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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/
Free.fr ~
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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
Columbia.edu ~
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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
Clemson.edu ~
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