TY - JOUR
AB - 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.
AU - Elsenhans, Andreas-Stephan
AU - Klüners, Jürgen
ID - 34843
JF - Journal of Symbolic Computation
KW - Computational Mathematics
KW - Algebra and Number Theory
SN - 0747-7171
TI - Computing subfields of number fields and applications to Galois group computations
VL - 93
ER -