#11758: Bug in global_height function
--------------------------------+-------------------------------------------
Reporter: dkrumm | Owner: cremona
Type: defect | Status: positive_review
Priority: major | Milestone: sage-4.8
Component: number theory | Keywords: global height
Work_issues: | Upstream: N/A
Reviewer: Frithjof Schulze | Author: David Krumm, Maarten Derickx
Merged: | Dependencies:
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Changes (by mderickx):
* reviewer: => Frithjof Schulze
Old description:
> 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.
New description:
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.
apply [attachment:trac_11758_global_height.2.patch]
--
Comment:
Thanks for reviewing.
If you review something you should set the reviewer field. And if there
are multiple patches you should specify wich to apply.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11758#comment:14>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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