[with revised patch, with positive review] General linear group over ZZ hangs in __call__

This has been around for a while, and it's been bugging me. I fixed it by writing methods __call__ and __contains__ for the class GeneralLinearGroup_generic, so that the GAP ones (which hang over ZZ) don't get used. A pleasant side effect is that things are now faster for the cases that were working before (i.e. over finite fields):

before:

sage: G = GL(5, GF(next_prime(6*10^4)))                                    
sage: m = [[1,0,1,0,2],[0,1,0,1,1],[0,0,1,0,0],[0,0,0,1,1],[0,0,0,0,1]]                              
sage: timeit("G(m)")                                                                                     
25 loops, best of 3: 9.56 ms per loop

after:

sage: G = GL(5, GF(next_prime(6*10^4)))                                    
sage: m = [[1,0,1,0,2], [0,1,0,1,1], [0,0,1,0,0], [0,0,0,1,1], [0,0,0,0,1]]                              
sage: timeit("G(m)")                                                                                     
625 loops, best of 3: 459 µs per loop

The same issue comes up for all the matrix groups. For the moment, I have only dealt with the really easy cases of GL and SL. If this gets approved and merged, I will open a new ticket for the other classes of groups and deal with them in a similar way.

Basically ok, but I would make the following changes to both cases (GL and SL):

Use a try: except: block to catch when coercion in the matrix space fails, with the error message "Cannot coerce ... to a matrix". Then catch the non-invertible matrices in the GL case with the error message "... is not an invertible matrix", and similarly in the SL case with "... does not have determinant 1".

I think this alternative error handling will produce better output.

PS As this is not "algebraic geometry" I changed the Component to Linear Algebra

Good idea. I have made the changes and replaced the patch with a new one.

Excellent. These are much more helpful messages.

The new patch applies ok to 3.1.2.alpha3 (there was a little fuzz:

applying /home/john/1834-gl_z_call.patch
patching file sage/groups/matrix_gps/matrix_group.py
Hunk #1 succeeded at 13 with fuzz 1 (offset 3 lines).

but nothing serious). All doctests in sage.groups.matrix_groups pass. Publish!

Merged in Sage 3.1.2.alpha4