[{"abstract":[{"text":"Let K be a global field and O be an order of K. We develop algorithms for the computation of the unit group of residue class rings for ideals O in . As an application we show how to compute the unit group and the Picard group of O provided that we are able to compute the unit group and class group of the maximal order O of K.","lang":"eng"}],"publication":"Journal of Algebra","keyword":["Algebra and Number Theory"],"language":[{"iso":"eng"}],"year":"2005","issue":"1","title":"Computing residue class rings and Picard groups of orders","publisher":"Elsevier BV","date_created":"2022-12-23T09:41:06Z","status":"public","type":"journal_article","_id":"34893","user_id":"93826","department":[{"_id":"102"}],"citation":{"apa":"Klüners, J., &#38; Pauli, S. (2005). Computing residue class rings and Picard groups of orders. <i>Journal of Algebra</i>, <i>292</i>(1), 47–64. <a href=\"https://doi.org/10.1016/j.jalgebra.2005.04.013\">https://doi.org/10.1016/j.jalgebra.2005.04.013</a>","mla":"Klüners, Jürgen, and Sebastian Pauli. “Computing Residue Class Rings and Picard Groups of Orders.” <i>Journal of Algebra</i>, vol. 292, no. 1, Elsevier BV, 2005, pp. 47–64, doi:<a href=\"https://doi.org/10.1016/j.jalgebra.2005.04.013\">10.1016/j.jalgebra.2005.04.013</a>.","bibtex":"@article{Klüners_Pauli_2005, title={Computing residue class rings and Picard groups of orders}, volume={292}, DOI={<a href=\"https://doi.org/10.1016/j.jalgebra.2005.04.013\">10.1016/j.jalgebra.2005.04.013</a>}, number={1}, journal={Journal of Algebra}, publisher={Elsevier BV}, author={Klüners, Jürgen and Pauli, Sebastian}, year={2005}, pages={47–64} }","short":"J. Klüners, S. Pauli, Journal of Algebra 292 (2005) 47–64.","ama":"Klüners J, Pauli S. Computing residue class rings and Picard groups of orders. <i>Journal of Algebra</i>. 2005;292(1):47-64. doi:<a href=\"https://doi.org/10.1016/j.jalgebra.2005.04.013\">10.1016/j.jalgebra.2005.04.013</a>","chicago":"Klüners, Jürgen, and Sebastian Pauli. “Computing Residue Class Rings and Picard Groups of Orders.” <i>Journal of Algebra</i> 292, no. 1 (2005): 47–64. <a href=\"https://doi.org/10.1016/j.jalgebra.2005.04.013\">https://doi.org/10.1016/j.jalgebra.2005.04.013</a>.","ieee":"J. Klüners and S. Pauli, “Computing residue class rings and Picard groups of orders,” <i>Journal of Algebra</i>, vol. 292, no. 1, pp. 47–64, 2005, doi: <a href=\"https://doi.org/10.1016/j.jalgebra.2005.04.013\">10.1016/j.jalgebra.2005.04.013</a>."},"intvolume":"       292","page":"47-64","publication_status":"published","publication_identifier":{"issn":["0021-8693"]},"doi":"10.1016/j.jalgebra.2005.04.013","date_updated":"2023-03-06T09:55:09Z","author":[{"last_name":"Klüners","id":"21202","full_name":"Klüners, Jürgen","first_name":"Jürgen"},{"first_name":"Sebastian","full_name":"Pauli, Sebastian","last_name":"Pauli"}],"volume":292},{"publication_identifier":{"isbn":["978-3-8322-4003-5"]},"year":"2005","place":"Universiät Kassel","citation":{"apa":"Klüners, J. (2005). <i>Über die Asymptotik von Zahlkörpern mit vorgegebener Galoisgruppe (Habilitation)</i>. Shaker Verlag.","bibtex":"@book{Klüners_2005, place={Universiät Kassel}, title={Über die Asymptotik von Zahlkörpern mit vorgegebener Galoisgruppe (Habilitation)}, publisher={Shaker Verlag}, author={Klüners, Jürgen}, year={2005} }","mla":"Klüners, Jürgen. <i>Über die Asymptotik von Zahlkörpern mit vorgegebener Galoisgruppe (Habilitation)</i>. Shaker Verlag, 2005.","short":"J. Klüners, Über die Asymptotik von Zahlkörpern mit vorgegebener Galoisgruppe (Habilitation), Shaker Verlag, Universiät Kassel, 2005.","chicago":"Klüners, Jürgen. <i>Über die Asymptotik von Zahlkörpern mit vorgegebener Galoisgruppe (Habilitation)</i>. Universiät Kassel: Shaker Verlag, 2005.","ieee":"J. Klüners, <i>Über die Asymptotik von Zahlkörpern mit vorgegebener Galoisgruppe (Habilitation)</i>. Universiät Kassel: Shaker Verlag, 2005.","ama":"Klüners J. <i>Über die Asymptotik von Zahlkörpern mit vorgegebener Galoisgruppe (Habilitation)</i>. Shaker Verlag; 2005."},"page":"114","date_updated":"2023-04-11T08:13:38Z","publisher":"Shaker Verlag","author":[{"full_name":"Klüners, Jürgen","id":"21202","last_name":"Klüners","first_name":"Jürgen"}],"date_created":"2023-03-07T09:05:29Z","title":"Über die Asymptotik von Zahlkörpern mit vorgegebener Galoisgruppe (Habilitation)","type":"misc","status":"public","_id":"42807","user_id":"93826","department":[{"_id":"102"}],"extern":"1","language":[{"iso":"ger"}]},{"title":"Konstruktive Idealtheorie in Quaternionenalgebren (Diplomarbeit)","date_updated":"2023-04-11T08:11:24Z","author":[{"first_name":"Markus","full_name":"Kirschmer, Markus","id":"82258","last_name":"Kirschmer"}],"date_created":"2023-04-11T08:09:29Z","place":"Universität Ulm","year":"2005","citation":{"apa":"Kirschmer, M. (2005). <i>Konstruktive Idealtheorie in Quaternionenalgebren (Diplomarbeit)</i>.","bibtex":"@book{Kirschmer_2005, place={Universität Ulm}, title={Konstruktive Idealtheorie in Quaternionenalgebren (Diplomarbeit)}, author={Kirschmer, Markus}, year={2005} }","mla":"Kirschmer, Markus. <i>Konstruktive Idealtheorie in Quaternionenalgebren (Diplomarbeit)</i>. 