On full rank differential systems with power series coefficients

We consider the following problem: given a linear ordinary differential system of arbitrary order with formal power series coefficients, decide whether the system has non-zero Laurent series solutions, and find all such solutions if they exist (in a truncated form preserving the space dimension). If the series coefficients of the original systems are represented algorithmically then these problems are algorithmically undecidable. However, it turns out that they are decidable in the case when we know in advance that a given system is of full rank.We define the width of a given full rank system S with formal power series coefficients as the smallest non-negative integer w such that any l-truncation of S   with l⩾wl⩾w is a full rank system. We prove that the value w exists for any full rank system and can be found algorithmically.We propose corresponding algorithms and their Maple implementation, and report some experiments.