#18620: Galois conjugates in universal cyclotomic field miss the previously
existing parameter m
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Reporter: stumpc5 | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-6.8
Component: number fields | Resolution:
Keywords: | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Comment (by vdelecroix):
Hello,
I did remove the argument on purpose. The Galois conjugates do not depend
on anything: it is the orbit of the Galois group (of `QQbar` over `QQ`).
The specifications you wrote
{{{
:param m: if given, it must be a multiple of :meth:`field_order`; the
Galois
conjugates are then computed with respect to the cyclotomics of order
``m``
}}}
is a nonsense to me. The way you compute something should not change the
result.
Moreover, what is used to do is to duplicate the output a certain number
of times (in a very inefficient way)
{{{
sage: E(6).galois_conjugates(6)
[-E(3)^2, -E(3)]
sage: E(6).galois_conjugates(12)
[-E(3)^2, -E(3), -E(3)^2, -E(3)]
}}}
Why not using
{{{
sage: E(6).galois_conjugates() * 2
[-E(3)^2, -E(3), -E(3)^2, -E(3)]
}}}
if you want to duplicate the list?
Vincent
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Ticket URL: <http://trac.sagemath.org/ticket/18620#comment:1>
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