#11601: Generic congruence subgroups
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Reporter: davidloeffler | Owner: craigcitro
Type: enhancement | Status: new
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, #5048,
#10453
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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.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11601>
Sage <http://www.sagemath.org>
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