On Monday, November 4, 2013 1:29:10 AM UTC-8, Georgi Guninski wrote: > > Isn't it possible to define the quality only in > terms of the norm and the integer radical, > something like this: > > q(a,b,c) = max( norm(a),norm(b),norm(c) ) / > (log(Delta(K)) + degree(K) * log(radical(norm(a*b*c))) ) > > with the restriction the norms of a,b,c to be coprime ? >
Assuming you mean to take log(max(...))): With this definition you don't get a quantity that's invariant under scaling: you want to have that q(a,b,c)=q(t*a,t*b,t*c) If a,b,c,t are integers you can accomplish this by dividing by doing something like: log ( max(norm(a),norm(b),norm(c))/norm(ideal(a,b,c)) ) [in case you're not familiar with ideals in rings of integers: think of it as an analogue to gcd(a,b,c)] -- 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.
