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Complex analysis of residues currents and computational algebraic analysis

Research Project

Project/Area Number 17540150
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionNiigata University

Principal Investigator

TAJIMA Shinichi  Niigata University, Graduate School of Science and Technology, Professor (70155076)

Co-Investigator(Kenkyū-buntansha) YOSHIHARA Hisao  Niigata Univ, Graduate School of Science and Technology, Professor (60114807)
KOJIMA Hideo  Niigata Univ, Graduate School of Science and Technology, Associate Professor (90332824)
TAKEUCHI Kiyoshi  Tsukuba Univ, Graduate School of Pure and Applied Sciences, Associate Professor (70281160)
NAKAMURA Yayoi  Kinki Univ, School of Science and Engineering, Lecturer (60388494)
Project Period (FY) 2005 – 2007
Project Status Completed (Fiscal Year 2007)
Budget Amount *help
¥3,630,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥330,000)
Fiscal Year 2007: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2006: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2005: ¥1,100,000 (Direct Cost: ¥1,100,000)
Keywordsmultidimensional residue / holonomic D-modules / singularity / algebraic local cohomology / standard bases / homological index / Grothendiecl local duality / algorithm / ホロノミー系 / ネター作用素 / グレブナ基底 / グレブナー基底 / ホロノミック系 / 多変数留数カレント / 孤立特異点
Research Abstract

Hypersurface isolated singularities and associated residues currents are considered in the context of algebraic analysis.
・An efficient algorithm that computes bases of a dual vector space of a Milnor algebra associated to a singular point has been constructed.
・A new method for computing standard bases of a zero-dimensional ideal in a power series ring has been proposed. The key ingredient in this approach is the concept of algebraic local cohomology and the Grothendieck local duality.
・An algorithm for construction holonomic D-modules attached to hypersurface isolated singularities has been derived and the structure of these holonomic D-modules have been investigated.
・An algorithmic method for computing homological indices of holomorphic vector fields has been proposed.

Report

(4 results)
  • 2007 Annual Research Report   Final Research Report Summary
  • 2006 Annual Research Report
  • 2005 Annual Research Report
  • Research Products

    (101 results)

All 2008 2007 2006 2005

All Journal Article (46 results) (of which Peer Reviewed: 10 results) Presentation (55 results)

  • [Journal Article] Annihilating ideals for an algebraic local cohomology class2008

    • Author(s)
      S. Tajima and Y. Nakamura
    • Journal Title

      J. of Symbolic Computation (In press)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] 一変数代数的局所コホモロジー類に対するRisa/Asir用パッケージTaji_alc2007

    • Author(s)
      庄司卓夢、田島慎一
    • Journal Title

      Risa Asir Journal 2

      Pages: 1-32

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] A new look at the local solvability condition of inhomogeneous ordinary differential equations2007

    • Author(s)
      S. Tajima
    • Journal Title

      Publ. Res. Inst. Math. Sci. 43

      Pages: 443-459

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Annual Research Report 2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] On weighted-degrees for algebraic local cohomologies associated with semiquasihomogeneous singularities2007

    • Author(s)
      Y. Nakamura and S. Tajima
    • Journal Title

      Advanced Studies in Pure mathematics 46

      Pages: 105-117

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] ネター作用素計算におけるモニックでない多項式による割り算の効率化2007

    • Author(s)
      庄司卓夢、田島慎一
    • Journal Title

      京都大学数理解析研究所講究録 1572

      Pages: 72-81

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Annual Research Report 2007 Final Research Report Summary
  • [Journal Article] コーシー問題の解法とアルゴリズム2007

    • Author(s)
      庄司卓夢、田島慎一
    • Journal Title

      京都大学数理解析研究所講究録 1568

      Pages: 67-73

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Annual Research Report 2007 Final Research Report Summary
  • [Journal Article] Syzygies を用いた Noether 作用素計算アルゴリズム2007

    • Author(s)
      田島慎一、中村弥生
    • Journal Title

      京都大学数理解析研究所講究録 1568

      Pages: 81-86

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] 零次元代数的局所コホモロジーの計算法とスタンダード基底計算について II2007

    • Author(s)
      田島慎一
    • Journal Title

      京都大学数理解析研究所講究録 1568

      Pages: 74-80

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] 多変数留数の計算代数解析とホロノミーD-加群2007

