% This is file `short-math-guide.tex'.
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% Copyright 1995-2017
% American Mathematical Society
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% conditions of the LaTeX Project Public License, either
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% later version. The latest version of this license is in
% http://www.latex-project.org/lppl.txt
% and version 1.3c or later is part of all distributions of LaTeX
% version 2005/12/01 or later.
%
% This file has the LPPL maintenance status "maintained".
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% The Current Maintainer of this work is the American Mathematical
% Society.
%
% Note: When updating, don't forget to update \smgversion, below
%%%
% ご覧の日本語訳は、もともとは私的目的で,上記の機関とは無関係につくりました.
% 内容の正確性については原文を確認してください.
%These Japanese translations were originally created for private purposes, regardless of the above organization.
%Please check the original about the accuracy of the contents.
%%%
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\end{filecontents}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\errorcontextlines=99
\documentclass{article}
\usepackage[dvipdfmx]{hyperref}
%
% for Japanese
\usepackage{pxjahyper}
\hypersetup{% hyperrefオプション
setpagesize=false,
bookmarksnumbered=true,%
bookmarksopen=true,%
colorlinks=true,%
linkcolor=blue,
pagecolor=cyan,
citecolor=green,
urlcolor=magenta,
}
%
\setlength{\parindent}{0.98em}
% end `for Japanese'
%
\pagestyle{myheadings}
%\usepackage{hthtml}
\usepackage{amsmath}
%\usepackage[cmex10]{amsmath}
\usepackage{amssymb}
\usepackage{mathrsfs}
%\usepackage[mathcal]{euscript}
\usepackage{euscript}
%\usepackage{mathtime}
%\usepackage{stmaryrd}
\numberwithin{equation}{section}
%% at the moment, using either url or hyperref crashes
%% get the content correct before debugging that problem
%\usepackage{url}
%\let\url\texttt
%\usepackage[breaklinks,colorlinks]{hyperref}
%\usepackage{xcolor}
%\definecolor{hycitecolor}{rgb}{0,0.65,0}
%
%
\usepackage{mathdoc}
\hoffset=-1 true in
\voffset=-1 true in
\topmargin=0.75 true in %% \oddsidemargin\topmargin
%\textwidth=210 true mm % A4
\textwidth=139 true mm
\textheight=11 true in \advance\textheight-2\topmargin
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\oddsidemargin=.5\oddsidemargin
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\hfuzz=14pt % suppress uninteresting warnings
\providecommand{\abs}[1]{\lvert#1\rvert}
\newcommand{\colhead}[1]{%
\textbf{\begin{tabular}[b]{@{}l@{}}#1\end{tabular}}%
}
%\newcommand{\secref}[1]{Section~\ref{#1}}
\newcommand{\secref}[1]{\ref{#1}節}
\newcommand{\tabref}[1]{Table~\ref{#1}}
\newcommand{\begend}[1]{%
\cn{begin}\texttt{\symbol{123}#1\symbol{125}}%
\ \dots\ \cn{end}\texttt{\symbol{123}#1\symbol{125}}%
}
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\begin{tabular}[#1]{@{}l@{}}%
}{%
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%%\newcommand{\lspx}{\mbox{\rule{5pt}{.6pt}\rule{.6pt}{6pt}}}
%%\newcommand{\rspx}{\mbox{\rule[-1pt]{.6pt}{7pt}%
%% \rule[-1pt]{5pt}{.6pt}}}
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%%\newcommand{\rspx}{\mathord{\odot}}
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\DeclareMathOperator{\esssup}{ess\,sup}
%\newcommand{\dotsref}{\leavevmode\unskip\space
% (see Section~\ref{dots})}
\newcommand{\dotsref}{\leavevmode\unskip\space
(\ref{dots}節をみてください)}
%\newcommand{\vertref}{\leavevmode\unskip\space
% (see Section~\ref{verts})}
\newcommand{\vertref}{\leavevmode\unskip\space
(\ref{verts}節をみてください)}
\providecommand{\pdfinfo}[1]{}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{document}
%\title{Short Math Guide for \LaTeX{}}
\title{はやわかり\LaTeX{}で数式組版}
\newcommand{\smgversion}{\textup{2.0 (2017/12/22)}}
%\markboth{Short Math Guide for \LaTeX{}, version \protect\smgversion}
% {Short Math Guide for \LaTeX{}, version \protect\smgversion}
\markboth{はやわかり\LaTeX{}で数式組版, version \protect\smgversion}
{はやわかり\LaTeX{}で数式組版, version \protect\smgversion}
\author{Michael Downes, updated by Barbara Beeton}
%\date{American Mathematical Society}
\date{アメリカ数学会}
\pdfinfo{
/Title (Short Math Guide for LaTeX)
/Author (Michael Downes, updated by Barbara Beeton)
/Subject (Short Math Guide for LaTeX)
/Keywords (LaTeX,amsmath,amsfonts,amssymb,equation,math,formula)
}
\maketitle
\begin{center}
%Version \smgversion, currently available from a link at
このドキュメントのバージョン\smgversion{}です.配布元は
%\mbox{\texttt{https://www.ams.org/tex/amslatex}}
\url{https://www.ams.org/tex/amslatex}\\
です.日本語訳は2018-09-04です.
