orderInPic -- order of a line bundle of degree 0 in Pic(E)

• Usage:

  N = orderInPic(L)

  N = orderInPic(phi)

• Inputs:
  • L, an instance of the type VectorBundleOnE, a line bundle of degree 0 on E
  • phi, a matrix, a matrix which is the yAction of VectorBundleOnE
• Outputs:
  • N, an integer, the order of L in Pic(E)

i1 : setRandomSeed 0
 -- setting random seed to 0

o1 = 0

i2 : kk=ZZ/101;

i3 : g=1;

i4 : rNP=randNicePencil(kk,g);

i5 : f=(cliffordModule(rNP.matFact1,rNP.matFact2,rNP.baseRing)).hyperellipticBranchEquation

          3       2 2        3      4
o5 = - 12s t - 50s t  - 16s*t  + 47t

o5 : kk[s, t]

i6 : L=randomLineBundle(0,f);

i7 : orderInPic L

o7 = 37