\sectiontitle{Control Sequences used in Mathematics (Plain \TeX)}
\label{pl-mthcs}

\subsectiontitle{Font Changes, Accents and Standard Functions}
\appenditem{Changing Fonts in Mathematical Expressions}
Fonts are changed using suitable control sequences.
\begin{quote}
\begin{tabular}{ll}
\verb?\mit? changes to the `math italic' font: & $\mit Math Italic$\\
\verb?\rm? changes to the roman font:          & $\rm Roman$\\
\verb?\sl? changes to a slanted roman font:    & $\sl Slanted$\\
\verb?\it? changes to an italic font:          & $\it Italic$\\
\verb?\tt? changes to an ``typewriter'' font:  & $\tt Typewriter$\\
\verb?\bf? changes to a boldface font:         & $\bf Boldface$\\
\verb?\cal? changes to a calligraphic font:    & $\cal CALLIGRAPHIC$
\end{tabular}
\end{quote}
The default font for mathematics is $Math Italic$.  The
$\cal CALLIGRAPHIC$ font is only available for uppercase letters.
Any change of font made within a group enclosed within curly
brackets \verb?{? and \verb?}? will only apply to text within
that group.  On leaving the group, the current font is restored
to what it was before entering the group.

\appenditem{Accents in Mathematics Mode}
Accents in mathematics mode are produced using appropriate
control sequences.  The effect of these on the letter $a$ is
exhibited in the following table.
\begin{quote}
\begin{tabular}{ll}
\verb?$\underline{a}$? & $\underline{a}$\\
\verb?$\overline{a}$?  & $\overline{a}$\\
\verb?$\hat{a}$?       & $\hat{a}$\\
\verb?$\check{a}$?     & $\check{a}$\\
\verb?$\tilde{a}$?     & $\tilde{a}$\\
\verb?$\acute{a}$?     & $\acute{a}$\\
\verb?$\grave{a}$?     & $\grave{a}$\\
\verb?$\dot{a}$?       & $\dot{a}$\\
\verb?$\ddot{a}$?      & $\ddot{a}$\\
\verb?$\breve{a}$?     & $\breve{a}$\\
\verb?$\bar{a}$?       & $\bar{a}$\\
\verb?$\vec{a}$?       & $\vec{a}$
\end{tabular}
\end{quote}
These control sequences should only be used for mathematics,
not for ordinary text.

You should bear in  mind that when a character is underlined in
a mathematical manuscript then it is normally typeset in
bold face without any underlining. Underlining is used very
rarely in print.

\appenditem{Standard Functions}
The names of certain standard functions and abbreviations are
obtained by typing a backlash \verb?\? before the name. The
complete list in \TeX\ is as follows:-

$$\vcenter{\halign{$\backslash${\tt #}&&\quad $\backslash${\tt #}\cr
arccos&cos&csc&exp&ker&limsup&min&sinh\cr
arcsin&cosh&deg&gcd&lg&ln&Pr&sup\cr
arctan&cot&det&hom&lim&log&sec&tan\cr
arg&coth&dim&inf&liminf&max&sin&tanh\cr}}$$


\def\displayandname#1{\rlap{$\displaystyle\csname #1\endcsname$}%
                      \qquad {\tt \char92 #1}}
\def\mathlexicon#1{$$\vcenter{\halign{\displayandname{##}\hfil&&\qquad
                   \displayandname{##}\hfil\cr #1}}$$}

\subsectiontitle{Control Sequences for Mathematical Symbols}
\appenditem{Lowercase Greek Letters}
\mathlexicon{alpha&iota&varrho\cr
beta&kappa&sigma\cr
gamma&lambda&varsigma\cr
delta&mu&tau\cr
epsilon&nu&upsilon\cr
varepsilon&xi&phi\cr
zeta&\omit\qquad \rlap{$o$}\qquad {\tt o}\hfil&varphi\cr
eta&pi&chi\cr
theta&varpi&psi\cr
vartheta&rho&omega\cr}

\appenditem{Uppercase Greek Letters}
\mathlexicon{Gamma&Xi&Phi\cr
Delta&Pi&Psi\cr
Theta&Sigma&Omega\cr
Lambda&Upsilon&\omit\hfil\cr}

\appenditem{Miscellaneous Symbols}
\mathlexicon{aleph&prime&forall\cr
hbar&emptyset&exists\cr
imath&nabla&neg\cr
jmath&surd&flat\cr
ell&top&natural\cr
wp&bot&sharp\cr
Re&|&clubsuit\cr
Im&angle&diamondsuit\cr
partial&triangle&heartsuit\cr
infty&backslash&spadesuit\cr}

\appenditem{``Large'' Operators}
\mathlexicon{sum&bigcap&bigodot\cr
prod&bigcup&bigotimes\cr
coprod&bigsqcup&bigoplus\cr
int&bigvee&biguplus\cr
oint&bigwedge&\omit\hfil\cr}

