Generic congruence subgroups

[davidloeffler]

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.

Apply 11601.4.patch​ on top of #5048. Once this is merged, #12001 can be closed as fixed.

[davidloeffler]

Patch against 4.7.1.alpha4 + dependencies as in ticket description

[davidloeffler]

New version rebased for 4.7.2.alpha3

[johanbosman]

I tried to apply trac_11601-congroups.2.patch to 4.8.alpha4 + #5048, but it failed.

[johanbosman]

I'm getting a warning when building the documentation, in is_CongruenceSubgroup in congroup_generic.py:

    Note that this may be False even if `x` really is a congruence subgroup --
    it tests whether `x` is "obviously" congruence, i.e.~whether it has a
    congruence subgroup datatype. To test whether or not an arithmetic subgroup
    of `SL(2, \ZZ)` is congruence, use the ``is_congruence()` method instead.

I guess a quote is missing at the end of is_congruence().

[davidloeffler]

Apply 11601.4.patch

(for the patchbot, so it knows the prerequisites for 11709)