@article{34843,
abstract = {{A polynomial time algorithm to find generators of the lattice of all subfields of a given number field was given in van 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 from van 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.}},
author = {{Elsenhans, Andreas-Stephan and Klüners, Jürgen}},
issn = {{0747-7171}},
journal = {{Journal of Symbolic Computation}},
keywords = {{Computational Mathematics, Algebra and Number Theory}},
pages = {{1--20}},
publisher = {{Elsevier BV}},
title = {{{Computing subfields of number fields and applications to Galois group computations}}},
doi = {{10.1016/j.jsc.2018.04.013}},
volume = {{93}},
year = {{2018}},
}