#4276: [with patch, needs review] move number fields to new coercion, implement
embeddings
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Reporter: robertwb | Owner: robertwb
Type: defect | Status: new
Priority: major | Milestone: sage-3.2.2
Component: coercion | Resolution:
Keywords: |
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Old description:
> I'm not sure what is supposed to happen, but this probably isn't it.
> AFAICT, these embeddings are *not* compatible. Or they are only after
> some work, that makes the results at the end strange.
>
> Please explain why this is correct if it is!
>
> {{{
> sage: F1 = NumberField(x^3 + 2, 'a', embedding=2)
> sage: F1.coerce_embedding()
>
> Generic morphism:
> From: Number Field in a with defining polynomial x^3 + 2
> To: Real Lazy Field
> Defn: a -> -1.259921049894873?
> sage: F2 = NumberField(x^3 + 2, 'a', embedding=CC.0)
> sage: F2.coerce_embedding()
>
> Generic morphism:
> From: Number Field in a with defining polynomial x^3 + 2
> To: Complex Lazy Field
> Defn: a -> 0.6299605249474365? + 1.091123635971722?*I
>
> sage: F1.gen() + F2.gen()
> 2*a
> sage: (F1.gen() + F2.gen()).parent()
> Number Field in a with defining polynomial x^3 + 2
> sage: (F1.gen() + F2.gen()).parent().coerce_embedding()
>
> Generic morphism:
> From: Number Field in a with defining polynomial x^3 + 2
> To: Real Lazy Field
> Defn: a -> -1.259921049894873?
> sage: CC(F1.gen())
> -1.25992104989487
> sage: CC(F1.gen()) + CC(F2.gen())
> -0.629960524947436 + 1.09112363597172*I
> sage: CC(F1.gen() + F2.gen())
> -2.51984209978975
> sage: CC(F2.gen() + F1.gen())
> 1.25992104989487 + 2.18224727194344*I
> }}}
New description:
See summary.
Comment (by mabshoff):
Comment by Nick Alexander, but it ended up in the wrong box, so I am
appending it here:
I'm not sure what is supposed to happen, but this probably isn't it.
AFAICT, these embeddings are *not* compatible. Or they are only after
some work, that makes the results at the end strange.
Please explain why this is correct if it is!
{{{
sage: F1 = NumberField(x^3 + 2, 'a', embedding=2)
sage: F1.coerce_embedding()
Generic morphism:
From: Number Field in a with defining polynomial x^3 + 2
To: Real Lazy Field
Defn: a -> -1.259921049894873?
sage: F2 = NumberField(x^3 + 2, 'a', embedding=CC.0)
sage: F2.coerce_embedding()
Generic morphism:
From: Number Field in a with defining polynomial x^3 + 2
To: Complex Lazy Field
Defn: a -> 0.6299605249474365? + 1.091123635971722?*I
sage: F1.gen() + F2.gen()
2*a
sage: (F1.gen() + F2.gen()).parent()
Number Field in a with defining polynomial x^3 + 2
sage: (F1.gen() + F2.gen()).parent().coerce_embedding()
Generic morphism:
From: Number Field in a with defining polynomial x^3 + 2
To: Real Lazy Field
Defn: a -> -1.259921049894873?
sage: CC(F1.gen())
-1.25992104989487
sage: CC(F1.gen()) + CC(F2.gen())
-0.629960524947436 + 1.09112363597172*I
sage: CC(F1.gen() + F2.gen())
-2.51984209978975
sage: CC(F2.gen() + F1.gen())
1.25992104989487 + 2.18224727194344*I
}}}
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/4276#comment:25>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
Reinventing the Wheel
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