From: fateman@gmail.com   
      
   >   
   The question is, what should a CAS provide as an answer.   
   y=x^2 is, by common usage in CAS, incomplete or outright wrong.   
   Consider sqrt(y)=-5    (that is,  x=-5)   
   y=25  would seem to be the specific "answer".   
      
   Yet sqrt(25) is commonly held to be 5, not -5, and so the given   
   answer does not satisfy the equation.   
      
   If you view sqrt as multivalued, and  sqrt(25) is therefore the   
   set {-5,5},  then it is also false that the set {-5,5} is equal to   
   5   (or the set {5} ).   
      
   Maxima seems to be headed in the right direction, though perhaps the answer   
   could   
   be stated as some kind of conditional,  if (x is real and x>=0 ) then y=x^2   
   else....   
      
   The rule of thumb I was taught was that you can square (etc) both side of an   
   equation at   
   the risk of introducing extraneous solutions, and so they must be checked.   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)