2012 Fiscal Year Final Research Report
A New Development of Algorithms for Geometry Theorem Proving by Grobner Bases
| Project/Area Number |
22500004
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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 |
Fundamental theory of informatics
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| Research Institution | University of Tsukuba |
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Principal Investigator |
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| Project Period (FY) |
2010 – 2012
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| Keywords | アルゴリズム / 数式処理 / 計算幾何 |
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| Research Abstract |
We picked up several computational geometry problems, and among them, we succeeded in deriving new formulae for
(1) radius of inscribed polygons, and
(2) extension of Descartes circle theorem for Steiner n-cycles. We investigated both Grobner basis and resultant methods, and found the latter algorithm more effective for these problems. To our best knowledge, the obtained formulae are so complicated that they have never been computed before.
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