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Development of efficient algorithms for complex and real algebraic constraints

Research Project

Project/Area Number 18K03426
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Review Section Basic Section 12040:Applied mathematics and statistics-related
Research InstitutionTokyo University of Science

Principal Investigator

Sato Yosuke  東京理科大学, 理学部第一部応用数学科, 教授 (50257820)

Project Period (FY) 2018-04-01 – 2023-03-31
Project Status Completed (Fiscal Year 2022)
Budget Amount *help
¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000)
Fiscal Year 2020: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2019: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2018: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
KeywordsCGS / 根の連続性 / パラメーター / Border基底 / 飽和イデアル / 限量子記号消去 / グレブナー基底
Outline of Final Research Achievements

I proved an important property concerning continuity of the roots of a parametric system of algebraic equations. By this result, we can make a partition of the parameter space necessary for the computation of the saturation by parametric polynomial ideals. It enables us have a simple representation of the saturation by parametric polynomial ideals. I further proved that we can have a simpler representation if we use a parametric border bases instead of comprehensive Groebner system. I also showed that we can have a simpler representation of a comprehensive Groebner system if we use the computation of the saturation ideal by disequalities. Based on those results, I developed efficient algorithms of quantifier elimination for both complex and real algebraic constraints.

Academic Significance and Societal Importance of the Research Achievements

国立情報学研究所の東ロボ君プロジェクトで扱うような大学入試の問題をそれと等価な限量子記号消去の問題として代数制約式に表現したとき、既存の数式処理システムの限量子記号消去プログラムを用いても大抵の場合処理が可能である。しかしながら、国際数学オリンピックで出題されるような、より難易度の高い問題は等式制約を多く含む複雑な代数制約式として表現され、 Mathematica や Maple 等の数式処理システムにおける既存の限量子記号消去プログラムでは処理できないものが多い。等式制約を多く含む代数制約式に対して有効な新しい限量子記号消去アルゴリズムを開発したことで処理できる問題の範囲が格段に広がった。

Report

(6 results)
  • 2022 Annual Research Report   Final Research Report ( PDF )
  • 2021 Research-status Report
  • 2020 Research-status Report
  • 2019 Research-status Report
  • 2018 Research-status Report
  • Research Products

    (18 results)

All 2022 2021 2020 2019 2018

All Journal Article (5 results) (of which Peer Reviewed: 4 results,  Open Access: 3 results) Presentation (13 results) (of which Int'l Joint Research: 7 results)

  • [Journal Article] On parametric border bases2020

    • Author(s)
      Yosuke Sato, Hiroshi Sekigawa, Ryoya Fukasaku, Katsusuke Nabeshima
    • Journal Title

      Lecture Notes in Computer Science

      Volume: 11989 Pages: 10-15

    • DOI

      10.1007/978-3-030-43120-4_2

    • ISBN
      9783030431198, 9783030431204
    • Related Report
      2019 Research-status Report
    • Peer Reviewed
  • [Journal Article] On Multivariate Hermitian Quadratic Forms2019

    • Author(s)
      Ryoya Fukasaku, Hidenao Iwane, Yosuke Sato
    • Journal Title

      Mathematics in Computer Science

      Volume: 13 Issue: 1-2 Pages: 79-93

    • DOI

      10.1007/s11786-018-0387-8

    • Related Report
      2019 Research-status Report 2018 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] パラメトリックな連立代数方程式の根の連続性についてII2019

    • Author(s)
      佐藤洋祐,深作亮也,関川浩
    • Journal Title

      数式処理

      Volume: Vol.25 No.1 Pages: 87-89

    • Related Report
      2018 Research-status Report
  • [Journal Article] On Continuity of the Roots of a Parametric Zero Dimensional Multivariate Polynomial Ideal2018

    • Author(s)
      Sato Yosuke、Fukasaku Ryoya、Sekigawa Hiroshi
    • Journal Title

      Proceedings of the 2018 ACM on International Symposium on Symbolic and Algebraic Computation

