PS e.g. see http://portal.acm.org/citation.cfm?id=800204.806298 (found using Google Scholar): "Algebraic simplification a guide for the perplexed" 1971, has references back to 1960 at least -- and also mentioned Axiom.
2008/6/1 John Cremona <[EMAIL PROTECTED]>: > 2008/6/1 Henryk Trappmann <[EMAIL PROTECTED]>: >> >>> 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) >> > > You have only shifted the ambiguity to the multi-values proprty of > log! As I have often expleined to students, the "generic" proprty > that log(ab)=log(a)+log(b) just does not hold as an identity for > arbitrary complex numbers, and there is no branch convention which > will make that true. > >> I never said it is simple but I am sure that there are equality >> deciding algorithms. >> And I really want to learn about those. > > If they exist, I would like to see them too. But I am not optimistic. > However there must be a vast literature on the subject, which is at > least as old as computer algebra. > > John > >> >> >> > --~--~---------~--~----~------------~-------~--~----~ 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 -~----------~----~----~----~------~----~------~--~---
