Converting an equation to another form using sympy

Question

I have such a problem: I have an expression like x ** 3 - x ** 2 + x - 5 = 0. I need to convert it to the form x = g(x), such as x = root(x ** 2 - x + 5, 3).

Can sympy do this? If so, how? Thank you for your informative answer.

Answer 1

You can replace the x**3 term with y**3 and solve for y:

In [26]: lhs = x ** 3 - x ** 2 + x - 5                                                                                                         

In [27]: lhs                                                                                                                                   
Out[27]: 
 3    2        
x  - x  + x - 5

In [28]: lhs.subs(x**3, y**3)                                                                                                                  
Out[28]: 
   2        3    
- x  + x + y  - 5

In [29]: y1, y2, y3 = solve(lhs.subs(x**3, y**3), y)                                                                                           

In [30]: Eq(x, y3)                                                                                                                             
Out[30]: 
       ____________
    3 ╱  2         
x = ╲╱  x  - x + 5