login  home  contents  what's new  discussion  bug reports     help  links  subscribe  changes  refresh  edit

A glossary generated from the pages on this site.


A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

A

AXIOMsys
is the main Axiom program. It does not include graphics or hyperdoc browsing. Under Linux Axiom is usually started via a script called 'axiom' that also starts other processes such as sman (the ...
AboutAxiom
History
AboutMaxima
Maxima is a system for the manipulation of symbolic and numerical expressions, including differentiation, integration, Taylor series, Laplace transforms, ordinary differential equations, systems of ...
AboutReduce
REDUCE: Overview
AboutSage
SAGE is free and open software that supports research and teaching in algebra, geometry, number theory, cryptography, etc. Both the SAGE development model and the technology in SAGE itself is ...
AbstractFauser2007
Calculations in character Hopf algebras using SCHUR and Maple
Aldor
Aldor is a computer programming language, like Scheme, Java or C#.
AldorFibonacci
And below an Aldor version of the Fibonacci function that resembles a definition done in Haskell.
AldorForAxiom
It is possible to use the Aldor compiler WebSite:www.aldor.org to compile functions which you then can use Axiom. For details see:
AldorInEmacs
There are currently two packages available for emacs which support the "Aldor":http://www.aldor.org programming language.This page provides information and links to the available tools.
AlgebraGivenByStructuralConstants
\begin{axiom} )sh AlgebraGivenByStructuralConstants \end{axiom}
Arch Usage
Axiom development is now hosted on an Arch server running on axiom.developer.org.
Award Of Bounties
**Bounties:** -- relatively small promotional awards to be paid for programming work done to enhance Axiom.
AxServer
\documentclass{article} \usepackage{axiom} \begin{document} \title{\$SPAD/src/algebra axserver.spad} \author{Arthur C. Ralfs} \maketitle \begin{abstract} The AxiomServer package is designed to ...
AxWeb
AxWeb - A literate programming tool written in Common Lisp
Axiom Algebra
Adding new algebra in Axiom and OpenAxiom
Axiom Colloquium
The Colloquium's purpose is two-fold: 1) for the participants to share and discuss theory, practical experiences and insights regarding Axiom, and 2) to assist others concerned with Axiom and ...
Axiom Developer FAQ
This is an edited version of the FAQ file found in the Axiom source code distributions.
Axiom Strengths
This page's purpose is to collect strengths of Axiom in comparison to other CAS. Please add your thoughts.
Axiom Volume 1
Axiom Developers,Axiom Volume 1: Tutorial on Lulu.com Here is a link to the first volume of the new Axiom book on Lulu.com. Thanks Tim!Bill Page
Axiom and Maple
From: http://history.siam.org/pdfs2/Gonnet_final.pdf
Axiom meeting 2005
See also: [Next Axiom Meeting]
Axiom-developer
Selected Messages from the Axiom-developer email mailing list
AxiomBinaries
For current binaries see: InstallationFiles
AxiomBook
Introduction
AxiomCompiler
The language used for programming Axiom is called [SPAD]. In fact, [SPAD] has a cousin, originally intended as a successor called [Aldor] which can be used alternatively to 'spad'. There has not been ...
AxiomDevelopment
This page is intended for Axiom developers and those who might want to become developers. Here you can get an overview of what to do, and where to discuss issues with others.
AxiomDocumentation
The Axiom Book
AxiomEmacsMode
\documentclass{article} \usepackage{axiom} % % Note in processing this document - to produce the elisp file, run % the following command: % % notangle axiom.el.pamphlet > axiom.el % % To produce ...
AxiomProgrammingDiscussion
Meta-classes versus Categories
AxiomPromotion
1 Communities to inform of a release
AxiomScreenCast
Flash Presentations
AxiomSources
Axiom, as an open source program, makes the complete source code to the program available online. (Note: for those who are not interested in compiling Axiom binaries for different platforms are ...
AxiomUI
by [Kai Kaminski]
AxiomWindowsInstallerScript
\documentclass{article} \usepackage{axiom} \begin{document} \title{\textbf{Axiom Windows Installer Script}} \author{Jose Alfredo Perez} \maketitle
AxispBranch
Axisp is an experimental branch of Axiom. The focus of development is to rewrite the original Boot implementation into Common Lisp, and to improve and document the compiler and interpreter in the ...
algebra
\begin{axiom} )show Algebra \end{axiom}
B
BNatural
A new project has been proposed to attempt to implement BNatural using Aldor as an extension of the open source version of Axiom.
BasicOperator
\begin{axiom} )sh BasicOperator \end{axiom}
BeBold
Follow the Wikipedia guideline of "being bold":http://en.wikipedia.org/wiki/Wikipedia:Be_bold in updating wiki pages: Don't ask, just update (i.e. improve) the page.
BiCartesianTensor
BiCartesianTensor(dim,R) provides Cartesian tensors with components belonging to a commutative ring R. These tensors can have any number of covariant and contravariant indices. Each index takes ...
Binaries
PRE-COMPILED BINARIES
BitTorrent
http://www.dessent.net/btfaq
BootProgramming
Boot is used internally in Axiom for some of the interpreter and compiler code. Here is a detailed description of the "Boot Language":/axiom--test--1/src/boot/Makefile
BugTests
This page serves as parent for pages testing possibly buggy behaviour.
BugTracker
FriCAS bugs should be reported in FriCAS bug tracker at SourceForge: http://sourceforge.net/p/fricas/bugs/
BuildAxiom
Developers
BuildFriCAS
Building on Linux
BuildOnCygwin
Note: the text below should be identical to the contents of INSTALL.CYGWIN in the FriCAS distribution.
BuildOnWindows
Building Axiom on Windows
BuildOpenAxiom
Building on Linux
C
CaleyDickson
Ref:
Cartesian Product
++ This domain implements cartesian product
CartesianTensor
\documentclass{article} \usepackage{axiom} \begin{document} \title{\$SPAD/src/algebra carten.spad} \author{Stephen M. Watt} \date{May 20, 1991} \maketitle \begin{abstract} CartesianTensor(minix,dim,R)...
Category Theory and FriCAS
CliffordAlgebra
\begin{axiom}
ClosedLinearOperator
Introduction
CombinatorialFunction
\documentclass{article} \usepackage{axiom, amsmath, amsfonts} \begin{document} \title{\$SPAD/src/algebra combfunc.spad} \author{Manuel Bronstein, Martin Rubey} \maketitle \begin{abstract} \end{...
Common Mistakes
1 Omitting the {axiom} enviroment
CommonDenominator for polynomials
Note: Common denominator in FriCAS is extended in such a way.
Comparable
The class of sets equipped with possibly unnatural linear order (needed for technical reasons).
Complex
\documentclass{article} \usepackage{axiom} \begin{document} \title{\$SPAD/src/algebra gaussian.spad} \author{Barry Trager, James Davenport} \date{18 March 1994} \maketitle \begin{abstract} This ...
Complex Polynomial
*Andrea Bedini wrote:*
Computing with Vectors
How to multiply two vectors??
Creating New Pages
Suppose someone asks you: -- **I think it would be great if you could add your algoritm to the FriCASWiki web site.**
Cylindrical Algebraic Decomposition
Note: This package is currently included in FriCAS.
D
DancingSambaRamanujan
Dancing Samba with Ramanujan Partition Congruences
DeRhamComplex
\documentclass{article} \usepackage{axiom} \begin{document} \title{\$SPAD/src/algebra derham.spad} \author{Larry A. Lambe} \date{12/02/90} \maketitle \begin{abstract} LALG LeftAlgebra The category of ...
DebuggingFriCAS
Fortunately, FriCAS is rather easy to debug. Most of the source is very transparent, so once you have localized the bug there are mostly "design issues":DesignIssues to overcome. However, to find out ...
Definite Integration
Here are some integration problems.
DesignIssues
This should become a page where we document design issues.
DistributedExpression
Francois Maltey (FM) and Bill Page (BP) wrote::
DistributedMultivariatePolynomial
\begin{axiom} )show DistributedMultivariatePolynomial \end{axiom}
DocBook
http://www.docbook.org/
Doyen @ ASEE Mid-Atlantic Spring Conference 2006
Poster session showing the Doyen Project at New York City Tech. This is the website of the conference: http://websupport1.citytech.cuny.edu/Faculty/hli/asee/asee/default.asp .
DoyenCD
Doyen Live CD
DoyenDocs
\documentclass{article} \usepackage{axiom} \usepackage{graphics} \begin{document} \title{Doyen Build Instructions} \author{Tim Daly \and Jose Alfredo Perez \and Wilken Rivera} \maketitle \begin{...
DoyenFeedBack
DoyenVirtualMachine
Following Mr. Tim Daly's suggestion, I have uploaded a virtual machine configuration file for the DoyenCD using VMWare. This should allow to run the DoyenCD in different operating systems, ...
Dynamic Function Domains
On Wednesday, January 12, 2005 12:00 PM you wrote: Ralf Hemmecke wrote: Well, I haven't checked whether it should really work, but shouldn't be:: Foo: with { g: (n: PositiveInteger, k: ...
dirichlet.spad
Drichlet ring is now included in FriCAS
doyen
Doyen The {problem, need, market} seems to be to develop a scientific computation platform. The goal of such a platform would be to create an ecosystem where scientists can - develop ...
E
ElementaryFunctionStructurePackage
\documentclass{article} \usepackage{axiom} \begin{document} \title{\$SPAD/src/algebra efstruc.spad} \author{Manuel Bronstein, Waldek Hebisch} \maketitle \begin{abstract} \end{abstract} \eject \...
ElementaryIntegrationExample
\begin{axiom} )set output tex off )set output algebra on integrate(x/sqrt(x^4 + 10*x^2 - 96*x - 71),x) \end{axiom}
ExampleFreeAbelianGroup
How to use FreeAbelianGroup
ExampleGroebner
Application of Groebner Bases
ExampleIntegration
\begin{axiom} f := x/(x^3-x+1) )set output tex off )set output algebra on i := integrate(f, x) )set output tex on )set output algebra off D(i, x)
ExampleSkewPolynomial
Computing with non-commutative polynomials
ExampleXDistributedPolynomial
Demonstration of XDistributedPolynomial
ExpressionInteger
This page gives a few comments about the expression domain 'Expression Integer' and the use of more specific domains.
