Does this bug affect the height algorithm for points on elliptic curves? On Aug 29, 7:36 pm, dkrumm <dkr...@uga.edu> wrote: > There is a problem with the global_height function for elements of > number fields. The fix would be very simple, just need to add two > parentheses to the code. Below is an example of the problem. I'm > running Sage version 4.7 on Mac OS X version 10.6.8. > > 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. The > problem is explained in the comments made by the author of the code: > > "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. > > The current code of global_height is : > > self.global_height_non_arch(prec)+self.global_height_arch(prec)/ > self.number_field().absolute_degree() > > The problem would be fixed if this were replaced by: > > (self.global_height_non_arch(prec)+self.global_height_arch(prec))/ > self.number_field().absolute_degree
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