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

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