#11601: Generic congruence subgroups
-----------------------------+----------------------------------------------
Reporter: davidloeffler | Owner: craigcitro
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-4.7.2
Component: modular forms | Keywords: modular subgroup congruence
Work_issues: | Upstream: N/A
Reviewer: | Author: David Loeffler
Merged: | Dependencies: #10335, #11422, #11598, #10453,
#5048
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Changes (by davidloeffler):
* dependencies: #10335, #11422, #11598, #5048, #10453 => #10335, #11422,
#11598, #10453, #5048
Old description:
> This ticket adds functionality to work with arbitrary congruence
> subgroups of the modular group (specified by a level N and a subgroup of
> the finite group {{{ SL(2, Z / N Z) }}}). These support all the basic
> functionality one would expect: computation of index, genus, elliptic
> points, cusps, etc. There is also a facility to compute the congruence
> closure of a (possibly noncongruence) subgroup.
>
> Some "rationalisation" is also included: e.g. one can no longer create
> {{{Gamma1(1)}}} or {{{GammaH(11, [2])}}}, which previously existed as
> less-functional duplicates of {{{SL2Z}}} and {{{Gamma0(11)}}}. (They
> previously played a role in "remembering" where certain degeneracy maps
> would go, but they didn't do this very well -- which was the cause of the
> issue at #10453 -- and the new more robust approach introduced at #10453
> means we can get rid of them at last.)
>
> Part of a series of tickets: #10335 - #11422 - #11598 - #5048 - #10453 -
> this one - #10546.
New description:
This ticket adds functionality to work with arbitrary congruence subgroups
of the modular group (specified by a level N and a subgroup of the finite
group {{{ SL(2, Z / N Z) }}}). These support all the basic functionality
one would expect: computation of index, genus, elliptic points, cusps,
etc. There is also a facility to compute the congruence closure of a
(possibly noncongruence) subgroup.
Some "rationalisation" is also included: e.g. one can no longer create
{{{Gamma1(1)}}} or {{{GammaH(11, [2])}}}, which previously existed as
less-functional duplicates of {{{SL2Z}}} and {{{Gamma0(11)}}}. (They
previously played a role in "remembering" where certain degeneracy maps
would go, but they didn't do this very well -- which was the cause of the
issue at #10453 -- and the new more robust approach introduced at #10453
means we can get rid of them at last.)
Part of a series of tickets: #10335 - #11422 - #11598 - #10453 - #5048 -
this one - #10546.
--
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11601#comment:3>
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