Now I have found myself an example, where my algorithm   
   still runs wrong. This is not desired:   
      
   ?- F is X*Y^2-X, G is Y*X^2-Y, R is F/G.   
   R is (X*Y-X*Y^3)/((1-X^2)*Y^2)   
      
   Checking my Gröbner Bases algorithm, there is something   
   going wrong somewhere:   
      
   ?- F is X*Y^2-X, G is Y*X^2-Y, S is F*Z, T is G*(1-Z),    
   sys_poly_groeb([T,S],H), R is H.   
   R is [(X-X^3)*Y^2-(X-X^3)*Y^4,   
   - (1-X^2)*Y^2-(X^2-Y^2)*Z,   
   - (1-X^2)*Y+(1-X^2)*Y*Z,   
   (X-X^3)*Y^2-(X-X^3)*Z]   
      
   Compare this with the maxima result, for the same    
   problem, the last element is just F*G, as desired:   
      
   (%i57) poly_buchberger([(x*y^2-x)*t,(y*x^2-y)*(1-t)],[t,x,y]);   
   (%o57) [t*x*y^2-t*x,(-t*x^2*y)+x^2*y+t*y-y,   
           (-x^2*y^2)-t*y^2+y^2+t*x^2,   
           (-x^2*y^3)-t*y^3+y^3+x^2*y+t*y-y,   
           x^3*y^3-x*y^3-x^3*y+x*y]   
      
   So going back to the lab, and    
   lets see what goes wrong.   
      
   Am Mittwoch, 5. Juli 2017 20:50:01 UTC+2 schrieb burs...@gmail.com:   
   > Maybe an effect of the used ordering. Dunno yet, might   
   > investigate more closely in the future. Dunno whether   
   > its a bad sign that maxima has a bigger base, or a good   
   > sign. Could be also a good sign.   
   >    
   > A more interesting case (test case) would be if my   
   > algorithm yields multiple members more than 3, and    
   > another system only yields 3. BTW: There are also   
   > situations where the resulting GB    
   >    
   > is single or two membered, more trivially:   
   >    
   > ?- X is 0, Y is A*B, S is X*Z, T is Y*(1-Z), sys_poly_groeb([S,T],H), R is H.   
   > R is [A*B-A*B*Z]   
   >    
   > ?- X is 1, Y is A*B, S is X*Z, T is Y*(1-Z), sys_poly_groeb([S,T],H), R is H.   
   > R is [Z,A*B],   
   >    
   > Quiz: Which one is the LCM?   
      
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