[{"keyword":["Computational Mathematics","Algebra and Number Theory"],"language":[{"iso":"eng"}],"publication":"Journal of Symbolic Computation","abstract":[{"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.","lang":"eng"}],"publisher":"Elsevier BV","date_created":"2022-12-23T09:57:28Z","title":"Explicit Galois Realization of Transitive Groups of Degree up to 15","issue":"6","year":"2000","_id":"34899","department":[{"_id":"102"}],"user_id":"93826","type":"journal_article","status":"public","date_updated":"2023-03-06T10:48:05Z","volume":30,"author":[{"last_name":"Klüners","full_name":"Klüners, Jürgen","id":"21202","first_name":"Jürgen"},{"full_name":"Malle, Gunter","last_name":"Malle","first_name":"Gunter"}],"doi":"10.1006/jsco.2000.0378","publication_identifier":{"issn":["0747-7171"]},"publication_status":"published","page":"675-716","intvolume":"        30","citation":{"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>","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.","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>.","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>.","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>"}},{"type":"journal_article","status":"public","department":[{"_id":"102"}],"user_id":"93826","_id":"34898","publication_identifier":{"issn":["0747-7171"]},"publication_status":"published","page":"733-737","intvolume":"        30","citation":{"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>","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>","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>.","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>."},"volume":30,"author":[{"id":"21202","full_name":"Klüners, Jürgen","last_name":"Klüners","first_name":"Jürgen"}],"date_updated":"2023-03-06T10:48:40Z","doi":"10.1006/jsco.2000.0380","publication":"Journal of Symbolic Computation","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)."}],"language":[{"iso":"eng"}],"keyword":["Computational Mathematics","Algebra and Number Theory"],"issue":"6","year":"2000","date_created":"2022-12-23T09:56:52Z","publisher":"Elsevier BV","title":"A Polynomial with Galois GroupSL2(11)"},{"status":"public","type":"journal_article","user_id":"93826","department":[{"_id":"102"}],"_id":"34902","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>.","short":"J. Klüners, Journal of Symbolic Computation 27 (1999) 261–269.","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} }","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>"},"page":"261-269","intvolume":"        27","publication_status":"published","publication_identifier":{"issn":["0747-7171"]},"doi":"10.1006/jsco.1998.0252","author":[{"first_name":"Jürgen","last_name":"Klüners","full_name":"Klüners, Jürgen","id":"21202"}],"volume":27,"date_updated":"2023-03-06T09:21:29Z","abstract":[{"lang":"eng","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."}],"publication":"Journal of Symbolic Computation","language":[{"iso":"eng"}],"keyword":["Computational Mathematics","Algebra and Number Theory"],"year":"1999","issue":"3","title":"On Polynomial Decompositions","date_created":"2022-12-23T10:01:15Z","publisher":"Elsevier BV"},{"language":[{"iso":"eng"}],"ddc":["000"],"keyword":["Computational Mathematics","Algebra and Number Theory"],"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"}],"date_created":"2022-12-23T10:02:24Z","publisher":"Elsevier BV","title":"KANT V4","issue":"3-4","year":"1997","user_id":"93826","department":[{"_id":"102"}],"_id":"34903","type":"journal_article","status":"public","author":[{"first_name":"M.","full_name":"DABERKOW, M.","last_name":"DABERKOW"},{"first_name":"C.","full_name":"FIEKER, C.","last_name":"FIEKER"},{"first_name":"Jürgen","last_name":"Klüners","full_name":"Klüners, Jürgen","id":"21202"},{"full_name":"POHST, M.","last_name":"POHST","first_name":"M."},{"full_name":"ROEGNER, K.","last_name":"ROEGNER","first_name":"K."},{"full_name":"SCHÖRNIG, M.","last_name":"SCHÖRNIG","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","publication_status":"published","publication_identifier":{"issn":["0747-7171"]},"has_accepted_license":"1","citation":{"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>.","short":"M. DABERKOW, C. FIEKER, J. Klüners, M. POHST, K. ROEGNER, M. SCHÖRNIG, K. WILDANGER, Journal of Symbolic Computation 24 (1997) 267–283.","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} }","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>","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>.","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>."},"intvolume":"        24","page":"267-283"},{"language":[{"iso":"eng"}],"keyword":["Computational Mathematics","Algebra and Number Theory"],"ddc":["000"],"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."}],"date_created":"2022-12-23T10:03:02Z","publisher":"Elsevier BV","title":"On Computing Subfields","issue":"3-4","year":"1997","department":[{"_id":"102"}],"user_id":"93826","_id":"34904","type":"journal_article","status":"public","volume":24,"author":[{"last_name":"Klüners","id":"21202","full_name":"Klüners, Jürgen","first_name":"Jürgen"},{"first_name":"Michael","full_name":"Pohst, Michael","last_name":"Pohst"}],"date_updated":"2023-03-06T10:36:21Z","doi":"10.1006/jsco.1996.0140","has_accepted_license":"1","publication_identifier":{"issn":["0747-7171"]},"publication_status":"published","page":"385-397","intvolume":"        24","citation":{"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>.","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} }","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>"}}]