[{"volume":52,"page":"17-34","publication":"Journal of Symbolic Computation","type":"journal_article","user_id":"93826","keyword":["Computational Mathematics","Algebra and Number Theory"],"title":"Generating subfields","doi":"10.1016/j.jsc.2012.05.010","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"}],"_id":"34846","date_updated":"2023-03-06T09:46:15Z","publisher":"Elsevier BV","date_created":"2022-12-22T10:54:15Z","status":"public","year":"2011","publication_identifier":{"issn":["0747-7171"]},"language":[{"iso":"eng"}],"publication_status":"published","citation":{"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.","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>","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>."},"department":[{"_id":"102"}],"author":[{"last_name":"van Hoeij","full_name":"van Hoeij, Mark","first_name":"Mark"},{"first_name":"Jürgen","full_name":"Klüners, Jürgen","id":"21202","last_name":"Klüners"},{"last_name":"Novocin","first_name":"Andrew","full_name":"Novocin, Andrew"}],"intvolume":"        52"},{"volume":4,"page":"493-508","issue":"5","publication":"Algebra &amp; Number Theory","type":"journal_article","keyword":["Algebra and Number Theory"],"user_id":"93826","title":"On the Spiegelungssatz for the 4-rank","abstract":[{"text":"Let d be a nonsquare positive integer. We give the value of the natural probability that the narrow ideal class groups of the quadratic fields ℚ(√d) and ℚ(√−d) have the same 4-ranks. ","lang":"eng"}],"doi":"10.2140/ant.2010.4.493","_id":"34887","date_updated":"2023-03-06T10:18:14Z","publisher":"Mathematical Sciences Publishers","date_created":"2022-12-23T09:10:12Z","status":"public","language":[{"iso":"eng"}],"publication_identifier":{"issn":["1937-0652"]},"year":"2010","publication_status":"published","citation":{"apa":"Fouvry, É., &#38; Klüners, J. (2010). On the Spiegelungssatz for the 4-rank. <i>Algebra &#38;amp; Number Theory</i>, <i>4</i>(5), 493–508. <a href=\"https://doi.org/10.2140/ant.2010.4.493\">https://doi.org/10.2140/ant.2010.4.493</a>","ama":"Fouvry É, Klüners J. On the Spiegelungssatz for the 4-rank. <i>Algebra &#38;amp; Number Theory</i>. 2010;4(5):493-508. doi:<a href=\"https://doi.org/10.2140/ant.2010.4.493\">10.2140/ant.2010.4.493</a>","bibtex":"@article{Fouvry_Klüners_2010, title={On the Spiegelungssatz for the 4-rank}, volume={4}, DOI={<a href=\"https://doi.org/10.2140/ant.2010.4.493\">10.2140/ant.2010.4.493</a>}, number={5}, journal={Algebra &#38;amp; Number Theory}, publisher={Mathematical Sciences Publishers}, author={Fouvry, Étienne and Klüners, Jürgen}, year={2010}, pages={493–508} }","mla":"Fouvry, Étienne, and Jürgen Klüners. “On the Spiegelungssatz for the 4-Rank.” <i>Algebra &#38;amp; Number Theory</i>, vol. 4, no. 5, Mathematical Sciences Publishers, 2010, pp. 493–508, doi:<a href=\"https://doi.org/10.2140/ant.2010.4.493\">10.2140/ant.2010.4.493</a>.","ieee":"É. Fouvry and J. Klüners, “On the Spiegelungssatz for the 4-rank,” <i>Algebra &#38;amp; Number Theory</i>, vol. 4, no. 5, pp. 493–508, 2010, doi: <a href=\"https://doi.org/10.2140/ant.2010.4.493\">10.2140/ant.2010.4.493</a>.","short":"É. Fouvry, J. Klüners, Algebra &#38;amp; Number Theory 4 (2010) 493–508.","chicago":"Fouvry, Étienne, and Jürgen Klüners. “On the Spiegelungssatz for the 4-Rank.” <i>Algebra &#38;amp; Number Theory</i> 4, no. 5 (2010): 493–508. <a href=\"https://doi.org/10.2140/ant.2010.4.493\">https://doi.org/10.2140/ant.2010.4.493</a>."},"department":[{"_id":"102"}],"author":[{"last_name":"Fouvry","full_name":"Fouvry, Étienne","first_name":"Étienne"},{"last_name":"Klüners","id":"21202","first_name":"Jürgen","full_name":"Klüners, Jürgen"}],"intvolume":"         4"},{"volume":21,"page":"15-39","issue":"1","publication":"Journal de Théorie des Nombres de Bordeaux","type":"journal_article","user_id":"93826","keyword":["Algebra and Number Theory"],"external_id":{"arxiv":["math/0409510 "]},"title":"Factoring polynomials over global fields","abstract":[{"lang":"eng","text":"We prove that van Hoeij’s original algorithm to factor univariate polynomials over the rationals runs in polynomial time, as well as natural variants. In particular, our approach also yields polynomial time complexity results for bivariate polynomials over a finite field."