2005.","short":"M. Kirschmer, Konstruktive Idealtheorie in Quaternionenalgebren (Diplomarbeit), Universität Ulm, 2005.","chicago":"Kirschmer, Markus. <i>Konstruktive Idealtheorie in Quaternionenalgebren (Diplomarbeit)</i>. Universität Ulm, 2005.","ieee":"M. Kirschmer, <i>Konstruktive Idealtheorie in Quaternionenalgebren (Diplomarbeit)</i>. Universität Ulm, 2005.","ama":"Kirschmer M. <i>Konstruktive Idealtheorie in Quaternionenalgebren (Diplomarbeit)</i>.; 2005."},"page":"147","language":[{"iso":"eng"}],"extern":"1","_id":"43455","user_id":"93826","department":[{"_id":"102"}],"status":"public","type":"mastersthesis"},{"status":"public","type":"journal_article","department":[{"_id":"102"}],"user_id":"93826","_id":"34896","intvolume":"        99","page":"318-337","citation":{"short":"C. Fieker, J. Klüners, Journal of Number Theory 99 (2003) 318–337.","bibtex":"@article{Fieker_Klüners_2003, title={Minimal discriminants for fields with small Frobenius groups as Galois groups}, volume={99}, DOI={<a href=\"https://doi.org/10.1016/s0022-314x(02)00071-9\">10.1016/s0022-314x(02)00071-9</a>}, number={2}, journal={Journal of Number Theory}, publisher={Elsevier BV}, author={Fieker, Claus and Klüners, Jürgen}, year={2003}, pages={318–337} }","mla":"Fieker, Claus, and Jürgen Klüners. “Minimal Discriminants for Fields with Small Frobenius Groups as Galois Groups.” <i>Journal of Number Theory</i>, vol. 99, no. 2, Elsevier BV, 2003, pp. 318–37, doi:<a href=\"https://doi.org/10.1016/s0022-314x(02)00071-9\">10.1016/s0022-314x(02)00071-9</a>.","apa":"Fieker, C., &#38; Klüners, J. (2003). Minimal discriminants for fields with small Frobenius groups as Galois groups. <i>Journal of Number Theory</i>, <i>99</i>(2), 318–337. <a href=\"https://doi.org/10.1016/s0022-314x(02)00071-9\">https://doi.org/10.1016/s0022-314x(02)00071-9</a>","ieee":"C. Fieker and J. Klüners, “Minimal discriminants for fields with small Frobenius groups as Galois groups,” <i>Journal of Number Theory</i>, vol. 99, no. 2, pp. 318–337, 2003, doi: <a href=\"https://doi.org/10.1016/s0022-314x(02)00071-9\">10.1016/s0022-314x(02)00071-9</a>.","chicago":"Fieker, Claus, and Jürgen Klüners. “Minimal Discriminants for Fields with Small Frobenius Groups as Galois Groups.” <i>Journal of Number Theory</i> 99, no. 2 (2003): 318–37. <a href=\"https://doi.org/10.1016/s0022-314x(02)00071-9\">https://doi.org/10.1016/s0022-314x(02)00071-9</a>.","ama":"Fieker C, Klüners J. Minimal discriminants for fields with small Frobenius groups as Galois groups. <i>Journal of Number Theory</i>. 2003;99(2):318-337. doi:<a href=\"https://doi.org/10.1016/s0022-314x(02)00071-9\">10.1016/s0022-314x(02)00071-9</a>"},"publication_identifier":{"issn":["0022-314X"]},"publication_status":"published","doi":"10.1016/s0022-314x(02)00071-9","volume":99,"author":[{"first_name":"Claus","full_name":"Fieker, Claus","last_name":"Fieker"},{"full_name":"Klüners, Jürgen","id":"21202","last_name":"Klüners","first_name":"Jürgen"}],"date_updated":"2023-03-06T09:19:16Z","abstract":[{"lang":"eng","text":"We apply class field theory to the computation of the minimal discriminants for certain solvable groups. In particular, we apply our techniques to small Frobenius groups and all imprimitive degree 8 groups such that the corresponding fields have only a degree 2 and no degree 4 subfield."}],"publication":"Journal of Number Theory","language":[{"iso":"eng"}],"keyword":["Algebra and Number Theory"],"year":"2003","issue":"2","title":"Minimal discriminants for fields with small Frobenius groups as Galois groups","date_created":"2022-12-23T09:53:23Z","publisher":"Elsevier BV"},{"_id":"35954","department":[{"_id":"102"}],"user_id":"93826","status":"public","type":"journal_article","date_updated":"2023-03-06T10:26:58Z","volume":11,"author":[{"last_name":"Klüners","id":"21202","full_name":"Klüners, Jürgen","first_name":"Jürgen"}],"intvolume":"        11","page":"171-181","citation":{"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} }","mla":"Klüners, Jürgen. “Algorithms for Function Fields.” <i>Experiment. Math. </i>, vol. 11, no. 2, Elsevier BV, 2002, pp. 171–81.","short":"J. Klüners, Experiment. Math.  11 (2002) 171–181.","apa":"Klüners, J. (2002). Algorithms for function fields. <i>Experiment. Math. </i>, <i>11</i>(2), 171–181.","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."