\end{center}
%%\begin{rawhtml}
%%
%%Download a PDF version of this documentation.
%%
%%
%%\end{rawhtml}
\setcounter{tocdepth}{3}
\tableofcontents
\vspace{\fill}
%\section*{Acknowledgments and plans for future work}
%Thanks to all who contributed suggestions, assistance and encouragement.
%Special thanks to David Carlisle for repairing unruly macros and to
%Jennifer Wright Sharp for applying consistent editing in AMS style.
\section*{謝辞と将来の計画}
提案,援助,励ましなど貢献してくださったすべての人に感謝します.
難しいマクロを修復したDavid Carlisleと
AMSスタイルにしたがように編集してくれたJennifer Wright Sharp
に特別に感謝します.
\smallskip\noindent
%Plans for a future edition include addition of an index.
将来の版の計画には,索引の追加が含まれます.
\smallskip\noindent
%Reports concerning errors and suggestions for improvement should be
%sent to\\[2pt]
エラーに関する報告と改善のための提案は,
\hspace*{\fill}
%\href{mailto:tech-support@ams.org}{\texttt{tech-support@ams.org}}\,.
\href{mailto:tech-support@ams.org}{\texttt{tech-support@ams.org}}
に送ってください.
\hspace{\fill}\null
\newpage
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\section{Introduction}
\section{イントロダクション}
%This is a concise summary of recommended features in \LaTeX{} and a
%couple of extension packages for \textbf{writing math formulas}. Readers
%needing greater depth of detail are referred to the sources listed in
%the bibliography, especially \cite{lamport}, \cite{amsldoc}, and
%\cite{fntguide}. A certain amount of familiarity with standard \LaTeX{}
%terminology is assumed; if your memory needs refreshing on the \LaTeX{}
%meaning of \emph{command}, \emph{optional argument}, \emph{environment},
%\emph{package}, and so forth, see \cite{lamport}.
これは\LaTeX{}と
\textbf{数式のあるドキュメントを作成}するためのいくつかの拡張パッケージの,
お勧めの機能についての簡潔な要約です.
詳細な説明に関心がある読者は,
参考文献(Reference)の,特に\cite{lamport},\cite{amsldoc},そして
\cite{fntguide}をみてください.
普通の\LaTeX{}については,ある程度の経験があることを想定しています.
\LaTeX{}が使う,
\emph{コマンド},\emph{オプションの引数},\emph{環境},
\emph{パッケージ}などを思い出す必要があれば,\cite{lamport}を参照してください.
%Most of the features described here are available to you if you use
%\LaTeX{} with two extension packages published by the American Mathematical
%Society: \pkg{amssymb} and \pkg{amsmath}. Thus, the source file for this
%document begins with
ここで説明している機能のほんとんどは,
\LaTeX{}をアメリカ数学会が作成した2つの拡張パッケージ
\pkg{amssymb}と\pkg{amsmath}を読み込んで使用すれば,
利用できます.
したがって,このドキュメントのソースファイルは
\begin{verbatim}
\documentclass{article}
\usepackage{amssymb,amsmath}
\end{verbatim}
%The \pkg{amssymb} package might be omissible for documents whose math
%symbol usage is relatively modest; in \secref{mathsymbols}, the symbols
%that require \pkg{amssymb} are marked with \textsuperscript{a} or
%\textsuperscript{b} (font \fn{msam} or \fn{msbm}). In \secref{alpha-digit},
%a few additional fonts are included; the necessary packages are identified
%there.
