Computing the torsion points of a variety defined by lacunary polynomials

TL;DR

This paper introduces an algorithm to compute torsion points on varieties defined by lacunary polynomials, with complexity depending on the number of terms and variables, offering an efficient approach for such problems.

Contribution

The paper presents a novel algorithm specifically designed for lacunary polynomial systems to compute torsion points efficiently.

Findings

Algorithm has quasilinear complexity in the degree's logarithm

Complexity is exponential in the number of non-zero terms and variables

Provides an effective method for lacunary polynomial systems

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.