#12509: computation of height of point on elliptic curve over Q(sqrt(5)) is
WRONG
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Reporter: was | Owner: was
Type: defect | Status: needs_review
Priority: critical | Milestone: sage-5.6
Component: elliptic curves | Resolution:
Keywords: heights | Work issues:
Report Upstream: N/A | Reviewers: Peter Bruin
Authors: John Cremona | Merged in:
Dependencies: | Stopgaps: #12692
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Comment (by pbruin):
The original precision problem seems to be solved by the patch, but there
is a remaining problem if the given place `v` has lower precision than
`prec` (the answer ends with a string of zeroes):
{{{
sage: K.<a> = NumberField(x^2-x-1)
sage: v = [0, a + 1, 1, 28665*a - 46382, 2797026*a - 4525688]
sage: E = EllipticCurve(v)
sage: P = E([72*a - 509/5, -682/25*a - 434/25])
sage: P.archimedian_local_height(v=K.places()[1],prec=1000)
2.81105581458853745263599796447519791747641640992814370122945754557165333149900887291328934930695388487942633879651281942220091469088330120430293759305481969374444866348067978423230783846520353108644485473632812500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
}}}
The precision of `v` shouldn't influence the result, of course.
Also, the default value of `prec` used when applying Silverman's Theorem
4.2 is currently the precision of the refined place `vv`, but it suffices
to take the same default precision to which the result is returned, namely
the precision of `v`.
I wrote a patch that fixes both issues; I am now going to test it.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12509#comment:11>
Sage <http://www.sagemath.org>
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