Hi, I'm trying to solve an equation-system with nsolve. One of the
equations includes the upper gamma function, which has one of the variables
as lower integral limit. When I run this I end up with an error massage :(
from sympy import *
p0, T0, n, g, a, F_s_1, F_s_2, F_i, k1, k2, D, t, t0, t_rc = symbols("p0 T0 n g
a F_s_1 F_s_2 F_i k1 k2 D t t0 t_rc")
ß = a*(g - 1)/g
o = 5.67 * 10**-8
F_plus_conv = o * T0**4 * exp(D*t) * (exp(-D*t0) + 1/((D*t0)**(4*ß/n)) *
(uppergamma(1 + 4*ß/n, D*t) - uppergamma(1 + 4*ß/n,D*t0)))
F_plus_rad = F_s_1/2 * (1 + D/k1 + (1 - D/k1) * exp(-k1*t)) + F_s_2/2 * (1 +
D/k2 + (1 - D/k2) * exp(-k2*t)) + F_i/2 * (2 + D*t)
F_plus_t_rc = Eq(F_plus_conv, F_plus_rad)
T_t_rc = Eq(o * T0**4 * (t_rc/t0)**(4*ß/n), F_s_1/2* (1 + D/k1 + (k1/D - D/k1)
* exp(-k1 * t_rc)) + F_s_2/2* (1 + D/k2 + (k2/D - D/k2) * exp(-k2 * t_rc)) +
F_i/2 * ( 1+ D * t_rc))
titan = [(n, 0.75), (g, 1.4), (a, 0.77), (F_s_1, 1.5), (F_s_2, 1.1), (F_i, 0),
(k1, 120), (k2, 0.2), (t, t_rc), (D, 1.6), (T0, 94), (p0, 1.5)]
print(nsolve((T_t_rc.subs(titan), F_plus_t_rc.subs(titan)), (t_rc,
t0),(4.8,5.3)))
Error msg:
Traceback (most recent call last): File
"/home/.../nsolve_uppergammma_problem.py", line 14, in <module>
print(nsolve((T_t_rc.subs(titan), F_plus_t_rc.subs(titan)), (t_rc,
t0),(4.8,5.3)))
File "/usr/lib/python3.6/site-packages/sympy/solvers/solvers.py", line 2772, in
nsolve x = findroot(f, x0, J=J, *kwargs)
File "/usr/lib/python3.6/site-packages/mpmath/calculus/optimization.py", line
928, in findroot fx = f(x0)
File "<string>", line 1, in <lambda> NameError: name 'uppergamma' is not defined
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