python - How to eliminate negative solutions from `sympy.solve` result?

Question

How can I make sympy.solve not return negative solutions?

This seems to be a different task than adding a constraint like positive=True to the symbol I'm solving for. While

import sympy

x = sympy.symbols("x")
print(sympy.solve(x**2-4, x))

x = sympy.symbols("x", positive=True)
print(sympy.solve(x**2-4, x))

prints

[-2, 2]
[2]

as expected - I still get a negative solve result for omega with

import sympy

omega, omega_0, gamma = sympy.symbols("omega, omega_0, gamma", real=True, positive=True)
zeta = 1/((omega_0**2 - omega**2)**2 + gamma**2*omega**2)

omega_R = sympy.solve(sympy.diff(zeta, omega), omega)
print(omega_R)

which returns

[-sqrt(2)*sqrt(-gamma**2 + 2*omega_0**2)/2, sqrt(2)*sqrt(-gamma**2 + 2*omega_0**2)/2]

even though -sqrt(2)*sqrt(-gamma**2 + 2*omega_0**2)/2 will never be positive for real and positive symbols omega_0 and gamma.

Alternatively, whats's the best way to eliminate the negative solutions afterwards?

Answer 1

SymPy's assumptions system isn't smart enough to know that -sqrt(2)*sqrt(-gamma**2 + 2*omega_0**2)/2 cannot be positive give the real and positive assumptions on omega_0 and gamma (I opened an issue for it). To be on the safe side, SymPy only filters solutions if it knows they cannot have the given assumptions. If the assumptions system gives None, meaning it doesn't know, it includes it anyway. For now your best bet is to just filter this solution manually.