Don't waste time programming! The Experimental Geometry Lab spends a great deal of time developing Mathematica functions for our own projects. As these tools are useful for anyone working in similar subject areas, we have assembled our most useful functions into easy-to-use packages.
Hyperbolic Toolbox v1.0
Hyperbolic Toolbox is a Mathematica package that contains functions to draw hyperbolic geodesics and circles in the Poincaré unit disc as well as the Upper Half Plane model, compute and apply linear fractional transformations of the isometry group PSL(2,R), map from the Upper Half Plane to the Unit Disc and vice versa, as well as compute distances, label points, and other useful tasks.
TurboTessellate uses a depth-first recursion method to quickly and easily display tessellations of the once-punctured torus (regular and flared) on the Poincaré unit disc model. Turbo Tessellate applies only those transformations that will provide visible results, greatly reducing rendering time. It can even perform tessellations in real-time!
Free Group Autos
This is a package of Mathematica functions to facilitate working with free groups. One can generate lists of words in a free group and work with such words by applying automorphisms, cyclically reducing them, and various other group operations.