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TitleInvolutive Division Technique: Some Generalizations and Optimizations
Author(s) Vladimir P. Gerdt
TypeArticle in Journal
AbstractIn this paper, in addition to the earlier introduced involutive divisions, we consider a new class of divisions induced by admissible monomial orderings. We prove that these divisions are noetherian and constructive. Thereby each of them allows one to compute an involutive Groebner basis of a polynomial ideal by se­quentially examining multiplicative reductions of nonmultiplicative prolongations. We study dependence of involutive algorithms on the completion ordering. Based on properties of particular involutive divisions two computational optimizations are suggested. One of them consists in a special choice of the completion ordering. Another optimization is related to recomputing multiplicative and nonmultiplica­tive variables in the course of the algorithm.
Keywordsinvolutive division, involutive Groebner basis, involutive algorithms,
URL http://invo.jinr.ru/papers.phtml
Translation No
Refereed No
Institution JINR (Joint Institute for Nuclear Research)