Involutive bases algorithm incorporating F5 criterion

Faugèreʼs F5 algorithm (Faugère, 2002) is the fastest known algorithm to compute Gröbner 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 non-incremental structure and in addition to the involutive form of Buchbergerʼs 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 (Gao et al., 2010a). To compare the proposed algorithm, via a set of benchmarks, with the Gerdt–Blinkov involutive algorithm (Gerdt and Blinkov, 1998) (which does not apply the F5 criterion) we use implementations of both algorithms done on the same platform in Maple.