Criteria for a split real polynomial

2024/03/06 by Jean‐Michel Billiot, Billiot, Jean-Michel, Éric Fontenas +1
Computer Science · Engineering · #Combinatorics (math.CO) #FOS: Mathematics #Material Science and Thermodynamics #Number Theory (math.NT) #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2403.19692

openalex publication_date 2024/03/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, we establish necessary and sufficient conditions for a polynomial of degree n to have exactly n real roots. A complete study of polynomials of degree five is carried out. The results are compared with those obtained using Sturm sequences.

Related

• An iterative approach for real roots of polynomials
• Note on the real rootedness of polynomials
• The number of real roots of a bivariate polynomial on a line
• Computing Real Roots of Real Polynomials
• Could René Descartes have known this?