Algorithms for D-modules and their applications
| Project/Area Number |
21540200
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Tokyo Woman's Christian University |
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Principal Investigator |
OAKU Toshinori 東京女子大学, 現代教養学部, 教授 (60152039)
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| Project Period (FY) |
2009-04-01 – 2014-03-31
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| Project Status |
Completed (Fiscal Year 2013)
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| Budget Amount *help |
¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2013: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2012: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2011: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2010: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2009: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
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| Keywords | 代数解析 / アルゴリズム / D加群 / 微分方程式 / 超関数 / 代数解析学 / グレブナー基底 / 差分方程式 / ホロノミック関数 / 微分差分方程式 / 局所コホモロジー / 留数 / 解析学 / 積分 / ホロノミック系 / ベルンステイン佐藤イデアル |
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| Research Abstract |
It is a primary purpose of analysis to study a function by using the differential equations which it satisfies. Hence one must find, first of all, the differential equations which a given function satisfies. I applied general algorithms for D-modules (algebraic counterpart of differential equations), which I had introduced, to some specific functions and obtained algorithms for computing the differential equations for functions such as the logarithm of a polynomial and the integral over a domain defined by polynomial inequalities. I also implemented these algorithms by using a Japanese software system.
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Report
(6 results)
Research Products
(33 results)
