I am trying to compute the quality of $abc$ triples over
number fields.

This is basically $l_K(x)$ from [1] p. 1 with x,1-x,1 replaced by
a,b,c.

My main pain is the definition of height in [1], 
is there a sage method for it - maybe global_height() or
local_height()?

The conductor N_K(a,b,c) is not clear to me too.

Implementation of the quality over number fields will be appreciated
(I suppose it will be one-liner if you have height() ).

Thanks.


[1] 
http://www.ams.org/mcom/2000-69-232/S0025-5718-99-01153-9/S0025-5718-99-01153-9.pdf
SOME EXAMPLES RELATED TO THE abc–CONJECTURE FOR ALGEBRAIC NUMBER FIELDS


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