For a plane curve of degree d with exactly 4 ordinary triple points, the pencil of conics through the 4 triple points cuts out a pencil of degree 2d-12 on the canonical model of this plane curve. This function computes the ideal of the scroll swept out by this pencil.
i1 : p=101; -- a prime number |
i2 : time L=random6gonalGenus11CurvekPencil(p,8);
-- used 2.77547 seconds
|
i3 : time S=scrollPencilOfConics4Triple(L_3,L_4);
-- used 0.420741 seconds
ZZ
o3 : Ideal of ---[r , r , r , r , r , r , r , r , r , r , r ]
101 0 1 2 3 4 5 6 7 8 9 10
|
i4 : betti res S
0 1 2 3 4 5
o4 = total: 1 15 40 45 24 5
0: 1 . . . . .
1: . 15 40 45 24 5
o4 : BettiTally
|