Convex geometry of the hyperbolic plane

[videlec]

This is a draft of notes that we took at a meeting in Bordeaux in early 2022. Please extend these notes.

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Geometry on the hyperbolic plane is not really implemented in SageMath. It's needed for our implementation of #155. While it might eventually go upstream into SageMath, we want to first implement it in sage-flatsurf.

Here are some objects that we think we should implement:

class flatsurf.geometry.HyperbolicPlane:
    # over a fixed base ring. Probably does nothing but store that base ring.

class flatsurf.geometry.HyperbolicHalfPlane:
    # implement sagemath containment for points

class flatsurf.geometry.HyperbolicPoint:

class flatsurf.geometry.HyperbolicPolytope:
    # intersection of half planes, as a list of edges.

class flatsurf.geometry.HyperbolicEdge:

It is not completely clear which hyperbolic model is the best to work with (probably the hyperboloid is more "linear").

[saraedum]

Superseded by #156 due to permission issues.