#18036: I should not be symbolic
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       Reporter:  vdelecroix     |        Owner:
           Type:  defect         |       Status:  new
       Priority:  major          |    Milestone:  sage-6.6
      Component:  number fields  |   Resolution:
       Keywords:                 |    Merged in:
        Authors:                 |    Reviewers:
Report Upstream:  N/A            |  Work issues:
         Branch:                 |       Commit:
   Dependencies:                 |     Stopgaps:
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Old description:

> As suggested in #17860, `I` (so that `I^2 = -1`) should be defined
> directly as the generator of `QuadraticField(-1)` and not wrapped into a
> symbolic expression.
>
> Currently, `I` is defined in `sage/symbolic/pynac.pyx` within the
> function `init_pynac_I`.

New description:

 As suggested in #7545, `I` (so that `I^2 = -1`) should be defined directly
 as the generator of `QuadraticField(-1)` and not wrapped into a symbolic
 expression.

 Currently, `I` is defined in `sage/symbolic/pynac.pyx` within the function
 `init_pynac_I`.

--

Comment (by kcrisman):

 Thank you all for working on this - this kind of thing has been on the
 radar for [comment:5:ticket:7545 years] but after Burcin left day-to-day
 operations around here there hasn't been the combination of energy and
 know-how to do this "correctly", whatever that might mean.  Just keep in
 mind it would be nice for `I in SR` to be true, though I'm sure it will be
 since `1 in SR` already is `True`.  I do like the idea of `abs(I)` being
 an `Integer` and not a symbolic expression.

--
Ticket URL: <http://trac.sagemath.org/ticket/18036#comment:6>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
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