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Algebraic aanalysis of non-isolated singularities and computational complex analysis algorithms

Research Project

Project/Area Number 18K03320
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Review Section Basic Section 12010:Basic analysis-related
Research InstitutionNiigata University

Principal Investigator

Tajima Shinichi  新潟大学, 自然科学系, フェロー (70155076)

Co-Investigator(Kenkyū-buntansha) 小原 功任  金沢大学, 数物科学系, 教授 (00313635)
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)
梅田 陽子  城西大学, 理学部, 准教授 (90606386)
渋田 敬史  九州産業大学, 理工学部, 講師 (40648200)
Project Period (FY) 2018-04-01 – 2022-03-31
Project Status Completed (Fiscal Year 2021)
Budget Amount *help
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2021: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2020: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2019: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2018: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Keywords特異点 / アルゴリズム / ホロノミーD-加群 / 多変数留数 / b-関数 / ネター作用素 / 特異点変形族 / torsion微分形式 / Bruce-Roberts-MIlnor数 / holonomic D-module / local cohomology / algorithm / 局所コホモロジー / 対数的ベクトル場 / 代数解析
Outline of Final Research Achievements

By utilizing the theory of algebraic analysis and the method of computer algebra, we construct a new framework for analyzing complex analytic properties of singularities. We invent new algorithms for computing several complex analytic invariant of singularities. We also implement resulting algorithms in a computer algebra system. Using these new device, we study singularities.
Based on the theory of comprehensive Groebner systems on the Poincare-Birkhoff-Witt algebra, we construct an algorithm for computing holonomic D-modules associated to a non-isolated hypersurface singularities. For some typical cases, we investigate the structure of holonomic D-modules in an explicit manner. We apply these result to the study of non-isolated hypersurface singularities.

Academic Significance and Societal Importance of the Research Achievements

特異点論は現代数学の重要な研究課題であり, 様々な観点から研究されている。特異点の複素解析的諸性質や不変量は, 基本的なものであっても一般には決定したり求めることが困難である。そのため, 計算法を確立することが重要となる。本研究では様々な複素解析的不変量を求めるアルゴリズムを導出し開発したプログラムを数式処理システムに実装した。この成果は今後の特異点研究の展開に有効である。
非孤立特異点を持つ超曲面に対し, それに付随するホロノミーD-加群を求めるアルゴリズムを構築した。さらにそれらホロノミーD-加群の構造を解析する方法を与えた。これにより非孤立特異点を解析する新たな方法を与えることが出来た。

Report

(5 results)
  • 2021 Annual Research Report   Final Research Report ( PDF )
  • 2020 Research-status Report
  • 2019 Research-status Report
  • 2018 Research-status Report
  • Research Products

    (106 results)

All 2022 2021 2020 2019 2018

All Journal Article (48 results) (of which Peer Reviewed: 32 results,  Open Access: 17 results) Presentation (58 results) (of which Int'l Joint Research: 14 results,  Invited: 2 results)

  • [Journal Article] Algebraic analysis of Siersma's non-isolated hypersurface singularities2022

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

      Hokkaido Mathematical Journal

      Volume: 51 Issue: 1 Pages: 117-151

    • DOI

      10.14492/hokmj/2020-305

    • Related Report
      2021 Annual Research Report
    • Peer Reviewed
  • [Journal Article] An effective method for computing Grothendieck point residue mappings2022

    • Author(s)
      S. Tajima and K. Nabeshima
    • Journal Title

      Journal of Algebra

      Volume: 593 Pages: 568-588

    • Related Report
      2021 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Holonomic <i>D</i>-Modules Associated with a Simple Line Singularity and the Vertical Monodromy2021

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

      Funkcialaj Ekvacioj

      Volume: 64 Issue: 1 Pages: 17-48

    • DOI

      10.1619/fesi.64.17

    • NAID

      130008023888

    • ISSN
      0532-8721
    • Year and Date
      2021-04-15
    • Related Report
      2021 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A new deterministic method for computing Milnor number of an ICIS2021

