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TitleOn the use of Buchberger criteria in $mathrm G^2mathrm V$ algorithm for calculating Gr\"obner bases.
Author(s) Vladimir P. Gerdt, Amir Hashemi
TypeArticle in Journal
AbstractIt 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 Buchbergerís 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.
ISSN0361-7688; 1608-3261/e
URL http://link.springer.com/article/10.1134%2FS0361768813020047
JournalProgram. Comput. Softw.
PublisherSpringer US, New York, NY; Pleiades Publishing, New York, NY; MAIK ``Nauka/Interperiodica
Translation No
Refereed No