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okicmd.tex
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% !TEX encoding = UTF-8 Unicode
% !TEX root = okicmd.tex
% !TEX spellcheck = en-US
% !TEX TS-program = latexmk
\documentclass[11pt,a4paper]{article}
% Margin
\usepackage[margin=1truein]{geometry}
% Fonts
\usepackage{lmodern}
\usepackage[T1]{fontenc}
\usepackage{textcomp}
% hyperref
\usepackage[bookmarksnumbered,pdfdisplaydoctitle,pdfusetitle]{hyperref}
% Tables
\usepackage{booktabs}
\usepackage{tablefootnote}
% Code execution and highlight
\usepackage{cnltx-example}
\newsourcecodeenv{cnltxexample}
\let\example\relax
\let\endexample\relax
% Misc
\usepackage{comment}
% okicmd
\usepackage{okicmd}
\usepackage{okithm}
\title{The \pkg*{okicmd} and \pkg*{okithm} Packages}
\author{Taihei Oki}
\begin{document}
\maketitle
\section{The \pkg*{okicmd} Package}
\subsection{Options}
Options can be passed as \cs{usepackage}\Oarg{\option{option1},\option{option2}}\Marg{okicmd}.
\begin{center}
\begin{tabular}{lcl} \toprule
Option name & Default? & Description \\\midrule
\option{loadams} & \checkmark & Load the \pkg*{amsmath} and \pkg*{amssymb} packages. \\
\option{noloadams} & & Stop loading the \pkg*{amsmath} and \pkg*{amssymb} packages. \\
\option{argminspace} & \checkmark & Make short spaces after ``arg'' in \cs{argmin} and \cs{argmax}. \\
\option{noargminspace} & & Stop making short spaces after ``arg'' in \cs{argmin} and \cs{argmax}. \\
\bottomrule
\end{tabular}
\end{center}
\subsection{Letters}
\begin{center}
\begin{tabular}{lcl} \toprule
\multicolumn{1}{c}{Input} & Output & \multicolumn{1}{c}{\LaTeX\ equivalent} \\\midrule
\code{l} & $l$ & \cs{ell} \\
\cs{ell} & $\ell$ & \code{l} \\
\cs{epsilon} & $\epsilon$ & \cs{varepsilon} \\
\cs{varepsilon} & $\varepsilon$ & \cs{epsilon} \\
\cs{phi} & $\phi$ & \cs{varphi} \\
\cs{varphi} & $\varphi$ & \cs{phi} \\
\bottomrule
\end{tabular}
\end{center}
\subsection{Parentheses}
Possible size options are \cs{normal}, \cs{big}, \cs{Big}, \cs{bigg}, and \cs{Bigg}.
If no size option is passed, parentheses' size is adjusted automatically by \cs{left} and \cs{right}.
\begin{center}
\begin{tabular}{lcl} \toprule
\multicolumn{1}{c}{Input} & Output & \multicolumn{1}{c}{\LaTeX\ (almost) equivalent} \\\midrule
\cs{prn}\Marg{\cs{cdot}} & $\prn{\cdot}$ & \code{\cs{left}(\cs{cdot}\cs{right})} \\
