Description
The set of D-homomorphisms between two holonomic modules
M and
N is a finite-dimensional vector space over the ground field. Since a homomorphism is defined by where it sends a set of generators, the output of this command is a list of matrices whose columns correspond to the images of the generators of
M. Here the generators of
M are determined from its presentation by generators and relations.
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 variable(s)
|
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
|