Computing Closed Form Solutions of Integrable Connections

In this talk, I will present algorithms for computing rational and hyperexponential solutions of linear D-finite partial differential systems written as integrable connections. In particular, I will show that these types of solutions can be computed recursively by adapting existing algorithms handling ordinary linear differential systems. The arithmetic complexity of the algorithms will be discussed. Finally, I will illustrate the result of a Maple implementation (available at http://www.ensil.unilim.fr/~cluzeau/PDS.html) on some examples.