Introduction

For positive integers $u$ and $v$, let

$$L_u=\begin{bmatrix} 1 & 0 \\ u & 1 \end{bmatrix},$$

$$R_v=\begin{bmatrix} 1 & v \\ 0 & 1 \end{bmatrix},$$

and $G_{u,v}$ be the group generated by $L_u$ and $R_v$.

The membership problem involves finding a relatively simple algorithmic way for determining membership in $G_{u,v}.$ For more details, see ....

This is joint work with Sandie Han, Ariane M. Masuda, and Satyanand Singh.

Content

The algorithm_implementation.ipynb file contains Sagemath code used for computational experiments (see ...).