Computing Grothendieck Point Residues via Solving Holonomic Systems of First Order Partial Differential Equations

Abstract

Grothendieck point residue is considered in the context of symbolic computation. Based on the theory of holonomic D-modules associated to a local cohomology class, a new effective method is given for computing Grothendieck point residue mappings. A basic strategy of our approach is the use of holonomic systems of first order linear partial differential equations. The resulting algorithm is easy to implement and can also be used to compute Grothendieck point residues in an effective manner. CCS CONCEPTSComputing methodologies → Algebraic algorithms.

Multidimensional algebraic interpolations

“…p n . The main properties of local residues and methods of their calculations are given in [5], [4], [11] and [9].…”