% hangulmath-doc.tex -- documentation for the hangulmath package % Copyright (C) 2026 Inkyu Park % LaTeX Project Public License 1.3c or later. % % Compile with: xelatex hangulmath-doc (twice) % Requires the Noto Serif CJK KR font for the Korean prose. \documentclass[11pt,a4paper]{article} \usepackage[margin=28mm]{geometry} \usepackage{amsmath,amssymb} \usepackage{hangulmath} \usepackage{array,booktabs,longtable} \usepackage{xcolor} \usepackage[hidelinks]{hyperref} \newfontfamily\koreanfont{Noto Serif CJK KR}[Scale=MatchLowercase] \newcommand\cs[1]{\texttt{\textbackslash#1}} \newcommand\meta[1]{\ensuremath{\langle}\textrm{\itshape#1}\ensuremath{\rangle}} \newcommand\marg[1]{\texttt{\{}\meta{#1}\texttt{\}}} \newcommand\ko[1]{{\koreanfont #1}} \newenvironment{koreanpar} {\par\koreanfont\sloppy\linespread{1.35}\selectfont}{\par} \newenvironment{preface}[1] {\begin{quote}\setlength\parindent{0pt}\setlength\parskip{0.6ex}% #1\linespread{1.3}\selectfont} {\end{quote}} \newenvironment{example} {\par\medskip\noindent\begin{minipage}{\linewidth}\small} {\end{minipage}\par\medskip} \setlength\parindent{0pt} \setlength\parskip{0.6ex} \title{\textsf{hangulmath}\\[0.5ex] \large Hangul jamo as mathematical symbols} \author{Inkyu Park \\ \texttt{icpark00@gmail.com}} \date{Version 0.5 \quad 2026/10/10} \begin{document} \maketitle \begin{center} {\LARGE\koreanfont 訓民正號}\\[0.5ex] {\large\koreanfont 훈민정호 \textrm{---} 백성을 가르치는 바른 기호}\\[0.3ex] {\itshape The Correct Symbols for the Instruction of the People} \end{center} \begin{preface}{\koreanfont\sloppy} 수식의 기호가 로마와 희랍의 글자에만 머물러 그 수가 넉넉지 아니하니, 이런 까닭으로 어리석은 수학자가 적고자 하는 바가 있어도 마침내 제 뜻을 수식에 실어 펴지 못하는 이가 많으니라. 내 이를 위하여 어여삐 여겨 새로 마흔 자를 수식에 들이노니, 자음 열아홉과 모음 스물하나라. \[ \#\{\giug,\ \niun,\ \diud,\ \dots,\ \uih,\ \euih\} = 19 + 21 = 40 \] 사람마다 쉬이 익혀 날마다 수식을 씀에 편안케 하고자 할 따름이니라. \hfill 병오년(2026) 한글날 \end{preface} \begin{preface}{} Because the symbols of mathematics dwell only among the letters of Rome and of Greece, they are not sufficient in number; and for this cause there be many a humble mathematician who, having something he would set down, can never at the last express his meaning in a formula. Taking pity upon them, I have newly brought forty letters into mathematics: nineteen consonants and twenty-one vowels. \[ \#\{\giug,\ \niun,\ \diud,\ \dots,\ \uih,\ \euih\} = 19 + 21 = 40 \] I desire only that every person may learn them with ease, and use them in comfort day by day. \hfill \textit{Given on Hangul Day, in the year 2026} \end{preface} \clearpage \tableofcontents \clearpage % =================================================================== \section{Introduction} Mathematical notation draws almost entirely on the Latin and Greek alphabets, and in a long paper one easily runs out of distinct letters. The Korean alphabet, Hangul, offers a clean supply of new symbols: its letters (\emph{jamo}) are built from simple geometric strokes, are visually distinct from Latin and Greek, and each has a well-established name. The \textsf{hangulmath} package makes the 40 jamo of modern Hangul available in mathematics: 14 basic consonants, 5 double consonants, 10 basic vowels and 11 compound vowels. Each symbol has a command named after the letter, so $\giyeok$ is \cs{giyeok}, much as $\alpha$ is \cs{alpha}. Consonants also have a four-letter alias that is