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.
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Ars, G., Hashemi, A. Computing Syzygies by Faugère’s F5 algorithm. Results. Math. 59, 35–42 (2011). https://doi.org/10.1007/s00025-010-0049-x
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DOI: https://doi.org/10.1007/s00025-010-0049-x