[{"abstract":[{"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.","lang":"eng"}],"publication":"Journal of Symbolic Computation","keyword":["Computational Mathematics","Algebra and Number Theory"],"language":[{"iso":"eng"}],"external_id":{"arxiv":["1610.06837 "]},"year":"2018","title":"Computing subfields of number fields and applications to Galois group computations","publisher":"Elsevier BV","date_created":"2022-12-22T10:52:18Z","status":"public","type":"journal_article","_id":"34843","department":[{"_id":"102"}],"user_id":"93826","page":"1-20","intvolume":"        93","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>","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>.","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>.","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>","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>.","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} }","short":"A.-S. Elsenhans, J. Klüners, Journal of Symbolic Computation 93 (2018) 1–20."},"publication_identifier":{"issn":["0747-7171"]},"publication_status":"published","doi":"10.1016/j.jsc.2018.04.013","date_updated":"2023-03-06T09:05:51Z","volume":93,"author":[{"last_name":"Elsenhans","full_name":"Elsenhans, Andreas-Stephan","first_name":"Andreas-Stephan"},{"first_name":"Jürgen","id":"21202","full_name":"Klüners, Jürgen","last_name":"Klüners"}]},{"abstract":[{"text":"Given a field extension K/k of degree n we are interested in finding the subfields of K containing k. There can be more than polynomially many subfields. We introduce the notion of generating subfields, a set of up to n subfields whose intersections give the rest. We provide an efficient algorithm which uses linear algebra in k or lattice reduction along with factorization in any extension of K. Implementations show that previously difficult cases can now be handled.","lang":"eng"}],"publication":"Journal of Symbolic Computation","language":[{"iso":"eng"}],"keyword":["Computational Mathematics","Algebra and Number Theory"],"year":"2011","title":"Generating subfields","date_created":"2022-12-22T10:54:15Z","publisher":"Elsevier BV","status":"public","type":"journal_article","department":[{"_id":"102"}],"user_id":"93826","_id":"34846","page":"17-34","intvolume":"        52","citation":{"ama":"van Hoeij M, Klüners J, Novocin A. Generating subfields. <i>Journal of Symbolic Computation</i>. 2011;52:17-34. doi:<a href=\"https://doi.org/10.1016/j.jsc.2012.05.010\">10.1016/j.jsc.2012.05.010</a>","ieee":"M. van Hoeij, J. Klüners, and A. Novocin, “Generating subfields,” <i>Journal of Symbolic Computation</i>, vol. 52, pp. 17–34, 2011, doi: <a href=\"https://doi.org/10.1016/j.jsc.2012.05.010\">10.1016/j.jsc.2012.05.010</a>.","chicago":"Hoeij, Mark van, Jürgen Klüners, and Andrew Novocin. “Generating Subfields.” <i>Journal of Symbolic Computation</i> 52 (2011): 17–34. <a href=\"https://doi.org/10.1016/j.jsc.2012.05.010\">https://doi.org/10.1016/j.jsc.2012.05.010</a>.","apa":"van Hoeij, M., Klüners, J., &#38; Novocin, A. (2011). Generating subfields. <i>Journal of Symbolic Computation</i>, <i>52</i>, 17–34. <a href=\"https://doi.org/10.1016/j.jsc.2012.05.010\">https://doi.org/10.1016/j.jsc.2012.05.010</a>","bibtex":"@article{van Hoeij_Klüners_Novocin_2011, title={Generating subfields}, volume={52}, DOI={<a href=\"https://doi.org/10.1016/j.jsc.2012.05.010\">10.1016/j.jsc.2012.05.010</a>}, journal={Journal of Symbolic Computation}, publisher={Elsevier BV}, author={van Hoeij, Mark and Klüners, Jürgen and Novocin, Andrew}, year={2011}, pages={17–34} }","mla":"van Hoeij, Mark, et al. “Generating Subfields.” <i>Journal of Symbolic Computation</i>, vol. 52, Elsevier BV, 2011, pp. 17–34, doi:<a href=\"https://doi.org/10.1016/j.jsc.2012.05.010\">10.1016/j.jsc.2012.05.010</a>.","short":"M. van Hoeij, J. Klüners, A. Novocin, Journal of Symbolic Computation 52 (2011) 17–34."