| Project/Area Number |
15K17592
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Foundations of mathematics/Applied mathematics
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| Research Institution | Tokai University |
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Principal Investigator |
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| Project Period (FY) |
2015-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Fiscal Year 2017: ¥520,000 (Direct Cost: ¥400,000、Indirect Cost: ¥120,000)
Fiscal Year 2016: ¥520,000 (Direct Cost: ¥400,000、Indirect Cost: ¥120,000)
Fiscal Year 2015: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
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| Keywords | グレブナー基底 / 超幾何関数 / 超幾何微分方程式 / 計算代数 |
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| Outline of Final Research Achievements |
To execute algorithms in D-modules, we need to obtain Groebner bases for ideals in the ring of differential operators. We have algorithms to compute Groebner bases, but for systems of differential equations including many variables or n variables, we cannot execute the algorithms.
In this research, we theoretically compute Groebner bases for systems of multivariable hypergeometric differential equations without computer. By using these Groebner bases we derive characteristic varieties, singular locus and Pfaffian systems for systems of multivariable hypergeometric differential eqautions.
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