Multidimensional continued fraction algorithm
| Project/Area Number |
22540037
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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 |
Algebra
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| Research Institution | Toho University (2012-2013)
Suzuka National College of Technology (2010-2011) |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
TAMURA Jun-ichi 津田塾大学, 付置研究所, 研究員 (90418905)
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| Project Period (FY) |
2010-04-01 – 2014-03-31
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| Project Status |
Completed (Fiscal Year 2013)
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| Budget Amount *help |
¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | 連分数 / 単数 / 高次元連分数 / substitution / stepped surface / タイリング / 高次元連分数展開 / 基本単数 / 高次元連分数アルゴリズム / Farey分割 / 同時近似問題 |
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| Research Abstract |
We were able to suggest a new class of multidimensional continued fraction algorithms, which improve our algorithms that we have studied. The numerical experiments support the extension of classical results of the Lagrange theorem
for the number field of degree less than 7 and the generation of fundamental units in number fields of degree less than 5. We have fundamental results about the relation between the class of algorithms and substitutions on two dimensional stepped surfaces.
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Report
(5 results)
Research Products
(33 results)
