#20826: AlgebraicExtensionFunctor should include number field structure
-----------------------------+-------------------------------
Reporter: pbruin | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-7.3
Component: number fields | Keywords:
Merged in: | Authors: Peter Bruin
Reviewers: | Report Upstream: N/A
Work issues: | Branch:
Commit: | Dependencies:
Stopgaps: |
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If a number field is equipped with structural morphisms, these are lost
when applying the functorial construction of the number field (via
`NumberField.construction()` and `AlgebraicExtensionFunctor`), which
happens for example in the construction of push-outs:
{{{
sage: R.<x> = ZZ[]
sage: K.<a> = NumberField(x^2 - 3)
sage: L0.<b> = K.change_names()
sage: L0.structure()
(Isomorphism given by variable name change map:
From: Number Field in b with defining polynomial x^2 - 3
To: Number Field in a with defining polynomial x^2 - 3,
Isomorphism given by variable name change map:
From: Number Field in a with defining polynomial x^2 - 3
To: Number Field in b with defining polynomial x^2 - 3)
sage: L1 = (b*x).parent().base_ring()
sage: L1.structure()
(Ring Coercion endomorphism of Number Field in b with defining polynomial
x^2 - 3,
Ring Coercion endomorphism of Number Field in b with defining polynomial
x^2 - 3)
}}}
This currently does not cause too much trouble because the two fields
(with and without the structural morphisms) are considered equal, although
they are not identical:
{{{
sage: L1 is L0
False
sage: L1 == L0
True
}}}
However, this becomes a nuisance when trying to implement "equality is
identity" for number fields (to be done on a future ticket).
--
Ticket URL: <http://trac.sagemath.org/ticket/20826>
Sage <http://www.sagemath.org>
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