Systems related to (Non)Commutative Algebra & Algebraic Geometry

GRB

GRB Version 1.0 provides a computational basis to do algebraic and homological manipulations on algebras and modules. The algebras in question should be given as a factor of a path algebra (which includes factors of free algebras). Things provided by the current program:

1. A basis of the algebra (if finite dimensional).
2. The reduced Groebner basis for the ideal of relations of the algebra.
3. The Cartan matrix and determinant of the algebra (if finite dimensional).
4. A package that allows one to add, multiply elements of the path algebra and then reduce by the ideal of relations.
5. Construction of the higher Gammas (overlaps) described in Anick - Green "On the homology of path algebras", Comm. Alg 15, 1987.
6. Construction of minimal projective resolutions of finite dimensional modules over finite dimensional algebras.
7. Coefficients of the Hilbert and Poincare' series of an algebra.

GRB runs on Unix workstations and PC compatibles running DOS. Original files can be obtained by anonymous ftp from ftp://math.vt.edu/pub/green/

Special Purpose Systems

Last updated: May 7, 1998