByPolynomial(FiniteField(3,3),?^3+2*?^2+1) @@ -531,7 +531,7 @@ g x -- fails -- from bmt --S 47 of 95 -a | a**8+a**4+a**3+a**2+(1::PF 2) +a | a^8+a^4+a^3+a^2+(1::PF 2) --R --R Your statement has resulted in the following assignments and --R declaration: @@ -581,7 +581,7 @@ T:=transpose tt --E 49 --S 50 of 95 -T0:=T**91 +T0:=T^91 --R --R --R +0 1 1 1 0 1 0 1+ @@ -603,7 +603,7 @@ T0:=T**91 --E 50 --S 51 of 95 -T1:=T**95 +T1:=T^95 --R --R --R +0 0 0 1 0 1 1 1+ diff --git a/src/input/r21bugsbig.input.pamphlet b/src/input/r21bugsbig.input.pamphlet index 85ff05f..036b43b 100644 --- a/src/input/r21bugsbig.input.pamphlet +++ b/src/input/r21bugsbig.input.pamphlet @@ -119,7 +119,7 @@ xi : E := generator()$E --S 12 of 22 bList : List(E) := _ - [reduce(+, [t(i+1) * xi**(i*j) for i in 0 .. #UZn-1]) for j in UZn] + [reduce(+, [t(i+1) * xi^(i*j) for i in 0 .. #UZn-1]) for j in UZn] --R --R --R (12) @@ -134,7 +134,7 @@ delta(j) = delta(j, 1) avec les nouvelles notations \begin{chunk}{*} --S 13 of 22 delta : List(E) := - [reduce(*, [b**((j*rapport(1,k)) quo n) for b in bList for k in UZn]) _ + [reduce(*, [b^((j*rapport(1,k)) quo n) for b in bList for k in UZn]) _ for j in UZn] --R --R Compiling function rapport with type (Integer,Integer) -> Integer @@ -247,7 +247,7 @@ delta : List(E) := verification en introduisant la liste B des Bj \begin{chunk}{*} --S 14 of 22 -B : List(E) := [reduce(*, [b**rapport(j,i) for b in bList for i in UZn]) _ +B : List(E) := [reduce(*, [b^rapport(j,i) for b in bList for i in UZn]) _ for j in UZn] --R --R @@ -840,13 +840,13 @@ B : List(E) := [reduce(*, [b**rapport(j,i) for b in bList for i in UZn]) _ --E 14 --S 15 of 22 -[B(1)**j - b * d**n for b in B for d in delta for j in UZn] +[B(1)^j - b * d^n for b in B for d in delta for j in UZn] --R --R (15) [0,0,0,0] --E 15 --S 16 of 22 -L := SimpleAlgebraicExtension(E, UP('C1, E), C1**n - B(1)) ; _ +L := SimpleAlgebraicExtension(E, UP('C1, E), C1^n - B(1)) ; _ C1 : L := generator()$L --R --R @@ -934,7 +934,7 @@ retraction(z : L) : Zt == --E 17 --S 18 of 22 -C : List(L) := [C1**j / d for j in UZn for d in delta] +C : List(L) := [C1^j / d for j in UZn for d in delta] --R --R --R (18) @@ -1413,11 +1413,11 @@ C : List(L) := [C1**j / d for j in UZn for d in delta] --E 18 \end{chunk} -en principe [c**n for c in C] = B +en principe [c^n for c in C] = B \begin{chunk}{*} --S 19 of 22 r : List(L) := _ - [reduce(+, [c * xi**(k*j) for j in UZn for c in C]) for k in 0 .. n-1] + [reduce(+, [c * xi^(k*j) for j in UZn for c in C]) for k in 0 .. n-1] --R --R --R (19) diff --git a/src/input/radff.input.pamphlet b/src/input/radff.input.pamphlet index b916236..cbc9998 100644 --- a/src/input/radff.input.pamphlet +++ b/src/input/radff.input.pamphlet @@ -40,7 +40,7 @@ P1 := UP(y, FRAC P0) curve given by $x^20 + y^20 = 1$ \begin{chunk}{*} --S 3 of 27 -R := RADFF(INT, P0, P1, 1 - x**20, 20) +R := RADFF(INT, P0, P1, 1 - x^20, 20) --R --R --R (3) @@ -147,7 +147,7 @@ trace y curve given by $y^4 = 2 x^2$ \begin{chunk}{*} --S 14 of 27 -R2 := RADFF(INT, P0, P1, 2 * x**2, 4) +R2 := RADFF(INT, P0, P1, 2 * x^2, 4) --R --R --R (14) @@ -216,7 +216,7 @@ y := generator()$R2 --E 21 --S 22 of 27 -integralCoordinates(y**3) +integralCoordinates(y^3) --R --R --R (22) [num= [0,0,0,x],den= 1] diff --git a/src/input/reclos.input.pamphlet b/src/input/reclos.input.pamphlet index 79b4344..901e758 100644 --- a/src/input/reclos.input.pamphlet +++ b/src/input/reclos.input.pamphlet @@ -305,7 +305,7 @@ sign(squareDiff8) --E 26 --S 27 of 70 -relativeApprox(squareDiff8,10**(-3))::Float +relativeApprox(squareDiff8,10^(-3))::Float --R --R --R (27) - 0.2340527771 5937700123 E -10 @@ -328,7 +328,7 @@ Check out if the sum of all roots is null. Example from P.V. Koseleff \begin{chunk}{*} --S 29 of 70 -l := allRootsOf((x**2-2)**2-2)$Ran +l := allRootsOf((x^2-2)^2-2)$Ran --R --R --R (29) [%A33,%A34,%A35,%A36] @@ -490,7 +490,7 @@ ee1::Boolean )cl prop pol r1 alpha beta --S 45 of 70 -pol : UP(x,Ran) := x**4+(7/3)*x**2+30*x-(100/3) +pol : UP(x,Ran) := x^4+(7/3)*x^2+30*x-(100/3) --R --R --R 4 7 2 100 @@ -580,7 +580,7 @@ beta2 := -sqrt(r2+11,5) --E 52 --S 53 of 70 -qol : UP(x,Ran) := x**5+10*x**3+20*x+22 +qol : UP(x,Ran) := x^5+10*x^3+20*x+22 --R --R --R 5 3 @@ -731,7 +731,7 @@ f27:Ran:=sqrt(27/5,5) --E 68 --S 69 of 70 -dst5:=sqrt((f32-f27,3)) = f25*(1+f3-f3**2) +dst5:=sqrt((f32-f27,3)) = f25*(1+f3-f3^2) --R --R --R +---------------+ diff --git a/src/input/reductio.input.pamphlet b/src/input/reductio.input.pamphlet index 6a0c809..b9592a4 100644 --- a/src/input/reductio.input.pamphlet +++ b/src/input/reductio.input.pamphlet @@ -31,7 +31,7 @@ reduce(_or,[x < 0 for x in u]) reduce(min,[i for i in 0.. while u.i > 0]) reduce(and,[x > 0 for x in u]) v := [1, 1, 0, 1, 0] -reduce(+,[v.(n - i) * 2**i for i in 0..(n := maxIndex v)]) +reduce(+,[v.(n - i) * 2^i for i in 0..