Tajima Shinichi

Profile Information

Affiliation: Niigata University

Degree: 理学博士(東京大学)

J-GLOBAL ID: 200901053358736585
researchmap Member ID: 1000018722

Research Areas

Natural sciences / Basic analysis /

Research History

Jan, 2010

Graduate School of Pure and Applied Sciences, University of Tsukuba
Apr, 2003 - Jan, 2010

Faculty of Engineering, Niigata University
Apr, 1994 - Mar, 2003

Faculty of Engineering, Niigata University
Jan, 1993 - Mar, 1994

Niigata University
Jul, 1982 - Jan, 1993

Niigata University
Jan, 1990 - Aug, 1990

maitre de conference, Universite de Paris Nord

Education

Apr, 1978 - Mar, 1981

数学専攻, 理学系研究科, 東京大学大学院
Apr, 1976 - Mar, 1978

数学専攻, 理学系研究科, 東京大学大学院
Apr, 1971 - Mar, 1976

Faculty of Science, Tokyo Institute of Technology

Papers

225

Effective Algorithm for Computing Noetherian Operators of Positive Dimensional Ideals

Katsusuke Nabeshima, Shinichi Tajima

Computer Algebra in Scientific Computing, 272-291, Aug 24, 2023
Computing holonomic D-modules associated to a family of non-isolated hypersurface singularities via comprehensive Gröbner systems of PBW algebra

Shinichi Tajima, Katsusuke Nabeshima, Katsuyoshi Ohara, Yoko Umeta

Mathematics in Computer Science, 17(1), Mar, 2023 Peer-reviewed
CSSg method for several genericities of parametric systems

Katsusuke Nabeshima, Shinichi Tajima

Japan Journal of Industrial and Applied Mathematics, Jul 14, 2022
An effective method for computing Grothendieck point residue mappings

Shinichi Tajima, Katsusuke Nabeshima

Journal of Algebra, 593 568-588, Mar, 2022
Computing Regular Meromorphic Differential Forms via Saito's Logarithmic Residues

Shinichi Tajima, Katsusuke Nabeshima

Symmetry, Integrability and Geometry: Methods and Applications, Feb 27, 2021
零次元準素イデアルのネター作用素の計算と応用

鍋島克輔, 田島慎一

京都大学数理解析研究所講究録, 2185 1-15, 2021
A New Deterministic Method for Computing Milnor Number of an ICIS

Shinichi Tajima, Katsusuke Nabeshima

Computer Algebra in Scientific Computing, 391-408, 2021
Testing Zero-Dimensionality of Varieties at a Point

Katsusuke Nabeshima, Shinichi Tajima

Mathematics in Computer Science, Jun 5, 2020
An Algorithm for Computing Torsion Differential Forms Associated with an Isolated Hypersurface Singularity

Shinichi Tajima, Katsusuke Nabeshima

Mathematics in Computer Science, Jun 5, 2020
An Algorithm for Computing Grothendieck Local Residues II: General Case

Katsuyoshi Ohara, Shinichi Tajima

Mathematics in Computer Science, 14(2) 483-496, Jan 14, 2020
Moving curve ideals, Rees algebra and parametric local cohomology systems

田島慎一, 鍋島克輔

京都大学数理解析研究所講究録, 2159 179-187, 2020
Computing Logarithmic Vector Fields Along an ICIS Germ via Matlis Duality.

Shinichi Tajima, Takafumi Shibuta, Katsusuke Nabeshima

Computer Algebra in Scientific Computing - 22nd International Workshop(CASC), 543-562, 2020
An algorithm for computing the Hilbert-Samuel multiplicities and reductions of zero-dimensional ideals of Cohen-Macaulay local rings.