    • Author(s)
      S. Tajima and K. Nabeshima,
    • Journal Title

      Lecture Notes in Computer Science

      Volume: 12865 Pages: 391-408

    • DOI

      10.1007/978-3-030-85165-1_22

    • ISBN
      9783030851644, 9783030851651
    • Related Report
      2021 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A new algorithm for computing logarithmic vector fields along an isolated singularity and Bruce-Roberts Milnor ideals2021

    • Author(s)
      K. Nabeshima and S. Tajima
    • Journal Title

      Journal of Symbolic Computation

      Volume: 107 Pages: 190-208

    • Related Report
      2021 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] 零次元準素イデアルのネター作用素の計算と応用2021

    • Author(s)
      鍋島克輔, 田島慎一
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 2185 Pages: 1-15

    • Related Report
      2021 Annual Research Report
    • Open Access
  • [Journal Article] 単純ホップ分岐判定法の実装, Implementation of criteria for simple Hopf bifurcations2021

    • Author(s)
      深作亮太, 田島慎一
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 2185 Pages: 113-122

    • Related Report
      2021 Annual Research Report
    • Open Access
  • [Journal Article] Testing zero-dimensionality of varieties at a point2021

    • Author(s)
      K. Nabeshima and S. Tajima
    • Journal Title

      Mathematics in Computer Science

      Volume: 15 Issue: 2 Pages: 317-331

    • DOI

      10.1007/s11786-020-00484-y

    • Related Report
      2021 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Computing Grothendieck point residues via solving holonomic systems of first order linear partial differential equations2021

    • Author(s)
      S. Tajima and K. Nabeshima
    • Journal Title

      Proceedings of the International Symposium on Symbolic and Algebraic Computation 2021

      Volume: 2021 Pages: 361-368

    • DOI

      10.1145/3452143.3465526

    • Related Report
      2021 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Computing Regular Meromorphic Differential Forms via Saito's Logarithmic Residues2021

    • Author(s)
      Tajima Shinichi、Nabeshima Katsusuke
    • Journal Title

      Symmetry, Integrability and Geometry: Methods and Applications

      Volume: 17

    • DOI

      10.3842/sigma.2021.019

    • Related Report
      2021 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Computing regular meromorphic differential forms via Saito's logarithmic residues2021

    • Author(s)
      S. Tajima and K. Nabeshima
    • Journal Title

      Symmetry, Integrability and Geometry: Methods and Applications

      Volume: 17 Pages: 019-019

    • Related Report
      2020 Research-status Report
    • Peer Reviewed
  • [Journal Article] Computation methods of b-functions associated with $\mu$-constant deformations -case of inner modality 2 --2021

    • Author(s)
      K. Nabeshima and S. Tajima
    • Journal Title

      Kyushu J. of Mathematics

      Volume: 75 Pages: 55-76

    • Related Report
      2020 Research-status Report
    • Peer Reviewed
  • [Journal Article] Holonomic D-modules associated with a simple line singularity and the vertical monodromy2021

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

      Funkcialaj Ekvacioj

      Volume: 64 Pages: 17-48

    • NAID

      130008023888

    • Related Report
      2020 Research-status Report
    • Peer Reviewed
  • [Journal Article] An algorithm for computing torsion differential forms associated to an isolated hypersurface singularity2020

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

      Mathematics in Computer Sciences

      Volume: - Issue: 2 Pages: 353-367

    • DOI

      10.1007/s11786-020-00486-w

    • Related Report
      2021 Annual Research Report 2019 Research-status Report
    • Peer Reviewed
  • [Journal Article] Computing logarithmic vector fields along an ICIS germ via Matlis duality2020

    • Author(s)
      S. Tajima, T. Shibuta and K. Nabeshima,
    • Journal Title

      Lecture Notes in Computer Science

      Volume: 12291 Pages: 543-562

    • Related Report
      2020 Research-status Report
    • Peer Reviewed
  • [Journal Article] 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,2020