},"publication_status":"published","related_material":{"link":[{"relation":"confirmation","url":"https://projecteuclid.org/journals/experimental-mathematics/volume-11/issue-2/Algorithms-for-function-fields/em/1062621213.full"}]},"keyword":["algorithms","decompositions","Galois groups","subfields"],"language":[{"iso":"eng"}],"abstract":[{"lang":"eng","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 \\!})."}],"publication":"Experiment. Math. ","title":"Algorithms for function fields","publisher":"Elsevier BV","date_created":"2023-01-11T09:45:40Z","year":"2002","issue":"2"},{"user_id":"93826","department":[{"_id":"102"}],"_id":"34897","type":"journal_article","status":"public","author":[{"last_name":"Klüners","full_name":"Klüners, Jürgen","id":"21202","first_name":"Jürgen"},{"full_name":"Malle, Gunter","last_name":"Malle","first_name":"Gunter"}],"volume":4,"date_updated":"2023-03-02T09:53:08Z","doi":"10.1112/s1461157000000851","publication_status":"published","publication_identifier":{"issn":["1461-1570"]},"citation":{"apa":"Klüners, J., &#38; Malle, G. (2001). A Database for Field Extensions of the Rationals. <i>LMS Journal of Computation and Mathematics</i>, <i>4</i>, 182–196. <a href=\"https://doi.org/10.1112/s1461157000000851\">https://doi.org/10.1112/s1461157000000851</a>","mla":"Klüners, Jürgen, and Gunter Malle. “A Database for Field Extensions of the Rationals.” <i>LMS Journal of Computation and Mathematics</i>, vol. 4, Wiley, 2001, pp. 182–96, doi:<a href=\"https://doi.org/10.1112/s1461157000000851\">10.1112/s1461157000000851</a>.","bibtex":"@article{Klüners_Malle_2001, title={A Database for Field Extensions of the Rationals}, volume={4}, DOI={<a href=\"https://doi.org/10.1112/s1461157000000851\">10.1112/s1461157000000851</a>}, journal={LMS Journal of Computation and Mathematics}, publisher={Wiley}, author={Klüners, Jürgen and Malle, Gunter}, year={2001}, pages={182–196} }","short":"J. Klüners, G. Malle, LMS Journal of Computation and Mathematics 4 (2001) 182–196.","ama":"Klüners J, Malle G. A Database for Field Extensions of the Rationals. <i>LMS Journal of Computation and Mathematics</i>. 2001;4:182-196. doi:<a href=\"https://doi.org/10.1112/s1461157000000851\">10.1112/s1461157000000851</a>","ieee":"J. Klüners and G. Malle, “A Database for Field Extensions of the Rationals,” <i>LMS Journal of Computation and Mathematics</i>, vol. 4, pp. 182–196, 2001, doi: <a href=\"https://doi.org/10.1112/s1461157000000851\">10.1112/s1461157000000851</a>.","chicago":"Klüners, Jürgen, and Gunter Malle. “A Database for Field Extensions of the Rationals.” <i>LMS Journal of Computation and Mathematics</i> 4 (2001): 182–96. <a href=\"https://doi.org/10.1112/s1461157000000851\">https://doi.org/10.1112/s1461157000000851</a>."},"intvolume":"         4","page":"182-196","external_id":{"arxiv":["math/0102232"]},"language":[{"iso":"eng"}],"keyword":["Computational Theory and Mathematics","General Mathematics"],"publication":"LMS Journal of Computation and Mathematics","abstract":[{"text":"This paper announces the creation of a database for number fields. It describes the contents and the methods of access, indicates the origin of the polynomials, and formulates the aims of this collection of fields.","lang":"eng"}],"date_created":"2022-12-23T09:56:22Z","publisher":"Wiley","title":"A Database for Field Extensions of the Rationals","year":"2001"},{"language":[{"iso":"eng"}],"keyword":["Computational Mathematics","Algebra and Number Theory"],"abstract":[{"text":"We describe methods for the computation of Galois groups of univariate polynomials over the rationals which we have implemented up to degree 15. These methods are based on Stauduhar’s algorithm. All computations are done in unramified p -adic extensions. For imprimitive groups we give an improvement using subfields. In the primitive case we use known subgroups of the Galois group together with a combination of Stauduhar’s method and the absolute resolvent method.","lang":"eng"}],"publication":"Journal of Symbolic Computation","title":"Galois Group Computation for Rational Polynomials","date_created":"2022-12-23T09:58:16Z","publisher":"Elsevier BV","year":"2000","issue":"6","department":[{"_id":"102"}],"user_id":"93826","_id":"34900","status":"public","type":"journal_article","doi":"10.1006/jsco.2000.0377","volume":30,"author":[{"last_name":"Geissler","full_name":"Geissler, Katharina","first_name":"Katharina"},{"first_name":"Jürgen","last_name":"Klüners","id":"21202","full_name":"Klüners, Jürgen"}],"date_updated":"2023-03-06T09:58:06Z","page":"653-674","intvolume":"        30","citation":{"chicago":"Geissler, Katharina, and Jürgen Klüners. “Galois Group Computation for Rational Polynomials.” <i>Journal of Symbolic Computation</i> 30, no. 6 (2000): 653–74. <a href=\"https://doi.org/10.1006/jsco.2000.0377\">https://doi.org/10.1006/jsco.2000.0377</a>.","ieee":"K. Geissler and J. Klüners, “Galois Group Computation for Rational Polynomials,” <i>Journal of Symbolic Computation</i>, vol. 30, no. 6, pp. 653–674, 2000, doi: <a href=\"https://doi.org/10.1006/jsco.2000.0377\">10.1006/jsco.2000.0377</a>.","ama":"Geissler K, Klüners J. Galois Group Computation for Rational Polynomials. <i>Journal of Symbolic Computation</i>. 