GB and FGB
Software for solving algebraic equations: GB computes Groebner bases and FGB solves polynomial systems.
http://www-calfor.lip6.fr/~jcf/
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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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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
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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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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
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CoCoA
A special-purpose system for computations in Commutative Algebra.
http://cocoa.dima.unige.it/
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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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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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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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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.html
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