From: boblatest@yahoo.com   
      
   antispam@math.uni.wroc.pl wrote:   
   > This is solved using usual quadratic formula, but since coefficients   
   > of the quadratic are complicated the result is large.  One could   
   > plug in this y into formula for x, but result would be equally large.   
   >   
   > Note: when you look at "general solution" there are subtleties.   
   > You can see this already from the first solution: there is   
   > division by d - a.  And indeed, depending on the other parameters   
   > beside normal case of two solutions there may be one solution,   
   > no solutions or infinitely many solutions.  Similarely, quadratic   
   > formula gives "generic solution" and ignores special cases.   
      
   I know all that. I didn't really *need* to find a general solution for the   
   intersections of two circles. I just took my daughter's homework assignment as   
   inspiration to play around with a CAS (which I always wanted but didn't have   
   any reason to). I expected a screenful of messy solutions, but not an empty   
   result.   
      
   > Normally a CAS will give you "generic solution", that is solution   
   > which is valid as long as there are no divisions and which may   
   > miss some special cases.  Some teachers insist of analysiong   
   > all cases, that quickly gets tedious both for people and at   
   > somewhat larger scale for computers.   
      
   Again, the homework assignment wasn't the general solution.   
      
   > If you have numbers in   
   > the problem, than it is possible to see during computation   
   > if there are special cases and handle such cases apropriately,   
      
   That's of course more along school homework lines.   
      
   > this avoids purely theoretical difficulties.  OTOH if you   
   > really need general solution, then there is some extra work   
   > to check usual CAS solution and write proper conditions.   
      
   Like I said, I don't. I was just curious.   
   >   
      
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