(n := maxIndex v)]) reduce(+,[x * y for x in u for y in v]) reduce(+,[r for x in u for y in v | (r := y/x) > 0]) reduce(max,[x for x in u for y in v | y = 1]) diff --git a/src/input/regset.input.pamphlet b/src/input/regset.input.pamphlet index b61359d..abc3b9c 100644 --- a/src/input/regset.input.pamphlet +++ b/src/input/regset.input.pamphlet @@ -103,7 +103,7 @@ T := REGSET(R,E,V,P) --E 10 --S 11 of 34 -p1 := x ** 31 - x ** 6 - x - y +p1 := x ^ 31 - x ^ 6 - x - y --R --R --R 31 6 @@ -112,7 +112,7 @@ p1 := x ** 31 - x ** 6 - x - y --E 11 --S 12 of 34 -p2 := x ** 8 - z +p2 := x ^ 8 - z --R --R --R 8 @@ -121,7 +121,7 @@ p2 := x ** 8 - z --E 12 --S 13 of 34 -p3 := x ** 10 - t +p3 := x ^ 10 - t --R --R --R 10 @@ -168,7 +168,7 @@ lts := zeroSetSplit(lp,false)$T --E 17 --S 18 of 34 -f1 := y**2*z+2*x*y*t-2*x-z +f1 := y^2*z+2*x*y*t-2*x-z --R --R --R 2 @@ -177,7 +177,7 @@ f1 := y**2*z+2*x*y*t-2*x-z --E 18 --S 19 of 34 -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 +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 --R 3 2 2 3 2 @@ -186,7 +186,7 @@ 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* --E 19 --S 20 of 34 -f3 := 2*y*z*t+x*t**2-x-2*z +f3 := 2*y*z*t+x*t^2-x-2*z --R --R --R 2 @@ -195,7 +195,7 @@ f3 := 2*y*z*t+x*t**2-x-2*z --E 20 --S 21 of 34 -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 +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 --R 3 2 2 3 2 2 @@ -282,10 +282,10 @@ u : R := 2 --E 28 --S 29 of 34 -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+ _ - t**2*(z-x)**2 +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+ _ + t^2*(z-x)^2 --R --R --R (29) @@ -299,7 +299,7 @@ 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)+ _ --S 30 of 34 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 + u*y*(x+u-z*x-1)+ u*(u+1)*z^2*t --R --R --R 2 @@ -308,7 +308,7 @@ q2 := t*(2*z+1)*(x-z)+ y*(z+2)*(1-x)+ u*(u-2)*t+ u*(1-2*u)*z*t+ _ --E 30 --S 31 of 34 -q3 := -u**2*(z-1)**2+ 2*z*(z-x)-2*(x-1) +q3 := -u^2*(z-1)^2+ 2*z*(z-x)-2*(x-1) --R --R --R 2 @@ -317,8 +317,8 @@ q3 := -u**2*(z-1)**2+ 2*z*(z-x)-2*(x-1) --E 31 --S 32 of 34 -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) +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 --R --R (32) diff --git a/src/input/roman.input.pamphlet b/src/input/roman.input.pamphlet index b9e8279..da5b4a0 100644 --- a/src/input/roman.input.pamphlet +++ b/src/input/roman.input.pamphlet @@ -55,7 +55,7 @@ x : UTS(ROMAN,'x,0) := x --E 4 --S 5 of 10 -recip(1 - x - x**2) +recip(1 - x - x^2) --R --R --R (5) diff --git a/src/input/roots.input.pamphlet b/src/input/roots.input.pamphlet index c7b7dca..d994074 100644 --- a/src/input/roots.input.pamphlet +++ b/src/input/roots.input.pamphlet @@ -22,10 +22,10 @@ )clear all \end{chunk} -This will compute all the roots of x**4 + 1 = 0 +This will compute all the roots of x^4 + 1 = 0 \begin{chunk}{*} --S 1 of 7 -lr:=rootsOf(x**4+1,x) +lr:=rootsOf(x^4+1,x) --R --R --R (1) [%x0,%x0 %x1,- %x0,- %x0 %x1] @@ -66,7 +66,7 @@ lr.1 * lr.2 * lr.3 --E 4 --S 5 of 7 -%**4 +%^4 --R --R --R (5) - 1 @@ -85,7 +85,7 @@ lr.1 + lr.2 + lr.3 --E 6 --S 7 of 7 -%**4 +%^4 --R --R --R (7) - 1 diff --git a/src/input/rules.input.pamphlet b/src/input/rules.input.pamphlet index 6a8ec0e..c8f2761 100644 --- a/src/input/rules.input.pamphlet +++ b/src/input/rules.input.pamphlet @@ -54,7 +54,7 @@ Now a pile of several rules --S 4 of 21 logrules := rule log(x) + log(y) == log(x * y) - y * log x == log(x ** y) + y * log x == log(x ^ y) --R --R --R y @@ -88,7 +88,7 @@ Example of a predicate attached to a pattern variable --S 7 of 21 logrules2 := rule log(x) + log(y) == log(x * y) - (y | integer? y) * log x == log(x ** y) + (y | integer? y) * log x == log(x ^ y) --R --R --R y @@ -115,8 +115,8 @@ trigLinearize := rule sin(x) * sin(y) == cos(x-y)/2 - cos(x+y)/2 cos(x) * cos(y) == cos(x+y)/2 + cos(x-y)/2 sin(x) * cos(y) == sin(x+y)/2 + sin(x-y)/2 - sin(x) ** (n | integer? n and n > 1) == (1-cos(2*x))/2 * sin(x)**(n-2) - cos(x) ** (n | integer? n and n > 1) == (1+cos(2*x))/2 * cos(x)**(n-2) + sin(x) ^ (n | integer? n and n > 1) == (1-cos(2*x))/2 * sin(x)^(n-2) + cos(x) ^ (n | integer? n and n > 1) == (1+cos(2*x))/2 * cos(x)^(n-2) --R --R --R (9) diff --git a/src/input/ruleset.input.pamphlet b/src/input/ruleset.input.pamphlet index de25e38..f426a17 100644 --- a/src/input/ruleset.input.pamphlet +++ b/src/input/ruleset.input.pamphlet @@ -29,8 +29,8 @@ TrigLinearRules := rule sin(x) * sin(y) == cos(x-y)/2 - cos(x+y)/2 cos(x) * cos(y) == cos(x+y)/2 + cos(x-y)/2 sin(x) * cos(y) == sin(x+y)/2 + sin(x-y)/2 - sin(x)**(n | integer? n and n > 0) == (1-cos(2*x))/2 * sin(x)**(n-2) - cos(x)**(n | integer? n and n > 0) == (1+cos(2*x))/2 * cos(x)**(n-2) + sin(x)^(n | integer? n and n > 0) == (1-cos(2*x))/2 * sin(x)^(n-2) + cos(x)^(n | integer? n and n > 0) == (1+cos(2*x))/2 * cos(x)^(n-2) --R --R --R (1) diff --git a/src/input/saddle.input.pamphlet b/src/input/saddle.input.pamphlet index 1237e43..9b91668 100644 --- a/src/input/saddle.input.pamphlet +++ b/src/input/saddle.input.pamphlet @@ -11,7 +11,7 @@ \tableofcontents \eject \begin{chunk}{*} -draw(x**2 - y**2,x = -2..2, y = -2..2) +draw(x^2 - y^2,x = -2..2, y = -2..2) \end{chunk} \eject \begin{thebibliography}{99} diff --git a/src/input/segbind.input.pamphlet b/src/input/segbind.input.pamphlet index 699b782..1d314d8 100644 --- a/src/input/segbind.input.pamphlet +++ b/src/input/segbind.input.pamphlet @@ -29,7 +29,7 @@ x = a..b --E 1 --S 2 of 6 -sum(i**2, i = 0..n) +sum(i^2, i = 0..n) --R --R --R 3 2 @@ -40,7 +40,7 @@ sum(i**2, i = 0..n) --E 2 --S 3 of 6 -draw(x**2, x = -2..2) +draw(x^2, x = -2..2) --R --I Compiling function %B with type DoubleFloat -> DoubleFloat --R Graph data being transmitted to the viewport manager... diff --git a/src/input/series.input.pamphlet b/src/input/series.input.pamphlet index caf40d1..42aedbb 100644 --- a/src/input/series.input.pamphlet +++ b/src/input/series.input.pamphlet @@ -210,7 +210,7 @@ xS := series(x) --E 14 --S 15 of 20 -sin(xS)**(1/3) - sin(xS**(1/3)) +sin(xS)^(1/3) - sin(xS^(1/3)) --R --R --R (15) diff --git a/src/input/series2.input.pamphlet b/src/input/series2.input.pamphlet index 5f8f9d2..e4e9824 100644 --- a/src/input/series2.input.pamphlet +++ b/src/input/series2.input.pamphlet @@ -30,7 +30,7 @@ Well not really, since we have $x^2$, not x. Otherwise, our series expansions would have fractional powers. \begin{chunk}{*} --S 1 of 38 -f1 := taylor(1 - x**2,x = 0) +f1 := taylor(1 - x^2,x = 0) --R --R --R 2 @@ -82,7 +82,7 @@ cos % --E 5 --S 6 of 38 -f2 := taylor(1 + x**2,x = 0) +f2 := taylor(1 + x^2,x = 0) --R --R --R 2 @@ -134,7 +134,7 @@ sec % --E 10 --S 11 of 38 -f3 := taylor(1 - (x - a)**2,x = a) +f3 := taylor(1 - (x - a)^2,x = a) --R --R --R 2 @@ -199,7 +199,7 @@ cos % --E 15 --S 16 of 38 -f4 := taylor(1 + (x - a)**2,x = a) +f4 := taylor(1 + (x - a)^2,x = a) --R --R --R 2 @@ -264,7 +264,7 @@ sec % --E 20 --S 21 of 38 -f5 := taylor(%i + x**2,x = 0) +f5 := taylor(%i + x^2,x = 0) --R --R --R 2 @@ -592,7 +592,7 @@ map(normalize,csch %) --E 29 --S 30 of 38 -f6 := taylor(%i + (x - a)**2,x = a) +f6 := taylor(%i + (x - a)^2,x = a) --R --R --R 2 diff --git a/src/input/set.input.pamphlet b/src/input/set.input.pamphlet index dd4ab85..79ff5af 100644 --- a/src/input/set.input.pamphlet +++ b/src/input/set.input.pamphlet @@ -21,7 +21,7 @@ )set message auto off )clear all --S 1 of 20 -s := set [x**2-1, y**2-1, z**2-1] +s := set [x^2-1, y^2-1, z^2-1] --R --R --R 2 2 2 @@ -30,7 +30,7 @@ s := set [x**2-1, y**2-1, z**2-1] --E 1 --S 2 of 20 -t := set [x**i - i+1 for i in 2..10 | prime? i] +t := set [x^i - i+1 for i in 2..10 | prime? i] --R --R --R 2 3 5 7 @@ -123,7 +123,7 @@ complement gs --E 12 --S 13 of 20 -a := set [i**2 for i in 1..5] +a := set [i^2 for i in 1..5] --R --R --R (13) {1,4,9,16,25} @@ -155,7 +155,7 @@ a --E 16 --S 17 of 20 -b := b0 := set [i**2 for i in 1..5] +b := b0 := set [i^2 for i in 1..5] --R --R --R (17) {1,4,9,16,25} diff --git a/src/input/skew.input.pamphlet b/src/input/skew.input.pamphlet index 54635f6..23fdb1a 100644 --- a/src/input/skew.input.pamphlet +++ b/src/input/skew.input.pamphlet @@ -74,7 +74,7 @@ Here are some functions chosen at random. \begin{chunk}{*} --S 5 of 36 -f:R:=x**2*y*z-5*x**3*y**2*z**5 +f:R:=x^2*y*z-5*x^3*y^2*z^5 --R --R --R 3 2 5 2 @@ -83,7 +83,7 @@ f:R:=x**2*y*z-5*x**3*y**2*z**5 --E 5 --S 6 of 36 -g:R:=z**2*y*cos(z)-7*sin(x**3*y**2)*z**2 +g:R:=z^2*y*cos(z)-7*sin(x^3*y^2)*z^2 --R --R --R 2 3 2 2 @@ -92,7 +92,7 @@ g:R:=z**2*y*cos(z)-7*sin(x**3*y**2)*z**2 --E 6 --S 7 of 36 -h:R:=x*y*z-2*x**3*y*z**2 +h:R:=x*y*z-2*x^3*y*z^2 --R --R --R 3 2 diff --git a/src/input/slowint.input.pamphlet b/src/input/slowint.input.pamphlet index b7ab413..b667bd4 100644 --- a/src/input/slowint.input.pamphlet +++ b/src/input/slowint.input.pamphlet @@ -35,7 +35,7 @@ k := 7/5 --E 1 --S 2 of 5 -mu := sqrt ( ((k-1)*m**2 + 2)/(2*k*m**2 -(k-1))) +mu := sqrt ( ((k-1)*m^2 + 2)/(2*k*m^2 -(k-1))) --R --R --R +-------+ @@ -48,7 +48,7 @@ mu := sqrt ( ((k-1)*m**2 + 2)/(2*k*m**2 -(k-1))) --E 2 --S 3 of 5 -km := 2/ ( (1+(2/(k+1)) * (1-mu**2)/mu)*(2*mu + 1 + 1/(m**2))) +km := 2/ ( (1+(2/(k+1)) * (1-mu^2)/mu)*(2*mu + 1 + 1/(m^2))) --R --R --R +-------+ @@ -68,7 +68,7 @@ km := 2/ ( (1+(2/(k+1)) * (1-mu**2)/mu)*(2*mu + 1 + 1/(m**2))) --E 3 --S 4 of 5 -f := - 2*m / ((m**2-1)*km) +f := - 2*m / ((m^2-1)*km) --R --R --R +-------+ diff --git a/src/input/solvetra.input.pamphlet b/src/input/solvetra.input.pamphlet index 93064eb..9ca8f29 100644 --- a/src/input/solvetra.input.pamphlet +++ b/src/input/solvetra.input.pamphlet @@ -53,7 +53,7 @@ solve(sin(x)-8,x) --E 4 --S 5 of 37 -solve(sin(x**2)-2,x) +solve(sin(x^2)-2,x) --R --R --R +-------+ +-------+ @@ -62,7 +62,7 @@ solve(sin(x**2)-2,x) --E 5 --S 6 of 37 -solve(sin(x**2)-3,x) +solve(sin(x^2)-3,x) --R --R --R +-------+ +-------+ @@ -71,7 +71,7 @@ solve(sin(x**2)-3,x) --E 6 --S 7 of 37 -solve(sin(x**2)**2-3,x) +solve(sin(x^2)^2-3,x) --R --R --R (7) @@ -90,7 +90,7 @@ solve(sin(x+2)-2,x) --E 8 --S 9 of 37 -solve(sin(x**2+2)-2,x) +solve(sin(x^2+2)-2,x) --R --R --R +-----------+ +-----------+ @@ -119,7 +119,7 @@ solve(sin(x-77)*cos(8)*tan(88)*567-y*3+3,x) --E 11 --S 12 of 37 -solve(sin(x**2-77)*cos(8)*tan(88)*567-y*3+3,x) +solve(sin(x^2-77)*cos(8)*tan(88)*567-y*3+3,x) --R --R --R (12) @@ -142,7 +142,7 @@ solve(sin(x)*cos(x)-2,x) --E 13 --S 14 of 37 -solve(sin(x**3-77)*cos(8)*tan(88)*567-y*3+3,x) +solve(sin(x^3-77)*cos(8)*tan(88)*567-y*3+3,x) --R --R --R (14) @@ -187,7 +187,7 @@ solve(3*tan(3*x)-tan(x)+2,x) --E 16 --S 17 of 37 -solve(3*sech(x)**2+4*tanh(x)+1,x) +solve(3*sech(x)^2+4*tanh(x)+1,x) --R --R --R +---+ +---+ +-+ +-+ @@ -317,7 +317,7 @@ solve(log(sqrt(sqrt(sqrt(x+1)+4)+7))+5,x) --E 27 --S 28 of 37 -solve(2**x-6,x) +solve(2^x-6,x) --R --R --R log(6) @@ -356,7 +356,7 @@ solve(sqrt(sin(x))+sqrt(cos(x))+1,x) --E 31 --S 32 of 37 -solve(sqrt(sin(x)+1)+(sin(x)+1)**(1/3)+7,x) +solve(sqrt(sin(x)+1)+(sin(x)+1)^(1/3)+7,x) --R --R --R (32) @@ -382,7 +382,7 @@ solve(sqrt(sqrt(sqrt(1+x)+7)+1)+8-2,x) --E 33 --S 34 of 37 -solve(sqrt(sin(x)+1)+(sin(x)+5)**(1/3)+7,x) +solve(sqrt(sin(x)+1)+(sin(x)+5)^(1/3)+7,x) --R --R --R (34) diff --git a/src/input/sqmatrix.input.pamphlet b/src/input/sqmatrix.input.pamphlet index 74f5bf8..8ec619c 100644 --- a/src/input/sqmatrix.input.pamphlet +++ b/src/input/sqmatrix.input.pamphlet @@ -47,7 +47,7 @@ m*m - m --E 3 --S 4 of 6 -mm := squareMatrix [[m, 1], [1-m, m**2]] +mm := squareMatrix [[m, 1], [1-m, m^2]] --R --R --R ++1 - %i+ +1 0+ + @@ -61,7 +61,7 @@ mm := squareMatrix [[m, 1], [1-m, m**2]] --E 4 --S 5 of 6 -p := (x + m)**2 +p := (x + m)^2 --R --R --R 2 + 2 - 2%i+ + 2 - 5%i+ diff --git a/src/input/sregset.input.pamphlet b/src/input/sregset.input.pamphlet index 2997e44..f235f14 100644 --- a/src/input/sregset.input.pamphlet +++ b/src/input/sregset.input.pamphlet @@ -105,7 +105,7 @@ ST := SREGSET(R,E,V,P) --E 10 --S 11 of 23 -p1 := x ** 31 - x ** 6 - x - y +p1 := x ^ 31 - x ^ 6 - x - y --R --R --R 31 6 @@ -114,7 +114,7 @@ p1 := x ** 31 - x ** 6 - x - y --E 11 --S 12 of 23 -p2 := x ** 8 - z +p2 := x ^ 8 - z --R --R --R 8 @@ -123,7 +123,7 @@ p2 := x ** 8 - z --E 12 --S 13 of 23 -p3 := x ** 10 - t +p3 := x ^ 10 - t --R --R --R 10 diff --git a/src/input/symbol.input.pamphlet b/src/input/symbol.input.pamphlet index 4dfd817..9f9f070 100644 --- a/src/input/symbol.input.pamphlet +++ b/src/input/symbol.input.pamphlet @@ -53,7 +53,7 @@ B := b --E 4 --S 5 of 24 -x**2 + 1 +x^2 + 1 --R --R --R 2 diff --git a/src/input/table.input.pamphlet b/src/input/table.input.pamphlet index c9c64a1..e1b697a 100644 --- a/src/input/table.input.pamphlet +++ b/src/input/table.input.pamphlet @@ -29,7 +29,7 @@ t: Table(Polynomial Integer, String) := table() --E 1 --S 2 of 18 -setelt(t, x**2 - 1, "Easy to factor") +setelt(t, x^2 - 1, "Easy to factor") --R --R --R (2) "Easy to factor" @@ -37,7 +37,7 @@ setelt(t, x**2 - 1, "Easy to factor") --E 2 --S 3 of 18 -t(x**3 + 1) := "Harder to factor" +t(x^3 + 1) := "Harder to factor" --R --R --R (3) "Harder to factor" @@ -77,7 +77,7 @@ t x --E 7 --S 8 of 18 -t.(x**2 - 1) +t.(x^2 - 1) --R --R --R (8) "Easy to factor" @@ -85,7 +85,7 @@ t.(x**2 - 1) --E 8 --S 9 of 18 -t (x**3 + 1) +t (x^3 + 1) --R --R --R (9) "Harder to factor" @@ -110,7 +110,7 @@ search(x, t) --E 11 --S 12 of 18 -search(x**2, t) +search(x^2, t) --R --R --R (12) "failed" @@ -118,7 +118,7 @@ search(x**2, t) --E 12 --S 13 of 18 -search(x**2, t) case "failed" +search(x^2, t) case "failed" --R --R --R (13) true @@ -126,7 +126,7 @@ search(x**2, t) case "failed" --E 13 --S 14 of 18 -remove!(x**2-1, t) +remove!(x^2-1, t) --R --R --R (14) "Easy to factor" diff --git a/src/input/test.input.pamphlet b/src/input/test.input.pamphlet index b32a718..1053d8b 100644 --- a/src/input/test.input.pamphlet +++ b/src/input/test.input.pamphlet @@ -28,7 +28,7 @@ Fixed by SCM, verified on 10/30/90 )clear all --S 1 of 188 -eq1:= A*x**2 + B*x*y + C*y**2 +D*x + E*y + F +eq1:= A*x^2 + B*x*y + C*y^2 +D*x + E*y + F --R --R --R 2 2 @@ -287,7 +287,7 @@ v := vector [1,2,3] --E 14 --S 15 of 188 -eval(x**2, x=1/2) +eval(x^2, x=1/2) --R --R --R 1 @@ -297,7 +297,7 @@ eval(x**2, x=1/2) --E 15 --S 16 of 188 -eval(x**2, x=0.5) +eval(x^2, x=0.5) --R --R --R (4) 0.25 @@ -305,7 +305,7 @@ eval(x**2, x=0.5) --E 16 --S 17 of 188 -eval(3**x, x=0.5) +eval(3^x, x=0.5) --R --R --R (5) 1.7320508075 688772935 @@ -456,7 +456,7 @@ Fixed by SCM, verified on 10/30/90 )clear all --S 33 of 188 -groebner [x**2 - y, y**3+1] +groebner [x^2 - y, y^3+1] --R --R --R 2 6 @@ -545,7 +545,7 @@ p(n,x) == if n=0 then 1 else (x+n-1)*p(n-1,x) --E 40 --S 41 of 188 -pp(n,x) == if n=0 then 1 else if n<0 then (-1)**n/p(-n,1-x) else p(n,x) +pp(n,x) == if n=0 then 1 else if n<0 then (-1)^n/p(-n,1-x) else p(n,x) --R --R Type: Void --E 41 @@ -648,7 +648,7 @@ Test interpreter list destructuring --S 47 of 188 mp(x,l) == l is [a,:b] => - a*x**(#b)+ mp(x,b) + a*x^(#b)+ mp(x,b) 0 --R --R Type: Void @@ -741,7 +741,7 @@ Input of GDMP types. Fixed by SCM on 1/22/91 )clear