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last edited 2 months ago by Martin Baker

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Editor: Martin Baker Time: 2011/11/17 07:31:51 GMT-8
Note:

changed:
-<a href="http://www.earlypaypdays.co.uk">payday loans</a> for people in the uk needing fast cash credit
[SandBoxCategoryTerms] -- Category theory terminology used in SPAD

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 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 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
SandBoxCL-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?
SandboxTypeDefinitions: What does the type means for you?
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 Functional Addition: "adding" two functions
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 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 Units and Dimensions: Scientific units and dimensions
SandBox Spad: Domain construction
SandBox Speed: Compilation speed

SandBox Zero

SandBox Axiom Strengths

SandBoxJohn2: Experiments with matrices and various other stuff
SandBox2: Experiments
SandBox3: Experiments
SandBoxSymbolicInverseTrig: Experiments
SandBoxGraphviz: Experiments with GraphViz and StructuredTables
SandBoxDifferentialEquations: Differential Equations etc.
SandBoxMatrixExample
SandBoxRotationMatrix: Here you can create your own SandBox.
SandBox9: Experiments with JET Bundles
SandBoxGnuDraw: Miscellaneous
SandBox11: Miscellaneous

SandBox12TestIndetAndComplex

SandBox13: Solving some nonlinear differential equations
SandBox42: Miscellaneous
SandBox DoOps: used to run Axiom without actually have to have it installed!

SandBoxKMG

SandBoxDGE

SandBoxMLE: Maximum likelihood estimation (statistics)
SandBoxFisher: Fisher's exact test for 2x2 tables (statistics)
SandBoxNewtonsMethod: Newton's method for numerically solving f(x)=0 (with examples of calling Axiom expressions and Spad functions from Lisp).
SandBoxVeryLongLaTeX: Test long lines
SandBox Complementsdalgebrelineaire: Francois Maltey
SandBoxFriCAS: page for testing friCAS
SandBoxEcfact: Aldor compiler problem?
SandBoxMyReduce: calling reduce with empty list
SandBoxCategoryTerms: Category theory terminology used in SPAD

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}

axiom

integrate(1/(a+z^3), z=0..1,"noPole")

$\label{eq1}{\left( \begin{array}{@{}l} \displaystyle -{{\sqrt{3}}\ {\log{\left({{3 \ {a^2}\ {{\root{3}\of{a^2}}^2}}+{{\left(-{2 \ {a^3}}+{a^2}\right)}\ {\root{3}\of{a^2}}}+{a^4}-{2 \ {a^3}}}\right)}}}+{2 \ {\sqrt{3}}\ {\log \left({{{\root{3}\of{a^2}}^2}+{2 \ a \ {\root{3}\of{a^2}}}+{a^2}}\right)}}+ \ \ \displaystyle {{12}\ {\arctan \left({{{2 \ {\sqrt{3}}\ {\root{3}\of{a^2}}}-{a \ {\sqrt{3}}}}\over{3 \ a}}\right)}}+{2 \ \pi}$

(1)

Type: Union(f1: OrderedCompletion?(Expression(Integer)),...)

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;

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

$\displaylines{\qdd \frac{a^{\frac{1}{ 3}}\cdot \(6\cdot \sqrt{3}\cdot \atan \(\frac{2\cdot a^{\frac{2}{ 3}}\cdot \sqrt{3} - \sqrt{3}\cdot a}{ 3\cdot a}$

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.

... --meliusja, Tue, 08 Apr 2008 10:33:39 -0700 reply

axiom

solve(a*x+b,x)

$\label{eq2}\left[{x = -{b \over a}}\right]$

(2)

Type: List(Equation(Fraction(Polynomial(Integer))))

exploring --Bill Page, Thu, 24 Apr 2008 07:00:25 -0700 reply

SandBoxNonAssociativeAlgebra

lexical scope --Bill Page, Sun, 11 May 2008 06:43:30 -0700 reply

Testing lexical scoping rules in SandBoxLexicalScope.

examples of overloading in SPAD --Bill Page, Fri, 16 May 2008 09:40:58 -0700 reply

