Computational Complex Analysis of logarithmic vector fields, singular varieties and Algebraic Analysis Algorithms

2014 Fiscal Year Final Research Report

• Project/Area Number: 24540162
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: University of Tsukuba
• Principal Investigator: TAJIMA Shinichi 筑波大学, 数理物質系, 教授 (70155076)
• Co-Investigator(Kenkyū-buntansha): OHARA Katsuyoshi 金沢大学, 数物科学系, 准教授 (00313635) ; NABESHIMA Katsusuke 徳島大学, ソシオアーツ・アンド・サイエンス研究部, 准教授 (00572629) ; NAKAMURA Yayoi 近畿大学, 理工学部, 准教授 (60388494)
• Co-Investigator(Renkei-kenkyūsha): OAKU Toshinori 東京女子大学, 現代教養学部, 教授 (60152039)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: 複素解析 / 代数解析 / 特異点 / アルゴリズム

Outline of Final Research Achievements

Complex analytic properties of hypersurface isolated singularities are considered in the context of algebraic analysis. An algorithm is constructed for computing Tjurina stratifications, the parameter dependency of Tjurina numbers, standard bases of relevant ideal quotients of semi quasihomogeneous hypersurface isolated singularities with deformation parameters. Polar varieties and logarithmic vector fields associated with hypersurface isolated singularities are studied. A new effective method is obtained for computing logarithmic vector fields associated with hypersurface isolated singularities.
Exact methods for computing generalized eigenvectors of given matrices are studied. An efficient method is constructed for conmuting annihilating polynomials of unit vectors. Efficient algorithms are constructed and also implemented in a computer algebra system for computing eigenvectors and also generalized eigenvectors.

Free Research Field

基礎解析学