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Dmodules :: singLocus

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 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)

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]

See also

Ways to use singLocus :

For the programmer

The object singLocus is a method function.