}],"doi":"10.5802/jtnb.655","_id":"34889","date_updated":"2023-03-06T09:09:56Z","publisher":"Cellule MathDoc/CEDRAM","date_created":"2022-12-23T09:33:37Z","status":"public","publication_identifier":{"issn":["1246-7405"]},"year":"2009","language":[{"iso":"eng"}],"publication_status":"published","citation":{"short":"K. Belabas, M. van Hoeij, J. Klüners, A. Steel, Journal de Théorie Des Nombres de Bordeaux 21 (2009) 15–39.","chicago":"Belabas, Karim, Mark van Hoeij, Jürgen Klüners, and Allan Steel. “Factoring Polynomials over Global Fields.” <i>Journal de Théorie Des Nombres de Bordeaux</i> 21, no. 1 (2009): 15–39. <a href=\"https://doi.org/10.5802/jtnb.655\">https://doi.org/10.5802/jtnb.655</a>.","ieee":"K. Belabas, M. van Hoeij, J. Klüners, and A. Steel, “Factoring polynomials over global fields,” <i>Journal de Théorie des Nombres de Bordeaux</i>, vol. 21, no. 1, pp. 15–39, 2009, doi: <a href=\"https://doi.org/10.5802/jtnb.655\">10.5802/jtnb.655</a>.","mla":"Belabas, Karim, et al. “Factoring Polynomials over Global Fields.” <i>Journal de Théorie Des Nombres de Bordeaux</i>, vol. 21, no. 1, Cellule MathDoc/CEDRAM, 2009, pp. 15–39, doi:<a href=\"https://doi.org/10.5802/jtnb.655\">10.5802/jtnb.655</a>.","ama":"Belabas K, van Hoeij M, Klüners J, Steel A. Factoring polynomials over global fields. <i>Journal de Théorie des Nombres de Bordeaux</i>. 2009;21(1):15-39. doi:<a href=\"https://doi.org/10.5802/jtnb.655\">10.5802/jtnb.655</a>","bibtex":"@article{Belabas_van Hoeij_Klüners_Steel_2009, title={Factoring polynomials over global fields}, volume={21}, DOI={<a href=\"https://doi.org/10.5802/jtnb.655\">10.5802/jtnb.655</a>}, number={1}, journal={Journal de Théorie des Nombres de Bordeaux}, publisher={Cellule MathDoc/CEDRAM}, author={Belabas, Karim and van Hoeij, Mark and Klüners, Jürgen and Steel, Allan}, year={2009}, pages={15–39} }","apa":"Belabas, K., van Hoeij, M., Klüners, J., &#38; Steel, A. (2009). Factoring polynomials over global fields. <i>Journal de Théorie Des Nombres de Bordeaux</i>, <i>21</i>(1), 15–39. <a href=\"https://doi.org/10.5802/jtnb.655\">https://doi.org/10.5802/jtnb.655</a>"},"department":[{"_id":"102"}],"author":[{"last_name":"Belabas","first_name":"Karim","full_name":"Belabas, Karim"},{"first_name":"Mark","full_name":"van Hoeij, Mark","last_name":"van Hoeij"},{"id":"21202","last_name":"Klüners","first_name":"Jürgen","full_name":"Klüners, Jürgen"},{"full_name":"Steel, Allan","first_name":"Allan","last_name":"Steel"}],"intvolume":"        21"},{"title":"Speech enhancement with a new generalized eigenvector blocking matrix for application in a generalized sidelobe canceller","author":[{"full_name":"Warsitz, Ernst","first_name":"Ernst","last_name":"Warsitz"},{"full_name":"Krueger, Alexander","first_name":"Alexander","last_name":"Krueger"},{"full_name":"Haeb-Umbach, Reinhold","first_name":"Reinhold","last_name":"Haeb-Umbach","id":"242"}],"abstract":[{"text":"The generalized sidelobe canceller by Griffith and Jim is a robust beamforming method to enhance a desired (speech) signal in the presence of stationary noise. Its performance depends to a high degree on the construction of the blocking matrix which produces noise reference signals for the subsequent adaptive interference canceller. Especially in reverberated environments the beamformer may suffer from signal leakage and reduced noise suppression. In this paper a new blocking matrix is proposed. It is based on a generalized eigenvalue problem whose solution provides an indirect estimation of the transfer functions from the source to the sensors. The quality of the new generalized eigenvector blocking matrix is studied in simulated rooms with different reverberation times and is compared to alternatives proposed in the literature.","lang":"eng"}],"doi":"10.1109/ICASSP.2008.4517549","citation":{"apa":"Warsitz, E., Krueger, A., &#38; Haeb-Umbach, R. (2008). Speech enhancement with a new generalized eigenvector blocking matrix for application in a generalized sidelobe canceller. In <i>IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2008)</i> (pp. 