Implicitizing rational hypersurfaces using approximation complexes

We describe an algorithm for implicitizing rational hypersurfaces with at most a finite number of base points, based on a technique already described by Busé and Jouanolou, where implicit equations are obtained as determinants of certain graded parts of an 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 present algorithms which involve only linear algebra routines