picrandtors

Function: picrandtors
Section: modular_forms
C-Name: PicRandTors
Prototype: GGDGDGDGD0,L,
Help: picrandtors(J,l,{Chi},{Phi},{randseed},{flag}): Random point of prime order l on the p-adic Jacobian J. Lp must be the chracteristic polynomial of Frob_p on J. If Chi is present, it must divide Lp mod l and be coprime with its cofactor, and we return a point of order l on the piece of J[l] where Frob_p acts with charpoly Chi. If Phi is present, it must be a cyclotomic polynomial dividing x^a-1, where a is the ineratial degree of the p-adic extension over which J is defined, and l and a must be coprime; and we return a point of order l in the piece of J killed by Phi(Frob_p). If randseed is present, use it to initialise the random generator. If flag is set, we instead return a vector [W,o,T,B], where W has order l^o exactly, T = l^{o-1}*W has order l, and B is such that B(Frob_p) kills T. We may also return 0 if the generation of a torsion point failed.
Doc: TODO 
 \bprog
 ? TODO
 %2 = 
 TODO
 @eprog