  We show that if a closed, oriented 3-manifold M is promised to be
homeomorphic to a lens space L(n,k) with n and k unknown, then we can compute
both n and k in polynomial time in the size of the triangulation of M. The
tricky part is the parameter k. The idea of the algorithm is to calculate
Reidemeister torsion using numerical analysis over the complex numbers, rather
than working directly in a cyclotomic field.