73–76). <a href=\"https://doi.org/10.1109/ICASSP.2008.4517549\">https://doi.org/10.1109/ICASSP.2008.4517549</a>","ama":"Warsitz E, Krueger A, Haeb-Umbach R. Speech enhancement with a new generalized eigenvector blocking matrix for application in a generalized sidelobe canceller. In: <i>IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2008)</i>. ; 2008:73-76. doi:<a href=\"https://doi.org/10.1109/ICASSP.2008.4517549\">10.1109/ICASSP.2008.4517549</a>","chicago":"Warsitz, Ernst, Alexander Krueger, and Reinhold Haeb-Umbach. “Speech Enhancement with a New Generalized Eigenvector Blocking Matrix for Application in a Generalized Sidelobe Canceller.” In <i>IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2008)</i>, 73–76, 2008. <a href=\"https://doi.org/10.1109/ICASSP.2008.4517549\">https://doi.org/10.1109/ICASSP.2008.4517549</a>.","ieee":"E. Warsitz, A. Krueger, and R. Haeb-Umbach, “Speech enhancement with a new generalized eigenvector blocking matrix for application in a generalized sidelobe canceller,” in <i>IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2008)</i>, 2008, pp. 73–76.","mla":"Warsitz, Ernst, et al. “Speech Enhancement with a New Generalized Eigenvector Blocking Matrix for Application in a Generalized Sidelobe Canceller.” <i>IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2008)</i>, 2008, pp. 73–76, doi:<a href=\"https://doi.org/10.1109/ICASSP.2008.4517549\">10.1109/ICASSP.2008.4517549</a>.","bibtex":"@inproceedings{Warsitz_Krueger_Haeb-Umbach_2008, title={Speech enhancement with a new generalized eigenvector blocking matrix for application in a generalized sidelobe canceller}, DOI={<a href=\"https://doi.org/10.1109/ICASSP.2008.4517549\">10.1109/ICASSP.2008.4517549</a>}, booktitle={IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2008)}, author={Warsitz, Ernst and Krueger, Alexander and Haeb-Umbach, Reinhold}, year={2008}, pages={73–76} }","short":"E. Warsitz, A. Krueger, R. Haeb-Umbach, in: IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2008), 2008, pp. 73–76."},"main_file_link":[{"open_access":"1","url":"https://groups.uni-paderborn.de/nt/pubs/2008/WaKrHa08.pdf"}],"keyword":["adaptive interference canceller","adaptive signal processing","array signal processing","beamforming method","eigenvalues and eigenfunctions","generalized eigenvector blocking matrix","generalized sidelobe canceller","interference suppression","matrix algebra","noise suppression","speech enhancement","transfer function estimation","transfer functions"],"user_id":"44006","oa":"1","department":[{"_id":"54"}],"date_created":"2019-07-12T05:31:06Z","publication":"IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2008)","language":[{"iso":"eng"}],"type":"conference","year":"2008","status":"public","_id":"11935","page":"73-76","date_updated":"2022-01-06T06:51:12Z"},{"publication_status":"published","citation":{"ieee":"M. Rösler, “Bessel convolutions on matrix cones,” <i>Compositio Mathematica</i>, vol. 143, no. 03, pp. 749–779, 2007, doi: <a href=\"https://doi.org/10.1112/s0010437x06002594\">10.1112/s0010437x06002594</a>.","chicago":"Rösler, Margit. “Bessel Convolutions on Matrix Cones.” <i>Compositio Mathematica</i> 143, no. 03 (2007): 749–79. <a href=\"https://doi.org/10.1112/s0010437x06002594\">https://doi.org/10.1112/s0010437x06002594</a>.","short":"M. Rösler, Compositio Mathematica 143 (2007) 749–779.","ama":"Rösler M. Bessel convolutions on matrix cones. <i>Compositio Mathematica</i>. 2007;143(03):749-779. doi:<a href=\"https://doi.org/10.1112/s0010437x06002594\">10.1112/s0010437x06002594</a>","bibtex":"@article{Rösler_2007, title={Bessel convolutions on matrix cones}, volume={143}, DOI={<a href=\"https://doi.org/10.1112/s0010437x06002594\">10.1112/s0010437x06002594</a>}, number={03}, journal={Compositio Mathematica}, publisher={Wiley}, author={Rösler, Margit}, year={2007}, pages={749–779} }","apa":"Rösler, M. (2007). Bessel convolutions on matrix cones. <i>Compositio Mathematica</i>, <i>143</i>(03), 749–779. <a href=\"https://doi.org/10.1112/s0010437x06002594\">https://doi.org/10.1112/s0010437x06002594</a>","mla":"Rösler, Margit. “Bessel Convolutions on Matrix Cones.” <i>Compositio Mathematica</i>, vol. 143, no. 03, Wiley, 2007, pp. 749–79, doi:<a href=\"https://doi.org/10.1112/s0010437x06002594\">10.1112/s0010437x06002594</a>."