#9557: fundamental domains for subgroups of PSL(2,ZZ)
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Reporter: vdelecroix | Owner: Vincent Delecroix
Type: enhancement | Status: new
Priority: major | Milestone: sage-4.5.2
Component: geometry | Keywords: hyperbolic geometry,
fundamental domains, Fuchsian groups
Author: Vincent Delecroix | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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Given a discrete subgroup of PSL(2,R) there exists a fundamental domain of
the action of this group on the hyperbolic plane. Knowing one fundamental
domain for a group, gives you the fundamental domain for any subgroups.
This module implement the passage from the fundamental domain of PSL(2,ZZ)
to any subgroup of finite index
The way is work concerns only the second part as I have to improve the
transition (subgroup of PSL(2,Z)) <-> (coset graph). The first line just
build the coset graph associated to the congruence subgroup Gamma(3).
{{{
sage: g = sage.geometry.fundamental_domains.gamma_triangle_graph(3)
sage: g
Triangle graph (2,3,infinty) with 12 vertices
sage: FundamentalDomain(g)
Fundamental domain of a subgroup of index 12
sage: FundamentalDomain(g).show()
}}}
Dependancy:
#9439 on hyperbolic geometry
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9557>
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