Opened 7 years ago

Closed 7 years ago

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

Reported by: Owned by: pbruin major sage-duplicate/invalid/wontfix number fields number field compositum Peter Bruin N/A

### Description

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.

### comment:2 Changed 7 years ago by pbruin

• Milestone changed from sage-6.7 to sage-duplicate/invalid/wontfix

This ticket is most likely a duplicate of #14164.

### comment:3 Changed 7 years ago by pbruin

• Reviewers set to Peter Bruin
• Status changed from new to needs_review

### comment:4 Changed 7 years ago by pbruin

• Status changed from needs_review to positive_review

### comment:5 Changed 7 years ago by vbraun

• Resolution set to duplicate
• Status changed from positive_review to closed
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