Wed 2018-08-08 22:08:16 UTC+2, Pat Hooper:

> I think Sage should support real transcendental extension fields.
> It does not as far as I can tell. For example it should support arithmetic
> and comparisons in Q(e) with e the usual constant e and in Q(r) where
> r is chosen at random in some interval with respect to Lebesgue measure.
> Ideally Sage would support Q(e,r), Q(sqrt(2),r), AA(r), Q(pi), Q(r_1, 
r_2), etc.

Excellent suggestion! I opened a ticket for that:

- Sage Trac ticket 26042:
  Real transcendental extension fields
  https://trac.sagemath.org/ticket/26042

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