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arXiv · 1610.06837

Computing subfields of number fields and applications to Galois group computations

Andreas-Stephan Elsenhans·Jürgen Klüners
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Abstract

A polynomial time algorithm to give a complete description of all subfields of a given number field was given in an article by van Hoeij et al. 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. 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.

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Andreas-Stephan Elsenhans, Jürgen Klüners. 2016-10-21. Computing subfields of number fields and applications to Galois group computations. https://arxiv.org/abs/1610.06837

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