},"publication_identifier":{"issn":["0747-7171"]},"publication_status":"published","doi":"10.1016/j.jsc.2012.05.010","volume":52,"author":[{"full_name":"van Hoeij, Mark","last_name":"van Hoeij","first_name":"Mark"},{"first_name":"Jürgen","id":"21202","full_name":"Klüners, Jürgen","last_name":"Klüners"},{"full_name":"Novocin, Andrew","last_name":"Novocin","first_name":"Andrew"}],"date_updated":"2023-03-06T09:46:15Z"},{"doi":"10.1006/jsco.2000.0377","date_updated":"2023-03-06T09:58:06Z","author":[{"first_name":"Katharina","last_name":"Geissler","full_name":"Geissler, Katharina"},{"first_name":"Jürgen","last_name":"Klüners","id":"21202","full_name":"Klüners, Jürgen"}],"volume":30,"citation":{"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>","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>","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>."},"page":"653-674","intvolume":"        30","publication_status":"published","publication_identifier":{"issn":["0747-7171"]},"_id":"34900","user_id":"93826","department":[{"_id":"102"}],"status":"public","type":"journal_article","title":"Galois Group Computation for Rational Polynomials","publisher":"Elsevier BV","date_created":"2022-12-23T09:58:16Z","year":"2000","issue":"6","keyword":["Computational Mathematics","Algebra and Number Theory"],"language":[{"iso":"eng"}],"abstract":[{"lang":"eng","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."}],"publication":"Journal of Symbolic Computation"},{"doi":"10.1006/jsco.2000.0361","date_updated":"2023-03-06T09:57:34Z","volume":30,"author":[{"first_name":"Vincenzo","full_name":"Acciaro, Vincenzo","last_name":"Acciaro"},{"last_name":"Klüners","full_name":"Klüners, Jürgen","id":"21202","first_name":"Jürgen"}],"page":"239-252","intvolume":"        30","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>"},"publication_identifier":{"issn":["0747-7171"]},"publication_status":"published","_id":"34901","department":[{"_id":"102"}],"user_id":"93826","status":"public","type":"journal_article","title":"Computing Local Artin Maps, and Solvability of Norm Equations","publisher":"Elsevier BV","date_created":"2022-12-23T09:58:48Z","year":"2000","issue":"3","keyword":["Computational Mathematics","Algebra and Number Theory"],"language":[{"iso":"eng"}],"abstract":[{"lang":"eng","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."}],"publication":"Journal of Symbolic Computation"},{"language":[{"iso":"eng"}],"keyword":["Computational Mathematics","Algebra and Number Theory"],"publication":"Journal of Symbolic Computation","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."}],"date_created":"2022-12-23T09:57:28Z","publisher":"Elsevier BV","title":"Explicit Galois Realization of Transitive Groups of Degree up to 15","issue":"6","year":"2000","department":[{"_id":"102"}],"user_id":"93826","_id":"34899","type":"journal_article","status":"public","volume":30,"author":[{"first_name":"Jürgen","last_name":"Klüners","id":"21202","full_name":"Klüners, Jürgen"},{"full_name":"Malle, Gunter","last_name":"Malle","first_name":"Gunter"}],"date_updated":"2023-03-06T10:48:05Z","doi":"10.1006/jsco.2000.0378","publication_identifier":{"issn":["0747-7171"]},"publication_status":"published","intvolume":"        30","page":"675-716","citation":{"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>.","short":"J. Klüners, G. Malle, Journal of Symbolic Computation 30 (2000) 675–716.","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>","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>"}},{"department":[{"_id":"102"}],"user_id":"93826","_id":"34898","type":"journal_article","status":"public","volume":30,"author":[{"first_name":"Jürgen","full_name":"Klüners, Jürgen","id":"21202","last_name":"Klüners"}],"date_updated":"2023-03-06T10:48:40Z","doi":"10.1006/jsco.2000.0380","publication_identifier":{"issn":["0747-7171"]},"publication_status":"published","intvolume":"        