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] |
The object singLocus is a method function.