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PencilsOfQuadrics :: orderInPic

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

Synopsis

Description

Computes the order of a degree 0 line bundle L on the hyperelliptic curve E by the most naive method.

i1 : kk=ZZ/101;
i2 : g=1;
i3 : rNP=randNicePencil(kk,g);
i4 : f=(cliffordModule(rNP.matFact1,rNP.matFact2,rNP.baseRing)).hyperellipticBranchEquation

          3       2 2        3      4
o4 = - 12s t - 50s t  - 16s*t  + 47t

o4 : kk[s, t]
i5 : L=randomLineBundle(0,f);
i6 : orderInPic L

o6 = 37

Caveat

The ground field kk has to be finite. It computes the order by checking inductively whether Lk is trivial, so it may fail when kk is not finite, or has too many elements. orderInPic(phi) may not terminate if it is not the yAction of a line bundle of degree 0 on E.

See also

Ways to use orderInPic :