# singLocus -- singular locus of a D-module

## Synopsis

• Usage:
singLocus M
singLocus I
• Inputs:
• M, , over the Weyl algebra D
• I, an ideal, which represents the module M = D/I
• Outputs:
• an ideal, the singular locus of M

## Description

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 C ^n.
More details can be found in [SST, Section 1.4].

 i1 : makeWA(QQ[x,y]) o1 = QQ[x..y, dx, dy] o1 : PolynomialRing, 2 differential variables 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 QQ[x..y, dx, dy] i3 : singLocus I o3 = ideal y o3 : Ideal of QQ[x..y, dx, dy]