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# Edit detail for SandBox revision 31 of 161

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 Editor: greg Time: 2008/03/15 05:13:00 GMT-7 Note:

added:

From greg Sat Mar 15 05:12:56 -0700 2008
From: greg
Date: Sat, 15 Mar 2008 05:12:56 -0700
Subject:
Message-ID: <20080315051256-0700@axiom-wiki.newsynthesis.org>

\begin{aldor}

#include "axiom"

fact(n: PositiveInteger): PositiveInteger == {
n <= 1 => 1;
res: PositiveInteger := 1;
while n > 1 repeat {
res := res * n;
n := n-1;
}
res
}
\end{aldor}

\begin{fricas}
fact 4
\end{fricas}


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 Axiom and Reduce. Please be curteous 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 click Save 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 who subscribe directly to MathAction?.

## Use Preview

If you click Preview instead of Save, 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 click Save or not.

## Use the SandBox

On this page or on any other page with a name beginning with SandBox? such as SandBoxJohn2?, SandBoxSimple?, SandBoxEtc?, clicking Save only sends email notices to users who subscribe directly to that specific SandBox? page. Saving and adding comments does not create an email to the email list. You can safely use these pages for testing without disturbing anyone who might not care to know about your experiments.

## New SandBox Pages

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.

[SandBox Aldor Category Theory]?
based on "Prospects for Category Theory in Aldor" by Saul Youssef, 2004 http://atlas.bu.edu/~youssef/papers/math/aldor/aldor.pdf
[SandBox Aldor Foreign]?
Using Aldor to call external C routines
[SandBox Aldor Generator]?
Aldor defines a generator for type Vector
[SandBox Aldor Join and Meet]?
Aldor has category constructor named Meet which appears to be analogous to (but opposite of) Join.
[SandBox Aldor Semantics]?
exports and constants
[SandBox Aldor Sieve]?
A prime number sieve in Aldor to count primes <= n.
[SandBox Aldor Testing]?
Using Aldor to write Axiom library routines
[SandBox Arrays]?
How fast is array access in Axiom?
[SandBox Axiom Syntax]?
Syntax of if then else
[SandBox Boolean]?
evaluating Boolean expressions and conditions
[SandBox Cast]?
Meaning and use of pretend vs. strong typing
[SandBox Categorical Relativity]?
Special relativity without the Lorentz group
[SandBox Category of Graphs]?
Graph theory in Axiom
[SandBox CL-WEB]?
Tangle operation for literate programming implemented in Common Lisp
[SandBox Combinat]?
A{ld,xi}o{r,m}Combinat
[SandBox Content MathML]?
Content vs. presentation MathML?

SandBoxCS224?

[SandBox Direct Product]?
A x B
[SandBox DistributedExpression]?
expression in sum-of-products form
[SandBox Domains and Types]?
What is the difference?
[AxiomEmacsMode]?
Beginnings of an Emacs mode for Axiom based off of Jay's work and others
[SandBox Embeded PDF]?
pdf format documents can be displayed inline
[SandBox EndPaper]?
Algebra and Data Structure Hierarchy (lattice) diagrams
[SandBox Folding]?
experiments with DHTML, javascript, etc.
[SandBox Functions]?
How do they work?
[SandBox Functors]?
What are they? In Axiom functors are also called domain constructors.
[SandBox Gamma]?
Numerical evaluation of the incomplete Gamma function
[SandBox GuessingSequence]?
Guessing integer sequences
[SandBox Integration]?
Examples of integration in Axiom and Reduce
[SandBox Kernel]?
What is a "kernel"?

[SandBox kaveh]?

[SandBox LaTeX]?
LaTeX? commands allowed in MathAction?
[SandBox Lisp]?
Using Lisp in Axiom
[SandBox Manip]?
expression manipulations
[SandBox Manipulating Domains]?
testing the domain of an expression
[SandBox Mapping]?
A->B is a type in Axiom

[MathMLFormat]?

