Computing the torsion points of a variety defined by lacunary polynomials

2009/11/13 by Louis Patrick Leroux, Leroux, Louis
Computer Science · Engineering · Mathematics · #11Y16 #12Y05 #68W30 #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.0911.2594

openalex publication_date 2009/11/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present an algorithm for computing the set of torsion points satisfying a given system of multivariate polynomial equations. Its complexity is quasilinear in the logarithm of the degree of the input equations and exponential in their number of non zero terms and variables.

Related

• Computing the torsion points of a variety defined by lacunary polynomials
• Solving algebraic equations in roots of unity
• Efficiently Detecting Torsion Points and Subtori
• Torsion Points on an Algebraic Subset of an Affine Torus
• Counting torsion points on subvarieties of the algebraic torus