Description
The derived integration modules of a D-module
M are the derived direct images in the category of D-modules. This routine computes integration for projection 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 take the Fourier transform of M, then compute the derived restriction, then inverse Fourier transform back.
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)
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i2 : I = ideal(x_1, D_2-1)
o2 = ideal (x , D - 1)
1 2
o2 : Ideal of R
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i3 : Dintegration(I,{1,0})
o3 = HashTable{0 => cokernel | D_2-1 |}
1 => 0
o3 : HashTable
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