Conjugacy classes and rational period functions for Hecke triangle groups

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Conjugacy classes and rational period functions for Hecke triangle groups #16976

Closed a1dd0ea6-9300-4f97-bb3c-0f25ba420caf closed 9 years ago

a1dd0ea6-9300-4f97-bb3c-0f25ba420caf commented 10 years ago

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
Linking numbers
improved documentation and minor additions/modifications

Some remarks:

The code to determine class numbers/representatives is very slow at the moment. :-(
The case n=infinity is excluded / not supported yet :(

Depends on #16936

CC: @videlec

Component: modular forms

Keywords: hecke triangle group conjugacy class rational period function

Author: Jonas Jermann

Branch/Commit: 7dcee34

Reviewer: Vincent Delecroix

Issue created by migration from https://trac.sagemath.org/ticket/16976

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 9 years ago

Changed commit from 67116d5 to 9fabb44

a1dd0ea6-9300-4f97-bb3c-0f25ba420caf commented 9 years ago

comment:35

Hi again

Is the code ok now? Or what remains to be done?

Best Jonas

videlec commented 9 years ago

Changed branch from u/jj/triangle_conjugacy to u/vdelecroix/16976

videlec commented 9 years ago

comment:36

I had to merge with 6.6.beta1 because of a trivial merge conflict due to #17694

You should really think about cleaning before implementing anything else. I already made many remarks about that are here are more:

The code of MatrixGroupElement is done in such way that there is no need to write a custom __init__. You only need to implement a ._matrix_check in the parent.
There is a .gitignore file in sage/modular/modform_hecketriangle/ because of

commit c8cbd7acfc81bdc1c24684f26d986f59491e0a3a
Author: Martin Raum <martin@raum-brothers.eu>
Date:   Thu May 8 16:32:54 2014 +0200

    Rename folder for Hecke triangle modforms.

Vincent

New commits:

6d73481 merge sage-6.6.beta1 in #16976

videlec commented 9 years ago

Changed commit from 9fabb44 to 6d73481

a1dd0ea6-9300-4f97-bb3c-0f25ba420caf commented 9 years ago

New commits:

7dcee34 remove .gitignore, add further explanations on `__init__`, change ValueError to TypeError for element checks

a1dd0ea6-9300-4f97-bb3c-0f25ba420caf commented 9 years ago

Changed commit from 6d73481 to 7dcee34

a1dd0ea6-9300-4f97-bb3c-0f25ba420caf commented 9 years ago

Changed branch from u/vdelecroix/16976 to u/jj/triangle_conjugacy

vbraun commented 9 years ago

Changed branch from u/jj/triangle_conjugacy to 7dcee34