2000;30(6):653-674. doi:<a href=\"https://doi.org/10.1006/jsco.2000.0377\">10.1006/jsco.2000.0377</a>","short":"K. Geissler, J. Klüners, Journal of Symbolic Computation 30 (2000) 653–674.","bibtex":"@article{Geissler_Klüners_2000, title={Galois Group Computation for Rational Polynomials}, volume={30}, DOI={<a href=\"https://doi.org/10.1006/jsco.2000.0377\">10.1006/jsco.2000.0377</a>}, number={6}, journal={Journal of Symbolic Computation}, publisher={Elsevier BV}, author={Geissler, Katharina and Klüners, Jürgen}, year={2000}, pages={653–674} }","mla":"Geissler, Katharina, and Jürgen Klüners. “Galois Group Computation for Rational Polynomials.” <i>Journal of Symbolic Computation</i>, vol. 30, no. 6, Elsevier BV, 2000, pp. 653–74, doi:<a href=\"https://doi.org/10.1006/jsco.2000.0377\">10.1006/jsco.2000.0377</a>.","apa":"Geissler, K., &#38; Klüners, J. (2000). Galois Group Computation for Rational Polynomials. <i>Journal of Symbolic Computation</i>, <i>30</i>(6), 653–674. <a href=\"https://doi.org/10.1006/jsco.2000.0377\">https://doi.org/10.1006/jsco.2000.0377</a>"},"publication_identifier":{"issn":["0747-7171"]},"publication_status":"published"},{"issue":"3","year":"2000","publisher":"Elsevier BV","date_created":"2022-12-23T09:58:48Z","title":"Computing Local Artin Maps, and Solvability of Norm Equations","publication":"Journal of Symbolic Computation","abstract":[{"text":"Let L = K(α) be an Abelian extension of degree n of a number field K, given by the minimal polynomial of α over K. We describe an algorithm for computing the local Artin map associated with the extension L / K at a finite or infinite prime v of K. We apply this algorithm to decide if a nonzero a ∈ K is a norm from L, assuming that L / K is cyclic.","lang":"eng"}],"keyword":["Computational Mathematics","Algebra and Number Theory"],"language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["0747-7171"]},"citation":{"ama":"Acciaro V, Klüners J. Computing Local Artin Maps, and Solvability of Norm Equations. <i>Journal of Symbolic Computation</i>. 2000;30(3):239-252. doi:<a href=\"https://doi.org/10.1006/jsco.2000.0361\">10.1006/jsco.2000.0361</a>","ieee":"V. Acciaro and J. Klüners, “Computing Local Artin Maps, and Solvability of Norm Equations,” <i>Journal of Symbolic Computation</i>, vol. 30, no. 3, pp. 239–252, 2000, doi: <a href=\"https://doi.org/10.1006/jsco.2000.0361\">10.1006/jsco.2000.0361</a>.","chicago":"Acciaro, Vincenzo, and Jürgen Klüners. “Computing Local Artin Maps, and Solvability of Norm Equations.” <i>Journal of Symbolic Computation</i> 30, no. 3 (2000): 239–52. <a href=\"https://doi.org/10.1006/jsco.2000.0361\">https://doi.org/10.1006/jsco.2000.0361</a>.","bibtex":"@article{Acciaro_Klüners_2000, title={Computing Local Artin Maps, and Solvability of Norm Equations}, volume={30}, DOI={<a href=\"https://doi.org/10.1006/jsco.2000.0361\">10.1006/jsco.2000.0361</a>}, number={3}, journal={Journal of Symbolic Computation}, publisher={Elsevier BV}, author={Acciaro, Vincenzo and Klüners, Jürgen}, year={2000}, pages={239–252} }","short":"V. Acciaro, J. Klüners, Journal of Symbolic Computation 30 (2000) 239–252.","mla":"Acciaro, Vincenzo, and Jürgen Klüners. “Computing Local Artin Maps, and Solvability of Norm Equations.” <i>Journal of Symbolic Computation</i>, vol. 30, no. 3, Elsevier BV, 2000, pp. 239–52, doi:<a href=\"https://doi.org/10.1006/jsco.2000.0361\">10.1006/jsco.2000.0361</a>.","apa":"Acciaro, V., &#38; Klüners, J. (2000). Computing Local Artin Maps, and Solvability of Norm Equations. <i>Journal of Symbolic Computation</i>, <i>30</i>(3), 239–252. <a href=\"https://doi.org/10.1006/jsco.2000.0361\">https://doi.org/10.1006/jsco.2000.0361</a>"},"intvolume":"        30","page":"239-252","date_updated":"2023-03-06T09:57:34Z","author":[{"first_name":"Vincenzo","last_name":"Acciaro","full_name":"Acciaro, Vincenzo"},{"first_name":"Jürgen","last_name":"Klüners","id":"21202","full_name":"Klüners, Jürgen"}],"volume":30,"doi":"10.1006/jsco.2000.0361","type":"journal_article","status":"public","_id":"34901","user_id":"93826","department":[{"_id":"102"}]},{"keyword":["Computational Mathematics","Algebra and Number Theory"],"language":[{"iso":"eng"}],"abstract":[{"lang":"eng","text":"We describe methods for the construction of polynomials with certain types of Galois groups. As an application we deduce that all transitive groups G up to degree 15 occur as Galois groups of regular extensions of ℚ (t), and in each case compute a polynomial f ∈ ℚ [ x ] with Gal(f)  = G."