Noetherian operators and primary decomposition. (May 2022) - Chen, Justin; Härkönen, Marc; Krone, Robert; Leykin, Anton
Abstract: 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.