约化算子之间的合合
Syzygies among reduction operators
摘要：
我们介绍的概念合的一组减少运营商和它的概念合代数介绍。本文给出了一种构造一组约化算子的合空间的线性基的方法。我们从重写理论的汇合性质来解释这些合合。这使我们能够优化完成过程的基础上检测无用的减少运营商的标准。我们用一个构造交换Gr{<$}bner基的例子来说明这个准则。
英文摘要：
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{ö}bner basis.
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