#18243: Wrong result of NumberField.composite_field() when embeddings are
specified
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Reporter: pbruin | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-6.7
Component: number fields | Keywords: number field compositum
Merged in: | Authors:
Reviewers: | Report Upstream: N/A
Work issues: | Branch:
Commit: | Dependencies:
Stopgaps: |
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Reported on [https://groups.google.com/forum/#!topic/sage-
support/N-O8FAHBQTM 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.
--
Ticket URL: <http://trac.sagemath.org/ticket/18243>
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