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D.6.9.12 delta

Procedure from library hnoether.lib (see hnoether_lib).

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).

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).

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.

LIB "hnoether.lib";
ring r = 32003,(x,y),ds;
poly f = x25+x24-4x23-1x22y+4x22+8x21y-2x21-12x20y-4x19y2+4x20+10x19y
==> 96
See also: deltaLoc; invariants.