Fix NumberFieldElement_quadratic.is_integral() when D is not square-free

[pjbruin]

Fixes #34800. The current implementation of is_integral() assumes that D is square-free. We implement the check for integrality of the trace and norm in a way that works for general D.

[github-actions]

Documentation preview for this PR (built with commit 7e8a6f1; changes) is ready! 🎉

[tscrim]

Does it make sense to keep the old test for the square-free case (which, of course, would include a check in the method for that)?

[pjbruin]

Does it make sense to keep the old test for the square-free case (which, of course, would include a check in the method for that)?

The problem with that is that knowing whether D is square-free requires factoring D, which we should certainly avoid. In my implementation, we only need to check one specific candidate for a square divisor, namely denom^2 or (denom/2)^2 depending on a parity condition.

[tscrim]

Thank you for the explanation. I wasn’t sure if this was already tested somewhere during the initialization (or could have been cached by some other computation) and if the new test would have been (relatively) slower than the old in the case it was already known.

Anyways, positive review.

[pjbruin]

Thank you!