    • Author(s)
      田島慎一
    • Journal Title

      京都大学数理解析研究所講究録 1532

      Pages: 43-59

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Annual Research Report 2007 Final Research Report Summary
  • [Journal Article] On weighted-degrees for algebraic local Cohomology associated with semiquasihomogeneous singularities2007

    • Author(s)
      Y, Nakamura, S., Tajima
    • Journal Title

      Advanced Studies in Pure Math Vol.46

      Pages: 105-117

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] A new look at the local solvability condition of inhomogeneous Ordinary differential equations2007

    • Author(s)
      S., Tajima
    • Journal Title

      Publ. Res. Inst. Math. Sci Vol.43

      Pages: 443-459

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] -変数代数的局所コホモロジー類に対するRisa/Asir用パッケージTaji_alc2007

    • Author(s)
      庄司卓夢、田島慎一
    • Journal Title

      Risa Asir Journal 2

      Pages: 1-32

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Syzygiesを用いたNoether作用素計算アルゴリズム2007

    • Author(s)
      田島慎一、中村弥生
    • Journal Title

      京都大学数理解析研究所講究録 1568

      Pages: 81-86

    • Related Report
      2007 Annual Research Report
  • [Journal Article] 零次元代数的局所コホモロジーの計算法とスタンダード基底計算についてII2007

    • Author(s)
      田島慎一
    • Journal Title

      京都大学数理解析研究所講究録 1568

      Pages: 74-80

    • Related Report
      2007 Annual Research Report
  • [Journal Article] 多変数留数の計算代数解析とホロノミーD加群2007

    • Author(s)
      田島慎一
    • Journal Title

      京都大学数理解析研究所講究録 1532

      Pages: 43-59

    • Related Report
      2006 Annual Research Report
  • [Journal Article] On weighted-degrees for algebraic local cohomologies associated with semiquasihomogeneous singularities2007

    • Author(s)
      Y.Nakamura, S.Tajima
    • Journal Title

      Advanced Studies in Pure Mathematics 46

      Pages: 105-117

    • Related Report
      2006 Annual Research Report
  • [Journal Article] 多項式剰余公式の計算アルゴリズム2006

    • Author(s)
      庄司卓夢、田島慎一
    • Journal Title

      京都大学数理解析研究所講究録 1514

      Pages: 108-114

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] 孤立特異点に付随する代数的局所コホモロジーとヤコビイデアルに対するグレブナ基底の計算法2006

    • Author(s)
      阿部隆行、田島慎一
    • Journal Title

      京都大学数理解析研究所講究録 1514

      Pages: 141-147

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] 剰余体 K[x]/<f>における逆冪計算2006

    • Author(s)
      田島慎一
    • Journal Title

      京都大学数理解析研究所講究録 1514

      Pages: 171-175

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Holonomic な定数係数線形偏微分方程式系とGrothendieck duality2006

    • Author(s)
      田島慎一
    • Journal Title

      京都大学数理解析研究所講究録 1509

      Pages: 1-23

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] 一変数留数計算アルゴリズムについて2006

    • Author(s)
      田島慎一
    • Journal Title

      京都大学数理解析研究所講究録 1509

      Pages: 24-50

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] 孤立特異点に付随する代数的局所コホモロジーとホロノミック系2006

    • Author(s)
      田島慎一、中村弥生
    • Journal Title

      京都大学数理解析研究所講究録 1501

      Pages: 168-180

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] An algorithm for computing exponential polynomial solutions of constant coefficients PDE' s2006

    • Author(s)
      S. Tajima
    • Journal Title

      Methods of Complex and Clifford Analysis

      Pages: 335-344

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] An algorithm for computing exponential polynomial solutions Of constant coefficients holonomic PDE's2006

    • Author(s)
      S., Tajima
    • Journal Title

      Methods of Complex and Clifford Analysis

      Pages: 335-344

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] 多項式剰余公式の計算アルゴリズム2006

    • Author(s)
      庄司卓夢, 田島慎一
    • Journal Title

      京都大学数理解析研究所講究録 1514

      Pages: 108-114

    • Related Report
      2006 Annual Research Report
  • [Journal Article] 孤立特異点に付随する代数的局所コホモロジーとヤコビイデアルに対するグレブナ基底の計算法2006

    • Author(s)
      阿部隆行, 田島慎一
    • Journal Title

      京都大学数理解析研究所講究録 1514

      Pages: 141-147

    • Related Report
      2006 Annual Research Report
  • [Journal Article] 孤立特異点に付随する代数的局所コホモロジーとホロノミック系2006

