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Albert
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.
http://www.cs.clemson.edu/~dpj/albertstuff/albert.html
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Aldor
Originally an extension to Axiom, now a separate product. Binaries are available free for non-profit use, with documentation, tips, projects and links.
http://www.aldor.org/
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Algebra Cheat
Program solves variable equations and gives explanations of steps used.
http://www.bacsoftware.co.uk/algebra/
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Algebra Helper
Helps students with equations and inequalities, simplifying expression, graphing and complex numbers. Includes problem solving exercises.
http://www.algebra-answer.com/
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Algebra Problem Solver
Personal Algebra Tutor - Enter your algebra problems and get instant step-by-step solutions with explanations.
http://www.cyberedinc.com/
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Algebra Word Problem Tutor:Miss Lindquist
The world's first web-delivered self-improving intelligent tutoring system able to tutor students in writing expressions for algebra word problems.
http://www.cs.cmu.edu/~neil
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AXIOM
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.
http://www.nag.co.uk/symbolic_software.asp
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Axiom Computer Algebra System
Savannah Free Software project for revival of Axiom as open source.
http://savannah.nongnu.org/projects/axiom
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CMAT
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.
http://www.numbertheory.org/cmat/krm_cmat.html
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CoCoA
A special-purpose system for computations in Commutative Algebra.
http://cocoa.dima.unige.it/
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Combinatorial Representation Theory (CREP)
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.
http://www.mathematik.uni-bielefeld.de/~sek/crep.html
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Comparison of Polynomial-Oriented Computer Algebra Systems
By Robert H. Lewis and Michael Wester. Presented as a poster to the 1999 ISSAC Conference.
http://www.fordham.edu/lewis/cacomp.html
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Computer Algebra and Problem Solving Environments
Abstract for Stanly Steinberg's article in "Comparative CAS Reviews and Philosophy", suggesting 6 ways in which computer algebra systems could be improved.
http://math.unm.edu/~wester/aca96/Steinberg_abstract.html
(Added: Mon Apr 04 2011 Hits: 0 Rating: 0.00 Votes: 0) Rate It Review It

Computer Algebra Benchmarks
Collated by Computer Algebra Fachgruppe, Mannheim.
http://krum.rz.uni-mannheim.de/cafgbench.html
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Computer Algebra Pages and Servers
A collection of links.
http://krum.rz.uni-mannheim.de/cabench/cawww.html
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Dolphinsoft Project
Offers Student Math, an advanced matrix operation tool, and Codegrinder's calculator, a simple but powerful calculator with expression calculation.
http://dolphinsoft.net
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Felix
Computer algebra system for computation in commutative and non-commutative rings and modules. Win32, Unix.
http://felix.hgb-leipzig.de/
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Fermat
Computer algebra system that does arithmetic of arbitrarily long integers and fractions, symbolic calculations, graphics, and other numerical calculations. Free download. Documentation.
http://www.bway.net/~lewis/
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FINITAS
Discussion group for this package for the construction and analysis of finite algebraic structures such as loops, quasigroups, and groups.
http://groups.yahoo.com/group/finitas/
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FRISCO - A Framework for Integrated Symbolic/Numeric Computation
The FRISCO project aims to develop highly efficient, versatile polynomial solvers for industrial users.
http://www.nag.co.uk/projects/FRISCO.html
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Galois Field Arithmetic Library
A simple opensource library in C++ for arithmetic between elements and polynomials over finite fields.
http://www.partow.net/projects/galois/
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GAP - Groups, Algorithms and Programming
A free system for computational discrete algebra.
http://www-history.mcs.st-and.ac.uk/~gap/
(Added: Mon Apr 04 2011 Hits: 0 Rating: 0.00 Votes: 0) Rate It Review It

GB and FGB
Software for solving algebraic equations: GB computes Groebner bases and FGB solves polynomial systems.
http://www-calfor.lip6.fr/~jcf/
(Added: Mon Apr 04 2011 Hits: 0 Rating: 0.00 Votes: 0) Rate It Review It

GIAC
Is A Computer algebra system. A semi-classical CAS by Bernard Parisse, available for Windows, Linux.
http://www-fourier.ujf-grenoble.fr/~parisse/english.html
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GiNaC
An open framework for symbolic computation within the C++ programming language. The name GiNaC is an iterated and recursive abbreviation for "GiNaC is Not a CAS", where CAS stands for Computer Algebra System. Its design is revolutionary in a sense that contrary to other CAS it does not try to provide extensive algebraic capabilities and a simple programming language but instead accepts a given language (C++) and extends it by a set of algebraic capabilities. It is published under the GNU Public License (GPL).
http://www.ginac.de/
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j'Abr Computer Algebra System
Collection of packages for computer algebra in Java. It contains the basics of a computer algebra system and important algorithms for solving both symbolic and numerical mathematical problems.
http://www.functologic.com/math/jAbr.html
(Added: Mon Apr 04 2011 Hits: 0 Rating: 0.00 Votes: 0) Rate It Review It

