Given the g pairs of points Pi,Qi we can proceed as follows:
Step 1. We compute g quadrics qi :=det(Pi | (x0,x1)t) * det(Qi | (x0,x1)t).
Step 2. We compute a basis of H0(C,ωC) by {si :=∏gj≠i,j=1qi | i=1,...,g } and multiply the matrix s=(s1,...,sg) wih a general matrix M∈GL(g,kk) to obtain more general sections.
i1 : (k,g,n)=(4,8,1000); |
i2 : (p,kk,S)=getFieldAndRing(n); |
i3 : (P,Q,multL,f)=pickGoodPoints(k,g,n); |
i4 : s=sub(sectionsFromPoints(P,Q),S);
1 8
o4 : Matrix S <--- S
|
i5 : T=kk[t_0..t_(g-1)]; |
i6 : I=ideal mingens ker map(S,T,s); o6 : Ideal of T |
i7 : betti res I
0 1 2 3 4 5 6
o7 = total: 1 15 39 50 39 15 1
0: 1 . . . . . .
1: . 15 35 25 4 . .
2: . . 4 25 35 15 .
3: . . . . . . 1
o7 : BettiTally
|