Involutive division generated by an antigraded monomial ordering

  • Authors:

  • Vladimir P. Gerdt;Yuri A. Blinkov

  • Affiliations:

  • Laboratory of Information Technologies, Institute for Nuclear Research, Dubna, Russia;Department of Mathematics and Mechanics, Saratov State University, Saratov, Russia

  • Venue:
  • CASC'11 Proceedings of the 13th international conference on Computer algebra in scientific computing
  • Year:
  • 2011

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Abstract

In the present paper we consider a class of involutive monomial divisions pairwise constructed by the partition of variables into multiplicative and nonmultiplicative generated by a total monomial ordering. If this ordering is admissible or the inverse of an admissible ordering, then the involutive division generated possesses all algorithmically important properties such as continuity, constructivity, and noetherianity. Among all such divisions, we single out those generated by antigraded monomial orderings. We demonstrate, by example of the antigraded lexicographic ordering, that the divisions of this class are heuristically better than the classical Janet division. The last division is pairwise generated by the pure lexicographic ordering and up to now has been considered as computationally best.