Efficient Computation of Syzygies by Faugère’s F5 algorithm
نویسندگان
چکیده
In this paper, we introduce a new algorithm for computing the syzygies of a sequence of polynomials. For this, we extend a given sequence to a Gröbner basis using Faugère’s F5 algorithm (see [1]). We show that if we keep all the reductions to zero during this computation, then at termination (by adding principal syzygies) we get a basis for the module of syzygies of input polynomials. We have implemented our algorithm in the computer algebra system Magma, and we evaluate its performance via some examples. Mathematics Subject Classification (2000). Primary 13P10; Secondary 68W30.
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