#17830: Comparison of number field elements dependent of real embedding
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Reporter: vdelecroix | Owner:
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.6
Component: number fields | Resolution:
Keywords: sd66 | Merged in:
Authors: Vincent | Reviewers:
Delecroix, Štěpán Starosta | Work issues:
Report Upstream: N/A | Commit:
Branch: | 96ac61e74d5dc073fe6d11570ed0be0934c50c77
u/vdelecroix/17830 | Stopgaps:
Dependencies: |
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Changes (by vdelecroix):
* cc: gagern (added)
Old description:
> Comparison of embedded number field elements should be identical to the
> comparison of the embedding. In other words, we should have:
> {{{
> sage: x = polygen(ZZ)
> sage: K.<cbrt2> = NumberField(x^3 - 2,
> embedding=AA.polynomial_root(x^3-2, RIF(0,3)))
> sage: 6064/4813 < cbrt2 < 90325/71691
> True
> }}}
> This has been done in #13213 for quadratic number fields. This ticket
> aims to implement this for all number fields by storing into the parent a
> list of interval approximations of the generator.
>
> This concerns only real embeddings.
New description:
Comparison of embedded number field elements should be identical to the
comparison of the embedding. In other words, we should have:
{{{
sage: x = polygen(ZZ)
sage: K.<cbrt2> = NumberField(x^3 - 2, embedding=AA.polynomial_root(x^3-2,
RIF(0,3)))
sage: 6064/4813 < cbrt2 < 90325/71691
True
}}}
This has been done in #13213 for quadratic number fields. This ticket aims
to implement this for all number fields by storing into the parent a list
of interval approximations of the generator.
This concerns only real embeddings.
To go further, one should consider:
- having a fast evaluation of integer polynomial with real intervals
(mpfi elements) input
- make better interaction with QQbar (see also #18103 and #18104)
--
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Ticket URL: <http://trac.sagemath.org/ticket/17830#comment:8>
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