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   sci.math.symbolic      Symbolic algebra discussion      10,432 messages   

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   Message 8,516 of 10,432   
   Axel Vogt to All   
   Re: when is sqrt(a/b) not the same as sq   
   01 Mar 14 22:35:06   
   
   From: &noreply@axelvogt.de   
      
   On 01.03.2014 22:19, Nasser M. Abbasi wrote:   
   ...   
      
   As Edgar already said:   
      
   [sqrt(a/b) , sqrt(a)/sqrt(b)]:   
   subs(a=1, %);   
                                     1/2   1   
                               [(1/b)   , ----]   
                                           1/2   
                                          b   
   subs(b=-1, %);   
                                   [I, -I]   
      
   You need that for x * 1/x = 1   
      
   The reason is the brunch cut: sqrt is 'only defined'   
   except the negative real axis and continued to that   
   by a special 'rule' in a non-continous way   
      
   In Maple that is named "winding number", K:   
      
      
   (z*w)^a = z^a*w^a * exp(-2*I*Pi*a*K(ln(z)+ln(w)))   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)   

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