1986 Fiscal Year Final Research Report Summary
Research on Formula Manipulation Expert System Based on Database of Mathematical Formulas
| Project/Area Number |
60580033
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
Informatics
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| Research Institution | The Institute of Physical and Chemical Research |
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Principal Investigator |
SASAKI Tateaki The Institute of Physical and Chemical Research (Researcher), その他, 研究員 (80087436)
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| Co-Investigator(Kenkyū-buntansha) |
MASUNAGA Yoshifumi University of Library and Information Science (Assistant Professor), 図書館情報学部, 助教授 (70006261)
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| Project Period (FY) |
1985 – 1986
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| Keywords | Mathematical formula / Database / Automatic application of formulas / Formula manipulation / 数式の簡単化 |
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| 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.
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Research Products
(10 results)