Takafumi Shibuta, Shinichi Tajima

J. Symb. Comput., 96 108-121, 2020 Peer-reviewed
Computing logarithmic vector fields and Bruce-Roberts Milnor numbers via local cohomology classes

Katsusuke Nabeshima, Shinichi Tajima

64(4) 521-538, Dec, 2019 Peer-reviewed
Alternative algorithms for computing generic μ ∗ -sequences and local Euler obstructions of isolated hypersurface singularities

Katsusuke Nabeshima, Shinichi Tajima

Journal of Algebra and its Applications, 18(8), Aug, 2019 Peer-reviewed
Solving Parametric Ideal Membership Problems and Computing Integral Numbers in a Ring of Convergent Power Series Via Comprehensive Gröbner Systems

Katsusuke Nabeshima, Shinichi Tajima

Mathematics in Computer Science, 13(1) 185-194, Jun, 2019 Peer-reviewed
An Implementation of the Lê–Teissier Method for Computing Local Euler Obstructions

Shinichi Tajima, Katsusuke Nabeshima

Mathematics in Computer Science, 13(1) 273-280, Jun, 2019 Peer-reviewed
パラメータ付きイデアルで定義された多様体の点でのゼロ次元性判定

鍋島克輔, 田島慎一

京都大学数理解析研究所講究録, 2138 130-137, 2019
Comprehensive Gröbner systems in PBW algebras, Bernstein–Sato ideals and holonomic D-modules

Katsusuke Nabeshima, Katsuyoshi Ohara, Shinichi Tajima

Journal of Symbolic Computation, 89 146-170, Nov, 2018 Peer-reviewed
A new method for computing the limiting tangent space of an isolated hypersurface singularity via algebraic local cohomology

Katsusuke Nabeshima, Shinichi Tajima

Advanced Studies in Pure Mathematics, 78 331-331, Sep, 2018 Peer-reviewed

Misc.

多項式函数のbifurcation setの計算法(1)—Methods for computing the bifurcation set of a polynomial function(1)—Computer Algebra : Foundations and Applications

田島慎一, 鍋島克輔

数理解析研究所講究録, (2255) 88-95, Jun, 2023
正次元イデアルのネター作用素の計算と特異点—Noetherian operators of positive dimensional ideals and hypersurface singularities—Computer Algebra : Foundations and Applications

鍋島克輔, 田島慎一

数理解析研究所講究録, (2255) 75-87, Jun, 2023
CSSg method for several genericities of deformations of hypersurface singularities—可微分写像の特異点論及びその応用

鍋島克輔, 田島慎一

数理解析研究所講究録, (2226) 1-15, Jul, 2022
ネター作用素を用いた零次元イデアルの準素イデアル分解と復元—日本数式処理学会第30回大会報告

鍋島克輔, 田島慎一

数式処理 = Bulletin of the Japan Society for Symbolic and Algebraic Computation, 28(1) 28-31, Apr, 2022
最小消去多項式を用いた一般固有ベクトル空間の構成—日本数式処理学会第30回大会報告

田島慎一, 小原功任, 照井章

数式処理 = Bulletin of the Japan Society for Symbolic and Algebraic Computation, 28(1) 32-35, Apr, 2022
有理関数体上の包括的スタンダード基底系を用いた特異点変形による不変量計算について—日本数式処理学会第29回大会報告

鍋島克輔, 田島慎一

数式処理 = Bulletin of the Japan Society for Symbolic and Algebraic Computation, 27(2) 41-44, Aug, 2021
孤立特異点を持つcomplete intersectionに沿う対数的ベクトル場の計算法について (可微分写像の特異点論とその応用)

田島慎一, 渋田敬史, 鍋島克輔

数理解析研究所講究録, (2156) 1-15, May, 2020
An algorithm for computing generalized integral dependence relations in a ring of convergent power series

鍋島克輔, 田島慎一

数理解析研究所講究録, (2104) 78-85, Feb, 2019
超曲面の孤立特異点に沿った対数的ベクトル場と応用 (第27回日本数式処理学会大会報告)

鍋島克輔, 田島慎一

数式処理 = Bulletin of the Japan Society for Symbolic and Algebraic Computation, 25(1) 83-86, Jan, 2019
収束冪級数環におけるintegral numberの計算法 (第26回日本数式処理学会大会報告)

鍋島克輔, 田島慎一

数式処理 = Bulletin of the Japan Society for Symbolic and Algebraic Computation, 24(2) 13-16, May, 2018
Fast Algorithm for Calculating the Minimal Annihilating Polynomials of Matrices via Pseudo Annihilating Polynomials

