Details:
Title  Computing syzygies by Faug`ere  Author(s)  Gwenole Ars, Amir Hashemi  Type  Article in Journal  Abstract  In 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 Faugère’s F5 algorithm (A new efficient algorithm for computing Gröbner bases without reduction to zero (F 5). ISSAC, ACM Press, pp 75–83, 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.  Keywords  Polynomial ideal, syzygy, block ordering, degree, reverse lexicographic ordering, Gröbner bases  ISSN  14226383; 03786218/e 
URL 
http://link.springer.com/article/10.1007%2Fs000250100049x 
Language  English  Journal  Result. Math.  Volume  59  Number  12  Pages  3542  Publisher  Springer (Birkh\"auser), Basel  Year  2011  Edition  0  Translation 
No  Refereed 
No 
