MINIMAL SETS OF CRITICAL PAIRS
Massimo Caboara, Martin Kreuzer, Lorenzo Robbiano · 2002
In the computation of a Grobner basis using Buchberger's algorithm, a key issue for improving the efficiency is to produce good 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 pairs. In this paper we show how to obtain that desired solution while retaining the same efficiency as with the classical implementation. As a consequence, we get a new Optimized Buchberger Algorithm.