| Project/Area Number |
22740065
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | The University of Tokushima |
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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)
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| Research Collaborator |
TAJIMA Shinichi 筑波大学, 大学院・数理物質系, 教授 (70155076)
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| Project Period (FY) |
2010 – 2012
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| Project Status |
Completed (Fiscal Year 2012)
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| 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)
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| 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 |
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| 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.
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