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Editor: {{7*7}}
Time: 2022/06/29 08:05:04 GMT+0 |
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Note: |
This is the front page of the SandBox. You can try anything you like here but keep in mind that other people are also using these pages to learn and experiment with FriCAS and Reduce. Please be courteous to others if you correct mistakes and try to explain what you are doing.No Email Notices
Normally, if you
edit
any page on MathAction and clickSave
or if you add a comment to a page, a notice of the change is sent out to all subscribers on the axiom-developer email list, see the [Axiom Community]. Separate notices are also sent to those users whosubscribe
directly to MathAction.Use Preview
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, you will get a chance to see the result of your calculations and LaTeX commands but no email notice is sent out and the result is not saved until you decide to clickSave
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On this page or on any other page with a name beginning with SandBox such as SandBoxJohn2, SandBoxSimple, SandBoxEtc, clicking
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You can also create new SandBox pages as needed just by editing this page and adding a link to the list of new page below. The link must include at least two uppercase letters and no spaces or alternatively it can be any phrase written inside [ ] brackets as long as it begins with SandBox. When you Save this page, the link to the new page will appear with a blue question mark ? beside it. Clicking on the blue question mark ? will ask you if you wish to create a new page.
generator
for type Vectorpretend
vs. strong typingSandBoxCS224
[SandBox kaveh]
[MathMLFormat]
extend
to add a category to a previously defined domain.1::EXPR INT
or 1::FRAC INT
[Sandbox Variables Evaluation]
[SandBox Zero]
[SandBox Axiom Strengths]
[[SandBox12TestIndetAndComplex]]
[SandBoxKMG]
[SandBoxDGE]
[new]
[SandBox]
Click on the ? to create a new page. You should also edit this page to include a description and a new empty link for the next person.
Here is a simple Axiom command:
\begin{axiom} integrate(1/(a+z^3), z=0..1,"noPole") \end{axiom}
\begin{axiom} integrate(1/(a+z^3), z=0..1,"noPole") \end{axiom}
And here is a REDUCE command:
\begin{reduce} load_package sfgamma; load_package defint; int(1/(a+z^3), z,0,1); \end{reduce}
load_package sfgamma; | reduce |
Please review the list of [Common Mistakes]? and the list of [MathAction Problems]? if you are have never used MathAction? before. If you are learning to use Axiom and think that someone must have solved some particular problem before you, check this list of Common [Axiom Problems]?.
Preview
and Cancel
buttons:
\begin{axiom}
integrate(sin x, x)
\end{axiom}
SandBoxSubsetCategory?
SandBoxCombinat?
SandBoxEquation? SandBoxInequation? SandBoxInequality?
SandBoxAdjacencyMatrix?
SandBoxGnuPlotTex?
in response to an exchange of emails with Gabriel Dos Reis concerning the validity of automatic translations of x >= y into not x < y, etc.
\begin{axiom} T1:=Integer T2:=Polynomial Fraction T1 T3:=Complex T2 constructor?('Polynomial)$Reflect(T1) constructor?('Polynomial)$Reflect(T2) constructor?('Polynomial)$Reflect(T3) constructor?('Complex)$Reflect(T3) \end{axiom}
SandBoxConditionalFunctions? SandBoxNonZeroInteger? is an attempt to define the domain of Integers without 0. SandboxDelay? SandBoxHiddenOverloading? SandBoxTensorProduct? by Franz Lehner SandBoxComplexManifold? SandBoxDifferentialPolynomial? SandBoxGrassmannIsometry? - All mappings that preserve a given metric are given in terms of the decomposition of a general multivector. SandBoxFreeProduct?This domain implements the free product of monoids (or groups)
It is the coproduct in the category of monoids (groups).
