#10832: bug in simon_two_descent()
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Reporter: cremona | Owner: cremona
Type: defect | Status: needs_review
Priority: major | Milestone:
Component: elliptic curves | Keywords:
Author: John Cremona | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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Comment(by cremona):
Replying to [comment:4 shin]:
> (* first comment ever)
>
> Works fine on snow leopard 10.6.6.
>
> But I'm not sure I understand. Sure, the "rank" should be returned as 2,
but if I ask for the generators - shouldn't we get the generators of the
torsion as well?
> I'm simply thinking of consistency with other groups such as unit
groups.
> The rank of the unit group of the cyclotomic field QQ(\zeta_5) is 1, but
there are two generators (and sage does return 2).
Welcome!
You are absolutely right from the mathematical point of view, the
generators should really include 0, 1 or 2 torsion generators. But there
is a tradition with elliptic curves of using "generators" to mean
"generators modulo torsion", and I think that to change the behaviour to
what you suggest would break a lot of code, hence a Bad Thing.
On the other hand it would be very reasonable to expect the docstring to
be more precise, and in fact it is: for curves over Q the docstring for
gens clearly states that it returns generaotors modulo torsion; while for
curves over other number fields it just says
{{{
Returns some generators of this elliptic curve. Check ``rank()`` or
``rank_bounds()`` to verify the number of generators.
}}}
so the user is not being misled.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10832#comment:5>
Sage <http://www.sagemath.org>
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