Ebook: Monomial representations for Groebner bases

Monomial representations and operations for Grobner 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 Grobner 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.