The procedure calls Drestriction, which uses w if specified.
The algorithm used appears in the paper 'Computing homomorphisms between holonomic D-modules' by Tsai-Walther(2000). The method is to combine isomorphisms of Bjork and Kashiwara with the restriction algorithm.
i1 : W = QQ[x, D, WeylAlgebra=>{x=>D}] o1 = W o1 : PolynomialRing, 1 differential variables |
i2 : M = W^1/ideal(D-1) o2 = cokernel | D-1 | 1 o2 : W-module, quotient of W |
i3 : N = W^1/ideal((D-1)^2) o3 = cokernel | D2-2D+1 | 1 o3 : W-module, quotient of W |
i4 : DHom(M,N) o4 = {| -xD+x+1 |, | -D+1 |} o4 : List |
The object DHom is a method function with options.