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.

这项研究是为了研究一般公式操作系统的结构和实施，（1）执行更高的数学，（2）统一数字，代数和图形计算，（3）配备了公式数据库及其自动利用设施。例如多项式和有理功能。我们非常仔细地确定了数据类型方案，以表现出清晰度而不降低效率。此外，我们开发了一个程序，用于自动生成许多典型的顶级程序，以及将类似工作统一工作与单个程序相似的机制。为了轻松实现算法而无需参考内部数据结构，我们准备了许多抽象处理数据的过程。通过这些，我们成功地开发了一个通用公式操纵系统的内核，该系统的效率是（2）的几倍。该机制已在UNIX上最初和成功实施。此外，我们使用数字和代数方法构建了几种算法。这些算法可以解决某些数字条件不良的问题，我们称它们为“近似代数算法”。作为（3），我们发现先前研究中开发的索引方法对串联公式不太有效。因此，我们改进了索引，以便在串联公式方面正常工作。但是，由于缺乏时间，我们无法研究公式的自动利用。