#9439: hyperbolic geometry
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Reporter: vdelecroix | Owner: vdelecroix
Type: enhancement | Status: new
Priority: major | Milestone: sage-4.8
Component: geometry | Keywords: hyperbolic geometry, Poincare
disc, upper half plane
Work_issues: | Upstream: N/A
Reviewer: | Author: vdelecroix
Merged: | Dependencies:
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Comment(by johanbosman):
Replying to [comment:4 vdelecroix]:
>
> I agree on the fact that near the real line it is unstable but disagree
on the fact that we need a 5 dimensional object (an element of SL(2,R) and
a complex number) to record a 2 dimensional object (a point in the half
plane). The best option would be to store only the SL(2,R) matrix m such
that the point is the image by z of the point i. Two matrices give the
same point iff they are congruent modulo SO(2).
>
Okay. Another possibility is to have the matrix ((a, b), (c, d)) in
SL_2(ZZ) and the complex number z in the standard fundamental domain for
this group. Or use both representations (and allow oneself to convert
between them).
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9439#comment:5>
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