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Clean up formulations and formatting related to 'is not provided' in …
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…'Synchronous Language Elements'

Two changes:
- Make sure symbolic argument is math-formatted.
- Remove redundant 'argument' before math-formatted symbolic reference to argument.
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henrikt-ma committed May 21, 2021
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Showing 1 changed file with 7 additions and 3 deletions.
10 changes: 7 additions & 3 deletions chapters/synchronous.tex
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Expand Up @@ -578,7 +578,10 @@ \subsection{Base-clock conversion operators}\label{base-clock-conversion-operato
sample($u$, $\mathit{clock}$)
\end{lstlisting}\end{synopsis}
\begin{semantics}
Input argument $u$ is a continuous-time expression according to \cref{continuous-time-expressions}. The optional input argument $\mathit{clock}$ is of type \lstinline!Clock!, and can in a call be given as a named argument (with the name $\mathit{clock}$), or as positional argument. The operator returns a clocked variable that has $\mathit{clock}$ as associated clock and has the value of the left limit of $u$ when $\mathit{clock}$ is active (that is the value of $u$ just before the event of \lstinline!c! is triggered). If argument $\mathit{clock}$ is not provided, it is inferred, see \cref{sub-clock-inferencing}.
Input argument $u$ is a continuous-time expression according to \cref{continuous-time-expressions}.
The optional input argument $\mathit{clock}$ is of type \lstinline!Clock!, and can in a call be given as a named argument (with the name $\mathit{clock}$), or as positional argument.
The operator returns a clocked variable that has $\mathit{clock}$ as associated clock and has the value of the left limit of $u$ when $\mathit{clock}$ is active (that is the value of $u$ just before the event of \lstinline!c! is triggered).
If $\mathit{clock}$ is not provided, it is inferred, see \cref{sub-clock-inferencing}.
\begin{nonnormative}
Since the operator returns the left limit of $u$, it introduces an infinitesimal small delay between the continuous-time and the clocked partition. This corresponds to the reality, where a sampled data system cannot act infinitely fast and even for a very idealized simulation, an infinitesimal small delay is present. The consequences for the sorting are discussed below.

Expand Down Expand Up @@ -673,7 +676,7 @@ \subsection{Sub-clock conversion operators}\label{sub-clock-conversion-operators
The clock of \lstinline!y = subSample($u$, $\mathit{factor}$)! is $\mathit{factor}$ times slower than the clock of $u$.
At every $\mathit{factor}$ ticks of the clock of $u$, the operator returns the value of $u$.
The first activation of the clock of \lstinline!y! coincides with the first activation of the clock of $u$, and then every activation of the clock of \lstinline!y! coincides with the every $\mathit{factor}$th activativation of the clock of $u$.
If argument $\mathit{factor}$ is not provided or is equal to zero, it is inferred, see \cref{sub-clock-inferencing}.
If $\mathit{factor}$ is not provided or is equal to zero, it is inferred, see \cref{sub-clock-inferencing}.
\end{semantics}
\end{operatordefinition}

Expand All @@ -686,7 +689,8 @@ \subsection{Sub-clock conversion operators}\label{sub-clock-conversion-operators
\begin{nonnormative}
Thus \lstinline!subSample(superSample($u$, $\mathit{factor}$), $\mathit{factor}$)! = $u$.
\end{nonnormative}
If argument factor is not provided or is equal to zero, it is inferred, see \cref{sub-clock-inferencing}. If an event clock is associated to a base-clock partition, all its sub-clock partitions must have resulting clocks that are sub-sampled with an \lstinline!Integer! factor with respect to this base-clock.
If $\mathit{factor}$ is not provided or is equal to zero, it is inferred, see \cref{sub-clock-inferencing}.
If an event clock is associated to a base-clock partition, all its sub-clock partitions must have resulting clocks that are sub-sampled with an \lstinline!Integer! factor with respect to this base-clock.

\begin{example}
\begin{lstlisting}[language=modelica]
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