ExpressionSpace
)abbrev category ES ExpressionSpace
editor
Just placeholder
F
FAQ
Frequently Asked Questions
FRISCO
This is just a link to a european project FRISCO in which software in Axiom and Aldor was developed.
FactorizationExample
The following example appeared on Maxima list. Maxima needs 3.5 GB memory and almost a hour to do it. In FriCAS it is much faster:
FormalFraction
Author -- M.G. Richardson
Found Objects
If you have a lot of spare time, you might want to classify those pages, accidentally stumbled across:
FractionFreeFastGaussianElimination
FractionFreeFastGaussianElimination implements an algorithm proposed by Bernhard Beckermann and George Labahn. It can be used to solve general rational interpolation problems like (usual) linerized ...
Free Aldor
Axiom is a sophisticated computer algebra system originally developed as an IBM research project. IBM sold Axiom to the Numerical Algorithms Group (NAG) who marketed it and continued its development....
FreeModule
A bi-module is a free module over a ring with generators indexed by an ordered set. Each element can be expressed as a finite linear combination of generators. Only non-zero terms are stored.
FreeModuleCategory
A domain of this category implements formal linear combinations of elements from a domain **S** with coefficients in a domain **R**. The coefficient ring may be non-commutative.
FreeRing
\begin{axiom} )lib FPROD )lib FSUM \end{axiom}
FriCAS
"!FriCAS/Axiom Project (Fork)":http://sourceforge.net/svn/?group_id=200168
FriCAS Algebra
In FriCAS the word 'algebra' normally means collection of constructors (categories, domains and packages) provided with FriCAS. The source code for algebra is contained in 'src/algebra' subdirectory ...
FriCAS Binaries
You can find Fricas installation files at http://fricas.sourceforge.net/download.html
FriCAS Library
The [FriCAS Library] contains over 1,000 strongly-typed mathematical domains and categories. It is written in "Spad":FriCASCompiler. The source code for the library is here:
FriCAS Problems
- [Unevaluated Expressions]
FriCAS Sources
Repository Info -- http://fricas.sourceforge.net/download.html
FriCAS Syntax
On January 19, 2006 5:53 AM Fabio Stumbo wrote:
FriCAS compiler
The language used for programming FriCAS is called Spad. Currently most of Axiom documentation still applies, see AxiomCompiler. However, there are changes, some mentioned at FriCASModifications.
FriCAS language
FriCAS has the [FriCAS interpreter] for interaction with the user and the [FriCAS compiler] for building library modules.
FriCASAdvantages
Compared to old Axiom FriCAS has following advantages:
FriCASContributions
The following are not included in current FriCAS:
FriCASDocumentation
FriCAS interface documentation
FriCASGraphics
Graphics in FriCAS
FriCASIcon
Some Proposed Site Icons
FriCASInVim
Syntax highlighting for FriCAS-files: .spad, .input
FriCASIntegration
FriCAS inherited from Axiom implementation of Risch algorithm for elementary integration. It can handle both easy cases \begin{axiom} integrate(x*exp(x^2), x) integrate(exp(1/x^2)/x^3, x) \end{axiom}...
FriCASInterpreter
The FriCAS interpreter is the part of FriCAS responsible for handling user input during an interactive session.
FriCASIssues
I have a number of issues that are somewhere between bug reports, new feature requests, problem workarounds and so on. Perhaps if I start to write them down some structure will appear. The issues on ...
FriCASModifications
Around August 2011 there have been made some changes that are described concisely in a Mail by Waldek: http://groups.google.com/group/fricas-devel/msg/1d069ca72125d17c?hl=en
FriCASOutputFormatting
One of the most frustrating things as a novice axiom user is to try to figure out how to get FriCAS output to appear in the desired form. For instance:
FriCASPreGenerated
This is a description of how to generate and how to use the new 'pre-generated' system.
FriCASProgramming
General programming
FriCASSpecialIntegration
FriCAS can now handle large class of integrals expressible in terms of exponential integral, error functions, incomplete Gamma function with rational first argument, logarithmic integral and ...
FriCASTimofeev1
Examples from Timofeev (1948) Ch. 1, divided into sections kindly provided by clicliclic vel Martin on sci.math.symbolic
FriCASTimofeev37
Examples from Timofeev Chapter 3 and Chapter 7
FriCASTimofeev5
Examples from Timofeev (1948) Ch. 5, divided into sections kindly provided by clicliclic vel Martin on sci.math.symbolic
FriCASTimofeev9
Timofeev Chapter 9 Integration Problems
FriCASTutorial
Most introductory material about Axiom applies to FriCAS. The [Axiom Volume 1]: Tutorial is available in printed format at http://publish-book.com and http://www.lulu.com/product/file-download/axiom-...
FriCASWiki
The FriCAS Wiki (this web site) is an online enviroment in which FriCAS users and developers can:
FriCASonCygwin
Martin Rubey provides the following instructions for running FriCAS on Cygwin:
Frobenius Algebra, Vector Spaces and Polynomial Ideals
References
FrontPage
[News]
FrontPageDiscussion
Please add comments about FrontPage here...
FunWithFunctions
\begin{spad} )abbrev package MYEXP MyExp
FunctionalProgramming
In pure functional programing there are no variables, there are only values. Values are immutable and logically exist "forever" from creation. Program creates new values from old ones, typically ...
finite field expressions
Here are some notes I took when I tried to allow expressions ove finite fields.
fricas-devel
The FriCAS developer email list is here:
G
GeneralDistributedMultivariatePolynomial
\begin{axiom} )show GeneralDistributedMultivariatePolynomial \end{axiom}
GenericNonAssociativeAlgebra
\begin{axiom} )sh GenericNonAssociativeAlgebra \end{axiom}
GradedAlgebra
\begin{spad}
GradedModule
\begin{spad} )abbrev category GRMOD GradedModule ++ Author: Stephen M. Watt ++ Date Created: May 20, 1991 ++ Date Last Updated: May 20, 1991 ++ Basic Operations: +, *, degree ++ Related Domains: ...
GraphViz
"An Introduction to GraphViz":http://www.linuxjournal.com/article/7275
Graphics on MathAction
Graphics?
GroebnerPackage
\begin{axiom} )show GroebnerPackage \end{axiom}
Group
\begin{axiom} )show Group \end{axiom}
GroupAlgorithms
FriCAS impements several algorithms for working with goups:
Guessing formulas for sequences
Author: "Martin Rubey":http://www.mat.univie.ac.at/~rubey/martin.html
groebner
From GroebnerPackage and PolynomialIdeals \begin{axiom} )display operation groebner \end{axiom}
H
HeapSort1
Heapsort
HelpPage
"What's going on here?":#whatisthis "User interface":#ui "Navigation":#navigation "Subscription":#email "Editing":#editing "Formatting rules in a nutshell":#rules "Finding out more":#more
HomogeneousDistributedMultivariatePolynomial
\begin{axiom} )show HomogeneousDistributedMultivariatePolynomial \end{axiom}
HowToSubmitAxiomPatches
This page describes how to submit a piece of code that corrects or extends the original Axiom project.
HyperDoc
The open source version of Axiom for Linux is a "feature complete" release of Axiom that includes all of the functionality of the original commercial release. It includes all of the algebra we have ...
HyperDocTracing
The Trace Facility
I
Imitation As Complement
MaplePrimes
Indefinite Types
Declaring Types The idea that one should be able to "declare the type" of a variable in Axiom by the command \begin{axiom} n:PositiveInteger \end{axiom}
IndexedUnion
Goal: To explore the issues and develop tools for implementing 'IndexedUnion', a new domain constructor proposed by William Sit.
InputForm
Domain of parsed forms which can be passed to the interpreter. This is also the interface between algebra code and facilities in the interpreter.
Installation Files
PRE-COMPILED BINARIES
InstallingMathAction
On 01/10/2004 4:05 PM Hans Peter Wuermli wrote:
Interval Arithmetic
Author -- Mike Dewar
IssueTracker
Bug reports and other issues. Please identify yourself and provide an email address using login before editing or adding a new issue. See also: ! ...
indexed variables
I am trying to create formulae for products with, say, p sub k as symbols. These are the results from two, at least naively identical formulae:
J
JenksSutorInXhtml
This is the Jenks-Sutor book in xhtml + mathml. The graphics are still included as images in the ps.tar file. The ps directory with the pictures and the graphicstyle.css file should be in the same ...
Jet Bundles
Note: In 2011 JET bundle package was included in FriCAS.
Jet Figure 4
\begin{axiom} jb := JBUNDLE(['x,'y,'z],['u]); jbx := JBX jb; jbl := JBLF(jb,jbx); de := JDE(jb,jbl); ck := CKP(jb,jbl); \end{axiom}
Jet Figure 5
\begin{axiom} jb := IJB('x,'u,'p,4,3); jbe := JBE jb; de := JDE(jb,jbe); ck := CKP(jb,jbe); \end{axiom}
Jet LUDecomposition
!LUDecomposition (LUD)
jEdit
Outline
K
Kai Kaminski
Biography
L
LaTeX
LaTeX ... is the world standard for writing technical documents. Authors in science and engineering are probably already familiar with it (or should be). If you've wrestled with and cursed at "...
LanguageDifferences
As mentioned on FriCASProgramming, there are a number of languages connected to PanAxiom. Since for actual users only 3 of them are relevant, namely, "Spad":AxiomCompiler, the "Axiom interpreter":...
LatexSymbols
\documentclass{article} %%% ==================================================================== %%% @LaTeX-file{ %%% filename = "symbols.tex", %%% version = "2.00", %%% ...
LatexTemplate
%% This file is used as a python printf() string. As such, the document we are %% trying to render is placed at the location of the percent-s below, and any %% comments in this file must be ...
LatexWiki
Test \begin{equation} \alpha = \frac{\beta}{\gamma} \end{equation}
Limits and Colimits
Limits
LineBreaker
From -- Bill Page
LinearOperator
Introduction
LinuxDoc
http://www.faqs.org/docs/Linux-mini/Linuxdoc-Reference.html
Lisp's Fraction Integer Domain
Original Date: Fri, 25 Mar 2005 12:01:44 -0600
LispInFriCAS
It is possible to enter Lisp expressions directly into FriCAS (including function definitions) using the ')lisp' command, but this is rather awkward for long Lisp programs. \begin{axiom} )lisp (defun ...
List To Matrix
Assume that I have a 'List', like: \begin{axiom} L := [[- 1,3,- 3,1],[3,- 6,3],[- 3,3],[1]] \end{axiom} (which is calculated from some earlier expressions). How can I convert it into a 'SquareMatrix'....