    • Author(s)
      田島慎一, 渋田敬史, 鍋島克輔
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 2156 Pages: 1-15

    • Related Report
      2020 Research-status Report
    • Open Access
  • [Journal Article] 半擬斉次孤立特異点の性質を利用した局所b-関数の計算2020

    • Author(s)
      鍋島克輔, 田島慎一
    • Journal Title

      京都大学数理解析研究所講究

      Volume: 2159 Pages: 188-199

    • NAID

      120006956641

    • Related Report
      2020 Research-status Report
    • Open Access
  • [Journal Article] Moving curve ideals, Rees algebra and parametric local cohomology systems2020

    • Author(s)
      田島慎一, 鍋島克輔
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 2159 Pages: 179-187

    • Related Report
      2020 Research-status Report
    • Open Access
  • [Journal Article] 多変数留数の計算アルゴリズム III2020

    • Author(s)
      小原功任, 田島慎一
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 2159 Pages: 101-107

    • Related Report
      2020 Research-status Report
    • Open Access
  • [Journal Article] An algorithm for computing the Hilbert-Samuel multiplicities and reductions of zero-dimensional ideals of Cohen-Macaulay local ring2020

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

      Journal of Symbolic Computation

      Volume: 96 Pages: 108-121

    • Related Report
      2019 Research-status Report
    • Peer Reviewed
  • [Journal Article] Generalized integral dependence relations2020

    • Author(s)
      Katsusuke Nabeshima, Shinichi Tajima
    • Journal Title

      Lecture Notes in Computer Science

      Volume: 11989 Pages: 48-63

    • DOI

      10.1007/978-3-030-43120-4_6

    • ISBN
      9783030431198, 9783030431204
    • Related Report
      2019 Research-status Report
    • Peer Reviewed
  • [Journal Article] Holonomic D-modules associated with a simple line singularity and the vertical monodromy2020

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

      Funkcialaj Ekvacioj

      Volume: -

    • NAID

      130008023888

    • Related Report
      2019 Research-status Report
    • Peer Reviewed
  • [Journal Article] An algorithm for computing Grothendieck local residues II2020

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

      Mathematics in Computer Sciences

      Volume: -

    • Related Report
      2019 Research-status Report
    • Peer Reviewed
  • [Journal Article] Testing zero-dimensionality of varieties at a point2020

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

      Mathematics in Computer Sciences

      Volume: -

    • Related Report
      2019 Research-status Report
    • Peer Reviewed
  • [Journal Article] A method for computing generic Le numbers associated with non-isolated hypersurface singularities2019

    • Author(s)
      田島慎一
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 2101 Pages: 133-138

    • Related Report
      2019 Research-status Report
    • Open Access
  • [Journal Article] 収束冪級数環におけるgeneralized integral dependence relationの計算について2019

    • Author(s)
      鍋島克輔, 田島慎一
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 2014 Pages: 78-85

    • Related Report
      2019 Research-status Report
    • Open Access
  • [Journal Article] Solving parametric ideal membership problems and computing integral numbers in a ring of convergent power series via comprehensive Groebner systems2019

    • Author(s)
      Katsusuke Nabeshima, Shinichi Tajima
    • Journal Title

      Mathematics in Computer Science

      Volume: 13 Issue: 1-2 Pages: 185-194

    • DOI

      10.1007/s11786-018-0354-4

    • Related Report
      2019 Research-status Report 2018 Research-status Report
    • Peer Reviewed
  • [Journal Article] An algorithm for computing Grothendieck local residues I2019

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

      Mathematics in Computer Sciences

      Volume: 13 Issue: 1-2 Pages: 205-216

    • DOI

      10.1007/s11786-019-00399-3

    • Related Report
      2019 Research-status Report
    • Peer Reviewed
  • [Journal Article] An implementation of the Le-Teissier method for computing local Euler obstructions2019