で始まります.
数式や記号の使用量が比較的少ないドキュメントの場合,
\pkg{amssymb}パッケージは使わなくても良いでしょう.
\secref{mathsymbols}では,\pkg{amssymb}を必要とする記号に
\textsuperscript{a}または\textsuperscript{b}(それぞれ\fn{msam}フォントまたは\fn{msbm}フォント)
とマークされます.\secref{alpha-digit}には,いくつかの追加フォントが含まれています.
必要なパッケージがそこで示されています.
%Many noteworthy features found in other packages are not covered here;
%see \secref{other-packages}. Regarding math symbols, please note
%especially that the list given here is not intended to be comprehensive,
%but to illustrate such symbols as users will normally find already
%present in their \lat/ system and usable without installing any
%additional fonts or doing other setup work.
その他の便利な機能を提供するパッケージもありますが,このドキュメントでは扱いません.
それらについては\secref{other-packages}を参照してください.
数学記号については,特にここで紹介したリストは,すべてではなく,
ユーザーの\lat{}システムに普通に備わっているものです.
フォントを使うためにインストールしたり他の設定をしなくても使用できるような記号だけを
扱っています.
%If you have a need for a symbol not shown here, you will probably want
%to consult \emph{The Comprehensive \LaTeX{} Symbol List}~\cite{comprehensive}.
%%\[\url{http://www.ctan.org/tex-archive/info/symbols/comprehensive/}\]
%If your \lat/ installation is based on \TeX\,Live, and includes documentation,
%the list can also be accessed by typing \texttt{texdoc comprehensive} at a
%system prompt.
ここに示されている記号以外が必要な読者は,
\emph{The Comprehensive \LaTeX{} Symbol List}
\cite{comprehensive}を参考にするとよいでしょう.
%\[\url{http://www.ctan.org/tex-archive/info/symbols/comprehensive/}\]
お使いの\lat/が\TeX\,Liveに基づいており,
ドキュメントも含まれていれば,システムプロンプトで
\texttt{texdoc comprehensive}と入力することで,
記号一覧を読むことができます.
\begin{table}[p]
%\caption[]{Multiline equations and equation groups\\
\caption[]{複数の行が必要な数式と数式のグループ\\
% \phantom{Table 1:} (vertical lines indicate nominal margins).}
\phantom{Table 1:} (縦棒は,通常のマージンを示しています).}
\label{displays}
\bigskip
\begin{makeimage}
\begin{minipage}{\textwidth}
\begin{eqxample}
\begin{verbatim}
\begin{equation}\label{xx}
\begin{split}
a& =b+c-d\\
& \quad +e-f\\
& =g+h\\
& =i
\end{split}
\end{equation}
\end{verbatim}
\producing
\begin{equation}\label{xx}
\begin{split}
a& =b+c-d\\
& \quad +e-f\\
& =g+h\\
& =i
\end{split}
\end{equation}
\end{eqxample}
\begin{eqxample}
\begin{verbatim}
\begin{multline}
a+b+c+d+e+f\\
+i+j+k+l+m+n\\
+o+p+q+r+s
\end{multline}
\end{verbatim}
\producing
\begin{multline}
a+b+c+d+e+f\\
+i+j+k+l+m+n\\
+o+p+q+r+s
\end{multline}
\end{eqxample}
\begin{eqxample}
\begin{verbatim}
\begin{gather}
a_1=b_1+c_1\\
a_2=b_2+c_2-d_2+e_2
\end{gather}
\end{verbatim}
\producing
\begin{gather}
a_1=b_1+c_1\\
a_2=b_2+c_2-d_2+e_2
\end{gather}
\end{eqxample}
\begin{eqxample}
\begin{verbatim}
\begin{align}
a_1& =b_1+c_1\\
a_2& =b_2+c_2-d_2+e_2
\end{align}
\end{verbatim}
\producing
\begin{align}
a_1& =b_1+c_1\\
a_2& =b_2+c_2-d_2+e_2
\end{align}
\end{eqxample}
\begin{eqxample}
\begin{verbatim}
\begin{align}
a_{11}& =b_{11}&
a_{12}& =b_{12}\\
