Opened 7 years ago
Closed 7 years ago
#18243 closed defect (duplicate)
Wrong result of NumberField.composite_field() when embeddings are specified
Reported by: | pbruin | Owned by: | |
---|---|---|---|
Priority: | major | Milestone: | sage-duplicate/invalid/wontfix |
Component: | number fields | Keywords: | number field compositum |
Cc: | Merged in: | ||
Authors: | Reviewers: | Peter Bruin | |
Report Upstream: | N/A | Work issues: | |
Branch: | Commit: | ||
Dependencies: | Stopgaps: |
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.
Change History (5)
comment:1 Changed 7 years ago by
comment:2 Changed 7 years ago by
- 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
- Reviewers set to Peter Bruin
- Status changed from new to needs_review
comment:4 Changed 7 years ago by
- Status changed from needs_review to positive_review
comment:5 Changed 7 years ago by
- Resolution set to duplicate
- Status changed from positive_review to closed
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See also the prehistoric ticket #252...