Minimal Free Resolutions of HomogenizedD-modules

Homogenizing a module over the ring of differential operators, we define the notion of a minimal free resolution that is adapted to a filtration. We show that one can apply a modification of the algorithm of La Scala and Stillman to compute such a free resolution. By dehomogenization, one gets a free resolution of the original module that is small enough to compute, e.g. its restriction and integration. We have implemented our algorithm in a computer algebra system Kan and give examples by using this implementation.