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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