L=preRandomLineBundle(f)
Ld=preRandomLineBundle(d,f)
Chooses a random line bundle on the hyperelliptic curve E of genus g given by the equation y^2-(-1)^{g}*f, where f is the branch equation of degree (2g+2). Input with an integer d gives a random line bundle of degree d on E.
Note that a line bundle on E is given by the y-action which is represented by a traceless 2x2 matrix
b c
a -b
whose determinant equals to (-1)^{g}*f. We find such a matrix over a finite ground field by picking randomly b, a homogeneous form of degree (g+1), since the binary form b^2 + (-1)^{g}*f frequently factors.
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The ground field kk has to be finite.
The object preRandomLineBundle is a method function.
The source of this document is in /build/reproducible-path/macaulay2-1.25.06+ds/M2/Macaulay2/packages/PencilsOfQuadrics.m2:3095:0.