Syzygies among reduction operators

Cyrille Chenavier

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arXiv · 1708.08709

Syzygies among reduction operators

Cyrille Chenavier

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Abstract

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 Gr{\"o}bner basis.

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Cyrille Chenavier. 2017-08-29. Syzygies among reduction operators. https://arxiv.org/abs/1708.08709

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