Research on Formula Manipulation Expert System Based on Database of Mathematical Formulas
Project/Area Number 
60580033

Research Category 
GrantinAid for General Scientific Research (C)

Allocation Type  Singleyear Grants 
Research Field 
Informatics

Research Institution  The Institute of Physical and Chemical Research 
Principal Investigator 
SASAKI Tateaki The Institute of Physical and Chemical Research (Researcher), その他, 研究員 (80087436)

CoInvestigator(Kenkyūbuntansha) 
MASUNAGA Yoshifumi University of Library and Information Science (Assistant Professor), 図書館情報学部, 助教授 (70006261)

Project Period (FY) 
1985 – 1986

Project Status 
Completed (Fiscal Year 1986)

Budget Amount *help 
¥1,600,000 (Direct Cost: ¥1,600,000)
Fiscal Year 1986: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 1985: ¥800,000 (Direct Cost: ¥800,000)

Keywords  Mathematical formula / Database / Automatic application of formulas / Formula manipulation / 数式の簡単化 
Research Abstract 
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.

Report
(1 results)
Research Products
(10 results)