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

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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