\cs{prn}\Oarg{\cs{normal}}\Marg{\cs{cdot}} & $\prn[\normal]{\cdot}$ & \code{(\cs{cdot})} \\
\cs{prn}\Oarg{\cs{big}}\Marg{\cs{cdot}} & $\prn[\big]{\cdot}$ & \code{\cs{bigl}(\cs{cdot}\cs{bigr})} \\
\cs{prn}\Oarg{\cs{Big}}\Marg{\cs{cdot}} & $\prn[\Big]{\cdot}$ & \code{\cs{Bigl}(\cs{cdot}\cs{Bigr})} \\
\cs{prn}\Oarg{\cs{bigg}}\Marg{\cs{cdot}} & $\prn[\bigg]{\cdot}$ & \code{\cs{biggl}(\cs{cdot}\cs{biggr})} \\
\cs{prn}\Oarg{\cs{Bigg}}\Marg{\cs{cdot}} & $\prn[\Bigg]{\cdot}$ & \code{\cs{Biggl}(\cs{cdot}\cs{Biggr})} \\
\cs{curl}\Marg{\cs{cdot}} & $\curl{\cdot}$ & \code{\cs{left}\cs{}\{\cs{cdot}\cs{right}\cs{}\}} \\
\cs{sqbr}\Marg{\cs{cdot}} & $\sqbr{\cdot}$ & \code{\cs{left}\lbrack\cs{cdot}\cs{right}\rbrack} \\
\cs{agbr}\Marg{\cs{cdot}} & $\agbr{\cdot}$ & \cs{left}\cs{langle}\cs{cdot}\cs{right}\cs{rangle} \\
\cs{dbbr}\Marg{\cs{cdot}} & $\dbbr{\cdot}$ & \cs{left}\cs{llbracket}\cs{cdot}\cs{right}\cs{rrbracket} \\
\cs{pipe}\Marg{\cs{cdot}} & $\pipe{\cdot}$ & \code{\cs{left}|\cs{cdot}\cs{right}|} \\
\cs{dbpp}\Marg{\cs{cdot}} & $\dbpp{\cdot}$ & \code{\cs{left}\cs{}|\cs{cdot}\cs{right}\cs{}|} \\
\cs{floor}\Marg{\cs{cdot}} & $\floor{\cdot}$ & \cs{left}\cs{lfloor}\cs{cdot}\cs{might}\cs{rfloor} \\
\cs{ceil}\Marg{\cs{cdot}} & $\ceil{\cdot}$ & \cs{left}\cs{lceil}\cs{cdot}\cs{right}\cs{rceil} \\
\cs{pprn}\Marg{\cs{cdot}} & $\pprn{\cdot}$ & \code{\cs{left}(\cs{left}(\cs{cdot}\cs{right})\cs{right})} \\
\cs{ccurl}\Marg{\cs{cdot}} & $\ccurl{\cdot}$ & \code{\cs{left}\cs{}\{\cs{left}\cs{}\{\cs{cdot}\cs{right}\cs{}\}\cs{right}\cs{}\}} \\
\cs{ssqbr}\Marg{\cs{cdot}} & $\ssqbr{\cdot}$ & \code{\cs{left}\lbrack\cs{left}\lbrack\cs{cdot}\cs{right}\rbrack\cs{right}\rbrack} \\
\cs{aagbr}\Marg{\cs{cdot}} & $\aagbr{\cdot}$ & \begin{tabular}[l]{@{}l@{}}\cs{left}\cs{langle}\cs{left}\cs{langle}\\\code{ \cs{cdot}\cs{right}\cs{rangle}\cs{right}\cs{rangle}}\end{tabular} \\
\bottomrule
\end{tabular}
\end{center}
\subsection{Logic}
\begin{center}
\begin{tabular}{lcl} \toprule
\multicolumn{1}{c}{Input} & Output & \multicolumn{1}{c}{\LaTeX\ equivalent} \\\midrule
\cs{bigland} & $\bigland$ & \cs{bigwedge} \\
\cs{biglor} & $\biglor$ & \cs{bigvee} \\
\code{a \cs{defeq} b} & $a \defeq b$ & \code{a \cs{coloneqq} b} \\
\code{a \cs{eqdef} b} & $b \eqdef a$ & \code{a \cs{eqqcolon} b} \\