SandBoxOverloading

Combinatorial Sum --Bill Page, Fri, 16 May 2008 13:38:20 -0700 reply

SandBoxSum (like Product)

Symbolic computations --Bill Page, Thu, 22 May 2008 12:58:29 -0700 reply

SandBoxSymbolic

add inheritance issue --Bill Page, Sun, 25 May 2008 11:26:13 -0700 reply

For example: SandBoxLeftFreeModule

Added Preview and Cancel to comment form --page, Tue, 27 May 2008 15:08:43 -0700 reply

This is a test of the Preview and Cancel buttons:

axiom

integrate(sin x, x)

$\label{eq3}-{\cos \left({x}\right)}$

(3)

Type: Union(Expression(Integer),...)

software archeology discovers another --Bill Page, Fri, 30 May 2008 21:01:37 -0700 reply

SandBoxSubsetCategory

try iso-experiment/combinat --Bill Page, Tue, 03 Jun 2008 13:24:13 -0700 reply

SandBoxCombinat

Equation, Inequation, and Inequality --Bill Page, Mon, 09 Jun 2008 18:28:56 -0700 reply

SandBoxEquation SandBoxInequation SandBoxInequality?

test aldor code --Bill Page, Wed, 18 Jun 2008 03:43:05 -0700 reply

SandBoxAdjacencyMatrix

gnuplottex --Bill Page, Tue, 24 Jun 2008 22:42:51 -0700 reply

SandBoxGnuPlotTex

implementing Integer from Cardinal (unsigned) numbers --Bill Page, Mon, 21 Jul 2008 06:34:23 -0700 reply

SandBoxDefineInteger

Attributes and categories --Bill Page, Fri, 25 Jul 2008 13:36:54 -0700 reply

SandBoxCommutativeCategory

Literal and Symbol in SPAD --Bill Page, Sun, 27 Jul 2008 02:09:57 -0700 reply

SandBoxLiteral

a category of partially ordered sets --Bill Page, Wed, 06 Aug 2008 17:26:50 -0700 reply

SandBoxPartiallyOrderedSet

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.

Document function selection process in the interpreter --Bill Page, Wed, 13 Aug 2008 18:10:26 -0700 reply

SandBox/interp/i-funsel.boot

Tensor Product of Polynomials --Bill Page, Sun, 24 Aug 2008 06:36:20 -0700 reply

SandBoxTensorProductPolynomial

Reflection --Bill Page, Mon, 08 Sep 2008 06:09:27 -0700 reply

spad

)abbrev package REFL Reflect
Reflect(T:Type): with
    constructor? : Symbol -> Boolean
  == add
    constructor?(p:Symbol):Boolean == car(devaluate(T)$Lisp)$SExpression = convert(p)$SExpression

spad

   Compiling FriCAS source code from file 
      /var/zope2/var/LatexWiki/2684009892188271010-25px004.spad using 
      old system compiler.
   REFL abbreviates package Reflect 
------------------------------------------------------------------------
   initializing NRLIB REFL for Reflect 
   compiling into NRLIB REFL 
   compiling exported constructor? : Symbol -> Boolean
Time: 0.02 SEC.

(time taken in buildFunctor:  0)

;;;     ***       |Reflect| REDEFINED

;;;     ***       |Reflect| REDEFINED
Time: 0 SEC.

   Cumulative Statistics for Constructor Reflect
      Time: 0.02 seconds

   finalizing NRLIB REFL 
   Processing Reflect for Browser database:
--->-->Reflect((constructor? ((Boolean) (Symbol)))): Not documented!!!!
--->-->Reflect(constructor): Not documented!!!!
--->-->Reflect(): Missing Description
; compiling file "/var/zope2/var/LatexWiki/REFL.NRLIB/REFL.lsp" (written 06 FEB 2012 07:25:41 PM):

; /var/zope2/var/LatexWiki/REFL.NRLIB/REFL.fasl written
; compilation finished in 0:00:00.101
------------------------------------------------------------------------
   Reflect is now explicitly exposed in frame initial 
   Reflect will be automatically loaded when needed from 
      /var/zope2/var/LatexWiki/REFL.NRLIB/REFL

