Description
The derived restriction modules of a D-module M are the derived inverse images in the sense of algebraic geometry but in the category of D-modules. This routine computes restrictions to coordinate subspaces, where the subspace is determined by the strictly positive entries of the weight vector
w, e.g.,
{x_i = 0 : w_i > 0} if
D = C<x_1,...,x_n,d_1,...,d_n>. The input weight vector should be a list of
n numbers to induce the weight
(-w,w) on
D.
The algorithm used appears in the paper 'Algorithms for D-modules' by Oaku-Takayama(1999). The method is to compute an adapted resolution with respect to the weight vector w and use the b-function with respect to w to truncate the resolution.
i1 : R = QQ[x_1,x_2,D_1,D_2,WeylAlgebra=>{x_1=>D_1,x_2=>D_2}]
o1 = R
o1 : PolynomialRing, 2 differential variable(s)
|
i2 : I = ideal(x_1, D_2-1)
o2 = ideal (x , D - 1)
1 2
o2 : Ideal of R
|
i3 : Drestriction(I,{1,0})
o3 = HashTable{0 => 0 }
1 => cokernel | D_2-1 |
o3 : HashTable
|