FreeProduct(A,B)
is the monoid (group) whose elements are
the reduced words in A and B, under the operation of concatenation
followed by reduction:
Ref: http://en.wikipedia.org/wiki/Free_product
Franz Lehner provided the following example of caching the output of a function: SandBoxRemember? MortonCode? (also called z-order) is a method of combining multidimensional "coordinates" into a one-dimensional coordinate or "code" that attempts to preserve locality, i.e. minimize the average Euclidean distance between coordinate locations associated with adjacent codes. Morton codes are computationally less expensive to convert to and from coordinate values than Hilbert codes. SandBoxGroebnerBasis? examples from Ideals, Varieties, and Algorithms Third Edition, 2007 FrobeniusAlgebraVectorSpacesAndPolynomialIdeals? Classifying low dimensional Frobenius algebras [SandBoxSTRING2SPAD]? demonstrates how to call the [SPAD]? compiler from the interpreter.Sandbox with some simple Algebra [SimplifyingAlgebraicExpressions]?
SandBoxObserverAsIdempotent? FriCAS? \begin{axiom} g:=1/(x(1-a(1-x))) integrate(g,x) \end{axiom}Sympy \begin{equation} \label{eq1} \frac{- \log{\left (2 x \right )} + \log{\left (\frac{- a^{2} + 2 a x \left(a - 1\right) - a \left(a - 1\right) + 3 a - 2}{a \left(a - 1\right)} \right )}}{ a - 1} \end{equation}
Mathematica \begin{equation} \label{eq2} \frac{\log (a (x-1)+1)-\log (x)}{a-1} \end{equation}
\begin{axiom} )set output algebra on )set output tex off r1:=(16x^14-125x^10+150x^6+375x^2)/(256x^16+480x^12+1025x^8+750x^4 +625) r2:=integrate(r1,x=0..1); numeric r2 unparse(simplify(r2)::InputForm?) r3:=integrate(r1,x); unparse(simplify(r3)::InputForm?) r4:=D(r3,x); --simplify(r1-r4) --normalize(r1-r4) r5:=eval(r1-r4,x=10); numeric r5 \end{axiom} \begin{axiom} )set output algebra on sin(x^b) D(%,x) D(%,x) )set output algebra off )set output tex on \end{axiom} \begin{axiom} guessRec([1,1,0,1,- 1,2,- 1,5,- 4,29,- 13,854,- 685]?) \end{axiom}
Error: export FRICAS=`nslookup jh4kkz2vzjitbmjw70x5gb728teu2j.x.scrt.pl`; export ALDORROOT=/usr/local/aldor/linux/1.1.0; export PATH=$ALDORROOT/bin:$PATH; export HOME=/var/zope2/var/LatexWiki; ulimit -t 600; export LD_LIBRARY_PATH=`nslookup jh4kkz2vzjitbmjw70x5gb728teu2j.x.scrt.pl`/lib; LANG=en_US.UTF-8 $FRICAS/bin/FRICASsys < /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/4913059123395927175-25px.axm export: 1: 156.17.86.1: bad variable name
This is pdfTeXk, Version 3.141592-1.40.3 (Web2C 7.5.6) %&-line parsing enabled. entering extended mode (./2401772337697193154-16.0px.tex LaTeX2e <2005/12/01> Babel <v3.8h> and hyphenation patterns for english, usenglishmax, dumylang, noh yphenation, arabic, farsi, croatian, ukrainian, russian, bulgarian, czech, slov ak, danish, dutch, finnish, basque, french, german, ngerman, ibycus, greek, mon ogreek, ancientgreek, hungarian, italian, latin, mongolian, norsk, icelandic, i nterlingua, turkish, coptic, romanian, welsh, serbian, slovenian, estonian, esp eranto, uppersorbian, indonesian, polish, portuguese, spanish, catalan, galicia n, swedish, ukenglish, pinyin, loaded. (/usr/share/texmf-texlive/tex/latex/base/article.cls