Data Computation and Software Development in Number Theory by Computers

计算机数论数据计算和软件开发

• 批准号: 10440012
• 负责人: NAKAMULA Ken
• 金额: $ 2.82万
• 依托单位: Tokyo Metropolitan University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 1998
• 资助国家: 日本
• 起止时间: 1998 至 1999
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-10440012/
• 关键词: number theory; computer; algorithm; software; database; network; mailing list; TNT

The objects of this study are to compute invariants on elementary number theory, algebraic number fields and elliptic curves computers using already known theorems and methods, then to gain realistic accumulation of data and to establish theoretical fundamentals in order to construct general-purpose system Tools on Number Theory, or TNT. The progress of this study for these two years spread, beyond the fields which was first planed mainly in number theory, widely to the study of computation by computers in general algebra including ring theory or algebraic geometry.A significant feature of our study is practical use of the mailing list TNT-ML in addition to file transfer service. In the first year, we collected several data and programs computed and written up to present, and reinstalled the TNT-SERVER for distribution of the results through network. New TNT-SERVER combines three servers for mailing list, anonymous ftp and world wide web together. In the second year, we sorted and classified these data and softwares, designed a method to link them with each other, and we organized a symposium "The 3rd Conference on Algebra and Computation" in order to discuss about the basic design for the TNT-SYSTEM (pre-release).Summarizing the computation and study above, we have almost finished fundamental preparation for a database on basic algorithms and tables on number theory. Moreover, we are ready to analyze necessary algorithms and important tables in this field, and have shown actual possibility to construct a general-purpose computer algebra system TNT-SYSTEM for software and database.

本研究的目的是使用已知的定理和方法计算初等数论，代数数域和椭圆曲线计算机上的不变量，然后获得现实的数据积累，并建立理论基础，以构建通用系统数论工具或TNT。这两年的研究进展，超出了最初计划的主要是数论的领域，广泛地扩展到一般代数（包括环论或代数几何）的计算机计算研究。我们研究的一个重要特点是除了文件传输服务之外，邮件列表TNT-ML的实际使用。在第一年，我们收集了一些数据和计算和编写的程序，到目前为止，并重新安装了TNT服务器的结果通过网络发布。新的TNT服务器结合了三个服务器的邮件列表，匿名FTP和万维网在一起。第二年，我们对这些数据和软件进行了整理和分类，设计了一种将它们相互连接起来的方法，并组织了一次研讨会“第三届代数和计算会议”，讨论了TNT-SYSTEM（预发行版）的基本设计。总结上述计算和研究，我们基本完成了基本算法数据库和数论表格的基本准备工作。此外，我们准备分析必要的算法和重要的表在这一领域，并显示了实际的可能性，建立一个通用的计算机代数系统TNT-SYSTEM的软件和数据库。

项目成果

N. Takao and H. Nakamura: "Galois rigidity of pro-l pure braid groups on algebraic curves"Trans. Amer. Math. Soc.. 350. 1079-1102 (1998)

N. Takao 和 H. Nakamura：“代数曲线上 pro-l 纯辫群的伽罗瓦刚性”Trans。

K.Hashimoto, K.Miyake: "Inverse Galois Problem for Dihedral Groups"Number Theory and its Applications. 165-181 (1999)

K.Hashimoto、K.Miyake：“二面群的逆伽罗瓦问题”数论及其应用。

Ken Nakamula: "Recent Developements of Computational Number Theory" Number Theory and its application, Kyoto 1997. 176-184 (1998)

Ken Nakamula：《计算数论的最新发展》数论及其应用，京都 1997 年。176-184 (1998)

Ken Nakamula: "A Survey on the Number Field Sieve" Number Theory and its Application. (1999)

Ken Nakamula：“数场筛的调查”数论及其应用。

K.Hashimoto K.Miyake: "Inverse Galois Problem for Dihedral Groups" to be appear in Number Theory and its Applications. (1998)

K.Hashimoto K.Miyake：“二面群的逆伽罗瓦问题”将出现在《数论及其应用》中。