a_{21}& =b_{21}&
a_{22}& =b_{22}+c_{22}
\end{align}
\end{verbatim}
\producing
\begin{align}
a_{11}& =b_{11}&
a_{12}& =b_{12}\\
a_{21}& =b_{21}&
a_{22}& =b_{22}+c_{22}
\end{align}
\end{eqxample}
\begin{eqxample}
\begin{verbatim}
\begin{alignat}{2}
a_1& =b_1+c_1& &+e_1-f_1\\
a_2& =b_2+c_2&{}-d_2&+e_2
\end{alignat}
\end{verbatim}
\producing
\begin{alignat}{2}
a_1& =b_1+c_1& &+e_1-f_1\\
a_2& =b_2+c_2&{}-d_2&+e_2
\end{alignat}
\end{eqxample}
\begin{eqxample}
\begin{verbatim}
\begin{flalign}
a_{11}& =b_{11}&
a_{12}& =b_{12}\\
a_{21}& =b_{21}&
a_{22}& =b_{22}+c_{22}
\end{flalign}
\end{verbatim}
\producing
\begin{flalign}
a_{11}& =b_{11}&
a_{12}& =b_{12}\\
a_{21}& =b_{21}&
a_{22}& =b_{22}+c_{22}
\end{flalign}
\end{eqxample}
\def\containsMSABM{TF}
\begin{notes}
%\item Applying \env{*} to any primary environment will suppress the
% assignment of equation numbers. However, \cn{tag} may be used to
% apply a visible label, and \cn{eqref} can be used to reference
% such manually tagged lines. Use of either \env{*} or a \cn{tag}
% on a subordinate environment is an error.
\item\env{*}を任意のプライマリ環境に適用すると,
数式番号の割り当てが抑止されます.
ただし,\cn{tag}はラベルを表示するために,
\cn{eqref}は手動でタグ付けされた行を参照するために使用できます.
従属環境で\env{*}または\cn{tag}を使用するとエラーになります.
%\item The \env{split} environment is something of a
% special case. It is a subordinate environment that can be used as the
% contents of an \env{equation} environment or the contents of one
% \qq{line} in a multiple-equation structure such as \env{align} or
% \env{gather}.
\item \env{split}環境は特殊なケースです.これは従属環境で,
複数の式をもつ構造の\env{equation}環境の内容や
\env{aligned}や\env{gather}のような複数式の中の
1ディスプレイ数式つの\qq{line}の内容として使用できます.
%\item The primary environments \env{gather}, \env{align} and \env{alignat}
% have subordinate ``\env{-ed}'' counterparts (\env{gathered},
% \env{aligned} and \env{alignedat}) that can be used as components of
% more complicated displays, or within in-line math. These ``\env{-ed}''
% environments can be positioned vertically using an optional argument
% \verb+[t]+, \verb+[c]+ or~\verb+[b]+.
\item 主要な環境\env{gather},\env{align}と\env{align}には,
その下位構造に``\env{-ed}''対応(\env{gather},\env{aligned},
\env{aligned})があります.より複雑なディスプレイ数式の構成要素として,
またはインライン数式の中で使用することができます.
これらの``\env{-ed}''環境は,オプションの\verb+[t]+,\verb+[c]+
または\verb+[b]+を使用して垂直に配置できます.
%\item The name \env{flalign} is meant as ``full length'', not
% ``flush left'' as often mistakenly reported. However, since a
% display occupying the full width will often begin at the left
% margin, this confusion is understandable. The indent applied to
% \env{flalign} from both margins is set with \cn{multlinegap}.
\item \env{flalign}という名前は,``全幅(full length)''を意味します.
よく``左寄せ(flush left)''だと誤解されます.しかし,ディスプレイ数式は
しばしば左端から始まり幅全体にわたるので,この混乱は納得できます.
両方のマージンから\env{flalign}に適用されるインデントは,
\cn{multlinegap}で設定されます.
