On Apr 1, 2:34 pm, Michael Orlitzky <mich...@orlitzky.com> wrote:

> Substitution doesn't even work pre-evaluation:
>
>    sage: f = function('f', x)
>    sage: f_prime = f.diff(x)
>    sage: g = function('g', x)
>    sage: f_prime.substitute_function(f,g)
>    D[0](f)(x)

That's because you're trying to substitute expressions, not functions:

sage: f,g
(f(x), g(x))

For that, you would have to use a different substitution function and
it wouldn't have any effect anyway because the expression f(x) does
not occur in f_prime.

If you fix this, the substitution does work:

sage: f = f.operator()
sage: g = g.operator()
sage: f,g
(f, g)
sage:  f_prime.substitute_function(f,g)
D[0](g)(x)

There is a different issue, which is fixed by 
http://trac.sagemath.org/sage_trac/ticket/12801

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