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Basic cleanup of table for overconstrained connections
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Expand Up @@ -854,78 +854,95 @@ \subsection{Overconstrained Equation Operators for Connection Graphs}\label{over
Additionally, corresponding nodes of the virtual connection graph have
to be defined as roots or as potential roots with functions
\lstinline!Connections.root! and \lstinline!Connections.potentialRoot!, respectively.
In the following table, \lstinline!A! and \lstinline!B! are connector instances that may be
hierarchically structured, e.g., \lstinline!A! may be an abbreviation for
\lstinline!EnginePort.Frame!.

\begin{longtable}[]{|p{5.1cm}|p{10cm}|}
\hline \endhead
\lstinline!connect(A,B);! &
Defines \firstuse{optional spanning-tree edge} from the
overdetermined type or record instances in connector instance \lstinline!A! to the
corresponding overdetermined type or record instances in connector
instance \lstinline!B! for a virtual connection graph. The types of the
corresponding overdetermined type or record instances shall be the
same.\\ \hline
\lstinline!Connections.branch(A.R,B.R);! &
Defines a \firstuse{required spanning-tree edge}
from the overdetermined type or record instance \lstinline!R! in connector instance
\lstinline!A! to the corresponding overdetermined type or record instance \lstinline!R! in
connector instance \lstinline!B! for a virtual connection graph. This function can
be used at all places where a \lstinline!connect! statement is allowed.
\par
\begin{nonnormative*}
E.g., it is not allowed to use this function in a when-clause. This definition shall be used if in a model with connectors \lstinline!A! and \lstinline!B! the overdetermined
records \lstinline!A.R! and \lstinline!B.R! are algebraically coupled in the model, e.g., due to \lstinline!B.R = f(A.R!, \textless{}other unknowns\textgreater{}).
\end{nonnormative*}
\\ \hline
\lstinline!Connections.root(A.R);! & The overdetermined type or record instance \lstinline!R! in
connector instance \lstinline!A! is a (definite) \firstuse{root node} in a virtual connection graph.
\par
\begin{nonnormative*}
This definition shall be used if in a model with connector \lstinline!A! the overdetermined record \lstinline!A.R! is (consistently) assigned, e.g., from a parameter expressions.
\end{nonnormative*}
\\ \hline
\begin{tabular}{@{}p{5.1cm}@{}}
\lstinline!Connections.potentialRoot(A.R);!\\
\lstinline!Connections.potentialRoot(!\\
\lstinline!A.R, priority = p)!;
\end{tabular}
& The overdetermined type or record instance \lstinline!R! in connector instance \lstinline!A! is
a \firstuse{potential root node} in a virtual connection graph with priority
\lstinline!p! ($p\ge 0$). If no second argument is provided, the priority is zero.
\lstinline!p! shall be a parameter expression of type \lstinline!Integer!. In a
virtual connection subgraph without a \lstinline!Connections.root! definition, one
of the potential roots with the lowest priority number is selected as
root.
\par
\begin{nonnormative*}
This definition may be used if in a model with connector \lstinline!A! the overdetermined record \lstinline!A.R! appears differentiated -- \lstinline!der(A.R)! -- together
with the \emph{constraint equations} of \lstinline!A.R!, i.e., a non-redundant subset of \lstinline!A.R! maybe used as states.
\end{nonnormative*}
%\strut
%\end{minipage}
\\ \hline
\lstinline!b = Connections.isRoot(A.R);! & Returns true, if the overdetermined type
or record instance \lstinline!R! in connector instance A is selected as a root in
the virtual connection graph.\\ \hline
\begin{tabular}{@{}p{5.1cm}@{}}
\lstinline!b = Connections.rooted(A.R);!\\
\lstinline!b = rooted(A.R); // deprecated!

The overconstrained equation operators for connection graphs are listed below. Here, \lstinline!A! and \lstinline!B! are connector instances that may be hierarchically structured, e.g., \lstinline!A! may be an abbreviation for \lstinline!EnginePort.Frame!.
\begin{center}
\begin{tabular}{l|l l}
\hline
\tablehead{Expression} & \tablehead{Description} & \tablehead{Details}\\
\hline
\hline
\lstinline!connect(A, B)! & Optional spanning-tree edge & \Cref{modelica:optional-spanning-tree-edge}\\
\lstinline!Connections.branch(A.R, B.R)! & Required spanning-tree edge & \Cref{modelica:Connections.branch}\\
\lstinline!Connections.root(A.R)! & Definite root node & \Cref{modelica:Connections.root}\\
\lstinline!Connections.potentialRoot(A.R, $\ldots$)! & Potential root node & \Cref{modelica:Connections.potentialRoot}\\
\lstinline!Connections.isRoot(A.R)! & Predicate for being selected as root & \Cref{modelica:Connections.isRoot}\\
\lstinline!Connections.rooted(A.R)! & Predicate for being closer to root & \Cref{modelica:Connections.rooted}\\
\hline
\end{tabular}
& If the operator \lstinline!Connections.rooted(A.R)!
is used, or the equivalent but deprecated operator \lstinline!rooted(A.R)!, then
there must be exactly one statement \lstinline!Connections.branch(A.R,B.R)!
involving \lstinline!A.R! (the argument of \lstinline!Connections.rooted! must be the first
argument of \lstinline!Connections.branch!). In that case \lstinline!Connections.rooted(A.R)!
returns true, if \lstinline!A.R! is closer to the root of the spanning tree than
\lstinline!B.R!; otherwise false is returned.
\par
\begin{nonnormative*}
\end{center}