},"department":[{"_id":"555"}],"author":[{"first_name":"Margit","full_name":"Rösler, Margit","last_name":"Rösler","id":"37390"}],"intvolume":"       143","_id":"39947","date_updated":"2023-01-26T17:47:42Z","publisher":"Wiley","date_created":"2023-01-25T09:55:18Z","status":"public","language":[{"iso":"eng"}],"publication_identifier":{"issn":["0010-437X","1570-5846"]},"year":"2007","keyword":["Algebra and Number Theory"],"user_id":"93826","extern":"1","title":"Bessel convolutions on matrix cones","doi":"10.1112/s0010437x06002594","volume":143,"page":"749-779","issue":"03","publication":"Compositio Mathematica","type":"journal_article"},{"publication":"Journal de Théorie des Nombres de Bordeaux","type":"journal_article","page":"607-615","volume":18,"issue":"3","title":"Asymptotics of number fields and the Cohen–Lenstra heuristics","doi":"10.5802/jtnb.561","abstract":[{"lang":"eng","text":"We study the asymptotics conjecture of Malle for dihedral groups Dℓ of order 2ℓ, where ℓ is an odd prime. We prove the expected lower bound for those groups. For the upper bounds we show that there is a connection to class groups of quadratic number fields. The asymptotic behavior of those class groups is predicted by the Cohen--Lenstra heuristics. Under the assumption of this heuristic we are able to prove the expected upper bounds. "}],"keyword":["Algebra and Number Theory"],"user_id":"93826","external_id":{"arxiv":["math/0512260 "]},"date_created":"2022-12-23T09:37:01Z","publisher":"Cellule MathDoc/CEDRAM","language":[{"iso":"eng"}],"year":"2006","publication_identifier":{"issn":["1246-7405"]},"status":"public","_id":"34891","date_updated":"2023-03-06T09:12:04Z","author":[{"last_name":"Klüners","id":"21202","full_name":"Klüners, Jürgen","first_name":"Jürgen"}],"intvolume":"        18","citation":{"short":"J. Klüners, Journal de Théorie Des Nombres de Bordeaux 18 (2006) 607–615.","chicago":"Klüners, Jürgen. “Asymptotics of Number Fields and the Cohen–Lenstra Heuristics.” <i>Journal de Théorie Des Nombres de Bordeaux</i> 18, no. 3 (2006): 607–15. <a href=\"https://doi.org/10.5802/jtnb.561\">https://doi.org/10.5802/jtnb.561</a>.","ieee":"J. Klüners, “Asymptotics of number fields and the Cohen–Lenstra heuristics,” <i>Journal de Théorie des Nombres de Bordeaux</i>, vol. 18, no. 3, pp. 607–615, 2006, doi: <a href=\"https://doi.org/10.5802/jtnb.561\">10.5802/jtnb.561</a>.","mla":"Klüners, Jürgen. “Asymptotics of Number Fields and the Cohen–Lenstra Heuristics.” <i>Journal de Théorie Des Nombres de Bordeaux</i>, vol. 18, no. 3, Cellule MathDoc/CEDRAM, 2006, pp. 607–15, doi:<a href=\"https://doi.org/10.5802/jtnb.561\">10.5802/jtnb.561</a>.","apa":"Klüners, J. (2006). Asymptotics of number fields and the Cohen–Lenstra heuristics. <i>Journal de Théorie Des Nombres de Bordeaux</i>, <i>18</i>(3), 607–615. <a href=\"https://doi.org/10.5802/jtnb.561\">https://doi.org/10.5802/jtnb.561</a>","bibtex":"@article{Klüners_2006, title={Asymptotics of number fields and the Cohen–Lenstra heuristics}, volume={18}, DOI={<a href=\"https://doi.org/10.5802/jtnb.561\">10.5802/jtnb.561</a>}, number={3}, journal={Journal de Théorie des Nombres de Bordeaux}, publisher={Cellule MathDoc/CEDRAM}, author={Klüners, Jürgen}, year={2006}, pages={607–615} }","ama":"Klüners J. Asymptotics of number fields and the Cohen–Lenstra heuristics. <i>Journal de Théorie des Nombres de Bordeaux</i>. 2006;18(3):607-615. doi:<a href=\"https://doi.org/10.5802/jtnb.561\">10.5802/jtnb.561</a>"},"publication_status":"published","department":[{"_id":"102"}]},{"issue":"2","page":"185-194","volume":122,"type":"journal_article","publication":"Acta Arithmetica","external_id":{"arxiv":["math/0411484"]},"user_id":"93826","keyword":["Algebra and Number Theory"],"abstract":[{"text":"We prove that the number of quartic S4--extensions of the rationals of given discriminant d is $O_\\eps(d^{1/2+\\eps})$ for all $\\eps>0$. For a prime number p we derive that the dimension of the space of octahedral modular forms of weight 1 and conductor p or p² is bounded above by