    • Author(s)
      田島慎一, 中村弥生
    • Journal Title

      京都大学数理解析研究所講究録 1501

      Pages: 168-180

    • Related Report
      2006 Annual Research Report
  • [Journal Article] An algorithm for computing exponential polynomial solutions of constant coefficients holonomic PDE's2006

    • Author(s)
      S.Tajima
    • Journal Title

      Methods of Complex and Clifford Analysis(SAS)

      Pages: 335-344

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Algebraic local cohomology classes attached to quasihomogeneous hypers urface isolated singularities2005

    • Author(s)
      S. Tajima and Y. Nakamura
    • Journal Title

      Publ. Res. Institute Math. Sci. 41

      Pages: 1-10

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Computational aspects of Grothendieck local residues2005

    • Author(s)
      S. Tajima and Y. Nakamura
    • Journal Title

      Seminaires et Congres 10

      Pages: 287-305

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Unimodal singularities and differential operators2005

    • Author(s)
      Y. Nakamura and S. Tajima
    • Journal Title

      Seminaires et Congres 10

      Pages: 191-208

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] On Noether differential operators attached to a zero-dimensional primary ideal2005

    • Author(s)
      S. Tajima
    • Journal Title

      Finite or Infinite Dimensional Complex Analysis and Applications

      Pages: 357-366

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] 高速留数計算アルゴリズム2005

    • Author(s)
      庄司卓夢、田島慎一
    • Journal Title

      京都大学数理解析研究所講究録 1456

      Pages: 133-143

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] 零次元代数的局所コホモロジーの計算法とスタンダード基底計算について2005

    • Author(s)
      田島慎一
    • Journal Title

      京都大学数理解析研究所講究録 1456

      Pages: 126-132

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary 2005 Annual Research Report
  • [Journal Article] Inner modality 4 以下の半擬斉次孤立特異点に付随したホロノミック系について2005

    • Author(s)
      中村弥生、田島慎一
    • Journal Title

      京都大学数理解析研究所講究録 1431

      Pages: 55-67

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Noether 作用素と多変数留数計算アルゴリズム2005

    • Author(s)
      田島慎一
    • Journal Title

      京都大学数理解析研究所講究録 1431

      Pages: 123-136

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] 零次元代数的局所コホモロジー類に付随するホロノミック系の構成アルゴリズム2005

    • Author(s)
      田島慎一、中村弥生
    • Journal Title

      京都大学数理解析研究所講究録 1412

      Pages: 189-198

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Unimodal singularities and differential Operators2005

    • Author(s)
      Y., Nakamura, S., Tajima
    • Journal Title

      Seminaires et Congres Vol.10

      Pages: 191-208

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Computational aspect s of Grothendieck Local residues2005

    • Author(s)
      S., Tajima, Y., Nakamura
    • Journal Title

      Seminaires et Congres Vol.10

      Pages: 287-305

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Algebraic local cohomology classes Attached to quasi-homogeneous hypersurface singularities2005

    • Author(s)
      S., Tajima, Y., Nakamura
    • Journal Title

      Publ. Res. Inst. Math. Sci Vol.41

      Pages: 1-10

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] On Noether differential operators attached to a zero-Dimensional primary ideal2005

    • Author(s)
      S., Tajima
    • Journal Title

      Finite or Infinite dimensional Complex Analysis

      Pages: 357-366

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Inner modality 4以下の半擬斉次孤立特異点に付随したホロノミック系について2005

    • Author(s)
      中村弥生, 田島慎一
    • Journal Title

      京都大学数理解析研究所講究録 1431

      Pages: 55-67

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Noether作用素と多変数留数計算アルゴリズム2005

    • Author(s)
      田島慎一
    • Journal Title

      京都大学数理解析研究所講究録 1431

      Pages: 123-136

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Unimodal singularities and differential operators2005

    • Author(s)
      Y.Nakamura, S.Tajima
    • Journal Title

      Seminaires et Congres, Soc. Math. France 8

      Pages: 191-208

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Computational aspects of Grothendieck local residues2005

    • Author(s)
      S.Tajima, Y.Nakamura
    • Journal Title

      Seminaires et Congres, Soc. Math. France 8

      Pages: 287-306

    • Related Report
      2005 Annual Research Report
  • [Journal Article] 高速留数計算アルゴリズム2005

    • Author(s)
      庄司卓夢, 田島慎一
    • Journal Title

      京都大学数理解析研究所講究録 1456

      Pages: 133-143

    • Related Report
      2005 Annual Research Report
  • [Presentation] 微分作用素を用いた留数計算とスペクトル分解2008

