An efficient reduction strategy for signature-based algorithms to compute Groebner basis

Abstract: This paper introduces a strategy for signature-based algorithms to compute Groebner basis. The signature-based algorithms generate S-pairs instead of S-polynomials, and use s-reduction instead of the usual reduction used in the Buchberger algorithm. There are two strategies for s-reduction: one is the only-top reduction strategy which is the way that only leading monomials are s-reduced. The other is the full reduction strategy which is the way that all monomials are s-reduced. A new strategy, which we call selective-full strategy, for s-reduction of S-pairs is introduced in this paper. In the experiment, this strategy is efficient for computing the reduced Groebner basis. For computing a signature Groebner basis, it is the most efficient or not the worst of the three strategies.