• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

Algorithms for systems of parametric polynomials

Research Project

Project/Area Number 22740065
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionThe University of Tokushima

Principal Investigator

NABESHIMA Katsusuke  徳島大学, 大学院・ソシオ・アーツ・アンド・サイエンス研究部, 准教授 (00572629)

Research Collaborator TAJIMA Shinichi  筑波大学, 大学院・数理物質系, 教授 (70155076)
Project Period (FY) 2010 – 2012
Project Status Completed (Fiscal Year 2012)
Budget Amount *help
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2010: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Keywordsアルゴリズム / 関数論 / 情報基礎 / 代数学 / 特異点 / 代数的局所コホモロジー / 数式処理 / 代数計算 / 包括的グレブナー基底 / グレブナー基底 / パラメータ / 標準基底 / 記号計算
Research Abstract

A new stability condition of monomial bases was introduced. This stability condition is stronger than other known one. The new algorithm for computing comprehensive Grobner systems, based on the new stability condition, was also introduced.Moreover, in this research, new efficient algorithms for computing algebraic local cohomology classes associated with (semi-quasihomogeneous) singularities, werepresented. The new algorithms were also generalized to parametric cases.

Report

(4 results)
  • 2012 Annual Research Report   Final Research Report ( PDF )
  • 2011 Annual Research Report
  • 2010 Annual Research Report
  • Research Products

    (42 results)

All 2013 2012 2011 2010

All Journal Article (11 results) (of which Peer Reviewed: 5 results) Presentation (31 results)

  • [Journal Article] On the computation of algebraic local cohomology classes associated with semi-quasihomogeneous singularities2013

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

      Advanced studies in pure mathematics

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] μ -constant deformation に対する代数的局所コホモロジーと Tjurina stratification2013

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

      数理解析研究所講究録

    • Related Report
      2012 Final Research Report
  • [Journal Article] Stability conditions of monomial bases and Comprehensive Grobner systems2012

    • Author(s)
      Katsusuke Nabeshima
    • Journal Title

      Proc. CASC 2012, Lecture Notes in Computer Science (Springer)

      Volume: Vol.7442 Pages: 248-259

    • URL

      http://www.springer.com/computer/theoretical+computer+science/book/978-3-642-32972-2

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] On an implementation of standard bases, Grobner bases and normal-form using algebraic local cohomology2012

    • Author(s)
      Katsusuke Nabeshima
    • Journal Title

      Communications of Japan Society of Symbolic and Algebraic Computations

      Volume: Vol.1 Pages: 1-25

    • URL

      http://www.jssac.org/Editor/CJssac/V01/index.html

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] パラメータ付き代数的局所コホモロジーの計算について--半擬斉次孤立特異点の場合--2012

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

      数理解析研究所講究録

      Volume: Vol.1785 Pages: 111-122

    • URL

      http://www.kurims.kyoto-u.ac.jp/~kyodo/kokyuroku/contents/1785.html

    • Related Report
      2012 Final Research Report
  • [Journal Article] Stability conditions of monomial bases and Comprehensive Groebner systems2012

    • Author(s)
      Katsusuke Nabeshima
    • Journal Title

      Proc. International Workshop on Computer Algebra 2012, Lecture Notes in Computer Science (Springer)

      Volume: 7442 Pages: 248-259

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On an implementation of standard bases, Groebner bases and normal-form using algebraic local cohomology2012

    • Author(s)
      Katsusuke Nabeshima
    • Journal Title

      Communications of Japan Society of Symbolic and Algebraic Computations

      Volume: 1 Pages: 1-25

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] パラメータ付き代数的局所コホモロジーの計算について--半擬斉次孤立特異点の場合--2012

    • Author(s)
      鍋島 克輔
    • Journal Title

      数理解析研究所講究録

      Volume: 1785 Pages: 111-122

    • Related Report
      2012 Annual Research Report
  • [Journal Article] CGS 計算アルゴリズムのさらなる改良2011

    • Author(s)
      鍋島 克輔
    • Journal Title

      数理解析研究所講究録

      Volume: Vol.1815 Pages: 29-40

    • URL

      http://www.kurims.kyoto-u.ac.jp/~kyodo/kokyuroku/contents/1815.html

    • Related Report
      2012 Final Research Report
  • [Journal Article] 代数的局所コホモロジーの計算法とそれを用いたスタンダード基底・グレブナー基底について2011