easy to remember (\cs{giug}). \begin{example} \[ \hangulsum\tiut_{k=1}^{n} \giug_k^{\,2} \;\le\; \Bigl(\hangulsum\tiut_{k=1}^{n} \giug_k\Bigr)^{2}, \qquad \mium^2 \vec{A} = -\mu_0 \vec{J}, \qquad \hangullim\liul_{x\to\infty} f(x) = b. \] \end{example} The symbols are taken from a bundled subset of the Noto Sans CJK KR typeface, so no Korean font needs to be installed. % =================================================================== \section{Requirements and installation} \textsf{hangulmath} requires \textbf{XeLaTeX or LuaLaTeX} (it uses \textsf{fontspec}) and a LaTeX kernel from 2022 or later. It does not work with pdfLaTeX; the package stops with an error if loaded there. \paragraph{TeX Live and MiKTeX.} Once the package is distributed via CTAN it is installed with the usual package manager (\texttt{tlmgr install hangulmath}, or automatically by MiKTeX). \paragraph{Manual installation.} Copy the following files into the directory of your document, or into your local \texttt{texmf} tree (\texttt{tex/latex/hangulmath/} and \texttt{fonts/opentype/public/hangulmath/}), then run \texttt{mktexlsr} if appropriate: \begin{quote}\ttfamily hangulmath.sty\\ hangulmath-metrics.def\\ hangulmath-sans.otf\\ hangulmath-sans-light.otf \end{quote} \paragraph{Overleaf.} Upload the four files above into your project and set the compiler to XeLaTeX (\emph{Menu} $\to$ \emph{Compiler}), or add a file \texttt{latexmkrc} containing \verb|$pdf_mode = 5;|. % =================================================================== \section{Usage} \begin{verbatim} \usepackage{hangulmath} ... $\giyeok + \nieun = \digeut$ or, with aliases, $\giug + \niun = \diud$ \end{verbatim} Every symbol command works in math mode and also in running text (it uses \cs{ensuremath}). The symbols are ordinary math symbols (\cs{mathord}): they take sub- and superscripts and scale correctly in script styles. They are always set upright, whatever the surrounding text font. \begin{example} \verb|$\giug_{\ah}(x)$, $\niun^{\ih j}$, $X\giug x\niun$| \hfill $\giug_{\ah}(x)$, $\niun^{\ih j}$, $X\giug x\niun$ \end{example} \subsection{Package options} \begin{longtable}{@{}>{\ttfamily}l p{0.62\linewidth}@{}} \toprule option & meaning\\ \midrule font=\meta{font} & Font for the symbols, given by name or file name. Default: the bundled \texttt{hangulmath-sans.otf} (HangulMath Sans DemiLight).\\ opfont=\meta{font} & Font for the large operator forms (Section~\ref{sec:operators}). Default: the bundled, lighter \texttt{hangulmath-sans-light.otf}.\\ metrics=\meta{file} & Name (without \texttt{.def}) of the metrics file that describes the glyphs of \texttt{font}. Default: \texttt{hangulmath-metrics}, which matches the bundled font. See Section~\ref{sec:fonts}.\\ scale=\meta{number} & Scale factor for the symbol font. Default: taken from the metrics file (about 1.24 for the bundled font).\\ sidebearing=\meta{em} & Space, in em, added to the left and right of each glyph. Default: \texttt{0.06}.