diff --git a/changelog b/changelog index 7c5d8fe..a4b3797 100644 --- a/changelog +++ b/changelog @@ -1,3 +1,26 @@ +20080106 tpd src/algebra/combfunc.spad \mathbb -> \bf +20080106 tpd src/algebra/op.spad revert dgamma change, reject patch +20080106 tpd src/scripts/tex/axiom.sty add binom for combfunc +20080106 tpd src/doc/axiom.sty add binom for combfunc +20080105 tpd src/input/Makefile add pfaffian +20080105 tpd src/input/pfaffian.input created +20080105 tpd src/algebra/acplot.spad fix output form of negative numbers +20080105 tpd src/algebra/sf.spad fix output form of negative numbers +20080105 tpd src/input/summation.input add mathml output +20080105 tpd src/input/r20bugs.input change spacing in S 17 +20080105 tpd src/input/pmint.input rewrite +20080105 tpd src/input/ndftip.input fix missing blank lines +20080105 tpd src/input/mathml.input new mathml sub/sup handling +20080105 tpd src/input/mapleok.input ignore gensyms +20080105 tpd src/input/kamke3.input mark random generation failure ok +20080105 tpd src/input/is.input type-declare the function f +20080105 tpd src/input/intg0.input ignore gensyms +20080105 tpd src/input/ico.input mark random generation failure ok +20080105 tpd src/input/grpthry.input mark random generation failure ok +20080105 tpd src/input/elemnum.input a + -bi now becomes a - bi +20080105 tpd src/input/dfloat.input fix output form of negative numbers +20080105 tpd src/input/classtalk.input ignore gensyms +20080105 tpd src/algebra/integer.spad transparent(?) category change 20080104 tpd changelog correct the author of besselk patches 20080104 mxr src/input/repa6.input fix function names (7093) 20080104 mxr src/input/knot2.input fix function names (7093) diff --git a/src/algebra/acplot.spad.pamphlet b/src/algebra/acplot.spad.pamphlet index 8a1ad4a..a39e3b6 100644 --- a/src/algebra/acplot.spad.pamphlet +++ b/src/algebra/acplot.spad.pamphlet @@ -228,8 +228,8 @@ makeSketch(x+y,x,y,-1/2..1/2,-1/2..1/2)$ACPLOT --R 1 1 1 1 --R y + x = 0, - - <= x <= -, - - <= y <= - --R 2 2 2 2 ---R [0.5,-0.5] ---R [-0.5,0.5] +--R [0.5,- 0.5] +--R [- 0.5,0.5] --R Type: PlaneAlgebraicCurvePlot --E 1 )spool diff --git a/src/algebra/combfunc.spad.pamphlet b/src/algebra/combfunc.spad.pamphlet index 9da05e9..24dd91a 100644 --- a/src/algebra/combfunc.spad.pamphlet +++ b/src/algebra/combfunc.spad.pamphlet @@ -110,7 +110,7 @@ $$\binom{n}{k}+\binom{n}{k+1}=\binom{n+1}{k+1}.$$ Alternatively, one can use the formula $$ \binom{n}{k}=\frac{\Gamma(n+1)}{\Gamma(k+1)\Gamma(n-k+1)}, $$ -and leave the case where $k\in\mathbb Z$, $n\in\mathbb Z$ and $k \leq n < 0$ +and leave the case where $k\in {\bf Z}$, $n\in {\bf Z}$ and $k \leq n < 0$ undefined, since the limit does not exist in this case: Since we then have that $n-k+1\geq 1$, $\Gamma(n-k+1)$ is finite. So it is @@ -123,7 +123,7 @@ $$\lim_{k_0\to k} \lim_{n_0\to n}\frac{\Gamma(n_0+1)}{\Gamma(k_0+1)}$$ does not exist, since for non-integral $k_0$, $\Gamma(k_0+1)$ is finite while $\Gamma(n_0+1)$ is unbounded. -However, since for $k\in\mathbb Z$, $n\in\mathbb Z$ and $0 < k < n$ both +However, since for $k\in {\bf Z}$, $n\in {\bf Z}$ and $0 < k < n$ both definitions agree, one could also combine them. This is what, for example, Mathematica does. It seems that MuPAD sets [[binomial(n,n)=1]] for all arguments [[n]], and returns [[binomial(-2, n)]] unevaluated. Provisos may help diff --git a/src/algebra/integer.spad.pamphlet b/src/algebra/integer.spad.pamphlet index 16ac727..c415a4e 100644 --- a/src/algebra/integer.spad.pamphlet +++ b/src/algebra/integer.spad.pamphlet @@ -1323,7 +1323,7 @@ Note that this code is not included in the generated catdef.spad file. ++ Keywords: positive integer ++ Description: \spadtype{PositiveInteger} provides functions for ++ positive integers. -PositiveInteger: Join(AbelianSemiGroup,OrderedSet,Monoid) with +PositiveInteger: Join(OrderedAbelianSemiGroup,Monoid) with gcd: (%,%) -> % ++ gcd(a,b) computes the greatest common divisor of two ++ positive integers \spad{a} and b. diff --git a/src/algebra/op.spad.pamphlet b/src/algebra/op.spad.pamphlet index 51d4d6c..cd18222 100644 --- a/src/algebra/op.spad.pamphlet +++ b/src/algebra/op.spad.pamphlet @@ -749,23 +749,7 @@ CommonOperators(): Exports == Implementation where dpi l == "%pi"::Symbol::O dfact x == postfix("!"::Symbol::O, (ATOM(x)$Lisp => x; paren x)) dquote l == prefix(quote(first(l)::O), rest l) -@ -It is certainly an abuse of OutputForm to produce a Gamma as done below. -Originally, it was even worse (Issue~\#6): -\begin{verbatim} dgamma l == prefix(hconcat("|"::Symbol::O, overbar(" "::Symbol::O)), l) -\end{verbatim} -which was TeXed to -$${|{\overline{\ }}} -\left( -{x} -\right). -$$ - -The right thing would be to introduce Greek letters in OutputForm, but -that should be coordinated with the new mathml package -<>= - dgamma l == prefix(super("|"::Symbol::O, "-"::Symbol::O), l) setDummyVar(op, n) == setProperty(op, DUMMYVAR, n pretend None) dexp x == diff --git a/src/algebra/sf.spad.pamphlet b/src/algebra/sf.spad.pamphlet index 571ccd0..1517c92 100644 --- a/src/algebra/sf.spad.pamphlet +++ b/src/algebra/sf.spad.pamphlet @@ -843,7 +843,7 @@ avg [3.4,9.7,-6.8] cos(3.1415926)$DoubleFloat --R --R ---R (9) -0.99999999999999856 +--R (9) - 0.99999999999999856 --R Type: DoubleFloat --E 9 @@ -851,7 +851,7 @@ cos(3.1415926)$DoubleFloat cos(3.1415926 :: DoubleFloat) --R --R ---R (10) -0.99999999999999856 +--R (10) - 0.99999999999999856 --R Type: DoubleFloat --E 10 )spool diff --git a/src/doc/axiom.sty.pamphlet b/src/doc/axiom.sty.pamphlet index cce87ad..a8ffdba 100644 --- a/src/doc/axiom.sty.pamphlet +++ b/src/doc/axiom.sty.pamphlet @@ -1613,6 +1613,8 @@ macro. There must be a more elegant way of coding the tests below\ldots % We use providecommand so it doesn't clash with amsmath package \providecommand{\eth}[1]{{#1}-th} +% add the binom function for combfunc +\providecommand{\binom}[2]{\left(\begin{array}{c}#1\\#2\end{array}\right)} @ \subsubsection{Support for English} diff --git a/src/input/Makefile.pamphlet b/src/input/Makefile.pamphlet index 8b79668..df8457c 100644 --- a/src/input/Makefile.pamphlet +++ b/src/input/Makefile.pamphlet @@ -313,6 +313,7 @@ REGRES= algaggr.regress algbrbf.regress algfacob.regress alist.regress \ float.regress fname1.regress fname.regress fnla.regress \ fns.regress fparfrac.regress fparfrc.regress fr1.regress \ fr2.regress frac.regress fr.regress galois.regress \ + gamma.regress \ gbf.regress genups.regress gonshor.regress grpthry.regress \ gstbl.regress heap.regress heat.regress help.regress \ herm.regress hexadec.regress ico.regress ideal.regress \ @@ -342,7 +343,7 @@ REGRES= algaggr.regress algbrbf.regress algfacob.regress alist.regress \ padic.regress parabola.regress pascal1.regress pascal.regress \ patch51.regress page.regress \ patmatch.regress pat.regress perman.regress perm.regress \ - pfr1.regress pfr.regress pmint.regress \ + pfaffian.regress pfr1.regress pfr.regress pmint.regress \ poly1.regress polycoer.regress poly.regress psgenfcn.regress \ quat1.regress quat.regress r20abugs.regress r20bugs.regress \ r21bugsbig.regress r21bugs.regress radff.regress radix.regress \ @@ -599,7 +600,7 @@ FILES= ${OUT}/algaggr.input ${OUT}/algbrbf.input ${OUT}/algfacob.input \ ${OUT}/pascal.input \ ${OUT}/patch51.input \ ${OUT}/patmatch.input ${OUT}/perman.input \ - ${OUT}/perm.input \ + ${OUT}/perm.input ${OUT}/pfaffian.input \ ${OUT}/pfr.input ${OUT}/pfr1.input \ ${OUT}/pinch.input ${OUT}/plotfile.input ${OUT}/pollevel.input \ ${OUT}/pmint.input ${OUT}/polycoer.input \ @@ -648,7 +649,7 @@ FILES2=${OUT}/arith.input ${OUT}/bugs.input \ ${OUT}/exlimit.input \ ${OUT}/expr.input ${OUT}/exprode.input ${OUT}/exseries.input \ ${OUT}/exsum.input ${OUT}/fns.input \ - ${OUT}/function.input ${OUT}/galois.input \ + ${OUT}/function.input ${OUT}/galois.input ${OUT}/gamma.input \ ${OUT}/grpthry.input \ ${OUT}/help.input ${OUT}/intef2.input \ ${OUT}/intmix2.input ${OUT}/knot2.input ${OUT}/linalg.input \ @@ -806,6 +807,7 @@ DOCFILES= \ ${DOC}/fr1.input.dvi ${DOC}/fr2.input.dvi \ ${DOC}/frac.input.dvi ${DOC}/fr.input.dvi \ ${DOC}/function.input.dvi ${DOC}/galois.input.dvi \ + ${DOC}/gamma.input.dvi \ ${DOC}/gary1.input.dvi ${DOC}/gbf.input.dvi \ ${DOC}/genups.input.dvi ${DOC}/gnarly1.input.dvi \ ${DOC}/gonshor.input.dvi ${DOC}/graphics.input.dvi \ @@ -881,7 +883,7 @@ DOCFILES= \ ${DOC}/pat.input.dvi ${DOC}/patch51.input.dvi \ ${DOC}/patmatch.input.dvi \ ${DOC}/pdecomp0.as.dvi ${DOC}/perman.input.dvi \ - ${DOC}/perm.input.dvi \ + ${DOC}/perm.input.dvi ${DOC}/pfaffian.input.dvi \ ${DOC}/pfr1.input.dvi \ ${DOC}/pfr.input.dvi ${DOC}/pinch.input.dvi \ ${DOC}/plotfile.input.dvi ${DOC}/plotlist.input.dvi \ diff --git a/src/input/classtalk.input.pamphlet b/src/input/classtalk.input.pamphlet index 7f89df1..2f3eca3 100644 --- a/src/input/classtalk.input.pamphlet +++ b/src/input/classtalk.input.pamphlet @@ -705,7 +705,7 @@ solve([x+y+z=8,3*x-2*y+z=0,x+2*y+2*z=17],[x,y,z]) --S 70 solve([x+2*y+3*z=2,2*x+3*y+4*z=2,3*x+4*y+5*z=2],[x,y,z]) --R ---R (2) [[x= %W - 2,y= - 2%W + 2,z= %W]] +--I (2) [[x= %W - 2,y= - 2%W + 2,z= %W]] --R Type: List List Equation Fraction Polynomial Integer --E 70 diff --git a/src/input/dfloat.input.pamphlet b/src/input/dfloat.input.pamphlet index f3e3468..75eeb5f 100644 --- a/src/input/dfloat.input.pamphlet +++ b/src/input/dfloat.input.pamphlet @@ -86,7 +86,7 @@ avg [3.4,9.7,-6.8] cos(3.1415926)$DoubleFloat --R --R ---R (9) -0.99999999999999856 +--R (9) - 0.99999999999999856 --R Type: DoubleFloat --E 9 @@ -94,7 +94,7 @@ cos(3.1415926)$DoubleFloat cos(3.1415926 :: DoubleFloat) --R --R ---R (10) -0.99999999999999856 +--R (10) - 0.99999999999999856 --R Type: DoubleFloat --E 10 )spool diff --git a/src/input/elemnum.input.pamphlet b/src/input/elemnum.input.pamphlet index 0581410..137b32d 100644 --- a/src/input/elemnum.input.pamphlet +++ b/src/input/elemnum.input.pamphlet @@ -176,7 +176,7 @@ x := 0.7::DoubleFloat --R --R --R (18) ---R [0.69999999999999996, 0.69999999999999996, 0.69999999999999996, +--R [0.69999999999999996, 0.70000000000000007, 0.69999999999999996, --R 0.69999999999999996] --R Type: List DoubleFloat --E 18 @@ -255,7 +255,7 @@ x := 1.1::DoubleFloat --R --R --R (26) ---R [1.1000000000000001, 1.1000000000000001, 1.1000000000000001, +--R [1.1000000000000003, 1.1000000000000001, 1.1000000000000001, --R 1.1000000000000001, 1.0999999999999999, 1.1000000000000001] --R Type: List DoubleFloat --E 26 @@ -351,25 +351,24 @@ qtest(sa, sb, 1) --R PositiveInteger) -> List Complex DoubleFloat --R --R (35) ---R [1.1102230246251565E-16, ---R 2.2204460492503131E-16 + -4.4408920985006262E-16 %i, ---R -2.2204460492503131E-16, ---R -4.4408920985006262E-16 + -2.2204460492503131E-16 %i, ---R 4.4408920985006262E-16, -1.1102230246251565E-16, ---R -2.2204460492503131E-16 + -2.2204460492503131E-16 %i, +--R [1.1102230246251565E-16, 2.2204460492503131E-16 - 4.4408920985006262E-16 %i, +--R - 2.2204460492503131E-16, +--R - 4.4408920985006262E-16 - 2.2204460492503131E-16 %i, +--R 4.4408920985006262E-16, - 1.1102230246251565E-16, +--R - 2.2204460492503131E-16 - 2.2204460492503131E-16 %i, --R 1.1102230246251565E-16, ---R -2.2204460492503131E-16 + -2.2204460492503131E-16 %i, +--R - 2.2204460492503131E-16 - 2.2204460492503131E-16 %i, --R 2.2204460492503131E-16 + 2.2204460492503131E-16 %i, ---R 1.1102230246251565E-16 + -2.2204460492503131E-16 %i, 0., ---R -6.6613381477509392E-16 %i, -1.1102230246251565E-16, ---R -4.4408920985006262E-16 + -4.4408920985006262E-16 %i, ---R 3.3306690738754696E-16 + -2.2204460492503131E-16 %i, ---R -3.3306690738754696E-16, ---R -4.4408920985006262E-16 + -4.4408920985006262E-16 %i, ---R 3.3306690738754696E-16 + -2.2204460492503131E-16 %i, ---R -5.5511151231257827E-16, -2.2204460492503131E-16, -1.1102230246251565E-16, ---R 1.1102230246251565E-16, 0., -1.1102230246251565E-16, ---R -1.1102230246251565E-16] +--R 1.1102230246251565E-16 - 2.2204460492503131E-16 %i, 0., +--R - 6.6613381477509392E-16 %i, - 1.1102230246251565E-16, +--R - 4.4408920985006262E-16 - 4.4408920985006262E-16 %i, +--R 3.3306690738754696E-16 - 2.2204460492503131E-16 %i, +--R - 3.3306690738754696E-16, +--R - 4.4408920985006262E-16 - 4.4408920985006262E-16 %i, +--R 3.3306690738754696E-16 - 2.2204460492503131E-16 %i, +--R - 5.5511151231257827E-16, - 2.2204460492503131E-16, +--R - 1.1102230246251565E-16, 1.1102230246251565E-16, 0., +--R - 1.1102230246251565E-16, - 1.1102230246251565E-16] --R Type: List Complex DoubleFloat --E 35 @@ -414,25 +413,24 @@ qtest(sa, sb, 2) --R --R --R (39) ---R [-1.1102230246251565E-16, ---R -2.2204460492503131E-16 + -4.4408920985006262E-16 %i, ---R -3.3306690738754696E-16, ---R 4.4408920985006262E-16 + -2.2204460492503131E-16 %i, ---R -4.4408920985006262E-16, ---R 1.1102230246251565E-16 + -2.2204460492503131E-16 %i, ---R 3.3306690738754696E-16 + -2.2204460492503131E-16 %i, ---R -1.1102230246251565E-16, ---R 4.4408920985006262E-16 + -2.2204460492503131E-16 %i, ---R -2.2204460492503131E-16 + 2.2204460492503131E-16 %i, ---R 2.2204460492503131E-16 + -2.2204460492503131E-16 %i, ---R -1.1102230246251565E-16 + -2.2204460492503131E-16 %i, ---R 2.2204460492503131E-16 + -2.2204460492503131E-16 %i, 0., ---R 4.4408920985006262E-16 + -4.4408920985006262E-16 %i, 0., ---R 3.3306690738754696E-16, ---R 4.4408920985006262E-16 + -4.4408920985006262E-16 %i, 0., ---R 8.8817841970012523E-16, 2.2204460492503131E-16, 1.1102230246251565E-16, ---R 3.3306690738754696E-16, -1.1102230246251565E-16, 1.1102230246251565E-16, ---R 2.2204460492503131E-16 + -2.2204460492503131E-16 %i] +--R [- 1.1102230246251565E-16, +--R - 2.2204460492503131E-16 - 4.4408920985006262E-16 %i, +--R - 3.3306690738754696E-16, +--R 4.4408920985006262E-16 - 2.2204460492503131E-16 %i, +--R - 4.4408920985006262E-16, +--R 1.1102230246251565E-16 - 2.2204460492503131E-16 %i, +--R 3.3306690738754696E-16 - 2.2204460492503131E-16 %i, +--R - 1.1102230246251565E-16, +--R 4.4408920985006262E-16 - 2.2204460492503131E-16 %i, +--R - 2.2204460492503131E-16 + 2.2204460492503131E-16 %i, +--R 2.2204460492503131E-16 - 2.2204460492503131E-16 %i, +--R - 1.1102230246251565E-16 - 2.2204460492503131E-16 %i, +--R 2.2204460492503131E-16 - 2.2204460492503131E-16 %i, 0., +--R 4.4408920985006262E-16 - 4.4408920985006262E-16 %i, 0., +--R 3.3306690738754696E-16, 4.4408920985006262E-16 - 4.4408920985006262E-16 %i, +--R 