[{"keyword":["algorithms","decompositions","Galois groups","subfields"],"language":[{"iso":"eng"}],"publication":"Experiment. Math. ","abstract":[{"text":"Let {\\ASIE K}\\,/{\\small \\ℚ}({\\ASIE t \\!}) be a finite extension. We describe algorithms for computing subfields and automorphisms of {\\ASIE K}\\,/{\\small \\ℚ}({\\ASIE t }\\!). As an application we give an algorithm for finding decompositions of rational functions in {\\small \\ℚ(α)}. We also present an algorithm which decides if an extension {\\ASIE L}\\,/{\\small \\ℚ}({\\ASIE t \\!}) is a subfield of {\\ASIE K}. In case [{\\ASIE K : \\;}{\\small\\ℚ}({\\ASIE t \\!})] = [{\\ASIE L : \\;}{\\small \\ℚ}({\\ASIE t \\!})] we obtain a {\\small \\ℚ}({\\ASIE t \\!})-isomorphism test. Furthermore, we describe an algorithm which computes subfields of the normal closure of {\\ASIE K}\\,/{\\small \\ℚ}({\\ASIE t \\!}).","lang":"eng"}],"publisher":"Elsevier BV","date_created":"2023-01-11T09:45:40Z","title":"Algorithms for function fields","issue":"2","year":"2002","_id":"35954","department":[{"_id":"102"}],"user_id":"93826","type":"journal_article","status":"public","date_updated":"2023-03-06T10:26:58Z","volume":11,"author":[{"last_name":"Klüners","id":"21202","full_name":"Klüners, Jürgen","first_name":"Jürgen"}],"publication_status":"published","related_material":{"link":[{"url":"https://projecteuclid.org/journals/experimental-mathematics/volume-11/issue-2/Algorithms-for-function-fields/em/1062621213.full","relation":"confirmation"}]},"page":"171-181","intvolume":"        11","citation":{"chicago":"Klüners, Jürgen. “Algorithms for Function Fields.” <i>Experiment. Math. </i> 11, no. 2 (2002): 171–81.","ieee":"J. Klüners, “Algorithms for function fields,” <i>Experiment. Math. </i>, vol. 11, no. 2, pp. 171–181, 2002.","ama":"Klüners J. Algorithms for function fields. <i>Experiment Math </i>. 2002;11(2):171-181.","bibtex":"@article{Klüners_2002, title={Algorithms for function fields}, volume={11}, number={2}, journal={Experiment. Math. }, publisher={Elsevier BV}, author={Klüners, Jürgen}, year={2002}, pages={171–181} }","short":"J. Klüners, Experiment. Math.  11 (2002) 171–181.","mla":"Klüners, Jürgen. “Algorithms for Function Fields.” <i>Experiment. Math. </i>, vol. 11, no. 2, Elsevier BV, 2002, pp. 171–81.","apa":"Klüners, J. (2002). Algorithms for function fields. <i>Experiment. Math. </i>, <i>11</i>(2), 171–181."}}]