clicliclic@freenet.de schrieb:   
   >   
   > clicliclic@freenet.de schrieb:   
   > >   
   > > Daniel Lichtblau schrieb:   
   > > >   
   > > > [...]   
   > > >   
   > >   
   > > Thanks for the private message, Daniel. So Mathematica does it in about   
   > > 25 seconds using "elimination order". Unfortunately the result of your   
   > > copy and paste operations was syntactically garbled. I have tried to   
   > > repair this by deleting some lines, as shown above, but the resulting   
   > > bivariate polynomial does not agree with Waldek's nor with my own from a   
   > > resultant computation (both were posted earlier). Bad for Mathematica.   
   > >   
   >   
   > Since Daniel doesn't respond, the private message ostensibly sent by him   
   > should be regarded as insider spam until proved genuine.   
   >   
      
   I am pleased to report that the private message initially attributed to   
   Daniel Lichtblau has been declared by him to be genuine. Moreover, his   
   discrepant result has been traced by him to a feature of Mathematica not   
   known to me: when parsing the 3rd and 4th lines   
      
   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) - ...   
      
   from my original 1st equation, for instance, Mathematica assumes   
   multiplication between the two lines! For input modified to be   
   understood correctly by Mathematica, Daniel now reports:   
      
   In[126]:= Timing[elim =   
       First[GroebnerBasis[polys3, {x3, x4}, {x1, x2},   
         MonomialOrder -> EliminationOrder]];]   
      
   Out[126]= {0.052000, Null}   
      
   In[127]:= InputForm[elim]   
      
   Out[127]//InputForm=   
   250*x3^3 + 10000*x3^5 + 100000*x3^7 + 250000*x3^9 - 150*x3^2*x4 -   
     9000*x3^4*x4 - 135000*x3^6*x4 - 450000*x3^8*x4 + 18*x3*x4^2 +   
     2820*x3^3*x4^2 + 97800*x3^5*x4^2 + 759000*x3^7*x4^2 +   
     1440000*x3^9*x4^2 - 748*x3^2*x4^3 - 64670*x3^4*x4^3 -   
     1010000*x3^6*x4^3 - 3648000*x3^8*x4^3 + 237*x3*x4^4 +   
     30066*x3^3*x4^4 + 771417*x3^5*x4^4 + 4434240*x3^7*x4^4 +   
     2764800*x3^9*x4^4 - 27*x4^5 - 6642*x3^2*x4^5 - 350499*x3^4*x4^5 -   
     3752256*x3^6*x4^5 - 9031680*x3^8*x4^5 + 364*x3*x4^6 +   
     110124*x3^3*x4^6 + 2476000*x3^5*x4^6 + 12951552*x3^7*x4^6 +   
     1769472*x3^9*x4^6 + 36*x4^7 - 27708*x3^2*x4^7 -   
     1198272*x3^4*x4^7 - 10788864*x3^6*x4^7 - 7077888*x3^8*x4^7 +   
     5004*x3*x4^8 + 382584*x3^3*x4^8 + 5849088*x3^5*x4^8 +   
     12533760*x3^7*x4^8 - 420*x4^9 - 72680*x3^2*x4^9 -   
     2199552*x3^4*x4^9 - 12894208*x3^6*x4^9 + 7056*x3*x4^10 +   
     593664*x3^3*x4^10 + 8491008*x3^5*x4^10 - 240*x4^11 -   
     113664*x3^2*x4^11 - 3710976*x3^4*x4^11 + 13968*x3*x4^12 +   
     1076224*x3^3*x4^12 - 816*x4^13 - 199680*x3^2*x4^13 +   
     21504*x3*x4^14 - 1024*x4^15   
      
   in agreement with all other results. Curiously enough, Mathematica's   
   echo of the incorrectly parsed input given in Daniel's first message is   
   found correct when read back into Derive ...   
      
   Martin.   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)