#9390: is_galois_relative() not always right
------------------------------+---------------------------------------------
Reporter: arminstraub | Owner: davidloeffler
Type: defect | Status: needs_review
Priority: major | Milestone: sage-4.6.1
Component: number fields | Keywords: galois extension
Author: Francis Clarke | Upstream: N/A
Reviewer: Marco Streng | Merged:
Work_issues: |
------------------------------+---------------------------------------------
Changes (by fwclarke):
* status: needs_work => needs_review
Comment:
With the #8451 patch, and with `is_galois` unchanged, I find
{{{
sage: set_verbose(1)
sage: EllipticCurve([1, -1, 0, -107,
-379]).galois_representation().image_type(7)
verbose 1 (1326: free_module.py, coordinate_module) rational in-place
Gauss elimination on 0 x 0 matrix
...
verbose 1 (811: gal_reps.py, image_type) field of degree 36. try to
compute galois group (time = 14.321421)
'The image is a group of order 36.'
}}}
deriving from the following lines in `gal_reps.py` (as patched by #8451):
{{{
if p <= 13:
K = _division_field(self.E,p)
d = K.absolute_degree()
misc.verbose("field of degree %s. try to compute galois
group"%(d),2)
try:
G = K.galois_group()
except:
self.__image_type[p] = "The image is a group of order
%s."%d
return self.__image_type[p]
}}}
So what's happening is that `K.is_galois()` (called via
`K.galois_group()`) is taking ages when my patch is implemented. The
unqualified `except:` is then catching the keyboard interrupt. But with
the existing implementation of `is_galois` applied to the degree 36 field
in question, a `NotImplementedError` is raised and caught.
Anyway, as you suggest, the way forward is a minimal patch which only
changes `is_galois_relative`. I'm attaching this.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9390#comment:12>
Sage <http://www.sagemath.org>
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