\\ \bottomrule \end{longtable} If a requested font is not installed, \textsf{hangulmath} issues a warning and uses the bundled font instead, so that documents always compile. % =================================================================== \section{The symbols} \subsection{Naming rules} \begin{itemize} \item \textbf{Official names} follow the Revised Romanization of Korean: \cs{giyeok}, \cs{nieun}, \dots, \cs{ssanggiyeok}. \item \textbf{Consonant aliases} have four letters: the consonant, \texttt{iu}, and the consonant again, imitating the shape of the Korean letter names (\ko{기역} $\to$ \cs{giug}, \ko{니은} $\to$ \cs{niun}). Their first letters are all different, so the first letter alone identifies the consonant. Two adjustments are needed: \ko{ㅇ} has no initial sound and is \cs{iung}; \ko{ㅊ} is written with \texttt{c} to keep four letters, \cs{ciuc}. \ko{ㄹ} uses \texttt{l}, its sound at the end of a syllable. \item \textbf{Double consonants} double the first letter of the alias: \cs{ggiug}, \cs{ddiud}, \cs{bbiub}, \cs{ssius}, \cs{jjiuj}. \item \textbf{Vowels} are written as pronounced, followed by \texttt{h}: \cs{ah}, \cs{eoh}, \cs{ih}. The trailing \texttt{h} avoids clashes with existing commands such as \cs{a}, \cs{o}, \cs{u} and \cs{i}. In compound vowels the glide \emph{w} is written \texttt{u} (\cs{uah} for \ko{ㅘ}). \ko{ㅢ} is \cs{euih} (\ko{ㅡ}+\ko{ㅣ}) to distinguish it from \ko{ㅟ}, \cs{uih}. \end{itemize} \subsection{Consonants} \noindent\begin{minipage}[t]{0.49\linewidth} \begin{tabular}{@{}c>{\ttfamily}l>{\ttfamily}l>{\ttfamily\small}l@{}} \toprule & official & alias & Unicode\\ \midrule $\giyeok$ & \textbackslash giyeok & \textbackslash giug & U+3131\\ $\nieun$ & \textbackslash nieun & \textbackslash niun & U+3134\\ $\digeut$ & \textbackslash digeut & \textbackslash diud & U+3137\\ $\rieul$ & \textbackslash rieul & \textbackslash liul & U+3139\\ $\mieum$ & \textbackslash mieum & \textbackslash mium & U+3141\\ $\bieup$ & \textbackslash bieup & \textbackslash biub & U+3142\\ $\siot$ & \textbackslash siot & \textbackslash sius & U+3145\\ \bottomrule \end{tabular} \end{minipage}\hfill \begin{minipage}[t]{0.49\linewidth} \begin{tabular}{@{}c>{\ttfamily}l>{\ttfamily}l>{\ttfamily\small}l@{}} \toprule & official & alias & Unicode\\ \midrule $\ieung$ & \textbackslash ieung & \textbackslash iung & U+3147\\ $\jieut$ & \textbackslash jieut & \textbackslash jiuj & U+3148\\ $\chieut$ & \textbackslash chieut & \textbackslash ciuc & U+314A\\ $\kieuk$ & \textbackslash kieuk & \textbackslash kiuk & U+314B\\ $\tieut$ & \textbackslash tieut & \textbackslash tiut & U+314C\\ $\pieup$ & \textbackslash pieup & \textbackslash piup & U+314D\\ $\hieut$ & \textbackslash hieut & \textbackslash hiuh & U+314E\\ \bottomrule \end{tabular} \end{minipage} \subsection{Double consonants} \begin{tabular}{@{}c>{\ttfamily}l>{\ttfamily}l>{\ttfamily\small}l@{}} \toprule & official & alias & Unicode\\ \midrule $\ssanggiyeok$ & \textbackslash ssanggiyeok & \textbackslash ggiug & U+3132\\ $\ssangdigeut$ & \textbackslash ssangdigeut & \textbackslash ddiud & U+3138\\ $\ssangbieup$ & \textbackslash ssangbieup & \textbackslash bbiub & U+3143\\ $\ssangsiot$ & \textbackslash ssangsiot & \textbackslash ssius & U+3146\\ $\ssangjieut$ & \textbackslash ssangjieut & \textbackslash jjiuj & U+3149\\ \bottomrule \end{tabular} \subsection{Vowels and compound vowels} \noindent\begin{minipage}[t]{0.49\linewidth} \begin{tabular}{@{}c>{\ttfamily}l>{\ttfamily\small}l@{}} \toprule & command & Unicode\\ \midrule $\ah$ & \textbackslash ah & U+314F\\ $\yah$ & \textbackslash yah & U+3151\\ $\eoh$ & \textbackslash eoh & U+3153\\ $\yeoh$ & \textbackslash yeoh & U+3155\\ $\oh$ & \textbackslash oh & U+3157\\ $\yoh$ & \textbackslash yoh & U+315B\\ $\uh$ & \textbackslash uh & U+315C\\ $\yuh$ & \textbackslash yuh & U+3160\\ $\euh$ & \textbackslash euh & U+3161\\ $\ih$ & \textbackslash ih & U+3163\\ \bottomrule \end{tabular} \end{minipage}\hfill \begin{minipage}[t]{0.49\linewidth} \begin{tabular}{@{}c>{\ttfamily}l>{\ttfamily\small}l@{}} \toprule & command & Unicode\\ \midrule $\aeh$ & \textbackslash aeh & U+3150\\ $\yaeh$ & \textbackslash yaeh & U+3152\\ $\eh$ & \textbackslash eh & U+3154\\ $\yeh$ & \textbackslash yeh & U+3156\\ $\uah$ & \textbackslash uah & U+3158\\ $\uaeh$ & \textbackslash uaeh & U+3159\\ $\oeh$ & \textbackslash oeh & U+315A\\ $\ueoh$ & \textbackslash ueoh & U+315D\\ $\ueh$ & \textbackslash ueh & U+315E\\ $\uih$ & \textbackslash uih & U+315F\\ $\euih$ & \textbackslash euih & U+3162\\ \bottomrule \end{tabular} \end{minipage} % =================================================================== \section{Operator forms}\label{sec:operators} The symbol commands produce ordinary symbols. To use a symbol as an operator, wrap it in one of the following commands. They accept any math symbol, not only Hangul. \begin{longtable}{@{}>{\ttfamily}l p{0.62\linewidth}@{}} \toprule command & behaviour\\ \midrule \textbackslash hangulsum\{\meta{sym}\} & Large; in display style, limits below and above (like \cs{sum}).\\ \textbackslash hangulint\{\meta{sym}\} & Large; limits at the side (like \cs{int}).\\ \textbackslash hangullim\{\meta{sym}\} & Normal size; in display style, limits below (like \cs{lim}).\\ \textbackslash hangulopscale\{\meta{d}\}\{\meta{t}\} & Sets the magnification of the large forms in display and text style (defaults 2.0 and 1.3).\\ \bottomrule \end{longtable} The large forms are drawn with the lighter operator font (\texttt{opfont}), so that magnification does not make their strokes heavier than those of \cs{sum} and \cs{int}. \begin{example} \begin{verbatim} \[ \hangulsum\tiut_{k=1}^{n} k^2 = \frac{n(n+1)(2n+1)}{6} \] \end{verbatim} \[ \hangulsum\tiut_{k=1}^{n} k^2 = \frac{n(n+1)(2n+1)}{6}, \qquad \hangulsum\tiut_{i=1}^{m}\hangulsum\tiut_{j=1}^{n} a_{ij} \quad\text{vs.}\quad \sum_{i=1}^{m}\sum_{j=1}^{n} a_{ij} \] Inline: $\hangulsum\tiut_{k=1}^{n} \giug_k = \sum_{k=1}^{n} \giug_k$. \end{example} \begin{example} \begin{verbatim} \[ \hangulint\diud_{x=0}^{x=1} f(x) = a \qquad \hangullim\liul_{x\to\infty} f(x) = b \] \end{verbatim} \[ \hangulint\diud_{x=0}^{x=1} f(x) = a \qquad \hangullim\liul_{x\to\infty} f(x) = b \qquad \hangullim\liul_{n\to\infty}\Bigl(1+\frac{1}{n}\Bigr)^{n} = e \] \end{example} % =================================================================== \section{More examples} \paragraph{\cs{mium} as the d'Alembertian.} The shape of $\mieum$ suggests the box operator. \begin{example} \begin{verbatim} \mium^2 \equiv \nabla^2 - \mu_0\epsilon_0 \frac{\partial^2}{\partial t^2}, \qquad \mium^2 \vec{A} = -\mu_0 \vec{J} \end{verbatim} \[ \mium^2 \equiv \nabla^2 - \mu_0 \epsilon_0 \frac{\partial^2}{\partial t^2}, \qquad \mium^2 \vec{A} = -\mu_0 \vec{J} \] \end{example} \paragraph{Pre- and post-scripts.} Like any ordinary symbol, a jamo can carry scripts on both sides, for instance in a hypergeometric-style notation. \begin{example} \begin{verbatim} {}_{123}\biub_{45}, \qquad {}_{2}\biub_{1}(a,b;c;z), \qquad {}^{\ih}_{\ah}\biub^{\uh}_{\oh} \end{verbatim} \[ {}_{123}\biub_{45}, \qquad {}_{2}\biub_{1}(a,b;c;z), \qquad {}^{\ih}_{\ah}\biub^{\uh}_{\oh} \] \end{example} \paragraph{Mixed with Latin and Greek.