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 H_I(M) in degree d, where I is an ideal in a polynomial ring and M is a D-module

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