}],"publication":"Journal of Symbolic Computation","title":"Explicit Galois Realization of Transitive Groups of Degree up to 15","publisher":"Elsevier BV","date_created":"2022-12-23T09:57:28Z","year":"2000","issue":"6","_id":"34899","user_id":"93826","department":[{"_id":"102"}],"status":"public","type":"journal_article","doi":"10.1006/jsco.2000.0378","date_updated":"2023-03-06T10:48:05Z","author":[{"id":"21202","full_name":"Klüners, Jürgen","last_name":"Klüners","first_name":"Jürgen"},{"first_name":"Gunter","full_name":"Malle, Gunter","last_name":"Malle"}],"volume":30,"citation":{"chicago":"Klüners, Jürgen, and Gunter Malle. “Explicit Galois Realization of Transitive Groups of Degree up to 15.” <i>Journal of Symbolic Computation</i> 30, no. 6 (2000): 675–716. <a href=\"https://doi.org/10.1006/jsco.2000.0378\">https://doi.org/10.1006/jsco.2000.0378</a>.","ieee":"J. Klüners and G. Malle, “Explicit Galois Realization of Transitive Groups of Degree up to 15,” <i>Journal of Symbolic Computation</i>, vol. 30, no. 6, pp. 675–716, 2000, doi: <a href=\"https://doi.org/10.1006/jsco.2000.0378\">10.1006/jsco.2000.0378</a>.","ama":"Klüners J, Malle G. Explicit Galois Realization of Transitive Groups of Degree up to 15. <i>Journal of Symbolic Computation</i>. 2000;30(6):675-716. doi:<a href=\"https://doi.org/10.1006/jsco.2000.0378\">10.1006/jsco.2000.0378</a>","apa":"Klüners, J., &#38; Malle, G. (2000). Explicit Galois Realization of Transitive Groups of Degree up to 15. <i>Journal of Symbolic Computation</i>, <i>30</i>(6), 675–716. <a href=\"https://doi.org/10.1006/jsco.2000.0378\">https://doi.org/10.1006/jsco.2000.0378</a>","short":"J. Klüners, G. Malle, Journal of Symbolic Computation 30 (2000) 675–716.","bibtex":"@article{Klüners_Malle_2000, title={Explicit Galois Realization of Transitive Groups of Degree up to 15}, volume={30}, DOI={<a href=\"https://doi.org/10.1006/jsco.2000.0378\">10.1006/jsco.2000.0378</a>}, number={6}, journal={Journal of Symbolic Computation}, publisher={Elsevier BV}, author={Klüners, Jürgen and Malle, Gunter}, year={2000}, pages={675–716} }","mla":"Klüners, Jürgen, and Gunter Malle. “Explicit Galois Realization of Transitive Groups of Degree up to 15.” <i>Journal of Symbolic Computation</i>, vol. 30, no. 6, Elsevier BV, 2000, pp. 675–716, doi:<a href=\"https://doi.org/10.1006/jsco.2000.0378\">10.1006/jsco.2000.0378</a>."},"page":"675-716","intvolume":"        30","publication_status":"published","publication_identifier":{"issn":["0747-7171"]}},{"keyword":["Computational Mathematics","Algebra and Number Theory"],"language":[{"iso":"eng"}],"abstract":[{"lang":"eng","text":"We compute a polynomial with Galois group SL₂(11) over ℚ. Furthermore we prove that SL₂(11) is the Galois group of a regular extension of ℚ (t)."}],"publication":"Journal of Symbolic Computation","title":"A Polynomial with Galois GroupSL2(11)","publisher":"Elsevier BV","date_created":"2022-12-23T09:56:52Z","year":"2000","issue":"6","_id":"34898","department":[{"_id":"102"}],"user_id":"93826","status":"public","type":"journal_article","doi":"10.1006/jsco.2000.0380","date_updated":"2023-03-06T10:48:40Z","volume":30,"author":[{"first_name":"Jürgen","last_name":"Klüners","id":"21202","full_name":"Klüners, Jürgen"}],"intvolume":"        30","page":"733-737","citation":{"apa":"Klüners, J. (2000). A Polynomial with Galois GroupSL2(11). <i>Journal of Symbolic Computation</i>, <i>30</i>(6), 733–737. <a href=\"https://doi.org/10.1006/jsco.2000.0380\">https://doi.org/10.1006/jsco.2000.0380</a>","bibtex":"@article{Klüners_2000, title={A Polynomial with Galois GroupSL2(11)}, volume={30}, DOI={<a href=\"https://doi.org/10.1006/jsco.2000.0380\">10.1006/jsco.2000.0380</a>}, number={6}, journal={Journal of Symbolic Computation}, publisher={Elsevier BV}, author={Klüners, Jürgen}, year={2000}, pages={733–737} }","short":"J. Klüners, Journal of Symbolic Computation 30 (2000) 733–737.","mla":"Klüners, Jürgen. “A Polynomial with Galois GroupSL2(11).” <i>Journal of Symbolic Computation</i>, vol. 30, no. 6, Elsevier BV, 2000, pp. 733–37, doi:<a href=\"https://doi.org/10.1006/jsco.2000.0380\">10.1006/jsco.2000.0380</a>.","ama":"Klüners J. A Polynomial with Galois GroupSL2(11). <i>Journal of Symbolic Computation</i>. 2000;30(6):733-737. doi:<a href=\"https://doi.org/10.1006/jsco.2000.0380\">10.1006/jsco.2000.0380</a>","chicago":"Klüners, Jürgen. “A Polynomial with Galois GroupSL2(11).” <i>Journal of Symbolic Computation</i> 30, no. 6 (2000): 733–37. <a href=\"https://doi.org/10.1006/jsco.2000.0380\">https://doi.org/10.1006/jsco.2000.0380</a>.","ieee":"J. Klüners, “A Polynomial with Galois GroupSL2(11),” <i>Journal of Symbolic Computation</i>, vol. 30, no. 6, pp. 733–737, 2000, doi: <a href=\"https://doi.org/10.1006/jsco.2000.0380\">10.1006/jsco.2000.0380</a>."