Non-compatibleな加群項順序の下でのsignature based algorithmについて

Abstract

The compatibility of a term ordering in a polynomial ring R = K[X] and a module term ordering in Rm is a sufficient condition of the termination of the signature based algorithm. Experiments show that a combination of non-compatible term orderings may give good performance for computing Groebner bases with respect to some term orderings. In such cases, we can apply the notion of Hilbert function for guaranteeing the termination. The hilbert function can be computed by using a Groebner basis with respect to another term ordering and thus this algorithm is a kind of change of ordering. We implement this algorithm in Risa/Asir and we compare its performance with the usual Hilbert driven algorithm.