Introduction
This package provides methods for computing with finite-index subgroups of the modular group ${\rm SL}_2(\mathbb{Z})$.
A convenient way to represent finite-index subgroups of ${\rm SL}_2(\mathbb{Z})$ is by specifying the action of generator matrices of ${\rm SL}_2(\mathbb{Z})$ on the right cosets by right multiplication. For example, one could choose the generators
\[S = \begin{pmatrix} 0 & -1 \\ 1 & 0 \end{pmatrix} \qquad T = \begin{pmatrix} 1 & 1 \\ 0 & 1 \end{pmatrix}\]
and represent a subgroup as a tuple of transitive permutations $(\sigma_S, \sigma_T)$ describing the action of $S$ and $T$. This is exactly the way this package internally treats such subgroups. We use the convention that $1$ corresponds to the coset of the identity matrix. Note that such a representation as a tuple of permutations is only unique up to relabeling of the cosets, i.e. up to simultaneous conjugation (fixing the $1$ coset by our convention).
Status
This part of OSCAR is in an experimental state; please see Adding new projects to experimental for what this means. See also the dedicated README.md for details.
Contact
Please direct questions about this part of OSCAR to the following people:
You can ask questions in the OSCAR Slack.
Alternatively, you can raise an issue on GitHub.