Hi,

I traced this down to integral_elements_with_trace not handling the
signs in pari's output of qfminim properly. It will only return a single
element from each pair of conjugates, and depending on
F.reduced_basis(), it might miss elements in ZZ with the required trace
entirely.

sage: F.<t> = NumberField(x^2-5)
sage: F.integral_elements_with_trace([8.0,12.0])
[3/2*t + 9/2, t + 5, t + 4, 1/2*t + 11/2, 1/2*t + 9/2, 6, 5, 4]
sage: (-1/2*t + 9/2).trace()
9
sage: F.integral_elements_with_trace([8.0,8.0])
[4]

On the machine where the doctest failed, I got an empty [] with this
final command.

Any opinions on if integral_elements_with_trace() should return both
conjugates, or only one?

-Willem Jan 

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