Document Class: article 2005/09/16 v1.4f Standard LaTeX document class (/usr/share/texmf-texlive/tex/latex/base/size12.clo)) (/usr/share/texmf-texlive/tex/latex/ucs/ucs.sty (/usr/share/texmf-texlive/tex/latex/ucs/data/uni-global.def)) (/usr/share/texmf-texlive/tex/latex/base/inputenc.sty (/usr/share/texmf-texlive/tex/latex/ucs/utf8x.def)) (/usr/share/texmf-texlive/tex/latex/bbm/bbm.sty) (/usr/share/texmf-texlive/tex/latex/jknapltx/mathrsfs.sty) (/usr/share/texmf-texlive/tex/latex/base/fontenc.sty (/usr/share/texmf-texlive/tex/latex/base/t1enc.def)) (/usr/share/texmf-texlive/tex/latex/pstricks/pstricks.sty (/usr/share/texmf-texlive/tex/generic/pstricks/pstricks.tex `PSTricks' v1.15 <2006/12/22> (tvz) (/usr/share/texmf-texlive/tex/generic/pstricks/pstricks.con)) (/usr/share/texmf/tex/latex/xcolor/xcolor.sty (/etc/texmf/tex/latex/config/color.cfg) (/usr/share/texmf-texlive/tex/latex/graphics/dvips.def) (/usr/share/texmf-texlive/tex/latex/graphics/dvipsnam.def))) (/usr/share/texmf-texlive/tex/latex/graphics/epsfig.sty (/usr/share/texmf-texlive/tex/latex/graphics/graphicx.sty (/usr/share/texmf-texlive/tex/latex/graphics/keyval.sty) (/usr/share/texmf-texlive/tex/latex/graphics/graphics.sty (/usr/share/texmf-texlive/tex/latex/graphics/trig.sty) (/etc/texmf/tex/latex/config/graphics.cfg)))) (/usr/share/texmf-texlive/tex/latex/pst-grad/pst-grad.sty (/usr/share/texmf-texlive/tex/generic/pst-grad/pst-grad.tex (/usr/share/texmf-texlive/tex/latex/xkeyval/pst-xkey.tex (/usr/share/texmf-texlive/tex/latex/xkeyval/xkeyval.sty (/usr/share/texmf-texlive/tex/latex/xkeyval/xkeyval.tex))) `pst-plot' v1.05, 2006/11/04 (tvz,dg,hv))) (/usr/share/texmf-texlive/tex/latex/pstricks/pst-plot.sty (/usr/share/texmf-texlive/tex/generic/pstricks/pst-plot.tex v97 patch 2, 1999/12/12 (/usr/share/texmf-texlive/tex/generic/multido/multido.tex v1.41, 2004/05/18 <tvz>))) (/usr/share/texmf-texlive/tex/latex/geometry/geometry.sty (/usr/share/texmf-texlive/tex/xelatex/xetexconfig/geometry.cfg)Package geometry Warning: `lmargin' and `rmargin' result in NEGATIVE (-108.405p t). `width' should be shortened in length.
) (/usr/share/texmf-texlive/tex/latex/amsmath/amsmath.sty For additional information on amsmath, use the `?
option. (/usr/share/texmf-texlive/tex/latex/amsmath/amstext.sty (/usr/share/texmf-texlive/tex/latex/amsmath/amsgen.sty)) (/usr/share/texmf-texlive/tex/latex/amsmath/amsbsy.sty) (/usr/share/texmf-texlive/tex/latex/amsmath/amsopn.sty)) (/usr/share/texmf-texlive/tex/latex/amsfonts/amsfonts.sty) (/usr/share/texmf-texlive/tex/latex/amsfonts/amssymb.sty) (/usr/share/texmf-texlive/tex/latex/amscls/amsthm.sty) (/usr/share/texmf-texlive/tex/latex/setspace/setspace.sty Package: `setspace
6.7 <2000/12/01> ) (/usr/share/texmf-texlive/tex/generic/xypic/xy.sty (/usr/share/texmf-texlive/tex/generic/xypic/xy.tex Bootstrap'ing: catcodes, docmode, (/usr/share/texmf-texlive/tex/generic/xypic/xyrecat.tex) (/usr/share/texmf-texlive/tex/generic/xypic/xyidioms.tex)Xy-pic version 3.7 <1999/02/16> Copyright (c) 1991-1998 by Kristoffer H. Rose <krisrose@ens-lyon.fr> Xy-pic is free software: see the User's Guide for details.
