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KeepSemanticRestrictionOutOfHeading
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HansOlsson committed Jan 4, 2022
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4 changes: 2 additions & 2 deletions chapters/arrays.tex
Expand Up @@ -1190,7 +1190,7 @@ \subsection{Array Element-wise Multiplication}\label{array-element-wise-multipli
\end{center}
\end{table}

\subsection{Matrix and Vector Multiplication of Numeric Arrays}\label{matrix-and-vector-multiplication-of-numeric-arrays}
\subsection{Multiplication of Matrices and Vectors}\label{matrix-and-vector-multiplication-of-numeric-arrays}\label{multiplication-of-matrices-and-vectors}

Multiplication \lstinline!a * b! of numeric vectors and matrices is defined only for the following combinations:
\begin{table}[H]
Expand Down Expand Up @@ -1315,7 +1315,7 @@ \subsection{Exponentiation of Scalars of Numeric Elements}\label{exponentiation-
literals solves the problem.
\end{example}

\subsection{Scalar Exponentiation of Square Matrices of Numeric Elements}\label{scalar-exponentiation-of-square-matrices-of-numeric-elements}
\subsection{Scalar Exponentiation of Matrices}\label{scalar-exponentiation-of-square-matrices-of-numeric-elements}\label{scalar-exponentiation-of-matrices}

Exponentiation \lstinline!a ^ s! is defined if \lstinline!a! is a square numeric matrix and \lstinline!s! is a scalar as a subtype of \lstinline!Integer!
with $\text{\lstinline!s!} \geq 0$. The exponentiation is done by repeated multiplication, e.g.:
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2 changes: 1 addition & 1 deletion chapters/connectors.tex
Expand Up @@ -671,7 +671,7 @@ \subsection{Balancing Restriction and Size of Connectors}\label{balancing-restri
\end{lstlisting}
\end{example}

\section{Equation Operators for Overconstrained Connection-Based Equation Systems}\label{equation-operators-for-overconstrained-connection-based-equation-systems1}
\section{Overconstrained Connection-Based Equation Systems}\label{equation-operators-for-overconstrained-connection-based-equation-systems1}\label{overconstrained-connection-based-equation-systems}

There is a special problem regarding equation systems resulting from \emph{loops} in connection graphs where the connectors contain \emph{non-flow} (i.e., potential) variables \emph{dependent} on each other.
When a loop structure occurs in such a graph, the resulting equation system will be \emph{overconstrained}, i.e., have more equations than variables, since there are implicit constraints between certain non-flow variables in the connector in addition to the connection equations around the loop.
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