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A Parametrized Nullstellensatz

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Computational Algebraic Geometry

Part of the book series: Progress in Mathematics ((PM,volume 109))

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Abstract

Let k be a field and f, F1,…,F3 ∈ k[X 1,…,X n], with deg(Fi) = d i and maxd 1,…, d 3 ≤ d. When there exist some polynomials A 1,…, A 3 and power N such that we have a representation 1 = A 1 F 1 + … + A 3F3 or f N = A 1 F 1 + … + A3F3, the question arises how to bound optimally a = sup deg {A i} and N.

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Author information

Authors and Affiliations

  1. URA 168 du CNRS, Université de Nice-Sophia Antipolis, Faculté des sciences, B.P. 71, 06108, Nice Cedex 2, France

    Frédéric Smietanski

Authors
  1. Frédéric Smietanski
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Editor information

Editors and Affiliations

  1. U.F.R. Faculté des Sciences Mathématiques, Université de Nice-Sophia Antipolis, 06108, Nice Cedex 2, France

    Frédéric Eyssette  & André Galligo  & 

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© 1993 Birkhäuser Boston

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Smietanski, F. (1993). A Parametrized Nullstellensatz. In: Eyssette, F., Galligo, A. (eds) Computational Algebraic Geometry. Progress in Mathematics, vol 109. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-2752-6_20

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  • DOI: https://doi.org/10.1007/978-1-4612-2752-6_20

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-7652-4

  • Online ISBN: 978-1-4612-2752-6

  • eBook Packages: Springer Book Archive

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