Signature Rewriting in Gröbner Basis Computation

Abstract : We introduce the RB algorithm for Gro ̈bner basis compu- tation, a simpler yet equivalent algorithm to F5GEN. RB contains the original unmodified F5 algorithm as a special case, so it is possible to study and understand F5 by con- sidering the simpler RB. We present simple yet complete proofs of this fact and of F5's termination and correctness. RB is parametrized by a rewrite order and it contains many published algorithms as special cases, including SB. We prove that SB is the best possible instantiation of RB in the following sense. Let X be any instantiation of RB (such as F5). Then the S-pairs reduced by SB are always a subset of the S-pairs reduced by X and the basis computed by SB is always a subset of the basis computed by X.