Systems related to (Non)Commutative Algebra & Algebraic Geometry
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:
GRB has been developed by C.D. Feustel and E.L.Green
of Virginia Polytechnic Institute and State University
Blacksburg, Virginia 24061, USA.
- A basis of the algebra (if finite dimensional).
- The reduced Groebner basis for the ideal of relations of
- The Cartan matrix and determinant of the algebra (if finite
- 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
Special Purpose Systems
Last updated: May 7, 1998