#18036: I.parent() should not be the symbolic ring
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Reporter: vdelecroix | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-6.6
Component: number fields | Resolution:
Keywords: | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Comment (by vdelecroix):
Replying to [comment:14 mmezzarobba]:
> Replying to [comment:13 vdelecroix]:
> > Anyway this will be instantiated at startup so why not keeping one
instance `QQi` in `sage.rings.number_field.number_field`? (like we have
for `ZZ`, `QQ`, etc).
>
> If I remember right, currently, just adding `QQi = ...()` in the module
currently doesn't work due to import order constraints. For now I just
kept the creation of QQ[i] happening at the same time as it used to. But
that's certainly something we should try to improve after this first
draft.
Here we can probably cheat with
{{{
_QQi = None
def NumberFieldQQi():
if _QQi is None:
# build it once for all
...
return _QQi
}}}
> > Then you can test identity when testing coercions.
>
> Yes. Having a separate class would also be natural if we want
`I.parent()` to display something less frightening than “Number Field in
`I` with defining polynomial `x^2 + 1`”, and more generally to implement
features specific to QQ[i]. But I can't really think of anything that
makes sense for this field and not for embedded quadratic number fields in
general, so perhaps it is better to encourage people to always implement a
more general version?
Yes! Having a custom representation should be done in the main class. It
is already possible:
{{{
sage: K = QuadraticField(2)
sage: K.rename('It's me')
sage: K
It's me
sage: K.rename(None)
sage: K
Number Field in a with defining polynomial x^2 - 2
}}}
> A related question is whether `QQi is NumberField(x^2+1, 'I',
embedding=CC.0)` should be true, or if there should be two separate
parents.
>
> What do you think?
More generally, do we want unique representation for (absolute) number
fields? I would tend to say yes. And the natural keys would be:
- the polynomial
- the variable name (not of the polynomial!)
- the embedding
Vincent
--
Ticket URL: <http://trac.sagemath.org/ticket/18036#comment:16>
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