Asymmetric approach to computation of Gr\"obner bases
Fundamentalʹnaâ i prikladnaâ matematika, Tome 12 (2006) no. 3, pp. 73-88
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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.
@article{FPM_2006_12_3_a4,
author = {E. V. Pankratiev and A. S. Semenov},
title = {Asymmetric approach to computation of {Gr\"obner} bases},
journal = {Fundamentalʹna\^a i prikladna\^a matematika},
pages = {73--88},
publisher = {mathdoc},
volume = {12},
number = {3},
year = {2006},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/FPM_2006_12_3_a4/}
}
E. V. Pankratiev; A. S. Semenov. Asymmetric approach to computation of Gr\"obner bases. Fundamentalʹnaâ i prikladnaâ matematika, Tome 12 (2006) no. 3, pp. 73-88. http://geodesic.mathdoc.fr/item/FPM_2006_12_3_a4/