   >> System error:
   The bounding indices 163 and 162 are bad for a sequence of length 162.
See also:
  The ANSI Standard, Glossary entry for "bounding index designator"
  The ANSI Standard, writeup for Issue SUBSEQ-OUT-OF-BOUNDS:IS-AN-ERROR

axiom

T1:=Integer

$\label{eq4}\hbox{\axiomType{Integer}\ }$

(4)

Type: Type

axiom

T2:=Polynomial Fraction T1

$\label{eq5}\hbox{\axiomType{Polynomial}\ } (\hbox{\axiomType{Fraction}\ } (\hbox{\axiomType{Integer}\ }))$

(5)

Type: Type

axiom

T3:=Complex T2

$\label{eq6}\hbox{\axiomType{Complex}\ } (\hbox{\axiomType{Polynomial}\ } (\hbox{\axiomType{Fraction}\ } (\hbox{\axiomType{Integer}\ })))$

(6)

Type: Type

axiom

constructor?('Polynomial)$Reflect(T1)

$\label{eq7} \mbox{\rm false}$

(7)

Type: Boolean

axiom

constructor?('Polynomial)$Reflect(T2)

$\label{eq8} \mbox{\rm true}$

(8)

Type: Boolean

axiom

constructor?('Polynomial)$Reflect(T3)

$\label{eq9} \mbox{\rm false}$

(9)

Type: Boolean

axiom

constructor?('Complex)$Reflect(T3)

$\label{eq10} \mbox{\rm true}$

(10)

Type: Boolean

Francois Maltey --Bill Page, Tue, 18 Nov 2008 19:11:35 -0800 reply

SandBoxConditionalFunctions

NonZeroInteger? --Bill Page, Tue, 02 Dec 2008 21:35:49 -0800 reply

SandBoxNonZeroInteger is an attempt to define the domain of Integers without 0.

Martin's "generator" mini-tutorial --Bill Page, Sat, 28 Feb 2009 09:00:14 -0800 reply

SandboxDelay

Ralf Hemmecke's example for hidden overloading --Bill Page, Mon, 23 Mar 2009 07:22:32 -0700 reply

SandBoxHiddenOverloading

prototype for tensor products --Bill Page, Tue, 12 May 2009 12:49:48 -0700 reply

SandBoxTensorProduct by Franz Lehner

Riemann Surface --Bill Page, Sat, 20 Jun 2009 13:15:37 -0700 reply

SandBoxComplexManifold

Differential Algebra --Bill Page, Wed, 29 Jul 2009 09:07:26 -0700 reply

SandBoxDifferentialPolynomial

Grassmann Algebra --Bill Page, Thu, 10 Sep 2009 09:05:28 -0700 reply

SandBoxGrassmannIsometry - All mappings that preserve a given metric are given in terms of the decomposition of a general multivector.

Free Product --Bill Page, Fri, 18 Sep 2009 03:20:41 -0700 reply

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:

Remove identity elements (of either A or B)
Replace a1a2 by its product in A and b1b2 by its product in B

Ref: http://en.wikipedia.org/wiki/Free_product

FunctionWithCache? --Bill Page, Tue, 27 Oct 2009 14:51:49 -0700 reply

Franz Lehner provided the following example of caching the output of a function: SandBoxRemember

Hash Functions --Bill Page, Wed, 04 Nov 2009 00:11:08 -0800 reply

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.

Groebner Basis and Polynomial Ideals --Bill Page, Tue, 08 Feb 2011 14:48:48 -0800 reply

SandBoxGroebnerBasis examples from Ideals, Varieties, and Algorithms Third Edition, 2007

Frobenius Algebra --Bill Page, Fri, 11 Feb 2011 17:12:43 -0800 reply

FrobeniusAlgebraVectorSpacesAndPolynomialIdeals Classifying low dimensional Frobenius algebras

Compiling SPAD code from a string --Bill Page, Mon, 07 Mar 2011 15:59:46 -0800 reply

SandBoxSTRING2SPAD demonstrates how to call the SPAD compiler from the interpreter.

Sandbox with some simple Algebra [SimplifyingAlgebraicExpressions]?