SymPy will find the solution eventually I think.
This is a polynomial of order 8 having only even powers so with a
substitution omega**2 -> x it's a quartic in x with complicated
symbolic coefficients. The general formula for a quartic is horrendous
and in this case your coefficients are already large expressions.
What this means is that the solution will take a while to compute and
will probably be too complicated to be useful when done anyway. Really
complicated analytic expressions can be difficult to use without
substituting numeric values in and it's much easier to find the roots
if you substitute the numbers in first.
I'm not sure why it is so slow though. You can get to the solutions
for omega^2 like this:
In [39]: coeffs = Poly(omega_nf_eq.rhs.subs(omega, sqrt(x)),
x).coeffs()
In [40]: a, b, c, d, e = symbols('a, b, c, d, e')
In [41]: p = Poly(a*x**4+b*x**3+c*x**2+d*x+e, x)
In [42]: rs = solve(p, x)
Print the first root:
In [43]: rs[0].subs(zip((a,b,c,d,e), coeffs))
(output omitted as it's long and complicated)
My suggestion is to consider why you need the solutions to this
equation. There may be a better way to reach your actual end goal then
getting the solutions in explicit analytic form.
--
Oscar
On Fri, 7 Jun 2019 at 00:13, pull_over93 <mattia.orempul...@gmail.com> wrote:
>
> Hi everybody, I'm tring to solve this equation without succes: omega_nf_eq = 0
>
> import sympy as sym
> m,J_d,J_p,y,Y,omega,Omega,phi,Phi,z,Z,theta,Theta,k_yy,k_zz,k_phiphi,k_yphi,k_ztheta,k_thetatheta,plane_xy1,plane_xy2,plane_xz1,plane_xz2
> =
> sym.symbols('m,J_d,J_p,y,Y,omega,Omega,phi,Phi,z,Z,theta,Theta,k_yy,k_zz,k_phiphi,k_yphi,k_ztheta,k_thetatheta,plane_xy1,plane_xy2,plane_xz1,plane_xz2',
> real = True)
> t, omega_nf = sym.symbols('t, omega_nf', real = True)
>
> omega_nf_eq = sym.Eq(omega_nf, -J_d**2*k_yy*k_zz*omega**4 +
> 0.382*J_d**2*k_yy*omega**6 + 0.382*J_d**2*k_zz*omega**6 -
> 0.145924*J_d**2*omega**8 + J_d*k_phiphi*k_yy*k_zz*omega**2 -
> 0.382*J_d*k_phiphi*k_yy*omega**4 - 0.382*J_d*k_phiphi*k_zz*omega**4 +
> 0.145924*J_d*k_phiphi*omega**6 + J_d*k_thetatheta*k_yy*k_zz*omega**2 -
> 0.382*J_d*k_thetatheta*k_yy*omega**4 - 0.382*J_d*k_thetatheta*k_zz*omega**4 +
> 0.145924*J_d*k_thetatheta*omega**6 - J_d*k_yphi**2*k_zz*omega**2 +
> 0.382*J_d*k_yphi**2*omega**4 - J_d*k_yy*k_ztheta**2*omega**2 +
> 0.382*J_d*k_ztheta**2*omega**4 + J_p**2*Omega**2*k_yy*k_zz*omega**2 -
> 0.382*J_p**2*Omega**2*k_yy*omega**4 - 0.382*J_p**2*Omega**2*k_zz*omega**4 +
> 0.145924*J_p**2*Omega**2*omega**6 - k_phiphi*k_thetatheta*k_yy*k_zz +
> 0.382*k_phiphi*k_thetatheta*k_yy*omega**2 +
> 0.382*k_phiphi*k_thetatheta*k_zz*omega**2 -
> 0.145924*k_phiphi*k_thetatheta*omega**4 + k_phiphi*k_yy*k_ztheta**2 -
> 0.382*k_phiphi*k_ztheta**2*omega**2 + k_thetatheta*k_yphi**2*k_zz -
> 0.382*k_thetatheta*k_yphi**2*omega**2 - k_yphi**2*k_ztheta**2)
>
> solution = sym.solve(omega_nf_eq.rhs, omega, dict = True , force=True,
> manual=True, set=True)
>
> Even after half an hour, sympy is unable to give a solution.
> I also tried sage math, but I had the same failure.
> Suggestions?
>
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