Noetherian operators are differential operators that encode primary components of a polynomial ideal. We develop a framework, as well as algorithms, for computing Noetherian operators with local dual spaces, both symbolically and numerically. For a primary ideal, such operators provide an alternative representation to one given by a set of generators. This description fits well with numerical algebraic geometry, taking a step toward the goal of numerical primary decomposition.

中文翻译：

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诺特算子和初级分解

诺特算子是对多项式理想的主要成分进行编码的微分算子。我们开发了一个框架和算法，用于计算具有局部对偶空间的 Noetherian 算子，包括符号和数字。对于主要理想，此类运算符提供了一组生成器给出的表示的替代表示。这种描述与数值代数几何非常吻合，朝着数值初级分解的目标迈出了一步。