Algebraic analysis of algebraic local cohomology and computational complex analysis of non-isolated singularities

在代数分析的背景下，研究了超表面孤立奇点上的代数局部上同类。提出了一种计算参数代数局部上同类的新算法。构造了一个研究对数向量场及相关完整d模的新框架。通过解析解，推导出一种计算方阵谱分解的有效算法。

Algebraic local cohomology classes attached to hypersurface isolated singularities are considered in the context of algebraic analysis. A new algorithm of computing parametric algebraic local cohomology classes is derived. A new framework to study logarithmic vector fields and associated holonomic D-modules is constructed. An efficient algorithm to compute spectral decomposition of square matrices is derived by analyzing resolvent.