Research on Formula Manipulation Expert System Based on Database of Mathematical Formulas

在本研究中，我们基本确立了数学公式数据库的构建方法，明确了数学公式数据库的有效性。1)找到了一种简单有效的数学公式索引方法；2)确定了一个简洁实用的语句供用户访问数据库；3)实现了一种高效的检索方法，并用大量公式进行了测试；4)开发了一个可以接受多种形式的公式的解析器；5)实现了一个通用的数学公式简化模式匹配器；6)给出了数学公式数据库的构建方法和有效性。特别是，我们的数据库检索方法不仅根据公式中包含的函数名检索数学公式，而且还检索公式的模式和性质，检索方式类似于从公式教科书中手工检索。但由于批准的研究术语较短，本研究在以下几个方面尚未完成研究：1)按人名、公式或科学学科和领域检索数据库；2)公式教科书中公式的重新排列；3)将数据库与计算机代数系统GA连接起来。由于公式数据库本身价值不高，但在计算积分、求解微分方程、简化数学表达式等方面有很大的应用价值。因此，在我们的研究基础上，公式数据库的应用在不久的将来将成为公式操作的一个重要主题。

We have almost established the construction method and clarified the effectiveness of database of mathematical formulas in this research. The items performed in this research are as follows:1) We found a simple and very effective indexing method for mathematical formulas; 2) We decided a concise and useful sentence for the user access to the databese; 3) We implemented an efficient retrieval method and tested it with many formulas; 4) We developed a parser which accepts quite many formulas in various forms; 5) We implemented a pattern matcher for general simplification of mathematical expressions; 6) We showed a construction method and effectiveness of database of mathematical formulas.In particular, our database retrieval method is such that the mathematical formulas are retrieved by not only the function names included in each formula but also the pattern and property of the formula, and that the retrieval is done in a similar way as the hand retrieval from formula textbooks.However, the research has not finished in the following points because of shortness of the research term approved:1) Retrieval of database by names of persons, formulas, or scientific subjects and fields; 2) Rearrangement of formulas in formula textbook; 3) Connecting the database with the computer algebra system GAL.These works are being carried out now.Since the formula database is not so worthy by itself but it becomes very useful when it is applied to calculating integrals, solving differential equations, simplifying mathematical expressions, and so on. Therefore, on the basis of our research, the application of formula database will become an important theme of formula manipulation in a very near future.