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D.4.25.9 deltaLoc
Procedure from library normal.lib (see normal_lib).
- Usage:
- deltaLoc(f,J); f poly, J ideal
- Assume:
- f is reduced bivariate polynomial; basering has exactly two variables;
J is irreducible prime component of the singular locus of f (e.g., one
entry of the output of
minAssGTZ(I); , I = <f,jacob(f)>).
- Return:
- list L:
L[1] ; int:
- the sum of (local) delta invariants of f at the (conjugated) singular
points given by J.
L[2] ; int:
- the sum of (local) Tjurina numbers of f at the (conjugated) singular
points given by J.
L[3] ; int:
- the sum of (local) number of branches of f at the (conjugated)
singular points given by J.
- Note:
- procedure makes use of
execute ; increasing printlevel displays
more comments (default: printlevel=0).
Example:
| LIB "normal.lib";
ring r=0,(x,y),dp;
poly f=(x2+y^2-1)^3 +27x2y2;
ideal I=f,jacob(f);
I=std(I);
list qr=minAssGTZ(I);
size(qr);
==> 6
// each component of the singular locus either describes a cusp or a pair
// of conjugated nodes:
deltaLoc(f,qr[1]);
==> [1]:
==> 1
==> [2]:
==> 2
==> [3]:
==> 1
deltaLoc(f,qr[2]);
==> [1]:
==> 1
==> [2]:
==> 2
==> [3]:
==> 1
deltaLoc(f,qr[3]);
==> [1]:
==> 1
==> [2]:
==> 2
==> [3]:
==> 1
deltaLoc(f,qr[4]);
==> [1]:
==> 1
==> [2]:
==> 2
==> [3]:
==> 1
deltaLoc(f,qr[5]);
==> [1]:
==> 2
==> [2]:
==> 2
==> [3]:
==> 4
deltaLoc(f,qr[6]);
==> [1]:
==> 2
==> [2]:
==> 2
==> [3]:
==> 4
| See also:
delta;
tjurina.
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