    • Author(s)
      Shinichi Tajima, Katsusuke Nabeshima
    • Journal Title

      Mathematics in Computer Science

      Volume: 13 Issue: 1-2 Pages: 273-280

    • DOI

      10.1007/s11786-018-0366-0

    • Related Report
      2019 Research-status Report 2018 Research-status Report
    • Peer Reviewed
  • [Journal Article] Local cohomology solutions of holonomic D-modules associated with non-isolated hypersurface singularities2019

    • Author(s)
      S. Tajima
    • Journal Title

      RIMS Kokyuroku Bessatsu

      Volume: 75 Pages: 61-72

    • Related Report
      2019 Research-status Report
  • [Journal Article] Computing logarithmic vector fields and Bruce-Roberts Milnor numbers via local cohomology classes2019

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

      Revue Roumaine Math. PUres et Appl.

      Volume: 64 Pages: 521-538

    • Related Report
      2019 Research-status Report
    • Peer Reviewed
  • [Journal Article] Alternative algorithms for computing generic \mu^{ast}-sequences and local Euler obstructions of isolated hypersurface isolated singularities2019

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

      J. Algebra and its Applications

      Volume: 18 Pages: 1950159-1950159

    • Related Report
      2019 Research-status Report
    • Peer Reviewed
  • [Journal Article] 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2019

    • Author(s)
      鍋島克輔, 田島慎一
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 2138 Pages: 130-137

    • Related Report
      2019 Research-status Report
  • [Journal Article] 行列の最小消去多項式候補を用いた逆行列の計算と連立1次方程式の解法2019

    • Author(s)
      田島慎一, 小原功任, 照井章
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 2138 Pages: 171-175

    • Related Report
      2019 Research-status Report
  • [Journal Article] 複素解析的不変量 \kappa の計算アルゴリズムについて2019

    • Author(s)
      田島慎一
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 2014 Pages: 128-132

    • Related Report
      2019 Research-status Report
  • [Journal Article] An algorithm for computing Grothendieck local residues I -shape basis case-2019

    • Author(s)
      K. Ohara and S. Tajima
    • Journal Title

      Mathematics in Computer Sciences

      Volume: 印刷中

    • Related Report
      2018 Research-status Report
    • Peer Reviewed
  • [Journal Article] An algorithm for computing the Hilbert-Samuel multiplicities and reductions of zero-dimensional ideals of Cohen-Macaulay local rings2019

    • Author(s)
      T. Shibuta and S. Tajima
    • Journal Title

      Journal of Symbolic Computation

      Volume: 印刷中

    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Alternative algorithms for computing generic mu^ast-sequences and local Euler obstructions of isolated hypersurface singularities2019

    • Author(s)
      K. Nabeshima and S. Tajima
    • Journal Title

      Journal of Algebra and its Applications

      Volume: 印刷中

    • Related Report
      2018 Research-status Report
    • Peer Reviewed
  • [Journal Article] Computing logarithmic vector fields and Bruce-Roberts Milnor numbers via local cohomology classes2019

    • Author(s)
      K. Nabeshima and S. Tajima
    • Journal Title

      Proc. Australian-Japanese workshop on real and complex singularities

      Volume: 印刷中

    • Related Report
      2018 Research-status Report
    • Peer Reviewed
  • [Journal Article] Holonomic D-modules associated with a simple line singularity and the vertical monodromy2019

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

      Funkcialaj Ekvacioj

      Volume: 印刷中

    • NAID

      130008023888

    • Related Report
      2018 Research-status Report
    • Peer Reviewed
  • [Journal Article] An algorithm for computing Grothendieck local residues II -general case-2019

    • Author(s)
      K. Ohara and S. Tajima
    • Journal Title

      Mathematics in Computer Sciences

      Volume: 印刷中

    • Related Report
      2018 Research-status Report
    • Peer Reviewed
  • [Journal Article] Computation methods of logarithmic vector fields associated with semi-weighted homogeneous isolated hypersurface singularities2018

