I have this polynomial for which I need to find the roots. The problem I'm running into is that my polynomial has an exogenously chosen parameter for which I need to find the roots in order to interpret. My approach has been to use the real_roots() method in SymPy:
from sympy.abc import x, c
from sympy import Poly, real_roots
Poly(4-2*c*c*x+c*c*x**3,x,domain='RR[c]').real_roots()
but I get the error NotImplementedError: sorted roots not supported over RR[c] which I'm having a hard time interpreting. Is this even the right way to go about approximating the roots of this polynomial? Ideally, the roots will be functions of c.
Unless you have need of Poly methods, it is not necessary to work with an explicit Poly expression. In this case, the real_roots method does not work unless the roots can be sorted (and they can't in this case). But if you just solve the expression without the Poly wrapper for x you will get the 3 roots of the cubic expression and can substitute in values of c afterwards. You may not be able to tell which is real without pugging in a value of c, however. (But if you know the value of c then real_roots will give you the answer.)
>>> sol = solve(c**2*x**3 - 2*c**2*x + 4, x) # sol is a list with 3 solution exprs