Clean up so-called "formal" definition of array concatenation

chapters/arrays.tex

@@ -673,48 +673,48 @@ \subsection{Array Concatenation}\doublelabel{array-concatenation}
 \end{lstlisting}
 \end{example}
 
-Concatenation is formally defined according to:
-\begin{lstlisting}[language=modelica, escapechar=!]
-!Let! R = cat(k,A,B,C,...)!, and let! n = ndims(A) = ndims(B) = ndims(C) =
-....!, then!
-  size(R,k) = size(A,k) + size(B,k) + size(C,k) + ...
-  size(R,j) = size(A,j) = size(B,j) = size(C,j) = ...., for 1 <=j <= n and j <> k.
-
-  R[i_1, ..., i_k, ..., i_n] = A[i_1, ..., i_k, ..., i_n], for i_k <= size(A,k),
-  R[i_1, ..., i_k, ..., i_n] = B[i_1, ..., i_k - size(A,i), ..., i_n], for i_k <= size(A,k) + size(B,k),
-    ....
-  where 1 <= i_j <= size(R,j) for 1 <= j <= n.
+Formally, the concatenation \lstinline[mathescape=true]!R = cat($k$, A, B, C, $\ldots$)! is defined as follows.  Let $n$ = \lstinline!ndims(A)! = \lstinline!ndims(B)! = \lstinline!ndims(C)! = \ldots  Then the size of \lstinline!R! is given by
+\begin{lstlisting}[language=modelica,escapechar=!,mathescape=true,frame=none,xleftmargin=1em]
+size(R,$k$) = size(A,$k$) + size(B,$k$) + size(C,$k$) + $\ldots$
+size(R,$j$) = size(A,$j$) = size(B,$j$) = size(C,$j$) = $\ldots$ !for! $1 \leq j \leq n$ and $j \neq k$
+\end{lstlisting}
+and the array elements of \lstinline!R! are given by
+\begin{lstlisting}[language=modelica,escapechar=!,mathescape=true,frame=none,xleftmargin=1em]
+R[$i_{1}$, $\ldots$, $i_{k}$, $\ldots$, $i_{n}$] = A[$i_{1}$, $\ldots$, $i_{k}$, $\ldots$, $i_{n}$]
+  !for! $0 < i_{k} \leq$ size(A,$k$)
+R[$i_{1}$, $\ldots$, $i_{k}$, $\ldots$, $i_{n}$] = B[$i_{1}$, $\ldots$, $i_{k}$ - size(A,$k$), $\ldots$, $i_{n}$]
+  !for! size(A,$k$) $< i_{k} \leq$ size(A,$k$) + size(B,$k$)
+R[$i_{1}$, $\ldots$, $i_{k}$, $\ldots$, $i_{n}$] = C[$i_{1}$, $\ldots$, $i_{k}$ - size(A,$k$) - size(B,$k$), $\ldots$, $i_{n}$]
+  !for! size(A,$k$) + size(B,$k$) $< i_{k} \leq$ size(A,$k$) + size(B,$k$) + size(C,$k$)
+$\ldots$
 \end{lstlisting}
+where $1 \leq i_{j} \leq$ \lstinline[mathescape=true]!size(R,$j$)! for $1 \leq j \leq n$.
 
 
 \subsubsection{Array Concatenation along First and Second Dimensions}\doublelabel{array-concatenation-along-first-and-second-dimensions}
 
-For convenience, a special syntax is supported for the concatenation
-along the first and second dimensions.
-
+For convenience, a special syntax is supported for the concatenation along the first and second dimensions:
 \begin{itemize}
 \item
   \emph{Concatenation along first dimension}:\\
-\lstinline![A; B; C; ...] = cat(1, promote(A,n), promote(B,n), promote(C,n),  ...)!
-where \lstinline!n = max(2, ndims(A), ndims(B), ndims(C), ....)!. If necessary, 1-sized
-  dimensions are added to the right of A, B, C before the operation is
-  carried out, in order that the operands have the same number of
-  dimensions which will be at least two.
+  \lstinline[mathescape=true]![A; B; C; $\ldots$] = cat(1, promote(A, n), promote(B, n), promote(C, n), $\ldots$)!
+  where \lstinline[mathescape=true]!n = max(2, ndims(A), ndims(B), ndims(C), $\ldots$)!.  If necessary, 1-sized
+  dimensions are added to the right of \lstinline!A!, \lstinline!B!, \lstinline!C! before the operation is
+  carried out, in order that the operands have the same number of dimensions which will be at least two.
 \item
   \emph{Concatenation along second dimension}:\\
-\lstinline![A, B, C, ...] = cat(2, promote(A,n), promote(B,n), promote(C,n), ...)!
-where \lstinline!n = max(2, ndims(A), ndims(B), ndims(C), ....)!. If necessary, 1-sized
-  dimensions are added to the right of A, B, C before the operation is
+  \lstinline[mathescape=true]![A, B, C, $\ldots$] = cat(2, promote(A, n), promote(B, n), promote(C, n), $\ldots$)!
+  where \lstinline[mathescape=true]!n = max(2, ndims(A), ndims(B), ndims(C), $\ldots$)!.  If necessary, 1-sized
+  dimensions are added to the right of \lstinline!A!, \lstinline!B!, \lstinline!C! before the operation is
   carried out, especially that each operand has at least two dimensions.
 \item
-  The two forms can be mixed. \lstinline![...,...]! has higher precedence than
- \lstinline![...;...]!, e.g., \lstinline![a, b; c, d]! is parsed as \lstinline![[a,b];[c,d]]!.
+  The two forms can be mixed.  \lstinline[mathescape=true]![$\ldots$, $\ldots$]! has higher precedence than
+  \lstinline[mathescape=true]![$\ldots$; $\ldots$]!, e.g., \lstinline![a, b; c, d]! is parsed as \lstinline![[a, b]; [c, d]]!.
 \item
-\lstinline![A] = promote(A,max(2,ndims(A)))!, i.e., \lstinline![A] = A!, if A has 2 or
-  more dimensions, and it is a matrix with the elements of A, if A is a
-  scalar or a vector.
+  \lstinline![A] = promote(A, max(2, ndims(A)))!, i.e., \lstinline![A] = A!, if \lstinline!A! has 2 or more dimensions, and it is a matrix
+  with the elements of \lstinline!A!, if \lstinline!A! is a scalar or a vector.
 \item
-  There must be at least one argument (i.e.\ \lstinline![]! is not defined)
+  There must be at least one argument (i.e.\ \lstinline![]! is not defined).
 \end{itemize}
 
 \begin{example}