| Project/Area Number |
18340008
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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 |
Algebra
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| Research Institution | Osaka University |
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Principal Investigator |
HIBI Takayuki Osaka University, 大学院・情報科学研究科, 教授 (80181113)
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| Co-Investigator(Kenkyū-buntansha) |
SAITO Mutsumi 北海道大学, 大学院・理学研究院, 准教授 (70215565)
TAKEMURA Akimichi 東京大学, 大学院・情報理工学系研究科, 教授 (10171670)
YOKOYAMA Kazuhiro 立教大学, 理学部, 教授 (30333454)
OHSUGI Hidefumi 立教大学, 理学部, 准教授 (80350289)
OAKU Toshinori 東京女子大学, 文理学部, 教授 (60152039)
MATSUI Yasuko 東海大学, 理学部, 准教授 (10264582)
SAITO Kyoji 東京大学, 数物連携宇宙機構, 主任研究員 (20012445)
TAKAYAMA Nobuki 神戸大学, 理学部, 教授 (30188099)
AOKI Satoshi 鹿児島大学, 理学部, 准教授 (90332618)
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| Project Period (FY) |
2006 – 2009
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| Project Status |
Completed (Fiscal Year 2009)
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| Budget Amount *help |
¥15,850,000 (Direct Cost: ¥13,600,000、Indirect Cost: ¥2,250,000)
Fiscal Year 2009: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2008: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2007: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2006: ¥6,100,000 (Direct Cost: ¥6,100,000)
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| Keywords | グレブナー基底 / 計算可換代数 / 計算代数解析 / 計算代数統計 / 凸多面体 / イニシャルイデアル / マルコフ基底 / 分割表 / アルゴリズム / トーリックイデアル / グレブナ-基底 / D加群 / generic initial ideal / 計算の効率化 / 凸多面体の組合せ論 |
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| Research Abstract |
With taking the persistence and the internationalization into consideration, in collaboration with many researchers in various field including computational commutative algebra, computational algebraic analysis, computational algebraic statistics as well as algebraic algorithm, this research project strongly developed the study on the theoretical effectivity and practical effectivity of Grobner bases and succeeded in establishing the foundations of the modern theory of Grobner bases. At present, in order for our research group to be one of the strongest international footholds on the theoretical and practical research of Grobner bases, the CREST research project "Harmony of Grobner bases and the modern industry society," whose team leader is Takayuki Hibi, which is supported by JST (Japan Science and Technology Agency) follows this research project.
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