Some results on counting roots of polynomials and the Sylvester resultant

2016/09/27 by Michael Monagan, Monagan, Michael, Baris Tuncer +1
Computer Science · Mathematics · #Combinatorics (math.CO) #Commutative Algebra and Its Applications #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Numerical Methods and Algorithms #Polynomial and algebraic computation #Symbolic Computation (cs.SC)

paper · pdf · doi:10.48550/arxiv.1609.08712

openalex publication_date 2016/09/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present two results, the first on the distribution of the roots of a polynomial over the ring of integers modulo n and the second on the distribution of the roots of the Sylvester resultant of two multivariate polynomials. The second result has application to polynomial GCD computation and solving polynomial diophantine equations.

Related

• Around the gcd of the values of two polynomials
• Roots of polynomials over division rings
• An Elementary Proof of Sylvester's Double Sums for Subresultants
• Counting polynomials over finite fields with given root multiplicities
• Counting Polynomial Roots in Isabelle/HOL: A Formal Proof of the Budan-Fourier Theorem