{"user_id":"93826","year":"1998","author":[{"first_name":"Jürgen","id":"21202","last_name":"Klüners","full_name":"Klüners, Jürgen"}],"publication_status":"published","date_created":"2022-12-23T10:24:43Z","doi":"https://jtnb.centre-mersenne.org/item/?id=JTNB_1998__10_2_243_0","status":"public","_id":"34905","type":"journal_article","publisher":"Elsevier BV","volume":10,"citation":{"bibtex":"@article{Klüners_1998, title={On computing subfields. A detailed description of the algorithm }, volume={10}, DOI={<a href=\"https://jtnb.centre-mersenne.org/item/?id=JTNB_1998__10_2_243_0\">https://jtnb.centre-mersenne.org/item/?id=JTNB_1998__10_2_243_0</a>}, number={2}, journal={Journal de Theorie des Nombres de Bordeaux}, publisher={Elsevier BV}, author={Klüners, Jürgen}, year={1998}, pages={243–271} }","ieee":"J. Klüners, “On computing subfields. A detailed description of the algorithm ,” <i>Journal de Theorie des Nombres de Bordeaux</i>, vol. 10, no. 2, pp. 243–271, 1998, doi: <a href=\"https://jtnb.centre-mersenne.org/item/?id=JTNB_1998__10_2_243_0\">https://jtnb.centre-mersenne.org/item/?id=JTNB_1998__10_2_243_0</a>.","ama":"Klüners J. On computing subfields. A detailed description of the algorithm . <i>Journal de Theorie des Nombres de Bordeaux</i>. 1998;10(2):243-271. doi:<a href=\"https://jtnb.centre-mersenne.org/item/?id=JTNB_1998__10_2_243_0\">https://jtnb.centre-mersenne.org/item/?id=JTNB_1998__10_2_243_0</a>","short":"J. Klüners, Journal de Theorie Des Nombres de Bordeaux 10 (1998) 243–271.","apa":"Klüners, J. (1998). On computing subfields. A detailed description of the algorithm . <i>Journal de Theorie Des Nombres de Bordeaux</i>, <i>10</i>(2), 243–271. <a href=\"https://jtnb.centre-mersenne.org/item/?id=JTNB_1998__10_2_243_0\">https://jtnb.centre-mersenne.org/item/?id=JTNB_1998__10_2_243_0</a>","mla":"Klüners, Jürgen. “On Computing Subfields. A Detailed Description of the Algorithm .” <i>Journal de Theorie Des Nombres de Bordeaux</i>, vol. 10, no. 2, Elsevier BV, 1998, pp. 243–71, doi:<a href=\"https://jtnb.centre-mersenne.org/item/?id=JTNB_1998__10_2_243_0\">https://jtnb.centre-mersenne.org/item/?id=JTNB_1998__10_2_243_0</a>.","chicago":"Klüners, Jürgen. “On Computing Subfields. A Detailed Description of the Algorithm .” <i>Journal de Theorie Des Nombres de Bordeaux</i> 10, no. 2 (1998): 243–71. <a href=\"https://jtnb.centre-mersenne.org/item/?id=JTNB_1998__10_2_243_0\">https://jtnb.centre-mersenne.org/item/?id=JTNB_1998__10_2_243_0</a>."},"date_updated":"2023-03-06T10:34:22Z","issue":"2","intvolume":"        10","language":[{"iso":"eng"}],"page":"243-271","related_material":{"link":[{"url":"http://www.numdam.org/item/JTNB_1998__10_2_243_0/","relation":"confirmation"}]},"abstract":[{"text":"Let ℚ(α) be an algebraic number field given by the\r\nminimal polynomial f of α. We want to determine all subfields\r\nℚ(β) ⊂ Q(α) of given degree. It is convenient to describe each\r\nsubfield by a pair (g, h) ∈ Z [t] x ℚ[t] such that g is the minimal\r\npolynomial of β = h(α) . There is a bijection between the block\r\nsystems of the Galois group of f and the subfields of ℚ(α). These\r\nblock systems are computed using cyclic subgroups of the Galois\r\ngroup which we get from the Dedekind criterion. When a block\r\nsystem is known we compute the corresponding subfield using p-\r\nadic methods. We give a detailed description for all parts of the\r\nalgorithm.","lang":"eng"}],"publication":"Journal de Theorie des Nombres de Bordeaux","title":"On computing subfields. A detailed description of the algorithm "}