On Sunday, November 3, 2013 6:36:35 AM UTC-8, John Cremona wrote: > > The function is called global_height(): > > sage: K.<a> = NumberField(x^3-2) > sage: b = a+1 > sage: b.global_height() > 0.366204096222703 > > John Cremona > That doesn't quite do the trick, though. For ABC, you'd need the height of the triple (a:b:c), not of the individual points. I think there are some tickets about heights for arithmetic dynamics? I'd think they would need naive height on projective space somewhere as well.
It should be pretty straightforward to write something yourself: - clear denominators on your triple (a,b,c) [not necessarily minimally - if your ring of integers isn't a PID you might not be able to] - compute the archimedean contribution by taking max abs of the complex (and real) embeddings (take complex places twice) - divide by Norm (ideal generated by integral representatives) -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/groups/opt_out.
