We show that if a closed, oriented 3–manifold is promised to be homeomorphic to a lens space with and unknown, then we can compute both and in polynomial time in the size of the triangulation of . The tricky part is the parameter . 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.
"Identifying lens spaces in polynomial time." Algebr. Geom. Topol. 18 (2) 767 - 778, 2018. https://doi.org/10.2140/agt.2018.18.767