Deciding linear-exponential problems

In our forthcoming article "Weyl closure of a linear differential operator", we give an algorithm to compute 1the Weyl closure when n = 1. This algorithm has been implemented in MAPLE. We also provide some applications, namely the algorithmic computat ion of Jordan-HSlder series for holonomic Dl-modules , a description of the possible initial ideals of left Dlideals with respect to the order filtration, and a description of the isomorphism classes of left Dl-ideals.