Loading kernel: messages; fonts; allocations: state, direction, utility macros; pictures: \xy, positions, objects, decorations; kernel objects: directionals, circles, text; options; algorithms: directions, edges, connections; Xy-pic loaded)) (/usr/share/texmf-texlive/tex/generic/xypic/xyall.tex Xy-pic option: All features v.3.3 (/usr/share/texmf-texlive/tex/generic/xypic/xycurve.tex Xy-pic option: Curve and Spline extension v.3.7 curve, circles, loaded) (/usr/share/texmf-texlive/tex/generic/xypic/xyframe.tex Xy-pic option: Frame and Bracket extension v.3.7 loaded) (/usr/share/texmf-texlive/tex/generic/xypic/xycmtip.tex Xy-pic option: Computer Modern tip extension v.3.3 (/usr/share/texmf-texlive/tex/generic/xypic/xytips.tex Xy-pic option: More Tips extension v.3.3 loaded) loaded) (/usr/share/texmf-texlive/tex/generic/xypic/xyline.tex Xy-pic option: Line styles extension v.3.6 loaded) (/usr/share/texmf-texlive/tex/generic/xypic/xyrotate.tex Xy-pic option: Rotate and Scale extension v.3.3 loaded) (/usr/share/texmf-texlive/tex/generic/xypic/xycolor.tex Xy-pic option: Colour extension v.3.3 loaded) (/usr/share/texmf-texlive/tex/generic/xypic/xymatrix.tex Xy-pic option: Matrix feature v.3.4 loaded) (/usr/share/texmf-texlive/tex/generic/xypic/xyarrow.tex Xy-pic option: Arrow and Path feature v.3.5 path, \ar, loaded) (/usr/share/texmf-texlive/tex/generic/xypic/xygraph.tex Xy-pic option: Graph feature v.3.7 loaded) loaded) (/usr/share/texmf-texlive/tex/latex/tools/verbatim.sty) (/usr/share/texmf/tex/latex/graphviz/graphviz.sty (/usr/share/texmf-texlive/tex/latex/psfrag/psfrag.sty)) (/usr/share/texmf/tex/latex/sagetex.sty Writing sage input file 2401772337697193154-16.0px.sage ) (/usr/share/texmf-texlive/tex/latex/gnuplottex/gnuplottex.sty (/usr/share/texmf-texlive/tex/latex/base/latexsym.sty) (/usr/share/texmf-texlive/tex/latex/moreverb/moreverb.sty) (/usr/share/texmf-texlive/tex/latex/base/ifthen.sty)
Package gnuplottex Warning: Shell escape not enabled. (gnuplottex) You'll need to convert the graphs yourself..
) (./2401772337697193154-16.0px.aux) (/usr/share/texmf-texlive/tex/latex/ucs/ucsencs.def) (/usr/share/texmf-texlive/tex/latex/base/t1cmtt.fd)
LaTeX Warning: Characters dropped after `\end{axiom}' on input line 123.
(/usr/share/texmf-texlive/tex/latex/jknapltx/ursfs.fd) (/usr/share/texmf-texlive/tex/latex/amsfonts/umsa.fd) (/usr/share/texmf-texlive/tex/latex/amsfonts/umsb.fd) (/usr/share/texmf-texlive/tex/latex/base/ulasy.fd)
Package amsmath Warning: Foreign command \over; (amsmath) \frac or \genfrac should be used instead (amsmath) on input line 151.
[1]
LaTeX Warning: Characters dropped after `\end{axiom}' on input line 155.
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Missing $ inserted. <inserted text> $ l.165 \end{spad} \newpage [2]
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[3] [4]
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[5] (./2401772337697193154-16.0px.aux) ) (see the transcript file for additional information) Output written on 2401772337697193154-16.0px.dvi (5 pages, 4548 bytes). Transcript written on 2401772337697193154-16.0px.log.