This is now <http://trac.sagemath.org/ticket/18243>.

> Hello,
>
>> The NumberField containing both embeddings should be larger. The
>> morphisms also clearly show that something is going wrong:
>>
>> sage: nf = NumberField(x^8 - 3*x^7 + 61/3*x^6 - 9*x^5 + 298*x^4 +
>> 458*x^3 + 1875*x^2 + 4293*x + 3099, 'z', embedding=-1.18126721294295 +
>> 3.02858651117832j)
>> sage: nf2 = NumberField(x^8 - 3*x^7 + 61/3*x^6 - 9*x^5 + 298*x^4 +
>> 458*x^3 + 1875*x^2 + 4293*x + 3099, 'z', embedding=-1.18126721294295 -
>> 3.02858651117832j)
>> sage: nf.composite_fields(nf2,both_maps = True)
>> [(Number Field in z with defining polynomial x^8 - 3*x^7 + 61/3*x^6 -
>> 9*x^5 + 298*x^4 + 458*x^3 + 1875*x^2 + 4293*x + 3099,
>> Ring endomorphism of Number Field in z with defining polynomial x^8 -
>> 3*x^7 + 61/3*x^6 - 9*x^5 + 298*x^4 + 458*x^3 + 1875*x^2 + 4293*x + 3099
>> Defn: z |--> z,
>> Ring morphism:
>> From: Number Field in z with defining polynomial x^8 - 3*x^7 + 61/3*x^6 -
>> 9*x^5 + 298*x^4 + 458*x^3 + 1875*x^2 + 4293*x + 3099
>> To: Number Field in z with defining polynomial x^8 - 3*x^7 + 61/3*x^6 -
>> 9*x^5 + 298*x^4 + 458*x^3 + 1875*x^2 + 4293*x + 3099
>> Defn: z |--> z,
>>  +Infinity)]
>>
>> I couldn't find a bug on trac for it. I think there should be one filed.
>
> Indeed, this looks like a bug.  It might be because the polynomials do
> not have integral coefficients.  I will open a ticket.
>
> Peter

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