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

Autor:	Sakata, Kosuke
Rok vydání:	2018
Předmět:	Computer Science - Symbolic Computation Mathematics - Commutative Algebra
Druh dokumentu:	Working Paper
Popis:	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. Comment: 13 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1811.12663 Zobrazit plný text záznamu View this record from Arxiv