LAUSR

Let $$\mathfrak {X}(\Gamma ,G)$$X(Γ,G) be the G-character variety of $$\Gamma $$Γ where G is a rank 1 complex affine algebraic group and $$\Gamma $$Γ is a finitely presentable discrete group. We describe an algorithm, which we implement in Mathematica, SageMath, and in Python, that takes a finite presentation for $$\Gamma $$Γ and produces a finite presentation of the coordinate ring of $$\mathfrak {X}(\Gamma ,G)$$X(Γ,G). We also provide a new description of the defining relations and local parameters of the coordinate ring when $$\Gamma $$Γ is free. Although the theorems used to create the algorithm are not new, we hope that as a well-referenced exposition with a companion computer program it will be useful for computation and experimentation with these moduli spaces.