O(p¹/²log(p)²). ","lang":"eng"}],"doi":"10.4064/aa122-2-3","title":"The number of S₄-fields with given discriminant","date_updated":"2023-03-06T09:52:41Z","_id":"34892","year":"2006","publication_identifier":{"issn":["0065-1036","1730-6264"]},"language":[{"iso":"eng"}],"status":"public","date_created":"2022-12-23T09:40:25Z","publisher":"Institute of Mathematics, Polish Academy of Sciences","department":[{"_id":"102"}],"citation":{"short":"J. Klüners, Acta Arithmetica 122 (2006) 185–194.","mla":"Klüners, Jürgen. “The Number of S₄-Fields with given Discriminant.” <i>Acta Arithmetica</i>, vol. 122, no. 2, Institute of Mathematics, Polish Academy of Sciences, 2006, pp. 185–94, doi:<a href=\"https://doi.org/10.4064/aa122-2-3\">10.4064/aa122-2-3</a>.","bibtex":"@article{Klüners_2006, title={The number of S₄-fields with given discriminant}, volume={122}, DOI={<a href=\"https://doi.org/10.4064/aa122-2-3\">10.4064/aa122-2-3</a>}, number={2}, journal={Acta Arithmetica}, publisher={Institute of Mathematics, Polish Academy of Sciences}, author={Klüners, Jürgen}, year={2006}, pages={185–194} }","chicago":"Klüners, Jürgen. “The Number of S₄-Fields with given Discriminant.” <i>Acta Arithmetica</i> 122, no. 2 (2006): 185–94. <a href=\"https://doi.org/10.4064/aa122-2-3\">https://doi.org/10.4064/aa122-2-3</a>.","ieee":"J. Klüners, “The number of S₄-fields with given discriminant,” <i>Acta Arithmetica</i>, vol. 122, no. 2, pp. 185–194, 2006, doi: <a href=\"https://doi.org/10.4064/aa122-2-3\">10.4064/aa122-2-3</a>.","ama":"Klüners J. The number of S₄-fields with given discriminant. <i>Acta Arithmetica</i>. 2006;122(2):185-194. doi:<a href=\"https://doi.org/10.4064/aa122-2-3\">10.4064/aa122-2-3</a>","apa":"Klüners, J. (2006). The number of S₄-fields with given discriminant. <i>Acta Arithmetica</i>, <i>122</i>(2), 185–194. <a href=\"https://doi.org/10.4064/aa122-2-3\">https://doi.org/10.4064/aa122-2-3</a>"},"publication_status":"published","intvolume":"       122","author":[{"full_name":"Klüners, Jürgen","first_name":"Jürgen","last_name":"Klüners","id":"21202"}]},{"abstract":[{"lang":"eng","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."}],"doi":"10.1016/j.jalgebra.2005.04.013","title":"Computing residue class rings and Picard groups of orders","keyword":["Algebra and Number Theory"],"user_id":"93826","type":"journal_article","publication":"Journal of Algebra","issue":"1","page":"47-64","volume":292,"intvolume":"       292","author":[{"first_name":"Jürgen","full_name":"Klüners, Jürgen","id":"21202","last_name":"Klüners"},{"last_name":"Pauli","first_name":"Sebastian","full_name":"Pauli, Sebastian"}],"department":[{"_id":"102"}],"citation":{"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>.","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>","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>","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} }","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>.","short":"J. Klüners, S. Pauli, Journal of Algebra 292 (2005) 47–64.","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>."},"publication_status":"published","language":[{"iso":"eng"}],"year":"2005","publication_identifier":{"issn":["0021-8693"]},"status":"public","date_created":"2022-12-23T09:41:06Z","publisher":"Elsevier BV","date_updated":"2023-03-06T09:55:09Z","_id":"34893"},{"department":[{"_id":"102"}],"citation":{"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>","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>.","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>.","short":"C. Fieker, J. Klüners, Journal of Number Theory 99 (2003) 318–337."