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D.6.9.12 delta
Procedure from library hnoether.lib (see hnoether_lib).
- Usage:
- delta(INPUT); INPUT a polynomial defining an isolated plane curve
singularity at 0, or the Hamburger-Noether expansion thereof, i.e.
the output of
develop(f), or the output of hnexpansion(f),
or the list of HN data computed by hnexpansion(f).
- Return:
- int, the delta invariant of the singularity at 0, that is, the vector
space dimension of R~/R, (R~ the normalization of the local ring of
the singularity).
- Note:
- In case the Hamburger-Noether expansion of the curve f is needed
for other purposes as well it is better to calculate this first
with the aid of
hnexpansion and use it as input instead of
the polynomial itself.
Example:
| | LIB "hnoether.lib";
ring r = 32003,(x,y),ds;
poly f = x25+x24-4x23-1x22y+4x22+8x21y-2x21-12x20y-4x19y2+4x20+10x19y
+12x18y2-24x18y-20x17y2-4x16y3+x18+60x16y2+20x15y3-9x16y
-80x14y3-10x13y4+36x14y2+60x12y4+2x11y5-84x12y3-24x10y5
+126x10y4+4x8y6-126x8y5+84x6y6-36x4y7+9x2y8-1y9;
delta(f);
==> 96
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See also:
deltaLoc;
invariants.
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