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Erschienen in:
2011 | OriginalPaper | Buchkapitel
Involutive Division Generated by an Antigraded Monomial Ordering
verfasst von : Vladimir P. Gerdt, Yuri A. Blinkov
Erschienen in: Computer Algebra in Scientific Computing
Verlag: Springer Berlin Heidelberg
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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.