      Volume: 2018 Pages: 359-365

    • DOI

      10.1145/3208976.3209004

    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] On Applications of Technology to Understanding Hierarchies of Elementary Geometry2018

    • Author(s)
      Yosuke Sato, Ryoya Fukasaku, Katsusuke Nabeshima
    • Journal Title

      Proceedings of the 23rd Asian Technology Conference in Mathematics

      Volume: 2018 Pages: 176-185

    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Open Access
  • [Presentation] 飽和イデアルの計算によるCGSの簡易化2022

    • Author(s)
      佐藤洋祐
    • Organizer
      日本数式処理学会第31回大会 山口東京理科大学
    • Related Report
      2022 Annual Research Report
  • [Presentation] Simplification of comprehensive Groebner systems using disequalities2022

    • Author(s)
      Yosuke Sato
    • Organizer
      26th International Conference on Applications of Computer Algebra
    • Related Report
      2022 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Comprehensive Groebner System(CGS)の簡易化とSageMathによる実装2022

    • Author(s)
      佐藤洋祐
    • Organizer
      限量子消去の効率的なアルゴリズムの構築と産業課題解決への応用 九州大学
    • Related Report
      2022 Annual Research Report
  • [Presentation] 包括的グレブナー基底系の改良とSageMathへの実装2022

    • Author(s)
      谷脇珠和,佐藤洋祐
    • Organizer
      Risa/Asir Conference 2022
    • Related Report
      2021 Research-status Report
  • [Presentation] Some tips on the implementation of CGS in SageMath2021

    • Author(s)
      Miwa Taniwaki, Yosuke Sato,
    • Organizer
      26th International Conference on Applications of Computer Algebra
    • Related Report
      2021 Research-status Report
    • Int'l Joint Research
  • [Presentation] SageMathでのCGSの実装について2021

    • Author(s)
      佐藤洋祐、田村俊太郎
    • Organizer
      Risa/Asir Conference 2021
    • Related Report
      2020 Research-status Report
  • [Presentation] On Parametric Border Bases2019

    • Author(s)
      Yosuke Sato, Hiroshi Sekigawa, Ryoya Fukasaku, Katsusuke Nabeshima
    • Organizer
      MACIS2019
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research
  • [Presentation] パラメトリックな連立代数方程式の根の連続性について II2018

    • Author(s)
      佐藤洋祐,深作亮也,関川浩
    • Organizer
      日本数式処理学会第27回大会
    • Related Report
      2018 Research-status Report
  • [Presentation] A canonical representation of continuity of the roots of a parametric zero dimensional multi-variate polynomial ideal2018

    • Author(s)
      Yosuke Sato,Ryoya Fukasaku,Hiroshi Sekigawa
    • Organizer
      24th Conference on Applications of Computer Algebra
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research
  • [Presentation] On Continuity of the Roots of a Parametric Zero Dimensional Multivariate Polynomial Ideal2018

    • Author(s)
      Yosuke Sato,Ryoya Fukasaku,Hiroshi Sekigawa
    • Organizer
      International Symposium on Symbolic and Algebraic Computation
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research
  • [Presentation] 初等幾何学の問題の階層付けとCASによる計算2018

    • Author(s)
      佐藤洋祐
    • Organizer
      京都大学数理解析研究所 共同研究(公開型) 数学ソフトウェアとその効果的教育利用に関する研究
    • Related Report
      2018 Research-status Report
  • [Presentation] Hierarchies of Elementary geometry problems and their computation by CAS2018

    • Author(s)
      Yosuke Sato
    • Organizer
      International Workshop on Mathematical Softwares in Educations and Researches
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research
  • [Presentation] On Applications of Technology to Understanding Hierarchies of Elementary Geometry2018

    • Author(s)
      Yosuke Sato, Ryoya Fukasaku, Katsusuke Nabeshima
    • Organizer
      The 23rd Asian Technology Conference in Mathematics
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research

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Published: 2018-04-23   Modified: 2024-01-30  

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