singLocus -- singular locus of a D-module

The singular locus of the system of PDE's given by I generalizes the notion of singular point of an ODE. Geometrically, the singular locus of a D-module M equals the projection of the characteristic variety of M minus the zero section of the cotangent bundle to the base affine space Cⁿ.

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