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 - AWAIC
- \begin{spad}
--- Disclaimer
--- The National Institute of Standards and Technology (NIST) uses its best
--- efforts to deliver a high quality copy of the Database and to verify that
--- the data ...
- 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.
- AldorForFriCAS
- It is possible to use the Aldor compiler WebSite:www.aldor.org
to compile functions which you then can use from FriCAS. Currently
the following commands work and install Aldor in '/opt/aldor':
- 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.
- 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 ...
- Axiom Algebra
- In FriCAS adding a new constructor (category, domain or package) is easy, just add
it and update algebra Makefile.in as indicated in note at top of Makefile.in
- Axiom Strengths
- See FriCASAdvantages. The page below is mostly historical.
- 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]
- AxiomBook
- This is historical entry. For up to date version go to
FriCASBook.
- AxiomCompiler
- See [FriCAS compiler]. The text below is mostly of historical interest.
The language used for programming Axiom is called SPAD. In fact, SPAD has a
cousin, originally intended as a successor called "...
- AxiomDocumentation
- The Axiom Book
- AxiomProgrammingDiscussion
- Meta-classes versus Categories
- AxiomPromotion
- 1 Communities to inform of a release
- AxiomScreenCast
- Flash Presentations
- AxiomSources
- For up-to-date information about Axiom see http://axiom-developer.org
- AxiomUI
- by [Kai Kaminski]
- AxiomWindowsInstallerScript
- \documentclass{article}
\usepackage{axiom}
\begin{document}
\title{\textbf{Axiom Windows Installer Script}}
\author{Jose Alfredo Perez}
\maketitle
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.
- 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 ...
- BootProgramming
- Boot (more precisely newer dialect called Shoe) is used internally in FriCAS for some of the interpreter
and compiler code. Here is a detailed description of the
"Boot Language":/axiom--test--1/src/...
- 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/
- BuildFriCAS
- Building on Linux
- BuildOnCygwin
- Note: the text below should be identical to the contents of INSTALL.CYGWIN in
the FriCAS distribution.
- BuildOnWindows
- Building FriCAS on Windows
- BuildOpenAxiom
- Building on Linux
C - CaleyDickson
- Ref:
- Cartesian Product
- This domain implements cartesian product, we give example usage here:
- Category Theory and FriCAS
- ClosedLinearOperator
- Introduction
- Common Mistakes
- 1 Omitting the {axiom} enviroment
- CommonDenominator for polynomials
- This page presented extension of UnivariatePolynomialCommonDenominator for arbitrary polynomial categories. FriCAS now
contains such extension, so we just present an example.
- Complex Polynomial
- Why this evalutate to zero ?
\begin{axiom}
A: Complex Polynomial Integer
A*conjugate A - A^2
\end{axiom}
Definitely wrong. It looks like the source of the problem is:
\begin{axiom}
conjugate(a)
\...
- Computing with Vectors
- How to multiply two vectors??
- Constant of integration
- By definition definite integral is determined only up to integration constant.
When integral depends on parameters constant of integration also depends
on parameters. Some choices of integration ...
- CopyrightPage
- Axiom was released under this license as of September 3, 2002.
- 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
- 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 ...
- DedekindEtaFunctions
- Some links related to Dedekind Eta Functions
- Definite Integration
- Here are some integration problems.
- DependentTypeTest1
- \begin{spad}
)abbrev category ACAT A_Categeroy
A_Categeroy() : Category == SetCategory with
degree : % -> Polynomial Integer
)abbrev domain BDOM B
B(p) : Exports == Implementation where
...
- DependentTypeTest2
- \begin{spad}
--)lisp (defvar |$inclAssertions| nil)
- DerivFunc
- \begin{axiom}
- Design By Contract
- Software and especially hardware frequently is treated as "given". More precisely,
hardware and software has properties and users depend on its properties. Some properties
are documented, some ...
- DesignIssues
- This should become a page where we document design issues.
- DistributedExpression
- Francois Maltey (FM) and Bill Page (BP) wrote::
- Division by zero during evaluation
- Evaluation may lead to spurious division by zero. This problem is not limited
to FriCAS, in fact it is general mathematical fact which limits what computers
(and people) can do. Simplest example is ...
- 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 example
- In FriCAS expression are represented as rational functions in kernels.
exp(2*x) and exp(x) are different kernels, so
\begin{axiom}
exp(2*x) - exp(x)^2
\end{axiom}
gives nonzero result. To recognize ...
