From: &noreply@axelvogt.de   
      
   On 05.04.2014 20:49, dwelz@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   
   >   
   ...   
   >   
   > 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.   
      
   Using Maple:   
      
   lhs1 respectively lhs2 are of degree (3,5) resp. (3,6)  in (x1,x2).   
      
   If I use 'eliminate' w.r.t. {x1, x2} I get three solutions for each   
   of the systems, allowing x2 to be chosen and all are (formally) not   
   polynomials but rational algebraic (roots and divisions).   
      
   Finally one can feed x2 by solving lhs3 = x2^2 + x4^2 - 2.   
      
   Due to degree(x2) = 5 in lhs1 a sqrt (formally) would survive.   
      
   So I have doubts one can do what you want to achieve.   
      
   And my dull understanding for 'eliminate' is to project a system   
   onto remaining coordinates [partially uniquely]).   
      
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