Quadratic Diophantine equations, the Heisenberg group and formal languages

2022/03/09 by Alex J. Levine, Levine, Alex · 1 citation
Mathematics · Computer Science · #Commutative Algebra and Its Applications #Polynomial and algebraic computation #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2203.04849

Abstract

We express the solutions to quadratic equations with two variables in the ring of integers using EDT0L languages. We use this to show that EDT0L languages can be used to describe the solutions to one-variable equations in the Heisenberg group. This is done by reducing the question of solving a one-variable equation in the Heisenberg group to solving an equation in the ring of integers, exploiting the strong link between the ring of integers and nilpotent groups.

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• Decidability of equations and first-order theory in Seifert 3-manifold groups

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