- 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}
- EtaRelations8
- Relations among eta functions of level 8
- ExampleCharacterTable
- We want to compute characters of wreath product Z_3^(Z_3)*Z_3
- ExampleCompositeFunction
- In practice we frequently need to deal with composite functions.
This is frequently formulated as 'y' depends in 'x' where 'x'
is a function (say of argument 't'). Unlike some other systems
in ...
- ExampleFreeAbelianGroup
- How to use FreeAbelianGroup
- ExampleGroebner
- Application of Groebner Bases
- ExampleInequalitiesViaCAD
- Recenty in sci.math.symbolic there was a question if
\begin{equation}
b^2 \geq (a - c)^2
\end{equation}
and
\begin{equation}
a^2 \geq b^2
\end{equation}
implies
\begin{equation}
c^2 \geq (a + b)^2
\...
- 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
- Note: 04-Apr-2021: This page is abandoned. It's new place is
https://fricas.github.io/fricas-notebooks/FriCAS-SkewPolynomial.html
- ExampleSolve
- This is motivated by discussion in Sage mailing list. We are given sum of ellipsis and
a strip symmetric with respect to one of the axis of the ellipsis. We want to
find circle with center on the ...
- ExampleSolve2
- The following example appeared in Maxima mailing list (Maxima could
not do it). Here we solve it using FriCAS. First we form
system of equations:
\begin{axiom}
-- Form system of equations
eqn1 := ...
- ExampleXDistributedPolynomial
- Demonstration of XDistributedPolynomial
- ExpressionInteger
- This page gives a few comments about the expression domain 'Expression Integer'
and the use of more specific domains.
- editor
- Just placeholder
F - FAQ
- Frequently Asked Questions
- FRICASsys
- is the main FriCAS program. It does not include graphics or
hyperdoc browsing. Under Linux FriCAS is usually started
via a script called 'fricas' that also starts other processes
such as sman (the ...
- 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:
- ForksInfo
- In 2007 open source Axiom project forked twice, leading to three
separate projects (forks):
- FriCAS is a fork of the original open source Axiom project created by Waldek Hebisch on July 9, 2007 ...
- 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
- Aldor is now free. Most of material below is only of historical interest.
- FreeModule
- FreeModule implements free module
over a ring with generators indexed by a 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.
- FreeMonoid
- The free monoid on a set S is the monoid of finite products of
the form reduce(*, [si ^ ni]) where the si's are in S, and the ni's
are nonnegative integers. The multiplication is not commutative.
...
- FreeRing
- \begin{axiom}
)lib FPROD
)lib FSUM
\end{axiom}
- FriCAS
- "!FriCAS Project":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. For this meaning
see [FriCAS Library]. The source code
for algebra is ...
- FriCAS Binaries
- You can find Fricas installation files at http://fricas.sourceforge.net/download.html
- FriCAS Book
- FriCAS Book is up to date version of Axiom Book by Jenks and Sutor. Master sources are bundled
with FriCAS. HyperDoc shows it when you choose 'Reference' and then 'FriCAS Book'.
Up to date '.pdf' ...
- FriCAS Colloquium
- The Colloquium's purpose is two-fold: 1) for the participants to share and discuss theory, practical experiences and insights regarding FriCAS, and 2) to assist others concerned with FriCAS and ...
- 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 Library Examples
- Here we collect some examples of using FriCAS library
- FriCAS Problems
- - [Unevaluated Expressions]
- FriCAS Sources
- Links to release tarballs -- 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 detailed
and up to date documentation is in FriCAS book at http://fricas.github.io/book.pdf There
are changes compared to ...
- 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
- FriCASEmacsMode
- FriCAS contains up-to date Emacs mode. You can start FriCAS inside Emacs typing 'efricas'.
- FriCASGraphics
- Graphics in FriCAS
- FriCASHelpSet
- )help set
- 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 FriCAS 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
- FriCASProgrammingModel
- FriCAS language (both interpreter and Spad) is imperative, basic operation is an assignment like
\begin{axiom}
a : Integer := 5
b : Integer := a + 2
\end{axiom}
FriCAS language is typed, each ...
