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Hilbert Stratification and Parametric Gröbner Bases

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Computer Algebra in Scientific Computing (CASC 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3718))

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Abstract

In 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.

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Author information

Authors and Affiliations

  1. Dpto. Matemáticas, Estadística y Computación, Facultad de Sciencias, Universidad de Cantabria, Avenida de Los Castros s/n, E-39071, Santander, Spain

    Laureano Gonzalez–Vega

  2. Dipartimento di Matematica “Leonida Tonelli”, Università di Pisa, Via F. Buonarroti 2, 56127, Pisa, Italy

    Carlo Traverso & Alberto Zanoni

Authors
  1. Laureano Gonzalez–Vega
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  2. Carlo Traverso
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  3. Alberto Zanoni
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Editor information

Editors and Affiliations

  1. Institute of Informatics, Technische Universität München, Boltzmannstr. 3, 85748, Garching, Germany

    Victor G. Ganzha  & Ernst W. Mayr  & 

  2. Institute of Theoretical and Applied Mechanics, Russian Academy of Sciences, 630090, Novosibirsk, Russia

    Evgenii V. Vorozhtsov

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© 2005 Springer-Verlag Berlin Heidelberg

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Gonzalez–Vega, L., Traverso, C., Zanoni, A. (2005). Hilbert Stratification and Parametric Gröbner Bases. In: Ganzha, V.G., Mayr, E.W., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2005. Lecture Notes in Computer Science, vol 3718. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11555964_19

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  • DOI: https://doi.org/10.1007/11555964_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-28966-1

  • Online ISBN: 978-3-540-32070-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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