A canonical form for the continuous piecewise polynomial functions

Abstract

We present in this paper a canonical form for the elements in the ring of continuous piecewise polynomial functions. This new representation is based on the use of a particular class of functionswhere α is the i-th real root of the polynomial P . These functions will allow us to represent and manipulate easily every continuous piecewise polynomial function through the use of the corresponding canonical form.It will be also shown how to produce a "rational" representation of each function Ci(P ) allowing its evaluation by performing only operations in Q and avoiding the use of any real algebraic number.