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\subsection{/}
\label{labdivide}
\noindent Name: \textbf{/}\\
\phantom{aaa}division function\\[0.2cm]
\noindent Library names:\\
\verb| sollya_obj_t sollya_lib_div(sollya_obj_t, sollya_obj_t)|\\
\verb| sollya_obj_t sollya_lib_build_function_div(sollya_obj_t, sollya_obj_t)|\\
\verb| #define SOLLYA_DIV(x,y) sollya_lib_build_function_div((x), (y))|\\[0.2cm]
\noindent Usage:
\begin{center}
\emph{function1} \textbf{/} \emph{function2} : (\textsf{function}, \textsf{function}) $\rightarrow$ \textsf{function}\\
\emph{interval1} \textbf{/} \emph{interval2} : (\textsf{range}, \textsf{range}) $\rightarrow$ \textsf{range}\\
\emph{interval1} \textbf{/} \emph{constant} : (\textsf{range}, \textsf{constant}) $\rightarrow$ \textsf{range}\\
\emph{interval1} \textbf{/} \emph{constant} : (\textsf{constant}, \textsf{range}) $\rightarrow$ \textsf{range}\\
\end{center}
Parameters:
\begin{itemize}
\item \emph{function1} and \emph{function2} represent functions
\item \emph{interval1} and \emph{interval2} represent intervals (ranges)
\item \emph{constant} represents a constant or constant expression
\end{itemize}
\noindent Description: \begin{itemize}
\item \textbf{/} represents the division (function) on reals.
The expression \emph{function1} \textbf{/} \emph{function2} stands for
the function composed of the division function and the two
functions \emph{function1} and \emph{function2}, where \emph{function1} is
the numerator and \emph{function2} the denominator.
\item \textbf{/} can be used for interval arithmetic on intervals
(ranges). \textbf{/} will evaluate to an interval that safely
encompasses all images of the division function with arguments
varying in the given intervals. If the intervals given contain points
where the division function is not defined, infinities and NaNs will be
produced in the output interval. Any combination of intervals with
intervals or constants (resp. constant expressions) is
supported. However, it is not possible to represent families of
functions using an interval as one argument and a function (varying in
the free variable) as the other one.
\end{itemize}
\noindent Example 1:
\begin{center}\begin{minipage}{15cm}\begin{Verbatim}[frame=single]
> 5 / 2;
2.5
\end{Verbatim}
\end{minipage}\end{center}
\noindent Example 2:
\begin{center}\begin{minipage}{15cm}\begin{Verbatim}[frame=single]
> x / 2;
x * 0.5
\end{Verbatim}
\end{minipage}\end{center}
\noindent Example 3:
\begin{center}\begin{minipage}{15cm}\begin{Verbatim}[frame=single]
> x / x;
1
\end{Verbatim}
\end{minipage}\end{center}
\noindent Example 4:
\begin{center}\begin{minipage}{15cm}\begin{Verbatim}[frame=single]
> 3 / 0;
NaN
\end{Verbatim}
\end{minipage}\end{center}
\noindent Example 5:
\begin{center}\begin{minipage}{15cm}\begin{Verbatim}[frame=single]
> diff(sin(x) / exp(x));
(exp(x) * cos(x) - sin(x) * exp(x)) / exp(x)^2
\end{Verbatim}
\end{minipage}\end{center}
\noindent Example 6:
\begin{center}\begin{minipage}{15cm}\begin{Verbatim}[frame=single]
> [1;2] / [3;4];
[0.25;0.66666666666666666666666666666666666666666666666668]
> [1;2] / 17;
[5.8823529411764705882352941176470588235294117647059e-2;0.1176470588235294117647
0588235294117647058823529412]
> -13 / [4;17];
[-3.25;-0.76470588235294117647058823529411764705882352941175]
\end{Verbatim}
\end{minipage}\end{center}
See also: \textbf{$+$} (\ref{labplus}), \textbf{$-$} (\ref{labminus}), \textbf{$*$} (\ref{labmult}), \textbf{$\mathbf{\hat{~}}$} (\ref{labpower})
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