#17830: Comparison of number field elements dependent of real embedding
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Reporter: vdelecroix | Owner:
Type: enhancement | Status: new
Priority: major | Milestone: sage-6.6
Component: number fields | Resolution:
Keywords: | Merged in:
Authors: Vincent Delecroix | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/vdelecroix/17830 | 5f7f57b445adebb118d1d80acb4e930911265494
Dependencies: | Stopgaps:
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Description changed by vdelecroix:
Old description:
> Comparison of embedded number field elements should be identical to the
> comparison of the embedding. In other words, we should have:
> {{{
> age: x = polygen(ZZ)
> sage: K.<cbrt2> = NumberField(x^3 - 2,
> embedding=AA.polynomial_root(x^3-2, RIF(0,3)))
> sage: 6065/4813 < 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.
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.
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Ticket URL: <http://trac.sagemath.org/ticket/17830#comment:2>
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