Shinichi Tajima, Katsuyoshi Ohara, Akira Terui

Jan 26, 2018
Tangent coneを用いた局所環でのパラメトリック・イデアルの次元判定 (合同分科会報告)

鍋島克輔, 田島慎一

数式処理 = Bulletin of the Japan Society for Symbolic and Algebraic Computation, 24(1) 50-53, Jan, 2018
グレブナー基底を用いた収束冪級数環での拡張イデアル所属アルゴリズムについて (数式処理とその周辺分野の研究)

鍋島克輔, 田島慎一

数理解析研究所講究録, (2054) 118-125, Oct, 2017
パラメトリック局所コホモロジーを用いたμ[*]の計算 (第25回日本数式処理学会大会報告)

鍋島克輔, 田島慎一

数式処理 = Bulletin of the Japan Society for Symbolic and Algebraic Computation, 23(2) 89-91, May, 2017
マトリス双対を用いた有限なcolengthを持つ加群の被約標準基底の計算アルゴリズム (第25回日本数式処理学会大会報告)

渋田敬史, 田島慎一

数式処理 = Bulletin of the Japan Society for Symbolic and Algebraic Computation, 23(2) 85-88, May, 2017
代数的局所コホモロジーを用いたスタンダード基底の項順序変換について(2) (第24回日本数式処理学会大会報告)

鍋島克輔, 田島慎一

数式処理, 22(2) 59-62, May, 2016
代数的局所コホモロジーを用いたスタンダード基底の項順序変換について (第23回日本数式処理学会大会報告)

鍋島克輔, 田島慎一

数式処理, 21(2) 56-59, Aug, 2015
マトリス双対定理を用いた代数的コホモロジー類の満たす偏微分方程式系の計算アルゴリズム (第23回日本数式処理学会大会報告)

渋田敬史, 田島慎一

数式処理, 21(2) 52-55, Aug, 2015
On $b$-functions and algebraic local cohomology classes attached to hypersurfaces with line singularities : Dedicated to Professor Takashi Aoki on the occasion of his sixtieth birthday (Exponential Analysis of Differential Equations and Related Topics)

Tajima Shinichi

RIMS Kokyuroku Bessatsu, 52 175-191, Nov, 2014
最小消去多項式候補を用いた行列の一般固有空間の構造の計算アルゴリズム (数式処理とその周辺分野の研究)

小原功任, 田島慎一

数理解析研究所講究録, 1907 62-70, Jul, 2014

Books and Other Publications

SINGULARITIES IN GEOMETRY AND TOPOLOGY 2011

Nabeshima, Katsusuke, Tajima, Shinichi

MATH SOC JAPAN, 2015 (ISBN: 9784864970266)
Analyse microlocale sur les varietes de Cauchy-Riemann et problemes du prolongement des solutions holomorphes des equations aux derivees partielles

Tajima,Shinichi

Mar, 1981

Presentations

Integral dependence relation と半擬斉次孤立特異点の $b$-関数

Tajima, Shinichi, 鍋島克輔

日本数学会函数論分科会, Sep 11, 2017
収束冪級数環でのintegral numberの計算グレブナー基底 vs 代数的局所コホモロジー類

Tajima, Shinichi, 加藤満生, 鍋島克輔

日本数学会函数論分科会, Sep 11, 2017
Transformation law による Grothendieck local residue の計算

Tajima, Shinichi, 鍋島克輔

日本数学会函数論分科会, Sep 11, 2017
b-関数の根に付随したホロノミー系の局所コホモロジー解の計算

Tajima, Shinichi, 鍋島克輔

数式処理の新たな発展--その最新研究, Sep 6, 2017
Local cohomology, Grothendieck local residues and algorithms,

Tajima,Shinichi

Workshop on Rresidues, dynamics and hyperfunctions, Jul 24, 2017 Invited
An algorithm for computing Grothendieck local residues I -- shape basis case --

Tajima, Shinichi, Ohara, K

Applications of Computer Algebra 2017, Jul 16, 2017
Computing integral numbers for a parametric ideal in a ring of convergent power s eries via comprehensive Gröbner systems