    • Author(s)
      鍋島 克輔, 中村 弥生, 田島 慎一
    • Journal Title

      数理解析研究所講究録

      Volume: Vol.1764 Pages: 102-125

    • URL

      http://www.kurims.kyoto-u.ac.jp/~kyodo/kokyuroku/contents/1785.html

    • Related Report
      2012 Final Research Report
  • [Journal Article] 代数的局所コホモロジーの計算法とそれを用いたスタンダード基底・グレブナー基底計算について2011

    • Author(s)
      鍋島克輔
    • Journal Title

      数理解析研究所講究録

      Volume: 1764号 Pages: 102-125

    • Related Report
      2011 Annual Research Report
  • [Presentation] μ-constant deformation 代数的局所コホモロジーを用いた Tjurina 数のパラメータ依存性の解析2013

    • Author(s)
      鍋島 克輔 , 田 島 慎 一
    • Organizer
      日本数学会 中国・四国支部例会
    • Place of Presentation
      高知大学 (高知県)
    • Year and Date
      2013-01-27
    • Related Report
      2012 Final Research Report
  • [Presentation] μ-constant deformation 代数的局所コホモロジーを用いた Tjurina 数のパラメータ依存性の解析2013

    • Author(s)
      鍋島 克輔
    • Organizer
      日本数学会 中国・四国支部例会
    • Place of Presentation
      高知大学(高知県)
    • Related Report
      2012 Annual Research Report
  • [Presentation] μ-constant deformation に対する代数的局所コホモロジーとTjurina stratification2012

    • Author(s)
      鍋島 克輔
    • Organizer
      数理解析研究所研究集会 「 Computer Algebra-Degign of Algorithm, Implementations and the Next Grneration」
    • Place of Presentation
      京都大学 (京都府)
    • Year and Date
      2012-12-26
    • Related Report
      2012 Final Research Report
  • [Presentation] CGSとminimal CGSの計算について2012

    • Author(s)
      鍋島克輔
    • Organizer
      第4回日本数式処理学会理論分科会&システム分科会合同研究会
    • Place of Presentation
      仙台青葉カルチャーセンター(宮城県)
    • Year and Date
      2012-01-22
    • Related Report
      2011 Annual Research Report
  • [Presentation] CGS と minimal CGS の計算について2012

    • Author(s)
      鍋島 克輔
    • Organizer
      第4回日本数式処理学会理論分科会&システム分科会合同研究会
    • Place of Presentation
      仙台青葉カルチャーセンター (宮城県)
    • Year and Date
      2012-01-21
    • Related Report
      2012 Final Research Report
  • [Presentation] μ-constant deformation に対する代数的局所コホモロジーとTjurina stratification2012

    • Author(s)
      鍋島 克輔
    • Organizer
      数理解析研究所研究集会 「Computer Algebra-Degign of Algorithm, Implementations and the Next Grneration」
    • Place of Presentation
      京都大学(京都府)
    • Related Report
      2012 Annual Research Report
  • [Presentation] Stability conditions of monomial bases and Comprehensive Groebner systems2012

    • Author(s)
      Katsusuke Nabeshima
    • Organizer
      The 14th International Workshop on Computer Algebra in Scientific Computing
    • Place of Presentation
      University of Maribor(スロベニア)
    • Related Report
      2012 Annual Research Report
  • [Presentation] パラメータ付き代数的局所コホモロジーの計算について--半擬斉次の場合--2011

    • Author(s)
      鍋島 克輔, 田島 慎一
    • Organizer
      数理解析研究所研究集会「 Computer Algebra-Degign of Algorithm, Implementations and the Next Generation]
    • Place of Presentation
      京都大学 (京都府)
    • Year and Date
      2011-12-08
    • Related Report
      2012 Final Research Report
  • [Presentation] パラメータ付き代数的局所コホモロジーの計算について--半擬斉次の場合--2011

