Development of a practical algorithm to solve polynomial systems with parameters

• Project/Area Number: 20500013
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Fundamental theory of informatics
• Research Institution: Kobe University
• Principal Investigator: SUZUKI Akira Kobe University, 情報科学研究科, 研究員 (50330519)
• Co-Investigator(Renkei-kenkyūsha): SATO Yosuke 東京理科大学, 理学部・第一部, 教授 (50257820)
• Project Period (FY): 2008 – 2010
• Project Status: Completed (Fiscal Year 2010)
• Budget Amount: ¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000); Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2009: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2008: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
• Keywords: アルゴリズム理論 / グレブナー基底 / アルゴリズム / 媒介変数 / 代数学

Research Abstract

We can use Groebner basis in order to solve (non-liner) polynomial systems. If the systems contain parameters, the situation becomes extremely harder to solve them. We aimed to develop practical algorithm for such problem, and we provide several tools for them.

Research Products

• [Journal Article] パラメーターを含む多項式剰余環における逆元の計算について (2008)
  • Author(s): 佐藤洋祐, 向田康平, 井上秀太郎, 鈴木晃
  • Journal Title: 数式処理Bulletin of JSSAC (2008) 15-2 Pages: 132-134
  • NAID: 10023902629
• [Presentation] グラフ表示を行うモバイルアプリのマルチプラットフォーム化 (2011)
  • Author(s): 鈴木晃
  • Organizer: 日本数式処理学会システム分科会
  • Place of Presentation: 福岡大学
  • Year and Date: 2011-01-23
• [Presentation] グラフ表示を行なうモバイルアプリのマルチプラットフォーム化 (2011)
  • Author(s): 鈴木晃
  • Organizer: 第3回日本数式処理学会システム分科会研究会
  • Place of Presentation: 福岡大学理学部
  • Year and Date: 2011-01-23
• [Presentation] スマートフォンならではのグラフ表示 (2010)
  • Author(s): 鈴木晃
  • Organizer: 数学ソフトウェアとフリードキュメント10
  • Place of Presentation: 慶應大学日吉キャンパス
  • Year and Date: 2010-03-23
• [Presentation] Computing Boolean Groenber Bases within Linear Algebra (2009)
  • Author(s): 鈴木晃
  • Organizer: ASCM 2009, Fukuoka
  • Place of Presentation: Japan
  • Year and Date: 2009-12-14
• [Presentation] Computing Groenber Bases within Linear Algebra (2009)
  • Author(s): 鈴木晃
  • Organizer: Computer Algebra in Scientific Computing (CASC 2009)
  • Place of Presentation: Kobe (Japan)
  • Year and Date: 2009-09-15
• [Presentation] Computing Gr obner Bases within Linear Algebra (2009)
  • Author(s): Akira Suzuki
  • Organizer: CASC 2009
  • Place of Presentation: 神戸大学(兵庫県)
  • Year and Date: 2009-09-15
• [Presentation] Computing Groenber Bases within Linear Algebra and Its Implementation (2009)
  • Author(s): 鈴木晃
  • Organizer: International Symposium on Symbolic and Algebraic Computation (ISSAC 2009; Poster)
  • Place of Presentation: Seoul (Korea)
  • Year and Date: 2009-07-30
• [Presentation] Computing Gr obner Bases within Linear Algebra and Its Implementation (2009)
  • Author(s): Akira Suzuki
  • Organizer: ISSAC 2009(Poster)
  • Place of Presentation: ソウル(韓国)
  • Year and Date: 2009-07-30
• [Presentation] Computation of Inverses in Residue Class Rings of Parametric Polynomial Ideals (2009)
  • Author(s): Yosuke Sato, Akira Suzuki
  • Organizer: ISSAC 2009
  • Place of Presentation: ソウル(韓国)
  • Year and Date: 2009-07-29
• [Presentation] Groebner bases computation within linear algebra and its application to comprehensive Groebner systems (2009)
  • Author(s): 鈴木晃
  • Organizer: Application of Computer Algebra (ACA2009)
  • Place of Presentation: Montreal (Canada)
  • Year and Date: 2009-06-25
• [Presentation] 行列演算によるグレブナー基底計算とその実装 (2009)
  • Author(s): 鈴木晃
  • Organizer: 第18回日本数式処理学会大会
  • Place of Presentation: 龍谷大学
  • Year and Date: 2009-06-12
• [Presentation] Implementation of CGS on small devices (2008)
  • Author(s): 鈴木晃
  • Organizer: Application of Computer Algebra (ACA2008)
  • Place of Presentation: Linz (Austria)
  • Year and Date: 2008-07-29
• [Presentation] Implementation of CGS on small devices (2008)
  • Author(s): Akira Suzuki
  • Organizer: Applications for Computer Algebra 2008
  • Place of Presentation: Linz (オーストリア)
  • Year and Date: 2008-07-29
• [Presentation] Boolean Groebner Bases and Sudoku (2008)
  • Author(s): Yosuke Sato, Akira Suzuki
  • Organizer: Shutaro Inoue and Katsusuke Nabeshima
  • Place of Presentation: Application of Computer Algebra (ACA2008), Linz (Austria)
  • Year and Date: 2008-07-27
• [Presentation] Boolean Groebner Bases and Sudoku (2008)
  • Author(s): Y. Sato, A. Suzuki, S. Inoue, K. Nabeshima
  • Organizer: Applications for Computer Algebra 2008
  • Place of Presentation: Linz (オーストリア)
  • Year and Date: 2008-07-27
• [Presentation] Computation of Inverses in Residue Class Rings with Parameters (2008)
  • Author(s): S. Inoue, K. Mukaida, A. Suzuki, Y. Sato
  • Organizer: ISSAC 2008 (Poster)
  • Place of Presentation: Linz (オーストリア)
  • Year and Date: 2008-07-22
• [Remarks] ホームページ等