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TitleApplying IsRewritten criterion on Buchberger algorithm
Author(s) Amir Hashemi, Benyamin M.-Alizadeh
TypeArticle in Journal
AbstractFaugère’s F 5 algorithm is one of the fastest algorithms to compute Gröbner bases. It uses two criteria namely the F 5 criterion and the IsRewritten criterion to detect the useless critical pairs (see Faugère (2002) [8]). The IsRewritten criterion has been used in the F 5 algorithm, but it has not been explicitly declared in the related paper. In this paper, we give first a complete proof for the IsRewritten criterion and then using a signature structure on Buchberger’s algorithm, we apply this criterion on Buchberger’s algorithm. We have implemented a new algorithm (based on the above results) in Maple to compute a Gröbner basis of a general ideal and we evaluate its performance via some examples.
KeywordsGröbner bases, Buchberger’s algorithm, IsRewritten criterion
URL http://www.sciencedirect.com/science/article/pii/S0304397511003495
JournalTheoretical Computer Science
Pages4592 - 4603
Translation No
Refereed No