all --S 56 of 188 -g: GDMP([x,y], INT, DIRPROD(2, NNI)) := x**2 + y +g: GDMP([x,y], INT, DIRPROD(2, NNI)) := x^2 + y --R --R --R 2 @@ -1049,7 +1049,7 @@ factorp(poly,p,e) == --E 73 --S 74 of 188 -factorp(x**2+x+5,7,1) +factorp(x^2+x+5,7,1) --R --R Cannot compile the declaration for ppoly because its (possible --R partial) type contains a local variable. @@ -1159,7 +1159,7 @@ factorp(poly,p,e) == --E 85 --S 86 of 188 -factorp(x**2+x+5,7,1) +factorp(x^2+x+5,7,1) --R --R Cannot compile conversion for types involving local variables. In --R particular, could not compile the expression involving :: UP(x,PF @@ -1268,7 +1268,7 @@ s:Mat := matrix [[ 2*x + 1, x], [x, 1]] --E 94 --S 95 of 188 -s**3 +s^3 --R --R --R + 3 2 3 2 + @@ -1295,7 +1295,7 @@ Parsing bug. Fixed by BURGE on 4/18/91 )clear all --S 97 of 188 --2**2 -- Should return -4 +-2^2 -- Should return -4 --R --R --R (1) - 4 @@ -1308,7 +1308,7 @@ Parsing bug. Fixed by BURGE on 4/18/91 )clear all --S 98 of 188 -f: DMP([x,y], INT) := x**2-y**2 +f: DMP([x,y], INT) := x^2-y^2 --R --R --R 2 2 @@ -1364,7 +1364,7 @@ Fixed by several people over a period of time )clear all --S 103 of 188 -eval(m**2, m=[[1,2],[2,3]]) +eval(m^2, m=[[1,2],[2,3]]) --R --R --R +5 8 + @@ -1416,7 +1416,7 @@ Fast generation of POLY FLOAT graphics code )clear all --S 107 of 188 -p: POLY FLOAT := (x-1)**30 +p: POLY FLOAT := (x-1)^30 --R --R --R (1) @@ -1497,7 +1497,7 @@ RFI := FRAC POLY INT --E 112 --S 113 of 188 -g:DMP([x,y], RFI) := a**2*x**2/b**2 - c**2*y**2/d**2 +g:DMP([x,y], RFI) := a^2*x^2/b^2 - c^2*y^2/d^2 --R --R --R 2 2 @@ -1891,7 +1891,7 @@ Passing ADEFs to functions which require specific mapping types. \begin{chunk}{*} )clear all ---draw((x,y) +-> x**2 - y**2, -1..1, -1..1) +--draw((x,y) +-> x^2 - y^2, -1..1, -1..1) \end{chunk} DP bug. Don't know where this came from, but its fixed. DP makes problems: @@ -1907,7 +1907,7 @@ dmp := DMP([u1,u2,u3],Fraction INT) --E 147 --S 148 of 188 -p : dmp := 2*u1**4*u2*u3 +p : dmp := 2*u1^4*u2*u3 --R --R --R 4 diff --git a/src/input/triglim.input.pamphlet b/src/input/triglim.input.pamphlet index 9cba036..6af1408 100644 --- a/src/input/triglim.input.pamphlet +++ b/src/input/triglim.input.pamphlet @@ -40,7 +40,7 @@ limit(atan(1/sin(x)),x = 0) --E 1 --S 2 of 6 -limit(atan(sqrt(1 - x**2)/x),x = 0) +limit(atan(sqrt(1 - x^2)/x),x = 0) --R --R --R %pi %pi @@ -70,7 +70,7 @@ limit(atan(sin(x)/(cos(x) + a)),x = acos(-a)) --E 4 \end{chunk} -We'll get these next two if sqrt(1 - a**2) is considered to be +We'll get these next two if sqrt(1 - a^2) is considered to be positive by SIGNEF \begin{chunk}{*} --S 5 of 6 diff --git a/src/input/tschirn.input.pamphlet b/src/input/tschirn.input.pamphlet index b1f0cc9..85fad97 100644 --- a/src/input/tschirn.input.pamphlet +++ b/src/input/tschirn.input.pamphlet @@ -11,7 +11,7 @@ \tableofcontents \eject \begin{chunk}{*} -draw(curve(3*(t**2-3),t*(t**2-3)),t = -3..3, [title "Tschirnhausen's Cubic"]) +draw(curve(3*(t^2-3),t*(t^2-3)),t = -3..3, [title "Tschirnhausen's Cubic"]) \end{chunk} \eject \begin{thebibliography}{99} diff --git a/src/input/tsetcatbutcher.input.pamphlet b/src/input/tsetcatbutcher.input.pamphlet index 4c84e9c..9910d92 100644 --- a/src/input/tsetcatbutcher.input.pamphlet +++ b/src/input/tsetcatbutcher.input.pamphlet @@ -38,13 +38,13 @@ v: P := 'v; w: P := 'w; f0 := b1 + y + z - t - w; -f1 := 2*z*u + 2*y*v + 2*t*w - 2*w**2 - w - 1 ; -f2 := 3*z*u**2 + 3*y*v**2 - 3*t*w**2 + 3*w**3 + 3*w**2 - t + 4*w ; -f3 := 6*x*z*v - 6*t*w**2 + 6*w**3 - 3*t*w + 6*w**2 - t + 4*w ; -f4 := 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 ; -f5 := 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 ; -f6 := 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; -f7 := -24*t*w**3 + 24*w**4 - 24*t*w**2 + 36*w**3 - 8*t*w + 26*w**2 + 7*w + 1 ; +f1 := 2*z*u + 2*y*v + 2*t*w - 2*w^2 - w - 1 ; +f2 := 3*z*u^2 + 3*y*v^2 - 3*t*w^2 + 3*w^3 + 3*w^2 - t + 4*w ; +f3 := 6*x*z*v - 6*t*w^2 + 6*w^3 - 3*t*w + 6*w^2 - t + 4*w ; +f4 := 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 ; +f5 := 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 ; +f6 := 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; +f7 := -24*t*w^3 + 24*w^4 - 24*t*w^2 + 36*w^3 - 8*t*w + 26*w^2 + 7*w + 1 ; lp := [f0,f1,f2,f3,f4,f5,f6,f7]; diff --git a/src/input/tsetcatchemical.input.pamphlet b/src/input/tsetcatchemical.input.pamphlet index e6ee72a..f8487eb 100644 --- a/src/input/tsetcatchemical.input.pamphlet +++ b/src/input/tsetcatchemical.input.pamphlet @@ -34,10 +34,10 @@ x4: P := 'x4; t: P := 't; -p1 := 2 - 7 * x1 + x1 ** 2 * x2 + t * (x3 - x1) ; -p2 := 6 * x1 - x1 ** 2 * x2 + 10 * t * (x4 - x2) ; -p3 := 2 - 7 * x3 + x3 ** 2 * x4 + t * (x1 - x3) ; -p4 := 6 * x3 - x3 **2 * x4 + 1 - t * (x2 - x4) ; +p1 := 2 - 7 * x1 + x1 ^ 2 * x2 + t * (x3 - x1) ; +p2 := 6 * x1 - x1 ^ 2 * x2 + 10 * t * (x4 - x2) ; +p3 := 2 - 7 * x3 + x3 ^ 2 * x4 + t * (x1 - x3) ; +p4 := 6 * x3 - x3 ^2 * x4 + 1 - t * (x2 - x4) ; lp := [p1,p2,p3,p4]; diff --git a/src/input/tsetcatvermeer.input.pamphlet b/src/input/tsetcatvermeer.input.pamphlet index e864a16..6c35c3d 100644 --- a/src/input/tsetcatvermeer.input.pamphlet +++ b/src/input/tsetcatvermeer.input.pamphlet @@ -105,28 +105,28 @@ w: P := 'w; --E 11 --S 12 of 21 -p1 := (x - u) ** 2 + (y - v) ** 2 - 1 ; +p1 := (x - u) ^ 2 + (y - v) ^ 2 - 1 ; --R --R --IType: NewSparseMultivariatePolynomial(Integer,... --E 12 --S 13 of 21 -p2 := v ** 2 - u ** 3 ; +p2 := v ^ 2 - u ^ 3 ; --R --R --IType: NewSparseMultivariatePolynomial(Integer,... --E 13 --S 14 of 21 -p3 := 2 * v * (x - u) + 3 * u ** 2 * (y - v) ; +p3 := 2 * v * (x - u) + 3 * u ^ 2 * (y - v) ; --R --R --IType: NewSparseMultivariatePolynomial(Integer,... --E 14 --S 15 of 21 -f1 := (3 * w * u ** 2 - 1) ; +f1 := (3 * w * u ^ 2 - 1) ; --R --R --IType: NewSparseMultivariatePolynomial(Integer,... diff --git a/src/input/up.input.pamphlet b/src/input/up.input.pamphlet index ebace9a..1a13b1f 100644 --- a/src/input/up.input.pamphlet +++ b/src/input/up.input.pamphlet @@ -16,9 +16,9 @@ )clear all (p,q) : UP(x,INT) -p := (3*x-1)**2 * (2*x + 8) -q := (1 - 6*x + 9*x**2)**2 -p**2 + p*q +p := (3*x-1)^2 * (2*x + 8) +q := (1 - 6*x + 9*x^2)^2 +p^2 + p*q leadingCoefficient p degree p reductum p @@ -32,14 +32,14 @@ q(p) l := coefficients p reduce(gcd,l) content p -ux := (x**4+2*x+3)::UP(x,INT) +ux := (x^4+2*x+3)::UP(x,INT) vectorise(ux,5) squareTerms(p) == - reduce(+,[t**2 for t in monomials p]) + reduce(+,[t^2 for t in monomials p]) p squareTerms p (r,s) : UP(a1,FRAC INT) -r := a1**2 - 2/3 +r := a1^2 - 2/3 s := a1 + 4 r quo s r rem s @@ -48,7 +48,7 @@ r - (d.quotient * s + d.remainder) integrate r integrate s t : UP(a1,FRAC POLY INT) -t := a1**2 - a1/b2 + (b1**2-b1)/(b2+3) +t := a1^2 - a1/b2 + (b1^2-b1)/(b2+3) u : FRAC POLY INT := t u :: UP(b1,?) \end{chunk} diff --git a/src/input/wester.input.pamphlet b/src/input/wester.input.pamphlet index d68dd54..dabef09 100644 --- a/src/input/wester.input.pamphlet +++ b/src/input/wester.input.pamphlet @@ -292,7 +292,7 @@ simplify(s1) -- Numbers are nice, but symbols allow for variability---try some high school -- algebra: rational simplification --S 21 of 216 -(x**2 - 4)/(x**2 + 4*x + 4) +(x^2 - 4)/(x^2 + 4*x + 4) --R --R --R x - 2 @@ -303,7 +303,7 @@ simplify(s1) -- This example requires more sophistication --S 22 of 216 -(%e**x - 1)/(%e**(x/2) + 1) +(%e^x - 1)/(%e^(x/2) + 1) --R --R --R x @@ -329,7 +329,7 @@ normalize(%) -- Expand and factor polynomials --S 24 of 216 -(x + 1)**20 +(x + 1)^20 --R --R --R (24) @@ -370,7 +370,7 @@ factor(%) --E 26 --S 27 of 216 -x**100 - 1 +x^100 - 1 --R --R --R 100 @@ -396,7 +396,7 @@ factor(%) -- Factor polynomials over finite fields and field extensions --S 29 of 216 -p:= x**4 - 3*x**2 + 1 +p:= x^4 - 3*x^2 + 1 --R --R --R 4 2 @@ -414,7 +414,7 @@ factor(p) --E 30 --S 31 of 216 -phi:= rootOf(phi**2 - phi - 1); +phi:= rootOf(phi^2 - phi - 1); --R --R --R Type: AlgebraicNumber @@ -448,7 +448,7 @@ expand(%) -- Partial fraction decomposition --S 35 of 216 -(x**2 + 2*x + 3)/(x**3 + 4*x**2 + 5*x + 2) +(x^2 + 2*x + 3)/(x^3 + 4*x^2 + 5*x + 2) --R --R --R 2 @@ -531,7 +531,7 @@ sincosAngles r -- ---------- Determining Zero Equivalence ---------- -- The following expressions are all equal to zero --S 42 of 216 -sqrt(997) - (997**3)**(1/6) +sqrt(997) - (997^3)^(1/6) --R --R --R (42) 0 @@ -539,7 +539,7 @@ sqrt(997) - (997**3)**(1/6) --E 42 --S 43 of 216 -sqrt(999983) - (999983**3)**(1/6) +sqrt(999983) - (999983^3)^(1/6) --R --R --R (43) 0 @@ -547,7 +547,7 @@ sqrt(999983) - (999983**3)**(1/6) --E 43 --S 44 of 216 -s1:=(2**(1/3) + 4**(1/3))**3 - 6*(2**(1/3) + 4**(1/3)) - 6 +s1:=(2^(1/3) + 4^(1/3))^3 - 6*(2^(1/3) + 4^(1/3)) - 6 --R --R --R 3+-+3+-+2 3+-+2 3+-+ 3+-+ @@ -592,7 +592,7 @@ rhs select (z+-> _ -- Thi49s expression is zero for x, y > 0 and n not equal to zero --S 49 of 216 -x**(1/n)*y**(1/n) - (x*y)**(1/n) +x^(1/n)*y^(1/n) - (x*y)^(1/n) --R --R --R 1 1 1 @@ -744,8 +744,8 @@ eval(expr, x = 0) --E 58 --S 59 of 216 -(4*r + 4*sqrt(r) + 1)**(sqrt(r)/(2*sqrt(r) + 1)) _ - * (2*sqrt(r) + 1)**(1/(2*sqrt(r) + 1)) - 2*sqrt(r) - 1 +(4*r + 4*sqrt(r) + 1)^(sqrt(r)/(2*sqrt(r) + 1)) _ + * (2*sqrt(r) + 1)^(1/(2*sqrt(r) + 1)) - 2*sqrt(r) - 1 --R --R --R (59) @@ -828,7 +828,7 @@ simplify(rectform(tan(x + %i*y))) -- September 1991. This first expression can simplify to sqrt(x y)/sqrt(x), -- but no further in general (consider what happens when x, y = -1). --S 64 of 216 -sqrt(x*y*abs(z)**2) / (sqrt(x)*abs(z)) +sqrt(x*y*abs(z)^2) / (sqrt(x)*abs(z)) --R --R --R +-----------+ @@ -869,7 +869,7 @@ sqrt(1/z) - 1/sqrt(z) -- If z = 3 pi i, log(exp(z)) is not equal to z --S 67 of 216 -log(%e**z) +log(%e^z) --R --R --R (67) z @@ -886,7 +886,7 @@ normalize(%) -- The principal value of this expression is (10 - 4 pi) i --S 69 of 216 -log(%e**(10*%i)) +log(%e^(10*%i)) --R --R --R 10%i @@ -914,7 +914,7 @@ atan(tan(z)) -- If z = 2 pi i, sqrt(exp(z)) is not equal to exp(z/2) --S 