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

      Tsukuba Journal of Mathematics

      Volume: 42 Pages: 191-231

    • Related Report
      2018 Research-status Report
    • Peer Reviewed
  • [Journal Article] Comprehensive Groebner systems in PBW algebras, Bernstein-Sato ideals and holonomic D-modules2018

    • Author(s)
      Katsusuke Nabeshima, Katsuyoshi Ohara, Shinichi Tajima
    • Journal Title

      Journal of Symbolic Computation

      Volume: 印刷中 Pages: 146-170

    • DOI

      10.1016/j.jsc.2017.11.010

    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] A new method for computing limiting tangent spaces of isolated hypersurface singularity via algebraic local cohomology2018

    • Author(s)
      K. Nabeshima and S. Tajima
    • Journal Title

      Advanced Studies in Pure Mathematics

      Volume: 78 Pages: 331-344

    • Related Report
      2018 Research-status Report
    • Peer Reviewed
  • [Journal Article] Poincare-Birkhoff-Witt代数上のグレブナ基底計算とRisa/Asirへの実装2018

    • Author(s)
      小原功任, 田島慎一
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 2054 Pages: 134-138

    • Related Report
      2018 Research-status Report
    • Open Access
  • [Journal Article] D. Siersmaの非孤立特異点に付随するD-加群とPoincare-Birkhoff-Witt代数2018

    • Author(s)
      田島慎一
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 2054 Pages: 126-133

    • Related Report
      2018 Research-status Report
    • Open Access
  • [Journal Article] グレブナ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2018

    • Author(s)
      鍋島克輔, 田島慎一
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 2054 Pages: 118-125

    • Related Report
      2018 Research-status Report
    • Open Access
  • [Journal Article] Local Euler obstructionの計算法について2018

    • Author(s)
      田島慎一
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 2085 Pages: 97-103

    • Related Report
      2018 Research-status Report
    • Open Access
  • [Presentation] 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2021

    • Author(s)
      鍋島克輔, 田島慎一
    • Organizer
      日本数式処理学会
    • Related Report
      2021 Annual Research Report
  • [Presentation] 最小消去多項式を用いた一般固有ベクトル空間の構成2021

    • Author(s)
      田島慎一, 小原功任, 照井章
    • Organizer
      日本数式処理学会
    • Related Report
      2021 Annual Research Report
  • [Presentation] Computing Grothendieck point residues via solving holonomic systems of first oeder partial differential equations2021

    • Author(s)
      S. Tajima and K. Nabeshima
    • Organizer
      International Symposium on Symbolic and Algebraic Computation
    • Related Report
      2021 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Noetherina representations for zero-dimensional ideals2021

    • Author(s)
      K. Nabeshima and S. Tajima
    • Organizer
      International Conference on Applications of Computer Algebra
    • Related Report
      2021 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Computing holonomic D-modules associated to a family of non-isolated hypersurface singularities via comprehensive Greobner systems in PBW algebra2021

    • Author(s)
      S. Tajima and K. Nabeshima
    • Organizer
      International Conference on Applications of Computer Algebra,
    • Related Report
      2021 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 孤立特異点を持つ complete intersection の Milnor 数の deterministic な計算法について2021

    • Author(s)
      田島慎一, 鍋島克輔
    • Organizer
      日本数学会函数論分科会
    • Related Report
      2021 Annual Research Report
  • [Presentation] A new deterministic method for computing Milnor number of an ICIS2021

    • Author(s)
      S. Tajima and K. Nabeshima
    • Organizer
      Computer Algebra in Scinetific Computing
    • Related Report
      2021 Annual Research Report
    • Int'l Joint Research
  • [Presentation] CSSg method for several genericities of deformations of hypersurface singularities2021

    • Author(s)
      鍋島克輔, 田島慎一
    • Organizer
      可微分写像の特異点論及びその応用
    • Related Report
      2021 Annual Research Report
  • [Presentation] 一変数留数計算アルゴリズムについて2021

    • Author(s)
      深作亮也, 田島慎一
    • Organizer
      Computer Algebra-Foundations and Applications
    • Related Report
      2021 Annual Research Report
  • [Presentation] Grothendieck residue mappings and holonomic D-modules2021

