Fix quaternion algebras over number field

[videlec]

In this sage devel thread was mentioned the following bug

sage: K = NumberField(x**3 + x - 1, 'a')
sage: D.<i,j,k> = QuaternionAlgebra(K, -1, -3)
sage: j/3 + (2*j)/3 == j
False

CC: @NathanDunfield @williamstein

Component: algebra

Author: Vincent Delecroix

Branch/Commit: 5497084

Reviewer: Nathan Dunfield

Issue created by migration from https://trac.sagemath.org/ticket/17099

[videlec]

New commits:

f0f8599	trac #17099: fix quaternion algebra over number fields
5497084	trac #17099: doc

[videlec]

Commit: 5497084

[videlec]

Branch: u/vdelecroix/17099

[NathanDunfield]

comment:2

I looked at Vincent's patch and tested it on my own machine. It definitely fixes the issue and the new doctest passes. However, buildbot reports doctest failures in other modules (including ones almost certainly unconnected with the quaternion algebra code, like "src/sage/rings/real_double.pyx"). Am I allowed to move the status to "positive review" in this situation?

[NathanDunfield]

comment:3

Ok, of the five doctests that failed on buildbot, on my machine two fail in what Vincent branched from (sr.py and pbori.py) and the other three (polynomial_element.pyx, modform/numerical.py, and real_double.pyx) pass both before and after. I think this looks good, so moving to positive review.

[videlec]

comment:4

Thanks Nathan! The buildbot has some trouble... (there is a thread about that on sage devel)

Vincent

[videlec]

Reviewer: Nathan Dunfield

[NathanDunfield]

comment:5

Yeah, I saw that thread, which is another reason I when ahead to "positive review"...

[vbraun]

Changed branch from u/vdelecroix/17099 to 5497084