#11758: Bug in global_height function
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Reporter: dkrumm | Owner: somebody
Type: defect | Status: new
Priority: major | Milestone: sage-4.7.2
Component: number theory | Keywords: global height
Work_issues: | Upstream: N/A
Reviewer: | Author:
Merged: | Dependencies:
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The global_height function for elements of number fields gives incorrect
results. Here is an example:
{{{
sage: K.<s> = QuadraticField(2)
sage: s.global_height()
0.346573590279973
sage: (1/s).global_height()
0.693147180559945
}}}
This is incorrect since s and 1/s should have the same height. I'm running
Sage 4.7 on Mac OS X 10.6.8.
I believe the reason for the error is explained in the author's comments
in the code for this function:
"The absolute logarithmic height of this number field element; that is,
the sum of the local heights at all finite and infinite places, with the
contributions from the infinite places scaled by the degree to make the
result independent of the parent field."
However, it is both the arch. and non-arch. contributions that need to be
scaled by the degree.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11758>
Sage <http://www.sagemath.org>
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