    • Author(s)
      S. Tajima
    • Organizer
      Silver workshop 2022 -Complex geometry and related topics-
    • Related Report
      2021 Annual Research Report
    • Invited
  • [Presentation] 柏原の bon operateur と Poincare-Birkhoff-Witt 代数2021

    • Author(s)
      田島慎一
    • Organizer
      Recent Topics in Algebraic Analysis
    • Related Report
      2021 Annual Research Report
  • [Presentation] 効率的な一変数留数計算アルゴリズム2021

    • Author(s)
      深作亮也, 田島慎一
    • Organizer
      日本数学会函数論分科会
    • Related Report
      2021 Annual Research Report
  • [Presentation] 特異点変形に付随した$\kappa$-不変量の計算2021

    • Author(s)
      鍋島克輔, 田島慎一
    • Organizer
      日本数学会函数論分科会
    • Related Report
      2020 Research-status Report
  • [Presentation] 特異平面代数曲線に沿う対数的ベクトル場とCamacho-Sad-Suwa指数について2021

    • Author(s)
      田島慎一, 鍋島克輔
    • Organizer
      日本数学会函数論分科会
    • Related Report
      2020 Research-status Report
  • [Presentation] Computation of $\kappa$-invariants associated to deformations of isolated hypersurface singularities2020

    • Author(s)
      K. Nabeshima and S. Tajima
    • Organizer
      Computer Algebra in Scientific Computing
    • Related Report
      2020 Research-status Report
    • Int'l Joint Research
  • [Presentation] Computing logarithmic vector fields along an ICIS germ via Matlis duality2020

    • Author(s)
      S. Tajima. T. Shibuta and K. Nabeshima
    • Organizer
      Computer Algebra in Scientific Computing
    • Related Report
      2020 Research-status Report
    • Int'l Joint Research
  • [Presentation] Versal unfoldings of singular holomorphic foliations --諏訪アルゴリズムの実装-2020

    • Author(s)
      田島慎一, 鍋島克輔
    • Organizer
      日本数学会関数論分科会
    • Related Report
      2020 Research-status Report
  • [Presentation] D. Barletのregular meromorphic differential formsとK. Saitoのlogarithmic residues2020

    • Author(s)
      田島慎一, 鍋島克輔
    • Organizer
      日本数学会関数論分科会
    • Related Report
      2020 Research-status Report
  • [Presentation] 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おける不変量計算について2020

    • Author(s)
      鍋島克輔, 田島慎一
    • Organizer
      日本数式処理学会
    • Related Report
      2020 Research-status Report
  • [Presentation] ネター作用素を用いた零次元準素イデアル成分の表現法と計算2020

    • Author(s)
      鍋島克輔, 田島慎一
    • Organizer
      Computer Algebra - Theory and its Applications
    • Related Report
      2020 Research-status Report
  • [Presentation] 単純ホップ分岐判定法の実装2020

    • Author(s)
      (深作亮也, 田島慎一
    • Organizer
      Computer Algebra - Theory and its Applications
    • Related Report
      2020 Research-status Report
  • [Presentation] Brieskorn lattice の saturationと一般化されたintegral dependence relations について2020

    • Author(s)
      田島慎一
    • Organizer
      超幾何方程式研究会
    • Related Report
      2019 Research-status Report
  • [Presentation] 2次元特異点を持つA. Zahariaの超曲面に付随するホロノミーD-加群について2020

    • Author(s)
      田島慎一, 梅田陽子
    • Organizer
      接触構造, 特異点, 微分方程式及びその周辺
    • Related Report
      2019 Research-status Report
  • [Presentation] 特異点の複素解析的不変量と parametric local cohomology system2020

    • Author(s)
      田島慎一
    • Organizer
      北海道大学, 応用特異点ラボ/幾何学コロキウム
    • Related Report
      2019 Research-status Report
  • [Presentation] Computing torsions and logarithmic differential forms via local cohomology2020

