Study of General Formula Manipulation System

通用公式操作系统的研究

基本信息

批准号：
62580029
负责人：
SASAKI Tateaki
金额：
$ 1.09万
依托单位：
The Institute of Physical and Chemical Research
依托单位国家：
日本
项目类别：
Grant-in-Aid for General Scientific Research (C)
财政年份：
1987
资助国家：
日本
起止时间：
1987 至 1989
项目状态：
已结题

项目摘要

This research is to study the structure and implementation of general formula manipulation system, which (1) performs higher mathematics, (2) unifies numeric, algebraic, and graphics computations, and (3) is equipped with formula database and its automatic utilization facility.As for (1), the system requires many data types such as algebraic number, algebraic function, set expression, group, etc., in addition to conventional data types such as polynomial and rational function. We determined the data type scheme very carefully, so as to manifest clarity and not to decrease efficiency. Furthermore, we developed a program for automatic generation of many typical top-level procedures, as well as mechanism for unifying similar jobs to a single program. In order to implement algorithms easily without referring to internal data structure, we have prepared many procedures for handling the data abstractly. By these, we succeeded in developing a kernnel of general formula manipulation system which is several times as efficient as REDUCE.As for (2), we devised a simple mechanism of combining FORTRAN programs, Lisp programs, etc. by using the process communication facility of OS. The mechanism has been implemented preliminarily and successfully on UNIX. Furthermore, we constructed several algorithms using both numeric and algebraic methods combinedly. The algorithms can solve some kinds of numerically ill-conditioned problems, and we call them "approximate algebraic algorithms".As for (3), we have found that the indexing method developed in a previous research does not work well for series formulas. So, we improved the indexing so as to work well for series formulas. However, we could not study the automatic utilization of formulas because of lack of time.

本研究的目的是研究通用公式运算系统的结构和实现，该系统（1）执行高等数学，（2）统一数值、代数和图形计算，（3）配备公式数据库及其自动利用设施。对于(1)，除了多项式、有理函数等常规数据类型外，系统还需要代数数、代数函数、集合表达式、群等多种数据类型。我们非常仔细地确定了数据类型方案，以便表现清晰而不降低效率。此外，我们开发了一个自动生成许多典型顶级程序的程序，以及将类似作业统一到单个程序的机制。为了在不参考内部数据结构的情况下轻松实现算法，我们准备了许多抽象处理数据的程序。通过这些，我们成功地开发了一个通用公式处理系统的内核，其效率是 REDUCE 的几倍。对于（2），我们设计了一种通过使用过程通信设施来组合 FORTRAN 程序、Lisp 程序等的简单机制。操作系统的。该机制已在UNIX上初步成功实现。此外，我们结合使用数值和代数方法构建了几种算法。这些算法可以解决一些数值病态问题，我们称之为“近似代数算法”。对于（3），我们发现先前研究中开发的索引方法对于级数公式效果不佳。因此，我们改进了索引，以便更好地适用于级数公式。但由于时间不够，我们未能研究公式的自动运用。