},"publication_identifier":{"issn":["0747-7171"]},"publication_status":"published"},{"title":"On Polynomial Decompositions","date_created":"2022-12-23T10:01:15Z","publisher":"Elsevier BV","year":"1999","issue":"3","language":[{"iso":"eng"}],"keyword":["Computational Mathematics","Algebra and Number Theory"],"abstract":[{"text":"We present a new polynomial decomposition which generalizes the functional and homogeneous bivariate decomposition of irreducible monic polynomials in one variable over the rationals. With these decompositions it is possible to calculate the roots of an imprimitive polynomial by solving polynomial equations of lower degree.","lang":"eng"}],"publication":"Journal of Symbolic Computation","doi":"10.1006/jsco.1998.0252","volume":27,"author":[{"full_name":"Klüners, Jürgen","id":"21202","last_name":"Klüners","first_name":"Jürgen"}],"date_updated":"2023-03-06T09:21:29Z","page":"261-269","intvolume":"        27","citation":{"apa":"Klüners, J. (1999). On Polynomial Decompositions. <i>Journal of Symbolic Computation</i>, <i>27</i>(3), 261–269. <a href=\"https://doi.org/10.1006/jsco.1998.0252\">https://doi.org/10.1006/jsco.1998.0252</a>","mla":"Klüners, Jürgen. “On Polynomial Decompositions.” <i>Journal of Symbolic Computation</i>, vol. 27, no. 3, Elsevier BV, 1999, pp. 261–69, doi:<a href=\"https://doi.org/10.1006/jsco.1998.0252\">10.1006/jsco.1998.0252</a>.","bibtex":"@article{Klüners_1999, title={On Polynomial Decompositions}, volume={27}, DOI={<a href=\"https://doi.org/10.1006/jsco.1998.0252\">10.1006/jsco.1998.0252</a>}, number={3}, journal={Journal of Symbolic Computation}, publisher={Elsevier BV}, author={Klüners, Jürgen}, year={1999}, pages={261–269} }","short":"J. Klüners, Journal of Symbolic Computation 27 (1999) 261–269.","ieee":"J. Klüners, “On Polynomial Decompositions,” <i>Journal of Symbolic Computation</i>, vol. 27, no. 3, pp. 261–269, 1999, doi: <a href=\"https://doi.org/10.1006/jsco.1998.0252\">10.1006/jsco.1998.0252</a>.","chicago":"Klüners, Jürgen. “On Polynomial Decompositions.” <i>Journal of Symbolic Computation</i> 27, no. 3 (1999): 261–69. <a href=\"https://doi.org/10.1006/jsco.1998.0252\">https://doi.org/10.1006/jsco.1998.0252</a>.","ama":"Klüners J. On Polynomial Decompositions. <i>Journal of Symbolic Computation</i>. 1999;27(3):261-269. doi:<a href=\"https://doi.org/10.1006/jsco.1998.0252\">10.1006/jsco.1998.0252</a>"},"publication_identifier":{"issn":["0747-7171"]},"publication_status":"published","department":[{"_id":"102"}],"user_id":"93826","_id":"34902","status":"public","type":"journal_article"},{"language":[{"iso":"eng"}],"abstract":[{"text":"Let L = ℚ(α) be an abelian number field of degree n. Most\r\nalgorithms for computing the lattice of subfields of L require the computation\r\nof all the conjugates of α. This is usually achieved by factoring the minimal\r\npolynomial mα(x) of α over L. In practice, the existing algorithms for factoring\r\npolynomials over algebraic number fields can handle only problems of moderate\r\nsize. In this paper we describe a fast probabilistic algorithm for computing\r\nthe conjugates of α, which is based on p-adic techniques. Given mα(x) and a\r\nrational prime p which does not divide the discriminant disc(mα(x)) of mα(x),\r\nthe algorithm computes the Frobenius automorphism of p in time polynomial\r\nin the size of p and in the size of mα(x). By repeatedly applying the algorithm\r\nto randomly chosen primes it is possible to compute all the conjugates of α.","lang":"eng"}],"publication":"Mathematics of Computation","title":"Computing Automorphisms of Abelian Number Fields","publisher":"American Mathematical Society (AMS)","date_created":"2023-01-11T09:31:21Z","year":"1999","issue":"227","_id":"35941","department":[{"_id":"102"}],"user_id":"93826","status":"public","type":"journal_article","date_updated":"2023-03-06T10:28:52Z","volume":68,"author":[{"first_name":"Jürgen","full_name":"Klüners, Jürgen","id":"21202","last_name":"Klüners"},{"first_name":"Vincenzo","last_name":"Acciaro","full_name":"Acciaro, Vincenzo"}],"intvolume":"        68","page":"1179-1186","citation":{"bibtex":"@article{Klüners_Acciaro_1999, title={Computing Automorphisms of Abelian Number Fields}, volume={68}, number={227}, journal={Mathematics of Computation}, publisher={American Mathematical Society (AMS)}, author={Klüners, Jürgen and Acciaro, Vincenzo}, year={1999}, pages={1179–1186} }","short":"J. Klüners, V. Acciaro, Mathematics of Computation 68 (1999) 1179–1186.","mla":"Klüners, Jürgen, and Vincenzo Acciaro. “Computing Automorphisms of Abelian Number Fields.” <i>Mathematics of Computation</i>, vol. 68, no. 227, American Mathematical Society (AMS), 1999, pp. 1179–86.","apa":"Klüners, J., &#38; Acciaro, V. (1999). Computing Automorphisms of Abelian Number Fields. <i>Mathematics of Computation</i>, <i>68</i>(227), 1179–1186.","ieee":"J. Klüners and V. Acciaro, “Computing Automorphisms of Abelian Number Fields,” <i>Mathematics of Computation</i>, vol. 68, no. 227, pp. 1179–1186, 1999.","chicago":"Klüners, Jürgen, and Vincenzo Acciaro. “Computing Automorphisms of Abelian Number Fields.” <i>Mathematics of Computation</i> 68, no. 227 (1999): 1179–86.","ama":"Klüners J, Acciaro V. Computing Automorphisms of Abelian Number Fields. <i>Mathematics of Computation</i>. 