On efficient algorithms for computing parametric local cohomology classes associated with semi-quasihomogeneous singularities and standard bases

A new algorithm is given for computing parametric local cohomology classes associated with semi-quasihomogeneous singularities. The essential point of the proposed algorithm involves Poincaré polynomials and weighted degrees. The proposed algorithm gives a suitable decomposition of the parameter space depending on the structure of the parametric local cohomology classes. As an application, an algorithm for computing parametric standard bases of zero-dimensional ideals, is given. These algorithms work for non-parametric cases, too.