Data Computation and Software Development in Number Theory by Computers

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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.