MG-MAMPOSSt, a code to test gravity at galaxy-cluster scales: a technical introduction

The \textsc{MG-MAMPOSSt} code is a license-free \textsc{Fortran95} code to perform tests of General Relativity (GR) through the analyses of kinematical data of galaxy clusters based on the Jeans' equation. The code is based on the \textsc{MAMPOSSt} method, and extends the original code through new parametrisations of the gravitational potential for general families of gravity theories beyond GR aimed to explain dark energy. \textsc{MG-MAMPOSSt} is further supplemented with a new capability to produce weak lensing forecasts for joint kinematic+lensing analysis. This document provides a technical description of the code's new features, functionality with respect to the original version, and instructions on its installation and use. Finally, we explain how the code could be further modified to include a wider family of gravity models and/or density profiles, that could allow its application in broader theoretical frameworks as well as other physical systems such as stellar clusters. A detailed forecast analysis for the modified gravity models currently implemented in the code can be found in the paper of Pizzuti et al., 2021.