1999;68(227):1179-1186."},"publication_identifier":{"issn":["1088-6842","0025-5718"]},"publication_status":"published","related_material":{"link":[{"url":"https://www.ams.org/journals/mcom/1999-68-227/S0025-5718-99-01084-4/S0025-5718-99-01084-4.pdf","relation":"confirmation"}]}},{"citation":{"bibtex":"@article{DABERKOW_FIEKER_Klüners_POHST_ROEGNER_SCHÖRNIG_WILDANGER_1997, title={KANT V4}, volume={24}, DOI={<a href=\"https://doi.org/10.1006/jsco.1996.0126\">10.1006/jsco.1996.0126</a>}, number={3–4}, journal={Journal of Symbolic Computation}, publisher={Elsevier BV}, author={DABERKOW, M. and FIEKER, C. and Klüners, Jürgen and POHST, M. and ROEGNER, K. and SCHÖRNIG, M. and WILDANGER, K.}, year={1997}, pages={267–283} }","short":"M. DABERKOW, C. FIEKER, J. Klüners, M. POHST, K. ROEGNER, M. SCHÖRNIG, K. WILDANGER, Journal of Symbolic Computation 24 (1997) 267–283.","mla":"DABERKOW, M., et al. “KANT V4.” <i>Journal of Symbolic Computation</i>, vol. 24, no. 3–4, Elsevier BV, 1997, pp. 267–83, doi:<a href=\"https://doi.org/10.1006/jsco.1996.0126\">10.1006/jsco.1996.0126</a>.","apa":"DABERKOW, M., FIEKER, C., Klüners, J., POHST, M., ROEGNER, K., SCHÖRNIG, M., &#38; WILDANGER, K. (1997). KANT V4. <i>Journal of Symbolic Computation</i>, <i>24</i>(3–4), 267–283. <a href=\"https://doi.org/10.1006/jsco.1996.0126\">https://doi.org/10.1006/jsco.1996.0126</a>","ama":"DABERKOW M, FIEKER C, Klüners J, et al. KANT V4. <i>Journal of Symbolic Computation</i>. 1997;24(3-4):267-283. doi:<a href=\"https://doi.org/10.1006/jsco.1996.0126\">10.1006/jsco.1996.0126</a>","ieee":"M. DABERKOW <i>et al.</i>, “KANT V4,” <i>Journal of Symbolic Computation</i>, vol. 24, no. 3–4, pp. 267–283, 1997, doi: <a href=\"https://doi.org/10.1006/jsco.1996.0126\">10.1006/jsco.1996.0126</a>.","chicago":"DABERKOW, M., C. FIEKER, Jürgen Klüners, M. POHST, K. ROEGNER, M. SCHÖRNIG, and K. WILDANGER. “KANT V4.” <i>Journal of Symbolic Computation</i> 24, no. 3–4 (1997): 267–83. <a href=\"https://doi.org/10.1006/jsco.1996.0126\">https://doi.org/10.1006/jsco.1996.0126</a>."},"intvolume":"        24","page":"267-283","publication_status":"published","publication_identifier":{"issn":["0747-7171"]},"has_accepted_license":"1","doi":"10.1006/jsco.1996.0126","date_updated":"2023-03-06T09:23:30Z","author":[{"first_name":"M.","last_name":"DABERKOW","full_name":"DABERKOW, M."},{"full_name":"FIEKER, C.","last_name":"FIEKER","first_name":"C."},{"last_name":"Klüners","id":"21202","full_name":"Klüners, Jürgen","first_name":"Jürgen"},{"last_name":"POHST","full_name":"POHST, M.","first_name":"M."},{"last_name":"ROEGNER","full_name":"ROEGNER, K.","first_name":"K."},{"first_name":"M.","last_name":"SCHÖRNIG","full_name":"SCHÖRNIG, M."},{"last_name":"WILDANGER","full_name":"WILDANGER, K.","first_name":"K."}],"volume":24,"status":"public","type":"journal_article","_id":"34903","user_id":"93826","department":[{"_id":"102"}],"year":"1997","issue":"3-4","title":"KANT V4","publisher":"Elsevier BV","date_created":"2022-12-23T10:02:24Z","abstract":[{"lang":"eng","text":"The software packageKANT V4for computations in algebraic number fields is now available in version 4. In addition a new user interface has been released. We will outline the features of this new software package."}],"publication":"Journal of Symbolic Computation","ddc":["000"],"keyword":["Computational Mathematics","Algebra and Number Theory"],"language":[{"iso":"eng"}]},{"keyword":["Computational Mathematics","Algebra and Number Theory"],"ddc":["000"],"language":[{"iso":"eng"}],"abstract":[{"text":"The purpose of this article is to determine all subfields ℚ(β) of fixed degree of a given algebraic number field ℚ(α). It is convenient to describe each subfield by a pair (h,g) of polynomials in ℚ[t] resp. Z[t] such thatgis the minimal polynomial of β = h(α). The computations are done in unramifiedp-adic extensions and use information concerning subgroups of the Galois group of the normal closure of ℚ(α) obtained from the van der Waerden criterion.","lang":"eng"}],"publication":"Journal of Symbolic Computation","title":"On Computing Subfields","publisher":"Elsevier BV","date_created":"2022-12-23T10:03:02Z","year":"1997","issue":"3-4","_id":"34904","department":[{"_id":"102"}],"user_id":"93826","status":"public","type":"journal_article","doi":"10.1006/jsco.1996.0140","date_updated":"2023-03-06T10:36:21Z","volume":24,"author":[{"last_name":"Klüners","full_name":"Klüners, Jürgen","id":"21202","first_name":"Jürgen"},{"first_name":"Michael","last_name":"Pohst","full_name":"Pohst, Michael"}],"intvolume":"        24","page":"385-397","citation":{"ieee":"J. Klüners and M. Pohst, “On Computing Subfields,” <i>Journal of Symbolic Computation</i>, vol. 24, no. 3–4, pp. 385–397, 1997, doi: <a href=\"https://doi.org/10.1006/jsco.1996.0140\">10.1006/jsco.1996.0140</a>.","chicago":"Klüners, Jürgen, and Michael Pohst. “On Computing Subfields.” <i>Journal of Symbolic Computation</i> 24, no. 3–4 (1997): 385–97. <a href=\"https://doi.org/10.1006/jsco.1996.0140\">https://doi.org/10.1006/jsco.1996.0140</a>.","ama":"Klüners J, Pohst M. On Computing Subfields. <i>Journal of Symbolic Computation</i>. 