%!TEX root = "../thesis.tex"
\section*{Symbol Classes}
            \begin{longtable}{lc|lc}
                \toprule
                \LaTeX & Rendered & \LaTeX & Rendered \\
                \midrule
                \endhead
                \hline \multicolumn{4}{r}{{Continued on next page}} \\
                \endfoot
                \bottomrule
                \caption{112 symbols of \dbName.}
                \endlastfoot
\verb+\&+ & $\&$ &\verb+\nmid+ & $\nmid$\\
\verb+\Im+ & $\Im$ &\verb+\nvDash+ & $\nvDash$\\
\verb+\Re+ & $\Re$ &\verb+\int+ & $\int$\\
\verb+\S+ & $\S$ &\verb+\fint+ & $\fint$\\
\verb+\Vdash+ & $\Vdash$ &\verb+\odot+ & $\odot$\\
\verb+\aleph+ & $\aleph$ &\verb+\oiint+ & $\oiint$\\
\verb+\amalg+ & $\amalg$ &\verb+\oint+ & $\oint$\\
\verb+\angle+ & $\angle$ &\verb+\varoiint+ & $\varoiint$\\
\verb+\ast+ & $\ast$ &\verb+\ominus+ & $\ominus$\\
\verb+\asymp+ & $\asymp$ &\verb+\oplus+ & $\oplus$\\
\verb+\backslash+ & $\backslash$ &\verb+\otimes+ & $\otimes$\\
\verb+\between+ & $\between$ &\verb+\parallel+ & $\parallel$\\
\verb+\blacksquare+ & $\blacksquare$ &\verb+\parr+ & $\parr$\\
\verb+\blacktriangleright+ & $\blacktriangleright$ &\verb+\partial+ & $\partial$\\
\verb+\bot+ & $\bot$ &\verb+\perp+ & $\perp$\\
\verb+\bowtie+ & $\bowtie$ &\verb+\pitchfork+ & $\pitchfork$\\
\verb+\boxdot+ & $\boxdot$ &\verb+\pm+ & $\pm$\\
\verb+\boxplus+ & $\boxplus$ &\verb+\prime+ & $\prime$\\
\verb+\boxtimes+ & $\boxtimes$ &\verb+\prod+ & $\prod$\\
\verb+\bullet+ & $\bullet$ &\verb+\propto+ & $\propto$\\
\verb+\checkmark+ & $\checkmark$ &\verb+\rangle+ & $\rangle$\\
\verb+\circ+ & $\circ$ &\verb+\rceil+ & $\rceil$\\
\verb+\circledR+ & $\circledR$ &\verb+\rfloor+ & $\rfloor$\\
\verb+\circledast+ & $\circledast$ &\verb+\rrbracket+ & $\rrbracket$\\
\verb+\circledcirc+ & $\circledcirc$ &\verb+\rtimes+ & $\rtimes$\\
\verb+\clubsuit+ & $\clubsuit$ &\verb+\sharp+ & $\sharp$\\
\verb+\coprod+ & $\coprod$ &\verb+\sphericalangle+ & $\sphericalangle$\\
\verb+\copyright+ & $\copyright$ &\verb+\sqcap+ & $\sqcap$\\
\verb+\dag+ & $\dag$ &\verb+\sqcup+ & $\sqcup$\\
\verb+\dashv+ & $\dashv$ &\verb+\sqrt{}+ & $\sqrt{}$\\
\verb+\diamond+ & $\diamond$ &\verb+\square+ & $\square$\\
\verb+\diamondsuit+ & $\diamondsuit$ &\verb+\star+ & $\star$\\
\verb+\div+ & $\div$ &\verb+\sum+ & $\sum$\\
\verb+\ell+ & $\ell$ &\verb+\times+ & $\times$\\
\verb+\flat+ & $\flat$ &\verb+\top+ & $\top$\\
\verb+\frown+ & $\frown$ &\verb+\triangle+ & $\triangle$\\
\verb+\guillemotleft+ & $\guillemotleft$ &\verb+\triangledown+ & $\triangledown$\\
\verb+\hbar+ & $\hbar$ &\verb+\triangleleft+ & $\triangleleft$\\
\verb+\heartsuit+ & $\heartsuit$ &\verb+\trianglelefteq+ & $\trianglelefteq$\\
\verb+\infty+ & $\infty$ &\verb+\triangleq+ & $\triangleq$\\
\verb+\langle+ & $\langle$ &\verb+\triangleright+ & $\triangleright$\\
\verb+\lceil+ & $\lceil$ &\verb+\uplus+ & $\uplus$\\
\verb+\lfloor+ & $\lfloor$ &\verb+\vDash+ & $\vDash$\\
\verb+\lhd+ & $\lhd$ &\verb+\varnothing+ & $\varnothing$\\
\verb+\lightning+ & $\lightning$ &\verb+\varpropto+ & $\varpropto$\\
\verb+\llbracket+ & $\llbracket$ &\verb+\vartriangle+ & $\vartriangle$\\
\verb+\lozenge+ & $\lozenge$ &\verb+\vdash+ & $\vdash$\\
\verb+\ltimes+ & $\ltimes$ &\verb+\with+ & $\with$\\
\verb+\mathds{1}+ & $\mathds{1}$ &\verb+\wp+ & $\wp$\\
\verb+\mathsection+ & $\mathsection$ &\verb+\wr+ & $\wr$\\
\verb+\mid+ & $\mid$ &\verb+\{+ & $\{$\\
\verb+\models+ & $\models$ &\verb+\|+ & $\|$\\
\verb+\mp+ & $\mp$ &\verb+\}+ & $\}$\\
\verb+\multimap+ & $\multimap$ &\verb+\vee+ & $\vee$\\
\verb+\nabla+ & $\nabla$ &\verb+\wedge+ & $\wedge$\\
\verb+\neg+ & $\neg$ &\verb+\barwedge+ & $\barwedge$
    \label{table:symbols-of-db-0}
    \end{longtable}


