Residue polynomial systems

In this paper, we present the basic ideas of the residue polynomial system (RPS), a polynomial analog of the familiar residue number systems (RNS) of integer arithmetic. Many of the properties of the RNS are shared by the RPS. The main exception is that division of polynomials in the RPS is much more tractable than its integer counterpart. Examples are included throughout. The underlying field of coefficients for polynomials under consideration can be the reals or the rationals, though extension to the complex field will be needed for division by irreducible quadratic factors.