Plotting geodesics in SL2(Z)∖H
In here there are functions that allow to plot geodesics in the upper half plane (namely, half circles perpendicular to the x axis and vertical lines). Are there similar functions that do the same thing but only in the fundamental domain of SL2(Z), so that the geodesic is folded up into the domain |x|<12 and x2+y2>1?
What I would like to have is something like the picture in page 5 of this paper.
There is no straightforward function to do it. However a simple algorithm is not hard to implement. You just need to look at the next intersection with the boundary, and apply the appropriate isometry... though the intersection feature is broken: see #23427.