The {\tt uservariable} command represents a variable that changes with user interaction such as touch or mouse events over the graphic.

\begin{verbatim}
\uservariable{variable}(x1,y1){f(x,y)}
\end{verbatim}

{\tt variable} is the variable that you can use in {\tt psplot} and {\tt userline} parameters and equations. Eventually it should be something you can use everywhere, but for the scope of this project, we kept it limited.


{\tt x1} and {\tt y1} are the initial values of {\tt x} and {\tt y} for the function $f(x,y)$ that is that last argument for the command. If there are no user interactions, the function is evaluated with the specified inital values.


On any user event, such as a touch or mouse event, the function $f(x,y)$ is evaluated and any dependent commands, namely {\tt psplot} and {\tt userline} are immediately notified and re-rendered with updated execution contexts.


Here is an example of teaching somebody integration, for example, you can represent $\int_a^b f(x) dx$ as:

\begin{interactive}

\begin{center}
\begin{pspicture}(-4,-3)(4,3)
    
\uservariable{alpha}(0,0){x}

\psplot[algebraic,linewidth=2pt,fillstyle=solid, fillcolor=lightblue]{-4}{alpha}{sin(x)}
\psplot[algebraic,linewidth=2pt]{-4}{4}{sin(x)}
  
\psline{->}(-4,0)(4,0)

   
\end{pspicture}
\end{center}
\end{interactive}

\begin{print}

\begin{center}
\begin{pspicture}(-4,-3)(4,3)
    
\psplot[algebraic,linewidth=2pt,fillstyle=solid, fillcolor=lightblue]{-3.14}{3.14}{sin(x)}
\psplot[algebraic,linewidth=2pt]{-4}{4}{sin(x)}
  
\psline{->}(-4,0)(4,0)
   
\end{pspicture}
\end{center}
\end{print}

which can be produced with the following \TeX:

\begin{verbatim}
\begin{pspicture}(-4,-3)(4,3)
\uservariable{alpha}(0,0){x}
\psplot[algebraic,linewidth=2pt,fillstyle=solid, fillcolor=lightblue]{-4}{alpha}{sin(x)}
\psplot[algebraic,linewidth=2pt]{-4}{4}{sin(x)}
\psline{->}(-4,0)(4,0)
\end{pspicture}
\end{verbatim}

The next example allows you to move the height of the graph and also demonstrates how to specify an interval:

\begin{interactive}
\begin{center}
\begin{pspicture}(-4,-3)(4,3)

\uservariable{alpha}(0,0){x}
\uservariable{beta}(0,0){y}

\psplot[algebraic,linewidth=2pt,fillstyle=solid, fillcolor=lightblue]{alpha-3}{alpha}{beta + sin(x)}
\psplot[algebraic,linewidth=2pt]{-4}{4}{beta + sin(x)}

\psline{->}(-4,0)(4,0)

\end{pspicture}
\end{center}
\end{interactive}
\begin{print}
\begin{center}
\begin{pspicture}(-4,-3)(4,3)

\psplot[algebraic,linewidth=2pt,fillstyle=solid, fillcolor=lightblue]{-3.14}{0}{sin(x)}
\psplot[algebraic,linewidth=2pt]{-4}{4}{sin(x)}

\psline{->}(-4,0)(4,0)

\end{pspicture}
\end{center}
\end{print}

which can be produced with the following source:

\begin{verbatim}
\begin{pspicture}(-4,-3)(4,3)
\uservariable{alpha}(0,0){x}
\uservariable{beta}(0,0){y}
\psplot[algebraic,linewidth=2pt,fillstyle=solid, fillcolor=lightblue]{alpha-3}{alpha}{beta + sin(x)}
\psplot[algebraic,linewidth=2pt]{-4}{4}{beta + sin(x)}
\psline{->}(-4,0)(4,0)
\end{pspicture}
\end{verbatim}