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TitleReduced Gröbner bases under composition
Author(s) Jaime Gutierrez, Rosario Rubio San Miguel
TypeArticle in Journal
AbstractIn this paper we contribute with one main result to the interesting problem initiated by Hong (1998, J. Symb. Comput. 25, 643-663) on the behaviour of Gröbner bases under composition of polynomials. Polynomial composition is the operation of replacing the variables of a polynomial with other polynomials. The main question of this paper is: When does composition commute with reduced Gröbner bases computation under the same term ordering? We give a complete answer for this question: let Theta be a polynomial map, then for every reduced Gröbner basis G, G &cir Theta is a reduced Gröbner basis if and only if the composition by Theta is compatible with the term ordering and Theta is a list of permuted univariate and monic polynomials. Besides, we also include other minor results concerned with this problem; in particular, we provide a sufficient condition to determine when composition commutes with reduced Gröbner bases computation (possibly) under different term ordering.
Length12
ISSN0747-7171
CopyrightAcademic Press
File
URL dx.doi.org/10.1006/jsco.1998.0222
LanguageEnglish
JournalJournal of Symbolic Computation
Volume26
Number4
Pages433-444
PublisherAcademic Press, Inc.
AddressDuluth, MN, USA
Year1998
MonthOctober
Translation No
Refereed No
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