\code{P \cs{defiff} Q} & $P \defiff Q$ & \code{P \cs{overset}\Marg{\cs{mathrm}\Marg{def}}\Marg{\cs{iff}} Q} \\
\bottomrule
\end{tabular}
\end{center}
\subsection{Sets}
\begin{center}
\begin{tabular}{lcl} \toprule
\multicolumn{1}{c}{Input} & Output & \multicolumn{1}{c}{\LaTeX\ (almost) equivalent} \\\midrule
\cs{set}\Marg{a, b, c} & $\set{a, b, c}$ & \code{\cs{left}\cs{\{}a, b, c\cs{\}}} \\
\cs{set}\Marg{a \cs{in} S}\Oarg{a\string^2 = 1} & $\set{a \in S}[a^2 = 1]$ & \begin{tabular}[l]{@{}l@{}}\code{\cs{left}\cs{\{}a \cs{in} S\cs{mathrel}\Marg{}\cs{middle}|}\\\code{ \cs{mathrel}\Marg{}a\string^2 = 1\cs{right}\cs{\}}}\end{tabular} \\ % chktex 44
\code{\cs{set}*\Marg{a}\Oarg{\string$a\string$ is odd}} & $\set*{a}[$a$ is odd]$ & \begin{tabular}[l]{@{}l@{}}\code{\cs{left}\cs{\{}a\cs{mathrel}\Marg{}\cs{middle}|}\\\code{ \cs{mathrel}\Marg{}\cs{text}\Marg{\string$a\string$ is odd}\cs{right}\cs{\}}}\end{tabular} \\ % chktex 44
\cs{card}\Marg{X} & $\card{X}$ & \code{\cs{left}|X\cs{right}|} \\
\code{X \cs{symdif} Y} & $X \symdif Y$ & \code{X \cs{mathbin}\Marg{\cs{triangle}} Y} \\
\cs{N} & $\N$ & \cs{mathbb}\Marg{N} \\
\cs{Z} & $\Z$ & \cs{mathbb}\Marg{Z} \\
\cs{Q} & $\Q$ & \cs{mathbb}\Marg{Q} \\
\cs{R} & $\R$ & \cs{mathbb}\Marg{R} \\
\cs{C} & $\C$ & \cs{mathbb}\Marg{C} \\
\cs{Zp} & $\Zp$ & \code{\cs{mathbb}\Marg{Z}\_\{\cs{ge}0\}} \\
\cs{Qp} & $\Qp$ & \code{\cs{mathbb}\Marg{Q}\_\{\cs{ge}0\}} \\
\cs{Rp} & $\Rp$ & \code{\cs{mathbb}\Marg{R}\_\{\cs{ge}0\}} \\
\cs{Npp} & $\Npp$ & \code{\cs{mathbb}\Marg{N}\_\{>0\}} \\
\cs{Zpp} & $\Zpp$ & \code{\cs{mathbb}\Marg{Z}\_\{>0\}} \\
\cs{Qpp} & $\Qpp$ & \code{\cs{mathbb}\Marg{Q}\_\{>0\}} \\
\cs{Rpp} & $\Rpp$ & \code{\cs{mathbb}\Marg{R}\_\{>0\}} \\
\cs{setH} & $\setH$ & \cs{mathbb}\Marg{H} \\
\cs{setF} & $\setF$ & \cs{mathbb}\Marg{F} \\
\cs{setK} & $\setK$ & \cs{mathbb}\Marg{K} \\
\bottomrule
\end{tabular}
\end{center}
\subsection{Maps}
\begin{center}
\begin{tabular}{lcl} \toprule
\multicolumn{1}{c}{Input} & Output & \multicolumn{1}{c}{\LaTeX\ (almost) equivalent} \\\midrule
\cs{doms}\Marg{X}\Marg{Y} & $\doms{X}{Y}$ & \code{\{X\}\cs{to}\{Y\}} \\
\cs{funcdoms}\Marg{f}\Marg{X}\Marg{Y} & $\funcdoms{f}{X}{Y}$ & \code{\{f\}\cs{vcentcolon}\{X\}\cs{to}\{Y\}} \\
\cs{restr}\Marg{f}\Marg{S} & $\restr{f}{S}$ & \code{\cs{left}.f\cs{right}|\_\{S\}} \\
\code{\cs{id}\_K} & $\id_K$ & \code{\cs{operatorname}\Marg{id}\_K} \\
