#16976: Conjugacy classes and rational period functions for Hecke triangle
groups
-------------------------------------+-------------------------------------
Reporter: jj | Owner:
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.4
Component: modular forms | Resolution:
Keywords: hecke triangle | Merged in:
group conjugacy class rational | Reviewers:
period function | Work issues: want: positive block
Authors: Jonas Jermann | exponents
Report Upstream: N/A | Commit:
Branch: | d14ee40b27fc54f5dc2e0ffe1bbb5a5f1c57e5cc
u/jj/triangle_conjugacy | Stopgaps:
Dependencies: #16936 |
-------------------------------------+-------------------------------------
Changes (by jj):
* status: needs_work => needs_review
Old description:
> The ticket adds several new features to Hecke triangle groups (resp.
> elements):
>
> - "Block" decomposition of elements. This determines the conjugacy type
> of elements
> - Several alternative representation methods for elements
> - Lambda-continued fraction expansion of fixed points (exact!)
> In particular the primitive part of a group element can be determined
> - Checks and generation of reduced and simple elements, Checks for Hecke
> symmetry
> - Slash operator
> - Rational period functions associated to hyperbolic elements (resp.
> their fixed point)
> - class number and class representatives for a given discriminant
> In particular discriminants can be listed, so can all simple/reduced
> elements
> for a given discriminant
> - improved documentation and minor additions/modifications
>
> The code to determine class numbers/representatives is very slow at the
> moment. :-(
New description:
The ticket adds several new features to Hecke triangle groups (resp.
elements):
- "Block" decomposition of elements. This determines the conjugacy type of
elements
- Several alternative representation methods for elements
- Lambda-continued fraction expansion of fixed points (exact!)
In particular the primitive part of a group element can be determined
- Checks and generation of reduced and simple elements, Checks for Hecke
symmetry
- Slash operator
- Rational period functions associated to hyperbolic elements (resp. their
fixed point)
- class number and class representatives for a given discriminant
In particular discriminants can be listed, so can all simple/reduced
elements
for a given discriminant
- improved documentation and minor additions/modifications
Some remarks:
1. The code to determine class numbers/representatives is very slow at the
moment. :-(
2. In some (complex) cases calculations seem to fail (see
continued_fraction),
probably because of issues / too high complexity in underlying sage
objects
(AA, NumberField, etc)
3. The case n=infinity is excluded / not supported yet
--
--
Ticket URL: <http://trac.sagemath.org/ticket/16976#comment:8>
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