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PolyBoRi is implemented as a C++ library for Polynomials over Boolean Rings, which provides high-level data types for Boolean polynomials. A python-interface yields extensible algorithms for computing Groebner bases over Boolean Rings.
Many computational problems need arithmetic operations in polynomial finite rings over Z/nZ, where n is an integer (n>1). This library provides efficient operations for applications such as integer factorization and primality testing.
The project aims to provide the basic functions and algorithms
needed for computations in polynomial rings over the ring of
integers, including polynomial arithmetic and D-Groebner Bases.
It might evolve in some
kind of computer algebra system
GJAL is a collection of generic class definitions in GJ/Generic Java/JSR-014 that outlines algebraic structures such as Monoids, SemiGroups, Groups, Rings, Fields and various Domains.
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PerMuVAR was a library for the Computer Algebra System MuPAD (http://www.mupad.de) for computations in invariant rings of permutation groups. It's now part of the algebraic combinatorics package MuPAD-Combinat (http://mupad-combinat.sf.net/)