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@ -5,7 +5,18 @@ The repository contains code for running experiments for
[Marek Kaluba](https://kalmar.faculty.wmi.amu.edu.pl/) and [Marek Kaluba](https://kalmar.faculty.wmi.amu.edu.pl/) and
[Stefan Witzel](https://www.math.uni-bielefeld.de/~switzel/). [Stefan Witzel](https://www.math.uni-bielefeld.de/~switzel/).
There are three disjoint computations covered in this repository. # Introduction
If you arrived here after reading the article looking for groups and
1. you don't understand any of this, you probably want to visit [this page](https://kalmarek.github.io/SmallHyperbolic/) instead;
2. you want just the machine-readable data, then the `json` file is available [here](https://github.com/kalmarek/SmallHyperbolic/blob/master/data/triangle_groups.json) (the file was generated by calling `julia ./scripts/create_json/create_json.jl`);
3. you want to re-run some of the computations that lead to the results, then continue reading.
# Computations
There are three disjoint computations covered in this repository:
1. certified eigenvalue computations for _PSL₂(p)_,
2. sum of squares computations in an attempt to prove property (T) by estimating spectral gap of the group Laplacian,
3. generation of magma files used to compute e.g. witnesses for non-hyperbolicity, rank of abelianization, etc.
## Eigenvalues computations for _PSL₂(p)_ ## Eigenvalues computations for _PSL₂(p)_