In the computation of a Grobner basis using Buchberger's algorithm, a key issue for improving the eciency is to produce techniques for avoiding as many unnecessary critical pairs as possible. A good solution would be to avoid all non-minimal critical pairs, and hence to process only a minimal set of generators of the module generated by the critical syzygies. In this paper we show how to obtain that desired solution in the homogeneous case while retaining the same eciency as with the classical implementation. As a consequence, we get a new Optimized Buchberger Algorithm.
['Massimo Caboara', 'Martin Kreuzer', 'Lorenzo Robbiano']
Efficiently Computing Minimal Sets of Critical Pairs