符合F5准则的对合基算法
Involutive Bases Algorithm Incorporating F5 Criterion
摘要：
Faugere的F5算法是已知的计算Groebner基的最快算法。它有一个基于特征的渐进式结构，允许应用F5标准删除不必要的削减。本文给出了一个输出最小对合基的对合完备化算法。我们的完成算法有一个nonincremental结构，除了对合形式的Buchberger的标准，它适用于F5标准每当这个标准是适用于在完成对合的过程中。在这样做时，我们使用G2 V形式的F5标准开发的高，关和Volny IV。为了比较所提出的算法，通过一组基准测试，与Gerdt-Blinkov对合算法（不适用F5准则），我们使用在Maple中的同一平台上完成的两种算法的实现。
英文摘要：
Faugere's F5 algorithm is the fastest known algorithm to compute Groebner bases. It has a signature-based and an incremental structure that allow to apply the F5 criterion for deletion of unnecessary reductions. In this paper, we present an involutive completion algorithm which outputs a minimal involutive basis. Our completion algorithm has a nonincremental structure and in addition to the involutive form of Buchberger's criteria it applies the F5 criterion whenever this criterion is applicable in the course of completion to involution. In doing so, we use the G2V form of the F5 criterion developed by Gao, Guan and Volny IV. To compare the proposed algorithm, via a set of benchmarks, with the Gerdt-Blinkov involutive algorithm (which does not apply the F5 criterion) we use implementations of both algorithms done on the same platform in Maple.
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