#18103: cleanup number fields coerce embeddings
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Reporter: vdelecroix | Owner:
Type: enhancement | Status: new
Priority: major | Milestone: sage-6.6
Component: number fields | Resolution:
Keywords: sd66 | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: #17830 | Stopgaps:
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Changes (by vdelecroix):
* keywords: => sd66
* dependencies: => #17830
Old description:
> Currently, the default coerce embedding uses RLF (or CLF) but heavily
> relies on AA (or QQbar). It is bad for several reasons:
> - there is no coercion from RLF to AA
> - 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.
New 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.
--
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Ticket URL: <http://trac.sagemath.org/ticket/18103#comment:1>
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