Syzygies among reduction operators

Cyrille Chenavier (1, 2)

1 IRIF (UMR_8243) - Institut de Recherche en Informatique Fondamentale
2 PI.R2 - Design, study and implementation of languages for proofs and programs

We introduce the notion of syzygy for a set of reduction operators and relate it to the notion of syzygy for presentations of algebras. We give a method for constructing a linear basis of the space of syzygies for a set of reduction operators. We interpret these syzygies in terms of the confluence property from rewriting theory. This enables us to optimise the completion procedure for reduction operators based on a criterion for detecting useless reductions. We illustrate this criterion with an example of construction of commutative Gröbner basis.

Mots clés: reduction operators; syzygies; completion procedures; commutative Gröbner bases

Domaines: Anneaux et algèbres [math.RA]; Calcul formel [cs.SC]

Cyrille Chenavier. Syzygies among reduction operators. 2017. ⟨hal-01578555v1⟩