Monomial Representations for Gröbner Bases Computations

Olaf Bachmann       Hans Schönemann
Centre for Computer Algebra
Department of Mathematics
University of Kaiserslautern
Kaiserslautern, Germany
[obachman,hannes]@mathematik.uni-kl.de

January 1998

Abstract:

Monomial representations and operations for Gröbner bases computations are investigated from an implementation point of view. The technique of vectorized monomial operations is introduced and it is shown how it expedites computations of Gröbner bases. Furthermore, a rank-based monomial representation and comparison technique is examined and it is concluded that this technique does not yield an additional speedup over vectorized comparisons. Extensive benchmark tests with the Computer Algebra System SINGULAR are used to evaluate these concepts.