FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2006, VOLUME 12, NUMBER 3, PAGES 73-88

Asymmetric approach to computation of Gröbner bases

E. V. Pankratiev
A. S. Semenov

Abstract

View as HTML     View as gif image

A new approach to Buchberger's algorithm based on the use of essential multiplications and nonmultiplicative prolongations instead of traditional $S$-polynomials is described. In the framework of this approach, both Buchberger's algorithm for computing Gröbner bases and Gerdt--Blinkov algorithm for computing involutive bases obtain a unified form of description. The new approach is based on consideration of the process of determining an $S$-polynomial as a process of constructing a nonmultiplicative prolongation of a polynomial and its subsequent reducing with respect to an essential multiplication. An advantage of the method is that some "redundant" $S$-pairs are automatically excluded from consideration.

Location: http://mech.math.msu.su/~fpm/eng/k06/k063/k06305h.htm
Last modified: July 22, 2006