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() -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
