  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 functions
$$\{C_i(P):P\in\Q[x],i=0,\ldots,\deg(P)\}$$ defined by $$C_i(P)(x)= \left\{
\begin{array}{cll}0 & \mbox{ if } & x \leq \alpha \\ P(x) & \mbox{ if } & x
\geq \alpha \end{array} \right.$$ where $\alpha$ 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 $C_{i}(P)$ allowing its evaluation by performing only operations in
$\Q$ and avoiding the use of any real algebraic number.
