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On the Real Nullstellensatz

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Algorithmic Algebra and Number Theory

Abstract

We give a survey of three implemented real quantifier elimination methods: partial cylindrical algebraic decomposition, virtual substitution of test terms, and a combination of Grabner basis computations with multivariate real root counting. We examine the scope of these implementations for applications in various fields of science, engineering, and economics.

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Authors and Affiliations

  1. Fachbereich Mathematik, Universität Dortmund, 44221, Dortmund, Germany

    Eberhard Becker & Joachim Schmid

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  1. Eberhard Becker
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  2. Joachim Schmid
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Editors and Affiliations

  1. Interdisziplinäres Zentrum für Wissenschaftliches Rechnen, der Universität Heidelberg, Im Neuenheimer Feld 368, D-69120, Heidelberg, Germany

    B. Heinrich Matzat

  2. Fachbereich Mathematik, Universität Kaiserslautern, Postfach 3049, D-67653, Kaiserslautern, Germany

    Gert-Martin Greuel

  3. Lehrstuhl D für Mathematik, RWTH Aachen, Templergraben 64, D-52062, Aachen, Germany

    Gerhard Hiss

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© 1999 Springer-Verlag Berlin Heidelberg

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Becker, E., Schmid, J. (1999). On the Real Nullstellensatz. In: Matzat, B.H., Greuel, GM., Hiss, G. (eds) Algorithmic Algebra and Number Theory. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-59932-3_9

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  • DOI: https://doi.org/10.1007/978-3-642-59932-3_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64670-9

  • Online ISBN: 978-3-642-59932-3

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