1 research outputs found
Involutive Bases Algorithm Incorporating F5 Criterion
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.Comment: 24 pages, 2 figure