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Computable Infinite Power Series in the Role of Coefficients of Linear Differential Systems

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Computer Algebra in Scientific Computing (CASC 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8660))

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Abstract

We consider linear ordinary differential systems over a differential field of characteristic 0. We prove that testing unimodularity and computing the dimension of the solution space of an arbitrary system can be done algorithmically if and only if the zero testing problem in the ground differential field is algorithmically decidable. Moreover, we consider full-rank systems whose coefficients are computable power series and we show that, despite the fact that such a system has a basis of formal exponential-logarithmic solutions involving only computable series, there is no algorithm to construct such a basis.

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Author information

Authors and Affiliations

  1. Computing Centre of the Russian Academy of Sciences, Vavilova, 40, Moscow, 119333, Russia

    Sergei A. Abramov

  2. Institut XLIM, Département Mathématiques et Informatique, Université de Limoges ; CNRS, 123, Av. A. Thomas, 87060, Limoges cedex, France

    Moulay A. Barkatou

Authors
  1. Sergei A. Abramov
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  2. Moulay A. Barkatou
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Editor information

Editors and Affiliations

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

    Vladimir P. Gerdt

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

    Wolfram Koepf

  3. Institut für Mathematik, Universität Kassel, 34132, Kassel, Germany

    Werner M. Seiler

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

    Evgenii V. Vorozhtsov

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Abramov, S.A., Barkatou, M.A. (2014). Computable Infinite Power Series in the Role of Coefficients of Linear Differential Systems. In: Gerdt, V.P., Koepf, W., Seiler, W.M., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2014. Lecture Notes in Computer Science, vol 8660. Springer, Cham. https://doi.org/10.1007/978-3-319-10515-4_1

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  • DOI: https://doi.org/10.1007/978-3-319-10515-4_1

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-10514-7

  • Online ISBN: 978-3-319-10515-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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