Development of efficient algorithms for complex and real algebraic constraints
| Project/Area Number |
18K03426
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Review Section |
Basic Section 12040:Applied mathematics and statistics-related
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| Research Institution | Tokyo University of Science |
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Principal Investigator |
Sato Yosuke 東京理科大学, 理学部第一部応用数学科, 教授 (50257820)
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| Project Period (FY) |
2018-04-01 – 2023-03-31
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| Project Status |
Completed (Fiscal Year 2022)
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| 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)
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| Keywords | CGS / 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 |
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| 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.
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| 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。
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Report
(6 results)
Research Products
(18 results)
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[Journal Article] On parametric border bases2020
Author(s)
Yosuke Sato, Hiroshi Sekigawa, Ryoya Fukasaku, Katsusuke Nabeshima
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Journal Title
Lecture Notes in Computer Science
Volume: 11989
Pages: 10-15
DOI
ISBN
9783030431198, 9783030431204
Related Report
Peer Reviewed
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