For details of the algorithm for computing singular locus see the book 'Groebner deformations of hypergeometric differential equations' by Saito-Sturmfels-Takayama (1999).
i1 : W = QQ[x,y,Dx,Dy, WeylAlgebra => {x=>Dx,y=>Dy}] o1 = W o1 : PolynomialRing |
i2 : I = ideal (x*Dx+2*y*Dy-3, Dx^2-Dy) 2 o2 = ideal (x*Dx + 2y*Dy - 3, Dx - Dy) o2 : Ideal of W |
i3 : singLocus I o3 = ideal(y) o3 : Ideal of W |