Math: Algebra: Software

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A Tutorial Introduction To AXIOM
http://www.dcs.st-and.ac.uk/~mnd/documentation/axiom_tutorial/axiom.html
By Martin N. Dunstan.

Albert
http://www.cs.clemson.edu/~dpj/albertstuff/albert.html
Albert is an interactive program to assist the specialist in the study of nonassociative algebra: the main problem addressed is the recognition of polynomial identities in varieties of nonassociative algebras. Download source code in C.

Aldor
http://www.aldor.org/
Originally an extension to Axiom, now a separate product. Binaries are available free for non-profit use, with documentation, tips, projects and links.

Algebra Cheat
http://www.bacsoftware.co.uk/algebra/
Program solves variable equations and gives explanations of steps used.

Algebra Helper
http://www.algebra-answer.com/
Helps students with equations and inequalities, simplifying expression, graphing and complex numbers. Includes problem solving exercises.

Algebra Problem Solver
http://www.cyberedinc.com/
Personal Algebra Tutor - Enter your algebra problems and get instant step-by-step solutions with explanations.

Algebra Word Problem Tutor:Miss Lindquist
http://www-2.cs.cmu.edu/~neil/
The world's first web-delivered self-improving intelligent tutoring system able to tutor students in writing expressions for algebra word problems.

AXIOM
http://www.nag.co.uk/symbolic_software.asp
Symbolic solver complete with a high-level interactive language, user extensible library and visualisation tool for the manipulation of graphical output. For Unix and Windows. No longer produced: support ceases at the end of 2001.

Axiom Computer Algebra System
http://savannah.nongnu.org/projects/axiom
Savannah Free Software project for revival of Axiom as open source.

CMAT
http://www.numbertheory.org/cmat/krm_cmat.html
A matrix calculator program, written in C. Calculations can be performed on matrices with complex rational coefficients using exact arithmetic routines, as well as on matrices with elements mod p.

CoCoA
http://cocoa.dima.unige.it/
A special-purpose system for computations in Commutative Algebra.

Combinatorial Representation Theory (CREP)
http://www.mathematik.uni-bielefeld.de/~sek/crep.html
CREP is designed to deal with categories whose morphism spaces are finite-dimensional over a field k. The main example of a category with this property is the category of finite-dimensional representations of an associative unital k-algebra.

Comparison of Polynomial-Oriented Computer Algebra Systems
http://www.fordham.edu/lewis/cacomp.html
By Robert H. Lewis and Michael Wester. Presented as a poster to the 1999 ISSAC Conference.

Computer Algebra and Problem Solving Environments
http://math.unm.edu/~wester/aca96/Steinberg_abstract.html
Abstract for Stanly Steinberg's article in "Comparative CAS Reviews and Philosophy", suggesting 6 ways in which computer algebra systems could be improved.

Computer Algebra Benchmarks
http://krum.rz.uni-mannheim.de/cafgbench.html
Collated by Computer Algebra Fachgruppe, Mannheim.

Computer Algebra Pages and Servers
http://krum.rz.uni-mannheim.de/cabench/cawww.html
A collection of links.

Edu2000 Visual Algebra
http://www.mathematicssoftware.com/mathematics-software-html/algebra-1-software.php
Designed to ease the difficulties many students experience during the transition from arithmetic into the world of algebra using visualization. Covers linear and quadratic equations.

Felix
http://felix.hgb-leipzig.de/
Computer algebra system for computation in commutative and non-commutative rings and modules. Win32, Unix.

Fermat
http://www.bway.net/~lewis/
Computer algebra system that does arithmetic of arbitrarily long integers and fractions, symbolic calculations, graphics, and other numerical calculations. Free download. Documentation.

FINITAS
http://groups.yahoo.com/group/finitas
Discussion group for this package for the construction and analysis of finite algebraic structures such as loops, quasigroups, and groups.

FRISCO - A Framework for Integrated Symbolic/Numeric Computation
http://www.nag.co.uk/projects/FRISCO.html
The FRISCO project aims to develop highly efficient, versatile polynomial solvers for industrial users.

Galois Field Arithmetic Library
http://www.partow.net/projects/galois/
A simple opensource library in C++ for arithmetic between elements and polynomials over finite fields.

GAP - Groups, Algorithms and Programming
http://www-history.mcs.st-and.ac.uk/~gap/
A free system for computational discrete algebra.

GB and FGB
http://www-calfor.lip6.fr/~jcf/
Software for solving algebraic equations: GB computes Groebner bases and FGB solves polynomial systems.

GIAC
http://www-fourier.ujf-grenoble.fr/~parisse/english.html
Is A Computer algebra system. A semi-classical CAS by Bernard Parisse, available for Windows, Linux.

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