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7.5.14.0. DsingularLocus
Procedure from library dmodloc.lib (see dmodloc_lib).
- Usage:
- DsingularLocus(I); I ideal
- Assume:
- The basering is the n-th Weyl algebra over a field of
characteristic 0 and for all 1<=i<=n the identity
var(i+n)*var(i)=var(i)*var(i+1)+1 holds, i.e. the sequence of
variables is given by x(1),...,x(n),D(1),...,D(n), where D(i)
is the differential operator belonging to x(i).
- Return:
- ideal, describing the singular locus of the D-module D/I
- Note:
- If printlevel>=1, progress debug messages will be printed,
if printlevel>=2, all the debug messages will be printed
Example:
| | LIB "dmodloc.lib";
// (OTW), Example 8
ring @D3 = 0,(x,y,z,Dx,Dy,Dz),dp;
def D3 = Weyl();
setring D3;
poly f = x^3-y^2*z^2;
ideal I = f^2*Dx + 3*x^2, f^2*Dy-2*y*z^2, f^2*Dz-2*y^2*z;
// I annihilates exp(1/f)
DsingularLocus(I);
==> _[1]=y^2*z^2-x^3
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