#9407: fixed fields for dirichlet characters and conductors and dirichlet
characters for abelian fields
-----------------------------------------------------------+----------------
Reporter: wuthrich | Owner:
davidloeffler
Type: enhancement | Status: new
Priority: minor | Milestone:
sage-4.5.2
Component: number fields | Keywords:
Dirichlet characters, abelian fields, class field theory
Author: Michael Daub, John Bergdall, Chris Wuthrich | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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Comment(by wuthrich):
Apart from the above the patch here also introduces the function
{{{is_abelian}}} and improves {{{is_galois}}} for number fields. Subfields
of abelian fields inherit both.
There are a few minor things that could be improved at a later state
(which I write down here so that I won't forget) :
* The 2-part of the conductor needs adjustment
* We can prove that a field is NOT abelian even if we can not decide that
it is Galois, by finding that a prime congruent to 1 modulo the
hypothetical conductor that does not completely split.
* Is there some effective Chebotarev that can be used to prove that a
field is Galois ?
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9407#comment:1>
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