On Mon, Nov 04, 2013 at 07:30:43AM -0800, Nils Bruin wrote: > 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)]
Thanks. I meant log(max()), sorry for the typo. Since abc for integers doesn't allow scaling (coprimality), I tried to avoid scaling too with coprimality of the norms, but didn't do it properly. I meant: If the norms of a,b,c are not coprime integers, q(a,b,c)=0 otherwise q(a,b,c)=log(max()) / .... -- 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.
