CoCoA: A special-purpose
system for doing Computations in Commutative Algebra.
Its principal area of expertise is that of operations over
commutative rings of polynomials.
GiNaC (which stands for
GiNaC is Not a CAS) is a C++ library, designed to allow the
creation of integrated systems that embed symbolic manipulations
together with more established areas of computer science under one
roof.