  We consider the notion of a connection on a module over a commutative ring,
and recall the obstruction calculus for such connections. The obstruction
calculus is defined using Hochschild cohomology. However, in order to compute
with Grobner bases, we need the conversion to a description using free
resolutions. We describe our implementation in Singular 3.0, available as the
library conn.lib. Finally, we use the library to verify some known results and
to obtain a new theorem for maximal Cohen-Macaulay (MCM) modules on isolated
singularities. For a simple hypersurface singularity of dimension one or two,
it is known that all MCM modules admit connections. We prove that for a simple
threefold hypersurface singularity of type A_n, D_n or E_n, only the free MCM
modules admit connections if n is at most 50.
