数学研究支援のための自己学習型数式処理系の設計と開発

支持数学研究的自学习公式处理系统的设计与开发

• 批准号: 09874010
• 负责人: 野海 正俊
• 金额: $ 1.41万
• 依托单位: Kobe University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Exploratory Research
• 财政年份: 1997
• 资助国家: 日本
• 起止时间: 1997 至 1998
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09874010/
• 关键词: 数式処理; グレプナ基底; ネットワーク

本研究では,自己学習型の数式処理系の設計・開発を目標としつつ,数学研究の現状に照らし合わせて,その支援のための数式処理系のあり方についての検討を行った.その要点は,(1)無限個の変数や非可換な変数を含む数式処理の実際的研究と,(2)複数の数式処理システム間で数式データを相互にやりとりするためのプロトコルの問題,の2点である.研究代表者は,主に(1)を担当し,非線形の可積分な微分・差分方程式系と,Lie環とWeyl群の表現の研究における数式処理の実践を通じて,無限変数の問題の雛形として微分多項式のグレプナ基底について,また非可換変数の問題の雛形としてCoxeter群の数式処理について,実際的アルゴリスムの検討を行った.その成果についてはもう少し完成度を高めた上で公表したい.研究分担者は主に(2)を担当し,分散数式処理系のプロトコルである,openXMの設計と実装を行い,Risa/AsirとKan/smlの間で数式処理系のネットワークを実現した.当初の研究課題の実現には未だ遠いが,そのための第一歩を踏み出すことができたと思う.

In the course of this study, the design of the Department of Mathematical Science, the design of the Department of Mathematical Science, the program of mathematical research, the combination of mathematical research, and the support of the Department of Mathematical Science, the Department of Mathematical Science. In this paper, the main points are as follows: (1) there is no limit to the number of non-linear variables, including the study of mathematical mathematics, (2) complex mathematical models, mathematical equations, mathematical models, mathematical models, mathematical models The representative of the research, the principal (1) is responsible for the system of differential and difference equations of non-linear equations, the Lie environment Weyl group shows the research of mathematical equations, mathematical equations, mathematical practice, unlimited numerical problems, numerical problems, differential multinomial problems, basic mathematical problems, non-scalable problems, mathematical equations, Coxeter group problems, mathematical equations, mathematical equations, numerical The international market is in full swing. The results show that there is a high degree of completion and a high degree of completion. The research contributor (2) is responsible for the research, the distributed data management system is based on the data management system, the openXM software is used to design the industry, and the Risa/Asir Kan/sml system is used to analyze the performance of the system. At the beginning, the research project has not yet been completed, and the first step of the research project is to think about it.

项目成果

M.Noumi: "Higher order Painleve equations of type A^<(1)>_l" Funkcial.Ekvac.41. 483-503 (1998)

M.Noumi：“A^<(1)>_l 类型的高阶 Painleve 方程”Funkcial.Ekvac.41。

M.Saito: "Hypergeometric polynomials and Integer Programming" Compositio Math.(to appear). (1999)

M.Saito：“超几何多项式和整数规划”复合数学（即将出现）。

M.Noumi: "Symmetries in the fourth Painleve equation and Okamoto polynomials" Nagoya Math.J.(to appear). (1999)

M.Noumi：“第四 Painleve 方程和冈本多项式中的对称性”Nagoya Math.J.（即将出现）。

M.Noumi and Y.Yamada: "Symmetries in the fourth Painleve equation and Okamoto polynomials" Nagoya Math,J.(to appear).

M.Noumi 和 Y.Yamada：“第四 Painleve 方程和冈本多项式中的对称性”Nagoya Math,J.（即将出现）。

M.Noumi: "Notes on the flat structures associated with simple and simply elliptic singularities" Proceedings of the Taniguchi Symposium 1997:"Integrable Systems and Algebraic Geometry"(eds.M.-H.Saito et al),World Scientific. 373-383 (1998)

M.Noumi：“关于与简单和简单椭圆奇点相关的平面结构的注释”1997 年谷口研讨会论文集：“可积系统和代数几何”（eds.M.-H.Saito 等人），世界科学。