#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:
Authors: Peter Bruin | Merged in:
Dependencies: #12509, #13953 | Stopgaps:
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Comment (by pbruin):
Replying to [comment:9 cremona]:
> A second comment, of a different kind: how can it have happened and
never been noticied that these related functions are all spelled wrong!
It is "archimedean" and not "archimedian" (think "Archimedes").
I agree with the spelling "archimedean". (It is "archimedisch" in German
and Dutch, and "archimédien" in French, but in these cases the "i" is part
of the suffix. Similarly, "Euclidean geometry" vs. "géométrie
euclidienne" etc.)
If we are changing the spelling anyway, should we also write
"non_archimedean_local_height" instead of "nonarchimedean_local_height"
for readability?
I also noticed that "independent" is spelled "independant" in three places
in the documentation.
> I don't think I will be able to resist correcting all these: about 24
occurrences including doctests. Interestingly, in almost all places the
word is spelled correctly in comments. But should we just deprecate the
old spelling? I will consult sage-devel.
>
> 1. In line 2858 of the patched file I removed the division by
K.degree() since that is 1. This appeared to cut the time to doctest this
file (with --long) by a few seconds, but that might have been a freak!
Yes, the division by K.degree() should clearly be omitted.
> 2. The global height function would now work without calling pari,
hence with no special case needed for K==QQ. Alternatively, we could
easily add an "algorithm" parameter which could be either "sage" or
"pari", with "pari" the default. I think that over QQ pari uses Mestre's
AGM method for the real place, which is likely to be faster. Having the
choice of algorithm would make it easy to add a doctest to compare the
two; there should already be a doctest showing that the global height is
the sum of the arch. and non-arch. heights which would actually be a test
since we are computing them entirely indepependently!
As far as I can see the doctest verifying that the height equals the sum
of the archimedean and non-archimedean local heights is not there yet, but
there should certainly be one!
> 3. The non-arch. height has a parameter "weighted" which is not
documented and should be, with doctests shoing its use. Similarly with
the is_minimal parameter. And for consistency, surely the arch. height
should also have a weighted parameter?
Yes, that sounds reasonable.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/13951#comment:12>
Sage <http://www.sagemath.org>
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