| Project/Area Number |
24540040
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Kyoto University of Education |
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Principal Investigator |
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| Project Period (FY) |
2012-04-01 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Fiscal Year 2014: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2012: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
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| Keywords | サグビー基底 / 不変式 / 高次元配列 / テンソル / グレブナー基底 / 行列式イデアル / 不変式論 |
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| Outline of Final Research Achievements |
Sagbi basis is an analogue of Groebner basis for ideals, which is very widely investigated by many researchers in these days.
In this research, we investigated the action of groups to high dimensional array of datum, which is called a tensor and is widely investigated by many researchers in relation to data analysis, and the ring of invariants with respect to this group action. And we have succeeded in some cases of 3-dimensional tensors, finding the sagbi basis of the ring of invariants and therefore the ring of invariants under the action of special linear groups.
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