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TitleAsymmetric approach to computation of Gr\"obner bases.
Author(s) Eugeny V. Pankratiev, A.S. Semenov
TypeArticle in Journal
AbstractA 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 the 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.
ISSN1072-3374; 1573-8795/e
URL http://link.springer.com/article/10.1007%2Fs10958-008-0062-8
LanguageEnglish
JournalJ. Math. Sci., New York
Volume149
Number3
Pages1235--1245
PublisherSpringer US, New York, NY
Year2008
Edition0
Translation No
Refereed No
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