Formal solutions of a class of Pfaffian systems in two variables

Abstract

In this article, we present an algorithm which computes a fundamental matrix of formal solutions of completely integrable Pfaffian systems with normal crossings in two variables, based on [Barkatou, 1997]. A first step was set in [Barkatou et al., 2006] where the problem of rank reduction was tackled via the approach in [Levelt, 1991]. We give instead a Moser-based approach following [Barkatou et al., 2014;Barkatou, 1995]. And, as a complementary step, we associate to our problem a system of ordinary linear singular differential equations from which the formal invariants can be efficiently derived via the package ISOLDE [Barkatou et al., 2013], implemented in the computer algebra system Maple.