    • Author(s)
      田島慎一, 庄司卓夢
    • Organizer
      Risa/Asir Conference
    • Place of Presentation
      神戸大学
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Annual Research Report 2007 Final Research Report Summary
  • [Presentation] 特異点と局所コホモロジーの代数解析2008

    • Author(s)
      田島慎一
    • Organizer
      幾何学と物理学セミナー
    • Place of Presentation
      早稲田大学
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] A computation for the homological index of a vector field on an isolated complete intersection singularity2008

    • Author(s)
      中村弥生、田島慎一、諏訪立雄
    • Organizer
      Geometry and Analysis on Complex Algebraic Variety(学術振興会日露二国間共同事業)
    • Place of Presentation
      東京農工大
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] 特異点と局所コホモロジーの代数解析2008

    • Author(s)
      田島慎一
    • Organizer
      早稲田大學談話会
    • Place of Presentation
      早稲田大學
    • Related Report
      2007 Annual Research Report
  • [Presentation] Le cycles and Noether operators2007

    • Author(s)
      田島慎一
    • Organizer
      Computer Algebra
    • Place of Presentation
      京都大学数理解析研究所
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Annual Research Report 2007 Final Research Report Summary
  • [Presentation] 多変数留数2007

    • Author(s)
      田島慎一
    • Organizer
      第5回計算数学研究会
    • Place of Presentation
      クロスパル新潟
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] 孤立特異点の代数解析とアルゴリズム2007

    • Author(s)
      田島慎一
    • Organizer
      特異点解析の理論と方法
    • Place of Presentation
      東京工業大学
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Annual Research Report 2007 Final Research Report Summary
  • [Presentation] Computing Grothendieck local residues via Noether differential operators2007

    • Author(s)
      S. Tajima
    • Organizer
      Niigata Workshop on Complex Geometry and Singularities
    • Place of Presentation
      Niigata
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Standard bases and algebraic local cohomology classes2007

    • Author(s)
      S. Tajima
    • Organizer
      Analysis and Geometry on Complex Varieties(日本学術振興会日露二国間共同事業)
    • Place of Presentation
      Krasnoyarsk Univ.(ロシア)
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] #NAME?2007

    • Author(s)
      庄司卓夢、田島慎一
    • Organizer
      Risa Consortium
    • Place of Presentation
      神戸大学
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Grothendieck双対性と広中の標準基底2007

    • Author(s)
      S. Tajima
    • Organizer
      計算可換代数と計算代数幾何
    • Place of Presentation
      京都大学数理解析研究所
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Standard bases and algebraic local cohomology2007

    • Author(s)
      S, Tajima
    • Organizer
      Analysis and geometry on Complex Varieties Krasnoyarsk Univ
    • Place of Presentation
      Russi
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Computing Grothendieck local residues via Noetherian Differential operators2007

    • Author(s)
      S, Tajima
    • Organizer
      Niigata Workshop on Complex Geometry and Singularities
    • Place of Presentation
      Niigata
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] A computation for the homological indices of a vector Fields on an isolated complete intersection singularities2007

    • Author(s)
      Y, Nakamura
    • Organizer
      Geometry and Analysis on Complex Algebraic Varieties
    • Place of Presentation
      Tokyo Univ. of Agriculture and Technology
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Computation for the homological index of a vector field on an isolated complete intersection singularity2007

    • Author(s)
      中村弥生、田島慎一、諏訪立雄
    • Organizer
      Geometry and Analysis on Complex Algebraic Variety
    • Place of Presentation
      東京農工大
    • Related Report
      2007 Annual Research Report
  • [Presentation] 多変数留数の話2007

    • Author(s)
      田島慎一
    • Organizer
      第5回計算数学研究会
    • Place of Presentation
      クロスパル新潟
    • Related Report
      2007 Annual Research Report
  • [Presentation] Computing Grothendieck local residues via Noetherian differential operators2007

    • Author(s)
      S. Tajima
    • Organizer
      Niigata Workshop on Complex Geometry and Singularities
    • Place of Presentation
      クロスパル新潟
    • Related Report
      2007 Annual Research Report
  • [Presentation] 非斉次な単独常微分方程式の形式冪級数の空間での可解条件2006

    • Author(s)
      田島慎一
    • Organizer
      超幾何方程式
    • Place of Presentation
      神戸大学
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] コーシー問題の解法とアルゴリズム2006