ListProgramming
List is a sequence of nodes storing data and links to other node. Each node has place for single piece of data and a single link. First node of the list contains link to second node, second node ...
LiterateProgramming
The standard form for all Axiom programs and documentation is the [noweb] literate programming extension of LaTeX (called "pamphlet files" in Axiom terminology). Pamphlet files contain both ...
LyX
!**LyX** is a fully featured document processor, including:
M
Manipulating Expressions
The domain InputForm can be quite useful for manipulating parts of expressions. For example
MathAction
Welcome to !MathAction - The Interactive Mathematical Web!
MathAction Problems
Some special Axiom-specific LaTeX commands might not be understood by MathAction. For example::
MathActionAssistantHelp
The MathAction Assistant is a new interactive toolbar that appears at the bottom of the 'edit' and 'Add comments' windows. It helps users edit text containing LaTeX, Axiom and Reduce commands. ...
MathActionDevelopment
Design Goals and Issues
MathActionRepository
MathAction is maintained as "darcs":http://darcs.net clone of the repository for "ZWiki":http://www.zwiki.org and is located at:
MathML
http://www.w3.org/Math/
MathMLFormat
The MathML package
Mathaction2Input
\documentclass{article} \usepackage{axiom} \begin{document} \title{mathaction2input} \author{Bill Page and David Cyganski} \date{5 July 2007} \maketitle \begin{abstract} This script converts the ...
MiKTeX
MiKTeX is an up-to-date TeX implementation for the Windows operating system.
MinGW
What is MinGW?
Mirrors
.hover-red:hover {background-color: pink; text-decoration: none } .hover-red:link {text-decoration: none } .hover-red:active {text-decoration: none } .hover-red:visited {text-decoration: none } ....
MortonCode
References to Morton codes (also known as z-order and Lebesgue curves):
MultiVariableCalculusFunctions
\begin{axiom} )show MultiVariableCalculusFunctions \end{axiom}
Multivariate Resultants
Here is what I got so far by translating Amit Khetans bires.mpl into Axiom (I'm struggling with guessing the right coercions...) Help is very much appreciated!::
Mutual Recursion
Here we give two examples of defining functions by mutual recursion in Axiom
MyComplex
\begin{spad} )abbrev domain MYPLEX MyComplex ++ Description: ++ Based on \spadtype{Complex(R)}, ++ \spadtype{MyComplex(R)} creates the domain of elements of the form ++ \spad{a + b * i} where \spad{a}...
mathematical algorithms
Computer algebra systems like FriCAS implement a very large number of [mathematical algorithms]. By that we mean:
mathml.spad.pamphlet
The material in the wiki was obsolete. See FriCAS sources ('src/algebra/mathml.spad') for current version.
N
News
Please post notices and information about events, conferences and meetings related to Axiom and computer algebra here.
Next Axiom Meeting
**On November 19, 2005 10:34 AM Tim Daly (root) wrote:**
NoWeb
\documentclass{article} \usepackage{axiom} \begin{document} \title{Autodoc} \author{Tim Daly} \maketitle \begin{abstract} We want to generate the reference information from axiom source files ...
NonAssociative
$$ a*(b*c) \ne (a*b)*c $$
NonNegativeInteger
See also PositiveInteger
NumericalIntegration
The package 'NumericalQuadrature' implements several operations for numerical integration. Here I provide just some examples. Documentation is to be found in the corresponding '.spad' or '.pamphlet' ...
NumericalQuadrature
Numeric integration routines \begin{axiom} )sh NumericalQuadrature \end{axiom}
noncommutative Groebner bases
FriCAS can compute Groebner bases for noncommutative polynomial rings of solvable type (of category SolvableSkewPolynomialCategory). Below we give example using partial differential operators: \begin{...
normalForm
From GroebnerPackage \begin{axiom} )display operation normalForm \end{axiom}
numerical linear algebra
I'm new to Axiom, so maybe I'm doing things in a stupid way.
O
Octonion Algebra is Frobenius in Just One Way
Octonion Algebra Is Frobenius In Just One Way
OldFrontPage
**Welcome!**
OldGnuDraw
**Demonstrate how graphs may be plotted and displayed from !MathAction**
OldSummerOfCode
Summer of Code: Axiom Projects
OldTeXmacs
"GNU TeXmacs":http://www.texmacs.org/tmweb/home/welcome.en.html is a free scientific text editor, which was both inspired by TeX and GNU Emacs. The editor allows you to write structured documents via ...
OldTodoList
The last release was "Axiom 3.0 Beta":Axiom-Release-3.0-Beta. Tim keeps a detailed "current state":AxiomCurrentState of Axiom. Those items which should be completed for the first stable public ...
OldWishList
This is the AXIOM wishlist, add items and descriptions of stuff that you would like to see done in AXIOM.
OpenAxiom
"!OpenAxiom Project (Fork):":http://www.open-axiom.org Open source development project on SourceForge with emphasis on becoming the "Axiom of Choice" by improving the build system and through the ...
OpenAxiom Sources
Repository -- http://www.open-axiom.org/download.html
OpenAxiomWindows
Installing OpenAxiom on Windows
OrderedDirectProduct
\begin{axiom} )show OrderedDirectProduct \end{axiom}
OrderedVariableList
\begin{axiom} )show OrderedVariableList \end{axiom}
OtherComputerAlgebraSystems
Someday (maybe) we will also include online access to other systems such as:
OutputForm
Returns -- a domain of category SetCategory with explicit exports
OverloadProb
**Type Conversion and Overloading problems**
P
PAFF
"PAFF":http://www-rocq.inria.fr/codes/Gaetan.Hache/PAFF.html : Package for Algebraic Function Fields in one variable
Pamphlet Files
**Based on an email from Tim Daly on June 27, 2005 1:24 AM:**
PamphletExample
\documentclass{article} \usepackage{axiom} \begin{document} \title{Autodoc} \author{Tim Daly} \maketitle \begin{abstract} We want to generate the reference information from axiom source files ...
PamphletSyntax
This page discusses the pros and cons of a change in pamphlet syntax away from the currently (23-Jul-2007) used "noweb":http://www.eecs.harvard.edu/~nr/noweb/ syntax.
PanAxiom
This page explains what PanAxiom stands for.
PanAxiomCommunity
Besides frequently visiting the [FriCAS Wiki] website. There are several ways to stay in contact with the PanAxiom community.
ParticipantsRISC2007
- Rafal ABLAMOWICZ (Tennessee Technological University)
PascalTriangle
Below there is a function which generates Pascal triangle by iteratively filling rows of a matrix using recurence formula. Spad array indexing is one based, so we cheat and add 1 to indices. \begin{...
PascalTriangleNopile
\begin{spad} )nopile )abbrev package PASCALN PascalNopile PascalNopile : with { make_pascal : Integer -> Matrix(Integer) } == add { make_pascal(N : Integer) : Matrix(Integer) == { nn := N::...
Pattern Matching
Say, I have \begin{axiom} test:=D(sin(z)^2, z) \end{axiom}
PerCent
There are some identifiers in Axiom that start with a percent sign.
Permutation
\begin{axiom} )show Permutation \end{axiom}
Piecewise Functions
Consider the following function, given in recursive manner: \begin{axiom} N0(t|(t1))==0 N0(t|(t>=0) and (t0)==(t-i)/p*N(t,i,p-1)+(i+1-t)/p*N(t,i+1,p-1) \end{axiom} This is a way to create (uniform) ...
PolyMake
http://www.math.tu-berlin.de/polymake
PolySpad
\documentclass{article} \usepackage{axiom} \begin{document} \title{\$SPAD/src/algebra poly.spad} \author{Dave Barton, James Davenport, Barry Trager, Patrizia Gianni, Marc Moreno Maza} \date{June 2009}...
Polynomial Coefficients
Let's examine a simple case: \begin{axiom} Dg := [p3 - 3*p2 + 3*p1 - p0,3*p2 - 6*p1 + 3*p0,3*p1 - 3*p0,p0] \end{axiom} Now calculate coefficients in two ways: \begin{axiom} map(coefficients, Dg::...
PolynomialIdeals
\begin{axiom} )show PolynomialIdeal \end{axiom}
PositiveInteger
See also NonNegativeInteger
ProgrammingSPAD
A very brief introduction to programming in SPAD
Q
QuadraticForm
\begin{axiom} )show QuadraticForm \end{axiom}
R
RandomAlgebra
(the maths inside is not meant to be taken seriously; 'tis a silly idea that can't work)
Rational Interpolation
Introduction
RealClosure
Real Algebraic Numbers
RealNumbers
Axiom implements the number domains Integer, Float and even Fraction(Integer) i.e. rational numbers, but it does not implement anything called Real numbers. *Why is that?*
RebuildDoyen
------------------------------------------------------- Instructions to make a new Doyen image file. -------------------------------------------------------
RecurrenceRelationOperator
Here is a simple implemention of a recurrence relation operator. It is far from finished, but might serve as a starting point. I experienced the following difficulties:
ReduceAppendixB
Appendix B  Examples
ReferenceSemantics
Traditional imperative languages like C, Pascal etc. have value semantic: variables store possibly complicated compound values. Normal calling sequence copies values of function parameters so that ...
Rep and Per
Aldor programming philosophy from the point of view of it's evolution from previous incarnations of the Axiom library compiler, is described here:
RichExp1
Examples involving exponential function from Albert Rich testsuite.
RichExp2
Examples involving exponential function from Albert Rich testsuite.
RischImplementationStatus
In FriCAS Risch algorithm is split into two stages, preparatory one when integrand is rewritten to express it in terms of differential fields and the core part.
Rosetta
\documentclass{article} \normalsize\baselineskip=12pt \parskip=0pt \parindent=10pt \tolerance=5000 \pretolerance=5000 \frenchspacing \hangindent=10pt \skip\footins=18pt \global\textwidth 31pc \global\...
RosettaStone
 1  Rosetta Translations
reading structures from a file
This package provides operations that all take a filename and return an axiom structure which is supposed to be in some standard notation in this file. Geared towards polymake. Needs '...
realElementary
\begin{axiom} realElementary sinh x realElementary cosh x \end{axiom}
robots.txt
# Define access-restrictions for robots/spiders # http://www.robotstxt.org/wc/norobots.html
S
SanBoxIntPar
---------- Forwarded message ----------::
SandBox
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 ...
