請用此 Handle URI 來引用此文件：
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/34948完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 陳其誠(Ki-Seng Tan) | |
| dc.contributor.author | Yi-Chih Chou | en |
| dc.contributor.author | 周奕志 | zh_TW |
| dc.date.accessioned | 2021-06-13T06:37:24Z | - |
| dc.date.available | 2005-10-14 | |
| dc.date.copyright | 2005-10-14 | |
| dc.date.issued | 2005 | |
| dc.date.submitted | 2005-10-11 | |
| dc.identifier.citation | [1]Buchmann, J.: “A subexponential algorithm for the determination of class groups and regulators of algebraic number fields.” pp. 27-41 in C. Goldstein (ed): Seminaire de Th´eorie des Nombres, Paris 1988V1989, BirkhLauser Boston 1990.
[2] Buchmann, J. and Hollinger, C.: “On smooth ideals in number fields.” J. of Number Theory 59 (1996), 82-87. [3] Cohen, H.: “A Course in Computational Algebraic Number Theory.” Graduate Texts in Mathematics 138, Springer-Verlag, Berlin 1993. [4] Cohen, H., Diaz y Diaz, F. and Olivier, M.:“Subexponential algorithm for class group and unit computations.” J. Symbolic Computation 24 (1997), 433-441. [5] Groenewegen, R.P.: “The size function for number fields.” Proceedings of the XXI Journees Arithmetiques, Journal de Theorie de Nombres de Bordeaux 13 (2001), 143- 156. [6] Hafner, J. and McCurley, K.: “A rigorous subexponential algorithm for computation of class groups.” Journal of the AMS 2 (1989), 837-850. [7] LiDIA: “ A C++ Library For Computational Number Theory” Homepage:www.informatik. tu-darmstadt.de/TI/LiDIA. [8] Lenstra, A.K., Lenstra, H.W. and Lovasz, L.: “Factoring polynomials with rational coefficients.” Math. Annalen 261 (1982), 515-534. [9] Pari-GP, Homepage: www.parigp-home.de. [10] Schoof, R.: “Computing Arakelov Class Groups”, Roma (2004) [11] Shanks, D.: “The infrastructure of a real quadratic field and its applications” Proceedings of the 1972 Number Theory Conference, Boulder (1972) 217V224. [12] Stewart, I. and Tall, D.: “Algebraic Number Theory and Fermat’s Last Theorem.” 2002 A K Peters, Ltd. [13] “The Magma Computational Algebra System for Algebra, Number Theory and Geometry.” Homepage: magma.maths.usyd.edu.au/magma.42 [14] Van der Geer, G. and Schoof, R.: “Effectivity of Arakelov divisors and the Theta divisor of a number field.” Selecta Mathematica, New Ser. 6 (2000), 377V398. Preprint 9802121 at: http://xxx.lanl.gov/list/math.AG/9802. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/34948 | - |
| dc.description.abstract | 本篇論文主要介紹 Buchamnn 的演算法和 Arakelov 類群 | zh_TW |
| dc.description.abstract | This thesis focuses not only on Buchmann’s algorithm for computing the class group together with the regulator of an arbitrary number field but also on the basic properties on Arakelov class groups which is relevant to Buchmann’s algorithm. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-13T06:37:24Z (GMT). No. of bitstreams: 1 ntu-94-R92221018-1.pdf: 380120 bytes, checksum: cb06947dfabbd4a6fe1405c45bc15d90 (MD5) Previous issue date: 2005 | en |
| dc.description.tableofcontents | Contents
1 Introduction 2 2 Basic Definitions, Notations and Results 3 2.1 Class groups, fundamental units and regulators 3 2.2 Methods for computing class number and class group 5 2.3 Computations on ideals 7 2.4 Arakelov class group 8 2.5 The idea of Buchmann's algorithm 11 3 Arakelov Class Groups 14 3.1 Inside and outside metrics on Arakelov divisors 14 3.2 The oriented Arakelov class 18 3.3 Reduced Arakelov divisors 20 4 Buchmann’s Algorithm 27 4.1 The LLL-reduced algorithm 27 4.2 Computation on reduced Arakelov divisor 32 4.3 The main steps of Buchmann’s algorithm 34 4.3.1 Finding Ic 34 4.3.2 Looking for relations 34 4.3.3 Producing a generating system 36 4.3.4 Determine the class group and the regulator 37 4.4 The complexity of Buchmann’s algorithm 38 4.5 Application the class group to the principal ideal problem 40 | |
| dc.language.iso | en | |
| dc.subject | Arakelov類群 | zh_TW |
| dc.subject | Buchmann演算法 | zh_TW |
| dc.subject | class group | en |
| dc.subject | class number | en |
| dc.subject | regulator | en |
| dc.subject | Arakelov class group | en |
| dc.title | 介紹 Buchmann 的演算法和 Arakelov 類群 | zh_TW |
| dc.title | Introduction to Buchmann's Algorithm and Arakelov Class Groups | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 94-1 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 紀文鎮,許志農 | |
| dc.subject.keyword | Buchmann演算法,Arakelov類群, | zh_TW |
| dc.subject.keyword | Arakelov class group,regulator,class group,class number, | en |
| dc.relation.page | 43 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2005-10-12 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 數學研究所 | zh_TW |
| 顯示於系所單位： | 數學系 | |
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