    • Author(s)
      鍋島克輔
    • Organizer
      京都大学数理解析研究所研究集会「Computer Algebra-Degign of Algorithm, Implementations and the Next Grneration]
    • Place of Presentation
      京都大学(京都府)
    • Year and Date
      2011-12-08
    • Related Report
      2011 Annual Research Report
  • [Presentation] 半擬斉次孤立特異点に付随する代数的局所コホモロジーについて2011

    • Author(s)
      鍋島克輔
    • Organizer
      2011年度日本数学会秋季総合分科会(函数論)
    • Place of Presentation
      信州大学(長野県)
    • Year and Date
      2011-10-01
    • Related Report
      2011 Annual Research Report
  • [Presentation] 半擬斉次孤立特異点に付随する代数的局所コホモロジーについて2011

    • Author(s)
      鍋島 克輔, 田島 慎一
    • Organizer
      日本数学会秋季総合分科会(函数論)
    • Place of Presentation
      信州大学 (長野県)
    • Year and Date
      2011-09-29
    • Related Report
      2012 Final Research Report
  • [Presentation] Semi-quasihomogeneous isolated sungularityに付随する代数的局所コホモロジーについて2011

    • Author(s)
      鍋島克輔
    • Organizer
      第20回日本数式処理学会
    • Place of Presentation
      神戸大学(兵庫県)
    • Year and Date
      2011-09-11
    • Related Report
      2011 Annual Research Report
  • [Presentation] Semi-quasihomogeneous isolated singularity に付随する代数的局所コホモロジーについて2011

    • Author(s)
      鍋島 克輔 , 田島 慎一
    • Organizer
      日本数式処理学会
    • Place of Presentation
      神戸大学, (兵庫県)
    • Year and Date
      2011-09-08
    • Related Report
      2012 Final Research Report
  • [Presentation] On the computation for algebraic local cohomogies associated with semi-quasihomogeneous singularities2011

    • Author(s)
      Katsusuke Nabeshima and Tajima Shinichi
    • Organizer
      The 6th Franco-Japan Symposium on Singularities
    • Place of Presentation
      Kyushu University (福岡県)
    • Year and Date
      2011-09-05
    • Related Report
      2012 Final Research Report
  • [Presentation] On the computation for algebraic local cohomogies associated with semi-quasihomogeneous singularities2011

    • Author(s)
      鍋島克輔
    • Organizer
      The 6th Franco-Japan Symposium on Singularities
    • Place of Presentation
      九州大学(福岡県)
    • Year and Date
      2011-09-05
    • Related Report
      2011 Annual Research Report
  • [Presentation] イデアルはいつ安定か?---強い安定条件を探そう!---2011

    • Author(s)
      鍋島克輔
    • Organizer
      JST CREST「現代社会の産業とグレブナー基底の調和」若手研究集会
    • Place of Presentation
      山口大学
    • Year and Date
      2011-02-17
    • Related Report
      2010 Annual Research Report
  • [Presentation] イデアルはいつ安定か?2011

    • Author(s)
      鍋島 克輔
    • Organizer
      JST CREST 「現代社会の産業とグレブナー基底の調和」 若手研究集会
    • Place of Presentation
      山口大学 (山口県)
    • Year and Date
      2011-02-15
    • Related Report
      2012 Final Research Report
  • [Presentation] グレブナー基底とその応用-- 集合制約と共振について--2010

    • Author(s)
      鍋島 克輔
    • Organizer
      徳島数学談話会
    • Place of Presentation
      徳島大学(徳島県)
    • Year and Date
      2010-12-17
    • Related Report
      2012 Final Research Report
  • [Presentation] ダレブナー基底とその応用--集合制約と共振について--2010

    • Author(s)
      鍋島克輔
    • Organizer
      徳島数学談話会
    • Place of Presentation
      徳島大学
    • Year and Date
      2010-12-17
    • Related Report
      2010 Annual Research Report
  • [Presentation] CGS 計算アルゴリズムのさらなる改良2010

    • Author(s)
      鍋島 克輔
    • Organizer
      数理解析研究所研究集会「Computer Algebra -Design of Algorithms, Implementations and Applications」
    • Place of Presentation
      京都大学 (京都府)
    • Year and Date
      2010-12-03
    • Related Report
      2012 Final Research Report
  • [Presentation] On an implementation of standard bases and Grobner bases using algebraic local cohomology2010

