PyRigi—A General-Purpose Python Package for the Rigidity and Flexibility of Bar-and-Joint Frameworks

We present PyRigi, a novel Python package designed to study the rigidity properties of graphs and frameworks. Among many other capabilities, PyRigi can determine whether a graph admits only finitely many ways, up to isometries, of placing the vertices in the plane so that the corresponding edge lengths are not altered, it can check whether the graph satisfies such a property even after the removal of any of its edges, and whether it has a unique vertex placement. By implementing algorithms from the scientific literature, PyRigi enables the exploration of rigidity properties of structures that would be out of reach for computations by hand. With reliable and robust algorithms, as well as clear, well-documented methods that are closely connected to the underlying mathematical definitions and results, PyRigi aims to be a practical and powerful general-purpose tool for the working mathematician interested in rigidity theory. PyRigi is open source and easy to use, and awaits researchers to benefit from its computational potential.