i1 : W = QQ[X, dX, Y, dY, Z, dZ, WeylAlgebra=>{X=>dX, Y=>dY, Z=>dZ}]
o1 = W
o1 : PolynomialRing
|
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
| -XdX-2 -XdX+YdY -Z2dZ-2Z -dYZdZ-2dY
2 => cokernel | -X2Y2Z2 X2Y2-2X2YZ+X2Z2 YdY+ZdZ+6 XdX+4
------------------------------------------------------------------------
0 0 0 0
XdXdZ-YdYdZ -XdXdY-2dY XdX^2+3dX 2XdX^2-3dXYdY
YZdZ-Z2dZ+2Y-4Z dYZ2dZ+Z2dZ^2+4dYZ+8ZdZ+10 |
------------------------------------------------------------------------
-dYdZ-dZ^2 -XdX-YdZ+ZdZ dXdY+dXdZ 0
-dYZ2dZ-Z2dZ^2-2dYZ-4ZdZ-2 -YZ2dZ+Z3dZ-2YZ+2Z2 dXZ2dZ+2dXZ dXdYZdZ+2dXdY
------------------------------------------------------------------------
0 0 0 4Y2-8YZ+4Z2
dX^2ZdZ+2dX^2 XdXdYdZ+2dYdZ -2XdX^2dZ+3dXYdYdZ 4Y2Z2
------------------------------------------------------------------------
-XdX+2YdY-3dYZ-ZdZ+2 XdX+2 XdX+4YdZ-4ZdZ-6 0
-XdXZ2+2YdYZ2-Z3dZ XdXZ2+2Z2 XdXZ2+4YZ2dZ+4Z3dZ+8YZ+10Z2 dX^2YdY+2dX^2
------------------------------------------------------------------------
0 2XdX^2+3dXYdZ-3dXZdZ -dX^2dY-dX^2dZ
XdX^2dY+3dXdY 3dXYZ2dZ-3dXZ3dZ+6dXYZ-6dXZ2 -dX^2Z2dZ-2dX^2Z
------------------------------------------------------------------------
XdXdZ+2dZ 0 0
XdXZ2dZ+2XdXZ+2Z2dZ+4Z -dX^2dYZdZ-2dX^2dY -dX^2YdYdZ-2dX^2dZ
------------------------------------------------------------------------
0 -4dXY2+8dXYZ-4dXZ2 -2XdXY+3XdXZ-4Y+6Z
-XdX^2dYdZ-3dXdYdZ -4dXY2Z2 -2XdXYZ2-XdXZ3-4YZ2-2Z3
------------------------------------------------------------------------
-XdX^2-3dX -XdX^2-6dXYdZ+6dXZdZ+9dX
-XdX^2Z2-3dXZ2 -XdX^2Z2-6dXYZ2dZ-6dXZ3dZ-12dXYZ-15dXZ2
------------------------------------------------------------------------
2XdX^2-6dXYdY+9dXdYZ+3dXZdZ-6dX
2XdX^2Z2-6dXYdYZ2+3dXZ3dZ
------------------------------------------------------------------------
3dXdYdZ+3dXdZ^2
-2XdX^2YdY+3dXdYZ2dZ+3dXZ2dZ^2-4XdX^2+6dXdYZ+12dXZdZ+6dX
------------------------------------------------------------------------
-4dX^2YdZ+4dX^2ZdZ+8dX^2 2dX^2YdZ-2dX^2ZdZ-4dX^2
-4dX^2YZ2dZ-8dX^2YZ 2dX^2YZ2dZ+2dX^2Z3dZ+4dX^2YZ+4dX^2Z2
------------------------------------------------------------------------
-XdX^2dZ-3dXdZ
-XdX^2Z2dZ-2XdX^2Z-3dXZ2dZ-6dXZ
------------------------------------------------------------------------
-dX^2dYdZ-dX^2dZ^2
dX^2YdYZdZ-dX^2dYZ2dZ-dX^2Z2dZ^2-2dX^2dYZ-2dX^2ZdZ-2dX^2
------------------------------------------------------------------------
2dX^2YdY-3dX^2dYZ+2dX^2YdZ-3dX^2ZdZ 4dX^2Y2-8dX^2YZ+4dX^2Z2
2dX^2YdYZ2+2dX^2YZ2dZ+dX^2Z3dZ+4dX^2YZ+6dX^2Z2 4dX^2Y2Z2
------------------------------------------------------------------------
2XdX^2Y-3XdX^2Z+6dXY-9dXZ |, | X2Y2-2X2YZ+X2Z2 dY+dZ YdZ-ZdZ-2
2XdX^2YZ2+XdX^2Z3+6dXYZ2+3dXZ3 | | X2Y2Z2 0 0
------------------------------------------------------------------------
XdX+2 0 0 0 |)}
0 ZdZ+2 YdY+2 XdX+2 |
o3 : HashTable
|