Higher-Order Linear Differential Systems with Truncated Coefficients - Archive ouverte HAL Accéder directement au contenu
Communication Dans Un Congrès Année : 2011

Higher-Order Linear Differential Systems with Truncated Coefficients

Sergei Abramov
  • Fonction : Auteur
Moulay A. Barkatou
DMI
Eckhard Pfluegel
  • Fonction : Auteur

Résumé

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].

Dates et versions

hal-00685032 , version 1 (03-04-2012)

Identifiants

Citer

Sergei Abramov, Moulay A. Barkatou, Eckhard Pfluegel. Higher-Order Linear Differential Systems with Truncated Coefficients. CASC 2011, Sep 2011, Kassel, Germany. pp.10-24, ⟨10.1007/978-3-642-23568-9_2⟩. ⟨hal-00685032⟩

Collections

UNILIM CNRS XLIM
27 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More