Sounds right, can you open a ticket?


On Tuesday, September 1, 2015 at 1:41:06 PM UTC-4, Antonio Francisco Behn 
Von Schmieden wrote:
>
> There seems to be a bug in the implementation of the coercion from 
> universal cyclotomic field.  The rational part disappears when converting.
> For example:
>
>    F.<c>=CyclotomicField(4)
>    F(-1/2 + 1/2*E(4))
>
> 1/2*c^2
>
>
> Reading the code:
>             from sage.rings.number_field.number_field import 
> CyclotomicField
>             k = self._obj.Conductor().sage()
>             Rcan = CyclotomicField(k)
>             if R is None:
>                 R = Rcan
>             obj = self._obj
>             if obj.IsRat():
>                 return R(obj.sage())
>             zeta = Rcan.gen()
>             coeffs = obj.CoeffsCyc(k).sage()
>             return R(sum(coeffs[a] * zeta**a for a in range(1,k)))
>
> I believe the problem is in the range(1,k) which should be range(0,k)
>

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