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Grothendieck point residue is considered in the context of computationalcomplex analysis. A new effective method is proposed for computing Grothendieckpoint residues mappings and residues. Basic ideas of our approach are the useof Grothendieck local duality and a transformation law for local cohomologyclasses. A new tool is devised for efficiency to solve the extended idealmembership problems in local rings. The resulting algorithms are described withan example to illustrate them. An extension of the proposed method toparametric cases is also discussed as an application.

An effective method for computing Grothendieck point residue mappings