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TitleComputing syzygies by Faug`ere
Author(s) Gwenole Ars, Amir Hashemi
TypeArticle in Journal
AbstractIn this paper, we introduce a new algorithm for computing a set of generators for the syzygies on a sequence of polynomials. For this, we extend a given sequence of polynomials to a Gröbner basis using Faugères F5 algorithm (A new efficient algorithm for computing Gröbner bases without reduction to zero (F 5). ISSAC, ACM Press, pp 7583, 2002). We show then that if we keep all the reductions to zero during this computation, then at termination (by adding principal syzygies) we obtain a basis for the module of syzygies on the input polynomials. We have implemented our algorithm in the computer algebra system Magma, and we evaluate its performance via some examples.
KeywordsPolynomial ideal, syzygy, block ordering, degree, reverse lexicographic ordering, Gröbner bases
ISSN1422-6383; 0378-6218/e
URL http://link.springer.com/article/10.1007%2Fs00025-010-0049-x
JournalResult. Math.
PublisherSpringer (Birkh\"auser), Basel
Translation No
Refereed No