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Dmodules :: localCohom(List,Ideal)

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

Synopsis

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 variables
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({1,2}, I)

o3 = HashTable{1 => subquotient (| 0          0      0           -dXdY-dXdZ dXY-dXZ XdX+1  0               0        XdXdZ-dY   -XdXZ-Y      |, | XY-XZ dY+dZ XdX+YdZ-ZdZ -YdZ+ZdZ+1 0       0       0     |)}
                                 | -YdY-ZdZ-2 -XdX-1 -3dXZdZ-3dX -dXZdZ-dX  dXYZ    XdXZ+Z dXYdY+dXZdZ+2dX XdXdY+dY XdXZdZ+XdX -XdXZ2-YZ-Z2 |  | XYZ   0     0           0          YdY-ZdZ XdX-ZdZ ZdZ+1 |
               2 => cokernel | -XYZ XY-XZ 3XdX-2YdY-2ZdZ YdY+ZdZ+3 Y2dY-2YdYZ-2YZdZ+Z2dZ |

o3 : HashTable
i4 : pruneLocalCohom h

o4 = HashTable{1 => | dZ dY X |               }
               2 => | Y-Z Z2 dYZ+ZdZ+2 XdX+2 |

o4 : HashTable

See also