\begin{operatordefinition*}[connect]\label{modelica:optional-spanning-tree-edge}
\begin{synopsis}\begin{lstlisting}
connect(A, B)
\end{lstlisting}\end{synopsis}
\begin{semantics}
Defines \firstuse{optional spanning-tree edge} from the overdetermined type or record instances in connector instance \lstinline!A! to the corresponding overdetermined type or record instances in connector instance \lstinline!B! for a virtual connection graph. The types of the corresponding overdetermined type or record instances shall be the same.
\end{semantics}
\end{operatordefinition*}

\begin{operatordefinition}[Connections.branch]
\begin{synopsis}\begin{lstlisting}
Connections.branch(A.R, B.R)
\end{lstlisting}\end{synopsis}
\begin{semantics}
Defines a \firstuse{required spanning-tree edge} from the overdetermined type or record instance \lstinline!R! in connector instance \lstinline!A! to the corresponding overdetermined type or record instance \lstinline!R! in connector instance \lstinline!B! for a virtual connection graph. This function can be used at all places where a \lstinline!connect! statement is allowed.

\begin{nonnormative}
E.g., it is not allowed to use this function in a when-clause. This definition shall be used if in a model with connectors \lstinline!A! and \lstinline!B! the overdetermined records \lstinline!A.R! and \lstinline!B.R! are algebraically coupled in the model, e.g., due to \lstinline!B.R = f(A.R!, \textless{}other unknowns\textgreater{}).
\end{nonnormative}
\end{semantics}
\end{operatordefinition}

\begin{operatordefinition}[Connections.root]
\begin{synopsis}\begin{lstlisting}
Connections.root(A.R)
\end{lstlisting}\end{synopsis}
\begin{semantics}
The overdetermined type or record instance \lstinline!R! in connector instance \lstinline!A! is a (definite) \firstuse{root node} in a virtual connection graph.

\begin{nonnormative}
This definition shall be used if in a model with connector \lstinline!A! the overdetermined record \lstinline!A.R! is (consistently) assigned, e.g., from a parameter expressions.
\end{nonnormative}
\end{semantics}
\end{operatordefinition}

\begin{operatordefinition}[Connections.potentialRoot]
\begin{synopsis}\begin{lstlisting}
Connections.potentialRoot(A.R)
Connections.potentialRoot(A.R, priority=$p$)
\end{lstlisting}\end{synopsis}
\begin{semantics}
The overdetermined type or record instance \lstinline!R! in connector instance \lstinline!A! is a \firstuse{potential root node} in a virtual connection graph with priority \lstinline!p! ($p \geq 0$). If no second argument is provided, the priority is zero. \lstinline!p! shall be a parameter expression of type \lstinline!Integer!. In a virtual connection subgraph without a \lstinline!Connections.root! definition, one of the potential roots with the lowest priority number is selected as root.

\begin{nonnormative}
This definition may be used if in a model with connector \lstinline!A! the overdetermined record \lstinline!A.R! appears differentiated -- \lstinline!der(A.R)! -- together with the \emph{constraint equations} of \lstinline!A.R!, i.e., a non-redundant subset of \lstinline!A.R! maybe used as states.
\end{nonnormative}
\end{semantics}
\end{operatordefinition}

\begin{operatordefinition}[Connections.isRoot]
\begin{synopsis}\begin{lstlisting}
Connections.isRoot(A.R)
\end{lstlisting}\end{synopsis}
\begin{semantics}
Returns true, if the overdetermined type or record instance \lstinline!R! in connector instance \lstinline!A! is selected as a root in the virtual connection graph.
\end{semantics}
\end{operatordefinition}

\begin{operatordefinition}[Connections.rooted]
\begin{synopsis}\begin{lstlisting}
Connections.rooted(A.R)
rooted(A.R) // deprecated!
\end{lstlisting}\end{synopsis}
\begin{semantics}
If the operator \lstinline!Connections.rooted(A.R)! is used, or the equivalent but deprecated operator \lstinline!rooted(A.R)!, then there must be exactly one statement \lstinline!Connections.branch(A.R, B.R)! involving \lstinline!A.R! (the argument of \lstinline!Connections.rooted! must be the first argument of \lstinline!Connections.branch!). In that case \lstinline!Connections.rooted(A.R)! returns true, if \lstinline!A.R! is closer to the root of the spanning tree than \lstinline!B.R!; otherwise false is returned.

\begin{nonnormative}
This operator can be used to avoid equation systems by providing analytic inverses, see \lstinline!Modelica.Mechanics.MultiBody.Parts.FixedRotation!.
\end{nonnormative*}
\\ \hline
\end{longtable}
\end{nonnormative}
\end{semantics}
\end{operatordefinition}

\begin{nonnormative}
Note, that \lstinline!Connections.branch!, \lstinline!Connections.root!,
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