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
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@ -674,43 +674,42 @@ This visualization helps to show intuitively how the classification system
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{}\monoidop s^0\monoidop\cdots\monoidop s^n%
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}
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}
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\def\classmatlines#1{%
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\begin{alignedat}{2}
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\Big( &M^0_{{#1}_0} \monoidops {}&&M^l_{{#1}_0} \Big)
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\monoidop
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v^0_{#1} \monoidops v^m_{#1}
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\monoidop
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s^0 \monoidops s^n \\
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&\quad\!\vdots &&\quad\!\vdots \\
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\Big( &M^0_{{#1}_k} \monoidops {}&&M^l_{{#1}_k} \Big)
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\monoidop
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v^0_{#1} \monoidops v^m_{#1}
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\monoidop
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s^0 \monoidops s^n
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\end{alignedat}
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}
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\begin{align*}
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&\quad\raisebox{-3mm}[0mm]{%
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&\quad\raisebox{-11mm}[0mm]{%
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\begin{turn}{45}
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$\equiv$
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\end{turn}%
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}
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\left(M^0_{0_0} \monoidops M^0_{0_k}\right)
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\monoidops
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\left(M^l_{0_0} \monoidops M^l_{0_k}\right)
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\monoidop
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v^0_0 \monoidops v^m_0
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\monoidop
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s^0 \monoidops s^n
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&\Gamma^2_0 \\[-2mm]
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}\; \classmatlines{0} &\Gamma^2_0 \\[-2mm]
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&\fbox{\raisebox{0mm}[0mm][6mm]{\hphantom{$\classmateq$}}} \\[-8mm]
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%
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&\classmateq &\vdots\; \\[-10mm]
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%
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&\fbox{\raisebox{0mm}[0mm][6mm]{\hphantom{$\classmateq$}}} \\
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&\quad\raisebox{3mm}[0mm]{%
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&\quad\raisebox{11mm}[0mm]{%
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\begin{turn}{-45}
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$\equiv$
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\end{turn}%
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}
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\left(M^0_{j_0} \monoidops M^0_{j_k}\right)
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\monoidops
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\left(M^l_{j_0} \monoidops M^l_{j_k}\right)
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\monoidop
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v^0_j \monoidops v^m_j
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\monoidop
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s^0 \monoidops s^n
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&\Gamma^2_j
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}\; \classmatlines{j} &\Gamma^2_j
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\end{align*}
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\caption{Visual interpretation of classification by \axmref{class-mat-not}.
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For each boxed row of the matrix notation there is an equivalence
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to the first-order logic of \axmref{class-yield}.}
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to the first-order logic of \thmref{class-compose}.}
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\label{f:class-mat-boxes}
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\end{figure}
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\endgroup
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