\begin{table}[ht]
        \centering

            \begin{tabular}{lc|lc|lc|lc}
                \toprule
                \LaTeX & Rendered & \LaTeX & Rendered & \LaTeX & Rendered & \LaTeX & Rendered \\
                \midrule
\verb+\#+ & $\#$ &\verb+A+ & $A$ &\verb+S+ & $S$ &\verb+i+ & $i$\\
\verb+\$+ & $\$$ &\verb+B+ & $B$ &\verb+T+ & $T$ &\verb+j+ & $j$\\
\verb+\%+ & $\%$ &\verb+C+ & $C$ &\verb+U+ & $U$ &\verb+k+ & $k$\\
\verb+++ & $+$ &\verb+D+ & $D$ &\verb+V+ & $V$ &\verb+l+ & $l$\\
\verb+-+ & $-$ &\verb+E+ & $E$ &\verb+W+ & $W$ &\verb+m+ & $m$\\
\verb+/+ & $/$ &\verb+F+ & $F$ &\verb+X+ & $X$ &\verb+n+ & $n$\\
\verb+0+ & $0$ &\verb+G+ & $G$ &\verb+Y+ & $Y$ &\verb+o+ & $o$\\
\verb+1+ & $1$ &\verb+H+ & $H$ &\verb+Z+ & $Z$ &\verb+p+ & $p$\\
\verb+2+ & $2$ &\verb+I+ & $I$ &\verb+[+ & $[$ &\verb+q+ & $q$\\
\verb+3+ & $3$ &\verb+J+ & $J$ &\verb+]+ & $]$ &\verb+r+ & $r$\\
\verb+4+ & $4$ &\verb+K+ & $K$ &\verb+a+ & $a$ &\verb+s+ & $s$\\
\verb+5+ & $5$ &\verb+L+ & $L$ &\verb+b+ & $b$ &\verb+u+ & $u$\\
\verb+6+ & $6$ &\verb+M+ & $M$ &\verb+c+ & $c$ &\verb+v+ & $v$\\
\verb+7+ & $7$ &\verb+N+ & $N$ &\verb+d+ & $d$ &\verb+w+ & $w$\\
\verb+8+ & $8$ &\verb+O+ & $O$ &\verb+e+ & $e$ &\verb+x+ & $x$\\
\verb+9+ & $9$ &\verb+P+ & $P$ &\verb+f+ & $f$ &\verb+y+ & $y$\\
\verb+<+ & $<$ &\verb+Q+ & $Q$ &\verb+g+ & $g$ &\verb+z+ & $z$\\
\verb+>+ & $>$ &\verb+R+ & $R$ &\verb+h+ & $h$ &\verb+|+ & $|$\\

