# localCohom(ZZ,Ideal,Module) -- local cohomology of a D-module

## Synopsis

• Function: localCohom
• Usage:
localCohom(d,I,M)
• Inputs:
• Optional inputs:
• LocStrategy => ..., default value null, specify localization strategy for local cohomology
• Strategy => ..., default value Walther, specify strategy for local cohomology
• Outputs:
• , the local cohomology HI(M) in degree d, where I is an ideal in a polynomial ring and M is a D-module

## Description

See localCohom(Ideal,Module) for the full description.
 i1 : W = QQ[X, dX, Y, dY, Z, dZ, WeylAlgebra=>{X=>dX, Y=>dY, Z=>dZ}] o1 = W o1 : PolynomialRing, 3 differential variables i2 : I = ideal (X*(Y-Z), X*Y*Z) o2 = ideal (X*Y - X*Z, X*Y*Z) o2 : Ideal of W i3 : h = localCohom(2, I, W^1 / ideal{dX,dY,dZ}) WARNING! Dlocalization is an obsolete name for Dlocalize WARNING! Dlocalization is an obsolete name for Dlocalize WARNING! Dlocalization is an obsolete name for Dlocalize o3 = HashTable{2 => cokernel | -X2Y2Z2 X2Y2-2X2YZ+X2Z2 -YdY-ZdZ-6 -XdX-4 YZdZ-Z2dZ+2Y-4Z |} o3 : HashTable i4 : pruneLocalCohom h o4 = HashTable{2 => | dYZ+YdZ+2 YdY+ZdZ+6 Y2-2YZ+Z2 XdX+4 YZdZ-Z2dZ+2Y-4Z 2YZ3-Z4 Z4dZ+2YZ2+4Z3 Z5 |} o4 : HashTable