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:

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