Identifying lens spaces in polynomial time

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.