Data Computation and Software Development in Number Theory by Computers

本研究的目的是利用已知的定理和方法，在初等数论、代数数域和椭圆曲线计算机上计算不变量，从而获得实际的数据积累，为构建通用的数论工具（TNT）系统奠定理论基础。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中的计算机计算研究，包括环论或代数几何。我们研究的一个重要特点是除了文件传输服务外，还实际使用了邮件列表TNT-ML。在第一年，我们收集了一些数据和程序，计算和编写到现在，并重新安装了TNT-SERVER，通过网络分发结果。新的TNT-SERVER结合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，设计了一种相互联系的方法，并组织了“第三届代数与计算大会”研讨会，讨论了TNT-SYSTEM（预发布）的基本设计。总结以上的计算和学习，我们已经基本完成了一个关于数论基本算法和表的数据库的基本准备工作。此外，我们还准备分析该领域中必要的算法和重要的表，并展示了构建通用计算机代数系统TNT-SYSTEM的实际可能性。

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.