From: rpearcea@gmail.com   
      
   On Saturday, April 5, 2014 11:49:11 AM UTC-7, dw...@web.de wrote:   
   > Maybe you can do this faster than Derive 6.10. I want to eliminate the   
   > two variables x1, x2 from the three polynomial equations   
      
   In Maple:   
      
   with(PolynomialIdeals);   
   J := <{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,   
   - 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))),   
   x2^2 + x4^2 - 2}>:   
   E := EliminationIdeal(J, {x3,x4});   
   Generators(E);  # as a set   
      
   The lone generator is:   
      
   1769472*x3^9*x4^6-7077888*x3^8*x4^7+12533760*x3^7*x4^8-12894208*   
   3^6*x4^9+8491008*x3^5*x4^10-3710976*x3^4*x4^11+1076224*x3^3*x4^1   
   -199680*x3^2*x4^13+21504*x3*x4^14-1024*x4^15+2764800*x3^9*x4^4-9   
   31680*x3^8*x4^5+12951552*x3^7*x4^6-10788864*x3^6*x4^7+   
   5849088*x3^5*x4^8-2199552*x3^4*x4^9+593664*x3^3*x4^10-113664*x3^   
   *x4^11+13968*x3*x4^12-816*x4^13+1440000*x3^9*x4^2-3648000*x3^8*x   
   ^3+4434240*x3^7*x4^4-3752256*x3^6*x4^5+2476000*x3^5*x4^6-1198272   
   x3^4*x4^7+382584*x3^3*x4^8-72680*x3^2*x4^9+7056*x3*x4^10-   
   240*x4^11+250000*x3^9-450000*x3^8*x4+759000*x3^7*x4^2-1010000*x3   
   6*x4^3+771417*x3   
   ^5*x4^4-350499*x3^4*x4^5+110124*x3^3*x4^6-27708*x3^2*x4^7+5004*x   
   *x4^8-420*x4^9+100000*x3^7-135000*x3^6*x4+97800*x3^5*x4^2-64670*   
   3^4*x4^3+30066*   
   x3^3*x4^4-6642*x3^2*x4^5+364*x3*x4^6+36*x4^7+10000*x3^5-9000*x3^   
   *x4+2820*x3^3*x4^2-748*x3^2*x4^3+237*x3*x4^4-27*x4^5+250*x3^3-15   
   *x3^2*x4+18*x3*x4^2   
      
   Maple also says the ideal is prime.   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)