\end{notes}
\end{minipage}
\end{makeimage}
\end{table}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\section{Inline math formulas and displayed equations}\label{first-step}
\section{文章中の数式(インライン数式)と数式だけの行(ディスプレイ数式)}\label{first-step}
%\subsection{The fundamentals}
\subsection{基本}
%Entering and leaving math mode in \LaTeX{} is normally done with the
%following commands and environments.%
\LaTeX{}で数式作成モードに入ったり出たりするのは,
通常以下のコマンドと環境で行われます.
\begin{center}
\begin{tabular}{ccc}
%\colhead{inline formulas}&& \colhead{displayed equations}\\[3pt]
\colhead{インライン数式}&& \colhead{ディスプレイ数式}\\[3pt]
\cline{1-1}\cline{3-3}\noalign{\medskip}
\begin{cstack}
\verb'$' \dots\ \verb'$'\\
\verb'\(' \dots\ \verb'\)'
\end{cstack}%
&&
\begin{llstack}
\begin{lstack}\verb'\[...\]'\\[6pt]\end{lstack}&
% unnumbered\\
数式番号がつかない \\
\begin{lstack}
\verb'\begin{equation*}'\\
\dots\\
\verb'\end{equation*}'\\[6pt]
\end{lstack}&
% unnumbered\\
数式番号がつかない \\
\begin{lstack}
\verb'\begin{equation}'\\
\dots\\
\verb'\end{equation}'
\end{lstack}&
% \begin{lstack}automatically\\numbered\end{lstack}
\begin{lstack}自動的に数式番号が\\つけられる\end{lstack}
\end{llstack}
\end{tabular}
\begin{notes}
% \singlenote
%\item Do not leave a blank line between text and a displayed equation.
% This allows a page break at that location, which is bad style. It
% also causes the spacing between text and display to be incorrect,
% usually larger than it should be.
% If a visual break is desired in the input, insert a line containing
% only a \verb+%+ at the beginning.
% Leave a blank line between a display and following text only if a new
% paragraph is intended.
\item 本文とディスプレイ数式の間に空白行を入れないでください.
そうしてしまうと,その場所での改ページが可能になります.
これは悪いスタイルです.
また,文章とディスプレイ数式の間隔が不正確になり,通常は望ましい値よりも大きくなります.
ドキュメント作成時の見やすさのために改行が必要な場合は,先頭に\verb+%+だけの行を挿入します.
新しい段落が意図されている場合にのみ,ディスプレイ数式の後と次のテキストとの間に空白行を置きます.
%\item Do not group multiple display structures in the input (\verb+\[...\]+,
% \env{equation}, etc.). Instead, use a multiline structure with
% substructures (\env{split}, \env{aligned}, etc.)\ as appropriate.
\item 入力(\verb+\[...\]+,\env{equation}など)に複数のディスプレイ数式をグループ化しないでください.
その代わりに,(\env{split},\env{aligned}など)などの複数行構造のためのコマンドを適切に使用してください.
%\item The alternative environments \begend{math} and\\
% \begend{displaymath} are seldom needed in practice. Using the plain
% \TeX{} notation \dbldollars\ for displayed equations is strongly
% discouraged. Although it is not expressly forbidden in \LaTeX{}, it
% is not documented anywhere in the \LaTeX{} book as being part of the
% \LaTeX{} command set, and it interferes with the proper operation of
% various features such as the \opt{fleqn} option.
\item 実際には,\verb+\begin{math}+と\verb+\begin{displaymath}+の両方が必要になることはめったにありません.
ディスプレイ数式の作成にplain\,\TeX{}表記\dbldollars{}を使用することは避けてください.
\LaTeX{}では明示的に禁止されていませんが,\LaTeX{}コマンドの一部として\LaTeX{}の本のどこにも
説明されておらず,\LaTeX{}コマンドの一部としてドキュメント化されていません.
これはたとえば\opt{fleqn}オプションを使用するときに特別な問題をおこします.
%\item The \env{eqnarray} and \env{eqnarray*} environments described
% in \cite{lamport} are strongly discouraged because they produce
% inconsistent spacing of the equal signs and make no attempt to prevent
% overprinting of the equation body by the equation number.
\item \cite{lamport}に記述されている\env{eqnarray}環境と\env{eqnarray*}環境の使用も避けてください.
これを使うと等号の間隔が不均一になり,式番号と方程式本体が重なるのを防げません.
\end{notes}
\end{center}
%Environments for handling equation groups and multiline equations are
%shown in \tabref{displays}.
方程式のグループ化と複数行を扱うための環境は,\tabref{displays}に示されています.
