This article is cited in 1 paper

Asymmetric approach to computation of Gröbner bases

E. V. Pankratiev^a, A. S. Semenov<sup>b

a</sup> M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
^b M. V. Lomonosov Moscow State University

Abstract: 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.

UDC: 512.62

 English version: Journal of Mathematical Sciences (New York), 2008, 149:3, 1235–1245

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