SandBox Aldor Category Theory
This project is intended to implement the code and concepts presented by Saul Youssef in "Prospects for Category Theory in Aldor", 2004.
SandBox Aldor Category Theory 3
\begin{aldor}[slicecategories] #include "axiom" #pile
SandBox Aldor Category Theory 4
\begin{aldor}[morphisms] #include "axiom" #pile #library lBasics "basics.ao" import from lBasics
SandBox Aldor Category Theory 5
\begin{aldor}[categories] #include "axiom" #pile
SandBox Aldor Category Theory 6
\begin{aldor} #include "axiom" #pile
SandBox Aldor Category Theory 7
\begin{aldor}[subobjects] #pile #include "axiom" +++ +++ Quotients +++ define Quotient(Obj:Category):Category == with Quotient: (A:Obj,B:Obj) -> (A->B) -> (Quo:Obj,A->Quo,(X:Obj)->(A->X)->(Quo-...
SandBox Aldor Category Theory Basics
Miscellaneous Logical helper functions
SandBox Aldor Category Theory Categories
\begin{aldor}[categories] #include "axiom" #pile
SandBox Aldor Foreign
On Wednesday, May 31, 2006 2:54 AM Gernot Hueber wrote: Due to that I want to call external library functions from within Aldor/Axiom I did some trials with Aldors "Foreign" and GCL "defentry" ...
SandBox Aldor Generator
Aldor has generators:
SandBox Aldor Join and Meet
Aldor-Meet
SandBox Aldor Semantics
The following Aldor code was given as an example by Ralf Hemmecke and added to the wiki by Martin Rubey. See the thread:
SandBox Aldor Sieve
From section 1.2 of Aldor Users Guide
SandBox Arrays
Adding new functions to PrimitiveArray in an attempt to improve performance.
SandBox Boolean
On Wed, 1 Feb 2006 10:29:24 -0700 Robert Dodier asked C Y:
SandBox Cast
This is an example of using 'pretend' to perform a type unsafe operation.
SandBox Categorical Relativity
Special relativity without Lorentz transformations.
SandBox Category of Graphs
Axiom currently lacks an implementation of the mathematical concept of *graph* in the sense of "Graph Theory":http://en.wikipedia.org/wiki/Graph_theory. See also: "Graph_(mathematics)":http://en....
SandBox Category of Graphs 2
This seems to work if the category is defined in the same source file (i.e. same section in MathAction). The code is based on the Spad version [SandBox Category of Graphs in Spad] \begin{aldor} # ...
SandBox Category of Graphs in SPAD
First we define the general category of graphs. \begin{spad} )abbrev category GRAPHS GraphCategory GraphCategory(nodes:Type, edges:Type): Category == with source:edges->nodes target:edges->nodes
SandBox Direct Product
The direct product of two functions over the same domain is another function over that domain whose co-domain is the product of the co-domains their co-domains.
SandBox DoOps
\begin{axiom} zerosOf(7-5*x+5*x^2-x^3,x) \end{axiom}
SandBox Domains and Types
Note: In FriCAS 'Domain' is no longer used as a type.
SandBox Einstein Velocity
Einstein Velocity and Non-associative Addition
SandBox Embeded PDF
This is how a pamphlet file will look in MathAction
SandBox EndPaper
Basic Algebra Hierarchy
SandBox Experimenting
\begin{axiom}
SandBox Folding
Real Easy Folding
SandBox Functional Addition
This library code is based directly on MappingPackage3 in 'mappkg.spad.pamphlet'
SandBox Functions
SandBox Gamma
From Numerical Recipes in C, 2nd edition
SandBox Grassmann Algebra Is Frobenius In Many Ways
Grassmann Algebra Is Frobenius In Many Ways
SandBox Idempotent Observers
Preliminaries
SandBox Integration
Integration
SandBox LaTeX
$x^2$
SandBox Lisp
Testing Lisp under Axiom Interpreter \begin{axiom} )lisp (setq $dalymode t) (+ 2 3) \end{axiom}
SandBox Lorentz Transformations
Lorentz transformations relate one object or observer (represented by a time-like 4-vector) to another object or observer. A Lorentz transformation is **not** uniquely given by the relative velocity ...
SandBox Manip
Demonstration of modifying and testing a SPAD file
SandBox Manipulating Domains
On Sunday, March 19, 2006 5:54 AM Francois Maltey wrote:
SandBox Mapping
This domain provides a function-like type that can be queried for domain and co-domain. \begin{aldor}[sig] #include "axiom.as" T ==> SetCategory;
SandBox Matrix
Symbolic Matrices
SandBox Monoid
\begin{spad} )abbrev category MM MyMonoid )if false -- Does not work now Monoid(m:Symbol,u:Symbol): Category == with() m: (%,%) -> % ++ returns the product of x and y u: () -> % ...
SandBox Monoid Extend
Martin's beautiful idea:
SandBox NNI
This is an experiment to see what the differences are between defining NonNegativeInteger (NNI) as a SubDomain of Integer, versus defining it simply based on Integer itself.
SandBox Noncommutative Polynomials
There is are some domains in Axiom for doing computations with non-commuting variables developed by Michel Petitot. You can find some examples in the Axiom book under the title XPolynomial but ...
SandBox Numerical Integration
On March 10, 2006 10:53 PM Donald J Bindner wrote:
SandBox Object
Type-safe Objects in SPAD
SandBox Polynomials
Testing a change from::
SandBox ProblemSolving
Mathe-Abi ab 2004
SandBox Quaternion Algebra is Frobenius in Many Ways
Quaternion Algebra Is Frobenius In Many Ways
SandBox Qubic
\begin{axiom} digits 20 -- n:=x^3+a1*x^2+a2*x+a3 ::Polynomial Fraction Integer
SandBox Reflection in Aldor
On July 28, 2006 3:21 AM Christian Aistleitner wrote:
SandBox SPAD for Python
In Python we might write:
SandBox SPAD for Python 2
Aldor and SPAD allow domains to have parameters. For example let's generalize the previous Complex domain to form complex numbers over any ring.
SandBox Sedenion Algebra is Frobenius In Just One Way
Sedenion Algebra is Frobenius in just one way!
SandBox Set Any
In Issue #347 it is shown that set equality fails after applying a map to a set: \begin{axiom} A:Set Integer := set [-2,-1,0] B:Set Integer := set [0,1,4] C:=map(x +-> x^2,A) test(C=B) \end{axiom}
SandBox Shortcoming
Please try the two solve statements at the bottom The first one runs in a short time but the second runs a long time. The only differenct is '*R*P' in eq1. Examining eq1a shows that in fact p=1 has ...
SandBox Sockets in SPAD
SocketsInSpad
SandBox Solve
Solving Equations
SandBox Spad
A minimal exemple of my trouble.
SandBox Speed
\begin{aldor} #include "axiom.as"
SandBox Statistics
Testing Martin's statistics code
SandBox SubDomain
Exposing the SubDomain constructor: \begin{spad} )abbrev domain SUB SubDom SubDom(X:Type,C:Type):Type with if C has IntegralDomain then IntegralDomain == SubDomain(X,true) \end{spad}
SandBox Tail Recursion
On Tuesday, August 30, 2005 3:44 PM Jens Axel Søgaard wrote:
SandBox Text Files
This is a simple example of writing to and reading from a text file: \begin{axiom} f1: TextFile := open("/tmp/test", "output") writeLine!(f1, "abcdefg") close! f1 f2: TextFile := open("/tmp/test", "...
SandBox Trace Analysed
This page is work in progress, to be continued ...
SandBox Trace EXPR and FRAC
Trace may affect correct output of '1::EXPR INT' . This page should be read in conjunction with IssueTracker #283. To suppress the infinite loop being displayed till overflow, add ')math' to the ...
SandBox Trace in Windows
I want to point out a bug in Windows version: where the Linux version below refers to 'Integer.=,64' the Windows version (shown next) shows 'Integer.random,63'.
SandBox Trace with )math
The addition of ')math' below stopped the infinite loop from occurring! For the version without ')math', see [SandBox Trace in Windows] ::
SandBox Zero
We are trying to create a Zero
SandBox kaveh
\begin{axiom}
SandBox polymake
Here we demonstrate the PolyMake wrappers 'Polytope' and 'SimplicialComplex'.
SandBox.GuessingSequence
This page makes test uses of the guessing package by Martin Rubey. Feel free to add new sequences or change the sequences to ones you like to try.
SandBox/interp/i-funsel.boot
The purpose of this page is to begin the process of documenting the function selection process used by the Axiom interpreter.
SandBox11
SandBox12_Test_Indet_and_Complex
\begin{axiom} 2^0.5 -1^0.5 sqrt(2) :: Float sqrt(-1) :: Complex Float 0^0 0.0^0.0 \end{axiom}
SandBox2
\begin{axiom} )set output tex on )set output algebra off )set output mathml off \end{axiom}
SandBox3
quad Bezier/line Intersection
SandBox42
\begin{axiom}
SandBox9
looking for completion of pendulum (constrained motion)
SandBoxAbelianDuck
During the Aldor/Axiom Workshop 2008 at RISC in one of his presentations Stephen Watt began with::
SandBoxAbs
This is how FriCAS currently differentiates the absolute value function. \begin{axiom} differentiate(abs(x),x) \end{axiom}
SandBoxActiveAxiomDevelopers
The Core Axiom developers in alphabetical order
SandBoxAdjacencyMatrix
*On Tue, Jun 17, 2008 at 10:07 AM Franz Lehner wrote:*
SandBoxAldorDomainList
This is an experimental page to implement cartesian product over an indexed set of domains in Aldor. The constructor Product constructs a domain which is the cartesian product of $f(i)$ for $i \in I$.
SandBoxAldorInductiveTypes
This implementation of an Inductive (recursive) data type involves the categorical co-product construction. See: LimitsAndColimits \begin{axiom} )library colimits \end{axiom}
SandBoxAldorTesting
Based on the Aldor presentation by Stephen Watt: http://www.aldor.org/docs/reports/ukqcd-2000/intro1-ukqcd00.pdf and http://www.aldor.org/docs/HTML/chap2.html
SandBoxAldorTuples
**On Date: Jun 26, 2007 8:19 AM Ralf Hemmecke wrote:((
SandBoxAlgfunc
Add conjugate \begin{spad} )abbrev category ACF AlgebraicallyClosedField ++ Author: Manuel Bronstein ++ Date Created: 22 Mar 1988 ++ Date Last Updated: 27 November 1991 ++ Description: ++ Model for ...
