I like working with Octave/Matlab's compact numerical polynomial form, and recently started doing some work with rational polynomials. I started working through some functions for multiplying and in particular, adding and simplifying rational polynomials using some of the built in polynomial and root finding functions. Before I got too far in was wondering if anyone had already done so. I could see a ratpoly class possibly being of some use.
I see that I could use tf objects for this and/or work symbolically, but at the moment am evaluating how practical it would be to keep this numerical and compatible with base Matlab. (I know, self imposed handcuff.)
My google-fu finds me some stuff for rat. poly curve fitting, but otherwise is lacking.
if you have recommended references for useful algorithms to do this, I'd appreciate a pointer.