\section{Defining a function}

It is possible to define \Index{functions} usable in a PostScript environment.

The domain can be  $\mathbb{R}$, $\mathbb{R}^2$
or $\mathbb{R}^3$, and the codomain can be $\mathbb{R}$, $\mathbb{R}^2$ or $\mathbb{R}^3$.

The definition is made with the macro \verb+\defFunction+. This macro comes with six
arguments, where the first is optional.


\verb!\defFunction[<options>]{<name>}(<var>){<x(var)>}{<y(var)>}{<z(var)>}!

\begin{table}[h]
\begin{tabular}{p{2cm}p{11cm}}
\verb!<options>! & We insert the options typical to PSTricks, like
\verb!linewidth! etc., and, some of them defined by
\verb!pst-solides3d!. A very nice and helpful option is \verb!algebraic!,
with which one can avoid  RPN (Reverse Polish
Notation). All the options are key value pairs separated with commas.\\

\verb!<name>! & This is a unique name of your choice---but be careful: avoid
names that contain accents, PostScript doesn't like them at all.\\

\verb!<var>! & We insert at most three variables, arbitrarily chosen and separated with commas.\\

\verb!<x(var)>! \verb!<y(var)>! \verb!<z(var)>! &
Here, we place functions defining the three Euclidean components $x,\,y,\,z$.
If one of the three components is not wanted, just enter a 0 within
 parentheses---this will also allow you to define some projections of the lines of functions.
\end{tabular}
\end{table}

Once you have defined a function, this function is always called by its chosen name \verb!<name>!.

Here some examples:
\begin{compactitem}
\item \verb!\defFunction{moncercle}(t){t cos 3 mul}{0}{t sin 3 mul}!

    draws a circle with radis 3 in the $xOz$ plane (notation RPN).
    \item \verb!\defFunction[algebraic]{helice}(t){cos(t)}{sin(t)}{t}!

    draws a helix in algebraic notation.
    \item \verb!\defFunction[algebraic]{F}(t){t}{}{}!

    draws a function from $\mathbb{R}$ in $\mathbb{R}$
    \item \verb!\defFunction[algebraic]{F}(t){t}{t}{}!

    draws a function from $\mathbb{R}$ in $\mathbb{R}^2$
    \item \verb!\defFunction[algebraic]{F}(t){t}{t}{t}!

    draws a function from $\mathbb{R}$ in $\mathbb{R}^3$

\end{compactitem}

There remains work to be done on this macro.  For the moment it does not permit an arbitrary
choice of names of variables, as this risks conflict with existing names.  Please use
names analogous to those used in the documentation.  A good strategy is to systematically use
one or more numerical characters at the end of the names of your variables.

\endinput