First, some background on what I'm actually trying to achieve: I have a reflectance filter (a discrete IIR) for use in an FDTD boundary condition:
$$R_{(z)}=\frac{b_0+b_1z^{-1}+b_2z^{-2}}{a_0+a_1z^{-1}+a_2z^{-2}}=\frac{B_{(z)}}{A_{(z)}}$$
As you can see, both the numerator and denominator polynomials are univariate, of the same order, and their powers change by 1 per coefficient. However, I need to turn it into an impedance filter (also represented by an IIR of the same type), according to Kowalczyk 2008 it is done by:
$$\xi_{(z)}=\frac{1+R_{(z)}}{1-R_{(z)}}$$
So my plan was to simply divide $B_{(z)}$ by $A_{(z)}$ to get a single polynomial, and then adjust the first coefficient by $\pm1$.
Only my plan fell at the first hurdle because every polynomial division implementation I've found returns a quotient and remainder. Why are there no implementations that return non-integer (floating point in computer parlance) coefficients? Is it fundamentally impossible for a polynomial division result to be represented in any form other than quotient and remainder?
Or have I just gotten completely confused and the solution to my real problem is far simpler?