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

Research Project

Project/Area Number 60580033
Research Category

Grant-in-Aid for General Scientific Research (C)

Allocation TypeSingle-year Grants
Research Field Informatics
Research InstitutionThe 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)

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)
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)
KeywordsMathematical 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)
  • 1986 Final Research Report Summary
  • Research Products

    (10 results)

All Other

All Publications (10 results)

  • [Publications] 増永良文,阿部昭博,元吉文男,佐々木建昭: 数式処理通信. 3. 16-21 (1985)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] 佐々木建昭,元吉文男: 数式処理通信. 4. 6-18 (1986)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] 佐々木建昭: Proceedings of SYMSAC'86(ACM). 115-120 (1986)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] 三枝義典,増永良文,佐々木建昭,佐々木睦子: 数式処理通信. (1987)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] 佐々木建昭,元吉文男,渡辺隼郎: "数式処理システム(ソフトウェア講座第36巻)" 昭晃堂, 207 (1986)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] Yoshifumi Masunaga, Akihiro Abe, Fumio Motoyoshi, Tateaki Sasaki: "Database of Mathematical Formulas in GAL (in Japanese)" Sushikishori-Tsushin. 3. 16-21 (1985)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] Tateaki Sasaki, Fumio Motoyoshi: "Japanese Computer Algebra System GAL (in Japanese)" Sushikishori-Tsushin. 4. 6-18 (1986)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] Tateaki Sasaki: "Simplification of Algebraic Expressions by Multiterm Rewriting Rules" Proceedings of SYMSAC'86 (ACM). 115-120 (1986)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] Yoshinori Saigusa, Yoshifumi Masunaga, Tateaki Sasaki, Mutsuko Sasaki: "Database of Mathematical Formulas in Japanese Computer Algebra System GAL --- Preliminary Report --- (in Japanese)" Sushikishori-Tsushin. 5. (1987)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] Tateaki Sasaki, Fumio Motoyoshi, Shunro Watanabe: Shoukoudo. Formula Manipulation System (Software Science Series No.36) (in Japanese), 207 (1986)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1986 Final Research Report Summary

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Published: 1987-03-31   Modified: 2016-04-21  

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