#19229: Bug in elliptic curve Galois Representation
-------------------------------------+-------------------------------------
Reporter: cremona | Owner:
Type: defect | Status: needs_work
Priority: major | Milestone: sage-6.10
Component: elliptic curves | Resolution:
Keywords: Galois | Merged in:
representations | Reviewers:
Authors: John Cremona | Work issues:
Report Upstream: N/A | Commit:
Branch: u/cremona/19229 | 62accc077ff28e2306364abaa60199846e292fdd
Dependencies: | Stopgaps:
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Comment (by cremona):
Replying to [comment:17 jdemeyer]:
> Obvious question: what is the performance impact of the earlier CM
checks? It seems that the old code was careful to postpone CM checks.
Good question. When the code was first written there was no CM check
available, so the presence of CM was detected indirectly; not that for CM
curves the output will always be trivial. So I thought it simpler to put
the CM check in early. On the other hand, whil it is often easy to see
that a curve does *not* have CM (e.g. if j is not an algebraic integer),
proving that it does have CM is harder. So perhaps it was better to
discover the presence of CM the old way. I will investigate that.
>
> All the methods where you added a check for CM should have a doctest for
the case when there is no CM. Many don't have such a doctest.
OK.
>
> Like I said before, this should be replaced by real caching (you
implemented the caching, but forgot to remove this part):
> {{{
> #!diff
> + self._has_cm = E.has_cm()
> + self._has_rational_cm = E.has_rational_cm()
> }}}
To be fixed.
>
> I think this comment is not very clear:
> {{{
> #!diff
> + # See #19229: can cause problems if this name is 'a' but it has
to be something!
> + F = NumberField(y**2 - a, 'grnf_a')
> }}}
I'll explain here and also make the comment clearer. The original bug was
only triggered when the base field already had 'a' as the name for its
generator. Here we need to construct a number field and so we need a name
which must not be a name used before in a similar context. So I cam up
with such a name (I think grnfstands for "Galois Rep Number Field").
--
Ticket URL: <http://trac.sagemath.org/ticket/19229#comment:20>
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