- FriCASSpecialIntegration
- FriCAS can now handle large class of integrals expressible in terms of exponential
integral, error functions, incomplete Gamma function with constant
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 first chapters of FriCAS book http://fricas.github.io/book.pdf
may serve as a tutorial.
- 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 - GraphViz
- "An Introduction to GraphViz":http://www.linuxjournal.com/article/7275
- Graphics on MathAction
- Graphics?
- GroupAlgorithms
- FriCAS implements several algorithms for working with groups:
- Guessing formulas for sequences
- Author: "Martin Rubey":http://www.mat.univie.ac.at/~rubey/martin.html
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
- HistoricAxiom
- History
- HyperDoc
- FriCAS in X11 environment (for example Linux) includes graphics and working HyperDoc browser.
- HyperDocTracing
- The Trace Facility
- HyperG
- \begin{spad}
)abbrev package SPI SumProdInt
SumProdInt(R): Exports == Implementation where
R:Join(Comparable,IntegralDomain,RTZZ,LEZZ)
I - Imitation As Complement
- MaplePrimes
- Indefinite Types
- Declaring Types
The idea that one should be able to "declare the type" of a
variable in FriCAS 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
- Interval Arithmetic
- Interval arithmetic for Axiom was implemented by Mike Dewar in form of Aldor files.
Juergen Weiss converted the files to Spad and they are included in current FriCAS
distribution.
- 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":FriCASCompiler,
the "FriCAS 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
- Note: this is historical info. FriCAS sources are just Spad
files and Axiom changed its format.
- 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 FriCAS-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
- 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):
- 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 FriCAS
- 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:
N - Nature of expressions
- FriCAS expression domains are based on notion of differential field. This
have advantages, for example some otherwise unsolvable problems became
solvable when dealing with differential fields. But ...
- News
- Please post notices and information about events, conferences
and meetings related to FriCAS and computer algebra here.
- Next Axiom Meeting
- **On November 19, 2005 10:34 AM Tim Daly (root) wrote:**
- NonCommutativeLaurentPolynomials
- Consider a noncommutative group ring over commuting polynomials
\begin{axiom}
NPOLY:=MonoidRing(Polynomial(Fraction(Integer)),FreeGroup(Symbol))
\end{axiom}
- NoncommutativePolynomials
- There is are some domains in FriCAS for doing computations with
non-commuting variables developed by Michel Petitot. You can find
some examples in the FriCAS book under the title XPolynomial but
...
- 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}
- new
- begin/{axiom}
[1/7, 3/4, 5/6]
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{...
- numerical linear algebra
- I want to get (estimates of) the eigenvalues of a 10x10 matrix of floats:
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 ...
- OldWishList
- This is the old AXIOM wish list, kept for historical reasons.
- OpenAxiom
- Note: Apparently OpenAxiom developement stopped in 2015. Currently there
is no runnable OpenAxiom in the wiki. The rest of the page is just for
historical record.
- OpenAxiom Sources
- Repository -- http://www.open-axiom.org/download.html
- OpenAxiomWindows
- Installing OpenAxiom on Windows
- OrderedSet
- The class of totally ordered sets, that is, sets such that for each pair of elements (a, b)
exactly one of the following relations holds a < b or a=b or b < a
and the relation is transitive, i.e. a <...
- OrderedVariableList
- This domain implements ordered variables
\begin{axiom}
)sh OrderedVariableList
\end{axiom}
- OtherComputerAlgebraSystems
- Someday (maybe) we will also include online access to
other systems such as:
- OverloadProblems
- **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
- 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 FriCAS that start with a percent sign.
- 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
- 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::...
- PolynomialOverFiniteField
- \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{...
- 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
- This contribution is included in FriCAS. Info below is partly
historical, parlty adds documentation.
- RealNumbers
- FriCAS 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 the Risch algorithm is split into two stages, a preparatory one
where the integrand is rewritten to express it in terms of differential
fields, and the core part.
- Root denesting
- FriCAS can denest many nested roots. This is implemented in an extra package so
befor use we need to expose it:
\begin{axiom}
)expose RootSimplification
\end{axiom}
- 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 - 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 FriCAS and Reduce. Please be ...
- SandBox 1D output Form
- **How to have an output similar to a 1D input form?**
- 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
- FriCAS currently has a subsystem for*graphs*. The discussion below
is morstly of historical interest. Note that some names in code below
are the same as names in current implementation which
...
