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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))$returns the function only in terms of z . How can we self compose functions with a placeholder variable for a coefficient? coefficient?  3 None slelievre 17654 ●22 ●160 ●348 http://carva.org/samue... Self composition of a function with symbolic variable I have a function in one variable with a placeholder variable, variable, and would like to find the nth iterate. For example, using:$f(z) = z^3 + az^2$, a z^2$, a function in variable z $z$ with placeholder coefficient a. $a$.

then I would like to see

$f(f(z)) = ( z^3 (z^3 + az^2)^3 + a( z^3 a(z^3 + az^2)^2$

However I am struggling to perform this in sage.Sage.

$f(f)$ f(f) returns $(az^2 (a*z^2 + z^3)z^2 z^3)*z^2 + z^3$ z^3, so it substitutes for a $a$ instead of z, $z$, and declaring $f(f(z))$ f(f(z)) returns the function only in terms of z .$z$.

How can we self compose functions with a placeholder variable for a coefficient?