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\chapter[REACTEQN: Chemical reaction equations]%
	{REACTEQN: Support for chemical reaction equations}
\label{REACTEQN}
\typeout{{REACTEQN: Support for chemical reaction equations}}

{\footnotesize
\begin{center}
Herbert Melenk \\
Konrad--Zuse--Zentrum f\"ur Informationstechnik Berlin \\
Takustra\"se 7 \\
D--14195 Berlin--Dahlem, Germany \\[0.05in]
e--mail: melenk@zib.de
\end{center}
}
\ttindex{REACTEQN}

The \REDUCE\ package REACTEQN allows one to transform chemical reaction
systems into ordinary differential equation systems corresponding to
the laws of pure mass action.

It provides the single function

\begin{verbatim}
    reac2ode {   <reaction> [,<rate> [,<rate>]]
               [,<reaction> [,<rate> [,<rate>]]]
                       ....
                  };
\end{verbatim}

A rate is any \REDUCE\ expression, and two rates are applicable only
for forward and backward reactions.  A reaction is coded as a linear
sum of the series variables, with the operator $->$ for forward
reactions and $<>$ for two-way reactions.

The result is a system of explicit ordinary differential equations
with polynomial righthand sides.  As side effect the following
variables are set:
\newpage
\begin{description}
\item[{\tt rates}]
\index{reacteqn ! {\tt rates}} A list of the rates in the system.
\item[{\tt species}]
\index{reacteqn ! {\tt species}} A list of the species in the system.
\item[{\tt inputmat}]
\index{reacteqn ! {\tt inputmat}} A matrix of the input coefficients.
\item[{\tt outputmat}]
\index{reacteqn ! {\tt outputmat}} A matrix of the output coefficients.
\end{description}

In the matrices the row number corresponds to the input reaction
number, while the column number corresponds to the species index.

If the rates are numerical values, it will be in most cases
appropriate to select a \REDUCE\ evaluation mode for floating point numbers.

{\tt Inputmat} and {\tt outputmat} can be used for linear algebra type
investigations of the reaction system.  The classical reaction
matrix is the difference of these matrices; however, the two
matrices contain more information than their differences because
the appearance of a species on both sides is not reflected by
the reaction matrix.