Buchberger's algorithm and staggered linear bases

Abstract

The most time consuming part is the S-polynomial reduction. Consequently Buchbergcr developed criteria for predicting that certain reductions lead to the zero polynomial, hence allowing the elimination of these reductions [Bu79]. A new interpretation of these criteria and an efficient implcmcntation of them is given in [GM861 and installed in Reduce 3.2 and in Scratchpad II. However there arc still many instances of s~~pcrfluous zero reductions not covered by these criteria.