Let σ be an algebraic local cohomology class, and κ a natural number. The purpose of this paper is to present an algorithm for computing the right D-ideal Ann~(κ) (σ) generated by linear differential operators annihilating σ and of order less than or equal to κ. This algorithm is based on Matlis duality theorem, and is applicable to the case where σ has parameters in its coefficients. Our main interest is where algebraic local cohomology classes σ is a generator of the dual space of the Milnor algebra of a hypersurface isolated singularity.
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