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TitleGröbner bases for polynomial systems with parameters
Author(s) Antonio Montes, Michael Wimber
TypeArticle in Journal
AbstractGröbner bases are the computational method par excellence for studying polynomial systems. In the case of parametric polynomial systems one has to determine the reduced Gröbner basis in dependence of the values of the parameters. In this article, we present the algorithm GröbnerCover which has as inputs a finite set of parametric polynomials, and outputs a finite partition of the parameter space into locally closed subsets together with polynomial data, from which the reduced Gröbner basis for a given parameter point can immediately be determined. The partition of the parameter space is intrinsic and particularly simple if the system is homogeneous.
KeywordsGröbner cover; Comprehensive; Reduced; Canonical; Parameters; Locally closed sets
LanguageEnglish
JournalJournal of Symbolic Computation
Volume45
Number12
Pages1391-1425
PublisherACM Press
Year2010
MonthDecember
Translation No
Refereed Yes
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