Séminaire Calcul Formel

Simple Forms and Rational Solutions of Pseudo-Linear Systems

by Ali El Hajj (XLIM / MATHIS)

Salle XR203 (Bâtiment XLIM)

Salle XR203

Bâtiment XLIM


Simple forms for systems of functional equations have been proved to be an important tool both for the local analysis and for computing global solutions. In this talk, we first provide a unified algorithm for computing a simple form for any system of pseudo-linear equations. We prove that the existing methods for differential and difference systems can be extended to handle every pseudo-linear system. We also provide a complexity estimate of our algorithm. We show how this algorithm can be used for determining the nature of a given singularity and for computing local regular solutions. We then propose an alternative, based on simple forms, to previous algorithms for computing rational solutions of q-difference systems. Moreover we develop a new algorithm for computing rational solutions of systems of linear differential and difference equations. We prove that the latter algorithm can be generalized to the case of several pseudo-linear systems. All the algorithms developed in this paper have been implemented in Maple and some examples are provided.