2006 Fiscal Year Final Research Report Summary
Computational Analysis of Hypergeometric Differential Equations
| Project/Area Number |
15340045
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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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 | KOBE UNIVERSITY |
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Principal Investigator |
TAKAYAMA Nobuki Kobe University, Faculty of Science, Professor, 理学部, 教授 (30188099)
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| Co-Investigator(Kenkyū-buntansha) |
NORO Masayuki Kobe University, Faculty of Science, Professor, 理学部, 教授 (50332755)
FUKUYAMA Katsushi Kobe University, Faculty of Science, Professor, 理学部, 教授 (60218956)
MASUDA Tetsu Kyoto University, Graduate School of Science, COE Researche, 理学研究科, COE研究員 (00335457)
OAKU Toshinori Tokyo Women's Christian University, Faculty of Literature and Science, Professor, 文理学部, 教授 (60152039)
SAITO Mutsumi Hokaido University, Graduate School of Science, Associate Profsor, 理学研究科, 助教授 (70215565)
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| Project Period (FY) |
2003 – 2006
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| Keywords | A-hypergeometric function / A-hypergeometric equation / D-modules / Computational D-modules / Grobner basis / Mathematical formula / Special function / random numbers and integration |
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| Research Abstract |
We have obtained the following results
1. We constructed vol(A)-linearly independent convergent series solutions for A-hypergeometric differential-difference equations.
2. We prove that any local Grober fan is a polyhedral fan. As an application of this fact, we give an algorithm of computing local BS polynomials, that of computing local tropical varieties, and discuss a relation of slopes and local Grobner fan.
3. We gave a tangent cone algorithm to study D-modules locally.
We have more results. As to these, refer to Japanese version of this research report and papers.
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