Maybe you can do this faster than Derive 6.10. I want to eliminate the   
   two variables x1, x2 from the three polynomial equations   
      
   2*x1^3*x2*(4*x2^2 - 3*(4*x4^2 + 1)) - x1^2*(12*x2^4 + 3*x2^2*(24*x3*x4 -   
   24*x4^2 - 1) - 6*x3*x4*(4*x4^2 + 3) + 12*x4^4 + 3*x4^2 - 2) +   
   6*x1*x2*(x2^4 - 2*x2^2*(2*x3^2 - 8*x3*x4 + 5*x4^2) + 3*x3^2*(4*x4^2 + 1)   
   - 2*x3*x4*(8*x4^2 + 1) + 5*x4^4) - x2^6 + 3*x2^4*(4*x3^2 - 10*x3*x4 +   
   5*x4^2) + 3*x2^2*(8*x3^3*x4 - x3^2*(24*x4^2 + 1) + 20*x3*x4^3 - 5*x4^4)   
   - 2*x3^3*x4*(4*x4^2 + 3) + x3^2*(12*x4^4 + 3*x4^2 - 2) - 6*x3*x4^5 +   
   x4^6 = 0   
      
   - 2*(x1^3*x4*(12*x2^2 - 4*x4^2 - 3) + 3*x1^2*x2*(4*x2^2*(x3 - 2*x4) -   
   3*x3*(4*x4^2 + 1) + x4*(8*x4^2 + 1)) - x1*(3*x2^4*(4*x3 - 5*x4) +   
   3*x2^2*(12*x3^2*x4 - x3*(24*x4^2 + 1) + 10*x4^3) - 3*x3^2*x4*(4*x4^2 +   
   3) + x3*(12*x4^4 + 3*x4^2 - 2) - 3*x4^5) + x2*(x3 - x4)*(3*x2^4 -   
   2*x2^2*(2*x3^2 - 10*x3*x4 + 5*x4^2) + 3*(x3^2*(4*x4^2 + 1) - 4*x3*x4^3 +   
   x4^4))) = 0   
      
   x2^2 + x4^2 - 2 = 0   
      
   Thus I started GROEBNER_BASIS([lhs1, lhs2, lhs3], [x1, x2, x3, x4]) on   
   Derive, where lhs1, lhs2, lhs3 are the left-hand sides of the three   
   equations; the computation is still running. However, I am interested   
   only in the basis elements not involving x1 and x2.   
      
   Thanks,   
      
   Martin.   
      
   --- SoupGate-Win32 v1.05   
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