    • Author(s)
      田島慎一
    • Organizer
      平坦構造と特異点
    • Related Report
      2019 Research-status Report
  • [Presentation] 孤立特異点を持つcomplete intersectionに沿う対数的ベクトル場の構成2020

    • Author(s)
      田島慎一, 渋田敬史, 鍋島克輔
    • Organizer
      日本数学会函数論分科会
    • Related Report
      2019 Research-status Report
  • [Presentation] 非孤立特異点とホロノミーD-加群のモノドロミー構造2019

    • Author(s)
      田島慎一
    • Organizer
      金沢大学理工学域談話会
    • Related Report
      2019 Research-status Report
    • Invited
  • [Presentation] 孤立特異点を持つ超曲面のtorsion微分形式2019

    • Author(s)
      田島慎一
    • Organizer
      特異点論による空間研究
    • Related Report
      2019 Research-status Report
  • [Presentation] An algorithm for computing torsion differential forms associated to an isolated hypersurface singularity2019

    • Author(s)
      S. Tajima, K. Nabeshima
    • Organizer
      Computer Algebra in Scientific Computating
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research
  • [Presentation] Testing zero-dimensionality of varieties at a point2019

    • Author(s)
      K. Nabeshima, S. Tajima
    • Organizer
      Computer Algebra in Scinetific Computing
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research
  • [Presentation] 孤立特異点を持つ超曲面のtorsion微分形式について2019

    • Author(s)
      田島慎一, 鍋島克輔
    • Organizer
      日本数学会函数論分科会
    • Related Report
      2019 Research-status Report
  • [Presentation] Vanishing cycle sheaves -Le cycles vs holonomic D-modules -2019

    • Author(s)
      田島慎一
    • Organizer
      トポロジーとコンピュータ2019
    • Related Report
      2019 Research-status Report
  • [Presentation] Generalized integral dependence relations2019

    • Author(s)
      K. Nabeshima, S. Tajima
    • Organizer
      Mathematical Aspects of Computer and Information Sciences
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research
  • [Presentation] On the Suwa method for computing versal unfoldings of codimension one complex analytic singular foliations2019

    • Author(s)
      田島慎一
    • Organizer
      葉層の複素解析幾何と力学系
    • Related Report
      2019 Research-status Report
  • [Presentation] Computation methods of Ann(f^s) and local b-functions using properties of semi-quasihomogeneous singularities2019

    • Author(s)
      K. Nabeshima, S. Tajima
    • Organizer
      Differential Systems: from theory to computer mathematics
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research
  • [Presentation] An implementation of the Suwa method for computing versal unfoldings of holomorphic foliations2019

    • Author(s)
      S. Tajima
    • Organizer
      Hyperplane Arrangement and Japanese-Australian Workshop on Real and Complex Singularities
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research
  • [Presentation] Computing logarithmic vector fields along ICIS via Matlis duality2019

    • Author(s)
      田島慎一, 渋田敬史, 鍋島克輔
    • Organizer
      可微分写像の特異点とその応用
    • Related Report
      2019 Research-status Report
  • [Presentation] 多変数留数の計算アルゴリズム III2019

    • Author(s)
      小原功任, 田島慎一
    • Organizer
      Computer Algebra
    • Related Report
      2019 Research-status Report
  • [Presentation] 代数曲線に付随するRees代数とパラメータ付き局所コホモロジー系2019

    • Author(s)
      田島慎一, 鍋島克輔
    • Organizer
      Computer Algebra
    • Related Report
      2019 Research-status Report
  • [Presentation] 半擬斉次特異点の性質を利用したAnn(f^s)とb-関数の計算について2019

    • Author(s)
      鍋島克輔, 田島慎一
    • Organizer
      Computer Algebra
    • Related Report
      2019 Research-status Report
  • [Presentation] Grothendiecl local residues 計算アルゴリズムとその実装2019

