The Gauß-Manin connection is a regular -module associated to an isolated hypersurface singularity . The V-filtration on is defined by the -module structure. One can describe in terms of integrals of holomorphic differential forms over vanishing cycles . Classes of these differential forms in the Brieskorn lattice can be considered as elements of . The V-filtration on reflects the embedding of in and determines the singularity spectrum which is an important invariant of the singularity.
E. Brieskorn  gave an algorithm to compute the complex monodromy based on the -module structure which is implemented in the computer algebra system SINGULAR  in the library mondromy.lib . In many respects, the microlocal structure of and  seems to be more natural.
After a brief introduction to the theory of the Gauß-Manin connection, we describe how to use this structure for computing in and give an explicit algorithm to compute the V-filtration on . This also leads to a much more efficient algorithm to compute the complex monodromy and the singularity spectrum of an arbitrary isolated hypersurface singularity. All algorithms are implemented in the SINGULAR library gaussman.lib  and are distributed with version 2.0.
For more theoretical background on this section see .