bursejan@gmail.com schrieb:   
   >   
   > I would only test the groebner bases algorithm, not some   
   > other poly_gcd algorithm, since as the thread title says,   
   > the goal is to improve the groebner bases algorithm.   
   >   
      
   All right. Standard test inputs for Groebner-basis computations are the   
   cyclic polynomials:   
      
   cyclic4:=[x1+x2+x3+x4,x1*x2+x2*x3+x3*x4+x1*x4,x1*x2*x3+x2*x3*x4+~   
   x1*x3*x4+x1*x2*x4,x1*x2*x3*x4-1]   
      
   cyclic5:=[x1+x2+x3+x4+x5,x1*x2+x2*x3+x3*x4+x4*x5+x1*x5,x1*x2*x3+~   
   x2*x3*x4+x3*x4*x5+x1*x4*x5+x1*x2*x5,x1*x2*x3*x4+x2*x3*x4*x5+x1*x~   
   3*x4*x5+x1*x2*x4*x5+x1*x2*x3*x5,x1*x2*x3*x4*x5-1]   
      
   cyclic6:=[x1+x2+x3+x4+x5+x6,x1*x2+x2*x3+x3*x4+x4*x5+x5*x6+x1*x6,~   
   x1*x2*x3+x2*x3*x4+x3*x4*x5+x4*x5*x6+x1*x5*x6+x1*x2*x6,x1*x2*x3*x~   
   4+x2*x3*x4*x5+x3*x4*x5*x6+x1*x4*x5*x6+x1*x2*x5*x6+x1*x2*x3*x6,x1~   
   *x2*x3*x4*x5+x2*x3*x4*x5*x6+x3*x4*x5*x6*x1+x4*x5*x6*x1*x2+x5*x6*~   
   x1*x2*x3+x6*x1*x2*x3*x4,x1*x2*x3*x4*x5*x6-1]   
      
   and so on for higher degrees, and the Katsura polynomials:   
      
   kat4:=[-1+2*x4+2*x3+2*x2+x1,-x1+2*x4^2+2*x3^2+2*x2^2+x1^2,-x2+2*~   
   x4*x3+2*x3*x2+2*x2*x1,-x3+2*x4*x2+2*x3*x1+x2^2]   
      
   kat5:=[-1+2*x5+2*x4+2*x3+2*x2+x1,-x1+2*x5^2+2*x4^2+2*x3^2+2*x2^2~   
   +x1^2,-x2+2*x5*x4+2*x4*x3+2*x3*x2+2*x2*x1,-x3+2*x5*x3+2*x4*x2+2*~   
   x3*x1+x2^2,-x4+2*x5*x2+2*x4*x1+2*x3*x2]   
      
   kat6:=[-1+2*x6+2*x5+2*x4+2*x3+2*x2+x1,-x1+2*x6^2+2*x5^2+2*x4^2+2~   
   *x3^2+2*x2^2+x1^2,-x2+2*x6*x5+2*x5*x4+2*x4*x3+2*x3*x2+2*x2*x1,-x~   
   3+2*x6*x4+2*x5*x3+2*x4*x2+2*x3*x1+x2^2,-x4+2*x6*x3+2*x5*x2+2*x4*~   
   x1+2*x3*x2,-x5+2*x6*x2+2*x5*x1+2*x4*x2+x3^2]   
      
   and so on for higher degrees. On a modern computer, Derive 6.10 needs   
   of the order of one minute for:   
      
     GROEBNER_BASIS(cyclic5, [x1, x2, x3, x4, x5])   
      
   and of the order of ten minutes for:   
      
     GROEBNER_BASIS(kat5, [x1, x2, x3, x4, x5])   
      
   I gather that Singular (also using a deterministic algorithm over QQ   
   and lexicographic ordering of monomials) can even compute the basis of   
   cylic8 or kat11 in an hour or so.   
      
   Martin.   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)