},"publication_status":"published","intvolume":"        99","author":[{"last_name":"Fieker","first_name":"Claus","full_name":"Fieker, Claus"},{"last_name":"Klüners","id":"21202","first_name":"Jürgen","full_name":"Klüners, Jürgen"}],"date_updated":"2023-03-06T09:19:16Z","_id":"34896","language":[{"iso":"eng"}],"year":"2003","publication_identifier":{"issn":["0022-314X"]},"status":"public","date_created":"2022-12-23T09:53:23Z","publisher":"Elsevier BV","keyword":["Algebra and Number Theory"],"user_id":"93826","abstract":[{"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.","lang":"eng"}],"doi":"10.1016/s0022-314x(02)00071-9","title":"Minimal discriminants for fields with small Frobenius groups as Galois groups","issue":"2","page":"318-337","volume":99,"type":"journal_article","publication":"Journal of Number Theory"},{"doi":"10.1109/DATE.2001.915002","abstract":[{"text":"We present a rigorous but transparent semantics definition of SystemC that covers method, thread, and clocked thread behavior as well as their interaction with the simulation kernel process. The semantics includes watching statements, signal assignment, and wait statements as they are introduced in SystemC V1.O. We present our definition in form of distributed Abstract State Machines (ASMs) rules reflecting the view given in the SystemC User's Manual and the reference implementation. We mainly see our formal semantics as a concise, unambiguous, high-level specification for SystemC-based implementations and for standardization. Additionally, it can be used as a sound basis to investigate SystemC interoperability with Verilog and VHDL.","lang":"eng"}],"place":"Munich, Germany ","author":[{"last_name":"Müller","id":"16243","full_name":"Müller, Wolfgang","first_name":"Wolfgang"},{"last_name":"Ruf","full_name":"Ruf, Jürgen","first_name":"Jürgen"},{"full_name":"Hoffmann, D. W.","first_name":"D. W.","last_name":"Hoffmann"},{"last_name":"Gerlach","first_name":"Joachim","full_name":"Gerlach, Joachim"},{"last_name":"Kropf","first_name":"Thomas","full_name":"Kropf, Thomas"},{"first_name":"W.","full_name":"Rosenstiehl, W.","last_name":"Rosenstiehl"}],"title":"The Simulation Semantics of SystemC","conference":{"name":" Proceedings Design, Automation and Test in Europe. Conference and Exhibition 2001"},"department":[{"_id":"672"}],"keyword":["Yarn","Formal verification","Kernel","Hardware design languages","Electronic design automation and methodology","Algebra","Computational modeling","Logic functions","Computer languages","Clocks"],"user_id":"5786","citation":{"mla":"Müller, Wolfgang, et al. “The Simulation Semantics of SystemC.” <i>Proceedings of the Design, Automation, and Test in Europe (DATE’01)</i>, IEEE, 2001, doi:<a href=\"https://doi.org/10.1109/DATE.2001.915002\">10.1109/DATE.2001.915002</a>.","bibtex":"@inproceedings{Müller_Ruf_Hoffmann_Gerlach_Kropf_Rosenstiehl_2001, place={Munich, Germany }, title={The Simulation Semantics of SystemC}, DOI={<a href=\"https://doi.org/10.1109/DATE.2001.915002\">10.1109/DATE.2001.915002</a>}, booktitle={Proceedings of the Design, Automation, and Test in Europe (DATE’01)}, publisher={IEEE}, author={Müller, Wolfgang and Ruf, Jürgen and Hoffmann, D. W. and Gerlach, Joachim and Kropf, Thomas and Rosenstiehl, W.}, year={2001} }","short":"W. Müller, J. Ruf, D.W. Hoffmann, J. Gerlach, T. Kropf, W. Rosenstiehl, in: Proceedings of the Design, Automation, and Test in Europe (DATE’01), IEEE, Munich, Germany , 2001.","apa":"Müller, W., Ruf, J., Hoffmann, D. W., Gerlach, J., Kropf, T., &#38; Rosenstiehl, W. (2001). The Simulation Semantics of SystemC. <i>Proceedings of the Design, Automation, and Test in Europe (DATE’01)</i>.  Proceedings Design, Automation and Test in Europe. Conference and Exhibition 2001. <a href=\"https://doi.org/10.1109/DATE.2001.915002\">https://doi.org/10.1109/DATE.2001.915002</a>","ama":"Müller W, Ruf J, Hoffmann DW, Gerlach J, Kropf T, Rosenstiehl W. The Simulation Semantics of SystemC. In: <i>Proceedings of the Design, Automation, and Test in Europe (DATE’01)</i>. IEEE; 2001. doi:<a href=\"https://doi.org/10.1109/DATE.2001.915002\">10.1109/DATE.2001.915002</a>","chicago":"Müller, Wolfgang, Jürgen Ruf, D. W. Hoffmann, Joachim Gerlach, Thomas Kropf, and W. Rosenstiehl. “The Simulation Semantics of SystemC.” In <i>Proceedings of the Design, Automation, and Test in Europe (DATE’01)</i>. Munich, Germany : IEEE, 2001. <a href=\"https://doi.org/10.1109/DATE.2001.915002\">https://doi.org/10.1109/DATE.2001.915002</a>.","ieee":"W. Müller, J. Ruf, D. W. Hoffmann, J. Gerlach, T. Kropf, and W. Rosenstiehl, “The Simulation Semantics of SystemC,” presented at the  Proceedings Design, Automation and Test in Europe. Conference and Exhibition 2001, 2001, doi: <a href=\"https://doi.org/10.1109/DATE.2001.915002\">10.1109/DATE.2001.915002</a>."