    • Author(s)
      鍋島 克輔, 中村 弥生, 田島 慎一
    • Organizer
      数理解析研究所研究集会「実閉体上の幾何と特異点論への応用」
    • Place of Presentation
      京都大学 (京都府)
    • Year and Date
      2010-12-02
    • Related Report
      2012 Final Research Report
  • [Presentation] On an Implementation of Standard Bases and Grobner Bases Using Algebraic Local Cohomology2010

    • Author(s)
      鍋島克輔, 中村弥生, 田島慎一
    • Organizer
      京都大学数理解析研究所研究集会「実閉体上の幾何と特異点論への応用」
    • Place of Presentation
      京都大学,数理解析研究所
    • Year and Date
      2010-12-02
    • Related Report
      2010 Annual Research Report
  • [Presentation] CGS計算アルゴリズムのさらなる改良2010

    • Author(s)
      鍋島克輔
    • Organizer
      京都大学数理解析研究所研究集会「Computer Algebra-Design of Algorithms, Implementations and Applications」
    • Place of Presentation
      京都大学,数理解析研究所
    • Year and Date
      2010-12-01
    • Related Report
      2010 Annual Research Report
  • [Presentation] ブーリアン・グレブナー基底2010

    • Author(s)
      鍋島克輔
    • Organizer
      JST CREST「現代社会の産業とグレブナー基底の調和」若手研究集会
    • Place of Presentation
      神戸大学
    • Year and Date
      2010-10-10
    • Related Report
      2010 Annual Research Report
  • [Presentation] ブーリアン・グレブナー基底2010

    • Author(s)
      鍋島 克輔
    • Organizer
      JST CREST 「現代社会の産業とグレブナー基底の調和」 若手研究集会
    • Place of Presentation
      神戸大学 (兵庫県)
    • Year and Date
      2010-09-09
    • Related Report
      2012 Final Research Report
  • [Presentation] Using Algebraic Local Cohomology with Parameters2010

    • Author(s)
      鍋島克輔, 中村弥生, 田島慎一
    • Organizer
      International Conference on Applications of Computer Algebra
    • Place of Presentation
      University of Vlore(アルバニア)
    • Year and Date
      2010-06-27
    • Related Report
      2010 Annual Research Report
  • [Presentation] Derivation of resonant conditions with CGS2010

    • Author(s)
      鍋島克輔, 吉田寛
    • Organizer
      International Conference on Applications of Computer Algebra
    • Place of Presentation
      University of Vlore(アルバニア)
    • Year and Date
      2010-06-27
    • Related Report
      2010 Annual Research Report
  • [Presentation] Using algebraic local cohomology with parameters2010

    • Author(s)
      Katsusuke Nabeshima, Nakamura Yayoiand Tajima Shinichi
    • Organizer
      International Conference on Applications of Computer Algebra (ACA 10)
    • Place of Presentation
      University of Vlora (アルバニア)
    • Year and Date
      2010-06-25
    • Related Report
      2012 Final Research Report
  • [Presentation] Derivation of resonant conditions with CGS2010

    • Author(s)
      Katsusuke Nabeshima and Yoshida Hiroshi
    • Organizer
      International Conference on Applications of Computer Algebra (ACA10)
    • Place of Presentation
      University of Vlora (アルバニア)
    • Year and Date
      2010-06-25
    • Related Report
      2012 Final Research Report
  • [Presentation] CGS を用いた共振条件導出2010

    • Author(s)
      鍋島 克輔, 吉田 寛
    • Organizer
      日本数式処理学会大会
    • Place of Presentation
      名古屋大学 (愛知県)
    • Year and Date
      2010-06-13
    • Related Report
      2012 Final Research Report
  • [Presentation] CGSを用いた共振条件導出2010

    • Author(s)
      鍋島克輔, 吉田寛
    • Organizer
      第19回日本数式処理学会大会
    • Place of Presentation
      名古屋大学
    • Year and Date
      2010-06-13
    • Related Report
      2010 Annual Research Report

URL: 

Published: 2010-08-23   Modified: 2019-07-29  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi