Involutive bases algorithm incorporating F5 criterion

  • Authors:

  • Vladimir P. Gerdt;Amir Hashemi;Benyamin M.-Alizadeh

  • Affiliations:

  • Laboratory of Information Technologies, Joint Institute for Nuclear Research, 141980 Dubna, Russia;Department of Mathematical Sciences, Isfahan University of Technology, Isfahan, 84156-83111, Iran;Young Researchers and Elites Club, Science and Research Branch, Islamic Azad University, Tehran 461/15655, Iran

  • Venue:
  • Journal of Symbolic Computation
  • Year:
  • 2013

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Abstract

Faugere@?s F"5 algorithm (Faugere, 2002) is the fastest known algorithm to compute Grobner bases. It has a signature-based and an incremental structure that allow to apply the F"5 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 Buchberger@?s criteria it applies the F"5 criterion whenever this criterion is applicable in the course of completion to involution. In doing so, we use the G^2V form of the F"5 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 F"5 criterion) we use implementations of both algorithms done on the same platform in Maple.