Singular is a computer algebra system for singularity theory and algebraic geometry developed by G.-M. Greuel, G. Pfister, H.Schoenemann, and others, at the Department of Mathematics of the University of Kaiserslautern. Singular can compute with ideals and modules generated by polynomials or polynomial vectors over polynomial or power series rings or, more generally, over the localization of a polynomial ring with respect to any ordering on the set of monomials which is compatible with the semigroup structure. There is also the possibility to do standard base calculations and hence computations of resolutions in modules over supercommutative superalgebras and Weyl algebras if you compile Singular with the appropriate options. Hence, there is a wide range of applications in local and global algebraic geometry (but Singular is not limited to these areas).
Singular is avaiblable via anonymous ftp from ftp://www.mathematik.uni-kl.de/pub/Math/Singular/bin/.