        \bottomrule
    \end{tabular}

    \caption{72 ASCII symbols of \dbName, including all
             ten digits, the Latin alphabet in lower and upper case and
             a few more symbols.}
    \label{table:symbols-of-db-1}
\end{table}


\begin{table}[ht]
        \centering
            \begin{tabular}{lc|lc|lc}
                \toprule
                \LaTeX & Rendered & \LaTeX & Rendered & \LaTeX & Rendered \\
                \midrule
\verb+\approx+ & $\approx$ &\verb+\geqslant+ & $\geqslant$ &\verb+\lesssim+ & $\lesssim$\\
\verb+\doteq+ & $\doteq$ &\verb+\neq+ & $\neq$ &\verb+\backsim+ & $\backsim$\\
\verb+\simeq+ & $\simeq$ &\verb+\not\equiv+ & $\not\equiv$ &\verb+\sim+ & $\sim$\\
\verb+\equiv+ & $\equiv$ &\verb+\preccurlyeq+ & $\preccurlyeq$ &\verb+\succ+ & $\succ$\\
\verb+\geq+ & $\geq$ &\verb+\preceq+ & $\preceq$ &\verb+\prec+ & $\prec$\\
\verb+\leq+ & $\leq$ &\verb+\succeq+ & $\succeq$ &\verb+\gtrless+ & $\gtrless$\\
\verb+\leqslant+ & $\leqslant$ &\verb+\gtrsim+ & $\gtrsim$ &\verb+\cong+ & $\cong$\\
        \bottomrule
    \end{tabular}

    \caption{21 symbols which are in \dbName and indicate a relationship.}
    \label{table:symbols-of-db-2}
\end{table}


\begin{table}[ht]
        \centering

            \begin{tabular}{lc|lc}
                \toprule
                \LaTeX & Rendered & \LaTeX & Rendered \\
                \midrule
\verb+\Downarrow+ & $\Downarrow$ &\verb+\nrightarrow+ & $\nrightarrow$\\
\verb+\Leftarrow+ & $\Leftarrow$ &\verb+\rightarrow+ & $\rightarrow$\\
\verb+\Leftrightarrow+ & $\Leftrightarrow$ &\verb+\rightleftarrows+ & $\rightleftarrows$\\
\verb+\Longleftrightarrow+ & $\Longleftrightarrow$ &\verb+\rightrightarrows+ & $\rightrightarrows$\\
\verb+\Longrightarrow+ & $\Longrightarrow$ &\verb+\rightsquigarrow+ & $\rightsquigarrow$\\
\verb+\Rightarrow+ & $\Rightarrow$ &\verb+\searrow+ & $\searrow$\\
\verb+\circlearrowleft+ & $\circlearrowleft$ &\verb+\shortrightarrow+ & $\shortrightarrow$\\
\verb+\circlearrowright+ & $\circlearrowright$ &\verb+\twoheadrightarrow+ & $\twoheadrightarrow$\\
\verb+\curvearrowright+ & $\curvearrowright$ &\verb+\uparrow+ & $\uparrow$\\
\verb+\downarrow+ & $\downarrow$ &\verb+\rightharpoonup+ & $\rightharpoonup$\\
\verb+\hookrightarrow+ & $\hookrightarrow$ &\verb+\rightleftharpoons+ & $\rightleftharpoons$\\
\verb+\leftarrow+ & $\leftarrow$ &\verb+\longmapsto+ & $\longmapsto$\\
\verb+\leftrightarrow+ & $\leftrightarrow$ &\verb+\mapsfrom+ & $\mapsfrom$\\
\verb+\longrightarrow+ & $\longrightarrow$ &\verb+\mapsto+ & $\mapsto$\\
\verb+\nRightarrow+ & $\nRightarrow$ &\verb+\leadsto+ & $\leadsto$\\
\verb+\nearrow+ & $\nearrow$ &\verb+\upharpoonright+ & $\upharpoonright$\\

        \bottomrule
    \end{tabular}

    \caption{32 arrow symbols of \dbName.}
    \label{table:symbols-of-db-3}
\end{table}


\begin{table}[ht]
        \centering

            \begin{tabular}{lc|lc|lc}
                \toprule
                \LaTeX & Rendered & \LaTeX & Rendered & \LaTeX & Rendered \\
                \midrule
\verb+\alpha+ & $\alpha$ &\verb+\xi+ & $\xi$ &\verb+\Xi+ & $\Xi$\\
\verb+\beta+ & $\beta$ &\verb+\pi+ & $\pi$ &\verb+\Pi+ & $\Pi$\\
\verb+\gamma+ & $\gamma$ &\verb+\rho+ & $\rho$ &\verb+\Sigma+ & $\Sigma$\\
\verb+\delta+ & $\delta$ &\verb+\sigma+ & $\sigma$ &\verb+\Phi+ & $\Phi$\\
\verb+\epsilon+ & $\epsilon$ &\verb+\tau+ & $\tau$ &\verb+\Psi+ & $\Psi$\\
\verb+\zeta+ & $\zeta$ &\verb+\phi+ & $\phi$ &\verb+\Omega+ & $\Omega$\\
\verb+\eta+ & $\eta$ &\verb+\chi+ & $\chi$ &\verb+\varepsilon+ & $\varepsilon$\\
\verb+\theta+ & $\theta$ &\verb+\psi+ & $\psi$ &\verb+\varkappa+ & $\varkappa$\\
\verb+\iota+ & $\iota$ &\verb+\omega+ & $\omega$ &\verb+\varpi+ & $\varpi$\\
\verb+\kappa+ & $\kappa$ &\verb+\Gamma+ & $\Gamma$ &\verb+\varrho+ & $\varrho$\\
\verb+\lambda+ & $\lambda$ &\verb+\Delta+ & $\Delta$ &\verb+\varphi+ & $\varphi$\\
\verb+\mu+ & $\mu$ &\verb+\Theta+ & $\Theta$ &\verb+\vartheta+ & $\vartheta$\\
\verb+\nu+ & $\nu$ &\verb+\Lambda+ & $\Lambda$ &\verb+ + & $ $\\

