from formulas to pari implementations

[Gottfried]

Hey!
Almost everybody knows Schröder's equation:
Psi o y(x) = s × Psi(x)
(...)
The bigger is the matrix, the more precise is the represantation.

My pari/gp implementation of this conversions:
(...)

It is much less precise as Sheldon's and others' fatou.gp programme; it works without using Schröder and Abel equations but using Carleman matrices and diagonalization.
(...)

Hmm, I don't really get it what you are after.      
For one: perhaps my very introductiory essay ContinuousfunctionalIteration  is enough to explain the method which leads to the Carleman-method and Schroeder-function (where I did not know in my first writing that already known/used terms and concepts and thus had rediscovered them on my own), and for second, this is all done for examples with a not too large set of procedures (mostly matrix-functions) in Pari/GP.