[SandBox Matrix]?
Examples of working with matrices in Axiom
[SandBox Maxima]?
Testing the Maxima interface
[SandBox Monoid]?
Rings and things
[SandBox Monoid Extend]?
Martin Rubey's beautiful idea about using extend to add a category to a previously defined domain.
[SandBox Noncommutative Polynomials]?
XPOLY and friends
[SandBox Numerical Integration]?
Simpson method
[SandBox NNI]?
NonNegative? Integer without using SubDomain?
[SandBox Pamphlet]?
[Literate Programming]? support on MathAction?
[SandBoxPartialFraction]?
Trigonometric expansion example
SandBoxPfaffian?
Computing the Pfaffian of a square matrix
[SandBox Polymake]?
an interface between Axiom and PolyMake?
[SandBox Polynomials]?
Axiom's polynomial domains are certainly rich and complex!
[SandBox ProblemSolving]?
Test page for educational purposes
[SandBox Qubic]?
Solving cubic polynomials
[SandBox Reduce And MathML]?
Reduce can use MathML? for both input and output
[SandBox Reflection in Aldor]?
a reflection framework
[SandBoxRelativeVelocity]?
Slides for IARD 2006: Addition of Relative Velocites is Associative
[SandBox RenameTitle]?
trying to re-create a crash due to renaming pages
[SandBox Sage]?
This is a test of Sage in MathAction?
[SandBox Shortcoming]?
Implementation of solve
[SandBox Solve]?
Solving equations
[SandBox Statistics]?
calculating statistics in Axiom
[SandBox SubDomain]?
What is a SubDomain??
[SandBox Tail Recursion]?
When does Axiom replace recursion with iteration?
[SandBox Text Files]?
How to access text files in Axiom
[SandBox Trace Analysed]?
Tracing can affect output of 1::EXPR INT or 1::FRAC INT
[SandBox Tuples Products and Records]?
Basic structured data types in Axiom
[SandBox Units and Dimensions]?
Scientific units and dimensions
Domain construction
[SandBox Speed]?
Compilation speed

[SandBox Zero]?

[SandBox Axiom Strengths]?

SandBoxJohn2?
Experiments with matrices and various other stuff
SandBox2?
Experiments
SandBox3?
Experiments
SandBox4?
Experiments
SandBox5?
Experiments with GraphViz? and StructuredTables?
SandBox6?
Differential Equations etc.
[SandBox7]?
[SandBox8]?
Here you can create your own SandBox?.
[SandBox9]?
Experiments with JET Bundles
[SandBox10]?
Miscellaneous
[SandBox11]?
Miscellaneous

[[SandBox12TestIndetAndComplex]]?

[SandBox DoOps]?
used to run Axiom without actually have to have it installed!

[SandBoxKMG]?

[SandBoxDGE]?

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.

## Examples

Here is a simple Axiom command:

    \begin{axiom}
integrate(1/(a+z^3), z=0..1,"noPole")
\end{axiom}


axiomintegrate(1/(a+z^3), z=0..1,"noPole")
 (1)
Type: Union(f1: OrderedCompletion? Expression Integer,...)

And here is a REDUCE command:

  \begin{reduce}
int(1/(a+z^3), z,0,1);
\end{reduce}


 load_package sfgamma; load_package defint; *** gamma declared operator *** ci already defined as operator *** si already defined as operator int(1/(a+z^3), z,0,1); reduce

## Common Mistakes

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]?.

int(1/(a+z^3), z,0,1);
Sat, 24 Nov 2007 08:14:35 -0800 reply
int(1/(a+z^3), z,0,1)
Sat, 24 Nov 2007 08:15:26 -0800 reply

Test long lines --page, Mon, 26 Nov 2007 19:29:57 -0800 reply
[SandBoxVeryLongLaTeX]?

Francois Maltey --Bill Page, Fri, 18 Jan 2008 13:22:29 -0800 reply
[SandBox Complementsdalgebrelineaire]?

page for testing friCAS --Bill Page, Mon, 18 Feb 2008 11:16:46 -0800 reply
SandBoxFriCAS?

Aldor compiler problem? --Bill Page, Fri, 14 Mar 2008 07:30:19 -0700 reply
[SandBoxEcfact]?

... --greg,  Sat, 15 Mar 2008 05:12:56 -0700 replyaldor#include "axiom"
fact(n: PositiveInteger): PositiveInteger == {
n <= 1 => 1;
res: PositiveInteger := 1;
while n > 1 repeat {
res := res * n;
n := n-1;
}
res
}
aldor   Compiling FriCAS source code from file
/var/zope2/var/LatexWiki/5597251742083727311-25px001.as using
AXIOM-XL compiler and options
-O -Fasy -Fao -Flsp -laxiom -Mno-AXL_W_WillObsolete -DAxiom -Y \$AXIOM/algebra
Use the system command )set compiler args to change these
options.
#1 (Warning) Deprecated message prefix: use ALDOR_' instead of _AXL'
Compiling Lisp source code from file
./5597251742083727311-25px001.lsp
Issuing )library command for 5597251742083727311-25px001
\begin{fricas}
fact 4
\end{fricas}

