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D.4.6.4 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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