SandBoxAxiomAndThe30YearHorizon
Intent
SandBoxAxiomSourcesReST
.. contents:: Table of Contents .. section-numbering::
SandBoxBen2
\begin{axiom} 4^(4^(3)+2) \end{axiom}
SandBoxBiQuaternions
The Biquaternion calculus support function collection
SandBoxBiQuaternions2
Biquaternion Calculus Domain
SandBoxBiQuaternions3
Biquaternion Calculus Domain
SandBoxBootStrap
On Monday, October 16, 2006 7:30 PM Gabriel Dos Reis wrote:
SandBoxBootStrap2
\begin{spad} )lisp (setq |$bootStrapMode| t) )abbrev domain T T
SandBoxBugFactor
\begin{axiom} t:=(4*x^3+2*y^2+1)*(12*x^5-x^3*y+12)*(x+1)*(y^2+3)*(x^2-1) factor t \end{axiom}
SandBoxBugLaurentSeries
\begin{axiom} Z==>Integer; Q==>Fraction Z z: Symbol := 'z; P==>UnivariatePolynomial(z,Q) t:P := monomial(1,1) p:P := (1-t)*(1-t^2)*(1-t^3) L==>UnivariateLaurentSeries(Q,z,0) R ==> Record(k: Z, c: Q) ...
SandBoxCL-WEB
\documentclass{article} \usepackage{axiom} \usepackage{geometry} \usepackage{hyperref} \geometry{verbose,letterpaper,tmargin=1in,bmargin=1in,lmargin=1in,rmargin=1in} \usepackage{graphics} \...
SandBoxCS224
\begin{axiom} [1/2, 3/4, 2/3] \end{axiom}
SandBoxCachedFunction
A generic way to define function that cache their values.
SandBoxCartesianTensor
Try to make it a little faster. \begin{spad} )abbrev domain CARTEN CartesianTensor ++ Author: Stephen M. Watt ++ Date Created: December 1986 ++ Date Last Updated: May 15, 1991 ++ Basic Operations: ++ ...
SandBoxCategories
This page was renamed to AnonymousCategories. You can delete this one if no longer needed.
SandBoxCategoryTerms
The aim of this page is to relate mathematical terms, such as those from category theory or type theory, to the way these terms are used in SPAD. So a reader who has some acquaintance with a given ...
SandBoxChoose
\begin{equation} \left( {\begin{array}{*{20}c} S \\ k \\ \end{array}} \right) \end{equation}
SandBoxCliffordAlgebra
We want to test some properties of the CliffordAlgebra domain implemented in FriCAS
SandBoxClosedLinearOperator
Introduction
SandBoxCoMultiplication
\begin{axiom} n:=2 T:=CartesianTensor(1,n,FRAC POLY INT) Y:T := unravel concat concat [[[script(y,[[i,j],[k]]) for i in 1..n] for j in 1..n] for k in 1..n] A:T := unravel(concat ...
SandBoxCollect
**Collect terms in x with given factor k.** \begin{spad} )abbrev package COLL Collect I==>Integer E==>Expression I K==>Kernel E Q==>PolynomialCategoryQuotientFunctions( _ IndexedExponents K, K, ...
SandBoxCombfunc
Add conjugate \begin{axiom} )library BOP BOP1 \end{axiom} \begin{spad} )abbrev category COMBOPC CombinatorialOpsCategory ++ Category for summations and products ++ Author: Manuel Bronstein ++ Date ...
SandBoxCombfuncDiscussion
Nicer display from binomials: \begin{axiom} --)set output tex off --)set output algebra on binomial(n,m) opbinom := operator(operator 'binomial)$CombinatorialFunction(INT,EXPR INT) setProperty(...
SandBoxCombinat
This page demonstrates one of the very early attempts to do something similar to MuPAD combinat's "decomposable objects" in Aldor/Axiom. Meanwhile, we adopted the point of view of species, as shown ...
SandBoxCommutativeCategory
Note: In FriCAS the 'commutative("*")' attribute is replaced by 'CommutativeStar' catogory. The disscussion below is kept as it raises some issues that are still relevant.
SandBoxComplementsdalgebrelineaire
\documentclass{article} % % linalg.ltx % Francois Maltey - janvier 2008 % \usepackage[utf-8]{inputenc} \usepackage{amsmath} \usepackage{amsfonts} \usepackage[french]{babel} \usepackage{xspace} \...
SandBoxComplexManifold
Complex domain constructor done differently.
SandBoxConditionalFunctions
**Conditional for inner functions in a package.**
SandBoxDGE
Something is going wrong with the formatting of the output. \begin{axiom} s:=integrate(sqrt(a*t^2+b*t+c),t); #s s.1 s.2 \end{axiom} It is not being wrapped as expected.
SandBoxDefineInteger
Why are the domains PositiveInteger and NonNegativeInteger defined as [SubDomain]s of Integer insteadof the other way around? Here is a (still somewhat imperfect) example of one way of defining ...
SandBoxDifferentialEquations
Differential Equations
SandBoxDifferentialGeometry
Subject: DeRhamComplex
SandBoxDifferentialPolynomial
Description -- DifferentialSparseMultivariatePolynomial implements an ordinary differential polynomial ring by combining a domain belonging to the category DifferentialVariableCategory with the ...
SandBoxDiracDelta
Distributions
SandBoxDiscussion
Time to clean out the SandBox!
SandBoxDomainConstructor
\begin{axiom} )set output tex off )set output algebra on \end{axiom}
SandBoxDomainOfComputation
An "assume" system based on equational reasoning.
SandBoxDoublePowerSeries
\begin{axiom} a! !:=operator '! a(i,j)==(1+(j-1)*i)/!(2*i+4*j) a0:=matrix [[a(i,j)*k^i*l^j for i in 0..5] for j in 1..4] a(i:INT,j:INT):FRAC INT == (1+(j-1)*i)/Gamma(1+2*i+4*j) aa:DMP([k,l], FRAC INT)...
SandBoxDoyen
PRE-COMPILED BINARIES
SandBoxEcfact
Subject: aldor/axiom interoperability
SandBoxElementaryFunctionStructurePackage
\begin{axiom} )lib FSPECX \end{axiom}
SandBoxElemntry
Add conjugate \begin{spad} )abbrev package EF ElementaryFunction ++ Author: Manuel Bronstein ++ Date Created: 1987 ++ Date Last Updated: 10 April 1995 ++ Keywords: elementary, function, logarithm, ...
SandBoxEllipticCurves
Elliptic curve computations mod N in projective coordinates
SandBoxEqualizerInOpenAxiom
In FriCAS 'Equalizer' (See: LimitsAndColimits) can be defined as a 'SubDomain' as follows, but this does not work in the most recent version of OpenAxiom
SandBoxEtc
\begin{axiom} integrate(x, x) \end{axiom}
SandBoxExpOfEnd
Exponential of endomorphism with minimal polynomial
SandBoxExpr
Add conjugate \begin{spad} )abbrev domain EXPR Expression ++ Top-level mathematical expressions ++ Author: Manuel Bronstein ++ Date Created: 19 July 1988 ++ Date Last Updated: October 1993 (P.Gianni),...
SandBoxExpression
\begin{axiom} fm:=FreeMonoid(OVAR [e1,e2]) EM:=Expression(fm) x1:=e1::Symbol::EM x2:=e2::Symbol::EM p:=operator('p) p(x1) x1*x2 \end{axiom}
SandBoxExpressionExpression
\begin{axiom} x:=coerce('x)$Expression(Expression Integer) ground(x) variables x ex1:=sin(x)$Expression(Expression Integer) kernels ex1 \end{axiom}
SandBoxExpresssionComplex
\begin{axiom} msqrt:=operator('msqrt) conj1:Ruleset(Integer,Complex Integer,Expression Complex Integer) := ruleset([ _ rule sqrt(-1)*:a==msqrt(-1)*a, _ rule -sqrt(-1)*:a==-msqrt(-1)*a _ ]$List ...
SandBoxF3lix
\begin{axiom} myExpr := simplify (1-e^x)^2 - (e^(2*x)- 2*e^x + 1) \end{axiom}
SandBoxFSpace
Add conjugate \begin{axiom} )lib BOP,BOP1,FSPECF \end{axiom}
SandBoxFileUploadTest
Here is a patch:
SandBoxFisher
How useful are the different CAS languages for implementing numerical routines? Prompted by a comparison of R and C for implementing Fisher's exact test for 2x2 tables (http://fluff.info/blog/arch/...
SandBoxFloatSegment
Split from #358
SandBoxFormalProduct
\begin{axiom} f:=operator 'f differentiate(f(x),x) = differentiate(f(y),y) test % integrate(f(x),x) = integrate(f(y),y) test % -- y is replaced with x? product(f(x),x) = product(f(y),y) test % ...
SandBoxFormann
f calculates the number of 0-1 matrices with row sums 'A' and column sums 'B'.
SandBoxFreeProduct
\begin{spad} )abbrev domain FPROD FreeProduct ++ Description: ++ This domain implements the free product of monoids (groups) ++ It is the coproduct in the category of monoids (groups). ++ FreeProduct(...
SandBoxFreeSum
\begin{spad} )abbrev domain FSUM FreeSum ++ Description: ++ This domain implements the free "product" of abelian monoids (groups) ++ It is the coproduct in the category of abelian monoids (groups). ++...
SandBoxFriCAS
This page is set to execute !\begin{axiom}... \end{axiom} commands using FriCAS. See also FriCASIntegration. \begin{axiom} )version \end{axiom}
SandBoxFriCAS2
Try FriCAS calculations here. For example, here is a simple FriCAS command::
SandBoxFrobeniusAlgebra
References
SandBoxFunctionalSpecialFunction
Changed derivative of abs(x) to $$ \frac{\overline{x}}{2\ abs(x)} $$ Added conjugate(x).
SandBoxFunctor
Gaby described how to obtain the type of a functor. A functor is an "unapplied" domain constructor. A domain constructor is an expression. So for example 'Complex Integer' is a domain constructor. '...
SandBoxGenericFunction
Generic Functions in FriCAS
SandBoxGeom1
\begin{spad} )abbrev domain RSPACE RealSpace ++ Author: kfp ++ Date Created: Thu Nov 06 03:51:56 CET 2014 ++ License: BSD (same as Axiom) ++ Date Last Updated: ++ Basic Operations: ++ Related ...
