Grothendieck point residue is considered in the context of computational complex analysis. A new effective method is proposed for computing Grothendieck point residues mappings and residues. Basic ideas of our approach are the use of Grothendieck local duality and a transformation law for local cohomology classes. A new tool is devised for efficiency to solve the extended ideal membership problems in local rings. The resulting algorithms are described with an example to illustrate them. An extension of the proposed method to parametric cases is also discussed as an application.

中文翻译：

---

一种计算格洛腾迪克点残差映射的有效方法

Grothendieck 点残差在计算复杂分析的上下文中被考虑。提出了一种新的有效方法来计算格洛腾迪克点残基映射和残基。我们方法的基本思想是使用 Grothendieck 局部对偶性和局部上同调类的变换定律。为了提高效率，设计了一种新工具来解决局部环中的扩展理想隶属度问题。生成的算法用一个例子来说明。还讨论了将所提出的方法扩展到参数情况的应用。