Computational complex analysis and algebraic analysis of singularities
| Project/Area Number |
15K04891
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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 |
Basic analysis
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| Research Institution | University of Tsukuba |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
福井 敏純 埼玉大学, 理工学研究科, 教授 (90218892)
山崎 晋 日本大学, 理工学部, 教授 (00349953)
鍋島 克輔 徳島大学, 大学院社会産業理工学研究部(理工学域), 准教授 (00572629)
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| Co-Investigator(Renkei-kenkyūsha) |
Oaku Toshinori 東京女子大学, 現代教養学部, 教授 (60152039)
Shibuta Takafumi 九州産業大学, 理工学部, 講師 (40648200)
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| Research Collaborator |
Umeta Yoko 山口大学, 創成科学研究科, 助教 (90606386)
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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 |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2017: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2016: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2015: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
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| Keywords | 複素解析 / 代数解析 / 特異点 / アルゴリズム / D-加群 / 局所コホモロジー / スタンダード基底 / integral number / ホロノミーD-加群 / Le numbers / b-関数 / 対数的ベクトル場 |
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| Outline of Final Research Achievements |
Based on the theory of algebraic analysis and computer algebra, complex analytic aspects of singularities are considered. Main results of our study are (i) an extended ideal membership algorithm in a ring of convergent power series. (ii) algorithms for computing integral numbers, and generalized integral dependence relations of an ideal in a local ring, (iii) algorithms for computing logarithmic vector fields and Bruce-Roberts Milnor numbers, (iv) an algorithm for computing b-functions and relevant holonomic D-modules associated to a hypersurface, (v) an algorithm for computing generic Le numbers.
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Report
(4 results)
Research Products
(70 results)
