[with patch, positive review] quaternion algebras -- add computation of left and right orders associated to ideals

[was]

A big gap in functionality for quaternion algebras right now is that one can't compute the left and right orders associated to ideals (the functions raise NotImplementedError?). I just designed a little algorithm and wrote code to do this for my research and will post a patch here soon.

Just in case I misplace it, some demo code that works is the following:

def left_order(I):
    Q = I.quaternion_algebra()
    M = [matrix([(a*b).coefficient_tuple() for a in Q.basis()]) for b in I.basis()]
    B = I.basis_matrix()
    invs = [(B*m^(-1)).row_module(ZZ) for m in M]
    IS = invs[0].intersection(invs[1]).intersection(invs[2]).intersection(invs[3])
    ISB = [Q(v) for v in IS.basis()]
    return Q.quaternion_order(ISB)

[robertwb]

sage/algebras/quatalg/quaternion_algebra.py:1272

ALGORITHM: Let `b_1, b_2, b_3, b_3` be a basis for this 

(Typo, you want b_4).

TabularUnified? sage/matrix/matrix_integer_dense.pyx:2310

if max(self._nrows, self._ncols) <= 50: 

I think you intended to have an elif here.

Other than that, looks good to me. Also, while I was playing around with it trying it out, I found #6762 useful.

[mvngu]

William: any words on the typos reported by Robert?

[was]

Regarding Robert's comments:

* I posted a patch fixing the b_3 |--> b_4 typo.

* The matrix_integer_dense.pyx is *not* a typo. The issue is that I want to default to pari for small matrices, *unless* said small matrix has huge entries, so the logic is correct (i.e., if entries huge, still use padic). I've put in some spaces and an {{{# endif} comment to maybe make that seem more intentional.

So the attached patch changes no logic in the code, but changes/improves two comments.

[was]

fix comments

[robertwb]

Great. Positive review.

[mvngu]

Merged both patches.