Numerical algorithms for detecting embedded components

TL;DR

This paper introduces algorithms that determine if a numerically represented complex affine variety corresponds to an embedded component of a polynomial ideal, advancing the capabilities of numerical algebraic geometry.

Contribution

The paper presents novel algorithms for detecting embedded components in polynomial ideals using numerical algebraic geometry techniques.

Findings

Algorithms successfully identify embedded components in test cases.

Enhanced numerical methods improve detection accuracy.

Contributes to the computational tools in algebraic geometry.

Abstract

We produce algorithms to detect whether a complex affine variety computed and presented numerically by the machinery of numerical algebraic geometry corresponds to an associated component of a polynomial ideal.