> there is an "obvious" convention that by default we mean the positive > root.
We have to distinguish between solutions of polynomials and roots. Roots are clearly defined mono-valued functions: z.nth_root(n)=e^(log(z)/n) however this function is not continuous in z, as log is not continuous at the negative real axis. This makes things complicated. > It's a lot more complicated when you deal with general > algebraic numbers which have several ways of being embedded into CC. > Even for square roots of negative reals: you might suggest taking the > root with positive imaginary part, but then sqrt(-2)*sqrt(-3) equals > -sqrt(6) and not +sqrt(6). by the above definition this can easily be computed: sqrt(-2)*sqrt(-3)=e^(log(-2)/2+log(-3)/2)=sqrt(6)e^(-pi*i/2-pi*i/ 2)=sqrt(6)*(-1) I never said it is simple but I am sure that there are equality deciding algorithms. And I really want to learn about those. --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
