
D.6.11.12 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 HamburgerNoether 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 HamburgerNoether 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+x244x231x22y+4x22+8x21y2x2112x20y4x19y2+4x20+10x19y
+12x18y224x18y20x17y24x16y3+x18+60x16y2+20x15y39x16y
80x14y310x13y4+36x14y2+60x12y4+2x11y584x12y324x10y5
+126x10y4+4x8y6126x8y5+84x6y636x4y7+9x2y81y9;
delta(f);
==> 96
 See also:
deltaLoc;
invariants.
