Implement sqrt() for QuaternionAlgebraElement

[sagetrac-epotash]

This method currently does not exist, but it should. For an outline of an algorithm see: http://www.mathreference.com/ring-q,sqr.html

The only issue is that, as far as I know, there is no standard for which square root to take like there is over C or R.

Component: algebra

Issue created by migration from https://trac.sagemath.org/ticket/3709

[sagetrac-fwclarke]

comment:2

In the quaternions there are infinitely many square-roots of -1: (xi + yj + zk)² = -1 for any real numbers x, y, z such that x² + y² + z² = 1.  I don't know how to prefer one of these.