Comments (1)
More generally I want to revamp the parts of the library which do hyperbolic computations. We require:
- a class to represent conformal maps/anticonformal maps, which wraps matrices and also keeps information about precomposition of \overline{z};
- a class to represent families of circles which has different views (as centre/radius pairs, etc.)
then the maps should be able to act on different kinds of objects:
- hyperbolic space, in the upper half-space model
- circle families
We also would like to include n-dimensional hyperbolic space, but perhaps as a start only 2 and 3 dimensions.
Proposal: a new module, geometry.py
, which includes the following classes:
- MobiusMap, which encapsulates matrices in PSL(2,C) and includes functions such as "act_on" (which is allowed to take any of the three following classes).
- CircleSet, which internally keeps track of circles/lines in the conformal boundary
- Pencil, which keeps track of an entire 1D pencil of circles
- HyperbolicPoint, which keeps track of a point in hyperbolic space.
We then have various geometric functions, e.g. cross-ratio, hyperbolic distance, construction of triangles, conformal product etc.
Next step is to produce a list of exactly which functions we will include with references to standard textbooks e.g. Beardon, Ratcliffe, Maskit.
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