F5C: a variant of Faugere's F5 algorithm with reduced Groebner bases

Details F5C: a variant of Faugere's F5 algorithm with reduced Groebner bases F5C: a variant of Faugere's F5 algorithm with reduced Groebner bases

2009-06-16

arxiv.org/abs/0906.2967v6

Journal of Symbolic Computation, vol. 45 (2010) pp. 1442-1458

Mathematics

Commutative Algebra

31 pages, 4 tables; updated proof of characterization theorem

Scientific paper

10.1016/j.jsc.2010.06.019

Faugere's F5 algorithm computes a Groebner basis incrementally, by computing a sequence of (non-reduced) Groebner bases. The authors describe a variant of F5, called F5C, that replaces each intermediate Groebner basis with its reduced Groebner basis. As a result, F5C considers fewer polynomials and performs substantially fewer polynomial reductions, so that it terminates more quickly. We also provide a generalization of Faugere's characterization theorem for Groebner bases.

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