  In this paper we describe an algorithm for implicitizing rational
hypersurfaces in case there exists at most a finite number of base points. It
is based on a technique exposed in math.AG/0210096, where implicit equations
are obtained as determinants of certain graded parts of a so-called
approximation complex. We detail and improve this method by providing an
in-depth study of the cohomology of such a complex. In both particular cases of
interest of curve and surface implicitization we also yield explicit algorithms
which only involves linear algebra routines.
