论文标题
关于Hermite投影仪的主要分解
On primary decomposition of Hermite projectors
论文作者
论文摘要
多项式空间上的理想投影仪$ \ mathbb {c} [\ MathBf {X}] = \ Mathbb {C} [X_ {1}，\ ldots，x_ {d}] $是投影仪的投影仪，其kernel的kernel在$ \ Mathbb {c} c} [c} [c} [c} [x \ math] $ {卡尔·德·博尔（Carl de Boor）提出了理想投影仪的特征性投影仪的特征问题。在本文中，我们为这个问题做出了贡献。每个理想的投影仪$ p $都可以写成理想投影仪$ \ sum p^{（k）} $ $ \ $的总和，这样$ \ cap \ ker p^{（k）} $是理想$ \ ker p $的主要分解。我们证明，$ p $是且仅当每个$ p^{（k）} $都是Lagrange投影仪的限制。作为一个应用程序，我们构建了一个理想的投影仪$ P $，其内核是对称的理想，但是$ p $不是Lagrange投影仪的限制。
An ideal projector on the space of polynomials $\mathbb{C} [\mathbf{x}]=\mathbb{C} [x_{1},\ldots ,x_{d}]$ is a projector whose kernel is an ideal in $\mathbb{C}[ \mathbf{x}]$. The question of characterization of ideal projectors that are limits of Lagrange projector was posed by Carl de Boor. In this paper we make a contribution to this problem. Every ideal projector $P$ can be written as a sum of ideal projector $\sum P^{(k)}$ $\ $such that $\cap \ker P^{(k)}$ is a primary decomposition of the ideal $\ker P$. We show that $P$ is a limit of Lagrange projectors if and only if each $P^{(k)}$ is. As an application we construct an ideal projector $P$ whose kernel is a symmetric ideal, yet $P$ is not a limit of Lagrange projectors.
