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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&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; User manual for <a href="http://www.singular.uni-kl.de/"><i>Singular</i></a> version 2-0-4, October 2002,
generated by <a href="http://www.gnu.org/software/texinfo/"><i>texi2html</i></a>.
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