SandBoxGlossary
**Glossary**
SandBoxGnuDraw
\begin{axiom} )clear completely m(0,p) == 0 m(n,p) == m(n-1,p) * p + 1 \end{axiom}
SandBoxGnuPlotTex
Gee, that's easy: \begin{gnuplot}[terminal=pslatex,terminaloptions=color,scale=1.4] plot [-pi:pi] cos(x) lw 4,sin(x) lw 4 \end{gnuplot}
SandBoxGradedTensor
\begin{spad} )abbrev domain GTEN GradedTensor GradedTensor(n:NonNegativeInteger, m:NonNegativeInteger, R:CommutativeRing,dim:NonNegativeInteger): Join(GradedAlgebra(R, NonNegativeInteger), ...
SandBoxGraphviz
\begin{latex} \digraph[scale=1.0]{SandBox5Graph1}{rankdir=LR; a->b->c; a->h; b->d; c->h; e->d e->f->g; f->h; g->h} \end{latex}
SandBoxGrassmannIsometry
Isometry from Grassmann Multivectors
SandBoxGroebnerBasis
Adapted from "Ideals, Varieties, and Algorithms Third Edition, 2007":http://www.cs.amherst.edu/~dac/iva.html
SandBoxHermitianIsomorphism3x
A complex vector CC-space $V$ possesses many different hermitian isomorphisms $h^\dagger=h \in iso(V,V^\dagger)$. In quantum mechanics a given operator $\rho \in End(V)$ may be said to be $h$-...
SandBoxHermitianIsomorphisms
A complex vector ℂ-space $V$ possesses many different hermitian isomorphisms $h^\dagger=h \in iso(V,V^\dagger)$. In quantum mechanics a given operator $\rho \in End(V)$ may be said to be $h$-...
SandBoxHermitianIsomorphisms3
A complex vector ℂ-space $V$ possesses many different hermitian isomorphisms $h^\dagger=h \in iso(V,V^\dagger)$. In quantum mechanics a given operator $\rho \in End(V)$ may be said to be $h$-...
SandBoxHermitianIsomorphisms4
EigenVectors and Diagonalization
SandBoxHiddenOverloading
This page discusses cases where instantiating of a parameter collapses two generically different functions.
SandBoxHopfAlgebra
**On Fri, May 15, 2009 at 03:23:33AM +0200, Franz Lehner wrote:**
SandBoxHyperDocReplacement
Here I demonstrate a possible way to start a replacement for HyperDoc.
SandBoxIOutput
Example for debugging boot code
SandBoxInductiveType
**On May 6, 2007 11:01 PM Gabriel Dos Reis wrote:**
SandBoxInequation
\begin{spad} )abbrev domain NEQ Inequation ++ Author: Bill Page ++ Based on: Equation by Stephen M. Watt, enhancements by Johannes Grabmeier ++ Date Created: June 2008 ++ Basic Operations: ~= ++ ...
SandBoxJacobianMatrix
\begin{axiom} )expose MCALCFN jacobian([x^2+y,x*y],[x,y]::List Symbol) \end{axiom}
SandBoxJohn2
This is a new SandBox test page. Since the page name begins with SandBox, no email notice should be generated if this page is changed.
SandBoxKMG
\begin{axiom}
SandBoxKernel
\begin{spad} )abbrev category PARTSET PartitionedSet ++ Sets whose elements are grouped into equivalence classes by a mapping ++ Author: Bill Page ++ Date Created: 20 March 2015 ++ Description: ++ ...
SandBoxLeftFreeModule
\begin{spad} )abbrev domain LFREEMOD LeftFreeModule LeftFreeModule(R: Ring, S: OrderedSet): Join(LeftModule R, IndexedDirectProductCategory(R,S)) with linearCombination: List Product(S,R) ->...
SandBoxLexicalScope
j is referenced out of scope \begin{axiom} for i in 1..5 repeat j:Integer := i^2 output(i::OutputForm)$OutputPackage output(j::OutputForm)$OutputPackage \end{axiom} The code above ...
SandBoxLimits
\begin{axiom} 1/sqrt(x^2 + 1) - sqrt(x^2 + 1)/(x^2 + 1) limit(1/sqrt(x^2 + 1),x=%i) limit(sqrt(x^2 + 1)/(x^2 + 1),x=%i) \end{axiom}
SandBoxLinearOperator
\begin{axiom} )lib CARTEN MONAL PROP \end{axiom}
SandBoxListLength
\begin{spad} )abbrev category MYLIST MyListPackage MyListPackage(T: Type): with length2: List T -> Integer == add len(count: Integer, l: List T): Integer == empty? l => count ...
SandBoxLiteral
Literals and Symbols in Axiom
SandBoxLorentzTransformation
Lorentz transformations.
SandBoxMIWHall
Many Interacting Worlds - Hall, et al. \begin{axiom} P:=operator('P); Q:=operator('Q); g:=operator('g); U:=operator('U); r:=operator('r); ℏ:=h; \end{axiom}
SandBoxMLE
I have recently been experimenting with using Axiom for maximum likelihood estimation, borrowing code (with permission) from "Compact Numerical Methods" by Nash.
SandBoxMatrixExample
Matrix Example
SandBoxMaxSingleInteger
The maximum of FriCASIssues is not really maximal.
SandBoxMaxima
Testing the Maxima interface
SandBoxMaxima2
Minimal Maxima
SandBoxMaxima3
Computing Christoffel symbols in Maxima \begin{maxima} load(ctensor); depends([a,b],[t,r]); ct_coords:[t,r,O,P]; lg:ident(4); lg[1,1]:-exp(2*a); lg[2,2]:exp(2*b); lg[3,3]:r^2; lg[4,4]:r^2*sin(O)^2; ...
SandBoxMaybe
SandBoxMonad
This may be a better definition of Monad in Axiom.
SandBoxMonads
**Bertfried Fauser** wrote:
SandBoxMorphism
Using OpenAxiom \begin{axiom} )version \end{axiom}
SandBoxMultivariatePolynomialDivision
A tutorial written by Angelos Mantzaflaris (webpage: http://users.uoa.gr/~amantzaf/proje.html )
SandBoxMyReduce
\begin{spad} )abbrev package MYRED MyReduce MyReduce(S:Type): with myred: ((S,S)->S,List S) -> S == add -- Waldek's local helper function ((f:(S,S)->S) = (g:(S,S)->S)):Boolean == --...
SandBoxMyReduceInFriCAS
\begin{axiom} )version \end{axiom} \begin{spad} )abbrev package MYRED MyReduce MyReduce(S:Type): with myred: ((S,S)->S,List S) -> S == add -- Waldek's local helper function ((f:(S,S)->S) = ...
SandBoxMyReduceInOpenAxiom
\begin{axiom} )version \end{axiom} \begin{spad} )abbrev package MYRED MyReduce MyReduce(S:Type): with myred: ((S,S)->S,List S) -> S == add -- Waldek's local helper function ((f:(S,S)->S) = ...
SandBoxNewAutodocPamphlet
\documentclass{article} \usepackage{axiom} \usepackage{hyperref} \begin{document} \title{NewAutodoc} \author{William Sit} \date{Original by Tim Daly\\ New Documentation August 13, 2006\\ Last updated ...
SandBoxNewtonsMethod
The following shows Newton's method for numerically solving f(x)=0. It is also shows examples of calling Axiom expressions and Spad functions from Lisp.
SandBoxNijenhuis
\documentclass[12pt,twoside]{article} %Marcel Dekker 2004 \usepackage{latexsym,amssymb,amsmath,amsfonts,amscd,amsthm,amstext} \usepackage[all]{xy} %epsfig,graphics %\setcounter{page}{1} \...
SandBoxNonAssociativeAlgebra
Ref: http://arxiv.org/abs/0711.3220
SandBoxNonCommutativeLaurentPolynomials
Consider a noncommutative group ring over commuting polynomials \begin{axiom} NPOLY:=MonoidRing(Polynomial(Fraction(Integer)),FreeGroup(Symbol)) \end{axiom}
SandBoxNonZeroInteger
Algebra
SandBoxNonZeroIntegerInOpenAxiom
Algebra
SandBoxObserverAsIdempotent
Obs(3) is a 9 dimensional Frobenius Algrebra \begin{axiom} )set output abbreviate on V := OrderedVariableList [p,q,r] M := FreeMonoid V gens:List M := enumerate()$V divisible := Record(lm: M,rm: M) ...
SandBoxObserverAsIdempotent2
Obs(2) is a 4 dimensional Frobenius Algebra
SandBoxObserverAsIdempotent4
Obs(4) is a 16 dimensional Frobenius Algrebra \begin{axiom} )set output abbreviate on V := OrderedVariableList [p,q,r,s] M := FreeMonoid V gens:List M := enumerate()$V divisible := Record(lm: M,rm: M)...
SandBoxOldFrontPage
Welcome to "Axiom":AboutAxiom!
SandBoxOp
Conjugate opertors \begin{spad} )abbrev domain BOP BasicOperator ++ Basic system operators ++ Author: Manuel Bronstein ++ Date Created: 22 March 1988 ++ Date Last Updated: 11 October 1993 ++ ...
SandBoxOpenAxiom
What version? \begin{axiom} )version \end{axiom}
SandBoxOperatorsAndSqrt
This fails unexpectedly: \begin{axiom} f:=operator 'f f(sin(-1)) f(sqrt(-1)) \end{axiom}
SandBoxOutputPackage
\begin{axiom} )set output algebra on \end{axiom}
SandBoxOverloading
This fails in SPAD: \begin{spad} )abbrev domain AAA Aaa Aaa: with bar: Integer -> Integer == add foo(x:Float):Integer == 1 foo(x:Integer):Integer == 2 a:Integer == 1 a:Float == ...
SandBoxPQTY
\begin{spad} ++++++++++++++++++++++++ ++ $Id: 01-AUG-2015$ +++ ++++++++++++++++++++++++ )abbrev domain RIA Q_INTERVAL ++ Author: Kurt Pagani ++ Date Created: 2012 ++ License: BSD (same as Axiom) ++ ==...
SandBoxPamphlet
\documentclass{article} \usepackage{axiom} \usepackage[final,pdfstartview=FitH]{hyperref} \begin{document} \title{\$SPAD/src/algebra dhmatrix.spad} \author{Richard Paul and Timothy Daly} \maketitle \...
