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Editor: horse
Time: 2010/08/02 03:55:24 GMT-7 |
||

Note: |

added:"Payday Loans":http://www.todayloan.co.ukadded:

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.

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?.

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.

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.

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

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}

axiom

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

(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; | 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]?.

axiom

solve(a*x+b,x)

(2) |

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

`Preview`

and `Cancel`

buttons:
axiom

integrate(sin x, x)

(3) |

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

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.

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: 0.03 SEC.

(time taken in buildFunctor: 0)

;;; *** |Reflect| REDEFINED

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

Cumulative Statistics for Constructor Reflect Time: 0.03 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 02 AUG 2010 03:55:14 AM): ; compiling (/VERSIONCHECK 2) ; compiling (DEFUN |REFL;constructor?;SB;1| ...) ; compiling (DEFUN |Reflect| ...) ; compiling (DEFUN |Reflect;| ...) ; compiling (MAKEPROP (QUOTE |Reflect|) ...)

; /var/zope2/var/LatexWiki/REFL.NRLIB/REFL.fasl written ; compilation finished in 0:00:00.053 ------------------------------------------------------------------------ Reflect is now explicitly exposed in frame initial Reflect will be automatically loaded when needed from /var/zope2/var/LatexWiki/REFL.NRLIB/REFL

axiom

T1:=Integer

(4) |

Type:Domain

axiom

T2:=Polynomial Fraction T1

(5) |

Type:Domain

axiom

T3:=Complex T2

(6) |

Type:Domain

axiom

constructor?('Polynomial)$Reflect(T1)

(7) |

Type:Boolean

axiom

constructor?('Polynomial)$Reflect(T2)

(8) |

Type:Boolean

axiom

constructor?('Polynomial)$Reflect(T3)

(9) |

Type:Boolean

axiom

constructor?('Complex)$Reflect(T3)

(10) |

Type:Boolean

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

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