Computing Homomorphisms Between HolonomicD-modules

Let K C be a subfield of the complex numbers, and let D be the ring of K -linear differential operators on R = K [ x1, . . . , xn]. If M and N are holonomic left D -modules we present an algorithm that computes explicit generators for the finite dimensional vector space Hom D(M, N). This enables us to answer algorithmically whether two given holonomic modules are isomorphic. More generally, our algorithm can be used to get explicit generators for Ext Di(M, N) for any i in the sense of Yoneda.