30","page":"733-737","citation":{"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>.","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>.","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>"},"language":[{"iso":"eng"}],"keyword":["Computational Mathematics","Algebra and Number Theory"],"publication":"Journal of Symbolic Computation","abstract":[{"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).","lang":"eng"}],"date_created":"2022-12-23T09:56:52Z","publisher":"Elsevier BV","title":"A Polynomial with Galois GroupSL2(11)","issue":"6","year":"2000"},{"page":"261-269","intvolume":"        27","citation":{"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>","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>.","short":"J. Klüners, Journal of Symbolic Computation 27 (1999) 261–269.","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} }","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>"},"publication_identifier":{"issn":["0747-7171"]},"publication_status":"published","doi":"10.1006/jsco.1998.0252","volume":27,"author":[{"first_name":"Jürgen","last_name":"Klüners","id":"21202","full_name":"Klüners, Jürgen"}],"date_updated":"2023-03-06T09:21:29Z","status":"public","type":"journal_article","department":[{"_id":"102"}],"user_id":"93826","_id":"34902","year":"1999","issue":"3","title":"On Polynomial Decompositions","date_created":"2022-12-23T10:01:15Z","publisher":"Elsevier BV","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","language":[{"iso":"eng"}],"keyword":["Computational Mathematics","Algebra and Number Theory"]},{"issue":"3-4","year":"1997","date_created":"2022-12-23T10:02:24Z","publisher":"Elsevier BV","title":"KANT V4","publication":"Journal of Symbolic Computation","abstract":[{"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.","lang":"eng"}],"language":[{"iso":"eng"}],"ddc":["000"],"keyword":["Computational Mathematics","Algebra and Number Theory"],"publication_status":"published","has_accepted_license":"1","publication_identifier":{"issn":["0747-7171"]},"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>","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>.","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>"},"page":"267-283","intvolume":"        24","author":[{"last_name":"DABERKOW","full_name":"DABERKOW, M.","first_name":"M."},{"first_name":"C.","last_name":"FIEKER","full_name":"FIEKER, C."},{"first_name":"Jürgen","full_name":"Klüners, Jürgen","id":"21202","last_name":"Klüners"},{"first_name":"M.","last_name":"POHST","full_name":"POHST, M."},{"first_name":"K.","full_name":"ROEGNER, K.","last_name":"ROEGNER"},{"last_name":"SCHÖRNIG","full_name":"SCHÖRNIG, M.","first_name":"M."},{"first_name":"K.","full_name":"WILDANGER, K.","last_name":"WILDANGER"}],"volume":24,"date_updated":"2023-03-06T09:23:30Z","doi":"10.1006/jsco.1996.0126","type":"journal_article","status":"public","user_id":"93826","department":[{"_id":"102"}],"_id":"34903"},{"issue":"3-4","year":"1997","publisher":"Elsevier BV","date_created":"2022-12-23T10:03:02Z","title":"On Computing Subfields","publication":"Journal of Symbolic Computation","abstract":[{"lang":"eng","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."}],"ddc":["000"],"keyword":["Computational Mathematics","Algebra and Number Theory"],"language":[{"iso":"eng"}],"publication_status":"published","has_accepted_license":"1","publication_identifier":{"issn":["0747-7171"]},"citation":{"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} }","short":"J. Klüners, M. Pohst, Journal of Symbolic Computation 24 (1997) 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>","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>"},"page":"385-397","intvolume":"        24","date_updated":"2023-03-06T10:36:21Z","author":[{"full_name":"Klüners, Jürgen","id":"21202","last_name":"Klüners","first_name":"Jürgen"},{"last_name":"Pohst","full_name":"Pohst, Michael","first_name":"Michael"}],"volume":24,"doi":"10.1006/jsco.1996.0140","type":"journal_article","status":"public","_id":"34904","user_id":"93826","department":[{"_id":"102"}]}]