I have a function in one variable with a placeholder variable, and would like to find the nth iterate. For example, using:
$f(z) = z^3 + az^2$, a function in variable z with placeholder coefficient a.
then I would like to see
$f(f(z)) = ( z^3 + az^2)^3 + a( z^3 + az^2)^2$
However I am struggling to perform this in sage.
$f(f)$ returns $(az^2 + z^3)z^2 + z^3$, so it substitutes for a instead of z, and declaring $f(f(z))$ returns the function only in terms of z .
How can we self compose functions with a placeholder variable for a coefficient?