    • Author(s)
      小原功任, 田島慎一
    • Organizer
      多変数関数論冬セミナー
    • Related Report
      2019 Research-status Report
  • [Presentation] 孤立特異点を持つ超曲面に対する対数的微分形式とtorsion微分形式2019

    • Author(s)
      田島慎一
    • Organizer
      多変数関数論冬セミナー
    • Related Report
      2019 Research-status Report
  • [Presentation] Local cohomologyと特異点の複素解析2019

    • Author(s)
      田島慎一
    • Organizer
      応用特異点論ラボ・セミナー
    • Related Report
      2018 Research-status Report
  • [Presentation] 対数的ベクトル場とCamacho-Sad指数2019

    • Author(s)
      田島慎一
    • Organizer
      接触構造, 特異点, 微分方程式及びその周辺
    • Related Report
      2018 Research-status Report
  • [Presentation] 孤立特異点を持つ超曲面のtorsion微分形式と対数的微分形式2019

    • Author(s)
      田島慎一
    • Organizer
      代数解析学の諸問題
    • Related Report
      2018 Research-status Report
  • [Presentation] genericな一次関数のブルース・ロバート・ミルナー数について2019

    • Author(s)
      鍋島克輔, 田島慎一
    • Organizer
      日本数学会
    • Related Report
      2018 Research-status Report
  • [Presentation] Chern-Schwartz-MacPherson classの計算法について2019

    • Author(s)
      鍋島克輔, 田島慎一
    • Organizer
      日本数学会
    • Related Report
      2018 Research-status Report
  • [Presentation] イデアル商を用いた点での多様体の次元判定2019

    • Author(s)
      鍋島克輔, 田島慎一
    • Organizer
      Risa/Asir Conference
    • Related Report
      2018 Research-status Report
  • [Presentation] Jordan-Chevalley 分解と非線形力学系について2019

    • Author(s)
      田島慎一
    • Organizer
      Risa/Asir Conference
    • Related Report
      2018 Research-status Report
  • [Presentation] 超曲面の孤立特異点に沿った対数的ベクトル場と応用2018

    • Author(s)
      鍋島克輔, 田島慎一
    • Organizer
      日本数式処理学会
    • Related Report
      2018 Research-status Report
  • [Presentation] An algorithm for computing Grothendieck local residues II2018

    • Author(s)
      K. Ohara and S. Tajima
    • Organizer
      Applications of Computer Algebra 2018
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research
  • [Presentation] An effective method for computing Grothendieck point residues2018

    • Author(s)
      S. Tajima and K. Nabeshima
    • Organizer
      Applications of Computer Algebra 2018
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research
  • [Presentation] Computation methods of b-functions associated with mu-constant deformations -case of inner modality 2-2018

    • Author(s)
      K. Nabeshima and S. Tajima
    • Organizer
      Applications of Computer Algebra 2018
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research
  • [Presentation] An algorithm for computing generic Le numbers2018

    • Author(s)
      田島慎一
    • Organizer
      トポロジーとコンピュータ2018
    • Related Report
      2018 Research-status Report
  • [Presentation] Computing Ann(f^s) via generalized integral dependence relations2018

    • Author(s)
      田島慎一
    • Organizer
      代数解析の諸問題
    • Related Report
      2018 Research-status Report
  • [Presentation] An algorithm for computing kappa invariants2018

    • Author(s)
      田島慎一
    • Organizer
      可微分写像の特異点論を用いたトポロジー・微分幾何学の研究
    • Related Report
      2018 Research-status Report
  • [Presentation] Testing zero-dimensionality of a parametric ideal in a local ring2018

    • Author(s)
      鍋島克輔, 田島慎一
    • Organizer
      Computer Algebra - Theory and its Applications
    • Related Report
      2018 Research-status Report
  • [Presentation] 最小消去多項式候補を用いた逆行列の計算2018

    • Author(s)
      照井章, 小原功任, 田島慎一
    • Organizer
      Computer Algebra - Theory and its Applications
    • Related Report
      2018 Research-status Report

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Published: 2018-04-23   Modified: 2023-01-30  

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