#18103: cleanup number fields coerce embeddings
----------------------------+----------------------------------------------
Reporter: | Owner:
vdelecroix | Status: needs_review
Type: | Milestone: sage-duplicate/invalid/wontfix
enhancement | Resolution:
Priority: major | Merged in:
Component: number | Reviewers:
fields | Work issues:
Keywords: sd66 | Commit:
Authors: | Stopgaps:
Report Upstream: N/A |
Branch: |
Dependencies: |
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Changes (by vdelecroix):
* status: new => needs_review
* dependencies: #17830 =>
* milestone: sage-6.6 => sage-duplicate/invalid/wontfix
Old description:
> Currently, the default coerce embedding uses RLF/CLF but heavily relies
> on AA/QQbar. It is bad for several reasons:
> - there is no coercion from RLF/CLF to AA/QQbar
> - equality and comparisons in RLF are completely broken (because it
> relies on finite approximations)
> {{{
> sage: K.<cbrt3> = NumberField(x^3 - 3, embedding=1)
> sage: b=(1+RLF(cbrt3))/2
> sage: c=1/2 + 3/2*(RLF(cbrt3)/3)
> sage: b == c
> False
> }}}
>
> In this ticket:
> - we get rid of RLF/CLF for number field embeddings and use AA/QQbar
> instead
> - we make the interaction between AA and number fields more friendly
> - we speed up a lot the approximations of number field elements using
> Cython
>
> In a ticket #18104, we will consider number fields with complex
> embeddings.
New description:
This ticket is a duplication of #12715.
Currently, the default coerce embedding uses RLF/CLF but heavily relies on
AA/QQbar. It is bad for several reasons:
- there is no coercion from RLF/CLF to AA/QQbar
- equality and comparisons in RLF are completely broken (because it
relies on finite approximations)
{{{
sage: K.<cbrt3> = NumberField(x^3 - 3, embedding=1)
sage: b=(1+RLF(cbrt3))/2
sage: c=1/2 + 3/2*(RLF(cbrt3)/3)
sage: b == c
False
}}}
In this ticket:
- we get rid of RLF/CLF for number field embeddings and use AA/QQbar
instead
- we make the interaction between AA and number fields more friendly
- we speed up a lot the approximations of number field elements using
Cython
In a ticket #18104, we will consider number fields with complex
embeddings.
--
Comment:
Replying to [comment:2 mmezzarobba]:
> Looks like a duplicate of #5355 and #12715.
It is (of #12715). Could you close it?
I will add some details in #12715 (I have an implementation which works
except for cyclotomic fields).
Vincent
--
Ticket URL: <http://trac.sagemath.org/ticket/18103#comment:3>
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