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classes/notebook.cls

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@@ -59,7 +59,6 @@
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\RequirePackage{numprint}
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\RequirePackage{blkarray}
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\RequirePackage{fancyvrb}
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\RequirePackage{diagbox}
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\RequirePackage{paracol}
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\RequirePackage{forest}
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packages/math_environments.sty

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% Annotations for the backnaur package
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\NewDocumentEnvironment {bnfextra} {}
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{
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\center
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\leavevmode
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\begingroup
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\RenewDocumentCommand \arraystretch {} {1.2}
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\tabular{R L L L}
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\begin{equation*}
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\RenewDocumentCommand \arraystretch {} {1.3}
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\begin{array}{r l l l}
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}
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{
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\endtabular
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\endgroup
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\endcenter
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\leavevmode
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\end{array}
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\end{equation*}
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}
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@@ -58,10 +54,10 @@
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{
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\begin{equation*}
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\begin{array}{| *{#1} {c |}}
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\hline
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\toprule
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}
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{
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\\ \hline
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\\ \bottomrule
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\end{array}
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\end{equation*}
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}

packages/math_macros.sty

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{ \mathrel { \text{#2} } }
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}
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% diagbox math mode wrapper
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\NewDocumentCommand \mdiagbox {mm}
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{
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\hbox
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{
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\diagbox {\( #1 \)} {\( #2 \)}
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}
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}
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\NewDocumentCommand \ParacolAlignmentHack {}
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{
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% For some reason, equations are positioned badly without this hack
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\NewDocumentCommand \oline {sm}
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{
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\IfBooleanTF {#1}
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{ \overline{ \nb_raisebox:nn { #2 } {2.3pt} } }
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% The lowered overline is based on https://tex.stackexchange.com/a/87615
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{ \overline{ \raisebox{0pt}[0.85\height]{ \( #2 \) } } }
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{ \overline{ #2 } }
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}
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text/group_actions.tex