SandBoxPartialFraction
Francois Maltey wrote:
SandBoxPartiallyOrderedSet
*On Tue, Aug 5, 2008 at 4:20 PM, Gabriel Dos Reis wrote:*
SandBoxPauliAlgebra
The Pauli Algebra Cl(3) Is Frobenius In Many Ways
SandBoxPfaffian
\documentclass{article} \usepackage{amsfonts} \usepackage{axiom} \begin{document} \title{\$SPAD/src/input pfaffian} \author{Timothy Daly, Gunter Rote, Martin Rubey} \maketitle \begin{abstract} In ...
SandBoxPileNotation
Example of wrong indentation.
SandBoxPoirier
Hall
SandBoxPolynomialOverFiniteField
\begin{axiom} p ==> 3 K ==> PrimeField p P ==> UnivariatePolynomial('x, K) x: P := monomial(1,1)$P f: P := (x+2)*(2*x^5 + x^3 + 2) g: P := 2*x^3 + x^2 -x +1 f/g factor f factor g k: K := 2 f/k \end{...
SandBoxPolynomialQuiz
\begin{axiom} )clear all variables (2*x+1/x)$DMP([x], EXPR INT) variables (2*y+1/y)$DMP([y], INT) a:=(2*x+1/x)$DMP([x], EXPR INT); variables a b:=(2*y+1/y)$DMP([y], INT); variables b x:DMP([x], EXPR ...
SandBoxPolynomialQuizExplained
Coming Soon! (Or you can provide them!) Please insert comments after each problem. Original quizzes on SandBoxPolynomials#quizzes
SandBoxProp
\begin{spad} )abbrev domain INEQTY InEquality ++ Author: kfp ++ Date Created: Sun Oct 26 02:21:23 CEST 2014 ++ License: BSD (same as Axiom) ++ Date Last Updated: ++ Basic Operations: ++ Related ...
SandBoxREN
\begin{axiom} As := matrix([ [-3,1,1,1], [1,1,1,1], [1,1,1,1], [1,1,1,1]]) A := subMatrix(As, 2,4,2,4) ob := orthonormalBasis(A) P : Matrix(Expression Integer) := new(3,3,0) setsubMatrix!(P,1,1,ob.3) ...
SandBoxRalf
\begin{axiom} 1+2 \end{axiom}
SandBoxRealSpace
\begin{spad} )abbrev domain RR Real ++ =================================== ++ THE REAL LINE MODELLED AS EXPR(INT) ++ =================================== ++ Modified version of Expression R ++ ...
SandBoxReduce
Try Reduce calculations here. For example::
SandBoxRelativeVelocity
\documentclass{slides} \usepackage{latexsym,amssymb,amsmath,amsfonts,amscd,amsthm,amstext} \newcommand{\bk}{\Bbbk}\newcommand{\Z}{\mathbb{Z}} \newcommand{\C}{\mathbb{C}}\newcommand{\R}{\mathbb{R}} \...
SandBoxRemember
On Tue, Oct 27, 2009 at 4:19 PM, Franz Lehner wrote::
SandBoxRepresentationTheory
From: input/repa6.input \begin{axiom}
SandBoxRibbonCategory
Refs:
SandBoxRotationMatrix
This says don't use LaTeX output. \begin{axiom} )set output tex off )set output algebra on \end{axiom}
SandBoxSPADParser
Parsing FriCAS/Axiom code
SandBoxSTRING2SPAD
Waldek Hebisch helped me to write the following Lisp code to call the SPAD compiler from the FriCAS/AXIOM interpreter.
SandBoxSage
This is a test of "Sage":http://modular.math.washington.edu/sage in MathAction.
SandBoxSageAxiomInterface
\documentclass{article} \def\code#1{{\tt #1}} \def\url#1{{\it #1}} \def\sage#1{{\bf #1}} \def\note#1{#1} \usepackage{axiom}
SandBoxSagePamphlet
\documentclass{article}
SandBoxScriptedSymbol
\begin{axiom} L ==> List OutputForm; rsl: List L := [[x1::OutputForm],[x2::OutputForm],[],[]]; sl: L := [commaSeparate(z)$OutputForm for z in rsl]; of: OutputForm := scripts(v::OutputForm, sl)$...
SandBoxSignum
Ref.
SandBoxSimple
SandBoxSinCosRules
Sin and Cos Rules
SandBoxSpecies
Test species in axiom/FriCAS.
SandBoxSpeciesAldor
Test species in axiom/FriCAS.
SandBoxSpeciesAldorSage
Test species in axiom/FriCAS and compare with the implementation in "Sage-Combinat":http://sage.math.washington.edu/home/mhansen/CombinatorialSpeciesDemo.html
SandBoxSpeciesBayreuth
\begin{axiom} )cd ~/combinat/src )re ../lib/combinat.input \end{axiom}
SandBoxSpeciesBayreuth2
Test the different Series defined for Species
SandBoxSpeciesCategory
\begin{spad} )abb category SPECCAT SpeciesCategory SpeciesCategory(L: SetCategory): Category == SetCategory with structures: Set L -> List % name: () -> String
SandBoxSqrt
Square root \begin{axiom} ksqrt:=kernels(sqrt(x))(1) name(ksqrt) argument(ksqrt) \end{axiom}
SandBoxSum
The Sum domain constructor is intended to be the "Categorical Dual":http://en.wikipedia.org/wiki/Dual_(category_theory) of the "Product":/axiom--test--1/src/algebra/ProductSpad domain constructor \...
SandBoxSurfaceComplex
\begin{axiom} )abbrev domain CMAP CellMap ++ CellMap(R,n) : Exports == Implementation where
SandBoxSymPy
Running SymPy in a SageBlock
SandBoxSymbol
Allow adding additional sub/superscripts to symbols. \begin{spad} )abbrev domain SYMBOL Symbol ++ Author: Stephen Watt ++ Date Created: 1986 ++ Date Last Updated: 7 Mar 1991, 29 Apr. 1994 (FDLL) ++ ...
SandBoxSymbolic
Symbolic Integers
SandBoxSymbolicExpressions
Unevaluated mathematical expressions
SandBoxSymbolicInverseTrig
How does FriCAS compute inverse trigonometric functions symbolically?
SandBoxSymbolicSumsAndProducts
Symbolic evaluation of sums and products
SandBoxSymbolicTrig
\begin{axiom} )lib AXIOM SINF SYMCAT SYMB AND SEXPR )lib ALTAX ALTAX- ALT )lib ASSAX ASSAX- ASSAX+ ASSAXS ASS+ ASSS )lib CANAX CANAX- CAN )lib COMAX COMAX- COMAX+ COM+ COMAX1 COMS COMAX2 COMAX3 )lib ...
SandBoxSyntax
\documentclass{article} \usepackage{axiom}
SandBoxTables
StructuredText supports tables with a simpler markup than HTML using this markup::
SandBoxTensorProduct
**Date: Fri, 15 May 2009 21:03:00 +0200 Franz Lehner wrote:**
SandBoxTensorProduct3
\begin{axiom} R ==> EXPR INT
SandBoxTensorProductPolynomial
http://en.wikipedia.org/wiki/Tensor_product
SandBoxTestTexOutput
\begin{axiom} integrate(cos(sqrt y)^3*y,y) integrate(cos(sqrt y)*y,y)/3::OutputForm+(integrate(cos(sqrt z)*z,z)/3)::OutputForm (z+1)^16 f:=operator 'f differentiate(f(1/sin(x)),x) integrate(1/sqrt(x^...
SandBoxThisFunctor
In a domain and in categories referenced in a domain the notation % represents "this domain" (or self in some programming languages). So we commonly write for example::
SandBoxThisFunctorAldor
In a domain and in categories referenced in a domain the notation % represents "this domain" (or self in some programming languages). So we commonly write for example::
SandBoxThisFunctorFriCAS
In a domain and in categories referenced in a domain the notation % represents "this domain" (or self in some programming languages). So we commonly write for example::
SandBoxTraceAffectsResults
\begin{axiom} integrate(sin(sqrt(x*x)),x) D(%,x) %-sin(sqrt(x*x)) normalize % )trace INTEF )math integrate(sin(sqrt(x*x)),x) D(%,x) %-sin(sqrt(x*x)) normalize % )trace INTEF )off integrate(sin(sqrt(x*...
SandBoxTroubleWithOperators
Operators are not immutable. Operator properties are dynamic and among other things affect equality! \begin{axiom} f:=operator 'f g:=operator 'f test(f=g) test(kernels f(x) = kernels g(x)) test(f(x)=...
SandBoxTryOutSPAD
Everyone is allowed to try out SPAD by editing this page. Don't be affraid to destroy anything. The purpose of this page is exactly to give a place for everyone to experiment.
SandBoxUnify
\begin{axiom} )abbrev package EQREASON EquationalReasoning ++ Author: Kurt Pagani ++ Date Created: Mon Mar 21 17:10:18 CET 2016 ++ License: BSD ++ References: ++ Description: ++ EquationalReasoning(R)...
SandBoxUnitsAndDimensions
See also the page named to [Units and Dimensions].
SandBoxUnparse
*On Tue, Sep 16, 2008 at 11:11 PM Waldek Hebisch wrote:*
SandBoxVeryLongLaTeX
Examples of Axiom output that causes problems for the LineBreaker program:
SandBoxWirtinger
Wirtinger Derivatives or Wirtinger Calculus (also called $\mathbb{CR}$-Calculus)
SandBoxXHashTable
A hash table implementation via double hashing
SandBoxXvfbRun
\begin{axiom} viewport1 := draw(sin x, x=-%pi..%pi) write(viewport1, "SandBoxXvfbRun1", "postscript") \end{axiom}
SandBoxZtransform
Alasdair McAndrew writes::
SandBox_pleblond
\begin{axiom} solve(p=n*log(n),n) \end{axiom}
Sandbox Errors
This is collection of popular errors made when entering FriCAS expressions.
SandboxDelay
delay vs. generate - yield
SandboxExportType
\begin{spad} )abbrev package TEST Test Test(x: Ring): with baseRing: () -> Ring == add baseRing() == x \end{spad} \begin{axiom}
SandboxFreeAndLocal
\begin{spad} )abbrev domain AAA Aaa Aaa: with foo: Integer -> Integer == add z: Integer := 0 zzz: () -> Integer foo(n: Integer): Integer == z := 1 n + 2*zzz() ...