\code{\cs{dom} f} & $\dom f$ & \code{\cs{operatorname}\Marg{dom} f} \\
\code{\cs{cod} f} & $\cod f$ & \code{\cs{operatorname}\Marg{cod} f} \\
\code{\cs{supp} f} & $\supp f$ & \code{\cs{operatorname}\Marg{supp} f} \\
\bottomrule
\end{tabular}
\end{center}
\subsection{Lattices}
\begin{center}
\begin{tabular}{lcl} \toprule
\multicolumn{1}{c}{Input} & Output & \multicolumn{1}{c}{\LaTeX\ equivalent} \\\midrule
\code{x \cs{meet} y} & $x \meet y$ & \code{x \cs{mathbin}\Marg{\cs{wedge}} y} \\
\code{x \cs{join} y} & $x \join y$ & \code{x \cs{mathbin}\Marg{\cs{vee}} y} \\
\cs{bigmeet} & $\bigmeet$ & \cs{bigwedge} \\
\cs{bigjoin} & $\bigjoin$ & \cs{bigvee} \\
\bottomrule
\end{tabular}
\end{center}
\subsection{Algebra}
\begin{center}
\begin{tabular}{lcl} \toprule
\multicolumn{1}{c}{Input} & Output & \multicolumn{1}{c}{\LaTeX\ (almost) equivalent} \\\midrule
\cs{Hom}\Darg{G} & $\Hom(G)$ & \code{\cs{operatorname}\Marg{Hom}(G)} \\
\code{\cs{End} R} & $\End R$ & \code{\cs{operatorname}\Marg{End} R} \\
\code{\cs{Aut}\_k K} & $\Aut_k K$ & \code{\cs{operatorname}\Marg{Aut}\_k K} \\
\cs{gen}\Marg{a,b} & $\gen{a,b}$ & \code{\cs{left}\cs{langle}a,b\cs{right}\cs{rangle}} \\
\cs{gen}\Marg{a,b}\Oarg{ab = e} & $\gen{a,b}[ab = e]$ & \begin{tabular}[l]{@{}l@{}}\code{\cs{left}\cs{langle}a,b\cs{mathrel}\Marg{}\cs{middle}|}\\\code{ \cs{mathrel}\Marg{}ab = e\cs{right}\cs{rangle}}\end{tabular} \\ % chktex 44
\cs{abel}\Marg{G} & $\abel{G}$ & \code{G\_\{\cs{mathrm}\Marg{ab}\}} \\
\cs{comm}\Marg{G} & $\comm{G}$ & \code{\cs{left}\lbrack G, G\cs{right}\rbrack} \\
\code{\cs{ord} G} & $\ord G$ & \code{\cs{operatorname}\Marg{ord} G} \\
\code{\cs{sym}\_n} & $\sym_n$ & \code{\cs{mathfrak}\Marg{S}\_n} \\
\cs{sgn}\Darg{\cs{sigma}} & $\sgn(\sigma)$ & \code{\cs{operatorname}\Marg{sgn}(\cs{sigma})} \\
\cs{mult}\Marg{R} & $\mult{R}$ & \code{R\string^\{\cs{times}\}} \\
\code{\cs{M}\_\string{m,n\string}\Darg{R}} & $\M_{m,n}(R)$ & \code{\cs{operatorname}\Marg{M}\_\{m,n\}(R)} \\
\code{\cs{GL}\_n\Darg{R}} & $\GL_n(R)$ & \code{\cs{operatorname}\Marg{GL}\_n(R)} \\
\code{\cs{SL}\_n\Darg{R}} & $\SL_n(R)$ & \code{\cs{operatorname}\Marg{SL}\_n(R)} \\
\cs{O}\Darg{n} & $\O(n)$ & \code{\cs{operatorname}\Marg{O}(n)} \\
\cs{SO}\Darg{n} & $\SO(n)$ & \code{\cs{operatorname}\Marg{SO}(n)} \\
\cs{U}\Darg{n} & $\U(n)$ & \code{\cs{operatorname}\Marg{U}(n)} \\
\cs{SU}\Darg{n} & $\SU(n)$ & \code{\cs{operatorname}\Marg{SU}(n)} \\