JACAL
An interactive symbolic mathematics program. JACAL can manipulate and simplify equations, scalars, vectors, and matrices of single and multiple valued algebraic expressions containing numbers, variables, radicals, and algebraic differential, and holonomic functions. Linux RPM distribution.
http://swissnet.ai.mit.edu/~jaffer/JACAL.html
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Java Algebra System
JAS is a software library using generic types for algebraic computations implemented in the Java programming language. The focus is on commutative and solvable polynomials, Groebner bases and applications.
http://freshmeat.net/projects/jas
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Java Algebra System (JAS) Project
JAS provides a software library using generic types for algebraic computations implemented in the Java programming language.
http://krum.rz.uni-mannheim.de/jas/
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KAN
Rings and Computer algebra software, part of OpenXM.
http://www.math.sci.kobe-u.ac.jp/KAN/
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LAPACK -- Linear Algebra PACKage
written in Fortran77; provides routines for solving systems of simultaneous linear equations, least-squares solutions of linear systems of equations, eigenvalue problems, and singular value problems.
http://netlib2.cs.utk.edu/lapack/
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LAPACK++: Linear Algebra Package in C++
(v. 1.1a) a software library for numerical linear algebra; however, it does not include all of the capabilities of original f77 LAPACK.
http://math.nist.gov/lapack++/
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Macaulay
Macaulay is a computer algebra system for mathematical computations in algebraic geometry and commutative algebra. At its core is a carefully tuned implementation of Grobner basis methods for manipulating systems of polynomial equations.
http://www.math.columbia.edu/~bayer/Macaulay/index.html
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Macaulay 2
A new software system devoted to supporting research in algebraic geometry and commutative algebra.
http://www.math.uiuc.edu/Macaulay2/
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MAS: The Modula-2 Algebra System
MAS is an experimental computer algebra system with algebraic specification capabilities for the design and study of algebraic algorithms. Downloads, documentation.
http://krum.rz.uni-mannheim.de/mas/
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Math Forum - Algebra Software
Algebra software resources compiled by The Math Forum.
http://mathforum.org/algebra/alg.software.html
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Math Symbolic Library
Evaluate, calculate, simplify and derive symbolic scalar, complex or vector expression. [OpenSource]
http://www.cdrnet.net/projects/nmath/
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MathPad - Scientific Matrices Calculator
Java applet based online Matrix calculation program for analyzing various simultaneous equations.
http://www.mathpad.com/public/htmls/main/left/matrix/MatrixInfo.html
(Added: Mon Apr 04 2011 Hits: 0 Rating: 0.00 Votes: 0) Rate It Review It

Mathscribe
Mathscribe is free dynamic graphing and modeling software for use in algebra classes. Lesson plans for linears and quadratics are included.
http://www.mathscribe.com/
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Matrix Expression Templates (MET)
C++ matrix class library which promotes the notational convenience of linear algebraic codes. Free download.
http://met.sourceforge.net/
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Maxima
A GPL CAS based on DOE-MACSYMA. A GPL project.
http://maxima.sourceforge.net/
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Maxima-Online
Browser based, web intrerface to Maxima computer algebra system.
http://maxima-online.lewalski.pl
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Online Gröbner Basis Calculations
Online computation of reduced ideal bases.
http://grobner.nuigalway.ie/grobner/basis.html
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perisic
A Java package for multivariate polynomials over polymorphic rings.
http://ring.perisic.com/
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Schur
A package for Lie groups by Brian G. Wybourne. DOS, Win32, Unix. Ordering information.
http://smc.vnet.net/Schur.html
(Added: Mon Apr 04 2011 Hits: 0 Rating: 0.00 Votes: 0) Rate It Review It

ScriviFacile Math Algebra
Voce Viva offers interactive multipurpose software for use in schools.
http://www.voceviva.it/page9.html
(Added: Mon Apr 04 2011 Hits: 0 Rating: 0.00 Votes: 0) Rate It Review It

SINGULAR
Computer Algebra System for polynomial computations with special emphasis on commutative algebra, algebraic geometry, and singularity theory.
http://www.singular.uni-kl.de/
(Added: Mon Apr 04 2011 Hits: 0 Rating: 0.00 Votes: 0) Rate It Review It

Software for Computing Primitive Polynomials.
Free C software for computing primitive polynomials of degree n modulo p for p^n up to about 2^60.
http://www.seanerikoconnor.freeservers.com/Mathematics/AbstractAlgebra/PrimitivePolynomials/overview.html
(Added: Mon Apr 04 2011 Hits: 0 Rating: 0.00 Votes: 0) Rate It Review It

SymbolicNet
Directory of links on symbolic algebraic computation: FAQ, live demos, software for download, events, bibliography, research groups and researcher directory.
http://www.symbolicnet.org/
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Symmetrica
A collection of routines, written in C, for computing in the representation theory of classical and symmetric groups, and related areas. Public domain.
http://www.mathe2.uni-bayreuth.de/axel/symneu_engl.html
(Added: Mon Apr 04 2011 Hits: 0 Rating: 0.00 Votes: 0) Rate It Review It

WinCoCoA Page
A version of CoCoA for Windows developed by a small group of mathematicians at Universität Regensburg, Germany.
http://www.uni-regensburg.de/Fakultaeten/nat_Fak_I/Kreuzer/WinCoCoA.html
(Added: Mon Apr 04 2011 Hits: 0 Rating: 0.00 Votes: 0) Rate It Review It

Yet Another Computer Algebra System
A general purpose easy program for It is built on top of its own programming language designed for symbolic manipulation of math symbols. Includes information on how to use the software.
http://yacas.sourceforge.net/
(Added: Mon Apr 04 2011 Hits: 0 Rating: 0.00 Votes: 0) Rate It Review It

ZEN
A toolbox for computation in finite rings, by Florent Chabaud and Reynald Lercier. ANSI-C source, free download, GPL.
http://fchabaud.free.fr/English/ZEN/
(Added: Mon Apr 04 2011 Hits: 0 Rating: 0.00 Votes: 0) Rate It Review It

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