Computing Parametric Standard Bases for Semi-weighted Homogeneous Isolated Hypersurface Singularities

An effective method for computing parametric standard bases of Jacobian ideals is introduced for semi-weighted homogeneous isolated hypersurface singularities. The advantage is that the proposed method is algorithmically simple. The main ideas of the method are the use of a negative weighted term ordering and coefficients in a field of rational functions. The correctness of the method is proved by utilizing algebraic local cohomology classes associated to semi-weighted homogeneous singularities.