Syzygies among reduction operators
Rings and Algebras
2018-04-10 v3 Symbolic Computation
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.
Cite
@article{arxiv.1708.08709,
title = {Syzygies among reduction operators},
author = {Cyrille Chenavier},
journal= {arXiv preprint arXiv:1708.08709},
year = {2018}
}