The * Gauß-Manin connection*
is a * regular*
-module associated to an isolated hypersurface singularity
[32]. The * V-filtration* on
is defined by the
-module structure. One can describe
in terms
of integrals of holomorphic differential forms over vanishing cycles
[1]. 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 [1] gave an algorithm to compute the *
complex monodromy* based on the
-module structure which
is implemented in the computer algebra system SINGULAR
[17] in the library ` mondromy.lib` [35].
In many respects, the * microlocal structure* of
and
[32] 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` [36] and are distributed
with version 2.0.

For more theoretical background on this section see [37].