From: &noreply@axelvogt.de   
      
   That - in my opinion - has not much to do with CAS per se. But more with some   
   consistent mathematical conventions. Where one also may want to look beyond   
   sqrt, avoiding similar discussions for cube roots etc.   
      
   It is a classical result that having 'enough' square roots one has logarithms,   
   which is a theorem of Hurwitz (Remmert, Funktionentheorie 1, "Die Kraft der   
   Quadratwurzel" for a proof, pointing to H. and his article Math. Ann 70 (1911),   
   p. 33 - 47). The converse 'powers if having log' is common in lectures.   
      
   That is for functions and thus much more general than discussed here. But it   
   shows that the proper setting is to consider Log. And Exp.   
      
   I have not looked further in Remmert (much material), but would suggest to   
   have a look into H. Cartan's 'little' book for a concise treatment, where one   
   finds exp & log (and variations/selections), covering a more formal view.   
      
      
   To come back to sqrt: the initial question was over the complex numbers.   
   One can not understand 'solutions' for that without basic complex analysis.   
      
   And in a brute way: not, sqrt is not a holomorphic function. It is not even   
   a continous function in the plane. It is just 1 selection (IIRC correctly   
   there was the notion of holomorphic correspondance [like in Topology] and   
   srqt becomes a fct after branch cut with semi-contious extension into   
   negatives,   
   if one wants to avoid Riemannian surfaces).   
      
   In school (which ones?) that is operationally reduced to "just do it in C++"   
      
   And I find it good that Maple et al refuse to follow that.   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)