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Dmodules :: localCohom(List,Ideal,Module)

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

Synopsis

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({1,2}, 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{1 => subquotient (| 0      0        -dY-dZ   0          0           0          0         0             dXdY+dXdZ   0             0             -dYdZ-dZ^2                               0             0                  4Y2-8YZ+4Z2 -3XdX-6YdZ+6ZdZ+6            -XdX+4YdY-6dYZ+4YdZ-6ZdZ-2          XdX+2     XdX+4YdZ-4ZdZ-6             0             0             -dX^2dY-dX^2dZ   XdXdZ+2dZ              0                  3dXdYdZ+3dXdZ^2                                            0                  0                  -4dXY2+8dXYZ-4dXZ2 -2XdXY+3XdXZ-4Y+6Z      -XdX^2-3dX     -XdX^2-6dXYdZ+6dXZdZ+9dX                3XdX^2+9dXYdZ-9dXZdZ-9dX              XdX^2-6dXYdY+9dXdYZ-6dXYdZ+9dXZdZ+3dX           -4dX^2YdZ+4dX^2ZdZ+8dX^2 2dX^2YdZ-2dX^2ZdZ-4dX^2              -XdX^2dZ-3dXdZ                  -dX^2dYdZ-dX^2dZ^2                                       2dX^2YdY-3dX^2dYZ+2dX^2YdZ-3dX^2ZdZ            4dX^2Y2-8dX^2YZ+4dX^2Z2 2XdX^2Y-3XdX^2Z+6dXY-9dXZ      |, | X2Y2-2X2YZ+X2Z2 dY+dZ YdZ-ZdZ-2 XdX+2 0     0     0     |)}
                                 | -XdX-2 -XdX+YdY -Z2dZ-2Z -dYZdZ-2dY XdXdZ-YdYdZ -XdXdY-2dY XdX^2+3dX 2XdX^2-3dXYdY dXZ2dZ+2dXZ dXdYZdZ+2dXdY dX^2ZdZ+2dX^2 -XdXZdZ+YdYZdZ-dYZ2dZ-Z2dZ^2-2dYZ-4ZdZ-2 XdXdYdZ+2dYdZ -2XdX^2dZ+3dXYdYdZ 4Y2Z2       -XdXZ2-6YZ2dZ-2Z3dZ-12YZ-6Z2 -XdXZ2+4YdYZ2+4YZ2dZ+2Z3dZ+8YZ+10Z2 XdXZ2+2Z2 XdXZ2+4YZ2dZ+4Z3dZ+8YZ+10Z2 dX^2YdY+2dX^2 XdX^2dY+3dXdY -dX^2Z2dZ-2dX^2Z XdXZ2dZ+2XdXZ+2Z2dZ+4Z -dX^2dYZdZ-2dX^2dY 2XdX^2ZdZ-3dXYdYZdZ+3dXdYZ2dZ+3dXZ2dZ^2+6dXdYZ+12dXZdZ+6dX -dX^2YdYdZ-2dX^2dZ -XdX^2dYdZ-3dXdYdZ -4dXY2Z2           -2XdXYZ2-XdXZ3-4YZ2-2Z3 -XdX^2Z2-3dXZ2 -XdX^2Z2-6dXYZ2dZ-6dXZ3dZ-12dXYZ-15dXZ2 XdX^2Z2+9dXYZ2dZ+3dXZ3dZ+18dXYZ+9dXZ2 XdX^2Z2-6dXYdYZ2-6dXYZ2dZ-3dXZ3dZ-12dXYZ-15dXZ2 -4dX^2YZ2dZ-8dX^2YZ      2dX^2YZ2dZ+2dX^2Z3dZ+4dX^2YZ+4dX^2Z2 -XdX^2Z2dZ-2XdX^2Z-3dXZ2dZ-6dXZ dX^2YdYZdZ-dX^2dYZ2dZ-dX^2Z2dZ^2-2dX^2dYZ-2dX^2ZdZ-2dX^2 2dX^2YdYZ2+2dX^2YZ2dZ+dX^2Z3dZ+4dX^2YZ+6dX^2Z2 4dX^2Y2Z2               2XdX^2YZ2+XdX^2Z3+6dXYZ2+3dXZ3 |  | X2Y2Z2          0     0         0     ZdZ+2 YdY+2 XdX+2 |
               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{1 => | dZ dY XdX+3 X3 |                                                              }
               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