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2017 Fiscal Year Final Research Report

Computational complex analysis and algebraic analysis of singularities

Research Project

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Project/Area Number 15K04891
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Basic analysis
Research InstitutionUniversity of Tsukuba

Principal Investigator

Tajima Shinichi  筑波大学, 数理物質系, 教授 (70155076)

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)
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)
Research Collaborator Umeta Yoko  山口大学, 創成科学研究科, 助教 (90606386)
Project Period (FY) 2015-04-01 – 2018-03-31
Keywords複素解析 / 代数解析 / 特異点 / アルゴリズム
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.

Free Research Field

解析学基礎

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Published: 2019-03-29  

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