Signature Rewriting in Gröbner Basis Computation

Christian Eder 1 Bjarke Hammersholt Roune 2
1 PolSys - Polynomial Systems
LIP6 - Laboratoire d'Informatique de Paris 6, Inria Paris-Rocquencourt
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.
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Christian Eder, Bjarke Hammersholt Roune. Signature Rewriting in Gröbner Basis Computation. Kauers, Manuel. ISSAC 2013 - International Symposium on Symbolic and Algebraic Computation, Jun 2013, Boston, United States. ACM, pp.331-338, 2013, 〈10.1145/2465506.2465522〉. 〈hal-00930273〉

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