#12509: computation of height of point on elliptic curve over Q(sqrt(5)) is
WRONG
---------------------------------+------------------------------------------
Reporter: was | Owner: was
Type: defect | Status: new
Priority: critical | Milestone: sage-5.6
Component: number theory | Resolution:
Keywords: | Work issues:
Report Upstream: N/A | Reviewers:
Authors: | Merged in:
Dependencies: | Stopgaps: #12692
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Comment (by cremona):
This is a completely TRIVIAL thing, and I cannot understand why I did not
spot this earlier. In the example, the height is computed as the sum of
archimedean and non-arch components. The latter is log(25)/2 and is
returned as such *using the python builtin log function*! This is where
the precision is lost, Compare
{{{
sage: P.height()
1.35648516097058
sage: P.archimedian_local_height() + P.nonarchimedian_local_height()
1/2*log(25) - 0.2206607955468278522013468194382
sage: RR(P.archimedian_local_height() + P.nonarchimedian_local_height())
1.38877711688727
}}}
and you wonder how it is possible to get this wrong:
{{{
sage: P.archimedian_local_height(prec=53) +
P.nonarchimedian_local_height(prec=53)
1.35648516097
}}}
I will make a patch now.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12509#comment:5>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
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