Dear Sympy list,
  I'm trying to solve a quartic equation that comes from the numerical
dispersion relation of a finite element method I am working on. If I
type

>>> solve(fn,w)

I get

[]

which is not what I expected. It's a rather complicated expression so
I have included it at the bottom of this file. I'd be most grateful if
someone could point out what I am doing wrong.

best wishes
--Colin

from sympy import *
p,q,w,g,f = symbols('pqwgf')
fn = w*((70400*f**2*g**2 - 2592000*g**3 + 12420*g*f**4 + 132*f**6)*cos
(p) + (70400*f**2*g**2 - 2592000*g**3 + 12420*g*f**4 + 132*f**6)*cos
(q) + (70400*f**2*g**2 - 2592000*g**3 + 12420*g*f**4 + 132*f**6)*cos(p
- q) + (1600*f**2*g**2 - 48000*g**3 + 180*g*f**4 - 12*f**6)*cos(-2*q +
2*p) + (25600*f**2*g**2 - 224000*g**3 - 360*g*f**4 + 12*f**6)*cos(p +
q) + (25600*f**2*g**2 - 224000*g**3 - 360*g*f**4 + 12*f**6)*cos(p -
2*q) + (25600*f**2*g**2 - 224000*g**3 - 360*g*f**4 + 12*f**6)*cos(q -
2*p)) + w**2*((-800*g**2 - 180*g*f**2 + 18*f**4)*cos(-2*q + 2*p) +
(-35200*g**2 - 12420*g*f**2 - 198*f**4)*cos(p) + (-35200*g**2 -
12420*g*f**2 - 198*f**4)*cos(q) + (-35200*g**2 - 12420*g*f**2 -
198*f**4)*cos(p - q) + (-12800*g**2 + 360*g*f**2 - 18*f**4)*cos(p + q)
+ (-12800*g**2 + 360*g*f**2 - 18*f**4)*cos(p - 2*q) + (-12800*g**2 +
360*g*f**2 - 18*f**4)*cos(q - 2*p)) + w**3*((-120*g + 12*f**2)*cos(p +
q) + (-120*g + 12*f**2)*cos(p - 2*q) + (-120*g + 12*f**2)*cos(q - 2*p)
+ (60*g - 12*f**2)*cos(-2*q + 2*p) + (4140*g + 132*f**2)*cos(p) +
(4140*g + 132*f**2)*cos(q) + (4140*g + 132*f**2)*cos(p - q)) + w**4*
(-33*cos(p) - 33*cos(q) - 33*cos(p - q) - 3*cos(p + q) - 3*cos(p -
2*q) - 3*cos(q - 2*p) + 3*cos(-2*q + 2*p)) + (-35200*f**4*g**2 +
2592000*f**2*g**3 - 47360000*g**4 - 4140*g*f**6 - 33*f**8)*cos(p) +
(-35200*f**4*g**2 + 2592000*f**2*g**3 - 47360000*g**4 - 4140*g*f**6 -
33*f**8)*cos(q) + (-35200*f**4*g**2 + 2592000*f**2*g**3 -
47360000*g**4 - 4140*g*f**6 - 33*f**8)*cos(p - q) + (-12800*f**4*g**2
+ 224000*f**2*g**3 - 3840000*g**4 + 120*g*f**6 - 3*f**8)*cos(p + q) +
(-12800*f**4*g**2 + 224000*f**2*g**3 - 3840000*g**4 + 120*g*f**6 -
3*f**8)*cos(p - 2*q) + (-12800*f**4*g**2 + 224000*f**2*g**3 -
3840000*g**4 + 120*g*f**6 - 3*f**8)*cos(q - 2*p) + (-800*f**4*g**2 +
48000*f**2*g**3 - 640000*g**4 - 60*g*f**6 + 3*f**8)*cos(-2*q + 2*p)

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