There are two different algorithms for localization implemented. The first appears in the paper 'A localization algorithm for D-modules' by Oaku-Takayama-Walther (1999). The second is due to Oaku and appears in the paper 'Algorithmic computation of local cohomology modules and the cohomological dimension of algebraic varieties' by Walther(1999)
i1 : W = QQ[x,y,Dx,Dy, WeylAlgebra => {x=>Dx,y=>Dy}] o1 = W o1 : PolynomialRing, 2 differential variables |
i2 : M = W^1/(ideal(x*Dx+1, Dy)) o2 = cokernel | xDx+1 Dy | 1 o2 : W-module, quotient of W |
i3 : f = x^2-y^3 3 2 o3 = - y + x o3 : W |
i4 : Mf = Dlocalize(M, f) o4 = cokernel | -3xDx-2yDy-15 -y3Dy+x2Dy-6y2 | 1 o4 : W-module, quotient of W |
The object Dlocalize is a method function with options.