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D.5.5.16 delta
Procedure from library hnoether.lib (see hnoether_lib).
- Usage:
- delta(f); f a polynomial defining an isolated plane curve
singularity at 0
- Return:
- the delta invariant of the singularity at 0, the vector space
dimension of R~/R, where R~ is the normalization of the
singularity R=basering/f
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);
==> finite HNE of one branch found
==> Change of basering (field extension) necessary!
==> HNE of one branch found
==> HNE of one branch found
==> HNE of one branch found
==> // result: 4 branch(es) successfully computed,
==> // basering has changed to HNEring
==> 96
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