  This paper deals with linear time-varying, delay systems. Extensions of the
concept of differential flatness \cite{Fliess_95} to this context have been
first proposed in \cite{Mounier_95,Fliess_96} (see also
\cite{Rudolph_03,Chyzak_05}), by the introduction of $\pi$-flat output. Roughly
speaking, it means that every system variable may be expressed as a function of
a particular output $y$, a finite number of its time derivatives, time delays,
and predictions, the latter resulting from the prediction operator $\pi^{-1}$.
We propose a simple and constructive algorithm for the computation of
$\pi$-flat outputs based on concepts of polynomial algebra, in particular
Smith-Jacobson decomposition of polynomial matrices. Some examples are provided
to illustrate the proposed methodology.
