Data Computation and Software Development in Number Theory by Computers

这项研究的目的是利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，从而获得实际的数据积累并建立理论基础，以构建数论或TNT的通用系统工具。这两年的研究进展超越了最初主要在数论中规划的领域，广泛地扩展到一般代数中的计算机计算的研究，包括环论或代数几何。我们研究的一个显著特点是除了文件传输服务之外，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计算和编写的程序，并重新安装了TNT-SERVER，通过网络发布结果。新的TNT-SERVER将邮件列表、匿名ftp和万维网的三个服务器组合在一起。在第二年，我们对这些数据和软件进行了整理和分类，设计了一种方法将它们联系起来，并组织了一次研讨会，讨论TNT系统(预发行)的基本设计。总结以上的计算和研究，我们基本完成了基本算法数据库和数论表格的准备工作。此外，我们已经准备好分析这一领域所需要的算法和重要的表，并展示了为软件和数据库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.