Computing quadratic subfields of number fields

A.-S. Elsenhans, J. Klüners, ArXiv:1907.13383 (2019).

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Elsenhans, Andreas-Stephan; Klüners, JürgenLibreCat
Abstract
Given a number field, it is an important question in algorithmic number theory to determine all its subfields. If the search is restricted to abelian subfields, one can try to determine them by using class field theory. For this, it is necessary to know the ramified primes. We show that the ramified primes of the subfield can be computed efficiently. Using this information we give algorithms to determine all the quadratic and the cyclic cubic subfields of the initial field. The approach generalises to cyclic subfields of prime degree. In the case of quadratic subfields, our approach is much faster than other methods.
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arXiv:1907.13383
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Elsenhans A-S, Klüners J. Computing quadratic subfields of number fields. arXiv:190713383. Published online 2019.
Elsenhans, A.-S., & Klüners, J. (2019). Computing quadratic subfields of number fields. In arXiv:1907.13383.
@article{Elsenhans_Klüners_2019, title={Computing quadratic subfields of number fields}, journal={arXiv:1907.13383}, author={Elsenhans, Andreas-Stephan and Klüners, Jürgen}, year={2019} }
Elsenhans, Andreas-Stephan, and Jürgen Klüners. “Computing Quadratic Subfields of Number Fields.” ArXiv:1907.13383, 2019.
A.-S. Elsenhans and J. Klüners, “Computing quadratic subfields of number fields,” arXiv:1907.13383. 2019.
Elsenhans, Andreas-Stephan, and Jürgen Klüners. “Computing Quadratic Subfields of Number Fields.” ArXiv:1907.13383, 2019.

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