SymPy cannot solve polynomial equation of 4th order

Question

I have an polynomial equation of 4th order and I need to find all roots. Simple example:

from sympy import (Symbol,solve,I)

a=4+5*I; b=3+7*I; c=12-56*I; d=33+56*I; e=345-67*I; x=Symbol('x')
eq=a*x**4 + b*x**3 + c*x**2 + d*x +e
solve(eq,x)

If a,b,c,d,e are pure real, then it work just fine. But in my case all of them are complex numbers. Then i did get call:

PolynomialError: 'cannot return general quartic solution'

I find kind of similar issue, and implement the fix: Description of the issue. Fix of the issue

but it doesn't really help. There is some kind of strange problem, as now the call is (as changed in the fix):

PolynomialError: Cannot determine if `-((12 - 56*I)/(4 + 5*I) - 3*(3 + 7*I)**2/(8*(4 + 5*I)**2))**2/12 + (3 + 7*I)*((33 + 56*I)/(4*(4 + 5*I)) + (3 + 7*I)*(3*(3 + 7*I)**2/(256*(4 + 5*I)**2) - (12 - 56*I)/(16*(4 + 5*I)))/(4 + 5*I))/(4 + 5*I) - (345 - 67*I)/(4 + 5*I)` is nonzero.

But to determine if expression above is nonzero is the most simplest thing, so don't know where the problem could be.

Answer 1

Upgrade to the most recent version of SymPy which supports arbitrary quartic solutions.