#### Conference abstracts

Session B3 - Symbolic Analysis

July 15, 16:00 ~ 16:25 - Room B2

## On the computation of simple forms and regular solutions of linear difference systems

### Thomas Cluzeau

### University of Limoges; XLIM , France - thomas.cluzeau@unilim.fr

In this talk, I will present a new algorithm for transforming any first-order linear difference system with factorial series coefficients into a simple system. Such an algorithm can be seen as a first step towards the computation of regular solutions since in a previous work we have developed an algorithm for computing regular solutions of simple linear difference system. Moreover, computing a simple form can also be used to characterize the nature of the singularity at infinity. If the singularity is regular, we are then reduced to a system of the first-kind. I will also present a direct algorithm for computing a formal fundamental matrix of regular solutions of such first-kind linear difference systems which yields an alternative to the algorithm for computing regular solutions of simple systems in the case of a regular singularity. Finally, the algorithms developed have been implemented in Maple thanks to our new package for handling factorial series. The talk will be illustrated by examples computed using our implementation.

Joint work with Moulay Barkatou (University of Limoges; XLIM, France) and Carole El Bacha (Lebanese University, Faculty of Sciences II, Lebanon).