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\subsection{$*$}
\label{labmult}
\noindent Name: \textbf{$*$}\\
\phantom{aaa}multiplication function\\[0.2cm]
\noindent Library names:\\
\verb| sollya_obj_t sollya_lib_mul(sollya_obj_t, sollya_obj_t)|\\
\verb| sollya_obj_t sollya_lib_build_function_mul(sollya_obj_t, sollya_obj_t)|\\
\verb| #define SOLLYA_MUL(x,y) sollya_lib_build_function_mul((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 multiplication (function) on reals.
The expression \emph{function1} \textbf{$*$} \emph{function2} stands for
the function composed of the multiplication function and the two
functions \emph{function1} and \emph{function2}.
\item \textbf{$*$} can be used for interval arithmetic on intervals
(ranges). \textbf{$*$} will evaluate to an interval that safely
encompasses all images of the multiplication function with arguments varying
in the given intervals. 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;
10
\end{Verbatim}
\end{minipage}\end{center}
\noindent Example 2:
\begin{center}\begin{minipage}{15cm}\begin{Verbatim}[frame=single]
> x * 2;
x * 2
\end{Verbatim}
\end{minipage}\end{center}
\noindent Example 3:
\begin{center}\begin{minipage}{15cm}\begin{Verbatim}[frame=single]
> x * x;
x^2
\end{Verbatim}
\end{minipage}\end{center}
\noindent Example 4:
\begin{center}\begin{minipage}{15cm}\begin{Verbatim}[frame=single]
> diff(sin(x) * exp(x));
sin(x) * exp(x) + exp(x) * cos(x)
\end{Verbatim}
\end{minipage}\end{center}
\noindent Example 5:
\begin{center}\begin{minipage}{15cm}\begin{Verbatim}[frame=single]
> [1;2] * [3;4];
[3;8]
> [1;2] * 17;
[17;34]
> 13 * [-4;17];
[-52;221]
\end{Verbatim}
\end{minipage}\end{center}
See also: \textbf{$+$} (\ref{labplus}), \textbf{$-$} (\ref{labminus}), \textbf{/} (\ref{labdivide}), \textbf{$\mathbf{\hat{~}}$} (\ref{labpower})
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