    • Author(s)
      庄司卓夢、田島慎一
    • Organizer
      Computer Aigebra
    • Place of Presentation
      京都大学数理解析研究所
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] 一般余次元の準素イデアルに対するネター作用素について2006

    • Author(s)
      田島慎一
    • Organizer
      Computer Algebra
    • Place of Presentation
      京都大学数理解析研究所
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] 零次元代数的局所コホモロジーの計算法とスタンダード基底計算についてII2006

    • Organizer
      Computer Algebra
    • Place of Presentation
      京都大学数理解析研究所
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] On holonomic D-modules attached to a family of nonquasihomogeneous hypersurface isolated singularities2006

    • Author(s)
      S. Tajima
    • Organizer
      複素多様体上の幾何と解析(日本学術振興会日露二国間共同事業)
    • Place of Presentation
      京都大学数理解析研究所
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] 代数的局所コホモロジーとスタンダード基底2006

    • Author(s)
      田島慎一
    • Organizer
      代数解析セミナー(COE)
    • Place of Presentation
      慶応大学
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] An invariants of hypersurface isolated singularity2006

    • Author(s)
      Y. Nakamura and S. Tajima
    • Organizer
      Encuentro de algebra computationaly Aplicaciones
    • Place of Presentation
      Sevilla Univ.(スペイン)
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Algebraic analysis of Hermite-Jacobi reproducing kernels and its applications2006

    • Author(s)
      S. Tajima
    • Organizer
      Geometry and Analysis on Complex Algebraic Varieties(日本学術振興会日露二国間共同事業)
    • Place of Presentation
      Krasnoyarsk State Univ.(ロシア)
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Grothendieck local residues and holonomic D-modules2006

    • Author(s)
      S. Tajima
    • Organizer
      Geometry and Analysis on Complex Algebraic Varieties(日本学術振興会日露二国間共同事業)
    • Place of Presentation
      Moscow Independent Uni.(ロシア)
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] 代数的局所コホモロジーを用いたヤコビイデアルの計算アルゴリズム2006

    • Author(s)
      田島慎一
    • Organizer
      グレブナ基底の効率的計算とそれを基盤とする数学アルゴリズム
    • Place of Presentation
      京都大学数理解析研究所
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] On holonomic D-modules attached to Bayer-Hefez plane curve singularities2006

    • Author(s)
      S. Tajima
    • Organizer
      KIAS-RIMS Joint Workshop on Computer Algebra
    • Place of Presentation
      Korean Institute for Advanced Study(韓国)
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Invariants of isolated singularities via holonomic systems2006

    • Author(s)
      Y. Nakamura and S. Tajima
    • Organizer
      Inter National Conference on Differential Equations and Dynamical Systems
    • Place of Presentation
      Suzdal(ロシア)
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] 多変数留数の計算代数解析とホロノミックD・加群2006

    • Author(s)
      田島慎一
    • Organizer
      情報物理学の数学的構造
    • Place of Presentation
      京都大学数理解析研究所
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] 孤立特異点に付随する代数的局所コホモロジーを用いたヤコビイデアルのグレブナ基底計算2006

    • Author(s)
      田島慎一
    • Organizer
      計算代数解析とその周辺
    • Place of Presentation
      京都大学数理解析研究所
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] 微分方程式を用いた部分分数分解アルゴリズムI2006

    • Author(s)
      田島慎一、庄司卓夢、加藤涼香
    • Organizer
      日本数学会応用数学分科会
    • Place of Presentation
      中央大学
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] 微分方程式を用いた部分分数分解アルゴリズムII2006

    • Author(s)
      田島慎一、斉藤加奈
    • Organizer
      日本数学会応用数学分科会
    • Place of Presentation
      中央大学
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Noetherian differential operators attached to holonomic D-modules and an algorithm for computing Grothendieck local residues2006

    • Author(s)
      S. Tajima
    • Organizer
      Seminaires on Computer Algebra
    • Place of Presentation
      Sevilla Univ.(スペイン)
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Noetherian differential operators and an algorithm for computing Grothendieck local residues2006

    • Author(s)
      S. Tajima
    • Organizer
      Special Semesters on Groebner Bases and Related Method
    • Place of Presentation
      Radon Institute for Computational and Applied mathematics and Applied mathematics and Research Institute for Symboic Computation(オーストリア)
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Noetherian differential operators and an algorithm for Computing Grothendieck local residues2006

