  The Koszul homology of modules of the polynomial ring $R$ is a central object
in commutative algebra.It is strongly related with the minimal free resolution
of these modules, and thus with regularity, Hilbert functions, etc. Here we
consider the case of modules of the form $R/I$ where $I$ is a monomial ideal.
So far, some good algorithms have been given in the literature and implemented
in different Computer Algebra Systems (e.g. CoCoa, Singular, Macaulay), which
compute minimal free resolutions of modules of the form $R/I$ with $I$ an ideal
in $R$, which include the case of $I$ being a monomial ideal as a particular
one (a good review is given in \cite {Sie}). Our goal is to build algorithms
especially teargeted to monomial ideals, taking into account the special
combinatorial and structural properties of these ideals. This being a first
goal, it is also a first step of an alternative approach to the computation of
the Koszul homology and minimal free resolutions of polynomial ideals.
