_richcmp_ for quaternion algebra elements

[fchapoton]

instead of the old-style _cmp_

CC: @tscrim @fchapoton

Component: algebra

Author: Frédéric Chapoton

Branch: c8425cb

Reviewer: Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/28398

[fchapoton]

Commit: c8425cb

[fchapoton]

New commits:

c8425cb

richcmp for quaternion algebras elements

[fchapoton]

Branch: u/chapoton/28398

[fchapoton]

comment:2

bot is morally green, please review

[tscrim]

comment:3

LGTM.

[tscrim]

Reviewer: Travis Scrimshaw

[vbraun]

Changed branch from u/chapoton/28398 to c8425cb

[mmasdeu]

comment:5

This breaks quaternion algebra comparisons quite badly. In Sage 9.0:

sage: B.<i,j,k> = QuaternionAlgebra(6)
sage: B(1) == B(-1)
False
sage: B(1) != B(-1)
False

[mmasdeu]

Changed commit from c8425cb to none

[tscrim]

comment:8

So this change did not cause that problem, but instead #28595. The problem comes from the fact that mpz_cmp yields arbitrary positive/negative numbers, but rich_to_bool assumes the input is in [-1, 0, 1]. Instead, we just need to use rich_to_bool_sgn. This is now #29094.