\code{L \cs{extends} K} & $L \extends K$ & \code{L \cs{mathbin}\Marg{/} K} \\
\cs{ch}\Darg{K} & $\ch(K)$ & \code{\cs{operatorname}\Marg{ch}(K)} \\
\cs{GF}\Darg{2} & $\GF(2)$ & \code{\cs{operatorname}\Marg{GF}(2)} \\
\bottomrule
\end{tabular}
\end{center}
\subsection{Number Theory}
\begin{center}
\begin{tabular}{lcl} \toprule
\multicolumn{1}{c}{Input} & Output & \multicolumn{1}{c}{\LaTeX\ (almost) equivalent} \\\midrule
\cs{abs}\Marg{x} & $\abs{x}$ & \code{\cs{left}|x\cs{right}|} \\
\cs{intset}\Marg{n} & $\intset{n}$ & \code{\cs{left}\lbrack n\cs{right}\rbrack} \\
\code{a \cs{coprime} b} & $a \coprime b$ & \code{a \cs{mathrel}\Marg{\cs{bot}} b} \\
\code{a \cs{divides} b} & $a \divides b$ & \code{a \cs{mid} b} \\
\code{a \cs{ndivides} b} & $a \ndivides b$ & \code{a \cs{nmid} b} \\
\bottomrule
\end{tabular}
\end{center}
\subsection{Linear Algebra}
\begin{center}
\begin{tabular}{lcl} \toprule
\multicolumn{1}{c}{Input} & Output & \multicolumn{1}{c}{\LaTeX\ (almost) equivalent} \\\midrule
\code{\cs{tr} A} & $\tr A$ & \code{\cs{operatorname}\Marg{tr} A} \\
\code{\cs{rank} A} & $\rank A$ & \code{\cs{operatorname}\Marg{rank} A} \\
\code{\cs{trank} A} & $\trank A$ & \code{\cs{operatorname}\Marg{t-rank} A} \\
\code{\cs{Det} A} & $\Det A$ & \code{\cs{operatorname}\Marg{Det} A} \\
\code{\cs{Pf} A} & $\Pf A$ & \code{\cs{operatorname}\Marg{Pf} A} \\
\code{\cs{perm} A} & $\perm A$ & \code{\cs{operatorname}\Marg{perm} A} \\
\code{\cs{Hf} A} & $\Hf A$ & \code{\cs{operatorname}\Marg{Hf} A} \\
\cs{diag}\Darg{a\_1,\cs{dotsc},a\_n} & $\diag(a_1,\dotsc,a_n)$ & \begin{tabular}[l]{@{}l@{}}\code{\cs{operatorname}\Marg{diag}}\\\code{ (a\_1,\cs{dotsc},a\_n)}\end{tabular} \\
\cs{blockdiag}\Darg{A\_1,\cs{dotsc},A\_n} & $\blockdiag(A_1,\dotsc,A_n)$ & \begin{tabular}[l]{@{}l@{}}\code{\cs{operatorname}\Marg{block-diag}}\\\code{ (A\_1,\cs{dotsc},A\_n)}\end{tabular} \\
\cs{vectorize}\Darg{A} & $\vectorize(A)$ & \code{\cs{operatorname}\Marg{vectorize}(A)} \\
\cs{Row}\Darg{A} & $\Row(A)$ & \code{\cs{operatorname}\Marg{Row}(A)} \\
\cs{Col}\Darg{A} & $\Col(A)$ & \code{\cs{operatorname}\Marg{Col}(A)} \\
\cs{trsp}\Marg{A} & $\trsp{A}$ & \code{A\string^\cs{top}} \\
\cs{adjo}\Marg{A} & $\adjo{A}$ & \code{A\string^*} \\
\cs{ones} & $\ones$ & \code{\cs{mathds}\Marg{1}} \\
\cs{norm}\Marg{x} & $\norm{x}$ & \code{\cs{left}\cs{}|x\cs{right}\cs{}|} \\