\newpage
%\subsection{Automatic numbering and cross-referencing}
\subsection{自動番号付けと相互参照}
%To get an auto-numbered equation, use the \env{equation} environment; to
%assign a label for cross-referencing, use the \cn{label} command:
自動的に数式番号が付く式を作るには,\env{equation}環境を使用します.
相互参照のラベルを割り当てるには,\cn{label}コマンドを使用します.
\begin{verbatim}
\begin{equation}\label{reio}
...
\end{equation}
\end{verbatim}
%To get a cross-reference to an auto-numbered equation, use the
自動的に番号付けた数式を相互参照するには,次のようにします.
%\cn{eqref} command:
\cn{eqref} コマンド:
\begin{verbatim}
... using equations~\eqref{ax1} and~\eqref{bz2}, we
can derive ...
\end{verbatim}
%The above example would produce something like
上に示した例では,
\begin{quote}
using equations (3.2) and (3.5), we can derive
\end{quote}
%In other words, \verb'\eqref{ax1}' is equivalent to \verb'(\ref{ax1})',
%but the parentheses produced by \cn{eqref} are always upright.
のように表示されます.
言い換えれば,\verb'\eqref{ax1}'は\verb'(\ref{ax1})'と同じですが,
\cn{eqref}で生成されたカッコは常に立体です.
%To give your equation numbers the form \textit{m.n}
%(\textit{section-number.equation-number}), use the \cn{numberwithin}
%command in the preamble of your document:
式番号を\textit{m.n}(\textit{節の番号.数式番号})という形にしたいときは,
ドキュメントのプレアンブルで\cn{numberwithin}コマンドを使います:
\begin{verbatim}
\numberwithin{equation}{section}
\end{verbatim}
%For more details on custom numbering schemes see \cite[\S 6.3,
%\S C.8.4]{lamport}.
番号付けの方針の詳細については,
\cite[\S 6.3,\S C.8.4]{lamport}
を参照してください.
%The \env{subequations} environment provides a convenient way to number
%equations in a group with a subordinate numbering scheme. For example,
%supposing that the current equation number is \theequation, write
\env{subequations}環境は,グループ内の方程式の番号付の方針ための便利な方法を提供します.
たとえば,現在の方程式の番号が\theequation{}であるなら,
\begin{verbatim}
\begin{equation}\label{first}
a=b+c
\end{equation}
この間に文章があるとして,
\begin{subequations}\label{grp}
\begin{align}
a&=b+c\label{second}\\
d&=e+f+g\label{third}\\
h&=i+j\label{fourth}
\end{align}
\end{subequations}
\end{verbatim}
%to get
とすれば
\begin{equation}\label{first}
a=b+c
\end{equation}
%some intervening text
この間に文章があるとして,
\begin{subequations}\label{grp}
\begin{align}
a&=b+c\label{second}\\
d&=e+f+g\label{third}\\
h&=i+j\label{fourth}
\end{align}
\end{subequations}
となります.
%By putting a \cn{label} command immediately after
%\verb'\begin{subequations}' you can get a reference to the parent
% number; \verb'\eqref{grp}' from the above example would produce \eqref{grp}
% while \verb'\eqref{second}' would produce \eqref{second}.
\verb'\begin{subequations}'の直後に\cn{label}コマンドを置くことで,
親の番号への参照を得ることができます.
上記の例の\verb'\eqref{grp}'は\eqref{grp}を生成し,
\verb'\eqref{second}'は\eqref{second}を生成します.
%An example at \url{https://tex.stackexchange.com/questions/220001/} shows
%a variant of the above example, with numbering like (2.1), (2.1a),
%\dots, rather than (2.1), (2.2a), \dots. This is accomplished by using
%\cn{tag} with a cross-reference to the principal component of the
%subequation number.
上で述べた数式番号の付け方のいくつかの変種が
\url{https://tex.stackexchange.com/questions/220001/}に
紹介されています.そこには
(2.1), (2.2a) \dots ではなく(2.1), (2.1a) \dots とする例などがあります.
これは,\cn{tag}を使って,子番号をもつ式の親の式に対して相互参照を行うことで実現されます.
