Work

Slices of stable polynomials and connections to the Grace-Walsh-Szegő theorem

Year: 2025

Type: article

Abstract: Univariate polynomials are called stable with respect to a domain D if all of their roots lie in D . We study linear slices of the space of stable univariate polynomials with respect to a half-plane. We show that a linear slice always contains a stable polynomial with only a few distinct roots. Subsequently, we apply these results to symmetric polynomials and varieties. We show that for varieties defined by few multiaffine symmetric polynomials, the existence of a point in D n with few distinct coordinates is necessary and sufficient for the intersection with D n to be non-empty. This is at the same time a generalization of the so-called degree principle to stable polynomials and a result similar to Grace-Walsh-Szegő's coincidence theorem.

Source: Journal of Symbolic Computation

DOI: 10.1016/j.jsc.2025.102488

Authors: Sebastian Debus, Cordian Riener, Robin Schabert

Institutions: Chemnitz University of Technology, UiT The Arctic University of Norway, University of Konstanz

Language: English

Topic: Polynomial and algebraic computation

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,160

Funder: Tromsø Forskningsstiftelse