Study of parametric system of equations for singularity theory
Project/Area Number |
25800029
|
Research Category |
Grant-in-Aid for Young Scientists (B)
|
Allocation Type | Multi-year Fund |
Research Field |
Algebra
|
Research Institution | Kyushu University |
Principal Investigator |
Shibuta Takafumi 九州大学, マス・フォア・インダストリ研究所, 助教 (40648200)
|
Project Period (FY) |
2013-04-01 – 2016-03-31
|
Project Status |
Completed (Fiscal Year 2015)
|
Budget Amount *help |
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2013: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
|
Keywords | 標準基底 / 代数的局所コホモロジー / マトリス双対 / アルゴリズム / 計算機代数 / 局所可換環論 / パラメトリック方程式系 / 計算代数 / 可換環論 / 孤立特異点 / 局所コホモロジー / 偏微分方程式系 |
Outline of Final Research Achievements |
In this research, the theory of Matlis duality with term orders over regular local rings was developed. Based on the theory, a new algorithm it for computing the holonomic system consisting of the linear differential operators of order at most n that vanishes a given algebraic local cohomology class was presented. An algebraic algorithm based on toric ideal theory for solving parametric linear integral programming was also presented.
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Report
(4 results)
Research Products
(12 results)