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@@ -225,27 +225,27 @@ \section{Group actions}\label{sec:group_actions}
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We have listed the functions permuting \( a \), \( b \) and \( ab \) in \cref{tab:ex:def:automorphism_group/v4}.
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\begin{table}[!ht]
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\begin{center}
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\begin{tabular}{l l l l}
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\begin{equation*}
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\begin{array}{l l l l}
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\toprule
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Cycle in \( S_3 \) & \( a \) & \( b \) & \( ab \) \\
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\T{Cycle in} S_3 & a & b & ab \\
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\midrule
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\( \id \) & \( a \) & \( b \) & \( ab \) \\
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\( \cycle{ 1, 2 } \) & \( b \) & \( a \) & \( ab \) \\
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\( \cycle{ 1, 3 } \) & \( ab \) & \( b \) & \( a \) \\
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\id & a & b & ab \\
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\cycle{ 1, 2 } & b & a & ab \\
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\cycle{ 1, 3 } & ab & b & a \\
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\bottomrule
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\end{tabular}
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\end{array}
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\quad
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\begin{tabular}{l c c c}
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\begin{array}{l c c c}
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\toprule
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Cycle in \( S_3 \) & \( a \) & \( b \) & \( ab \) \\
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\T{Cycle in} S_3 & a & b & ab \\
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\midrule
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\( \cycle{ 2, 3 } \) & \( a \) & \( ab \) & \( b \) \\
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\( \cycle{ 1, 2, 3 } \) & \( b \) & \( ab \) & \( a \) \\
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\( \cycle{ 1, 3, 2 } \) & \( ab \) & \( a \) & \( b \) \\
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\cycle{ 2, 3 } & a & ab & b \\
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\cycle{ 1, 2, 3 } & b & ab & a \\
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\cycle{ 1, 3, 2 } & ab & a & b \\
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\bottomrule
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\end{tabular}
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\end{center}
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\end{array}
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\end{equation*}
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\caption{Isomorphisms of the \hyperref[def:klein_four_group]{Klein four-group} \( V_4 \)}\label{tab:ex:def:automorphism_group/v4}
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\end{table}
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@@ -1157,14 +1157,16 @@ \section{Group actions}\label{sec:group_actions}
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\begin{equation*}
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\begin{array}{l !{\quad} *{6}{l}}
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\toprule
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\mdiagbox{\tau}{\sigma} & \id & \cycle{ 1, 2 } & \cycle{ 1, 3 } & \cycle{ 2, 3 } & \cycle{ 1, 2, 3 } & \cycle{ 1, 3, 2 } \\
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& \multicolumn{6}{c}{\sigma} \\
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\cmidrule{2-7}
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\multicolumn{1}{c}{\tau} & \id & \cycle{ 1, 2 } & \cycle{ 1, 3 } & \cycle{ 2, 3 } & \cycle{ 1, 2, 3 } & \cycle{ 1, 3, 2 } \\
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\midrule
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\id & \id & \cycle{ 1, 2 } & \cycle{ 1, 3 } & \cycle{ 2, 3 } & \cycle{ 1, 2, 3 } & \cycle{ 1, 3, 2 } \\
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\cycle{ 1, 2 } & \cycle{ 1, 2 } & \id & \cycle{ 1, 3, 2 } & \cycle{ 1, 2, 3 } & \cycle{ 2, 3 } & \cycle{ 1, 3 } \\
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\cycle{ 1, 3 } & \cycle{ 1, 3 } & \cycle{ 1, 2, 3 } & \id & \cycle{ 1, 3, 2 } & \cycle{ 1, 2 } & \cycle{ 2, 3 } \\
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\cycle{ 2, 3 } & \cycle{ 2, 3 } & \cycle{ 1, 3, 2 } & \cycle{ 1, 2, 3 } & \id & \cycle{ 1, 3 } & \cycle{ 1, 2 } \\
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\cycle{ 1, 2, 3 } & \cycle{ 1, 2, 3 } & \cycle{ 1, 3 } & \cycle{ 2, 3 } & \cycle{ 1, 2 } & \cycle{ 1, 3, 2 } & \id \\
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\cycle{ 1, 3, 2 } & \cycle{ 1, 3, 2 } & \cycle{ 2, 3 } & \cycle{ 1, 2 } & \cycle{ 1, 3 } & \id & \cycle{ 1, 2, 3 } \\
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\id & \id & \cycle{ 1, 2 } & \cycle{ 1, 3 } & \cycle{ 2, 3 } & \cycle{ 1, 2, 3 } & \cycle{ 1, 3, 2 } \\
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\cycle{ 1, 2 } & \cycle{ 1, 2 } & \id & \cycle{ 1, 3, 2 } & \cycle{ 1, 2, 3 } & \cycle{ 2, 3 } & \cycle{ 1, 3 } \\
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\cycle{ 1, 3 } & \cycle{ 1, 3 } & \cycle{ 1, 2, 3 } & \id & \cycle{ 1, 3, 2 } & \cycle{ 1, 2 } & \cycle{ 2, 3 } \\
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\cycle{ 2, 3 } & \cycle{ 2, 3 } & \cycle{ 1, 3, 2 } & \cycle{ 1, 2, 3 } & \id & \cycle{ 1, 3 } & \cycle{ 1, 2 } \\
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\cycle{ 1, 2, 3 } & \cycle{ 1, 2, 3 } & \cycle{ 1, 3 } & \cycle{ 2, 3 } & \cycle{ 1, 2 } & \cycle{ 1, 3, 2 } & \id \\
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\cycle{ 1, 3, 2 } & \cycle{ 1, 3, 2 } & \cycle{ 2, 3 } & \cycle{ 1, 2 } & \cycle{ 1, 3 } & \id & \cycle{ 1, 2, 3 } \\
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\bottomrule
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\end{array}
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\end{equation*}

text/heyting_algebras.tex

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@@ -405,7 +405,7 @@ \section{Heyting algebras}\label{sec:heyting_algebras}
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\Cref{thm:def:heyting_algebra/dist} implies that
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\begin{equation*}
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\underbrace{\bot \rightarrow (x \rightarrow \doline{x})}_\top \leq (\underbrace{(\bot \rightarrow x)}_\top \rightarrow (x \rightarrow \doline{x})).
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\underbrace{\bot \rightarrow (x \rightarrow \doline{x})}_\top \leq \parens[\big]{ \underbrace{(\bot \rightarrow x)}_\top \rightarrow (x \rightarrow \doline{x}) }.
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\end{equation*}
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\Cref{thm:def:heyting_algebra/top_left} allows us to conclude that
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\begin{equation*}
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\begin{array}{r !{\quad} *{3}{c}}
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\toprule
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\mdiagbox{x}{y} & F & N & T \\
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& \multicolumn{3}{c}{y} \\
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\cmidrule{2-4}
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x & F & N & T \\
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\midrule
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F & T & T & T \\
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N & F & T & T \\

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