0., 8.8817841970012523E-16, 2.2204460492503131E-16, 1.1102230246251565E-16, +--R 3.3306690738754696E-16, - 1.1102230246251565E-16, 1.1102230246251565E-16, +--R 2.2204460492503131E-16 - 2.2204460492503131E-16 %i] --R Type: List Complex DoubleFloat --E 39 @@ -472,20 +470,20 @@ qtest(sa, sb, 3) --R --R --R (43) ---R [-1.1102230246251565E-16, 0., ---R -2.2204460492503131E-16 + 4.4408920985006262E-16 %i, ---R -2.2204460492503131E-16, 1.1102230246251565E-16, -4.4408920985006262E-16, ---R -1.1102230246251565E-16, -1.1102230246251565E-16, +--R [- 1.1102230246251565E-16, 0., +--R - 2.2204460492503131E-16 + 4.4408920985006262E-16 %i, +--R - 2.2204460492503131E-16, 1.1102230246251565E-16, - 4.4408920985006262E-16, +--R - 1.1102230246251565E-16, - 1.1102230246251565E-16, --R 4.4408920985006262E-16 + 2.2204460492503131E-16 %i, ---R -2.2204460492503131E-16 + -2.2204460492503131E-16 %i, +--R - 2.2204460492503131E-16 - 2.2204460492503131E-16 %i, --R 2.2204460492503131E-16 + 2.2204460492503131E-16 %i, ---R -1.1102230246251565E-16 + 2.2204460492503131E-16 %i, +--R - 1.1102230246251565E-16 + 2.2204460492503131E-16 %i, --R 2.2204460492503131E-16 + 2.2204460492503131E-16 %i, 0., 0., ---R -3.3306690738754696E-16 + 2.2204460492503131E-16 %i, +--R - 3.3306690738754696E-16 + 2.2204460492503131E-16 %i, --R 2.2204460492503131E-16 %i, 0., ---R -3.3306690738754696E-16 + 2.2204460492503131E-16 %i, +--R - 3.3306690738754696E-16 + 2.2204460492503131E-16 %i, --R 8.8817841970012523E-16, 2.2204460492503131E-16, 1.1102230246251565E-16, ---R 3.3306690738754696E-16, -1.1102230246251565E-16, 1.1102230246251565E-16, +--R 3.3306690738754696E-16, - 1.1102230246251565E-16, 1.1102230246251565E-16, --R 2.2204460492503131E-16 + 2.2204460492503131E-16 %i] --R Type: List Complex DoubleFloat --E 43 @@ -529,16 +527,16 @@ qtest(sa, sb, 4) --R (47) --R [1.1102230246251565E-16, 0., --R 3.3306690738754696E-16 + 4.4408920985006262E-16 %i, 2.2204460492503131E-16, ---R -1.1102230246251565E-16, ---R 2.2204460492503131E-16 + -2.2204460492503131E-16 %i, +--R - 1.1102230246251565E-16, +--R 2.2204460492503131E-16 - 2.2204460492503131E-16 %i, --R 2.2204460492503131E-16 + 2.2204460492503131E-16 %i, 1.1102230246251565E-16, ---R -2.2204460492503131E-16 + 2.2204460492503131E-16 %i, ---R 2.2204460492503131E-16 + -2.2204460492503131E-16 %i, +--R - 2.2204460492503131E-16 + 2.2204460492503131E-16 %i, +--R 2.2204460492503131E-16 - 2.2204460492503131E-16 %i, --R 1.1102230246251565E-16 + 2.2204460492503131E-16 %i, 0., ---R 6.6613381477509392E-16 %i, -1.1102230246251565E-16, 0., 0., ---R 2.2204460492503131E-16 %i, 0., 0., -6.6613381477509392E-16, ---R -2.2204460492503131E-16, -1.1102230246251565E-16, 1.1102230246251565E-16, ---R 0., -1.1102230246251565E-16, -1.1102230246251565E-16] +--R 6.6613381477509392E-16 %i, - 1.1102230246251565E-16, 0., 0., +--R 2.2204460492503131E-16 %i, 0., 0., - 6.6613381477509392E-16, +--R - 2.2204460492503131E-16, - 1.1102230246251565E-16, 1.1102230246251565E-16, +--R 0., - 1.1102230246251565E-16, - 1.1102230246251565E-16] --R Type: List Complex DoubleFloat --E 47 diff --git a/src/input/grpthry.input.pamphlet b/src/input/grpthry.input.pamphlet index b0296a4..e713c5c 100644 --- a/src/input/grpthry.input.pamphlet +++ b/src/input/grpthry.input.pamphlet @@ -1697,7 +1697,7 @@ ma := meatAxe r28.1 --R Type: List List Matrix PrimeField 2 --E 34 ---S 35 of 68 +--S 35 of 68 random generation, FAILURE OK. isAbsolutelyIrreducible? ma.1 --R --R Random element in generated algebra does diff --git a/src/input/ico.input.pamphlet b/src/input/ico.input.pamphlet index 1643180..f096f56 100644 --- a/src/input/ico.input.pamphlet +++ b/src/input/ico.input.pamphlet @@ -344,7 +344,7 @@ p2:=point([real ca2,imag ca2,0.5])@Point(SF) p3:=point([real ca3,imag ca3,0.5])@Point(SF) --R --R ---R (34) [-0.80901699437494745,0.58778525229247314,0.5] +--R (34) [- 0.80901699437494745,0.58778525229247314,0.5] --R Type: Point DoubleFloat --E 35 @@ -352,7 +352,7 @@ p3:=point([real ca3,imag ca3,0.5])@Point(SF) p4:=point([real ca4,imag ca4,0.5])@Point(SF) --R --R ---R (35) [-0.80901699437494745,-0.58778525229247314,0.5] +--R (35) [- 0.80901699437494745,- 0.58778525229247314,0.5] --R Type: Point DoubleFloat --E 36 @@ -360,7 +360,7 @@ p4:=point([real ca4,imag ca4,0.5])@Point(SF) p5:=point([real ca5,imag ca5,0.5])@Point(SF) --R --R ---R (36) [0.30901699437494745,-0.95105651629515353,0.5] +--R (36) [0.30901699437494745,- 0.95105651629515353,0.5] --R Type: Point DoubleFloat --E 37 @@ -368,7 +368,7 @@ p5:=point([real ca5,imag ca5,0.5])@Point(SF) p6:=point([real cb1,imag cb1,-0.5])@Point(SF) --R --R ---R (37) [0.80901699437494745,0.58778525229247314,-0.5] +--R (37) [0.80901699437494745,0.58778525229247314,- 0.5] --R Type: Point DoubleFloat --E 38 @@ -376,7 +376,7 @@ p6:=point([real cb1,imag cb1,-0.5])@Point(SF) p7:=point([real cb2,imag cb2,-0.5])@Point(SF) --R --R ---R (38) [-0.30901699437494745,0.95105651629515353,-0.5] +--R (38) [- 0.30901699437494745,0.95105651629515353,- 0.5] --R Type: Point DoubleFloat --E 39 @@ -384,7 +384,7 @@ p7:=point([real cb2,imag cb2,-0.5])@Point(SF) p8:=point([real cb3,imag cb3,-0.5])@Point(SF) --R --R ---R (39) [-1.,0.,-0.5] +--R (39) [- 1.,0.,- 0.5] --R Type: Point DoubleFloat --E 40 @@ -392,7 +392,7 @@ p8:=point([real cb3,imag cb3,-0.5])@Point(SF) p9:=point([real cb4,imag cb4,-0.5])@Point(SF) --R --R ---R (40) [-0.30901699437494745,-0.95105651629515353,-0.5] +--R (40) [- 0.30901699437494745,- 0.95105651629515353,- 0.5] --R Type: Point DoubleFloat --E 41 @@ -400,7 +400,7 @@ p9:=point([real cb4,imag cb4,-0.5])@Point(SF) p10:=point([real cb5,imag cb5,-0.5])@Point(SF) --R --R ---R (41) [0.80901699437494745,-0.58778525229247314,-0.5] +--R (41) [0.80901699437494745,- 0.58778525229247314,- 0.5] --R Type: Point DoubleFloat --E 42 @@ -408,7 +408,7 @@ p10:=point([real cb5,imag cb5,-0.5])@Point(SF) p11:=point([0,0,-u-1/2])@Point(SF) --R --R ---R (42) [0.,0.,-1.1180339887498949] +--R (42) [0.,0.,- 1.1180339887498949] --R Type: Point DoubleFloat --E 43 diff --git a/src/input/intg0.input.pamphlet b/src/input/intg0.input.pamphlet index ea802ef..bc5a258 100644 --- a/src/input/intg0.input.pamphlet +++ b/src/input/intg0.input.pamphlet @@ -32,7 +32,7 @@ y := sqrt(a * x + b) --E 1 --S 2 of 25 -integrate(%,x) +integrate(y,x) --R --R --R +-------+ @@ -43,7 +43,7 @@ integrate(%,x) --E 2 --S 3 of 25 -x * y +t1:=x * y --R --R --R +-------+ @@ -52,7 +52,7 @@ x * y --E 3 --S 4 of 25 -integrate(%,x) +integrate(t1,x) --R --R --R 2 2 2 +-------+ @@ -74,7 +74,7 @@ z := sqrt(a**2 - x**2) --E 5 --S 6 of 25 -1 / z +t2:=1 / z --R --R --R 1 @@ -86,7 +86,7 @@ z := sqrt(a**2 - x**2) --E 6 --S 7 of 25 -integrate(%,x) +integrate(t2,x) --R --R --R +---------+ @@ -98,7 +98,7 @@ integrate(%,x) --E 7 --S 8 of 25 -x**2 * z +t3:=x**2 * z --R --R --R +---------+ @@ -108,7 +108,7 @@ x**2 * z --E 8 --S 9 of 25 -integrate(%,x) +integrate(t3,x) --R --R --R (9) @@ -133,7 +133,7 @@ integrate(%,x) --E 9 --S 10 of 25 -x**3 / (a+b*x)**(1/3) +t4:=x**3 / (a+b*x)**(1/3) --R --R --R 3 @@ -145,7 +145,7 @@ x**3 / (a+b*x)**(1/3) --E 10 --S 11 of 25 -integrate(%,x) +integrate(t4,x) --R --R --R 3 3 2 2 2 3 3+-------+2 @@ -157,7 +157,7 @@ integrate(%,x) --E 11 --S 12 of 25 -1 / (x**3 * (a+b*x)**(1/3)) +t5:=1 / (x**3 * (a+b*x)**(1/3)) --R --R --R 1 @@ -168,7 +168,7 @@ integrate(%,x) --E 12 --S 13 of 25 -integrate(%,x) +integrate(t5,x) --R --R --R (13) @@ -192,7 +192,7 @@ integrate(%,x) Examples of transcendentals over a curve of genus 0 <<*>>= --S 14 of 25 -x / (y + y**2) + log(y + 1) +t6:=x / (y + y**2) + log(y + 1) --R --R --R +-------+ +-------+ @@ -204,7 +204,7 @@ x / (y + y**2) + log(y + 1) --E 14 --S 15 of 25 -integrate(%,x) +integrate(t6,x) --R --R --R (15) @@ -220,7 +220,7 @@ integrate(%,x) --E 15 --S 16 of 25 -(2 + 1/sqrt(x)) * cos(x + sqrt x) +t7:=(2 + 1/sqrt(x)) * cos(x + sqrt x) --R --R --R +-+ +-+ @@ -232,7 +232,7 @@ integrate(%,x) --E 16 --S 17 of 25 -integrate(%,x) +integrate(t7,x) --R --R --R +-+ @@ -244,7 +244,7 @@ integrate(%,x) One which does not have an elementary integral <<*>>= --S 18 of 25 -log(1 + y) / x +t8:=log(1 + y) / x --R --R --R +-------+ @@ -255,13 +255,13 @@ log(1 + y) / x --E 18 --S 19 of 25 -integrate(%,x) +integrate(t8,x) --R --R --R x +--------+ ---R ++ log(\|b + %K a + 1) ---R (19) | -------------------- d%K ---R ++ %K +--I ++ log(\|b + %K a + 1) +--I (19) | -------------------- d%K +--I ++ %K --R Type: Union(Expression Integer,...) --E 19 @@ -269,7 +269,7 @@ integrate(%,x) Integrals of hyperbolic trigs are returned in terms of hyperb. trigs. <<*>>= --S 20 of 25 -(sinh(1+sqrt(x+b))+2*sqrt(x+b))/(sqrt(x+b)*(x+cosh(1+sqrt(x+b)))) +t9:=(sinh(1+sqrt(x+b))+2*sqrt(x+b))/(sqrt(x+b)*(x+cosh(1+sqrt(x+b)))) --R --R --R +-----+ +-----+ @@ -281,7 +281,7 @@ Integrals of hyperbolic trigs are returned in terms of hyperb. trigs. --E 20 --S 21 of 25 -integrate(%,x) +integrate(t9,x) --R --R --R +-----+ @@ -296,7 +296,7 @@ integrate(%,x) Examples of genus 0 functions presented as transcendentals <<*>>= --S 22 of 25 -tan(atan(x)/2) +t10:=tan(atan(x)/2) --R --R --R atan(x) @@ -306,7 +306,7 @@ tan(atan(x)/2) --E 22 --S 23 of 25 -integrate(%,x) +integrate(t10,x) --R --R --R (23) @@ -328,7 +328,7 @@ integrate(%,x) --E 23 --S 24 of 25 -tan(atan(x)/3) +t11:=tan(atan(x)/3) --R --R --R atan(x) @@ -338,7 +338,7 @@ tan(atan(x)/3) --E 24 --S 25 of 25 -integrate(%,x) +integrate(t11,x) --R --R --R atan(x) 2 atan(x) 2 atan(x) diff --git a/src/input/is.input.pamphlet b/src/input/is.input.pamphlet index 8ee12d6..7dd1ade 100644 --- a/src/input/is.input.pamphlet +++ b/src/input/is.input.pamphlet @@ -37,32 +37,37 @@ but we code using the pattern matching syntax: The 'integer' is to return an integer instead of a polynomial \end{verbatim} <<*>>= ---S 1 of 4 +--S 1 of 5 +f: INT -> INT +--R Type: Void +--E 1 + +--S 2 of 5 f n == not empty?(u := Is(n, 2*m%)) => integer eval(m%, u) 3 * n + 1 --R --R Type: Void ---E 1 +--E 2 )set stream showall on @ The function g generates the stream of the repeated applications of f <<*>>= ---S 2 of 4 +--S 3 of 5 g(n:INT):STREAM(INT) == generate(f, n) --R --R Function declaration g : Integer -> Stream Integer has been added to --R workspace. --R Type: Void ---E 2 +--E 3 @ There is a conjecture that g(n) gets into the cycle (1 4 2) for every n <<*>>= ---S 3 of 4 +--S 4 of 5 s := g 27 --R --R Compiling function f with type Integer -> Integer @@ -70,9 +75,9 @@ s := g 27 --R --R (3) [27,82,41,124,62,31,94,47,142,71,...] --R Type: Stream Integer ---E 3 +--E 4 ---S 4 of 4 +--S 5 of 5 extend(s, 150) --R --R @@ -88,7 +93,7 @@ extend(s, 150) --R 10, 5, 16, 8, 4, 2, 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, --R 2, 7, 22, 11, 34, 17, 52, 26, ...] --R Type: Stream Integer ---E 4 +--E 5 )spool )lisp (bye) diff --git a/src/input/kamke3.input.pamphlet b/src/input/kamke3.input.pamphlet index 2d9ac94..fc280ab 100644 --- a/src/input/kamke3.input.pamphlet +++ b/src/input/kamke3.input.pamphlet @@ -1249,7 +1249,7 @@ ode180 := (a*x**2+b*x+c)*(x*D(y(x),x)-y(x)) - y(x)**2 + x**2 --R Type: Expression Integer --E 84 ---S 85 of 139 +--S 85 of 139 random generation, FAILURE OK. yx:=solve(ode180,y,x) --R --R WARNING (genufact): No known algorithm to factor diff --git a/src/input/mapleok.input.pamphlet b/src/input/mapleok.input.pamphlet index c468cb3..1fb777d 100644 --- a/src/input/mapleok.input.pamphlet +++ b/src/input/mapleok.input.pamphlet @@ -662,50 +662,50 @@ in1185a:=integrate((z+1)^(1/2)/(1+z^4), z= 0..1,"noPole") --R ROOT --R +-----------------------------------------+ --R | 2 2 +-+ ---R \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 - 4\|2 %%BC1 +--I \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 - 4\|2 %%BC1 --R + --R +-+ ---R - 4\|2 %%BC0 +--I - 4\|2 %%BC0 --R / --R +-+ --R 2\|2 --R * --R log --R +-+ +-+ +-+ +-+ ---R ((24576\|2 %%BC0 - 768\|2 )%%BC1 - 768\|2 %%BC0 - 48\|2 ) +--I ((24576\|2 %%BC0 - 768\|2 )%%BC1 - 768\|2 %%BC0 - 48\|2 ) --R * --R +-----------------------------------------+ --R | 2 2 ---R \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 +--I \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 --R + --R 2 2 ---R (196608%%BC0 - 6144)%%BC1 + (196608%%BC0 + 384)%%BC1 +--I (196608%%BC0 - 6144)%%BC1 + (196608%%BC0 + 384)%%BC1 --R + --R 2 ---R - 6144%%BC0 + 384%%BC0 + 48 +--I - 6144%%BC0 + 384%%BC0 + 48 --R * --R ROOT --R +-----------------------------------------+ --R | 2 2 ---R \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 +--I \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 --R + --R +-+ +-+ ---R - 4\|2 %%BC1 - 4\|2 %%BC0 +--I - 4\|2 %%BC1 - 4\|2 %%BC0 --R / --R +-+ --R 2\|2 --R + ---R ((- 3072%%BC0 + 384)%%BC1 + 384%%BC0 - 12) +--I ((- 3072%%BC0 + 384)%%BC1 + 384%%BC0 - 12) --R * --R +-----------------------------------------+ --R | 2 2 ---R \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 +--I \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 --R + --R +-+ +-+ 2 ---R (- 12288\|2 %%BC0 + 1536\|2 )%%BC1 +--I (- 12288\|2 %%BC0 + 1536\|2 )%%BC1 --R + --R +-+ 2 +-+ +-+ 2 +-+ ---R (- 12288\|2 %%BC0 + 48\|2 )%%BC1 + 1536\|2 %%BC0 + 48\|2 %%BC0 +--I (- 12288\|2 %%BC0 + 48\|2 )%%BC1 + 1536\|2 %%BC0 + 48\|2 %%BC0 --R + --R +-+ --R 60\|2 @@ -717,55 +717,55 @@ in1185a:=integrate((z+1)^(1/2)/(1+z^4), z= 0..1,"noPole") --R ROOT --R +-----------------------------------------+ --R | 2 2 +-+ ---R \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 - 4\|2 %%BC1 +--I \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 - 4\|2 %%BC1 --R + --R +-+ ---R - 4\|2 %%BC0 +--I - 4\|2 %%BC0 --R / --R +-+ --R 2\|2 --R * --R log ---R ((24576%%BC0 - 768)%%BC1 - 768%%BC0 - 48) +--I ((24576%%BC0 - 768)%%BC1 - 768%%BC0 - 48) --R * --R +-----------------------------------------+ --R | 2 2 ---R \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 +--I \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 --R + --R +-+ +-+ 2 ---R (98304\|2 %%BC0 - 3072\|2 )%%BC1 +--I (98304\|2 %%BC0 - 3072\|2 )%%BC1 --R + --R +-+ 2 +-+ +-+ 2 ---R (98304\|2 %%BC0 + 192\|2 )%%BC1 - 3072\|2 %%BC0 +--I (98304\|2 %%BC0 + 192\|2 )%%BC1 - 3072\|2 %%BC0 --R + --R +-+ +-+ ---R 192\|2 %%BC0 + 24\|2 +--I 192\|2 %%BC0 + 24\|2 --R * --R ROOT --R +-----------------------------------------+ --R | 2 2 ---R \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 +--I \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 --R + --R +-+ +-+ ---R - 4\|2 %%BC1 - 4\|2 %%BC0 +--I - 4\|2 %%BC1 - 4\|2 %%BC0 --R / --R +-+ --R 2\|2 --R + ---R ((- 3072%%BC0 + 384)%%BC1 + 384%%BC0 - 12) +--I ((- 3072%%BC0 + 384)%%BC1 + 384%%BC0 - 12) --R * --R +-----------------------------------------+ --R | 2 2 ---R \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 +--I \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 --R + --R +-+ +-+ 2 ---R (- 12288\|2 %%BC0 + 1536\|2 )%%BC1 +--I (- 12288\|2 %%BC0 + 1536\|2 )%%BC1 --R + --R +-+ 2 +-+ +-+ 2 ---R (- 12288\|2 %%BC0 + 48\|2 )%%BC1 + 1536\|2 %%BC0 +--I (- 12288\|2 %%BC0 + 48\|2 )%%BC1 + 1536\|2 %%BC0 --R + --R +-+ +-+ ---R 48\|2 %%BC0 + 42\|2 +--I 48\|2 %%BC0 + 42\|2 --R / --R +-+ --R \|2 @@ -774,56 +774,56 @@ in1185a:=integrate((z+1)^(1/2)/(1+z^4), z= 0..1,"noPole") --R ROOT --R +-----------------------------------------+ --R | 2 2 +-+ ---R - \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 - 4\|2 %%BC1 +--I - \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 - 4\|2 %%BC1 --R + --R +-+ ---R - 4\|2 %%BC0 +--I - 4\|2 %%BC0 --R / --R +-+ --R 2\|2 --R * --R log --R +-+ +-+ +-+ ---R (24576\|2 %%BC0 - 768\|2 )%%BC1 - 768\|2 %%BC0 +--I (24576\|2 %%BC0 - 768\|2 )%%BC1 - 768\|2 %%BC0 --R + --R +-+ --R - 48\|2 --R * --R +-----------------------------------------+ --R | 2 2 ---R \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 +--I \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 --R + --R 2 ---R (- 196608%%BC0 + 6144)%%BC1 +--I (- 196608%%BC0 + 6144)%%BC1 --R + --R 2 2 ---R (- 196608%%BC0 - 384)%%BC1 + 6144%%BC0 - 384%%BC0 - 48 +--I (- 196608%%BC0 - 384)%%BC1 + 6144%%BC0 - 384%%BC0 - 48 --R * --R ROOT --R +-----------------------------------------+ --R | 2 2 ---R - \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 +--I - \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 --R + --R +-+ +-+ ---R - 4\|2 %%BC1 - 4\|2 %%BC0 +--I - 4\|2 %%BC1 - 4\|2 %%BC0 --R / --R +-+ --R 2\|2 --R + ---R ((3072%%BC0 - 384)%%BC1 - 384%%BC0 + 12) +--I ((3072%%BC0 - 384)%%BC1 - 384%%BC0 + 12) --R * --R +-----------------------------------------+ --R | 2 2 ---R \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 +--I \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 --R + --R +-+ +-+ 2 ---R (- 12288\|2 %%BC0 + 1536\|2 )%%BC1 +--I (- 12288\|2 %%BC0 + 1536\|2 )%%BC1 --R + --R +-+ 2 +-+ +-+ 2 ---R (- 12288\|2 %%BC0 + 48\|2 )%%BC1 + 1536\|2 %%BC0 +--I (- 12288\|2 %%BC0 + 48\|2 )%%BC1 + 1536\|2 %%BC0 --R + --R +-+ +-+ ---R 48\|2 %%BC0 + 60\|2 +--I 48\|2 %%BC0 + 60\|2 --R / --R +-+ --R \|2 @@ -831,52 +831,52 @@ in1185a:=integrate((z+1)^(1/2)/(1+z^4), z= 0..1,"noPole") --R ROOT --R +-----------------------------------------+ --R | 2 2 +-+ ---R - \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 - 4\|2 %%BC1 +--I - \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 - 4\|2 %%BC1 --R + --R +-+ ---R - 4\|2 %%BC0 +--I - 4\|2 %%BC0 --R / --R +-+ --R 2\|2 --R * --R log ---R ((24576%%BC0 - 768)%%BC1 - 768%%BC0 - 48) +--I ((24576%%BC0 - 768)%%BC1 - 768%%BC0 - 48) --R * --R +-----------------------------------------+ --R | 2 2 ---R \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 +--I \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 --R + --R +-+ +-+ 2 ---R (- 98304\|2 %%BC0 + 3072\|2 )%%BC1 +--I (- 98304\|2 %%BC0 + 3072\|2 )%%BC1 --R + --R +-+ 2 +-+ +-+ 2 ---R (- 98304\|2 %%BC0 - 192\|2 )%%BC1 + 3072\|2 %%BC0 +--I (- 98304\|2 %%BC0 - 192\|2 )%%BC1 + 3072\|2 %%BC0 --R + --R +-+ +-+ ---R - 192\|2 %%BC0 - 24\|2 +--I - 192\|2 %%BC0 - 24\|2 --R * --R ROOT --R +-----------------------------------------+ --R | 2 2 ---R - \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 +--I - \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 --R + --R +-+ +-+ ---R - 4\|2 %%BC1 - 4\|2 %%BC0 +--I - 4\|2 %%BC1 - 4\|2 %%BC0 --R / --R +-+ --R 2\|2 --R + ---R ((3072%%BC0 - 384)%%BC1 - 384%%BC0 + 12) +--I ((3072%%BC0 - 384)%%BC1 - 384%%BC0 + 12) --R * --R +-----------------------------------------+ --R | 2 2 ---R \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 +--I \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 --R + --R +-+ +-+ 2 ---R (- 12288\|2 %%BC0 + 1536\|2 )%%BC1 +--I (- 12288\|2 %%BC0 + 1536\|2 )%%BC1 --R + --R +-+ 2 +-+ +-+ 2 +-+ ---R (- 12288\|2 %%BC0 + 48\|2 )%%BC1 + 1536\|2 %%BC0 + 48\|2 %%BC0 +--I (- 12288\|2 %%BC0 + 48\|2 )%%BC1 + 1536\|2 %%BC0 + 48\|2 %%BC0 --R + --R +-+ --R 42\|2 @@ -888,55 +888,55 @@ in1185a:=integrate((z+1)^(1/2)/(1+z^4), z= 0..1,"noPole") --R ROOT --R +-----------------------------------------+ --R | 2 2 +-+ ---R - \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 - 4\|2 %%BC1 +--I - \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 - 4\|2 %%BC1 --R + --R +-+ ---R - 4\|2 %%BC0 +--I - 4\|2 %%BC0 --R / --R +-+ --R 2\|2 --R * --R log ---R ((- 24576%%BC0 + 768)%%BC1 + 768%%BC0 + 48) +--I ((- 24576%%BC0 + 768)%%BC1 + 768%%BC0 + 48) --R * --R +-----------------------------------------+ --R | 2 2 ---R \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 +--I \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 --R + --R +-+ +-+ 2 ---R (98304\|2 %%BC0 - 3072\|2 )%%BC1 +--I (98304\|2 %%BC0 - 3072\|2 )%%BC1 --R + --R +-+ 2 +-+ +-+ 2 ---R (98304\|2 %%BC0 + 192\|2 )%%BC1 - 3072\|2 %%BC0 +--I (98304\|2 %%BC0 + 192\|2 )%%BC1 - 3072\|2 %%BC0 --R + --R +-+ +-+ ---R 192\|2 %%BC0 + 24\|2 +--I 192\|2 %%BC0 + 24\|2 --R * --R ROOT --R +-----------------------------------------+ --R | 2 2 ---R - \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 +--I - \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 --R + --R +-+ +-+ ---R - 4\|2 %%BC1 - 4\|2 %%BC0 +--I - 4\|2 %%BC1 - 4\|2 %%BC0 --R / --R +-+ --R 2\|2 --R + ---R ((3072%%BC0 - 384)%%BC1 - 384%%BC0 + 12) +--I ((3072%%BC0 - 384)%%BC1 - 384%%BC0 + 12) --R * --R +-----------------------------------------+ --R | 2 2 ---R \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 +--I \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 --R + --R +-+ +-+ 2 ---R (- 12288\|2 %%BC0 + 1536\|2 )%%BC1 +--I (- 12288\|2 %%BC0 + 1536\|2 )%%BC1 --R + --R +-+ 2 +-+ +-+ 2 ---R (- 12288\|2 %%BC0 + 48\|2 )%%BC1 + 1536\|2 %%BC0 +--I (- 12288\|2 %%BC0 + 48\|2 )%%BC1 + 1536\|2 %%BC0 --R + --R +-+ +-+ ---R 48\|2 %%BC0 + 42\|2 +--I 48\|2 %%BC0 + 42\|2 --R / --R +-+ --R \|2 @@ -944,53 +944,53 @@ in1185a:=integrate((z+1)^(1/2)/(1+z^4), z= 0..1,"noPole") --R ROOT --R +-----------------------------------------+ --R | 2 2 +-+ ---R - \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 - 4\|2 %%BC1 +--I - \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 - 4\|2 %%BC1 --R + --R +-+ ---R - 4\|2 %%BC0 +--I - 4\|2 %%BC0 --R / --R +-+ --R 2\|2 --R * --R log --R +-+ +-+ +-+ ---R (- 24576\|2 %%BC0 + 768\|2 )%%BC1 + 768\|2 %%BC0 +--I (- 24576\|2 %%BC0 + 768\|2 )%%BC1 + 768\|2 %%BC0 --R + --R +-+ --R 48\|2 --R * --R +-----------------------------------------+ --R | 2 2 ---R \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 +--I \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 --R + --R 2 2 ---R (196608%%BC0 - 6144)%%BC1 + (196608%%BC0 + 384)%%BC1 +--I (196608%%BC0 - 6144)%%BC1 + (196608%%BC0 + 384)%%BC1 --R + --R 2 ---R - 6144%%BC0 + 384%%BC0 + 48 +--I - 