#18036: I should not be symbolic
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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 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.
> 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?
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?
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Ticket URL: <http://trac.sagemath.org/ticket/18036#comment:14>
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