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TitleEnumeration of finite monomial orderings and combinatorics of universal Gr\"obner bases.
Author(s) D.A. Pavlov, N.N. Vasiliev
TypeArticle in Journal
AbstractThe goal of this work is to analyze various classes of finite and total monomial orderings. The concept of monomial ordering plays the key role in the theory of Gröbner bases: every basis is determined by a certain ordering. At the same time, in order to define a Gröbner basis, it is not necessary to know ordering of all monomials. Instead, it is sufficient to know only a finite interval of the given ordering. We consider combinatorics of finite monomial orderings and its relationship with cells of a universal Gröbner basis. For every considered class of orderings (weakly admissible, convex, and admissible), an algorithm for enumerating finite orderings is discussed and combinatorial integer sequences are obtained. An algorithm for computing all minimal finite orderings for an arbitrary Gröbner basis that completely determine this basis is presented. The paper presents also an algorithm for computing an extended universal Gröbner basis for an arbitrary zero-dimensional ideal.
ISSN0361-7688; 1608-3261/e
URL link.springer.com/article/10.1134%2FS0361768809020030
LanguageEnglish
JournalProgram. Comput. Softw.
Volume35
Number2
Pages79--89
PublisherSpringer US, New York, NY; Pleiades Publishing, New York, NY; MAIK ``Nauka/Interperiodica
Year2009
Edition0
Translation No
Refereed No
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