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Tytuł artykułu

Intrinsic Factorization of Ideals in Dedekind Domains

Wybrane pełne teksty z tego czasopisma
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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We present a generalization of a polynomial factorization algorithm that works with ideals in maximal orders of global function fields. The method presented in this paper is intrinsic in the sense that it does not depend on the embedding of the ring of polynomials into the Dedekind domain in question.
Wydawca
Rocznik
Strony
325--338
Opis fizyczny
Bibliogr. 20 poz., tab.
Twórcy
  • Institute of Mathematics, University of Silesia, ul. Bankowa 14, 40-007 Katowice, Poland
  • Institute of Mathematics, University of Silesia, ul. Bankowa 14, 40-007 Katowice, Poland
Bibliografia
  • [1] Cohen H. Advanced topics in computational number theory, volume 193 of Graduate Texts in Mathematics. Springer-Verlag, New York, 2000. ISBN 0-387-98727-4. doi:10.1007/978-1-4419-8489-0. URL http://dx.doi.org/10.1007/978-1-4419-8489-0.
  • [2] Guàrdia J, Montes J, Nart E. A new computational approach to ideal theory in number fields. Found. Comput. Math., 2013. 13(5):729-762. URL https://doi.org/10.1007/s10208-012-9137-5.
  • [3] Bosma W, Cannon J, Playoust C. The Magma algebra system. I. The user language. J. Symbolic Comput., 1997. 24(3-4):235-265. doi:10.1006/jsco.1996.0125. Computational algebra and number theory (London, 1993), URL http://dx.doi.org/10.1006/jsco.1996.0125.
  • [4] Atiyah MF, Macdonald IG. Introduction to commutative algebra. Addison-Wesley Series in Mathematics. Westview Press, Boulder, CO, economy edition, 2016. ISBN 978-0-8133-5018-9; 0-201-00361-9; 0-201-40751-5. For the 1969 original see [ MR0242802].
  • [5] Seidenberg A. Constructions in algebra. Trans. Amer. Math. Soc., 1974. 197:273-313. doi:10.2307/1996938. URL https://doi.org/10.2307/1996938.
  • [6] Musser DR. Algorithms for polynomial factorization. Ph.D. thesis, University of Wisconsin, 1971.
  • [7] Cohn PM. Basic algebra. Springer-Verlag London, Ltd., London, 2003. ISBN 1-85233-587-4. Groups, rings and fields, URL https://doi.org/10.1007/978-0-85729-428-9.
  • [8] Gerhard J. Fast modular algorithms for squarefree factorization and Hermite integration. Appl. Algebra Engrg. Comm. Comput., 2001. 11(3):203-226. doi:10.1007/PL00004222. URL http://dx.doi.org/10.1007/PL00004222.
  • [9] Guersenzvaig NH, Szechtman F. Roots multiplicity and square-free factorization of polynomials using companion matrices. Linear Algebra Appl., 2012. 436(9):3160-3164. doi:10.1016/j.laa.2011.10.018. URL http://dx.doi.org/10.1016/j.laa.2011.10.018.
  • [10] Horowitz E. Algorithms for symbolic integration of rational functions. Ph.D. thesis, University of Wisconsin, 1969.
  • [11] Koprowski Pa. Roots multiplicity without companion matrices. Fund. Inform., 2017. 153(3):265-270. URL https://doi.org/10.3233/FI-2017-1540.
  • [12] Lorenzini D. An invitation to arithmetic geometry, volume 9 of Graduate Studies in Mathematics. American Mathematical Society, Providence, RI, 1996. ISBN 0-8218-0267-4.
  • [13] Stichtenoth H. Algebraic function fields and codes. Universitext. Springer-Verlag, Berlin, 1993. ISBN 3-540-56489-6.
  • [14] Tobey RG. Algorithms for antidifferentiation of rational functions. Ph.D. thesis, Harvard, 1967.
  • [15] Yun DY. On Square-free Decomposition Algorithms. In: Proceedings of the Third ACM Symposium on Symbolic and Algebraic Computation, SYMSAC ’76. ACM, New York, NY, USA, 1976 pp. 26-35. doi:10.1145/800205.806320. URL http://doi.acm.org/10.1145/800205.806320.
  • [16] RSFDGrC. International Conference on Rough Sets, Fuzzy Sets, Data Mining, and Granular-Soft Computing. http://dblp.uni-trier.de/db/conf/rsfdgrc/index.html. Accessed: 2015-08-29.
  • [17] Baker G, Hacker P. Wittgenstein: Understanding and Meaning, Volume 1 of an Analytical Commentary on the Philosophical Investigations, Part II: Exegesis 1-184. Wiley-Blackwell Publishing, 2004. ISBN 9780470753101. doi:10.1002/9780470753101. 2nd Edition.
  • [18] Szczuka MS, Sosnowski L, Krasuski A, Krenski K. Using Domain Knowledge in Initial Stages of KDD: Optimization of Compound Object Processing. Fundamenta Informaticae, 2014. 129(4):341-364. doi:10.3233/FI-2014-975.
  • [19] Krasuski A, Jankowski A, Skowron A, Ślęzak D. From Sensory Data to Decision Making: A Perspective on Supporting a Fire Commander. In: 2013 IEEE/WIC/ACM International Conferences on Web Intelligence and Intelligent Agent Technology, Atlanta, Georgia, USA, 17-20 November 2013, Workshop Proceedings [20], 2013 pp. 229-236. doi:10.1109/WI-IAT.2013.188. URL http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=6690661.
  • [20] 2013 IEEE/WIC/ACM International Conferences on Web Intelligence and Intelligent Agent Technology, Atlanta, Georgia, USA, 17-20 November 2013, Workshop Proceedings. IEEE Computer Society, 2013. ISBN 978-1-4799-2902-3. URL http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=6690661.
Uwagi
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).
Typ dokumentu
Bibliografia
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bwmeta1.element.baztech-40558557-52ef-4dac-9768-5d9998428f1d
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