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PseudoLinearSystems – A Maple Package for Studying Systems of Pseudo-Linear Equations

  • Moulay Barkatou
  • Thomas Cluzeau
  • Ali El HajjEmail author
Conference paper
  • 47 Downloads
Part of the Communications in Computer and Information Science book series (CCIS, volume 1125)

Abstract

Pseudo-linear systems constitute a large class of linear functional systems including the usual differential, difference and q-difference systems. The Maple package PseudoLinearSystems is dedicated to the study of this class of linear systems. It contains a generic procedure for computing a so-called simple form of a pseudo-linear system as well as local data useful for the local analysis: k-simple forms, super-irreducible forms, integer slopes of the Newton polygon, indicial equations, etc. It is also devoted to the computation of rational solutions (using simple forms) of a single linear differential, difference or q-difference system, as well as rational solutions of a system of mixed linear partial differential, difference and q-difference equations. In this software presentation, we demonstrate the use of several procedures of the package that are all based on the simple form procedure.

Keywords

Pseudo-linear systems Simple forms Rational solutions 

References

  1. 1.
    Barkatou, M., Cluzeau, T., El Hajj, A.: PseudoLinearSystems - A Maple Package for Studying Systems of Pseudo-Linear Equations (2019). http://www.unilim.fr/pages_perso/ali.el-hajj/PseudoLinearSystems.html
  2. 2.
    Barkatou, M., Cluzeau, T., El Hajj, A.: Simple forms and rational solutions of pseudo-linear systems. In: Proceedings of the ISSAC 2019 (2019)Google Scholar
  3. 3.
    Barkatou, M., El Bacha, C.: On \(k\)-simple forms of first-order linear differential systems and their computation. J. Symb. Comput. 54, 36–58 (2013)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.University of Limoges, CNRS, XLIM UMR 7252, MATHISLimogesFrance

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