Noetherian operators and primary decomposition

2020/06/24 by Chen, Justin, Härkönen, Marc, Krone, Robert +1
#13N05 #14-04 #14Q15 #65D05 #65L80 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Computer and information sciences #FOS: Mathematics #Symbolic Computation (cs.SC)

paper · doi:10.48550/arxiv.2006.13881

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.

Related

• Primary ideals and their differential equations
• Primary Decomposition with Differential Operators
• Noetherian operators, primary submodules and symbolic powers
• Primary decomposition of modules: a computational differential approach
• The noetherian properties of the rings of differential operators on central 2-arrangements