{"volume":93,"abstract":[{"lang":"eng","text":"A polynomial time algorithm to find generators of the lattice of all subfields of a given number field was given in van Hoeij et al. (2013).\r\n\r\nThis 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. (2013). For an early termination of these calls, we give a list of criteria that imply that further calls will not result in additional subfields.\r\n\r\nFinally, we explain how we use subfields to get a good starting group for the computation of Galois groups."}],"doi":"10.1016/j.jsc.2018.04.013","keyword":["Computational Mathematics","Algebra and Number Theory"],"publication":"Journal of Symbolic Computation","date_created":"2022-12-22T10:52:18Z","type":"journal_article","page":"1-20","_id":"34843","intvolume":"        93","publication_identifier":{"issn":["0747-7171"]},"year":"2018","status":"public","author":[{"first_name":"Andreas-Stephan","full_name":"Elsenhans, Andreas-Stephan","last_name":"Elsenhans"},{"full_name":"Klüners, Jürgen","last_name":"Klüners","id":"21202","first_name":"Jürgen"}],"publisher":"Elsevier BV","citation":{"ama":"Elsenhans A-S, Klüners J. Computing subfields of number fields and applications to Galois group computations. <i>Journal of Symbolic Computation</i>. 2018;93:1-20. doi:<a href=\"https://doi.org/10.1016/j.jsc.2018.04.013\">10.1016/j.jsc.2018.04.013</a>","bibtex":"@article{Elsenhans_Klüners_2018, title={Computing subfields of number fields and applications to Galois group computations}, volume={93}, DOI={<a href=\"https://doi.org/10.1016/j.jsc.2018.04.013\">10.1016/j.jsc.2018.04.013</a>}, journal={Journal of Symbolic Computation}, publisher={Elsevier BV}, author={Elsenhans, Andreas-Stephan and Klüners, Jürgen}, year={2018}, pages={1–20} }","chicago":"Elsenhans, Andreas-Stephan, and Jürgen Klüners. “Computing Subfields of Number Fields and Applications to Galois Group Computations.” <i>Journal of Symbolic Computation</i> 93 (2018): 1–20. <a href=\"https://doi.org/10.1016/j.jsc.2018.04.013\">https://doi.org/10.1016/j.jsc.2018.04.013</a>.","short":"A.-S. Elsenhans, J. Klüners, Journal of Symbolic Computation 93 (2018) 1–20.","apa":"Elsenhans, A.-S., &#38; Klüners, J. (2018). Computing subfields of number fields and applications to Galois group computations. <i>Journal of Symbolic Computation</i>, <i>93</i>, 1–20. <a href=\"https://doi.org/10.1016/j.jsc.2018.04.013\">https://doi.org/10.1016/j.jsc.2018.04.013</a>","ieee":"A.-S. Elsenhans and J. Klüners, “Computing subfields of number fields and applications to Galois group computations,” <i>Journal of Symbolic Computation</i>, vol. 93, pp. 1–20, 2018, doi: <a href=\"https://doi.org/10.1016/j.jsc.2018.04.013\">10.1016/j.jsc.2018.04.013</a>.","mla":"Elsenhans, Andreas-Stephan, and Jürgen Klüners. “Computing Subfields of Number Fields and Applications to Galois Group Computations.” <i>Journal of Symbolic Computation</i>, vol. 93, Elsevier BV, 2018, pp. 1–20, doi:<a href=\"https://doi.org/10.1016/j.jsc.2018.04.013\">10.1016/j.jsc.2018.04.013</a>."},"user_id":"93826","department":[{"_id":"102"}],"title":"Computing subfields of number fields and applications to Galois group computations","external_id":{"arxiv":["1610.06837 "]},"language":[{"iso":"eng"}],"publication_status":"published","date_updated":"2023-03-06T09:05:51Z"}