On the use of Buchberger criteria in G2V algorithm for calculating Gröbner bases

Authors:
Vladimir P. Gerdt;Amir Hashemi
Affiliations:
Laboratory of Information Technologies, Joint Institute for Nuclear Research, Dubna, Moscow oblast, Russia 141980;Department of Mathematical Sciences, Isfahan University of Technology, Isfahan, Iran 84156-83111
Venue:
Programming and Computing Software
Year:
2013

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Abstract

It has been experimentally demonstrated by Faugère that his F5 algorithm is the fastest algorithm for calculating Gröbner bases. Computational efficiency of F5 is due to not only applying linear algebra but also using the new F5 criterion for revealing useless zero reductions. At the ISSAC 2010 conference, Gao, Guan, and Volny presented G2V, a new version of the F5 algorithm, which is simpler than the original version of the algorithm. However, the incremental structure of G2V used in the algorithm for applying the F5 criterion is a serious obstacle from the point of view of application of Buchberger's second criterion. In this paper, a modification of the G2V algorithm is presented, which makes it possible to use both Buchberger criteria. To experimentally study computational effect of the proposed modification, we implemented the modified algorithm in Maple. Results of comparison of G2V and its modified version on a number of test examples are presented.