On 3 November 2013 17:51, Nils Bruin <[email protected]> wrote: > 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)
I do have a function somewhere for heights of points in projective space over number fields (for arbitrary class number). I'll see if I can find it. John > > -- > 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. -- 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.