- 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 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 FriCAS 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 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 Risch
- Let us integrate functions as explained in:
IV_ (https://math.stackexchange.com/users/292527/iv), Does someone know an online-applet for the Risch-algorithm?, URL (version: 2020-08-20): https://...
- SandBox SPAD dependent types
- ** Notations **
- 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-TDT
- 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 FriCAS 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)
- SandBoxA000230
- \begin{axiom}
a: (Integer) -> Integer
a(n) ==
i:=2
repeat
j:=nextPrime(i)
if j-i = 2*n or n = 0 then
return i
i:=j
- 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:((
- SandBoxAlgebraOfObservers2
- Obs(2) is a 4 dimensional Frobenius Algebra
- 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
- 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}
- SandBoxBugGroebnerFactorize
- \begin{axiom}
ideq:LIST(POLY(FRAC(SMP(INT,OVAR([mp,mq,mr,γqp,γrp,γrq]))))) := [ _
(γrp^2*mr^2*mp*%x5+(γrq*γrp*γqp*mr*mq*mp*%x4+γrp^2*mr*mp*%x1))*%x8+((γrq*γrp*γqp*mr*mq*mp*%x5+(γqp^2*mq^2*mp*%x4+γ...
- 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}
artanh:(Float) -> Float
artanh(x) ==
y := x
k := 1
for k in 1..precision() repeat
z := x^(2*k+1) / (2 * k + 1)
y := z + y
return y
- 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}
\...
- SandBoxComplexFunctionTest
- \begin{axiom}
Gamma(0.5+0.5*%i)
\end{axiom}
- SandBoxComplexManifold
- Complex domain constructor done differently.
- SandBoxConditionalFunctions
- **Conditional for inner functions in a package.**
- SandBoxDFORM
- \begin{spad}
)abbrev package DFORM DifferentialForms
++ Author: Kurt Pagani
++ Date Created: October 2014
++ Revised: Sat Sep 17 17:10:00 CET 2016
++ License: FriCAS/BSD
++ Description: Basic ...
- SandBoxDFT
- \begin{spad}
)abbrev package TYPEPKG TypePackage
TypePackage (T : Type) : Exports == Implementation where
Exports == with
typeof : T -> Type
Implementation == add
typeof(x:T) == T
- 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.
- SandBoxDOPT
- \begin{spad}
)abbrev package DOPT DiscreteOptimalTransport
++ Author: Kurt Pagani
++ Date Created: Thu Jun 21 01:42:00 CEST 2018
++ License: BSD
++ References:
++ Description:
++
...
- 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 ...
- SandBoxDemoXFreeAlgebra
- \begin{axiom}
-- Category: XFreeAlgebra(vl : OrderedSet, R : Ring) : Category
-- ++ Author: Michel Petitot petitot@lifl.fr
-- ++ Date Created: 91
-- should be enough to impl TensorAlgebra(R-Module), ...
- 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 := (1-e^x)^2 - (e^(2*x)- 2*e^x + 1)
\end{axiom}
- SandBoxFORMAN
- \begin{spad}
)abbrev package FORMAN FormalManipulations
++ Author: Kurt Pagani
++ Date Created: Tue Jun 19 19:09:16 CEST 2018
++ License: BSD
++ References:
++ Description:
++ Interactive Computer ...
- 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'.
- SandBoxFractionGCD
- \begin{axiom}
R := Integer
Q := Fraction R
gcd(8,4) = retract gcd(8::Q, 4::Q)
\end{axiom}
- 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.
- SandBoxHyperGeometric
- \begin{spad}
)abbrev package SUMMPACK SummPack
SummPack(): Exports == Implementation where
FPI ==> Fraction Polynomial Integer
X ==> Expression Integer
NNI ==> NonNegativeInteger
PI ==> ...
- SandBoxINFSUM
- \begin{spad}
)abbrev package UNIFY Unify
++ Author: Kurt Pagani
++ Date Created: Mon Feb 06 18:56:20 CET 2017
++ License: BSD
++ References:
++ Description:
++
Unify(X) : Exports == Implementation ...
- 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: ~=
++ ...
- SandBoxJacobiDiag
- \begin{spad}
)abbrev package JACDIAG JacobiDiagonalisation
++ Author: Kurt Pagani
++ Date Created: Sat Jun 16 23:37:27 CEST 2018
++ License: BSD
++ References:
++ Jacobi, C.G.J. (1846). "Über ein ...
