Computing subfields of number fields and applications to Galois group computations. (July 2019) - Elsenhans, Andreas-Stephan; Klüners, Jürgen
Abstract: A polynomial time algorithm to find generators of the lattice of all subfields of a given number field was given invan Hoeij et al. (2013) . This article reports on a massive speedup of this algorithm. This is primary achieved by our new concept of Galois-generating subfields . In general this is a very small set of subfields that determine all other subfields in a group-theoretic way. We compute them by targeted calls to the method fromvan Hoeij et al. (2013) . For an early termination of these calls, we give a list of criteria that imply that further calls will not result in additional subfields. Finally, we explain how we use subfields to get a good starting group for the computation of Galois groups.