#11709: FareySymbol
-------------------------------+--------------------------------------------
Reporter: hmonien | Owner: craigcitro
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-5.0
Component: modular forms | Resolution:
Keywords: Farey symbol | Work_issues:
Upstream: N/A | Reviewer: Martin Raum, Leif Leonhardy,
David Loeffler
Author: Hartmut Monien | Merged:
Dependencies: |
-------------------------------+--------------------------------------------
Old description:
> !FareySymbol is a '''fast''' implementation of the '''KFarey''' package
> for Sage.
>
> The major changes done by me:
>
> * created an object oriented coherent class interface
>
> * implemented a C++ module with pyx interface
>
> !FareySymbol allows the calculation of properties of a general arithmetic
> subgroup. The use with the congruence subgroups Gamma0, Gamma1, GammaH
> is trivial. For a group not implemented in Sage, the "user" has to define
> a class with a `__contains__(self, M)` attribute which returns `True` or
> `False` depending on `M` being in the group or not.
>
> The calculation of the generators, coset representation and genus of
> Gamma(32) takes 62.5 seconds on my laptop. Try this with Magma ... .
>
> {{{
> sage: time FareySymbol(Gamma(32))
> FareySymbol(Congruence Subgroup Gamma(32))
> Time: CPU 62.50 s, Wall: 62.52 s
> }}}
>
> ----
>
> Apply
> 1. [attachment:trac-11709_farey_symbol-sage-4.8.patch]
New description:
!FareySymbol is a '''fast''' implementation of the '''KFarey''' package
for Sage.
The major changes done by me:
* created an object oriented coherent class interface
* implemented a C++ module with pyx interface
!FareySymbol allows the calculation of properties of a general arithmetic
subgroup. The use with the congruence subgroups Gamma0, Gamma1, GammaH is
trivial. For a group not implemented in Sage, the "user" has to define a
class with a `__contains__(self, M)` attribute which returns `True` or
`False` depending on `M` being in the group or not.
The calculation of the generators, coset representation and genus of
Gamma(32) takes 62.5 seconds on my laptop. Try this with Magma ... .
{{{
sage: time FareySymbol(Gamma(32))
FareySymbol(Congruence Subgroup Gamma(32))
Time: CPU 62.50 s, Wall: 62.52 s
}}}
----
Apply
1. [attachment:trac-11709_farey_symbol-sage-5.0.patch]
2. [attachment:trac_11709-review.patch]
--
Comment(by davidloeffler):
I just realised that the patch breaks a line in William's old 2008
Bordeaux slides which are included as part of the documentation. The
slides complain about Farey symbols not being implemented, so I've added a
comment explaining that they are now implemented and changed the doctest.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11709#comment:35>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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