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International Workshop on Computer Algebra in Scientific Computing

CASC 2012: Computer Algebra in Scientific Computing pp 143–154Cite as

Complexity of Solving Systems with Few Independent Monomials and Applications to Mass-Action Kinetics

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7442))

Abstract

We design an algorithm for finding solutions with nonzero coordinates of systems of polynomial equations which has a better complexity bound than for known algorithms when a system contains a few linearly independent monomials. For parametric binomial systems we construct an algorithm of polynomial complexity. We discuss the applications of these algorithms in the context of chemical reaction systems.

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Author information

Authors and Affiliations

  1. CNRS, Mathématiques, Université de Lille, Villeneuve d’Ascq, 59655, France

    Dima Grigoriev

  2. Institut für Informatik II, Universität Bonn, Friedrich-Ebert-Allee 144, 53113, Bonn, Germany

    Andreas Weber

Authors
  1. Dima Grigoriev
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  2. Andreas Weber
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Editor information

Editors and Affiliations

  1. Laboratory of Information Technologies (LIT), Joint Institute for Nuclear Research (JINR), 141980, Dubna, Russia

    Vladimir P. Gerdt

  2. Institut für Mathematik, Universität Kassel, Heinrich-Plett-Straße 40, 34132, Kassel, Germany

    Wolfram Koepf

  3. Institut für Informatik, Lehrstuhl für Effiziente Algorithmen, Technische Universität München, Boltzmannstraße 3, 85748, Garching, Germany

    Ernst W. Mayr

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

    Evgenii V. Vorozhtsov

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© 2012 Springer-Verlag Berlin Heidelberg

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Grigoriev, D., Weber, A. (2012). Complexity of Solving Systems with Few Independent Monomials and Applications to Mass-Action Kinetics. In: Gerdt, V.P., Koepf, W., Mayr, E.W., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2012. Lecture Notes in Computer Science, vol 7442. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32973-9_12

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  • DOI: https://doi.org/10.1007/978-3-642-32973-9_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-32972-2

  • Online ISBN: 978-3-642-32973-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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