SandboxIsomorphic
This page deals with specification of isomorphic domains.
SandboxNullaryVsConstant
\begin{spad} )abbrev domain FOO Foo Foo(): Exports == Implementation where Exports ==> with myrandom: Integer -- myrandom: () -> Integer Implementation ==> add myrandom == 42 -- ...
SandboxOutputBug
\begin{axiom} OF ==> OutputForm R ==> Record(OUTPUTFORM:OF, SEXPRESSION: SExpression, TEXFORMAT:TexFormat) e x ==> (print(([x::OF, (x::OF) pretend SExpression, x::OF::TexFormat]$R)::OF);x) )set ...
SandboxOutputTest
\begin{axiom} )version OF==>OutputForm %pi message("%pi")$OF message(" %pi")$OF message("%pi ")$OF "%pi" %pii message("%pii")$OF "%pii" message("\")$OF \end{axiom}
SandboxPamphletStyle
This page describes how pamphlets should look like.
SandboxPermutations
\begin{axiom} PI ==> PositiveInteger LPS ==> List Permutation SetCategory PS ==> Permutation SetCategory LPSET ==> List Permutation Set Integer PSET ==> Permutation Set Integer lookup(lps2:LPS,i:PI): ...
SandboxPlex
\begin{axiom} OF ==> OutputForm -- e x ==> x::OF pretend SExpression e x ==> x e integral(x^x, x) e integral(x^x, x=a..b) e sum(x^x, x) e sum(x^x, x=a..b) e product(x^x, x) e product(x^x, x=a..b) e ...
SandboxTypeDefinitions
There seems to be different understandings of Type, domain, category, Category, etc. around. Here is an attempt to collect all these different opinions in order to make discussion about them clearer.
SandboxWorkShopRISC2008
Aldor & Axiom Workshop 2008 part of "RISC Summer 2008":http://www.risc.uni-linz.ac.at/about/conferences/summer2008/
Savannah
RemoteUrl: http://savannah.nongnu.org
ScratchPad
Scratchpad was a computer algebra system developed at IBM in the early 1970s. Like M&M (Maple and Mathematical) and other systems today, Scratchpad had one principal representation for mathematical ...
ScreenShots
A short demonstration of Axiom
SequenceIteration
Sequence Iteration
SeriesSolve
SeriesSolve implements a workaround to the broken package delivered with Axiom. It handles quite arbitrary functional equations, but uses a questionable algorithm. It certainly should be replaced by ...
Set
\begin{axiom} )show Set \end{axiom}
SetCategory
Returns -- a category
SimpleSpadExamples
This page is a hub to link to various simple examples. Currently: PascalTriangle, SequenceIteration, SymbolicDifferentiation, HeapSort1.
Simpson's method
This routine provides Simpson's method for numerical integration. Although Axiom already provides a Simpson's method, this version has a syntax that will be intuitive to anyone who has used the ...
SingleInteger
\begin{axiom} )show SingleInteger \end{axiom}
SiteIndex
A glossary generated from the pages on this site.
Snake Relation
Non-degeneracy of the pairing
Solving Differential Equations
Test 1: solve a simple nonlinear homogeneous differential equation
Source Repository
- [Axiom Sources]
SourceForge
RemoteUrl: http://sourceforge.net
SpadFileConvention
Conventions for writing .spad files after noweb has been dropped
SparseMultivariateTaylorSeries
How to work with multivariate Taylor series
SpeedOfUserCode
Here w show FriCAS version of benchmark presented at http://cosmosimple.blogspot.de/2013/12/some-benchmarks-of-mathematica-vs.html
Sqrt3Demo
Some demo involving the algebraic number $\sqrt{3}$.
Status Page
Adapted from ZopeWikiStats
StructuredTables
\begin{axiom} P:= [[1,0,0],[0,1,0],[0,0,0]] Q:= [[0,0,0],[0,0,0],[0,0,1]] CT := CARTEN(i0 := 1,3,Integer) epsilon:CT:=leviCivitaSymbol() permi1:= matrix[[e0,0,0],[0,e0,0],[0,0,e0]] permi2:= ...
StructuredText
Structured Text is a simple plain text markup format used by Zope and ZWiki. It's similar in effect to !WikiWikiWebMarkup but is more intuitive and standardized. The idea is to have text that is ...
SubDomain
PositiveInteger and NonNegativeInteger are subdomains of Integer.
Symbolic Integration
Errors in symbolic integration
SymbolicAssociativeExpressions
\begin{axiom} )lib AXIOM SINF SYMCAT SYMB AND SEXPR )lib ALTAX ALTAX- ALT )lib ASSAX ASSAX- ASSAX+ ASSAXS ASS+ ASSS )lib CANAX CANAX- CAN )lib COMAX COMAX- COMAX+ COM+ COMAX1 COMS COMAX2 COMAX3 )lib ...
SymbolicDifferentiation
Symbolic Differentiation Tutorial
SymbolicItoCalculus
itovsn3 (author: Wilfrid S. Kendall)
SymbolicNonAssociativeExpressions
\begin{axiom} )lib AXIOM SINF SYMCAT SYMB AND SEXPR )lib ALTAX ALTAX- ALT )lib ASSAX ASSAX- ASSAX+ ASSAXS ASS+ ASSS )lib CANAX CANAX- CAN )lib COMAX COMAX- COMAX+ COM+ COMAX1 COMS COMAX2 COMAX3 )lib ...
SymbolsAndVariables
Interpreter
SymmetricGroupCombinatoricFunctions
\begin{axiom} )show SymmetricGroupCombinatoricFunctions \end{axiom}
series
Carl McTague asked axiom to evaluate
simplify exponents
How to simplify exponents
simplifying Expressions
Simplification of Expressions
statistical functions
Anonymous shared the following library of statistical functions with us. Many thanks! (He added, that they are not checked...)
string conversions
Here is a package that converts strings to numbers. It is only to be considered as a starting point. There is no error checking, it is probably slow and certainly buggy...
T
TableAggregate
\begin{axiom} )sh TableAggregate \end{axiom}
TaylorSeries
Example for multivariate Taylor series expansion
TeX
and LaTeX are mathematical typesetting programs.
TeXmacs
"GNU TeXmacs":http://www.texmacs.org/tmweb/home/welcome.en.html is a free scientific text editor, which was both inspired by TeX and GNU Emacs. The editor allows you to write structured documents via ...
TensorProduct
\documentclass{article} \usepackage{axiom,amsthm,amsmath,url} \newtheorem{ToDo}{ToDo}[section] \usepackage{a4wide} \newcommand{\Axiom}{{\tt Axiom}}
The Algebra of Complex Numbers Is Frobenius In Many Ways
The Algebra of Complex Numbers Is Frobenius In Many Ways
ToDelete
Root for pages which probably should be deleted
TouchGraph
TouchGraph is a graphical web page navigator.
Tuples Products And Records
On Fri Jul 1 14:47:12 -0500 2005 Bill Page wrote:
TutorialIntroductionToAxiom
A Tutorial Introduction To AXIOM
TwistedSnakeRelation
Non-degeneracy of the pairing (snake relation)
Type Equivalence
Type equivalence of domains in Axiom and Aldor
TypeTowerDemo
This page demonstrates some features of Axiom.
TypedGcd
GCD and types
test
\begin{axiom} draw(5*sin(sqrt(x^2+y^2)) , x=-20..20 , y=-20..20); \end{axiom}
U
Unevaluated Expressions
Note: In FriCAS 'max' on expressions is currently undefined.
Unicode
The following Greek characters are supported as text::
UnicodeIssues
This page has more details about the unicode issue introduced on the FriCASIssues page.
Units and Dimensions
**On Friday, August 19, 2005 4:56 PM C Y wrote:**
UnivariatePolynomial
Section 9.83 UnivariatePolynomial
UnivariateTaylorSeriesODESolver
\begin{axiom} )show UnivariateTaylorSeriesODESolver \end{axiom}
UnrelatedSites
The following web sites are not related to the Axiom computer algebra system but have names that suggest that they might. We collect them here for easy reference and in case someone got here by ...
UserInterface
There are several options to interact with FriCAS:
V
VMWare
Run any virtual machine
VirtualBox
How to provide FriCAS as a VirtualBox VDI file ==============================================
W
WebSite
RemoteWikiURL: http://
WesterProblemSet
\documentclass{article} \usepackage{axiom} \usepackage{makeidx} \makeindex \begin{document} \title{The Wester Problem Set} \author{Timothy Daly} \maketitle \begin{abstract} I'm starting to construct ...
Where do variables belong?
Currently, Axiom allows \begin{axiom} (1/x)::UP(x, FRAC POLY INT) \end{axiom}
WikiWikiWeb
Ward Cunningham's WikiWikiWeb is the original and still one of the largest and most active wikis. It contains a wealth of information about wiki and many other things.
WindowsInstaller
\documentclass{article} \usepackage{axiom} \begin{document} \title{\textbf{OpenAxiom Windows Installer Script}} \author{Alfredo Portes} \maketitle
WindowsSetupNoBuild
Complete Setup on Windows With No Builds Required
Wish List
Assumptions/provisos: FriCAS shuld be able to do simplifications based on extra assumptions.
WorkShopRISC2006
will take place at the "Research Institute for Symbolic Computation":http://www.risc.uni-linz.ac.at in "Hagenberg":http://www.risc.uni-linz.ac.at/about/map, Austria from Thursday, April 27, 10 am, to ...
WorkShopRISC2007
AXIOM Workshop 2007 Symmetric Functions "RISC-Linz":http://www.risc.uni-linz.ac.at
WorkShopRISC2008
Aldor & Axiom Workshop 2008 part of "RISC Summer 2008":http://www.risc.uni-linz.ac.at/about/conferences/summer2008/
WorkshopRisc2006
will take place at the "Research Institute for Symbolic Computation":http://www.risc.uni-linz.ac.at in "Hagenberg":http://www.risc.uni-linz.ac.at/about/map, Austria from Thursday, April 27, 10 am, to ...
X
Xming
Xming X Server
Y
Yacas
From Yacas' web page:
Z
ZWiki
Zwiki is the software which drives this wiki site. It has been developed by "Joyful Systems":http://joyful.com and "contributors":http://zwiki.org/ZwikiContributors around the world, and is ...




  Subject:   Be Bold !!
  ( 12 subscribers )  
Please rate this page: