.subs_expr() method doesn't work for argument of D derivative operator

[gmhossain]

In computing functional derivative, one needs to vary a functional. For example, in sage-3.4 one can do as follows

sage: f(x) = function('f',x)
sage: df(x) = function('df',x)
sage: g = f(x).diff(x)
sage: g
diff(f(x), x, 1)
sage: g.subs_expr(f(x)==f(x)+df(x))
diff(f(x) + df(x), x, 1)

In new symbolics, if I do the same I get

sage: g
D[0](f)(x)
sage: g.subs_expr(f(x)==f(x)+df(x))
D[0](f)(x)

---

From #11842, the list of what does/doesn't work:

from sage.all import *


# 1. Fails.
x = var('x')
f = function('f', x)
g = function('g', x)
p = f
print p.substitute_function(f, g) # Outputs "f(x)"



# 2. Fails.
x = var('x')
f = function('f')
g = function('g')
p = f(x)
print p.substitute_function(f(x), g(x)) # Outputs "f(x)"



# 3. Works.
x = var('x')
f = function('f')
g = function('g')
p = f(x)
print p.substitute_function(f, g) # Outputs "g(x)"



# 4. Fails.
x = var('x')
f = function('f')
g = function('g')
p = f(1)
print p.substitute_function(f(1), g(1)) # Outputs "f(1)"



# 5. Works.
x = var('x')
f = function('f')
g = function('g')
p = f(1)
print p.substitute_function(f, g) # Outputs "g(1)"



# 6. Fails.
x = var('x')
f = function('f', x)
g = function('g', x)
p = f.diff()
print p.substitute_function(f, g) # Outputs "D[0](f)(x)"



# 7. Fails.
x = var('x')
f = function('f', x)
g = function('g', x)
p = f.diff()
print p.substitute_function(f(x), g(x)) # Outputs "D[0](f)(x)"



# 8. Works.
x = var('x')
f = function('f')
g = function('g')
p = f(x).diff()
print p.substitute_function(f, g) # Outputs "D[0](g)(x)"



# 9. Fails.
x = var('x')
f = function('f')
g = function('g')
p = f(x).diff()(1)
print p.substitute_function(f(x).diff(), g(x).diff()) # Outputs "D[0](f)(1)"



# 10. Works..
x = var('x')
f = function('f')
g = function('g')
p = f(x).diff()(1)
print p.substitute_function(f, g) # Prints D[0](g)(1).

[mjo]

I duped this in #11842. We might be able to make use of the test cases there when this gets fixed.

[eviatarbach]

.substitute_function seems to work:  http://ask.sagemath.org/question/2380/how-to-substitute-a-function-within-derivatives

[mjo]

One of the cases in #11842 that used to crash now works, but a lot of them still don't. I updated the list.

[kcrisman]

I feel like if that one is closed, we should have the list here, so I'm updating the description.