},"status":"public","language":[{"iso":"eng"}],"year":"2001","publication_identifier":{"isbn":["0-7695-0993-2"]},"type":"conference","publisher":"IEEE","date_created":"2023-01-24T10:39:33Z","publication":"Proceedings of the Design, Automation, and Test in Europe (DATE’01)","date_updated":"2023-01-24T10:39:38Z","_id":"39421"},{"date_updated":"2023-03-06T09:58:06Z","_id":"34900","status":"public","year":"2000","publication_identifier":{"issn":["0747-7171"]},"language":[{"iso":"eng"}],"publisher":"Elsevier BV","date_created":"2022-12-23T09:58:16Z","department":[{"_id":"102"}],"publication_status":"published","citation":{"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>","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>","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>.","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>.","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>.","short":"K. Geissler, J. Klüners, Journal of Symbolic Computation 30 (2000) 653–674."},"intvolume":"        30","author":[{"first_name":"Katharina","full_name":"Geissler, Katharina","last_name":"Geissler"},{"first_name":"Jürgen","full_name":"Klüners, Jürgen","last_name":"Klüners","id":"21202"}],"issue":"6","volume":30,"page":"653-674","type":"journal_article","publication":"Journal of Symbolic Computation","user_id":"93826","keyword":["Computational Mathematics","Algebra and Number Theory"],"doi":"10.1006/jsco.2000.0377","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"}],"title":"Galois Group Computation for Rational Polynomials"},{"intvolume":"        30","author":[{"first_name":"Vincenzo","full_name":"Acciaro, Vincenzo","last_name":"Acciaro"},{"last_name":"Klüners","id":"21202","full_name":"Klüners, Jürgen","first_name":"Jürgen"}],"department":[{"_id":"102"}],"citation":{"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>.","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.","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>","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>","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>.","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>."},"publication_status":"published","year":"2000","publication_identifier":{"issn":["0747-7171"]},"language":[{"iso":"eng"}],"status":"public","date_created":"2022-12-23T09:58:48Z","publisher":"Elsevier BV","date_updated":"2023-03-06T09:57:34Z","_id":"34901","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."}],"doi":"10.1006/jsco.2000.0361","title":"Computing Local Artin Maps, and Solvability of Norm Equations","user_id":"93826","keyword":["Computational Mathematics","Algebra and Number Theory"],"type":"journal_article","publication":"Journal of Symbolic Computation","issue":"3","page":"239-252","volume":30},{"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.","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>","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>."},"publication_status":"published","department":[{"_id":"102"}],"author":[{"last_name":"Klüners","id":"21202","first_name":"Jürgen","full_name":"Klüners, Jürgen"},{"full_name":"Malle, Gunter","first_name":"Gunter","last_name":"Malle"}],"intvolume":"        30","_id":"34899","date_updated":"2023-03-06T10:48:05Z","date_created":"2022-12-23T09:57:28Z","publisher":"Elsevier BV","language":[{"iso":"eng"}],"year":"2000","publication_identifier":{"issn":["0747-7171"]},"status":"public","keyword":["Computational Mathematics","Algebra and Number Theory"],"user_id":"93826","title":"Explicit Galois Realization of Transitive Groups of Degree up to 15","doi":"10.1006/jsco.2000.0378","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"}],"page":"675-716","volume":30,"issue":"6","publication":"Journal of Symbolic Computation","type":"journal_article"},{"publisher":"Elsevier BV","date_created":"2022-12-23T09:56:52Z","status":"public","language":[{"iso":"eng"}],"year":"2000","publication_identifier":{"issn":["0747-7171"]},"_id":"34898","date_updated":"2023-03-06T10:48:40Z","author":[{"full_name":"Klüners, Jürgen","first_name":"Jürgen","id":"21202","last_name":"Klüners"}],"intvolume":"        30","publication_status":"published","citation":{"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>.","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>","short":"J. Klüners, Journal of Symbolic Computation 30 (2000) 733–737.","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} }","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>."