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

- Function: localCohom
- Usage:
    `localCohom(d,I,M)`
- Inputs:
  - d, an integer
  - I, an ideal
  - M, a module
- Optional inputs:
  - LocStrategy => ..., default value null, specify localization strategy for local cohomology
  - Strategy => ..., default value Walther, specify strategy for local cohomology
- Outputs:
  - a hash table, 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 variable(s)

    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})

    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

## See also

- pruneLocalCohom -- prunes local cohomology modules

## Ways to use this method:

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

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/BernsteinSato/DOC/localCohom.m2:193:0.