[{"year":"2025","title":"Computing quadratic subfields of number fields","publisher":"Elsevier BV","date_created":"2025-08-05T07:01:39Z","abstract":[{"lang":"eng","text":"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."}],"publication":"Journal of Computational Algebra","language":[{"iso":"eng"}],"external_id":{"arxiv":["1907.13383"]},"intvolume":"        15","citation":{"apa":"Elsenhans, A.-S., &#38; Klüners, J. (2025). Computing quadratic subfields of number fields. <i>Journal of Computational Algebra</i>, <i>15</i>, Article 100039. <a href=\"https://doi.org/10.1016/j.jaca.2025.100039\">https://doi.org/10.1016/j.jaca.2025.100039</a>","bibtex":"@article{Elsenhans_Klüners_2025, title={Computing quadratic subfields of number fields}, volume={15}, DOI={<a href=\"https://doi.org/10.1016/j.jaca.2025.100039\">10.1016/j.jaca.2025.100039</a>}, number={100039}, journal={Journal of Computational Algebra}, publisher={Elsevier BV}, author={Elsenhans, Andreas-Stephan and Klüners, Jürgen}, year={2025} }","short":"A.-S. Elsenhans, J. Klüners, Journal of Computational Algebra 15 (2025).","mla":"Elsenhans, Andreas-Stephan, and Jürgen Klüners. “Computing Quadratic Subfields of Number Fields.” <i>Journal of Computational Algebra</i>, vol. 15, 100039, Elsevier BV, 2025, doi:<a href=\"https://doi.org/10.1016/j.jaca.2025.100039\">10.1016/j.jaca.2025.100039</a>.","ama":"Elsenhans A-S, Klüners J. Computing quadratic subfields of number fields. <i>Journal of Computational Algebra</i>. 2025;15. doi:<a href=\"https://doi.org/10.1016/j.jaca.2025.100039\">10.1016/j.jaca.2025.100039</a>","ieee":"A.-S. Elsenhans and J. Klüners, “Computing quadratic subfields of number fields,” <i>Journal of Computational Algebra</i>, vol. 15, Art. no. 100039, 2025, doi: <a href=\"https://doi.org/10.1016/j.jaca.2025.100039\">10.1016/j.jaca.2025.100039</a>.","chicago":"Elsenhans, Andreas-Stephan, and Jürgen Klüners. “Computing Quadratic Subfields of Number Fields.” <i>Journal of Computational Algebra</i> 15 (2025). <a href=\"https://doi.org/10.1016/j.jaca.2025.100039\">https://doi.org/10.1016/j.jaca.2025.100039</a>."},"publication_identifier":{"issn":["2772-8277"]},"publication_status":"published","doi":"10.1016/j.jaca.2025.100039","date_updated":"2025-08-05T07:10:25Z","volume":15,"author":[{"full_name":"Elsenhans, Andreas-Stephan","last_name":"Elsenhans","first_name":"Andreas-Stephan"},{"first_name":"Jürgen","last_name":"Klüners","full_name":"Klüners, Jürgen","id":"21202"}],"status":"public","type":"journal_article","article_number":"100039","_id":"60874","user_id":"82981"}]