some new functionality and doctests for congruence subgroups

[aghitza]

The attached patch does the following:

1. allow coercing a 2x2 matrix (or a list of 4 elements) into a congruence subgroup: Gamma0(5)([1,5,1,6]) now works

2. modified G.generators() so that it actually returns a list of elements of the group G instead of just matrices

3. added gens()

4. added a bunch of doctests

Right now, all these changes are for Gamma0 and Gamma1 subgroups; I will do the same with GammaH subgroups as soon as I figure out how these work.

Component: modular forms

Keywords: congruence subgroup

Issue created by migration from https://trac.sagemath.org/ticket/2995

[aghitza]

comment:1

Attachment: congroup.patch.gz

I've replaced the previous patch with one that also has the changes listed above for the groups Gamma_H.

[ncalexan]

comment:2

Patch looks good, doctests are good too.

I hate the name acton -- it looks like a typoed action. Could we change that to act_on?

[sagetrac-mabshoff]

comment:3

Merged in Sage 3.0.1.alpha0

[aghitza]

comment:4

Nick: good point about acton(). I am planning to do some more work on congroup.py and friends, and I'll fix this then.