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design/tpl (Matches): Refine matrix visualization figure 

This provides an element-level rather than row-level focus, which I feel is
more appropriate.

One could draw lines to connect each of the elements, but that'd likely be
too noisy and it'd be a lot of work.
master
Mike Gerwitz 2021-05-27 10:58:54 -04:00
parent 9e9d5fc16b
commit e3a583624c
1 changed files with 20 additions and 21 deletions
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41
design/tpl/sec/class.tex
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@ -674,43 +674,42 @@ This visualization helps to show intuitively how the classification system
{}\monoidop s^0\monoidop\cdots\monoidop s^n%
}
}
\def\classmatlines#1{%
\begin{alignedat}{2}
\Big( &M^0_{{#1}_0} \monoidops {}&&M^l_{{#1}_0} \Big)
\monoidop
v^0_{#1} \monoidops v^m_{#1}
\monoidop
s^0 \monoidops s^n \\
&\quad\!\vdots &&\quad\!\vdots \\
\Big( &M^0_{{#1}_k} \monoidops {}&&M^l_{{#1}_k} \Big)
\monoidop
v^0_{#1} \monoidops v^m_{#1}
\monoidop
s^0 \monoidops s^n
\end{alignedat}
}
\begin{align*}
&\quad\raisebox{-3mm}[0mm]{%
&\quad\raisebox{-11mm}[0mm]{%
\begin{turn}{45}
$\equiv$
\end{turn}%
}
\left(M^0_{0_0} \monoidops M^0_{0_k}\right)
\monoidops
\left(M^l_{0_0} \monoidops M^l_{0_k}\right)
\monoidop
v^0_0 \monoidops v^m_0
\monoidop
s^0 \monoidops s^n
&\Gamma^2_0 \\[-2mm]
}\; \classmatlines{0} &\Gamma^2_0 \\[-2mm]
&\fbox{\raisebox{0mm}[0mm][6mm]{\hphantom{$\classmateq$}}} \\[-8mm]
%
&\classmateq &\vdots\; \\[-10mm]
%
&\fbox{\raisebox{0mm}[0mm][6mm]{\hphantom{$\classmateq$}}} \\
&\quad\raisebox{3mm}[0mm]{%
&\quad\raisebox{11mm}[0mm]{%
\begin{turn}{-45}
$\equiv$
\end{turn}%
}
\left(M^0_{j_0} \monoidops M^0_{j_k}\right)
\monoidops
\left(M^l_{j_0} \monoidops M^l_{j_k}\right)
\monoidop
v^0_j \monoidops v^m_j
\monoidop
s^0 \monoidops s^n
&\Gamma^2_j
}\; \classmatlines{j} &\Gamma^2_j
\end{align*}
\caption{Visual interpretation of classification by \axmref{class-mat-not}.
For each boxed row of the matrix notation there is an equivalence
to the first-order logic of \axmref{class-yield}.}
to the first-order logic of \thmref{class-compose}.}
\label{f:class-mat-boxes}
\end{figure}
\endgroup