#12850: Fix coercions for CyclotomicField with different embeddings
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Reporter: stumpc5 | Owner: davidloeffler
Type: defect | Status: new
Priority: major | Milestone: sage-5.0
Component: number fields | Resolution:
Keywords: cyclotomic field | Work issues:
Report Upstream: N/A | Reviewers:
Authors: | Merged in:
Dependencies: | Stopgaps:
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Changes (by stumpc5):
* cc: nthiery (added)
Old description:
> With the current coercion between cyclotomic fields, we get an non-
> commutative coercion diagram:
>
> {{{
> sage: CF1 = CyclotomicField(5)
> sage: CF2 = CyclotomicField(5,embedding = (4 * CLF.pi() * CLF.gen() /
> 5).exp())
> sage: CC(CF1.gen()-CF2.gen())
> 0
> sage: CC(CF1.gen()) - CC(CF2.gen())
> 1.11803398874989 + 0.363271264002680*I
> }}}
New description:
With the current coercion between cyclotomic fields, we get an non-
commutative coercion diagram:
{{{
sage: CF1 = CyclotomicField(5)
sage: CF2 = CyclotomicField(5,embedding = (4 * CLF.pi() * CLF.gen() /
5).exp())
sage: CC(CF1.gen()-CF2.gen())
0
sage: CC(CF1.gen()) - CC(CF2.gen())
1.11803398874989 + 0.363271264002680*I
}}}
TODO: When this is done, we have to fix the embedding of cyclotomic fields
into the universal cyclotomic field.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12850#comment:1>
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