Wrong result of NumberField.composite_field() when embeddings are specified

[pbruin]

Reported on ​sage-support:

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)]

The NumberField containing both (complex conjugate) embeddings should be larger.

The cause is probably that the defining polynomial f does not have integral coefficients. When f is replaced by QQ['x'](pari(f).polredabs()) (which is x^8 - x^7 + x^6 - 2*x^5 - x^4 + x^3 + x^2 + 2*x + 1), the result is a number field of degree 32.

[pbruin]

See also the prehistoric ticket #252...

[pbruin]

This ticket is most likely a duplicate of #14164.