},"department":[{"_id":"102"}],"publication":"Journal of Symbolic Computation","type":"journal_article","volume":30,"page":"733-737","issue":"6","title":"A Polynomial with Galois GroupSL2(11)","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)."}],"doi":"10.1006/jsco.2000.0380","keyword":["Computational Mathematics","Algebra and Number Theory"],"user_id":"93826"},{"publisher":"Elsevier BV","date_created":"2022-12-23T10:01:15Z","status":"public","year":"1999","publication_identifier":{"issn":["0747-7171"]},"language":[{"iso":"eng"}],"_id":"34902","date_updated":"2023-03-06T09:21:29Z","author":[{"id":"21202","last_name":"Klüners","first_name":"Jürgen","full_name":"Klüners, Jürgen"}],"intvolume":"        27","publication_status":"published","citation":{"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} }","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>","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>.","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."},"department":[{"_id":"102"}],"publication":"Journal of Symbolic Computation","type":"journal_article","volume":27,"page":"261-269","issue":"3","title":"On Polynomial Decompositions","doi":"10.1006/jsco.1998.0252","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."}],"user_id":"93826","keyword":["Computational Mathematics","Algebra and Number Theory"]},{"title":"KANT V4","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."}],"has_accepted_license":"1","doi":"10.1006/jsco.1996.0126","keyword":["Computational Mathematics","Algebra and Number Theory"],"user_id":"93826","publication":"Journal of Symbolic Computation","ddc":["000"],"type":"journal_article","page":"267-283","volume":24,"issue":"3-4","author":[{"last_name":"DABERKOW","full_name":"DABERKOW, M.","first_name":"M."},{"last_name":"FIEKER","first_name":"C.","full_name":"FIEKER, C."},{"id":"21202","last_name":"Klüners","full_name":"Klüners, Jürgen","first_name":"Jürgen"},{"first_name":"M.","full_name":"POHST, M.","last_name":"POHST"},{"last_name":"ROEGNER","full_name":"ROEGNER, K.","first_name":"K."},{"first_name":"M.","full_name":"SCHÖRNIG, M.","last_name":"SCHÖRNIG"},{"first_name":"K.","full_name":"WILDANGER, K.","last_name":"WILDANGER"}],"intvolume":"        24","citation":{"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>.","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>","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} }","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>."},"publication_status":"published","department":[{"_id":"102"}],"date_created":"2022-12-23T10:02:24Z","publisher":"Elsevier BV","language":[{"iso":"eng"}],"year":"1997","publication_identifier":{"issn":["0747-7171"]},"status":"public","_id":"34903","date_updated":"2023-03-06T09:23:30Z"},{"publication":"Journal of Symbolic Computation","ddc":["000"],"type":"journal_article","page":"385-397","volume":24,"issue":"3-4","title":"On Computing Subfields","has_accepted_license":"1","doi":"10.1006/jsco.1996.0140","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"}],"user_id":"93826","keyword":["Computational Mathematics","Algebra and Number Theory"],"date_created":"2022-12-23T10:03:02Z","publisher":"Elsevier BV","publication_identifier":{"issn":["0747-7171"]},"year":"1997","language":[{"iso":"eng"}],"status":"public","_id":"34904","date_updated":"2023-03-06T10:36:21Z","author":[{"id":"21202","last_name":"Klüners","full_name":"Klüners, Jürgen","first_name":"Jürgen"},{"first_name":"Michael","full_name":"Pohst, Michael","last_name":"Pohst"}],"intvolume":"        24","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>.","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>","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>."},"publication_status":"published","department":[{"_id":"102"}]}]