From: fateman@cs.berkeley.edu   
      
   On 7/6/2017 10:05 AM, bursejan@gmail.com wrote:   
   > In the below paragraph there is possibly a negation   
   > of yours somewhere missing:   
   yep.   
      
   corrected it should read ...   
      
   Nevertheless, there are good reasons to believe that,   
   in any reasonably implemented CAS which   
   has  polynomial GCD and GB procedures,   that using GB to   
   implement a GCD  would   
   NOT   
     be faster than the GCD.   
      
   ..........   
      
   Since Jan mentions the classical Euclidean GCD ...   
      
      
   The classical Euclidean GCD algorithm directly implemented   
   for polynomial arithmetic is an obvious method. It is   
   lucidly described and compared to some far superior alternatives   
   in D.E. Knuth's Art of Computer Programming, vol. 2.   
   Yet more superior algorithms were subsequently developed   
   and are in fairly wide-spread implementations.   
      
   The Euclidean GCD's theoretically expected behavior, and its actual   
   behavior in practice are really quite poor.   
      
   I can think of a worse algorithm for gcd(a,b), which   
   is to use some method (perhaps a heuristic to make guesses)   
   to make a list L1 of the factors of   
   the polynomial a and L2 of the factors of   
     the polynomial b.  Then look   
   to see which factors are in common in L1 and L2.   
      
   (There is a generally slow but compact factoring algorithm   
   available in Maxima.  Set berlefact:false to try it out.   
   It is ok for really small degree small coefficient few variables.)   
      
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