Computing subfields of number fields and applications to Galois group computations
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Publication:1733297
DOI10.1016/J.JSC.2018.04.013zbMATH Open1419.11142arXiv1610.06837OpenAlexW2963138639WikidataQ130002429 ScholiaQ130002429MaRDI QIDQ1733297
Author name not available (Why is that?)
Publication date: 21 March 2019
Published in: (Search for Journal in Brave)
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.
Full work available at URL: https://arxiv.org/abs/1610.06837
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