#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:
---------------------------------------------+------------------------------
Comment (by cremona):
One small point: on line 2618 you set w=1, which will be a python int,
and then you multiply the final returned height by w (in 3 places, 2 with
the cached value and one when it is computed). Maybe I am old-fashioned,
but I don't like multiplying by 1: can we reply on python doing nothing
when that value of 1 is a plain python int? If it were not for this
scaling needing to be done in three places I would suggest not defining w
at all and ending the function with
{{{
if normalised:
return height
else:
return height * K.degree()
}}}
but it is not very nice to add that three times.
Perhaps multiplying by one in the usual (and default) case is not serious.
The only other thing to point out is that there is no new doctest to show
the effect of the normalisation parameter. How about:
{{{
sage: E = EllipticCurve('37a1')
sage: P = E([0,0])
sage: P.height()
0.0511114082399688
sage: P.height(normalised=False)
0.0511114082399688
sage: K.<z> = CyclotomicField(5) # or perhaps something simpler
sage: EK = E.change_ring(K)
sage: PK = EK([0,0])
sage: PK.height()
0.0511114082399688
sage: PK.height(normalised=False)
0.204445632959875
}}}
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/13951#comment:24>
Sage <http://www.sagemath.org>
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