The constructive membership problem for discrete two-generator subgroups of \(\operatorname{SL}_2(\mathbb{R})\) (Q524500)

Let \(G=\left\langle A,B\right\rangle \) be a discrete two generator subgroup of SL\(_{2}(\mathbb{R})\), where \(A,B\in \) SL\(_{2}(\mathbb{R})\). The constructive membership problem for \(G\) asks whether any given \(M\in \) SL\(_{2}(\mathbb{R})\) lies in \( G\) and if so, how to express \(M\) as a word in the generators \(A\) and \(B\). In the paper under review, the authors solve the constructive membership problem for all discrete two-generator subgroups of SL\(_{2}(\mathbb{R})\).