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
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A new approach to Buchberger's algorithm based on the use of
essential multiplications and nonmultiplicative prolongations instead
of traditional -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 -polynomial as
a process of constructing a nonmultiplicative prolongation
of a polynomial and its subsequent reducing with respect to an
An advantage of the method is that some "redundant" -pairs are automatically
excluded from consideration.
Last modified: July 22, 2006