I have trouble solving the following simple equation with sympy. Sympy seems to take way too much time to produce a result.
import sympy as sp
sp.solve(sp.Eq(1000/(sp.exp(log(39) - 1000*k) + 1), 100), k)
The solution is log(39)/1000 - log(3)/500, which can be verified by plugging that into the equation.
What can one do to "help" sympy to solve this equation for k?
I think solve is attempting to solve this as a polynomial equation of degree 1000 in exp(k) which is apparently slow.
You can use solveset instead:
In [16]: eq
Out[16]:
1000
─────────────── = 100
-1000⋅k
1 + 39⋅ℯ
In [17]: solveset(eq, k)
Out[17]:
⎧n⋅ⅈ⋅π log(13/3) │ ⎫ ⎧ⅈ⋅(2⋅n⋅π + π) log(39) │ ⎫
⎨───── + ───────── │ n ∊ ℤ⎬ \ ⎨───────────── + ─────── │ n ∊ ℤ⎬
⎩ 500 1000 │ ⎭ ⎩ 1000 1000 │ ⎭
In [18]: solveset(eq, k, Reals)
Out[18]:
⎧-log(3/13) ⎫
⎨───────────⎬
⎩ 1000 ⎭