- SandBoxJacobiDiagFloat
- \begin{axiom}
PI ==> PositiveInteger
NN ==> NonNegativeInteger
IF ==> Float
VIF ==> Vector Float
MIF ==> Matrix Float
- SandBoxJacobiDiagIntervalFloat
- \begin{axiom}
RR ==> Expression Integer
CC ==> Expression Complex Integer
- 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}
- SandBoxLinearProgramming
- \begin{spad}
)abbrev package LINPROG LinearProgramming
++ Author: Kurt Pagani
++ Date Created: Sun Jun 03 02:05:55 CEST 2018
++ License: BSD
++ References:
++ Description:
++ TODO: description, more ...
- 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
- SandBoxNonZeroInteger
- Algebra
- SandBoxNonZeroIntegerInOpenAxiom
- Algebra
- SandBoxObserverAsIdempotent
- Obs(3) is a 9 dimensional Frobenius Algrebra
\begin{axiom}
)set output abbreviate on
)set message type off
\end{axiom}
- 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 ...
- SandBoxPhysicalUnitSystem
- \begin{spad}
)abbrev category PUNIT PhysicalUnit
PhysicalUnit() : Category == with
"*" : (%,%) -> %
"/" : (%,%) -> %
"^" : (%,Integer) -> %
"=" : (%,%) -> Boolean
dim : % -...
- SandBoxPileNotation
- Example of wrong indentation.
- SandBoxPlotly
- \begin{spad}
)abbrev package PLOTLY Plotly
++ Author: Kurt Pagani
++ Date Created: Sat Jul 14 01:52:32 CEST 2018
++ License: BSD
++ References:
++ Description:
++
Plotly(R) : Exports == ...
- SandBoxPoirier
- Hall
- 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
- SandBoxProduct
- \begin{spad}
)abbrev domain PRD2 Product2
rep(x) ==> x @ % pretend Rep
per(x) ==> x @ Rep pretend %
Product2(X:SetCategory,Y:SetCategory): with
construct: (X,Y) -> %
coerce: % -> OutputForm
...
- 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}
E ==> Expression Integer
OF ==> OutputForm
macro R == Record(OUTPUTFORM:OF,_
SEXPRESSION: SExpression,_
SEXPRESSION: SExpression,_
...
- 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:
- SandBoxRootOfUnity
- \begin{spad}
)abbrev domain ROU RootOfUnity
++ Author: Kurt Pagani
++ Date Created: Fri Jun 01 17:24:19 CEST 2018
++ License: BSD
++ References:
++ https://en.wikipedia.org/wiki/Root_of_unity
++ ...
- SandBoxRotationMatrix
- This says don't use LaTeX output.
\begin{axiom}
)set output tex off
)set output algebra on
\end{axiom}
- SandBoxSEXPM
- \begin{spad}
)abbrev package UNIFY Unify
++ Author: Kurt Pagani
++ Date Created: Mon Feb 06 18:56:20 CET 2017
++ License: BSD
++ References:
++ Description:
++
Unify(X) : Exports == Implementation ...
- SandBoxSPADParser
- Parsing FriCAS/Axiom code
- SandBoxSSPM
- \begin{spad}
)abbrev package SSPM SuperSimplePatternMatcher
++ Author: Kurt Pagani
++ Date Created: Mon Feb 06 18:56:20 CET 2017
++ License: BSD
++ References:
++ www.cs.northwestern.edu/academics/...
- 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::
- SandBoxTensorAlgebra
- \begin{spad}
---)lisp (setq |$inclAssertions| nil)
--- https://en.wikipedia.org/wiki/Tensor_algebra
- SandBoxTensorAlgebra2
- \begin{spad}
)abbrev domain TENSALG TensorAlgebra
TensorAlgebra(M,R,B) : Exports == Implementation where
- SandBoxTensorAlgebra3
- \begin{spad}
)abbrev domain TENSALG TensorAlgebra
++ Author: Kurt Pagani
++ Date Created: Thu Jan 30 23:04:02 CET 2020
++ License: BSD
++ References:
++ https://en.wikipedia.org/wiki/
...
