Elements from a Field of Fractions that compare equal should have equal hashes

[sagetrac-Stefan]

Sage can't guarantee that p == q implies hash(p) == hash(q), but it is not unreasonable to strive to make this work in case p,q belong to the same ring or field.

This ticket deals with Fields of Fractions. The proposed solution from this post appears to do the trick:
https://groups.google.com/forum/#!topic/sage-devel/TOp_5LCBBR4

Example:

sage: R.<x> = ZZ['x']
sage: F = R.fraction_field()
sage: p = 1/(1-x)
sage: q = (-1)/(x-1)
sage: p == q
True
sage: hash(p) == hash(q)
False

CC: @yuan-zhou @mkoeppe

Component: algebra

Keywords: field of fractions, hashing

Issue created by migration from https://trac.sagemath.org/ticket/15297

[mkoeppe]

comment:5

Still broken even with #16268; see #26339.

[mkoeppe]

comment:6

Still broken in 9.1.rc2

[mkoeppe]

comment:8

Sage development has entered the release candidate phase for 9.3. Setting a new milestone for this ticket based on a cursory review of ticket status, priority, and last modification date.