    • Author(s)
      S, Tajima
    • Organizer
      Radon Institute for Computational and Applied Mathematics and Research Institute for Symbolic Computation
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Invariants of isolated singularities via holonomic systems2006

    • Author(s)
      Y, Nakamura
    • Organizer
      International Conference on Differential Equations and Dynamical systems
    • Place of Presentation
      Suzdal Russia
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] On holonomic D-modules attached to Bayer-Hefez plane curve Singularities2006

    • Author(s)
      S, Tajima
    • Organizer
      KIAS-RIMS joint workshop on Computer Algebra
    • Place of Presentation
      KIAS, Korea
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Grothendieck local residues and holonomic D-modules2006

    • Author(s)
      S, Tajima
    • Organizer
      Geometry and Analysis on Complex Algebraic Varieties
    • Place of Presentation
      Moscow Independent Univ
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Algebraic analysis of Hermite-Jacobi reproducing kernels and2006

    • Author(s)
      S, Tajima
    • Organizer
      Krasnoyarsk State Univ
    • Place of Presentation
      Russia
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] An invariant of hypersurface isolated singularities2006

    • Author(s)
      Y, Nakamura
    • Organizer
      Encuentro de algebra computacional y Aplicaciones, Sevilla Univ
    • Place of Presentation
      Spain
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] 多項式剰余公式アルゴリズム2005

    • Author(s)
      庄司卓夢、田島慎一
    • Organizer
      Computer Algebra
    • Place of Presentation
      京都大学数理解析研究所
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] 代数的局所コホモロジーを用いたグレブナ基底の計算法2005

    • Author(s)
      阿部隆行、田島慎一
    • Organizer
      Computer Algebra
    • Place of Presentation
      京都大学数理解析研究所
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] 剰余体における逆冪計算アルゴリズムとその応用2005

    • Author(s)
      田島慎一
    • Organizer
      Computer Algebra
    • Place of Presentation
      京都大学数理解析研究所
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] On holonomic D-modules attached to a hypersurface isolated singularity2005

    • Author(s)
      S. Tajima
    • Organizer
      The 7-th Asian Symposium on Computer Mathematics
    • Place of Presentation
      Korea Institute for Advanced Study(韓国)
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] 孤立特異点に付随する代数的局所コホモロジーとホロノミック系2005

    • Author(s)
      田島慎一、中村弥生
    • Organizer
      Recent Topics on Real and Complex Singularities
    • Place of Presentation
      京都大学数理解析研究所
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] #NAME?2005

    • Author(s)
      田島慎一
    • Organizer
      第48回函数論シンポジウム
    • Place of Presentation
      鹿児島大学
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Algorithm for computing Noetherian differential operators2005

    • Author(s)
      S. Tajima
    • Organizer
      Theoretical Effectivity and Practical Effectivity of Groebner Bases(日本学術振興会国際会議)
    • Place of Presentation
      立教大学
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Algorithm for local cohomology classes attached to an isolated hypersurface singularity2005

    • Author(s)
      T. Abe and S. Tajima
    • Organizer
      Applications of Computer Algebra
    • Place of Presentation
      奈良女子大学
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Algorithm for partial fraction decomposition via differential equations2005

    • Author(s)
      T. Shoji and S. Tajima
    • Organizer
      Applications of Computer Algebra
    • Place of Presentation
      奈良女子大学
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] 多変数Hermite-Jacobi再生核の複素解析と代数解析2005

    • Author(s)
      田島慎一
    • Organizer
      多変数函数論サマーセミナー
    • Place of Presentation
      湯沢グランドホテル
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] 剰余公式アルゴリズム2005

    • Author(s)
      庄司卓夢、田島慎一
    • Organizer
      コンピュータアルジェブラ研究の新たな発展
    • Place of Presentation
      京都大学数理解析研究所
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] 孤立特異点に付随する代数的局所コホモロジー2005

    • Author(s)
      田島慎一
    • Organizer
      特異点における不変量
    • Place of Presentation
      近畿大学理工学部
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Algorithm for computing Noetherian differential operators2005

    • Author(s)
      S, Tajima
    • Organizer
      Theoretical Effectivity and Practical Effectivity of Groebner Bases
    • Place of Presentation
      Rikkyo Univ
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] On holonomic D-modules attached to a hypersurface isolated Singularities2005

    • Author(s)
      S, Tajima
    • Organizer
      The 7-th Asian Symposium on Computer Korea Institute for Advanced Study
    • Place of Presentation
      S., Tajima
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary

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Published: 2005-04-01   Modified: 2016-04-21  

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