Nonlinear equations

 

In Reduce

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

inputs outputs

• using decomposition to solve high degree polynomials

  
      solve(x**8-8*x**7+34*x**6-92*x**5+175*x**4-236*x**3+226*x**2-140*x+46);
  

      Unknown: x
  
          sqrt( - sqrt( - 4*sqrt(3) - 3) - 3)*sqrt(2) + 2
      {x=-------------------------------------------------,
                                 2
  
           - sqrt( - sqrt( - 4*sqrt(3) - 3) - 3)*sqrt(2) + 2
       x=----------------------------------------------------,
                                  2
  
          sqrt( - sqrt(4*sqrt(3) - 3) - 3)*sqrt(2) + 2
       x=----------------------------------------------,
                               2
  
           - sqrt( - sqrt(4*sqrt(3) - 3) - 3)*sqrt(2) + 2
       x=-------------------------------------------------,
                                 2
  
          sqrt(sqrt( - 4*sqrt(3) - 3) - 3)*sqrt(2) + 2
       x=----------------------------------------------,
                               2
  
           - sqrt(sqrt( - 4*sqrt(3) - 3) - 3)*sqrt(2) + 2
       x=-------------------------------------------------,
                                 2
  
          sqrt(sqrt(4*sqrt(3) - 3) - 3)*sqrt(2) + 2
       x=-------------------------------------------,
                              2
  
           - sqrt(sqrt(4*sqrt(3) - 3) - 3)*sqrt(2) + 2
       x=----------------------------------------------}
                               2

• multiple use of inversion functions

      solve(log(acos(asin(x**(2/3)-b)-1))+2,x);
  

                   1             3/2
      {x=(sin(cos(----) + 1) + b)   ,
                    2
                   e
  
                      1             3/2
       x= - (sin(cos(----) + 1) + b)   }
                       2
                      e