#13951: (non)archimedian_local_height broken for rational points on elliptic
curves
over Q
---------------------------------------------+------------------------------
Reporter: pbruin | Owner: cremona
Type: defect | Status: needs_review
Priority: major | Milestone: sage-5.10
Component: elliptic curves | Resolution:
Keywords: local heights | Work issues:
Report Upstream: N/A | Reviewers: John Cremona,
Peter Bruin
Authors: Peter Bruin, John Cremona | Merged in:
Dependencies: #12509, #13953, #14609 | Stopgaps:
---------------------------------------------+------------------------------
Old description:
> Computing local heights uses functions that are only available when the
> base field is a NumberField, and not over the RationalField:
>
> {{{
> sage: E = EllipticCurve([0, 0, 0, -36, 0])
> sage: P = E(-3, 9)
> sage: P.archimedian_local_height()
> ...
> AttributeError: 'RationalField_with_category' object has no attribute
> 'places'
> sage: P.nonarchimedian_local_height()
> ...
> AttributeError: 'RationalField_with_category' object has no attribute
> 'factor'
> }}}
>
> Note: at the moment this bug only shows up for non-torsion points because
> of bug #13953 (asking for local heights of torsion points always returns
> 0, which is in general incorrect).
>
> Apply: trac13951-local_heights.patch
New description:
Computing local heights uses functions that are only available when the
base field is a NumberField, and not over the RationalField:
{{{
sage: E = EllipticCurve([0, 0, 0, -36, 0])
sage: P = E(-3, 9)
sage: P.archimedian_local_height()
...
AttributeError: 'RationalField_with_category' object has no attribute
'places'
sage: P.nonarchimedian_local_height()
...
AttributeError: 'RationalField_with_category' object has no attribute
'factor'
}}}
Note: at the moment this bug only shows up for non-torsion points because
of bug #13953 (asking for local heights of torsion points always returns
0, which is in general incorrect).
Apply: trac13951-local_heights.patch, trac13951-local_heights_2.patch
--
Comment (by pbruin):
Thanks! The only problem was a warning while building the documentation.
The new patch fixes this and polishes the documentation of
[[non_]archimedean_local_]height.
I now added a "weighted" flag to the global height function (only the
normalised height is cached) and to archimedean_local_height. For the
latter I reintroduced the ugly way of checking whether an Archimedean
place is real (v.im_gens()[0] in rings.RR). However, this is only needed
when the user directly calls archimedean_local_height(v, weighted=True),
not when v = None.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/13951#comment:21>
Sage <http://www.sagemath.org>
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