\section{With \tkzname{tkz-elements}}\label{sec:elements}

\tkzname{tkz-elements} works in centimeters, \tkzname{tkz-fn} in the units of the coordinate system. When \tkzname{tkz-elements} is loaded, every point defined with \tkzcname{tkzFnDefPoint} or \tkzcname{tkzFnDefPointXY} is also stored in the table \texttt{z}, with its coordinates in centimeters:

\[ \texttt{z.A} = \left(\frac{x_A}{\text{xstep}}, \frac{y_A}{\text{ystep}}\right) \]

The point can then be used with the objects of \tkzname{tkz-elements}: |circle(z.O, z.A)|, |line(z.A, z.B)|, etc. In the other direction, |tkzfn.point_from_z("B")| brings the point \texttt{z.B} back into the coordinate system, so that its coordinates can be written with \tkzcname{tkzFnPrintCoord}.

\tkzBomb If the units of the two axes are different, |circle(z.O, z.A)| is a circle on the page, not a circle in the coordinate system.

\tkzHand \tkzname{tkz-elements} is not loaded by \tkzname{tkz-fn}; the following example needs |\usepackage{tkz-elements}|.

\begin{tkzltxexample}[]
\tkzFnDef{f}{x^2/2}
\begin{tikzpicture}
  \tkzFnInit[xmin=-3,xmax=3,ymin=-2,ymax=6,ystep=2]
  \tkzFnGrid
  \tkzFnAxes
  \tkzFnDraw[thick,red](f)
  \tkzFnDefPoint(f,2){A}       % A(2,2) in the system, z.A = (2,1) in cm
  \tkzFnDefPointXY(0,0){O}
  \directlua{
    C.OA = circle(z.O, z.A)     % tkz-elements works in cm
    z.B  = C.OA.south
  }
  \tkzGetNodes
  \draw[blue] (O) circle [radius=\tkzUseLua{C.OA.radius}];
  \tkzFnDrawPoints[red](A,O)
  \fill[blue] (B) circle (1.5pt) node[below right] {$B$};
\end{tikzpicture}

\directlua{tkzfn.point_from_z("B")}
$B\tkzFnPrintCoord(B)$   % (0, -4.47) in the coordinate system
\end{tkzltxexample}

\subsection{In Lua}

The objects of \tkzname{tkz-fn} are available in Lua:
\begin{itemize}
  \item |FN.f(2)|: value of the function $f$ at 2;
  \item |tkzfn.fct("sin(x)")|: creates a function (|FN.g = tkzfn.fct("sin(x)")|); a Lua function can also be given;
  \item |tkzfn.derivative(f, x)|, |tkzfn.integral(f, a, b)|;
  \item |tkzfn.to_page(x, y)| and |tkzfn.to_user(X, Y)|: conversions between the coordinate system and the page;
  \item |tkzfn.points.A|: coordinates of $A$ in the coordinate system.
\end{itemize}

\endinput