Thomas Decomposition of Algebraic and Differential Systems

  • Thomas Bächler
  • Vladimir Gerdt
  • Markus Lange-Hegermann
  • Daniel Robertz
Conference paper

DOI: 10.1007/978-3-642-15274-0_4

Part of the Lecture Notes in Computer Science book series (LNCS, volume 6244)
Cite this paper as:
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

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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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Thomas Bächler
    • 1
  • Vladimir Gerdt
    • 2
  • Markus Lange-Hegermann
    • 1
  • Daniel Robertz
    • 1
  1. 1.Lehrstuhl B für MathematikRWTH-Aachen UniversityGermany
  2. 2.Joint Institute for Nuclear ResearchDubnaRussia

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