F5C: A variant of Faugère's F5 algorithm with reduced Gröbner bases

Faugère's F5 algorithm computes a Gröbner basis incrementally, by computing a sequence of (non-reduced) Gröbner bases. The authors describe a variant of F5, called F5C, that replaces each intermediate Gröbner basis with its reduced Gröbner 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 Faugère's characterization theorem for Gröbner bases.