2012 Fiscal Year Final Research Report
Algorithms for systems of parametric polynomials
| 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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| Keywords | アルゴリズム / 関数論 / 情報基礎 / 代数学 |
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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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