### How can I map functions into polynomial coefficients

Let's say I have the following expression (from a wide range of possibilities) :

`pol = 3*a*x^(-b)*log(x)*b^2 - `~~6*a*b*c*sinx(x*b) ~~6*a*b*c*sin(x*b) + 3*a*c^2 + 5

And I want to extract the coefficients of the polynomial over the polynomial ring over a & c, so that these result in:

```
a^0*c^0 : 5
a^1*c^0 : 3*x^(-b)*log(x)*b^2
a^0*c^1 : 0
a^1*c^1 :
```~~-6*b*sinx(x*b)
~~-6*b*sin(x*b)
etc.

How can I define the polynomial ring?

How can I map an existing expression that defines "pol" (which is the result of other manipulations) into such ring?