        \bottomrule
    \end{tabular}

    \caption{All Greek letters and some variations of Greek letters were
             used for evaluation. 38 of them are in this table, the rest
             is identical to Latin letters.}
    \label{table:symbols-of-db-4}
\end{table}


\begin{table}[ht]
        \centering

            \begin{tabular}{lc|lc|lc}
                \toprule
                \LaTeX & Rendered & \LaTeX & Rendered & \LaTeX & Rendered \\
                \midrule
\verb+\mathcal{A}+ & $\mathcal{A}$ &\verb+\mathcal{T}+ & $\mathcal{T}$ &\verb+\mathds{Z}+ & $\mathds{Z}$\\
\verb+\mathcal{B}+ & $\mathcal{B}$ &\verb+\mathcal{U}+ & $\mathcal{U}$ &\verb+\mathfrak{A}+ & $\mathfrak{A}$\\
\verb+\mathcal{C}+ & $\mathcal{C}$ &\verb+\mathcal{X}+ & $\mathcal{X}$ &\verb+\mathfrak{M}+ & $\mathfrak{M}$\\
\verb+\mathcal{D}+ & $\mathcal{D}$ &\verb+\mathcal{Z}+ & $\mathcal{Z}$ &\verb+\mathfrak{S}+ & $\mathfrak{S}$\\
\verb+\mathcal{E}+ & $\mathcal{E}$ &\verb+\mathbb{H}+ & $\mathbb{H}$ &\verb+\mathfrak{X}+ & $\mathfrak{X}$\\
\verb+\mathcal{F}+ & $\mathcal{F}$ &\verb+\mathbb{N}+ & $\mathbb{N}$ &\verb+\mathscr{A}+ & $\mathscr{A}$\\
\verb+\mathcal{G}+ & $\mathcal{G}$ &\verb+\mathbb{Q}+ & $\mathbb{Q}$ &\verb+\mathscr{C}+ & $\mathscr{C}$\\
\verb+\mathcal{H}+ & $\mathcal{H}$ &\verb+\mathbb{R}+ & $\mathbb{R}$ &\verb+\mathscr{D}+ & $\mathscr{D}$\\
\verb+\mathcal{L}+ & $\mathcal{L}$ &\verb+\mathbb{Z}+ & $\mathbb{Z}$ &\verb+\mathscr{E}+ & $\mathscr{E}$\\
\verb+\mathcal{M}+ & $\mathcal{M}$ &\verb+\mathds{C}+ & $\mathds{C}$ &\verb+\mathscr{F}+ & $\mathscr{F}$\\
\verb+\mathcal{N}+ & $\mathcal{N}$ &\verb+\mathds{E}+ & $\mathds{E}$ &\verb+\mathscr{H}+ & $\mathscr{H}$\\
\verb+\mathcal{O}+ & $\mathcal{O}$ &\verb+\mathds{N}+ & $\mathds{N}$ &\verb+\mathscr{L}+ & $\mathscr{L}$\\
\verb+\mathcal{P}+ & $\mathcal{P}$ &\verb+\mathds{P}+ & $\mathds{P}$ &\verb+\mathscr{P}+ & $\mathscr{P}$\\
\verb+\mathcal{R}+ & $\mathcal{R}$ &\verb+\mathds{Q}+ & $\mathds{Q}$ &\verb+\mathscr{S}+ & $\mathscr{S}$\\
\verb+\mathcal{S}+ & $\mathcal{S}$ &\verb+\mathds{R}+ & $\mathds{R}$ &\verb+ + & $ $\\

