Study of parametric system of equations for singularity theory

2015 Fiscal Year Final Research Report

• 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
• 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

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.

Free Research Field

可換環論, 計算機代数