论文标题
主要理想及其微分方程
Primary ideals and their differential equations
论文作者
论文摘要
多项式环中的理想是编码具有恒定系数的线性偏微分方程系统。主要分解组织了PDE的解决方案。本文为多项式环中的主要理想发展了一种新颖的结构理论。我们以PDE，守时希尔伯特方案，相对Weyl代数和联接结构来表征主要理想。用主要理想来解决的PDE，量是从Ehrenpreis和Palamodov的意义上计算Noetherian运营商的。我们为此任务开发了新的算法，并提出了有效的实现。
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.