        \bottomrule
    \end{tabular}

    \caption{44 variants of Latin letters in \dbName.}
    \label{table:symbols-of-db-5}
\end{table}


\begin{table}[ht]
        \centering

            \begin{tabular}{lc|lc|lc}
                \toprule
                \LaTeX & Rendered & \LaTeX & Rendered & \LaTeX & Rendered \\
                \midrule
\verb+\therefore+ & $\therefore$ &\verb+\cdot+  & $\cdot$  &\verb+\dots+  & $\dots$\\
\verb+\because+   & $\because$   &\verb+\vdots+ & $\vdots$ &\verb+\ddots+ & $\ddots$\\
\verb+\dotsc+     & $\dotsc$     &\verb+ +      &          &\verb+ +      &  \\
        \bottomrule
    \end{tabular}

    \caption{7 symbols that contain only dots in \dbName.}
    \label{table:symbols-of-db-6}
\end{table}


\begin{table}[ht]
        \centering
            \begin{tabular}{lc|lc|lc|lc|lc}
                \toprule
                \LaTeX & R & \LaTeX & R & \LaTeX & R &  \LaTeX & R & \LaTeX & R \\
                \midrule
\verb+\AA+ & {\r A}                                                           &\verb+\L+       & \includegraphics[height=12.3pt, keepaspectratio]{symbols/L.pdf} &\verb+\male+     & {\mbox {\wasyfamily \char 26}}                         &\verb+\ohm+      &  $\Omega $                     &\verb+\sun+       & {\mbox {\wasyfamily \char 46}} \\
\verb+\AE+ & \includegraphics[height=12.3pt, keepaspectratio]{symbols/AE.pdf} &\verb+\O+       & \includegraphics[height=12.3pt, keepaspectratio]{symbols/L.pdf} &\verb+\mars+     & {\leavevmode \lower 0.2ex\hbox {\wasyfamily \char 26}} &\verb+\fullmoon+ & {\mbox {\wasyfamily \char 35}} &\verb+\degree+    & {\ensuremath {^\circ }}\\
\verb+\aa+ & {\r a}                                                           &\verb+\o+       & \includegraphics[height=12.3pt, keepaspectratio]{symbols/o.pdf} &\verb+\female+   & {\mbox {\wasyfamily \char 25}}                         &\verb+\leftmoon+ & {\mbox {\wasyfamily \char 36}} &\verb+\iddots+    & \includegraphics[height=12.3pt, keepaspectratio]{symbols/iddots.pdf}\\
\verb+\ae+ & \includegraphics[height=12.3pt, keepaspectratio]{symbols/AE.pdf} &\verb+\Bowtie+  & {\mbox {\wasyfamily \char 49}}                                  &\verb+\venus+    & {\leavevmode \raise 0.2ex\hbox {\wasyfamily \char 25}} &\verb+\checked+  & {\mbox {\wasyfamily \char 8}}  &\verb+\diameter+  & {\mbox {\wasyfamily \char 31}} \\
\verb+\ss+ & \includegraphics[height=12.3pt, keepaspectratio]{symbols/ss.pdf} &\verb+\celsius+ & $^\circ \mathrm {C}$                                            &\verb+\astrosun+ & {\mbox {$\odot $}}                                     &\verb+\pounds+   & \textsterling                  &\verb+\mathbb{1}+ & \includegraphics{symbols/mathbb1.pdf}\\
        \bottomrule
    \end{tabular}
    \caption{25 symbols of \dbName.}
    \label{table:symbols-of-db-7}
\end{table}


\begin{table}[ht]
        \centering

            \begin{tabular}{lc|lc|lc}
                \toprule
                \LaTeX & Rendered & \LaTeX & Rendered & \LaTeX & Rendered \\
                \midrule
\verb+\cup+ & $\cup$ &\verb+\varsubsetneq+ & $\varsubsetneq$ &\verb+\exists+ & $\exists$\\
\verb+\cap+ & $\cap$ &\verb+\nsubseteq+ & $\nsubseteq$ &\verb+\nexists+ & $\nexists$\\
\verb+\emptyset+ & $\emptyset$ &\verb+\sqsubseteq+ & $\sqsubseteq$ &\verb+\forall+ & $\forall$\\
\verb+\setminus+ & $\setminus$ &\verb+\subseteq+ & $\subseteq$ &\verb+\in+ & $\in$\\
\verb+\supset+ & $\supset$ &\verb+\subsetneq+ & $\subsetneq$ &\verb+\ni+ & $\ni$\\
\verb+\subset+ & $\subset$ &\verb+\supseteq+ & $\supseteq$ &\verb+\notin+ & $\notin$\\

        \bottomrule
    \end{tabular}

    \caption{18 set related symbols of \dbName.}
    \label{table:symbols-of-db-8}
\end{table}
\clearpage