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Higher-Order Linear Differential Systems with Truncated Coefficients

  • S. A. Abramov
  • M. A. Barkatou
  • E. Pflügel
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6885)

Abstract

We consider the following problem: given a linear differential system with formal Laurent series coefficients, we want to decide whether the system has non-zero Laurent series solutions, and find all such solutions if they exist. Let us also assume we need only a given positive integer number l of initial terms of these series solutions. How many initial terms of the coefficients of the original system should we use to construct what we need?

Supposing that the series coefficients of the original systems are represented algorithmically, we show that these questions are undecidable in general. However, they are decidable in the scalar case and in the case when we know in advance that a given system has an invertible leading matrix. We use our results in order to improve some functionality of the Maple [17] package ISOLDE [11].

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • S. A. Abramov
    • 1
  • M. A. Barkatou
    • 2
  • E. Pflügel
    • 3
  1. 1.Computing Centre of the Russian Academy of SciencesMoscowRussia
  2. 2.Institut XLIM, Département Mathématiques et InformatiqueUniversité de Limoges ; CNRSLimoges cedexFrance
  3. 3.Faculty of CISMKingston UniversitySurreyUnited Kingdom

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