Primary Ideals and Their Differential Equations
Primary Ideals and Their Differential Equations
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基本理想及其微分方程
DOI：
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发表时间：
2020
影响因子：
3
通讯作者：
B. Sturmfels
中科院分区：
文献类型：
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作者：
Yairon Cid‐Ruiz;R. Homs;B. Sturmfels
多项式环上的理想编码常系数线性偏微分方程组。初级分解组织偏微分方程组的解。本文发展了多项式环中素理想的一种新的结构理论。我们用偏微分方程、点Hilbert格式、相对Weyl代数和并结构刻画了初等理想。求解由初等理想描述的偏微分方程组，相当于计算Ehrenpreis和Palamodov意义下的Noether算子。我们为这项任务开发了新的算法，并给出了有效的实现。
An ideal in a polynomial ring encodes a system of linear partial differential equations with constant coefficients. Primary decomposition organizes the solutions to the PDE. This paper develops a novel structure theory for primary ideals in a polynomial ring. We characterize primary ideals in terms of PDE, punctual Hilbert schemes, relative Weyl algebras, and the join construction. Solving the PDE described by a primary ideal amounts to computing Noetherian operators in the sense of Ehrenpreis and Palamodov. We develop new algorithms for this task, and we present efficient implementations.