Truncating out higher order polynomials in series of fractions

Question

I have taken sequential partial derivatives of a two variable polynomial fraction, resulting in a very long series of polynomials of form:

C*x^i*y^j/(some product series of (1-x^k*y)^n)

What I wish to do is a series of basic truncations. First, I eliminate all polynomials that have x^i*y^j with i or j > 4 in the numerator. I keep looking over the documentation and StackExchange and cannot find anything that works for me.

I am open to suggestions.

Edit: Thus far, I have merely sorted the long series, and picked out the valid fractions starting from the bottom. What is the solution that uses Mathematica functions?

Answer 1

I post this as a way to handle polynomials that could be modified to suit your needs:

func[exp_, vars_, pattern_] := 
 FromCoefficientRules[
  Cases[CoefficientRules[exp, vars], HoldPattern[pattern]], vars]

Example:

expr = (1 - x^2 y)^10;
Column[{Expand@expr, func[expr, {x, y}, Rule[{_?(# > 4 &), _}, _]]}, 
 Frame -> All]