6144%%BC0 + 384%%BC0 + 48 --R * --R ROOT --R +-----------------------------------------+ --R | 2 2 ---R - \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 +--I - \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 --R + --R +-+ +-+ ---R - 4\|2 %%BC1 - 4\|2 %%BC0 +--I - 4\|2 %%BC1 - 4\|2 %%BC0 --R / --R +-+ --R 2\|2 --R + ---R ((3072%%BC0 - 384)%%BC1 - 384%%BC0 + 12) +--I ((3072%%BC0 - 384)%%BC1 - 384%%BC0 + 12) --R * --R +-----------------------------------------+ --R | 2 2 ---R \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 +--I \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 --R + --R +-+ +-+ 2 ---R (- 12288\|2 %%BC0 + 1536\|2 )%%BC1 +--I (- 12288\|2 %%BC0 + 1536\|2 )%%BC1 --R + --R +-+ 2 +-+ +-+ 2 +-+ ---R (- 12288\|2 %%BC0 + 48\|2 )%%BC1 + 1536\|2 %%BC0 + 48\|2 %%BC0 +--I (- 12288\|2 %%BC0 + 48\|2 )%%BC1 + 1536\|2 %%BC0 + 48\|2 %%BC0 --R + --R +-+ --R 60\|2 @@ -1001,52 +1001,52 @@ in1185a:=integrate((z+1)^(1/2)/(1+z^4), z= 0..1,"noPole") --R ROOT --R +-----------------------------------------+ --R | 2 2 +-+ ---R \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 - 4\|2 %%BC1 +--I \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 - 4\|2 %%BC1 --R + --R +-+ ---R - 4\|2 %%BC0 +--I - 4\|2 %%BC0 --R / --R +-+ --R 2\|2 --R * --R log ---R ((- 24576%%BC0 + 768)%%BC1 + 768%%BC0 + 48) +--I ((- 24576%%BC0 + 768)%%BC1 + 768%%BC0 + 48) --R * --R +-----------------------------------------+ --R | 2 2 ---R \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 +--I \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 --R + --R +-+ +-+ 2 ---R (- 98304\|2 %%BC0 + 3072\|2 )%%BC1 +--I (- 98304\|2 %%BC0 + 3072\|2 )%%BC1 --R + --R +-+ 2 +-+ +-+ 2 ---R (- 98304\|2 %%BC0 - 192\|2 )%%BC1 + 3072\|2 %%BC0 +--I (- 98304\|2 %%BC0 - 192\|2 )%%BC1 + 3072\|2 %%BC0 --R + --R +-+ +-+ ---R - 192\|2 %%BC0 - 24\|2 +--I - 192\|2 %%BC0 - 24\|2 --R * --R ROOT --R +-----------------------------------------+ --R | 2 2 ---R \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 +--I \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 --R + --R +-+ +-+ ---R - 4\|2 %%BC1 - 4\|2 %%BC0 +--I - 4\|2 %%BC1 - 4\|2 %%BC0 --R / --R +-+ --R 2\|2 --R + ---R ((- 3072%%BC0 + 384)%%BC1 + 384%%BC0 - 12) +--I ((- 3072%%BC0 + 384)%%BC1 + 384%%BC0 - 12) --R * --R +-----------------------------------------+ --R | 2 2 ---R \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 +--I \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 --R + --R +-+ +-+ 2 ---R (- 12288\|2 %%BC0 + 1536\|2 )%%BC1 +--I (- 12288\|2 %%BC0 + 1536\|2 )%%BC1 --R + --R +-+ 2 +-+ +-+ 2 +-+ ---R (- 12288\|2 %%BC0 + 48\|2 )%%BC1 + 1536\|2 %%BC0 + 48\|2 %%BC0 +--I (- 12288\|2 %%BC0 + 48\|2 )%%BC1 + 1536\|2 %%BC0 + 48\|2 %%BC0 --R + --R +-+ --R 42\|2 @@ -1058,189 +1058,189 @@ in1185a:=integrate((z+1)^(1/2)/(1+z^4), z= 0..1,"noPole") --R ROOT --R +-----------------------------------------+ --R | 2 2 +-+ ---R \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 - 4\|2 %%BC1 +--I \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 - 4\|2 %%BC1 --R + --R +-+ ---R - 4\|2 %%BC0 +--I - 4\|2 %%BC0 --R / --R +-+ --R 2\|2 --R * --R log --R +-+ +-+ +-+ ---R (- 24576\|2 %%BC0 + 768\|2 )%%BC1 + 768\|2 %%BC0 +--I (- 24576\|2 %%BC0 + 768\|2 )%%BC1 + 768\|2 %%BC0 --R + --R +-+ --R 48\|2 --R * --R +-----------------------------------------+ --R | 2 2 ---R \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 +--I \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 --R + --R 2 ---R (- 196608%%BC0 + 6144)%%BC1 +--I (- 196608%%BC0 + 6144)%%BC1 --R + --R 2 2 ---R (- 196608%%BC0 - 384)%%BC1 + 6144%%BC0 - 384%%BC0 - 48 +--I (- 196608%%BC0 - 384)%%BC1 + 6144%%BC0 - 384%%BC0 - 48 --R * --R ROOT --R +-----------------------------------------+ --R | 2 2 ---R \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 +--I \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 --R + --R +-+ +-+ ---R - 4\|2 %%BC1 - 4\|2 %%BC0 +--I - 4\|2 %%BC1 - 4\|2 %%BC0 --R / --R +-+ --R 2\|2 --R + ---R ((- 3072%%BC0 + 384)%%BC1 + 384%%BC0 - 12) +--I ((- 3072%%BC0 + 384)%%BC1 + 384%%BC0 - 12) --R * --R +-----------------------------------------+ --R | 2 2 ---R \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 +--I \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 --R + --R +-+ +-+ 2 ---R (- 12288\|2 %%BC0 + 1536\|2 )%%BC1 +--I (- 12288\|2 %%BC0 + 1536\|2 )%%BC1 --R + --R +-+ 2 +-+ +-+ 2 ---R (- 12288\|2 %%BC0 + 48\|2 )%%BC1 + 1536\|2 %%BC0 +--I (- 12288\|2 %%BC0 + 48\|2 )%%BC1 + 1536\|2 %%BC0 --R + --R +-+ +-+ ---R 48\|2 %%BC0 + 60\|2 +--I 48\|2 %%BC0 + 60\|2 --R / --R +-+ --R \|2 --R + --R - --R +------+ ---R \|4%%BC1 +--I \|4%%BC1 --R * --R log --R +-+ +-+ 2 ---R (98304\|2 %%BC0 - 3072\|2 )%%BC1 +--I (98304\|2 %%BC0 - 3072\|2 )%%BC1 --R + --R +-+ 2 +-+ +-+ 3 ---R (98304\|2 %%BC0 + 192\|2 )%%BC1 + 98304\|2 %%BC0 +--I (98304\|2 %%BC0 + 192\|2 )%%BC1 + 98304\|2 %%BC0 --R + --R +-+ +-+ ---R 768\|2 %%BC0 - 36\|2 +--I 768\|2 %%BC0 - 36\|2 --R * --R +------+ ---R \|4%%BC1 +--I \|4%%BC1 --R + --R 2 2 ---R (12288%%BC0 - 1536)%%BC1 + (12288%%BC0 - 48)%%BC1 +--I (12288%%BC0 - 1536)%%BC1 + (12288%%BC0 - 48)%%BC1 --R + --R 3 ---R 12288%%BC0 + 96%%BC0 + 18 +--I 12288%%BC0 + 96%%BC0 + 18 --R + --R +------+ ---R \|4%%BC1 +--I \|4%%BC1 --R * --R log --R 2 2 ---R (98304%%BC0 - 3072)%%BC1 + (98304%%BC0 + 192)%%BC1 +--I (98304%%BC0 - 3072)%%BC1 + (98304%%BC0 + 192)%%BC1 --R + --R 3 ---R 98304%%BC0 + 768%%BC0 - 36 +--I 98304%%BC0 + 768%%BC0 - 36 --R * --R +------+ ---R \|4%%BC1 +--I \|4%%BC1 --R + --R 2 2 3 ---R (12288%%BC0 - 1536)%%BC1 + (12288%%BC0 - 48)%%BC1 + 12288%%BC0 +--I (12288%%BC0 - 1536)%%BC1 + (12288%%BC0 - 48)%%BC1 + 12288%%BC0 --R + ---R 96%%BC0 + 9 +--I 96%%BC0 + 9 --R + --R - --R +------+ ---R \|4%%BC1 +--I \|4%%BC1 --R * --R log --R 2 2 ---R (- 98304%%BC0 + 3072)%%BC1 + (- 98304%%BC0 - 192)%%BC1 +--I (- 98304%%BC0 + 3072)%%BC1 + (- 98304%%BC0 - 192)%%BC1 --R + --R 3 ---R - 98304%%BC0 - 768%%BC0 + 36 +--I - 98304%%BC0 - 768%%BC0 + 36 --R * --R +------+ ---R \|4%%BC1 +--I \|4%%BC1 --R + --R 2 2 ---R (12288%%BC0 - 1536)%%BC1 + (12288%%BC0 - 48)%%BC1 +--I (12288%%BC0 - 1536)%%BC1 + (12288%%BC0 - 48)%%BC1 --R + --R 3 ---R 12288%%BC0 + 96%%BC0 + 9 +--I 12288%%BC0 + 96%%BC0 + 9 --R + --R +------+ ---R \|4%%BC1 +--I \|4%%BC1 --R * --R log --R +-+ +-+ 2 ---R (- 98304\|2 %%BC0 + 3072\|2 )%%BC1 +--I (- 98304\|2 %%BC0 + 3072\|2 )%%BC1 --R + --R +-+ 2 +-+ +-+ 3 ---R (- 98304\|2 %%BC0 - 192\|2 )%%BC1 - 98304\|2 %%BC0 +--I (- 98304\|2 %%BC0 - 192\|2 )%%BC1 - 98304\|2 %%BC0 --R + --R +-+ +-+ ---R - 768\|2 %%BC0 + 36\|2 +--I - 768\|2 %%BC0 + 36\|2 --R * --R +------+ ---R \|4%%BC1 +--I \|4%%BC1 --R + --R 2 2 3 ---R (12288%%BC0 - 1536)%%BC1 + (12288%%BC0 - 48)%%BC1 + 12288%%BC0 +--I (12288%%BC0 - 1536)%%BC1 + (12288%%BC0 - 48)%%BC1 + 12288%%BC0 --R + ---R 96%%BC0 + 18 +--I 96%%BC0 + 18 --R + --R +------+ ---R \|4%%BC0 +--I \|4%%BC0 --R * --R log --R +-+ 3 +-+ 2 +-+ +-+ ---R (98304\|2 %%BC0 + 3072\|2 %%BC0 + 576\|2 %%BC0 - 60\|2 ) +--I (98304\|2 %%BC0 + 3072\|2 %%BC0 + 576\|2 %%BC0 - 60\|2 ) --R * --R +------+ ---R \|4%%BC0 +--I \|4%%BC0 --R + --R 3 2 ---R - 12288%%BC0 - 1536%%BC0 - 144%%BC0 + 30 +--I - 12288%%BC0 - 1536%%BC0 - 144%%BC0 + 30 --R + --R - --R +------+ ---R \|4%%BC0 +--I \|4%%BC0 --R * --R log --R 3 2 +------+ ---R (98304%%BC0 + 3072%%BC0 + 576%%BC0 - 60)\|4%%BC0 +--I (98304%%BC0 + 3072%%BC0 + 576%%BC0 - 60)\|4%%BC0 --R + --R 3 2 ---R - 12288%%BC0 - 1536%%BC0 - 144%%BC0 + 21 +--I - 12288%%BC0 - 1536%%BC0 - 144%%BC0 + 21 --R + --R +------+ ---R \|4%%BC0 +--I \|4%%BC0 --R * --R log --R 3 2 +------+ ---R (- 98304%%BC0 - 3072%%BC0 - 576%%BC0 + 60)\|4%%BC0 +--I (- 98304%%BC0 - 3072%%BC0 - 576%%BC0 + 60)\|4%%BC0 --R + --R 3 2 ---R - 12288%%BC0 - 1536%%BC0 - 144%%BC0 + 21 +--I - 12288%%BC0 - 1536%%BC0 - 144%%BC0 + 21 --R + --R - --R +------+ ---R \|4%%BC0 +--I \|4%%BC0 --R * --R log --R +-+ 3 +-+ 2 +-+ +-+ ---R (- 98304\|2 %%BC0 - 3072\|2 %%BC0 - 576\|2 %%BC0 + 60\|2 ) +--I (- 98304\|2 %%BC0 - 3072\|2 %%BC0 - 576\|2 %%BC0 + 60\|2 ) --R * --R +------+ ---R \|4%%BC0 +--I \|4%%BC0 --R + --R 3 2 ---R - 12288%%BC0 - 1536%%BC0 - 144%%BC0 + 30 +--I - 12288%%BC0 - 1536%%BC0 - 144%%BC0 + 30 --R / --R 4 --R Type: Union(f1: OrderedCompletion Expression Integer,...) @@ -2116,7 +2116,7 @@ in13:=integrate(cos(z)^2*sin(z)^n, z) --R --R z --R ++ 2 n ---R (48) | cos(%K) sin(%K) d%K +--I (48) | cos(%K) sin(%K) d%K --R ++ --R Type: Union(Expression Integer,...) --E 49 @@ -2818,8 +2818,8 @@ in160:=integrate((-z^2-z)^sin(z), z) --R --R --R z ---R ++ 2 sin(%K) ---R (79) | (- %K - %K) d%K +--I ++ 2 sin(%K) +--I (79) | (- %K - %K) d%K --R ++ --R Type: Union(Expression Integer,...) --E 80 @@ -3006,10 +3006,10 @@ in161:=integrate((-z^2)^(1/3), z) in163:=integrate(log(z)*abs(exp(z)/z), z) --R --R ---R z %K +--I z %K --R ++ %e ---R (98) | log(%K)abs(----)d%K ---R ++ %K +--I (98) | log(%K)abs(----)d%K +--I ++ %K --R Type: Union(Expression Integer,...) --E 100 @@ -3018,8 +3018,8 @@ in166:=integrate((1+z)^z, z) --R --R --R z ---R ++ %K ---R (99) | (%K + 1) d%K +--I ++ %K +--I (99) | (%K + 1) d%K --R ++ --R Type: Union(Expression Integer,...) --E 101 diff --git a/src/input/mathml.input.pamphlet b/src/input/mathml.input.pamphlet index 461f32c..0cbcf7b 100644 --- a/src/input/mathml.input.pamphlet +++ b/src/input/mathml.input.pamphlet @@ -209,15 +209,17 @@ y:=operator 'y --S 14 of 21 D(y(x,z),[x,x,z,x]) +--R --R --R (14) y (x,z) --R ,1,1,2,1 --R ---R∂4y∂x3∂z(x,z) +--Ry,1,1,2,1(x,z) --R --R --R Type: Expression Integer --E 14 + )clear all --S 15 of 21 @@ -234,12 +236,13 @@ y:=operator 'y --S 16 of 21 D(y x,x,2) +--R --R --R ,, --R (2) y (x) --R --R ---Rⅆ2yⅆx2⁡(x) +--Ry′′⁡(x) --R --R --R Type: Expression Integer diff --git a/src/input/ndftip.input.pamphlet b/src/input/ndftip.input.pamphlet index 7b838a5..bbed72e 100644 --- a/src/input/ndftip.input.pamphlet +++ b/src/input/ndftip.input.pamphlet @@ -298,6 +298,7 @@ hdftA := nagHermitianDFT seqA; --R Cannot convert from type Polynomial Integer to Vector Complex Float --R for value --R hdftA +--R --E 19 -- + 2.48361 + -- | | @@ -361,6 +362,7 @@ dftC :: Vector Float --RDaly Bug --R Cannot convert from type Variable dftC to Vector Float for value --R dftC +--R --E 22 -- [1.82616,1.86862,- 0.017503,0.502001,- 0.598725,- 0.0314404,- 2.62557] @@ -824,7 +826,7 @@ nagDFT badSeqs --RDaly Bug --R Cannot find a definition or applicable library operation named --R nagDFT with argument type(s) ---R List Symbol +--R Variable badSeqs --R --R Perhaps you should use "@" to indicate the required return type, --R or "$" to specify which version of the function you need. diff --git a/src/input/pmint.input.pamphlet b/src/input/pmint.input.pamphlet index 280ab6e..ede0da7 100644 --- a/src/input/pmint.input.pamphlet +++ b/src/input/pmint.input.pamphlet @@ -22,7 +22,7 @@ @ \section{Rational Functions} <<*>>= ---S 1 of 28 +--S 1 of 29 f:=(x^7-24*x^4-4*x^2+8*x-8)/(x^8+6*x^6+12*x^4+8*x^2) --R --R @@ -34,7 +34,7 @@ f:=(x^7-24*x^4-4*x^2+8*x-8)/(x^8+6*x^6+12*x^4+8*x^2) --R Type: Fraction Polynomial Integer --E 1 ---S 2 of 28 +--S 2 of 29 g:=integrate(f,x) --R --R @@ -46,7 +46,7 @@ g:=integrate(f,x) --R Type: Union(Expression Integer,...) --E 2 ---S 3 of 28 +--S 3 of 29 differentiate(g,x) --R --R @@ -63,7 +63,7 @@ differentiate(g,x) @ \section{Trigonometric Functions} <<*>>= ---S 4 of 28 +--S 4 of 29 f:=(x-tan(x))/tan(x)^2 + tan(x) --R --R @@ -75,7 +75,7 @@ f:=(x-tan(x))/tan(x)^2 + tan(x) --R Type: Expression Integer --E 4 ---S 5 of 28 +--S 5 of 29 g:=integrate(f,x) --R --R @@ -86,7 +86,7 @@ g:=integrate(f,x) --R Type: Union(Expression Integer,...) --E 5 ---S 6 of 28 +--S 6 of 29 differentiate(g,x) --R --R @@ -102,8 +102,8 @@ differentiate(g,x) @ \section{Log-Exp Functions} - ---S 7 of 28 +<<*>>= +--S 7 of 29 f:=(1+x+x*exp(x))*(x+log(x)+exp(x)-1)/(x+log(x)+exp(x))^2/x --R --R @@ -115,7 +115,7 @@ f:=(1+x+x*exp(x))*(x+log(x)+exp(x)-1)/(x+log(x)+exp(x))^2/x --R Type: Expression Integer --E 7 ---S 8 of 28 +--S 8 of 29 g:=integrate(f,x) --R --R @@ -127,7 +127,7 @@ g:=integrate(f,x) --R Type: Union(Expression Integer,...) --E 8 ---S 9 of 28 +--S 9 of 29 differentiate(g,x) --R --R @@ -144,7 +144,7 @@ differentiate(g,x) @ \section{Liouvillian special functions} <<*>>= ---S 10 of 28 +--S 10 of 29 f:=exp(-x^2)+erf(x)/(erf(x)^3-erf(x)^2-erf(x)+1) --R --R @@ -157,82 +157,154 @@ f:=exp(-x^2)+erf(x)/(erf(x)^3-erf(x)^2-erf(x)+1) --R Type: Expression Integer --E 10 ---S 11 of 28 +--S 11 of 29 +g:=integrate(f,x) +--R +--R 2 +--I x 3 2 - %G +--I ++ (erf(%G) - erf(%G) - erf(%G) + 1)%e + erf(%G) +--I (2) | ---------------------------------------------------- d%G +--R ++ 3 2 +--I erf(%G) - erf(%G) - erf(%G) + 1 +--R Type: Union(Expression Integer,...) +--E 11 + +--S 12 of 29 +differentiate(g,x) +--R +--R 2 +--R 3 2 - x +--R (erf(x) - erf(x) - erf(x) + 1)%e + erf(x) +--R (3) ----------------------------------------------- +--R 3 2 +--R erf(x) - erf(x) - erf(x) + 1 +--R Type: Expression Integer +--E 12 + +)clear all + +--S 13 of 29 f:=(exp(-x^2)+erf(x))/(erf(x)^3-erf(x)^2-erf(x)+1) --R --R --R 2 --R - x --R %e + erf(x) ---R (2) ------------------------------ +--R (1) ------------------------------ --R 3 2 --R erf(x) - erf(x) - erf(x) + 1 --R Type: Expression Integer ---E 11 +--E 13 ---S 12 of 28 used to work! -integrate(f,x) +--S 14 of 29 used to work! +g:=integrate(f,x) --R --R --R 2 ---R x - %G ---R ++ %e + erf(%G) ---R (3) | --------------------------------- d%G +--I x - %G +--I ++ %e + erf(%G) +--I (3) | --------------------------------- d%G --R ++ 3 2 ---R erf(%G) - erf(%G) - erf(%G) + 1 +--I erf(%G) - erf(%G) - erf(%G) + 1 --R Type: Union(Expression Integer,...) ---E 12 +--E 14 -- should be: -- 1 sqrt(%pi) 1 1 -- - - ------------ - - sqrt(%pi) log(erf(x)+1) + - sqrt(%pi) log(erf(x)-1) -- 4 erf(x) - 1 8 8 +--S 15 of 29 +differentiate(g,x) +--R +--R 2 +--R - x +--R %e + erf(x) +--R (3) ------------------------------ +--R 3 2 +--R erf(x) - erf(x) - erf(x) + 1 +--R Type: Expression Integer +--E 15 + )clear all @ \section{Airy Functions} <<*>>= -- Axiom does not have a 2 argument form of the airyAi function ---S 13 of 28 will certainly fail -f:=(x-airyAi(x)*airyAi(1,x))/(x^2-airyAi(x)^2) ---R ---E 13 - ---S 14 of 28 will certainly fail -integrate(f,x) +-- f:=(x-airyAi(x)*airyAi(1,x))/(x^2-airyAi(x)^2) +--it has the integral --R --R 1 1 --R - log(x+airyAi(x)) + - log(x-airyAi(x)) --R 