#14472: some elliptic curve functions over number fields fail over relative
fields
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Reporter: cremona | Owner:
cremona
Type: defect | Status:
needs_review
Priority: major | Milestone:
sage-5.10
Component: elliptic curves | Resolution:
Keywords: elliptic curve relative number field | Work issues:
Report Upstream: N/A | Reviewers:
Authors: John Cremona | Merged in:
Dependencies: | Stopgaps:
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Comment (by cremona):
Replying to [comment:4 jdemeyer]:
> All the examples seem to be ''quadratic'' number fields, is this
intentional?
No, probably just laziness.
>
> I don't know why Sage returns the basis of `ZK` like that, because it's
not what PARI gives:
> {{{
> sage: K.<a> = NumberField(x^2-5)
> sage: K.integral_basis()
> [1/2*a + 1/2, a]
> sage: K._pari_integral_basis()
> [1, 1/2*y - 1/2]
> }}}
>
Well spotted. The integral_basis method calls maximal_order which does
call _pari_integral_basis, but then applies some Order constructor to the
generators (order.absolute_order_from_module_generators) which is where
this non-canonical ( to my mind) basis comes from. If that is to be
chaned for quadratic fields then that would be a separate ticket, and
would surely have a lot of doctest output consequences.
> As for reducing an element modulo an ideal (which is what you do here),
you could use PARI's `nfeltreduce()`.
Sure, but here we are only reducing modulo (2) or (3) so it seemed easier
to do it manually.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/14472#comment:5>
Sage <http://www.sagemath.org>
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