Some or all expressions may not have rendered properly, because Latex returned the following error:
This is pdfeTeX, Version 3.141592-1.21a-2.2 (Web2C 7.5.4)
\write18 enabled.
entering extended mode
(./5720973349192907468-18.0px.tex
LaTeX2e <2003/12/01>
Babel <v3.8d> and hyphenation patterns for american, french, german, ngerman, b
ahasa, basque, bulgarian, catalan, croatian, czech, danish, dutch, esperanto, e
stonian, finnish, greek, icelandic, irish, italian, latin, magyar, norsk, polis
h, portuges, romanian, russian, serbian, slovak, slovene, spanish, swedish, tur
(/usr/share/texmf-tetex/tex/latex/base/article.cls
Document Class: article 2004/02/16 v1.4f Standard LaTeX document class
(/usr/share/texmf-tetex/tex/latex/base/size12.clo))
(/usr/share/texmf-tetex/tex/latex/amsmath/amsmath.sty
For additional information on amsmath, use the ?' option.
(/usr/share/texmf-tetex/tex/latex/amsmath/amstext.sty
(/usr/share/texmf-tetex/tex/latex/amsmath/amsgen.sty))
(/usr/share/texmf-tetex/tex/latex/amsmath/amsbsy.sty)
(/usr/share/texmf-tetex/tex/latex/amsmath/amsopn.sty))
(/usr/share/texmf-tetex/tex/latex/amsfonts/amsfonts.sty)
(/usr/share/texmf-tetex/tex/latex/amsfonts/amssymb.sty)
(/usr/share/texmf-tetex/tex/latex/amscls/amsthm.sty)
(/usr/share/texmf-tetex/tex/generic/xypic/xy.sty
(/usr/share/texmf-tetex/tex/generic/xypic/xy.tex Bootstrap'ing: catcodes,
docmode, (/usr/share/texmf-tetex/tex/generic/xypic/xyrecat.tex)
(/usr/share/texmf-tetex/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.

utility macros; pictures: \xy, positions, objects, decorations;
kernel objects: directionals, circles, text; options; algorithms: directions,
(/usr/share/texmf-tetex/tex/generic/xypic/xyall.tex
Xy-pic option: All features v.3.3
(/usr/share/texmf-tetex/tex/generic/xypic/xycurve.tex
Xy-pic option: Curve and Spline extension v.3.7 curve, circles, loaded)
(/usr/share/texmf-tetex/tex/generic/xypic/xyframe.tex
Xy-pic option: Frame and Bracket extension v.3.7 loaded)
(/usr/share/texmf-tetex/tex/generic/xypic/xycmtip.tex
Xy-pic option: Computer Modern tip extension v.3.3
(/usr/share/texmf-tetex/tex/generic/xypic/xytips.tex
(/usr/share/texmf-tetex/tex/generic/xypic/xyline.tex
Xy-pic option: Line styles extension v.3.6 loaded)
(/usr/share/texmf-tetex/tex/generic/xypic/xyrotate.tex
Xy-pic option: Rotate and Scale extension v.3.3 loaded)
(/usr/share/texmf-tetex/tex/generic/xypic/xycolor.tex
Xy-pic option: Colour extension v.3.3 loaded)
(/usr/share/texmf-tetex/tex/generic/xypic/xymatrix.tex
Xy-pic option: Matrix feature v.3.4 loaded)
(/usr/share/texmf-tetex/tex/generic/xypic/xyarrow.tex
Xy-pic option: Arrow and Path feature v.3.5 path, \ar, loaded)
(/usr/share/texmf-tetex/tex/generic/xypic/xygraph.tex
(/usr/share/texmf-tetex/tex/latex/graphics/graphicx.sty
(/usr/share/texmf-tetex/tex/latex/graphics/keyval.sty)
(/usr/share/texmf-tetex/tex/latex/graphics/graphics.sty
(/usr/share/texmf-tetex/tex/latex/graphics/trig.sty)
(/usr/share/texmf-tetex/tex/latex/graphics/graphics.cfg)
(/usr/share/texmf-tetex/tex/latex/graphics/dvips.def)))
(/usr/share/texmf-tetex/tex/latex/tools/verbatim.sty)
(/usr/share/texmf-tetex/tex/latex/graphviz/graphviz.sty
(/usr/share/texmf-tetex/tex/latex/psfrag/psfrag.sty))
(/usr/share/texmf-tetex/tex/latex/sage/sagetex.sty
Writing sage input file 5720973349192907468-18.0px.sage
(./5720973349192907468-18.0px.sout)) (./5720973349192907468-18.0px.aux) LaTeX Error: Environment fricas undefined.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
...
l.60 \begin{fricas}
LaTeX Error: \begin{document} ended by \end{fricas}.
See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
...
l.62 \end{fricas}
[1] (./5720973349192907468-18.0px.aux) )
(see the transcript file for additional information)
Output written on 5720973349192907468-18.0px.dvi (1 page, 228 bytes).
Transcript written on 5720973349192907468-18.0px.log.
`