Ticket #11758 (closed defect: fixed)
Bug in global_height function
|Reported by:||dkrumm||Owned by:||cremona|
|Component:||number theory||Keywords:||global height|
|Cc:||cremona, mderickx||Work issues:|
|Report Upstream:||N/A||Reviewers:||Frithjof Schulze|
|Authors:||David Krumm, Maarten Derickx||Merged in:||sage-4.8.alpha5|
Description (last modified by mderickx) (diff)
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.
- Owner changed from somebody to cremona
comment:10 follow-up: ↓ 11 Changed 19 months ago by mderickx
- Status changed from new to needs_review
- Authors set to David Krumm, Maarten Derickx
comment:14 Changed 18 months ago by mderickx
- Reviewers set to Frithjof Schulze
- Description modified (diff)