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

• Published in: Programming and computer software Vol. 39; no. 2; pp. 81 - 90
• Main Authors: Gerdt, Vladimir P., Hashemi, Amir
• Format: Journal Article
• Language: English
• Published: Dordrecht SP MAIK Nauka/Interperiodica 01.03.2013; Springer Nature B.V
• Subjects: Algorithms; Artificial Intelligence; Computer Science; Criteria; Linear algebra; Mathematical analysis; Operating Systems; Software Engineering; Software Engineering/Programming and Operating Systems; Incremental Algorithm; Computational Effect; Standard Representation; Algorithm Operation; System Singular
• ISSN: 0361-7688; 1608-3261
• DOI: 10.1134/S0361768813020047

It has been experimentally demonstrated by Faugère that his F 5 algorithm is the fastest algorithm for calculating Gröbner bases. Computational efficiency of F 5 is due to not only applying linear algebra but also using the new F 5 criterion for revealing useless zero reductions. At the ISSAC 2010 conference, Gao, Guan, and Volny presented G 2 V, a new version of the F 5 algorithm, which is simpler than the original version of the algorithm. However, the incremental structure of G 2 V used in the algorithm for applying the F 5 criterion is a serious obstacle from the point of view of application of Buchberger’s second criterion. In this paper, a modification of the G 2 V 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 G 2 V and its modified version on a number of test examples are presented.