From: nma@12000.org   
      
   was looking at a thread in Maple group. I was surprised that   
   Maple does not consider   
      
   Sqrt[1/Sin[a]] the same as  1/Sqrt[Sin[a]]] for all a.   
      
   I have always thought that sqrt(a/b) and sqrt(a)/sqrt(b) are   
   exactly the same (but I am an engineering student, so   
   may be I am missing something mathematically advanced here :)   
      
   Mathematica simplifies this to zero with no assumptions:   
      
   Simplify[Sqrt[1/Sin[a]] - 1/Sqrt[Sin[a]]]   
   (*  0  *)   
      
   Maxima:   
      
   (%i6) fullratsimp( sqrt(1/sin(a)) - sqrt(1)/sqrt(sin(a)));   
   (%o6)                                  0   
      
   While Maple will not   
      
   simplify(sqrt(1/sin(alpha))-1/sqrt(sin(alpha)));   
      
   The above returns unevaluated.  But when telling Maple   
   to assume  sin(alpha)>0 (thanks to the hint on the Maple group)   
   only then it returns zero:   
      
   simplify(sqrt(1/sin(alpha))-1/sqrt(sin(alpha))) assuming sin(alpha)>0;   
   (* 0 *)   
      
   Is Mathematica and Maxima wrong here? or is Maple wrong?   
      
   or in general, when is  sqrt(a/b) not the same as sqrt(a)/sqrt(b)   
   from computer algebra point of view?   
      
   --Nasser   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)