Involutive Algorithms for Computing Groebner Bases
Abstract
In this paper we describe an efficient involutive algorithm for constructing Groebner bases of polynomial ideals. The algorithm is based on the concept of involutive monomial division which restricts the conventional division in a certain way. In the presented algorithm a reduced Groebner basis is the internally fixed subset of an involutive basis, and having computed the later, the former can be output without any extra computational costs. We also discuss some accounts of experimental superiority of the involutive algorithm over Buchberger's algorithm.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 January 2005
 arXiv:
 arXiv:math/0501111
 Bibcode:
 2005math......1111G
 Keywords:

 Mathematics  Commutative Algebra;
 Mathematics  Algebraic Geometry;
 13P10;
 68W30
 EPrint:
 27 pages, Proceedings of the NATO Advanced Research Workshop "Computational commutative and noncommutative algebraic geometry" (Chishinau, June 611, 2004), IOS Press, to appear