#12269: coercion and conversion for absolute_field
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Reporter: mstreng | Owner: davidloeffler
Type: defect | Status: new
Priority: major | Milestone: sage-5.0
Component: number fields | Keywords: coercion conversion
absolute_field number field structure relative absolute
Work_issues: | Upstream: N/A
Reviewer: | Author:
Merged: | Dependencies:
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Comment(by mstreng):
The map {{{absolute_field().structure()[1]}}} (from relative to absolute)
cannot be a *coercion*, because it would lead to non-commuting diagrams of
coercions. In sage-4.8.alpha4:
{{{
sage: K.<a> = NumberField(x^2-2, embedding=-1)
sage: L.<b> = NumberField(x^2-2, embedding=1)
sage: xK = K['x'].gen()
sage: xL = L['x'].gen()
sage: M.<c> = NumberField(xK^2-3)
sage: N.<d> = NumberField(xL^2-3)
sage: O = M.absolute_field('e')
sage: P = N.absolute_field('e')
sage: b_in_a = K(0)+b
sage: map1 = O.structure()[1]
sage: map2 = P.structure()[1]
sage: b_in_a in map1.domain()
# True
sage: b in map2.domain()
# True
sage: map1(b_in_a) - map2(b)
# e^3 - 9*e, which is non-zero, so the diagrams don't commute!
}}}
Fast *conversions* in both directions would be very useful though. And
maybe coercion from absolute to relative?
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12269#comment:7>
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