\cs{inpr}\Marg{x}\Marg{y} & $\inpr{x}{y}$ & \begin{tabular}[l]{@{}l@{}}\code{\cs{left}\cs{langle}\{x\},\{y\}}\\\code{ \cs{right}\cs{rangle}}\end{tabular} \\
\bottomrule
\end{tabular}
\end{center}
\subsection{Analysis}
\begin{center}
\begin{tabular}{lcl} \toprule
\multicolumn{1}{c}{Input} & Output & \multicolumn{1}{c}{\LaTeX\ (almost) equivalent} \\\midrule
\cs{intoo}\Marg{a,b} & $\intoo{a,b}$ & \code{\cs{left}\lparen a,b\cs{right}\rparen} \\
\cs{intoc}\Marg{a,b} & $\intoc{a,b}$ & \code{\cs{left}\lparen a,b\cs{right}\rbrack} \\
\cs{intco}\Marg{a,b} & $\intco{a,b}$ & \code{\cs{left}\lbrack a,b\cs{right}\rparen} \\
\cs{intcc}\Marg{a,b} & $\intcc{a,b}$ & \code{\cs{left}\lbrack a,b\cs{right}\rbrack} \\
\cs{e} & $\e$ & \code{\cs{mathrm}\Marg{e}} \\
\cs{d} & $\d$ & \code{\cs{mathrm}\Marg{d}} \\
\cs{dif}\Marg{f}\Marg{x} & $\dif{f}{x}$ & \code{\cs{frac}\Marg{\cs{mathrm}\Marg{d} f}\Marg{\cs{mathrm}\Marg{d} x}} \\
\cs{pdif}\Marg{f}\Marg{x} & $\pdif{f}{x}$ & \code{\cs{frac}\Marg{\cs{partial} f}\Marg{\cs{partial} x}} \\
\cs{ddif}\Marg{f}\Marg{x} & $\ddif{f}{x}$ & \code{\cs{dfrac}\Marg{\cs{mathrm}\Marg{d} f}\Marg{\cs{mathrm}\Marg{d} x}} \\
\cs{dpdif}\Marg{f}\Marg{x} & $\dpdif{f}{x}$ & \code{\cs{dfrac}\Marg{\cs{partial} f}\Marg{\cs{partial} x}} \\
\bottomrule
\end{tabular}
\end{center}
\subsection{Complex Analysis}
\begin{center}
\begin{tabular}{lcl} \toprule
\multicolumn{1}{c}{Input} & Output & \multicolumn{1}{c}{\LaTeX\ equivalent} \\\midrule
\cs{i} & $\i$ & \code{\cs{mathrm}\Marg{i}} \\
\code{\cs{Re} z} & $\Re z$ & \code{\cs{operatorname}\Marg{Re} z} \\
\code{\cs{Im} z} & $\Im z$ & \code{\cs{operatorname}\Marg{Im} z} \\
\code{\cs{Arg} z} & $\Arg z$ & \code{\cs{operatorname}\Marg{Arg} z} \\
\code{\cs{Log} z} & $\Log z$ & \code{\cs{operatorname}\Marg{Log} z} \\
\code{\cs{Sin} z} & $\Sin z$ & \code{\cs{operatorname}\Marg{Sin} z} \\
\code{\cs{Cos} z} & $\Cos z$ & \code{\cs{operatorname}\Marg{Cos} z} \\
\code{\cs{Tan} z} & $\Tan z$ & \code{\cs{operatorname}\Marg{Tan} z} \\
\code{\cs{Res}\_\string{z=0\string} f\Darg{z}} & $\Res_{z=0} f(z)$ & \code{\cs{operatorname*}\Marg{Res}\_\{z=0\} f(z)} \\
\bottomrule
\end{tabular}
\end{center}
\subsection{Computer Science, Optimization}
Spaces after ``arg'' in \cs{argmin} and \cs{argmax} are omitted by passing the \option{noargminspace} option.