72 of 216 -sqrt(%e**z) - %e**(z/2) +sqrt(%e^z) - %e^(z/2) --R --R --R z @@ -938,7 +938,7 @@ sqrt(%e**z) - %e**(z/2) -- Solve various nonlinear equations---this cubic polynomial has all real roots --S 74 of 216 -radicalSolve(3*x**3 - 18*x**2 + 33*x - 19 = 0, x) +radicalSolve(3*x^3 - 18*x^2 + 33*x - 19 = 0, x) --R --R --R (74) @@ -1038,7 +1038,7 @@ map(e +-> lhs(e) = rectform(rhs(e)), %) -- Some simple seeming problems can have messy answers --S 76 of 216 -eqn:= x**4 + x**3 + x**2 + x + 1 = 0 +eqn:= x^4 + x^3 + x^2 + x + 1 = 0 --R --R --R 4 3 2 @@ -1485,7 +1485,7 @@ eval(eqn, %.1) --E 78 --S 79 of 216 -%e**(2*x) + 2*%e**x + 1 = z +%e^(2*x) + 2*%e^x + 1 = z --R --R --R 2x x @@ -1504,7 +1504,7 @@ solve(%, x) -- This equation is already factored and so *should* be easy to solve --S 81 of 216 -(x + 1) * (sin(x)**2 + 1)**2 * cos(3*x)**3 = 0 +(x + 1) * (sin(x)^2 + 1)^2 * cos(3*x)^3 = 0 --R --R --R 3 4 3 2 3 @@ -1525,7 +1525,7 @@ solve(%, x) -- The following equations have an infinite number of solutions (let n be an -- arbitrary integer): z = 0 [+ n 2 pi i] --S 83 of 216 -solve(%e**z = 1, z) +solve(%e^z = 1, z) --R --R --R (83) [z= 0] @@ -1564,7 +1564,7 @@ solve(sin(x) = tan(x), x) -- This equation has no solutions --S 87 of 216 -solve(sqrt(x**2 + 1) = x - 2, x) +solve(sqrt(x^2 + 1) = x - 2, x) --R --R --R (87) [] @@ -1607,7 +1607,7 @@ solve([eq1, eq2, eq3], [x, y, z]) -- Solve a system of nonlinear equations --S 92 of 216 -eq1:= x**2*y + 3*y*z - 4 = 0 +eq1:= x^2*y + 3*y*z - 4 = 0 --R --R --R 2 @@ -1616,7 +1616,7 @@ eq1:= x**2*y + 3*y*z - 4 = 0 --E 92 --S 93 of 216 -eq2:= -3*x**2*z + 2*y**2 + 1 = 0 +eq2:= -3*x^2*z + 2*y^2 + 1 = 0 --R --R --R 2 2 @@ -1625,7 +1625,7 @@ eq2:= -3*x**2*z + 2*y**2 + 1 = 0 --E 93 --S 94 of 216 -eq3:= 2*y*z**2 - z**2 - 1 = 0 +eq3:= 2*y*z^2 - z^2 - 1 = 0 --R --R --R 2 @@ -1695,8 +1695,8 @@ m * minv --S 99 of 216 matrix([[1, 1, 1, 1 ], _ [w, x, y, z ], _ - [w**2, x**2, y**2, z**2], _ - [w**3, x**3, y**3, z**3]]) + [w^2, x^2, y^2, z^2], _ + [w^3, x^3, y^3, z^3]]) --R --R --R +1 1 1 1 + @@ -1775,7 +1775,7 @@ solve(% = 0, lambda) -- ---------- Sums and Products ---------- -- Sums: finite and infinite --S 105 of 216 -summation(k**3, k = 1..n) +summation(k^3, k = 1..n) --R --R --R n @@ -1787,7 +1787,7 @@ summation(k**3, k = 1..n) --E 105 --S 106 of 216 -sum(k**3, k = 1..n) +sum(k^3, k = 1..n) --R --R --R 4 3 2 @@ -1798,7 +1798,7 @@ sum(k**3, k = 1..n) --E 106 --S 107 of 216 -limit(sum(1/k**2 + 1/k**3, k = 1..n), n = %plusInfinity) +limit(sum(1/k^2 + 1/k^3, k = 1..n), n = %plusInfinity) --R --R --R (107) "failed" @@ -1821,7 +1821,7 @@ product(k, k = 1..n) -- ---------- Calculus ---------- -- Limits---start with a famous example --S 109 of 216 -limit((1 + 1/n)**n, n = %plusInfinity) +limit((1 + 1/n)^n, n = %plusInfinity) --R --R --R (109) %e @@ -1829,7 +1829,7 @@ limit((1 + 1/n)**n, n = %plusInfinity) --E 109 --S 110 of 216 -limit((1 - cos(x))/x**2, x = 0) +limit((1 - cos(x))/x^2, x = 0) --R --R --R 1 @@ -1868,7 +1868,7 @@ D(y(x(t)), t, 2) -- ---------- Indefinite Integrals ---------- --S 114 of 216 -1/(x**3 + 2) +1/(x^3 + 2) --R --R --R 1 @@ -2034,7 +2034,7 @@ integrate(1/x, x = -1..1) --E 126 --S 127 of 216 -integrate(1/x**2, x = -1..1) +integrate(1/x^2, x = -1..1) --R --R --R >> Error detected within library code: @@ -2107,7 +2107,7 @@ integrate(sqrt(x + 1/x - 2), x = 0..2, "noPole") -- Contour integrals --S 134 of 216 -integrate(cos(x)/(x**2 + a**2), x = %minusInfinity..%plusInfinity) +integrate(cos(x)/(x^2 + a^2), x = %minusInfinity..%plusInfinity) --R --R --R (132) potentialPole @@ -2115,7 +2115,7 @@ integrate(cos(x)/(x**2 + a**2), x = %minusInfinity..%plusInfinity) --E 134 --S 135 of 216 -integrate(cos(x)/(x**2 + a**2), x = %minusInfinity..%plusInfinity, "noPole") +integrate(cos(x)/(x^2 + a^2), x = %minusInfinity..%plusInfinity, "noPole") --R --R --R (133) "failed" @@ -2124,7 +2124,7 @@ integrate(cos(x)/(x**2 + a**2), x = %minusInfinity..%plusInfinity, "noPole") -- Integrand with a branch point --S 136 of 216 -integrate(t**(a - 1)/(1 + t), t = 0..%plusInfinity) +integrate(t^(a - 1)/(1 + t), t = 0..%plusInfinity) --R --R --R (134) potentialPole @@ -2132,7 +2132,7 @@ integrate(t**(a - 1)/(1 + t), t = 0..%plusInfinity) --E 136 --S 137 of 216 -integrate(t**(a - 1)/(1 + t), t = 0..%plusInfinity, "noPole") +integrate(t^(a - 1)/(1 + t), t = 0..