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Thomas Decomposition of Algebraic and Differential Systems

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Computer Algebra in Scientific Computing (CASC 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6244))

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Abstract

In this paper we consider disjoint decomposition of algebraic and non-linear partial differential systems of equations and inequations into so-called simple subsystems. We exploit Thomas decomposition ideas and develop them into a new algorithm. For algebraic systems simplicity means triangularity, squarefreeness and non-vanishing initials. For differential systems the algorithm provides not only algebraic simplicity but also involutivity. The algorithm has been implemented in Maple.

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Author information

Authors and Affiliations

  1. Lehrstuhl B für Mathematik, RWTH-Aachen University, Germany

    Thomas Bächler, Markus Lange-Hegermann & Daniel Robertz

  2. Joint Institute for Nuclear Research, Dubna, Russia

    Vladimir Gerdt

Authors
  1. Thomas Bächler
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  2. Vladimir Gerdt
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  3. Markus Lange-Hegermann
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  4. Daniel Robertz
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Editor information

Editors and Affiliations

  1. JINR, Moscow region, 141980, Dubna, Russia

    Vladimir P. Gerdt

  2. University of Kassel, 34109 l, Kasse, Germany

    Wolfram Koepf

  3. Technische Universität München, 85748, Garching, Germany

    Ernst W. Mayr

  4. Russian Academy of Sciences,, 630090, Novosibirsk, Russia

    Evgenii V. Vorozhtsov

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Bächler, T., Gerdt, V., Lange-Hegermann, M., Robertz, D. (2010). Thomas Decomposition of Algebraic and Differential Systems. In: Gerdt, V.P., Koepf, W., Mayr, E.W., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2010. Lecture Notes in Computer Science, vol 6244. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15274-0_4

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  • DOI: https://doi.org/10.1007/978-3-642-15274-0_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-15273-3

  • Online ISBN: 978-3-642-15274-0

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