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kGonalNodalCurves :: idealOfNodalCurve

idealOfNodalCurve -- computes the ideal I of a k-gonal g-nodal canonical curve.

Synopsis

Description

Constructs the ideal of a rational k-gonal g-nodal canonical curve.

Step 1: computes the matrix s of sections that defines the canonical embedding with the function getSections.

Step 2: computes I as the kernel of the map s: kk[x0,x1]->kk[t0,..,tg-1].

i1 : (k,g,n)=(4,8,1000);
i2 : time I=idealOfNodalCurve(k,g,n);
     -- used 0.694035 seconds

               ZZ
o2 : Ideal of ----[t , t , t , t , t , t , t , t ]
              1009  0   1   2   3   4   5   6   7
i3 : time betti res I
     -- used 2.6243 seconds

            0  1  2  3  4  5 6
o3 = total: 1 15 39 50 39 15 1
         0: 1  .  .  .  .  . .
         1: . 15 35 25  4  . .
         2: .  .  4 25 35 15 .
         3: .  .  .  .  .  . 1

o3 : BettiTally

See also

Ways to use idealOfNodalCurve :

  • idealOfNodalCurve(ZZ,ZZ,ZZ)