#10448: Extensions of ZZ are not unique parents
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Reporter: SimonKing | Owner: davidloeffler
Type: defect | Status: new
Priority: major | Milestone: sage-4.6.1
Component: number fields | Keywords: uniqueness of parents
Author: | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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Changes (by SimonKing):
* component: elliptic curves => number fields
* priority: critical => major
* owner: cremona => davidloeffler
* keywords: torsion_group, uniqueness of parents, coerce map =>
uniqueness of parents
Old description:
> We have
> {{{
> sage: K.<i>=NumberField(x^2 + 1)
> sage: R = ZZ.extension(x**2+1,'i')
> sage: f1 = K.coerce_map_from(R)
> sage: f1.domain() is R
> True
> sage: E = EllipticCurve(K,[0,0,0,1,0])
> sage: E.torsion_subgroup()
> Torsion Subgroup isomorphic to Z/2 + Z/2 associated to the Elliptic Curve
> defined by y^2 = x^3 + x over Number Field in i with defining polynomial
> x^2 + 1
> sage: R = ZZ.extension(x**2+1,'i')
> sage: f2 = K.coerce_map_from(R)
> sage: f2.domain() is R
> False
> sage: f2.domain() == R
> True
> }}}
>
> Hence, on the one hand, computing the torsion group destroys uniqueness
> of parents, and moreover, it makes the coerce map from an order to its
> ambient field have a domain that is not the same that is requested.
New description:
With an unpatched sage-4.6, we have:
{{{
sage: R1 = ZZ.extension(x**2+1,'i')
sage: R1 is ZZ.extension(x**2+1,'i')
False
sage: R1 is ZZ.extension(x**2+1,'i')
False
}}}
I think that should be changed.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10448#comment:1>
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