Extraction of Transfer Function Coefficients/Transfer Function Determination

Hello Dear Friends,

I'm trying to do the following:

1) I have a transfer function in the z domain and I want to build a function in Mathcad to which if I give the respective transfer function in the z domain at the exit of this function to obtain the values ​​of the coefficients.

2) Having at my disposal the coefficients of the transfer function in the z domain, I would like to construct a function in Mathcad that would do the inverse of point 1, namely at the exit of this function to obtain a transfer function in the z domain, ie the function from point 1.

For example, the transfer function in the z domain has the degree of the numerator and the degree of the denominator equal to 3, as shown in the figure below (for simplicity).

How could this be achieved?

Attached is the Mathcad 15 file.

Thank you.
Best regards.