\begin{center}
\begin{tabular}{lcl} \toprule
\multicolumn{1}{c}{Input} & Output & \multicolumn{1}{c}{\LaTeX\ equivalent} \\\midrule
\code{\cs{argmin}\_\string{x \cs{in} S\string} f\Darg{x}} & $\argmin_{x \in S} f(x)$ & \begin{tabular}[l]{@{}l@{}}\code{\cs{operatorname*}\Marg{arg\string~min}}\\\code{ \_\{x \cs{in} S\} f(x)}\end{tabular} \\
\code{\cs{argmax}\_\string{x \cs{in} S\string} f\Darg{x}} & $\argmax_{x \in S} f(x)$ & \begin{tabular}[l]{@{}l@{}}\code{\cs{operatorname*}\Marg{arg\string~max}}\\\code{ \_\{x \cs{in} S\} f(x)}\end{tabular} \\
\cs{Order}\Darg{n} & $\Order(n)$ & \code{\cs{mathrm}\Marg{O}(n)} \\
\cs{order}\Darg{n} & $\order(n)$ & \code{\cs{mathrm}\Marg{o}(n)} \\
\cs{poly}\Darg{n} & $\poly(n)$ & \code{\cs{operatorname}\Marg{poly}(n)} \\
\cs{polylog}\Darg{n} & $\polylog(n)$ & \code{\cs{operatorname}\Marg{polylog}(n)} \\
\bottomrule
\end{tabular}
\end{center}
\section{The \pkg*{okithm} Package}
\subsection{Theorems}
If the language is set to Japanese like by \cs{usepackage}\Oarg{\keyis-{main}{japanese}}\Marg{\pkg{babel}}, \pkg{okithm} will translate all the environment titles (Theorem, Definition, etc.) into Japanese.
You can disable theorems by giving the option \option{notheorem} to \pkg{okicmd}.
\begin{cnltxexample}
\begin{theorem}[Awesome theorem]
The square root $\sqrt{2}$ of two is irrational.
\end{theorem}
\begin{definition}[Coprime]
Integers $a$ and $b$ are said to be \emph{coprime} if their greatest common divisor is one.
\end{definition}
\begin{lemma}
If $a$ and $b$ are coprime, so are $a^2$ and $b^2$.
\end{lemma}
\begin{proposition}
If $\sqrt{2} = a/b$, then $a^2 = 2b^2$.
\end{proposition}
\begin{corollary}
If $\sqrt{2} = a/b$ with $a$ and $b$ being coprime, then $a$ is even.
\end{corollary}
\begin{example}
If $a = 2$ and $b = 1$, then $a$ is even but $\sqrt{2} \ne a/b$.
\end{example}
\begin{remark}
Note that $a$ and $b$ must be integers.
\end{remark}
\begin{proof}[of Awesome theorem]
Suppose to the contrary that $\sqrt{2} = a/b$ with coprime $a$ and $b$.
Then both $a$ and $b$ are even, which contradicts the assumption.
\end{proof}
\end{cnltxexample}
\subsection{Algorithms}
You can disable algorithms by setting the option \option{noalgorithm}.
\begin{cnltxexample}
\begin{algorithmic}[1]
\Input{$n \in \N$}
\Output{$n(n+1)/2$}
\State{$s \gets 0$}
\ForTo{$i = 1$}{$n$}
\State{$s \gets s + i$}
\EndFor
\State{\Return $s$}
\end{algorithmic}
\end{cnltxexample}
\subsection{Optimization Problems}
You can change \texttt{minimize}, \texttt{maximize} and \texttt{subject to} into \texttt{min}, \texttt{max} and \texttt{s.t.}, respectively, by setting the option \keyis-{optstyle}{short}.
\begin{comment}
\begin{cnltxexample}
\Minimize[name={(P)}]{
\sum_{\condit{x \in S}[x^2 = 1]} w (x) + \sum_{i=1}^n (p_i + q_i)
}{
S \subseteq V, \\
p_i \ge 0 & (i = 1, \ldots, n), \\
q_i \ge 0 & (i = 1, \ldots, n)
}
\end{cnltxexample}
\end{comment}
\end{document}