\appenditem{Binary Operations}
\mathlexicon{pm&cap&vee\cr
mp&cup&wedge\cr
setminus&uplus&oplus\cr
cdot&sqcap&ominus\cr
times&sqcup&otimes\cr
ast&triangleleft&oslash\cr
star&triangleright&odot\cr
diamond&wr&dagger\cr
circ&bigcirc&ddagger\cr
bullet&bigtriangleup&amalg\cr
div&bigtriangledown&\omit\hfil\cr}

\appenditem{Relations}
\mathlexicon{leq&geq&equiv\cr
prec&succ&sim\cr
preceq&succeq&simeq\cr
ll&gg&asymp\cr
subset&supset&approx\cr
subseteq&supseteq&cong\cr
sqsubseteq&sqsupseteq&bowtie\cr
in&ni&propto\cr
vdash&dashv&models\cr
smile&mid&doteq\cr
frown&parallel&perp\cr}

\appenditem{Negated Relations}
\def\negdisplayandname#1{\rlap{$\displaystyle\not\csname #1\endcsname$}%
\qquad {\tt \char92 not\char92 #1}}
$$\vcenter{\halign{\negdisplayandname{#}\hfil&&\qquad
        \negdisplayandname{#}\hfil\cr
\omit\rlap{$\not<$}\qquad{\tt \char92 not<}\hfil&\omit
\qquad\rlap{$\not>$}\qquad{\tt \char92 not>}\hfil&\omit
\qquad\rlap{$\not=$}\qquad{\tt \char92 not=}\hfil\cr
leq&geq&equiv\cr
prec&succ&sim\cr
preceq&succeq&simeq\cr
subset&supset&approx\cr
subseteq&supseteq&cong\cr
sqsubseteq&sqsupseteq&asymp\cr}}$$

\appenditem{Arrows}
\mathlexicon{leftarrow&longleftarrow&uparrow\cr
Leftarrow&Longleftarrow&Uparrow\cr
rightarrow&longrightarrow&downarrow\cr
Rightarrow&Longrightarrow&Downarrow\cr
leftrightarrow&longleftrightarrow&updownarrow\cr
Leftrightarrow&Longleftrightarrow&Updownarrow\cr
mapsto&longmapsto&nearrow\cr
hookleftarrow&hookrightarrow&searrow\cr
leftharpoonup&rightharpoonup&swarrow\cr
leftharpoondown&rightharpoondown&nwarrow\cr
rightleftharpoons&\omit\hfil&\omit\hfil\cr}

\appenditem{Openings}
\mathlexicon{lbrack&lfloor&lciel\cr
lbrace&langle&\omit\hfil\cr}

\appenditem{Closings}
\mathlexicon{rbrack&rfloor&rciel\cr
rbrace&rangle&\omit\hfil\cr}

\appenditem{Alternative Names}
$$\vcenter{\halign{\displayandname{#}\hfil&\qquad
(same as {\tt \char92 #})\hfil\cr
\omit\rlap{$\not=$}\qquad
      {\tt  \char92 ne} or {\tt \char92 neq}\hfil&not=\cr
le&leq\cr
ge&geq\cr
\omit\rlap{$\{$}\qquad{\tt \char92 \char123}\hfil&lbrace\cr
\omit\rlap{$\}$}\qquad{\tt \char92 \char125}\hfil&lbrace\cr
to&rightarrow\cr
gets&leftarrow\cr
owns&ni\cr
land&wedge\cr
lor&vee\cr
lnot&neg\cr
vert&\omit\qquad (same as {\tt |})\hfil\cr
Vert&\omit\qquad (same as {\tt \char92 |})\hfil\cr
iff&\omit\qquad (same as {\tt \char92 Longleftrightarrow}, but with\hfil\cr
\omit\hfil&\omit\qquad\ extra space at each end)\hfil\cr
colon&\omit\qquad (same as {\tt :}, but with less space around it and\hfil\cr
\omit\hfil&\omit
\qquad\ less likelihood of a line break after it)\hfil\cr}}$$

\subsectiontitle{Some frequently used Control Sequences of Plain \TeX}
We list some of the control sequences of Plain \TeX\ that are
frequently used when typesetting mathematical formulae.  The
list is by no means exhaustive.  For information on how to
apply these control sequences, consult the appropriate
manual (e.g. `The \TeX book').
\begin{quote}
\begin{tabular}{ll}
\verb?\over?          & produces fractions \\
\verb?\sqrt?          & produces square roots \\
\verb?\root?          & produces $n$th roots \\
\verb?\left?          & produces left delimiter of required size \\
\verb?\right?         & produces right delimiter of required size \\
\verb?\quad?          & produces a `quad' of blank space \\
\verb?\qquad?         & produces two `quads' of blank space \\
\verb?\,?             & produces a thin space \\
\verb?\!?             & removes a thin space \\
\verb?\hbox?          & creates a box of text within mathematics \\
\verb?\eqalign?       & creates a multiline formula \\
\verb?\eqalignno?     & creates a numbered multiline formula \\
\verb?\leqalignno?    & creates a multiline formula numbered on the left \\
\verb?\cases?         & creates an equation that splits into cases \\
\verb?\matrix?        & produces an array \\
\verb?\pmatrix?       & produces a matrix surrounded by parentheses
\end{tabular}
\end{quote}