1997;24(3-4):385-397. doi:<a href=\"https://doi.org/10.1006/jsco.1996.0140\">10.1006/jsco.1996.0140</a>","short":"J. Klüners, M. Pohst, Journal of Symbolic Computation 24 (1997) 385–397.","bibtex":"@article{Klüners_Pohst_1997, title={On Computing Subfields}, volume={24}, DOI={<a href=\"https://doi.org/10.1006/jsco.1996.0140\">10.1006/jsco.1996.0140</a>}, number={3–4}, journal={Journal of Symbolic Computation}, publisher={Elsevier BV}, author={Klüners, Jürgen and Pohst, Michael}, year={1997}, pages={385–397} }","mla":"Klüners, Jürgen, and Michael Pohst. “On Computing Subfields.” <i>Journal of Symbolic Computation</i>, vol. 24, no. 3–4, Elsevier BV, 1997, pp. 385–97, doi:<a href=\"https://doi.org/10.1006/jsco.1996.0140\">10.1006/jsco.1996.0140</a>.","apa":"Klüners, J., &#38; Pohst, M. (1997). On Computing Subfields. <i>Journal of Symbolic Computation</i>, <i>24</i>(3–4), 385–397. <a href=\"https://doi.org/10.1006/jsco.1996.0140\">https://doi.org/10.1006/jsco.1996.0140</a>"},"has_accepted_license":"1","publication_identifier":{"issn":["0747-7171"]},"publication_status":"published"},{"extern":"1","language":[{"iso":"eng"}],"user_id":"93826","department":[{"_id":"102"}],"_id":"42806","status":"public","type":"dissertation","title":"Über die Berechnung von Automorphismen und Teilkörpern algebraischer Zahlkörper (Dissertation)","author":[{"full_name":"Klüners, Jürgen","id":"21202","last_name":"Klüners","first_name":"Jürgen"}],"date_created":"2023-03-07T09:00:38Z","date_updated":"2023-03-07T09:24:39Z","citation":{"mla":"Klüners, Jürgen. <i>Über Die Berechnung von Automorphismen Und Teilkörpern Algebraischer Zahlkörper (Dissertation)</i>. 1997.","short":"J. Klüners, Über Die Berechnung von Automorphismen Und Teilkörpern Algebraischer Zahlkörper (Dissertation), TU Berlin, 1997.","bibtex":"@book{Klüners_1997, place={TU Berlin}, title={Über die Berechnung von Automorphismen und Teilkörpern algebraischer Zahlkörper (Dissertation)}, author={Klüners, Jürgen}, year={1997} }","apa":"Klüners, J. (1997). <i>Über die Berechnung von Automorphismen und Teilkörpern algebraischer Zahlkörper (Dissertation)</i>.","chicago":"Klüners, Jürgen. <i>Über Die Berechnung von Automorphismen Und Teilkörpern Algebraischer Zahlkörper (Dissertation)</i>. TU Berlin, 1997.","ieee":"J. Klüners, <i>Über die Berechnung von Automorphismen und Teilkörpern algebraischer Zahlkörper (Dissertation)</i>. TU Berlin, 1997.","ama":"Klüners J. <i>Über Die Berechnung von Automorphismen Und Teilkörpern Algebraischer Zahlkörper (Dissertation)</i>.; 1997."},"page":"93","place":"TU Berlin","year":"1997","related_material":{"link":[{"url":"https://math.uni-paderborn.de/fileadmin/mathematik/AG-Computeralgebra/Publications-klueners/diss.pdf","relation":"confirmation"}]}},{"status":"public","type":"mastersthesis","language":[{"iso":"eng"}],"extern":"1","_id":"42808","user_id":"93826","department":[{"_id":"102"}],"year":"1995","place":"TU Berlin","citation":{"apa":"Klüners, J. (1995). <i>Über die Berechnung von Teilkörpern algebraischer Zahlkörper (Diplomarbeit)</i>.","mla":"Klüners, Jürgen. <i>Über Die Berechnung von Teilkörpern Algebraischer Zahlkörper (Diplomarbeit)</i>. 1995.","bibtex":"@book{Klüners_1995, place={TU Berlin}, title={Über die Berechnung von Teilkörpern algebraischer Zahlkörper (Diplomarbeit)}, author={Klüners, Jürgen}, year={1995} }","short":"J. Klüners, Über Die Berechnung von Teilkörpern Algebraischer Zahlkörper (Diplomarbeit), TU Berlin, 1995.","ama":"Klüners J. <i>Über Die Berechnung von Teilkörpern Algebraischer Zahlkörper (Diplomarbeit)</i>.; 1995.","chicago":"Klüners, Jürgen. <i>Über Die Berechnung von Teilkörpern Algebraischer Zahlkörper (Diplomarbeit)</i>. TU Berlin, 1995.","ieee":"J. Klüners, <i>Über die Berechnung von Teilkörpern algebraischer Zahlkörper (Diplomarbeit)</i>. TU Berlin, 1995."},"page":"91","related_material":{"link":[{"url":"https://math.uni-paderborn.de/fileadmin/mathematik/AG-Computeralgebra/Publications-klueners/diplom.pdf","relation":"confirmation"}]},"title":"Über die Berechnung von Teilkörpern algebraischer Zahlkörper (Diplomarbeit)","date_updated":"2023-03-07T09:25:16Z","author":[{"full_name":"Klüners, Jürgen","id":"21202","last_name":"Klüners","first_name":"Jürgen"}],"date_created":"2023-03-07T09:12:39Z"}]