} Jamo combine freely with other symbols. \begin{example} \[ \giug_{\ah}(x) = \sum_{\niun=0}^{\infty} \frac{\diud^{\niun}}{\niun!}\, x^{\liul_{\ih}}, \qquad \alpha\giug\beta\niun\gamma, \qquad \ssius_{\uah} + \ggiug^{\euih} \] \end{example} % =================================================================== \section{Using other fonts}\label{sec:fonts} Hangul compatibility jamo are drawn small and high in the em square of most Korean fonts, with large side bearings. \textsf{hangulmath} therefore scales all glyphs by a common factor, lowers them by a common amount so that consonants sit on the baseline, and trims each glyph to its ink. These values depend on the font and are stored in a metrics file. To use another font, generate a metrics file with the Python script \texttt{hangulmath-metrics.py} (Python 3.10+, \texttt{pip install fonttools}): \begin{verbatim} python3 hangulmath-metrics.py "Nanum Gothic" -o nanum.def \end{verbatim} and load it together with the font: \begin{verbatim} \usepackage[font={Nanum Gothic}, metrics=nanum]{hangulmath} \end{verbatim} \cs{hangulmathfont}\marg{font} and \cs{hangulmathopfont}\marg{font} change the fonts later in the preamble. % =================================================================== \section{Caveats} \begin{itemize} \item \textbf{Look-alikes.} $\euh$ resembles a minus sign and $\ih$ a vertical bar. Use them with care, and say in the text which letter you mean. \item \textbf{Engines.} pdfLaTeX is not supported. Check whether your publisher or preprint server compiles with XeLaTeX or LuaLaTeX before relying on the package for a submission. \item \textbf{Searchability.} The symbols are real Unicode characters in the PDF, so they can be copied and searched. \end{itemize} % =================================================================== \section{Korean summary \ko{(한국어 요약)}} \begin{koreanpar} hangulmath는 현대 한글 자모 40자(기본 자음 14, 쌍자음 5, 기본 모음 10, 복모음 11)를 수식 기호로 쓸 수 있게 하는 패키지입니다. XeLaTeX 또는 LuaLaTeX에서 동작하며, 기호용 고딕체 글꼴이 함께 들어 있어 따로 한글 글꼴을 설치할 필요가 없습니다. 명령어는 로마자 표기법에 따른 공식 이름(\cs{giyeok})과 외우기 쉬운 네 글자 약어(\cs{giug})가 있습니다. 약어는 자음, iu, 자음의 순서이며, 쌍자음은 첫 글자를 두 번 씁니다(\cs{ggiug}). 모음은 소리 나는 대로 쓰고 끝에 h를 붙입니다(\cs{ah}, \cs{uah}). 합, 적분, 극한처럼 쓰려면 \cs{hangulsum}, \cs{hangulint}, \cs{hangullim}으로 감쌉니다. \begin{center}\verb|\hangulsum\tiut_{k=1}^{n} a_k|\quad $\Rightarrow$\quad $\displaystyle\hangulsum\tiut_{k=1}^{n} a_k$\end{center} \end{koreanpar} % =================================================================== \section{License} Copyright \copyright\ 2026 Inkyu Park. The package files may be distributed and/or modified under the conditions of the \LaTeX\ Project Public License, version 1.3c or (at your option) any later version. The bundled fonts \texttt{hangulmath-sans.otf} and \texttt{hangulmath-sans-light.otf} are modified (subset and renamed) versions of Noto Sans CJK KR, copyright 2014--2021 Adobe, and are distributed under the SIL Open Font License 1.1; see \texttt{OFL.txt}. They are rebuilt with \texttt{hangulmath-fonts.py}. \section{Change history} \begin{description} \item[v0.5 (2026/10/10)] First public release. \end{description} \end{document}