DsingularLocus -- singular locus of a D-module

Synopsis

Usage:

DsingularLocus M

DsingularLocus I
Inputs:
- M, a module, 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 variable(s)

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 : DsingularLocus I

o3 = ideal y

o3 : Ideal of QQ[x..y, dx, dy]

Ways to use DsingularLocus:

DsingularLocus(Ideal)
DsingularLocus(Module)

For the programmer

The object DsingularLocus is a method function.

DsingularLocus -- singular locus of a D-module

Synopsis

Description

See also

Ways to use DsingularLocus:

For the programmer