{"language":[{"iso":"eng"}],"type":"preprint","date_updated":"2023-03-02T09:10:59Z","publication":"arXiv:1907.13383","status":"public","year":"2019","abstract":[{"lang":"eng","text":"Given a number field, it is an important question in algorithmic number\r\ntheory to determine all its subfields. If the search is restricted to abelian\r\nsubfields, one can try to determine them by using class field theory. For this,\r\nit is necessary to know the ramified primes. We show that the ramified primes\r\nof the subfield can be computed efficiently. Using this information we give\r\nalgorithms to determine all the quadratic and the cyclic cubic subfields of the\r\ninitial field. The approach generalises to cyclic subfields of prime degree. In\r\nthe case of quadratic subfields, our approach is much faster than other\r\nmethods."}],"author":[{"full_name":"Elsenhans, Andreas-Stephan","last_name":"Elsenhans","first_name":"Andreas-Stephan"},{"id":"21202","last_name":"Klüners","full_name":"Klüners, Jürgen","first_name":"Jürgen"}],"title":"Computing quadratic subfields of number fields","_id":"42646","department":[{"_id":"102"}],"external_id":{"arxiv":["1907.13383"]},"user_id":"93826","citation":{"chicago":"Elsenhans, Andreas-Stephan, and Jürgen Klüners. “Computing Quadratic Subfields of Number Fields.” <i>ArXiv:1907.13383</i>, 2019.","short":"A.-S. Elsenhans, J. Klüners, ArXiv:1907.13383 (2019).","bibtex":"@article{Elsenhans_Klüners_2019, title={Computing quadratic subfields of number fields}, journal={arXiv:1907.13383}, author={Elsenhans, Andreas-Stephan and Klüners, Jürgen}, year={2019} }","apa":"Elsenhans, A.-S., &#38; Klüners, J. (2019). Computing quadratic subfields of number fields. In <i>arXiv:1907.13383</i>.","mla":"Elsenhans, Andreas-Stephan, and Jürgen Klüners. “Computing Quadratic Subfields of Number Fields.” <i>ArXiv:1907.13383</i>, 2019.","ama":"Elsenhans A-S, Klüners J. Computing quadratic subfields of number fields. <i>arXiv:190713383</i>. Published online 2019.","ieee":"A.-S. Elsenhans and J. Klüners, “Computing quadratic subfields of number fields,” <i>arXiv:1907.13383</i>. 2019."},"date_created":"2023-03-02T09:03:18Z"}