The first 3 test cases, are none of the **nasty    
   kind** of a GB for GCD algorithm. They all go through    
   very easily by the GB for GCD algorithm:   
      
   ?- D is X^2+X+3,    
   F is 2*X^2+2*X+1,    
   G is X^2+2*X+2,    
   H is (D*F)/(D*G).   
   H is 2-(3+2*X)/(2+2*X+X^2)   
      
   ?- D is X^2+X+3,    
   F is 2*X^2+2*X+1,    
   G is X^2+2*X+2,    
   time(_ is (D*F)/(D*G)).   
   % Up 12 ms, GC 0 ms, Thread Cpu 0 ms (Current 07/13/17 01:21:05)   
      
   ?- D is 2*X^2*Y^2+X*Y+2*X,   
   F is Y^2+2*X^2*Y+X^2+1,   
   G is X^2*Y^2+X^2*Y+X*Y+X^2+X,   
   H is (D*F)/(D*G).   
   H is (1+X^2+2*X^2*Y+Y^2)/(X+X^2+(X+X^2)*Y+X^2*Y^2)   
      
   ?- D is 2*X^2*Y^2+X*Y+2*X,   
   F is Y^2+2*X^2*Y+X^2+1,   
   G is X^2*Y^2+X^2*Y+X*Y+X^2+X,   
   time(_ is (D*F)/(D*G)).   
   % Up 405 ms, GC 35 ms, Thread Cpu 360 ms (Current 07/13/17 01:23:59)   
      
   ?- D is Y^2*Z^2+Y^2*Z+2*X^2*Y*Z+X*Z,   
   F is Z^2+Y^2*Z+X^2*Y*Z+X*Z+X^2*Y^2,   
   G is Y*Z+2*X*Z+Z+X,   
   H is (D*F)/(D*G).   
   H is 1/2-1/4*Y-1/4*Y^2+1/2*Y*X-((1/4+1/8*Y-3/4*Y^2-1/8*Y^3)*Z-1/   
   *Z^2+(1/4-1/8*Y-1/8*Y^2)*X+(1/4*Y-1/2*Y^2)*X^2)/((1/2+1/2*Y)*Z+(1/2+Z)*X)   
      
   ?- D is Y^2*Z^2+Y^2*Z+2*X^2*Y*Z+X*Z,   
   F is Z^2+Y^2*Z+X^2*Y*Z+X*Z+X^2*Y^2,   
   G is Y*Z+2*X*Z+Z+X,   
   time(_ is (D*F)/(D*G)).   
   % Up 2,773 ms, GC 344 ms, Thread Cpu 2,454 ms (Current 07/13/17 01:26:44)   
      
   But then number 4 is of the **nasty kind** for my    
   system and the current realization (as of now) of    
   GB for GCD algorithm.    
      
   ?- D is X^2*T^2+Y^2*Z*T+X^2*Y*T+Y*T+X^2*Y*Z,   
   F is X*Y*Z^2*T^2+X*Z^2*T^2+X*T^2+T^2+X*Z*T,   
   G is X*Z^2*T^2+Z^2*T^2+X*Y^2*Z*T+X*Y^2,   
   H is (D*F)/(D*G).   
   Error: Execution aborted since memory threshold exceeded.   
   	is/2   
   Ok lets see what maxima does today, to get a grip   
   of the time relationship (only CLISP for simplicity):   
      
   (%i7) D:X^2*T^2+Y^2*Z*T+X^2*Y*T+Y*T+X^2*Y*Z;   
   Evaluation took 0.0000 seconds (0.0000 elapsed) using 26.594 KB.   
                          2      2          2            2  2   
   (%o7)               T Y  Z + X  Y Z + T X  Y + T Y + T  X   
   (%i8) F:X*Y*Z^2*T^2+X*Z^2*T^2+X*T^2+T^2+X*Z*T;   
   Evaluation took 0.0000 seconds (0.0000 elapsed) using 21.836 KB.   
                        2      2    2    2            2      2   
   (%o8)               T  X Y Z  + T  X Z  + T X Z + T  X + T   
   (%i9) G:X*Z^2*T^2+Z^2*T^2+X*Y^2*Z*T+X*Y^2;   
   Evaluation took 0.0000 seconds (0.0000 elapsed) using 16.375 KB.   
                           2    2    2  2        2        2   
   (%o9)                  T  X Z  + T  Z  + T X Y  Z + X Y   
   (%i10) gcd(expand(D*F),expand(D*G));   
   Evaluation took 0.0156 seconds (0.0155 elapsed) using 734.891 KB.   
                           2    2            2           2  2   
   (%o10)              (T Y  + X  Y) Z + (T X  + T) Y + T  X   
      
   Cool, very good! Not bad.    
   This is something new to chew on.    
      
   Oki Doki.   
      
   Am Donnerstag, 13. Juli 2017 01:03:19 UTC+2 schrieb burs...@gmail.com:   
   > But I would need a better quality PDF, to   
   > make OmniPage OCR of the test cases.   
   >    
   > Am Donnerstag, 13. Juli 2017 00:51:00 UTC+2 schrieb burs...@gmail.com:   
   > > This paper contains a couple of GCD problems:   
   > >    
   > > http://www.cecm.sfu.ca/~monaganm/teaching/TopicsinCA15/zippel79.pdf   
   > >    
   > > 5. Appendix.   
   > > This appendix lists the polynomials that were used to test the various GCD   
   algorithms in scction 3. The di polynomials are the GCDs which are computed,   
   the fi and gi the cofactors. The polynomials that were fed to the various GCD   
   routines were di*fi    
   and di*gi.   
   > >    
   > > The algorithms EZ, mod, red all get easily killed!   
   > >    
   > > > . Zippel, R.: Probabilistic Algorithms for    
   > > > Sparse Polynomials. Lecture Notes in Computer   
   > > > Science Vol. 72. Berlin, Heidelberg, New York: Springer 1979   
      
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