Computing closed form solutions of integrable connections

Authors:
M. A. Barkatou;T. Cluzeau;C. El Bacha;J.-A. Weil
Affiliations:
University of Limoges, Limoges cedex, France;University of Limoges, Limoges cedex, France;University of Limoges, Limoges cedex, France;University of Limoges, Limoges cedex, France
Venue:
Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation
Year:
2012

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Abstract

We present algorithms for computing rational and hyperexponential solutions of linear D-finite partial differential systems written as integrable connections. We show that these types of solutions can be computed recursively by adapting existing algorithms handling ordinary linear differential systems. We provide an arithmetic complexity analysis of the algorithms that we develop. A Maple implementation is available and some examples and applications are given.