Nonlinear systems

 

In Mathematica

For comparison with other CAS choose from: Axiom Derive Macsyma Maple Reduce

inputs outputs

• polynomial systems by the use of Grobner bases

      Solve[ alpha c1 -beta c1^2 -gamma c1 c2 +epsilon c3 == 0,
             -gamma c1 c2 + (epsilon+theta) c3 - eta c2 == 0,
               gamma c1 c2 + eta c2 - (epsilon+theta) c3 == 0 ,
              c3,c2,c1 ]
  

      {{c3 -> (c1 (-alpha + beta c1 -
  
                 alpha c1 epsilon gamma
              ---------------------------- +
              epsilon eta - c1 gamma theta
  
                        2
                 beta c1  epsilon gamma
              ---------------------------- -
              epsilon eta - c1 gamma theta
  
                  alpha c1 gamma theta
              ---------------------------- +
              epsilon eta - c1 gamma theta
  
                         2
                  beta c1  gamma theta
              ----------------------------)) / epsilon,
              epsilon eta - c1 gamma theta
  
        c2 -> (c1 (alpha epsilon - beta c1 epsilon +
  
              alpha theta - beta c1 theta)) /
  
          (-(epsilon eta) + c1 gamma theta)}}

      Simplify[%]
  

              c1 (-alpha + beta c1) (eta + c1 gamma)
      {{c3 -> --------------------------------------,
                   epsilon eta - c1 gamma theta
  
              c1 (alpha - beta c1) (epsilon + theta)
        c2 -> --------------------------------------}}
                 -(epsilon eta) + c1 gamma theta

• c1 is an arbitrary complex number