%plusInfinity, "noPole") --R --R --R (135) "failed" @@ -2155,7 +2155,7 @@ integrate(integrate(integrate(1, z = 0..c*(1 - x/a - y/b)), _ -- ---------- Series ---------- -- Taylor series---this first example comes from special relativity --S 139 of 216 -1/sqrt(1 - (v/c)**2) +1/sqrt(1 - (v/c)^2) --R --R --R 1 @@ -2181,7 +2181,7 @@ series(%, v = 0) --E 140 --S 141 of 216 -1/%**2 +1/%^2 --R --R --R 1 2 8 @@ -2236,7 +2236,7 @@ series(tan(x), x = 0) )set streams calculate 1 --S 146 of 216 -log(x)**a*exp(-b*x) +log(x)^a*exp(-b*x) --R --R --R - b x a @@ -2546,7 +2546,7 @@ y:= operator('y); --E 169 --S 170 of 216 -x**2 * D(y(x), x) + 3*x*y(x) = sin(x)/x +x^2 * D(y(x), x) + 3*x*y(x) = sin(x)/x --R --R --R 2 , sin(x) @@ -2568,7 +2568,7 @@ solve(%, y, x) -- Nonlinear ODE --S 172 of 216 -D(y(x), x, 2) + y(x)*D(y(x), x)**3 = 0 +D(y(x), x, 2) + y(x)*D(y(x), x)^3 = 0 --R --R --R ,, , 3 @@ -2631,7 +2631,7 @@ solve(%, y, x) -- ODE with boundary conditions. This problem has nontrivial solutions -- y(x) = A sin([pi/2 + n pi] x) for n an arbitrary integer. --S 178 of 216 -solve(D(y(x), x, 2) + k**2*y(x) = 0, y, x) +solve(D(y(x), x, 2) + k^2*y(x) = 0, y, x) --R --R --R (170) [particular= 0,basis= [cos(k x),sin(k x)]] @@ -2816,7 +2816,7 @@ subst(L(subst(g(y), y = x)), x = y) --E 195 --S 196 of 216 -subst(L(subst(A * sin(z**2), z = x)), x = z) +subst(L(subst(A * sin(z^2), z = x)), x = z) --R --R --R 2 2 2 @@ -2826,9 +2826,9 @@ subst(L(subst(A * sin(z**2), z = x)), x = z) -- Truncated Taylor series operator --S 197 of 216 -T:= (f, xx, a) +-> subst((DD**0)(f(x)), x = a)/factorial(0) * (xx - a)**0 + _ - subst((DD**1)(f(x)), x = a)/factorial(1) * (xx - a)**1 + _ - subst((DD**2)(f(x)), x = a)/factorial(2) * (xx - a)**2 +T:= (f, xx, a) +-> subst((DD^0)(f(x)), x = a)/factorial(0) * (xx - a)^0 + _ + subst((DD^1)(f(x)), x = a)/factorial(1) * (xx - a)^1 + _ + subst((DD^2)(f(x)), x = a)/factorial(2) * (xx - a)^2 --R --R --R (189) @@ -2902,7 +2902,7 @@ T(Sin, z, c) )clear properties p --S 203 of 216 -p(n, x) == 1/(2**n*factorial(n)) * D((x**2 - 1)**n, x, n) +p(n, x) == 1/(2^n*factorial(n)) * D((x^2 - 1)^n, x, n) --R --R Type: Void --E 203 @@ -3013,7 +3013,7 @@ a:= operator('a) --E 210 --S 211 of 216 -sum(a(i)*x**i, i = 1..5) +sum(a(i)*x^i, i = 1..5) --R --R --R 5 4 3 2 diff --git a/src/input/wutset.input.pamphlet b/src/input/wutset.input.pamphlet index 452f6d7..57e9dd9 100644 --- a/src/input/wutset.input.pamphlet +++ b/src/input/wutset.input.pamphlet @@ -25,9 +25,9 @@ y: P := 'y z: P := 'z t: P := 't T := WUTSET(R,E,V,P) -p1 := x ** 31 - x ** 6 - x - y -p2 := x ** 8 - z -p3 := x ** 10 - t +p1 := x ^ 31 - x ^ 6 - x - y +p2 := x ^ 8 - z +p3 := x ^ 10 - t lp := [p1, p2, p3] characteristicSet(lp)$T zeroSetSplit(lp)$T diff --git a/src/input/xpoly.input.pamphlet b/src/input/xpoly.input.pamphlet index 5424a06..4d2f79d 100644 --- a/src/input/xpoly.input.pamphlet +++ b/src/input/xpoly.input.pamphlet @@ -19,12 +19,12 @@ pr2: poly := pr*pr pd := expand pr pd2 := pd*pd expand(pr2) - pd2 -qr := pr**3 -qd := pd**3 +qr := pr^3 +qd := pd^3 trunc(qd,2) trunc(qr,2) Word := OrderedFreeMonoid Symbol -w: Word := x*y**2 +w: Word := x*y^2 rquo(qr,w) sh(pr,w::poly) \end{chunk} diff --git a/src/input/xpr.input.pamphlet b/src/input/xpr.input.pamphlet index bfb73dd..4704b1d 100644 --- a/src/input/xpr.input.pamphlet +++ b/src/input/xpr.input.pamphlet @@ -22,12 +22,12 @@ p * q (p +q)^2 -p^2 -q^2 - 2*p*q M := SquareMatrix(2,Fraction Integer) poly1:= XPR(M,Word) -m1:M := matrix [[i*j**2 for i in 1..2] for j in 1..2] +m1:M := matrix [[i*j^2 for i in 1..2] for j in 1..2] m2:M := m1 - 5/4 -m3: M := m2**2 +m3: M := m2^2 pm:poly1 := m1*x + m2*y + m3*z - 2/3 qm:poly1 := pm - m1*x -qm**3 +qm^3 \end{chunk} \eject \begin{thebibliography}{99} diff --git a/src/input/zdsolve.input.pamphlet b/src/input/zdsolve.input.pamphlet index 9e58ec0..3575b35 100644 --- a/src/input/zdsolve.input.pamphlet +++ b/src/input/zdsolve.input.pamphlet @@ -16,9 +16,9 @@ R := Integer ls : List Symbol := [x,y,z,t] ls2 : List Symbol := [x,y,z,t,new()$Symbol] pack := ZDSOLVE(R,ls,ls2) -p1 := x**2*y*z + x*y**2*z + x*y*z**2 + x*y*z + x*y + x*z + y*z -p2 := x**2*y**2*z + x*y**2*z**2 + x**2*y*z + x*y*z + y*z + x + z -p3 := x**2*y**2*z**2 + x**2*y**2*z + x*y**2*z + x*y*z + x*z + z + 1 +p1 := x^2*y*z + x*y^2*z + x*y*z^2 + x*y*z + x*y + x*z + y*z +p2 := x^2*y^2*z + x*y^2*z^2 + x^2*y*z + x*y*z + y*z + x + z +p3 := x^2*y^2*z^2 + x^2*y^2*z + x*y^2*z + x*y*z + x*z + z + 1 lp := [p1, p2, p3] triangSolve(lp)$pack univariateSolve(lp)$pack @@ -26,10 +26,10 @@ lr := realSolve(lp)$pack # lr [ [approximate(r,1/1000000) for r in point] for point in lr] lpr := positiveSolve(lp)$pack -f0 := x**3 + y + z + t- 1 -f1 := x + y**3 + z + t -1 -f2 := x + y + z**3 + t-1 -f3 := x + y + z + t**3 -1 +f0 := x^3 + y + z + t- 1 +f1 := x + y^3 + z + t -1 +f2 := x + y + z^3 + t-1 +f3 := x + y + z + t^3 -1 lf := [f0, f1, f2, f3] lts := triangSolve(lf)$pack univariateSolve(lf)$pack @@ -39,7 +39,7 @@ realSolve(ts)$pack lr2 := realSolve(lf)$pack #lr2 lpr2 := positiveSolve(lf)$pack -[approximate(r,1/10**21)::Float for r in lpr2.1] +[approximate(r,1/10^21)::Float for r in lpr2.1] \end{chunk} \eject \begin{thebibliography}{99} diff --git a/src/input/zimmbron.input.pamphlet b/src/input/zimmbron.input.pamphlet index 13e1e8b..3ab395b 100644 --- a/src/input/zimmbron.input.pamphlet +++ b/src/input/zimmbron.input.pamphlet @@ -161,7 +161,7 @@ solve(eq,y,x) \subsection{First Order 4 } \begin{chunk}{*} --S 14 of 143 -eq := 2*(y x)*y'**2-2*x*y'-y x=0 +eq := 2*(y x)*y'^2-2*x*y'-y x=0 --R --R --R , 2 ,