2 2 ---E 14 ---S 15 of 28 + +--S 16 of 29 will certainly fail +f:=(x-airyAi(x))/(x^2-airyAi(x)^2) +--R +--R 1 +--R (1) ------------- +--R airyAi(x) + x +--R Type: Expression Integer +--E 16 + +--S 17 of 29 will certainly fail +g:=integrate(f,x) +--R +--R x +--R ++ 1 +--R (2) | --------------- d%G +--R ++ airyAi(%G) + %G +--R Type: Union(Expression Integer,...) +--E 17 + +--S 18 of 29 +differentiate(g,x) +--R +--R 1 +--R (3) ------------- +--R airyAi(x) + x +--R Type: Expression Integer +--E 18 + +)clear all + +--S 19 of 29 f:=x^2*airyAi(x) --R --R --R 2 --R (1) x airyAi(x) --R Type: Expression Integer ---E 15 +--E 19 ---S 16 of 28 used to work +--S 20 of 29 used to work g:=integrate(f,x) --R --R --R x --R ++ 2 ---R (2) | %G airyAi(%G)d%G +--I (2) | %G airyAi(%G)d%G --R ++ --R Type: Union(Expression Integer,...) ---E 16 +--E 20 -- should be: -- -airyAi(x) + airyAi(1,x) x +--S 21 of 29 +differentiate(g,x) +--R +--R 2 +--R (3) x airyAi(x) +--R Type: Expression Integer +--E 21 + )clear all @ \section{Bessel functions} ---S 17 of 28 +<<*>>= +--S 22 of 29 f:=besselJ(y+1,x)/besselJ(y,x) --R --R @@ -240,49 +312,96 @@ f:=besselJ(y+1,x)/besselJ(y,x) --R (1) ---------------- --R besselJ(y,x) --R Type: Expression Integer ---E 17 +--E 22 ---S 18 of 28 used to work +--S 23 of 29 used to work g:=integrate(f,x) --R --R --R x ---R ++ besselJ(y + 1,%G) ---R (2) | ----------------- d%G ---R ++ besselJ(y,%G) +--I ++ besselJ(y + 1,%G) +--I (2) | ----------------- d%G +--I ++ besselJ(y,%G) --R Type: Union(Expression Integer,...) ---E 18 +--E 23 -- should be: -- y log(x) - log(besselJ(y,x)) +--S 24 of 29 +differentiate(g,x) +--R +--R besselJ(y + 1,x) +--R (3) ---------------- +--R besselJ(y,x) +--R Type: Expression Integer +--E 24 + +)clear all + + -- Axiom does not have Maple's normal function ---S 19 of 28 used to work -f:=normal(y*besselJ(y,x)/x = besselJ(y+1,x)) +--S 25 of 29 used to work +--f:=normal(y*besselJ(y,x)/x - besselJ(y+1,x)) +f:=y*besselJ(y,x)/x - besselJ(y+1,x) --R ---E 19 --- should be: --- besselJ(y+1,x) x - y besselJ(y,x) --- - --------------------------------- --- x +--R - x besselJ(y + 1,x) + y besselJ(y,x) +--R (1) ------------------------------------- +--R x +--R Type: Expression Integer +--E 25 + +--S 26 of 29 +g:=integrate(f,x) +--R +--R x +--I ++ - %G besselJ(y + 1,%G) + y besselJ(y,%G) +--I (2) | ---------------------------------------- d%G +--I ++ %G +--R Type: Union(Expression Integer,...) +--E 26 +--S 27 of 29 +differentiate(g,x) +--R +--R - x besselJ(y + 1,x) + y besselJ(y,x) +--R (3) ------------------------------------- +--R x +--R Type: Expression Integer +--E 27 )clear all @ \section{Whittaker functions} ---S 20 of 28 used to work +<<*>>= +--S 28 of 29 used to work f:=WhittakerW(u+1,n,x)/(WhittakerW(u,n,x)*x) ---R ---E 20 +--R +--R There are no library operations named WhittakerW +--R Use HyperDoc Browse or issue +--R )what op WhittakerW +--R to learn if there is any operation containing " WhittakerW " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R WhittakerW with argument type(s) +--R Polynomial Integer +--R Variable n +--R Variable x +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 28 + -- Axiom does not implement WhittakerW -- should be: -- Whittaker(u+1,n,x) -- ------------------ -- Whittaker(u,n,x) x ---S 21 of 28 used to work -integrate(f,x) ---R ---E 21 +-- of 29 used to work +--integrate(f,x) +-- 22 -- should be: -- x -- - - u log(x) - log(WhattakerW(u,n,x)) @@ -294,25 +413,36 @@ integrate(f,x) \section{The Lambert W function} <<*>>= -- Axiom does not implement LambertW ---S 22 of 28 used to work +--S 29 of 29 used to work f:=LambertW(x) ---R ---E 22 - ---S 23 of 28 used to work -g:=integrate(f,x) ---R ---E 23 +--R +--R There are no library operations named LambertW +--R Use HyperDoc Browse or issue +--R )what op LambertW +--R to learn if there is any operation containing " LambertW " in its +--R name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R LambertW with argument type(s) +--R Variable x +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 29 + +-- of 29 used to work +-- g:=integrate(f,x) +-- 24 -- should be: -- 2 2 2 2 -- x + LambertW(x) x - LambertW(x) x -- ------------------------------------ -- x LambertW(x) ---S 24 of 28 used to work -integrate(sin(LambertW(x)),x) ---R ---E 24 +-- of 29 used to work +-- integrate(sin(LambertW(x)),x) +-- 25 --should be: -- +- -+ -- | 2 | @@ -343,10 +473,9 @@ integrate(sin(LambertW(x)),x) -- | +- -+ | -- +- -+ ---S 25 of 28 used to work -f:=((x^2+2)*LambertW(x^2)^2+x^2*(2*LambertW(x^2)+1))/(x*(1+LambertW(x^2)^3)) ---R ---E 25 +-- of 29 used to work +--f:=((x^2+2)*LambertW(x^2)^2+x^2*(2*LambertW(x^2)+1))/(x*(1+LambertW(x^2)^3)) +-- 26 --should be: -- 2 -- 2 2 2 2 @@ -356,10 +485,9 @@ f:=((x^2+2)*LambertW(x^2)^2+x^2*(2*LambertW(x^2)+1))/(x*(1+LambertW(x^2)^3)) -- 2 -- x (1 + LambertW(x )) ---S 26 of 28 used to work -integrate(f,x) ---R ---E 26 +-- of 29 used to work +--integrate(f,x) +-- 27 --should be: -- 2 4 --1 4 2 4 2 x 2 2 2 2 @@ -374,10 +502,10 @@ integrate(f,x) -- 2 -- log(1 + LambertW(x )) ---S 27 of 28 used to work -f:=(2*LambertW(x^2)*cos(LambertW(x^2))*(a*x+LambertW(x^2))+a*x*(1+LambertW(x^2)) + 2*LambertW(x^2))/((1+LambertW(x^2))*(a*x+LambertW(x^2))*x) ---R ---E 27 +-- of 29 used to work +--f:=(2*LambertW(x^2)*cos(LambertW(x^2))*(a*x+LambertW(x^2))+a*x*(1+LambertW(x^2)) + 2*LambertW(x^2))/((1+LambertW(x^2))*(a*x+LambertW(x^2))*x) +-- +-- 28 --+- -+ --| | --| 2 2 2 | @@ -392,10 +520,10 @@ f:=(2*LambertW(x^2)*cos(LambertW(x^2))*(a*x+LambertW(x^2))+a*x*(1+LambertW(x^2)) -- (1 + LambertW(x ))(a x+LambertW(x )) x -- ---S 28 of 28 used to work +-- 29 of 29 used to work integrate(f,x) ---R ---E 28 +-- +-- 29 -- -- +- -+ -- | 1 2 | diff --git a/src/input/r20bugs.input.pamphlet b/src/input/r20bugs.input.pamphlet index b28c18b..d91d6ff 100644 --- a/src/input/r20bugs.input.pamphlet +++ b/src/input/r20bugs.input.pamphlet @@ -196,7 +196,8 @@ positiveRemainder(-1::SINT,-5::SINT) complexRoots([u**2-v+1,v**2-4],[u,v],0.01) --R --R ---R (1) [[1.732421875 %i,- 2.0],[- 1.732421875 %i,- 2.0],[- 1.0,2.0],[1.0,2.0]] +--R (1) +--R [[1.732421875 %i,- 2.0],[- 1.732421875 %i,- 2.0],[- 1.0,2.0],[1.0,2.0]] --R Type: List List Complex Float --E 17 diff --git a/src/input/summation.input.pamphlet b/src/input/summation.input.pamphlet index 78b7aa7..a1e2c42 100644 --- a/src/input/summation.input.pamphlet +++ b/src/input/summation.input.pamphlet @@ -16,6 +16,7 @@ This is bug 7057: summation is ambiguous. <<*>>= )spool summation.output )set message test on +)set output mathml on )set message auto off )clear all diff --git a/src/scripts/tex/axiom.sty b/src/scripts/tex/axiom.sty index fdd8e27..3581b97 100755 --- a/src/scripts/tex/axiom.sty +++ b/src/scripts/tex/axiom.sty @@ -943,6 +943,8 @@ I'll try to avoid such incompatible changes in the future.}% % We use providecommand so it doesn't clash with amsmath package \providecommand{\eth}[1]{{#1}-th} +% add the binom function for combfunc +\providecommand{\binom}[2]{\left(\begin{array}{c}#1\\#2\end{array}\right)} % spadcommands are the actual text that you type at the axiom prompt \providecommand{\spadcommand}[1]%