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Dmodules :: localCohom(ZZ,Ideal,Module)

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

Synopsis

Usage:
localCohom(d,I,M)
Function: localCohom
Inputs:
- d, an integer
- I, an ideal
- M, a module
Optional inputs:
- LocStrategy => ..., -- specify localization strategy for local cohomology
- Strategy => ..., -- specify strategy for local cohomology
Outputs:
- a hash table, the local cohomology H_I(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

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 dYZ2dZ+Z2dZ^2+4dYZ+8ZdZ+10 |}

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