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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>","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>.","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>","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>."},"external_id":{"arxiv":["math/0409510 "]},"status":"public","volume":21,"user_id":"93826","publisher":"Cellule MathDoc/CEDRAM","_id":"34889","page":"15-39","abstract":[{"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.","lang":"eng"}],"issue":"1","publication":"Journal de Théorie des Nombres de Bordeaux","department":[{"_id":"102"}],"keyword":["Algebra and Number Theory"],"type":"journal_article","date_created":"2022-12-23T09:33:37Z","intvolume":"        21","date_updated":"2023-03-06T09:09:56Z","publication_status":"published","author":[{"full_name":"Belabas, Karim","last_name":"Belabas","first_name":"Karim"},{"full_name":"van Hoeij, Mark","last_name":"van Hoeij","first_name":"Mark"},{"last_name":"Klüners","first_name":"Jürgen","full_name":"Klüners, Jürgen","id":"21202"},{"full_name":"Steel, Allan","first_name":"Allan","last_name":"Steel"}],"publication_identifier":{"issn":["1246-7405"]},"year":"2009","title":"Factoring polynomials over global fields","doi":"10.5802/jtnb.655","language":[{"iso":"eng"}]},{"type":"book_chapter","department":[{"_id":"102"}],"date_created":"2023-01-11T09:48:17Z","place":"Berlin, Heidelberg","abstract":[{"text":"In this survey, we report about a new algorithm for factoring polynomials due to Mark van Hoeij. The main idea is that the combinatorial problem that occurs in the Zassenhaus algorithm is reduced to a very special knapsack problem. In case of rational polynomials, this knapsack problem can be very efficiently solved by the LLL algorithm. This gives a polynomial time algorithm, which also works very well in practice.","lang":"eng"}],"related_material":{"link":[{"relation":"confirmation","url":"https://www.researchgate.net/profile/Juergen-Klueners/publication/226764840_The_van_Hoeij_Algorithm_for_Factoring_Polynomials/links/00463532f2216a64ae000000/The-van-Hoeij-Algorithm-for-Factoring-Polynomials.pdf?origin=publication_detail"}]},"publication":"The LLL Algorithm","citation":{"ama":"Klüners J. The van Hoeij Algorithm for Factoring Polynomials. In: <i>The LLL Algorithm</i>. Springer Berlin Heidelberg; 2009. doi:<a href=\"https://doi.org/10.1007/978-3-642-02295-1_8\">10.1007/978-3-642-02295-1_8</a>","bibtex":"@inbook{Klüners_2009, place={Berlin, Heidelberg}, title={The van Hoeij Algorithm for Factoring Polynomials}, DOI={<a href=\"https://doi.org/10.1007/978-3-642-02295-1_8\">10.1007/978-3-642-02295-1_8</a>}, booktitle={The LLL Algorithm}, publisher={Springer Berlin Heidelberg}, author={Klüners, Jürgen}, year={2009} }","mla":"Klüners, Jürgen. “The van Hoeij Algorithm for Factoring Polynomials.” <i>The LLL Algorithm</i>, Springer Berlin Heidelberg, 2009, doi:<a href=\"https://doi.org/10.1007/978-3-642-02295-1_8\">10.1007/978-3-642-02295-1_8</a>.","chicago":"Klüners, Jürgen. “The van Hoeij Algorithm for Factoring Polynomials.” In <i>The LLL Algorithm</i>. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. <a href=\"https://doi.org/10.1007/978-3-642-02295-1_8\">https://doi.org/10.1007/978-3-642-02295-1_8</a>.","short":"J. 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Optimal trajectory generation for a dynamic glider in ocean flows modeled by 3d B-spline functions. In: <i>IEEE International Conference on Robotics and Automation</i>. ; 2008.","bibtex":"@inproceedings{Zhang_Inanc_Ober-Blöbaum_Marsden_2008, title={Optimal trajectory generation for a dynamic glider in ocean flows modeled by 3d B-spline functions}, booktitle={IEEE International Conference on Robotics and Automation}, author={Zhang, W. and Inanc, T. and Ober-Blöbaum, Sina and Marsden, J.E.}, year={2008} }","mla":"Zhang, W., et al. “Optimal Trajectory Generation for a Dynamic Glider in Ocean Flows Modeled by 3d B-Spline Functions.” <i>IEEE International Conference on Robotics and Automation</i>, 2008.","short":"W. Zhang, T. Inanc, S. Ober-Blöbaum, J.E. Marsden, in: IEEE International Conference on Robotics and Automation, 2008.","chicago":"Zhang, W., T. Inanc, Sina Ober-Blöbaum, and J.E. 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