翻訳と辞書 Words near each other ・ Infrared thermometer ・ Infrared vision ・ Infrared window ・ Infrarrealismo ・ Infrasonic burglar alarm ・ Infrasonic passive differential spectroscopy ・ Infrasound ・ Infraspecific name ・ Infraspeed ・ Infraspinatous fossa ・ Infraspinatus muscle ・ Infraspinous fascia ・ Infrasternal angle ・ Infrastructural power ・ Infrastructure ・ Infrastructure (number theory) ・ Infrastructure Act 2015 ・ Infrastructure and Communities ・ Infrastructure and economics ・ Infrastructure and Energy Committee ・ Infrastructure asset management ・ Infrastructure Australia ・ Infrastructure bias ・ Infrastructure Canada ・ Infrastructure Consortium for Africa ・ Infrastructure damage during the Russo-Georgian War ・ Infrastructure debt ・ Infrastructure Development Finance Company ・ Infrastructure for Peace ・ Infrastructure for Spatial Information in the European Community Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Infrastructure (number theory) ： ウィキペディア英語版 Infrastructure (number theory) In mathematics, an infrastructure is a group-like structure appearing in global fields. == Historic development == In 1972, D. Shanks first discovered the infrastructure of a real quadratic number field and applied his baby-step giant-step algorithm to compute the regulator of such a field in $\backslash mathcal(D^)$ binary operations (for every $\backslash varepsilon\; >\; 0$), where $D$ is the discriminant of the quadratic field; previous methods required $\backslash mathcal(D^)$ binary operations.〔D. Shanks: The infrastructure of a real quadratic field and its applications. Proceedings of the Number Theory Conference (Univ. Colorado, Boulder, Colo., 1972), pp. 217-224. University of Colorado, Boulder, 1972. 〕 Ten years later, H. W. Lenstra published〔H. W. Lenstra Jr.: On the calculation of regulators and class numbers of quadratic fields. Number theory days, 1980 (Exeter, 1980), 123–150, London Math. Soc. Lecture Note Ser., 56, Cambridge University Press, Cambridge, 1982. 〕 a mathematical framework describing the infrastructure of a real quadratic number field in terms of "circular groups". It was also described by R. Schoof〔R. J. Schoof: Quadratic fields and factorization. Computational methods in number theory, Part II, 235–286, Math. Centre Tracts, 155, Math. Centrum, Amsterdam, 1982. 〕 and H. C. Williams,〔H. C. Williams: Continued fractions and number-theoretic computations. Number theory (Winnipeg, Man., 1983). Rocky Mountain J. Math. 15 (1985), no. 2, 621–655. 〕 and later extended by H. C. Williams, G. W. Dueck and B. K. Schmid to certain cubic number fields of unit rank one〔H. C. Williams, G. W. Dueck, B. K. Schmid: A rapid method of evaluating the regulator and class number of a pure cubic field. Math. Comp. 41 (1983), no. 163, 235–286. 〕〔G. W. Dueck, H. C. Williams: Computation of the class number and class group of a complex cubic field. Math. Comp. 45 (1985), no. 171, 223–231. 〕 and by J. Buchmann and H. C. Williams to all number fields of unit rank one.〔J. Buchmann, H. C. Williams: On the infrastructure of the principal ideal class of an algebraic number field of unit rank one. Math. Comp. 50 (1988), no. 182, 569–579. 〕 In his habilitation thesis, J. Buchmann presented a baby-step giant-step algorithm to compute the regulator of a number field of ''arbitrary'' unit rank.〔J. Buchmann: Zur Komplexität der Berechnung von Einheiten und Klassenzahlen algebraischer Zahlkörper. Habilitationsschrift, Düsseldorf, 1987. (PDF )〕 The first description of infrastructures in number fields of arbitrary unit rank was given by R. Schoof using Arakelov divisors in 2008.〔R. Schoof: Computing Arakelov class groups. (English summary) Algorithmic number theory: lattices, number fields, curves and cryptography, 447–495, Math. Sci. Res. Inst. Publ., 44, Cambridge University Press, 2008. (PDF )〕 The infrastructure was also described for other global fields, namely for algebraic function fields over finite fields. This was done first by A. Stein and H. G. Zimmer in the case of real hyperelliptic function fields.〔A. Stein, H. G. Zimmer: An algorithm for determining the regulator and the fundamental unit of hyperelliptic congruence function field. In "Proceedings of the 1991 International Symposium on Symbolic and Algebraic Computation, ISSAC '91," Association for Computing Machinery, (1991), 183–184.〕 It was extended to certain cubic function fields of unit rank one by R. Scheidler and A. Stein.〔R. Scheidler, A. Stein: Unit computation in purely cubic function fields of unit rank 1. (English summary) Algorithmic number theory (Portland, OR, 1998), 592–606, Lecture Notes in Comput. Sci., 1423, Springer, Berlin, 1998. 〕〔R. Scheidler: Ideal arithmetic and infrastructure in purely cubic function fields. (English, French summary) J. Théor. Nombres Bordeaux 13 (2001), no. 2, 609–631. 〕 In 1999, S. Paulus and H.-G. Rück related the infrastructure of a real quadratic function field to the divisor class group.〔S. Paulus, H.-G. Rück: Real and imaginary quadratic representations of hyperelliptic function fields. (English summary) Math. Comp. 68 (1999), no. 227, 1233–1241. 〕 This connection can be generalized to arbitrary function fields and, combining with R. Schoof's results, to all global fields. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Infrastructure (number theory)」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.