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Self composition of a function with symbolic variable

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?

Self composition of a function with symbolic variable

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 $(az^2 + z^3)z^2 + z^3$, 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? coefficient?