#18620: Galois conjugates in universal cyclotomic field miss the previously
existing parameter m
---------------------------------+------------------------
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:
---------------------------------+------------------------
Comment (by vdelecroix):
Hello,
Replying to [comment:2 stumpc5]:
> What I find more important is that you broke my code without providing a
workaround. And I am also not a big fan of the rudeness or at least
missing politeness that seems to become standard in SageMath discussions.
I am sorry if I was rude or missed politeness.
> you might be right in the sense that you will see the same elements
multiple times or the same elements in a different order such as
> {{{
> sage: zeta.galois_conjugates(5)
> [E(5), E(5)^2, E(5)^3, E(5)^4]
> sage: zeta.galois_conjugates(10)
> [E(5), E(5)^3, E(5)^2, E(5)^4]
> sage: zeta.galois_conjugates(15)
> [E(5), E(5)^2, E(5)^4, E(5)^2, E(5)^3, E(5), E(5)^3, E(5)^4]
> }}}
> You can argue that these elements live in the {{{UCF}}} so their Galois
conjugates should be computed using {{{UCF/QQ}}}. But since every such
element is contained in {{{CF(n)}}} for multiple {{{n}}}s, one can as well
argue to compute it in one of those (recall that the Galois conjugates are
defined over a field extension
http://en.wikipedia.org/wiki/Conjugate_element_%28field_theory%29).
>
> The orbit **as a set** does not depend on your choice above, but the
order in which they come in the list depends on the field extension
{{{CF(n)}}} you chose, and you might want to further use that ordering for
something.
Here I do not agree with the terminology. I very much understand the
difference between:
- computing the galois conjugates
- computing the orbit of the Galois group `Gal(CF(n)/QQ)` as a list `[g_0
x, g_1 x, ..., g_k x]`.
What your function was doing is the second item (and there is a very
natural ordering of the Galois group).
Since you are mentioning wikipedia, you can read that the Galois
conjugates are the root of the minimal polynomial. So there are as many as
the degree of the minimal polynomial (which is just independent of any
choice of `CF(n)`).
I understand now that this feature was useful and I am sorry if I removed
it in an abrupt way. I can provide the branch if you wish (tell me). If
you write it, please be much clearer on the specifications.
Vincent
--
Ticket URL: <http://trac.sagemath.org/ticket/18620#comment:3>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
--
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To post to this group, send email to [email protected].
Visit this group at http://groups.google.com/group/sage-trac.
For more options, visit https://groups.google.com/d/optout.
