Research on Signature-based Grbner Basis Algorithms in Matrix Style

The current signature-based Grbner basis algorithms are mostly in Buchberger style and the researches related to matrix style often aim to analyze the complexity of algorithms. From a practical aspect, this paper provides a concrete Gao-Volny-Wang (GVW) algorithm in matrix style and presents optimization at the algorithmic level. Meanwhile, an efficient reduction criterion is given in the paper. Many popular criteria and strategies are compared by some experiments which show that the matrix version described in the paper is a combination of reasonable criteria and strategies. Moreover, the matrix-GVW is two to six times faster than the Buchberger style for some polynomial systems, e.g. Cyclic series and Katsura series.