Involutive Division Technique: Some Generalizations and Optimizations

Details Involutive Division Technique: Some Generalizations and Optimizations Involutive Division Technique: Some Generalizations and Optimizations

1999-12-04

arxiv.org/abs/math/9912030v2

Zapiski nauchgnyh seminarov POMI (St.Petersburg) 258, 1999, 185-206

Mathematics

Commutative Algebra

19 pages

Scientific paper

In 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.

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