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Faugere's F5 algorithm computes a Groebner basis incrementally, by computinga sequence of (non-reduced) Groebner bases. The authors describe a variant ofF5, called F5C, that replaces each intermediate Groebner basis with its reducedGroebner basis. As a result, F5C considers fewer polynomials and performssubstantially fewer polynomial reductions, so that it terminates more quickly.We also provide a generalization of Faugere's characterization theorem forGroebner bases.

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