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# localCohom(ZZ,Ideal) -- local cohomology of a polynomial ring

- Function: localCohom
- Usage:
    `localCohom(d,I)`
- Inputs:
  - d, an integer
  - I, an ideal
- 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 of I in degree d

## Description

See localCohom(Ideal) 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)

    o3 = cokernel | -XYZ XY-XZ 3XdX-2YdY-2ZdZ YdY+ZdZ+3 Y2dY-2YdYZ-2YZdZ+Z2dZ |

                                1
    o3 : W-module, quotient of W

    i4 : Dprune h

    o4 = cokernel | Y-Z Z2 dYZ+ZdZ+2 XdX+2 |

                                1
    o4 : W-module, quotient of W

## See also

- pruneLocalCohom -- prunes local cohomology modules

## Ways to use this method:

- localCohom(ZZ,Ideal) -- local cohomology of a polynomial ring

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/BernsteinSato/DOC/localCohom.m2:142:0.