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TitleHilbert Stratification and Parametric Gröbner Bases
Author(s) Laureano Gonzalez-Vega, Carlo Traverso, Alberto Zanoni
TypeArticle in Conference Proceedings
AbstractIn this paper we generalize a method to analyze inhomogeneous polynomial systems containing parameters. In particular, the Hilbert function is used as a tool to check that the specialization of a “generic” Gröbner basis of the parametric polynomial system (computed in a polynomial ring having both parameters and unknowns as variables) is a Gröbner basis of the specialized system. Extending the analysis, we can also build the so-called Hilbert stratification of the associated variety. We classify the possible specializations according to the value of the Hilbert function of the specialized system. Some computation examples with the PoSSoLib are reported.
KeywordsGröbner bases, Hilbert function, Specialization
ISBN3-540-28966-6
LanguageEnglish
JournalLecture Notes in Computer Science
Volume3718
Pages220-235
Publisher Springer
Year2005
EditorVictor G. Ganzha, Ernst W. Mayr, Evgenii V. Vorozhtsov
Edition0
Translation No
Refereed No
BookComputer Algebra in Scientific Computing: 8th International Workshop, CASC 2005, Kalamata, Greece, September 12-16, 2005. Proceedings
ConferencenameComputer Algebra in Scientific Computing: 8th International Workshop, CASC 2005
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