I am using sympy to evaluate a rather complex eigenvalue problem that relies on several state functions. I would like to be able to use placeholder functions that I can generate the integral and evaluate the dependence of the integral on the input function later.
import sympy as s
x, L = s.symbols('x L')
Q = s.Function('Q')(x)
# do some sort of integration
e = s.integrate(Q, (x, -L, L))
print(e)
# Integral(Q(x), (x, -L, L))
# evaluate a simple linear function
print(e.subs(Q, x))
# Integral(Q(x), (x, -L, L))
# Expected: Integral(x, (x, -L, L))
# Or: 0 (evaluation)
# intermediate work around
interm = Q
e = s.integrate(interm.subs(Q, x), (x, -L, L))
print(e)
# 0 (expected)
As you can see, the evaluation of the integral does not allow for function substitution. Of course, I can perform the substitution at any point before the x integration of Q, but it would be convenient to perform substitution later. Is there a way around this? Or, is there a reason why this is avoided by sympy by design?
The behavior of subs on Integral has been changed in the development version of SymPy (see https://github.com/sympy/sympy/wiki/release-notes-for-0.7.4#unification-of-sum-product-and-integral-classes). We plan to do a release within the next few weeks. Your example works in the development version:
>>> # This is in the development version
>>> print(e.subs(Q, x))
Integral(x, (x, -L, L))
As a workaround, you can use replace instead of subs:
>>> # This is in 0.7.3
>>> print(e.replace(Q, x))
Integral(x, (x, -L, L))