Thank you so much, for the answer. I have to try it . Really Thank you!
Il giorno sabato 8 giugno 2019 16:51:41 UTC+2, Chris Smith ha scritto:
>
> As Oscar said, the equation is essentially a quartic with symbolic
> coefficients for which it is not possible to write a single generally valid
> solution (since the solutions depend on the relationship between the
> coefficients);
>
> eq = Eq(omega_nf, C0 + C1*omega**2 + C2*omega**4 + C3*omega**6 + C4*omega
> **8)
> d = Dict({C0: -k_phiphi*k_thetatheta*k_yy*k_zz + k_phiphi*k_yy*k_ztheta**2
> + k_thetatheta*k_yphi**2*k_zz - k_yphi**2*k_ztheta**2,
> C1: J_d*k_phiphi*k_yy*k_zz + J_d*k_thetatheta*k_yy*k_zz - J_d*k_yphi**2*k_zz
> - J_d*k_yy*k_ztheta**2 + J_p**2*Omega**2*k_yy*k_zz + 0.382*k_phiphi*
> k_thetatheta*k_yy + 0.382*k_phiphi*k_thetatheta*k_zz - 0.382*k_phiphi*
> k_ztheta**2 - 0.382*k_thetatheta*k_yphi**2,
> C2: -J_d**2*k_yy*k_zz - 0.382*J_d*k_phiphi*k_yy - 0.382*J_d*k_phiphi*k_zz
> - 0.382*J_d*k_thetatheta*k_yy - 0.382*J_d*k_thetatheta*k_zz + 0.382*J_d*
> k_yphi**2 + 0.382*J_d*k_ztheta**2 - 0.382*J_p**2*Omega**2*k_yy - 0.382*J_p
> **2*Omega**2*k_zz - 0.145924*k_phiphi*k_thetatheta,
> C3: 0.382*J_d**2*k_yy + 0.382*J_d**2*k_zz + 0.145924*J_d*k_phiphi +
> 0.145924*J_d*k_thetatheta + 0.145924*J_p**2*Omega**2,
> C4: -0.145924*J_d**2, x: J_g1 + omega})
>
>
>
> real_roots(eq.xreplace(d.subs({...}))) should very quickly give you the
> real solution when you put in for {...} the known values, e.g. `{J_d: 1,
> k_zz: 2, etc...}`. If the solution is written in terms of RootOf you can
> evaluate those to whateve precision is needed, e.g.
> `RootOf(x+x**3-4*x**4,1).n(3) -> 0.725`
>
>
> BTW, I have been experimenting with a constant-extracting routine:
>
> def cify(eq, v):
> from sympy.core.rules import Transform
> sym=numbered_symbols('C')
> def do(e, x):
> if e.is_Add:
> e = collect(e, x)
> c, fx = e.as_independent(x)
> s = next(sym)
> did[s] = c
> return e.func(s,fx)
> did={}
> e = None
> while e != eq:
> e = eq
> eq = eq.xreplace(Transform(lambda x: do(x, v), lambda x:(x.is_Add or x.
> is_Mul) and x.as_independent(v)[0].args))
> r, d = cse(did.values())
> did = dict(zip(did.keys(), d))
> r = dict(r)
> return r, did, eq
> eq = omega_nf_eq.rhs
> print(cify(eq,omega))
> ({
> x0: k_ztheta**2,
> x1: k_phiphi*x0,
> x2: k_yphi**2,
> x3: k_thetatheta*x2,
> x4: k_phiphi*k_thetatheta,
> x5: k_yy*k_zz,
> x6: 0.382*k_yy,
> x7: 0.382*k_zz,
> x8: J_d*k_phiphi,
> x9: J_d*k_thetatheta,
> x10: J_d*x2,
> x11: J_d*x0,
> x12: J_p**2*Omega**2,
> x13: 0.145924*k_phiphi,
> x14: J_d**2,
> x15: k_yy*x14
> },
> {
> C0: k_yy*x1 + k_zz*x3 - x0*x2 - x4*x5,
> C1: -k_yy*x11 - k_zz*x10 - 0.382*x1 + x12*x5 - 0.382*x3 + x4*x6 + x4*x7 +
> x5*x8 + x5*x9,
> C2: -k_thetatheta*x13 - k_zz*x15 + 0.382*x10 + 0.382*x11 - x12*x6 - x12*x7
> - x6*x8 - x6*x9 - x7*x8 - x7*x9,
> C3: J_d*x13 + 0.145924*x12 + x14*x7 + 0.382*x15 + 0.145924*x9,
> C4: -0.145924*x14
> },
> C0 + C1*omega**2 + C2*omega**4 + C3*omega**6 + C4*omega**8)
>
>
>
>
> On Thursday, June 6, 2019 at 6:13:23 PM UTC-5, pull_over93 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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