- SandBoxTensorPower
- \begin{axiom}
n:=5000 -- whatever PI
- 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
- SandBoxTest1
- \begin{axiom}
1 + 2
\end{axiom}
- 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 FriCAS 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[Polynomial Sequences: Matrix]
- \begin{axiom}
--- Functions to facilitate Transforming Polynomial Generating Functions into
---- Coefficient arrays. With some examples
--- These are coefficient arrays (A) and can be rendered into ...
- SandBox_pleblond
- \begin{axiom}
solve(p=n*log(n),n)
\end{axiom}
- SandBox{{7*7}}
- This is the front page of the **SandBox**. You can try anything you like
here but keep in mind that other people are also using these pages to
learn and experiment with FriCAS and Reduce. Please be ...
- Sandbox Errors
- This is collection of popular errors made when entering FriCAS expressions.
- Sandbox Variables Evaluation
- ** Thoughts on Variables Evaluation **
- SandboxDelay
- delay vs. generate - yield
- SandboxDemoFreeMonoid/-Module
- \begin{axiom}
-- FreeMonoid(S: SetCategory)
-- S can be almost anything
- SandboxErik
- How do I find the n-root of a number?
- SandboxExportType
- \begin{spad}
)abbrev package TEST Test
Test(x: Ring): with
baseRing: () -> Ring
== add
baseRing() == x
\end{spad}
\begin{axiom}
- SandboxFactoringNoncommutativePolynomials
- Konrad Schrempf wrote::
- 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 ...
- SandboxSomos2Eta
- Translation from Somos notation to eta-function notation and back
- 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/
- ScratchPad
- Scratchpad was a large, general purpose computer algebra system
developed at IBM. Developement was started around 1965 by
J. Griesmer with creation of Lisp system. Later,
Richard Jenks joined ...
- ScreenShots
- A short demonstration
- SequenceIteration
- Sequence Iteration
- SeriesSolve
- This package is included in FriCAS. Compared to previous series solver
it handles quite arbitrary functional equations, but uses a questionable algorithm.
It certainly should be replaced by ...
- 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 FriCAS already provides a Simpson's method, this version has a syntax that will be intuitive to anyone who has used the ...
- 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
- - [FriCAS 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 we 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.
- SymbolInteger
- \begin{spad}
)abbrev package SYMINT SymbolInteger
++ Date Created: Fri Sep 02 01:11:15 CEST 2022
++ Description: _[-]d+ ; symbols as integers
++
SymbolInteger(T:Type) : Exports == Implementation ...
- 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
- series
- Currently FriCAS can not 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 - TaylorSeries
- Note 04-Apr-2021: This page is abandoned, it's new home is
https://fricas.github.io/fricas-notebooks/FriCAS-TaylorSeries.html
- 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 ...
- Test
- \begin{axiom}
integrate((atan(x))^n,x)
\end{axiom}
- Test12
- FriCAS
\begin{axiom}
1 + 1
\end{axiom}
Maxima
\begin{maxima}
1 + 1;
\end{maxima}
Reduce
\begin{reduce}
1 + 1;
\end{reduce}
- Test14
- Test
- TexFormat0
- \begin{axiom}
--- TexFormat (tex.spad)
--- Ugly primes (op PRIME) in derivatives and unwanted quotes (" ") are now gone
- TexFormat1
- \begin{spad}
)abbrev domain TEX TexFormat
++ Author: Robert S. Sutor
++ Date Created: 1987 through 1992
++ Basic Operations: coerce, convert, display, epilogue,
++ tex, new, prologue, setEpilogue!, ...
- 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
- ToDo
- A short list of things to implement:
- Topics
- This page should serve to link (dispatch) to more specific topics
- TouchGraph
- TouchGraph is a graphical web page navigator.
- Tuples Products And Records
- On Fri Jul 1 14:47:12 -0500 2005 Bill Page wrote:
- TutorialIntroductionToFriCAS
- A Tutorial Introduction To FriCAS
- TwistedSnakeRelation
- Non-degeneracy of the pairing (snake relation)
- Type Equivalence
- Type equivalence of domains in FriCAS and Aldor
- TypeTowerDemo
- This page demonstrates some features of FriCAS.
- TypedGcd
- GCD and types
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
- 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, FriCAS 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/
X - XDistributedPolynomial
- This type supports distributed multivariate polynomials
whose variables do not commute.
The coefficient ring may be non-commutative too.
However, coefficients and variables commute.
\begin{axiom}
)sh ...
- 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 ...