Tajima, Shinichi, Nabeshima, Katsusuke

Applications of Computer Algebra 2017, Jul 16, 2017
An implementation of the Lê -Teissier method for computing local Euler obstructions

Tajima, Shinichi, Nabeshima, Katsusuke

Applications of Computer Algebra 2017, Jul 16, 2017
Local Euler obstruction の計算法について

Tajima,Shinichi

日本数式処理学会, Jun 9, 2017
収束冪級数環における integral number の計算法について

Tajima, Shinichi, 鍋島克輔

日本数式処理学会, Jun 9, 2017
Generic Lê numbers の計算アルゴリズムとホロノミーD-加群

Tajima,Shinichi

微分幾何学と特異点論の応用, Jun 1, 2017
包括的グレブナー基底系を用いた$\mu$-stratification と$\mu^{\ast}$列の計算法について

Tajima, Shinichi, 鍋島克輔

Risa/Asir Conference, Mar 28, 2017
マトリス双対を用いた孤立特異点の不変量の計算

Tajima, Shinichi, 渋田敬史

日本数学会, 函数論分科会, Mar 24, 2017
パラメータ付きBernstein-SatoイデアルとホロノミーD加群の計算

Tajima, Shinichi, 鍋島克輔, 小原功任

日本数学会, 函数論分科会, Mar 24, 2017
多変数留数の計算アルゴリズム II (一般の場合)

Tajima, Shinichi, 小原功任

日本数学会, 函数論分科会, Mar 24, 2017
Computation method for $ \mu^{\ast} $-sequences of hypersurface isolated singularities

Tajima, Shinichi, Nabeshima, Katsusuke

Topology of Singularity in Hanoi, Feb 21, 2017
Tangent cone を用いた局所環でのパラメトリックイデアルの次元判定

Tajima, Shinichi, 鍋島克輔

数式処理学会合同分科会, Jan 21, 2017
特異点の計算複素解析 -- 留数, Samuel multiplicity, Chern-Schwartz-MacPherson class --

Tajima,Shinichi

多変数関数論冬セミナ, Dec 15, 2016
多変数留数の計算アルゴリズム II (一般の場合)

Tajima, Shinichi, 小原功任

数式処理とその周辺分野の研究, Dec 7, 2016
b-関数の因子チェックを用いたパラメータ付きb-関数の計算 -$\mu$-constant deformation の場合-

Tajima, Shinichi, 鍋島克輔

数式処理とその周辺分野の研究, Dec 7, 2016

Professional Memberships

Research Projects

Algebraic analysis of deformations of non-isolated singularities, computational complex analysis and algorithms

Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (C), Japan Society for the Promotion of Science, Apr, 2022 - Mar, 2027
Algebraic aanalysis of non-isolated singularities and computational complex analysis algorithms

Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (C), Japan Society for the Promotion of Science, Apr, 2018 - Mar, 2022

Tajima Shinichi
Singular statistics and computational algebraic analysis of machine learning models

Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (C), Japan Society for the Promotion of Science, Jul, 2015 - Mar, 2018

Tajima Shinichi, Hasegawa Makoto
Residue theory on singular varieties and its applications

Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (C), Japan Society for the Promotion of Science, Apr, 2012 - Mar, 2017

SUWA Tatsuo, ASUKE Taro, OHMOTO Toru, OKA Mutsuo, TAKEUCHI Kiyoshi, TAJIMA Shinichi, NAKAMURA Yayoi, YOKURA Shoji
Computational Complex Analysis of logarithmic vector fields, singular varieties and Algebraic Analysis Algorithms

Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (C), Japan Society for the Promotion of Science, Apr, 2012 - Mar, 2015

TAJIMA Shinichi, OHARA Katsuyoshi, NABESHIMA Katsusuke, NAKAMURA Yayoi, OAKU Toshinori
Algorithms for systems of parametric polynomials

Grants-in-Aid for Scientific Research, Grant-in-Aid for Young Scientists (B), Japan Society for the Promotion of Science, 2010 - 2012

NABESHIMA Katsusuke, TAJIMA Shinichi
Algebraic analysis of algebraic local cohomology and computational complex analysis of non-isolated singularities

Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (C), Japan Society for the Promotion of Science, 2009 - 2011

TAJIMA Shinichi, NAKAMURA Yayoi, OHARA Katsuyoshi, MATSUI Yutaka
Localization theory of Atiyah classes and its applications

Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (C), Japan Society for the Promotion of Science, 2009 - 2011

SUWA Tatsuo, OHMOTO Toru, OKA Mutsuo, KAWAZUMI Nariya, TAKEUCHI Kiyoshi, TAJIMA Shinichi, NAKAMURA Yayoi, YOKURA Shoji, YOSHIKAWA Kenichi
Applications of algebraic analysis to geometry

Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (C), Japan Society for the Promotion of Science, 2007 - 2009

TAKEUCHI Kiyoshi, SUWA Tatsuo, TAJIMA Shinichi, TANISAKI Toshiyuki
Residues on Singular Varieties

Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (B), Japan Society for the Promotion of Science, 2006 - 2007

SUWA Tatsuo, OHMOTO Toru, OKA Mutsuo, SAITO Kyoji, TAJIMA Shinichi, YOKURA Shoji
Complex analysis of residues currents and computational algebraic analysis

Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (C), Japan Society for the Promotion of Science, 2005 - 2007

TAJIMA Shinichi, YOSHIHARA Hisao, KOJIMA Hideo, TAKEUCHI Kiyoshi, NAKAMURA Yayoi
Algebraic study of non-local differential equations and operational calculus

Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (C), Japan Society for the Promotion of Science, 2005 - 2006

ISHIMURA Ryuichi, HINO Yoshiyuki, OKADA Yasunori, AOKI Takashi, TAJIMA Shin-ichi, TOSE Nobuyuki
Residues on Singular Varieties

Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (B), Japan Society for the Promotion of Science, 2003 - 2005

SUWA Tatsuo, ITO Toshikazu, OHMOTO Toru, OKA Mutsuo, TAJIMA Shinichi, YOKURA Shoji
Algebraic Analysis of residue currents and an algorithm for computing Noether operators

Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (C), Japan Society for the Promotion of Science, 2003 - 2004

TAJIMA Shinichi, OAKU Toshinori, KOJIMA Hidoe
Algebraic-analytical Study of non-local pseudo-differential equations in complex domains

Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (C), Japan Society for the Promotion of Science, 2003 - 2004

ISHIMURA Ryuichi, HINO Yoshiyuki, OKADA Yasunori, AOKI Takashi, TAJIMA Shin-ichi, TOSE Nobuyuki
ALGEBRAIC ANALYTICAL STUDY OF SHEAVES AND INFINITE ORDRE DIFFERENTIAL EQUATIONS

Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (C), Japan Society for the Promotion of Science, 2001 - 2002

ISHIMURA Ryuichi, AOKI Takashi, OKADA Yasunori, HINO Yoshiyuki, TOSE Nobuyuki, TAJIMA Shinichi
Research on the structures of hypersurfaces and their function fields

Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (C), Japan Society for the Promotion of Science, 2001 - 2002

YOSHIHARA Hisao, KONNO Kazuhiro, OHBUCHI Akira, TAJIMA Shinichi, TOKUNAGA Hiro-o, AKIYAMA Shigeki
Algebraic analysis of residue theory in several complex variables and algorithms

Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (C), Japan Society for the Promotion of Science, 2000 - 2001

TAJIMA Shinichi
ALGEBRAIC-ANALYTICAL STUDY OF PSEUDO-DIFFERENTIAL AND CONVOLUTION ERUATIONS

Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (C), Japan Society for the Promotion of Science, 1999 - 2000

ISHIMURA Ryuichi, AOKI Takashi, OKADA Yasunori, HINO Yoshiyuki, TOSE Nobuyuki, TAJIMA Shinichi
Comprehensive Study of Real Analysis and Functional Analysis

Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (A)., Japan Society for the Promotion of Science, 1999 - 2000

MIYACHI Akihiko, WAKAYAMA Masato, CHO Muneo, KOBAYASI Kazuo, OHYA Masanori, OKAJI Takashi

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Misc.

Books and Other Publications

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Professional Memberships

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