\newpage
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\providecommand{\dotsref}{\leavevmode\unskip\ignorespaces}
\providecommand{\vertref}{\leavevmode\unskip\ignorespaces}
%\section{Math symbols and math fonts}\label{mathsymbols}
\section{数学記号と数式フォント}\label{mathsymbols}
%\subsection{Classes of math symbols}
\subsection{数学記号の分類}
%The symbols in a math formula fall into different classes that
%correspond more or less to the part of speech each symbol would have if
%the formula were expressed in words. Certain spacing and positioning
%cues are traditionally used for the different symbol classes to increase
%the readability of formulas.
数式で使う記号は,いくつかの種類(クラス)に分けられます.
数式が単語で表されるなら,読み方に多少なりとも対応します.
式の可読性を高めるために,異なる記号クラスごとに伝統的に間隔および配置が使用されています.
\begin{center}
\begin{tabular}{clll}
%\colhead{Class\\number}& \colhead{Mnemonic}& \colhead{Description\\(part
%of speech)}& \colhead{Examples}\\\hline\noalign{\smallskip}
\colhead{クラス\\番号}& \colhead{ニーモニック}& \colhead{意味\\(読みのヒント)}& \colhead{例}\\\hline\noalign{\smallskip}
%0& Ord& simple/ordinary (\qq{noun})& $A\;0\;\Phi\;\infty$\\
0& Ord& 普通/通常(名詞) & $A\;0\;\Phi\;\infty$\\
%1& Op& prefix operator& $\sum\;\prod\;\int$\\
1& Op& 前に置かれる作用素& $\sum\;\prod\;\int$\\
%2& Bin& binary operator (conjunction)& ${+}\;{\cup}\;{\wedge}$\\
2& Bin& 二項作用素(結合)& ${+}\;{\cup}\;{\wedge}$\\
%3& Rel& relation/comparison (verb)& ${=}\;{<}\;{\subset}$\\
3& Rel& 関係/比較 (動詞)& ${=}\;{<}\;{\subset}$\\
%4& Open& left/opening delimiter& $(\;{[}\;{\lbrace}\;{\langle}$\\
4& Open& 左/開きのデリミタ& $(\;{[}\;{\lbrace}\;{\langle}$\\
%5& Close& right/closing delimiter& $)\;{]}\;{\rbrace}\;{\rangle}$\\
5& Close& 右/閉じのデリミタ& $)\;{]}\;{\rbrace}\;{\rangle}$\\
%6& Punct& postfix/punctuation& ${.}\;{,}\;{;}\;{!}$\\
6& Punct& 後置記号/文の終わり& ${.}\;{,}\;{;}\;{!}$\\
\end{tabular}
\end{center}
\begin{notes}
%\item The distinction in \TeX{} between class 0 and an additional
%class 7 has to do only with font selection issues, and it is immaterial
%here.
\item \TeX{}のクラス0とクラス7の区別は,フォント選択の問題にのみ影響します.
ここでは重要ではありません.
%\item Symbols of class 2 (Bin), notably the minus sign $-$, are
%automatically printed by \LaTeX{} as class~0 (no space) if they do not
%have a suitable left operand\mdash e.g., at the beginning of a math
%formula or after an opening delimiter.
\item クラス2(Bin)の記号,特にマイナス記号$-$は,\LaTeX{}によってクラス0(空白なし)として,自動的にプリントされます.つまり
適切な左オペランド\mdash{}がないとき,つまり数式の始まりまたは開始デリミタの受け側であるとしています.
\end{notes}
%The spacing for a few symbols follows tradition instead of the general
%rule: although $/$ is (semantically speaking) of class~2, we write $k/2$
%with no space around the slash rather than $k\mathbin{/}2$. And compare
%\verb'p|q' $p\vert q$ (no space) with \verb'p\mid q' $p\mid q$
%(class-3 spacing).
いくつかの記号の間隔は,日常ドキュメントではなく数式の伝統に従います:
$/$は(意味的に)クラス2のものですが,$k\mathbin{/}2$ではなく
スラッシュのまわりに空白を入れずに$k/2$と書きます.
そして,\verb'p|q' $p\vert q$(空白なし)と
\verb'p\mid q' $p\mid q$(クラス3の空白)と
を比べてみましょう.
%The proper way to define a new math symbol is discussed in
%\emph{\LaTeXe{} font selection} \cite{fntguide}. It is not really
%possible to give a useful synopsis here because one needs first to
%understand the ramifications of font specifications. But supposing one
%knows that a Cyrillic font named \fn{wncyr10} is available, here is a
%minimal example showing how to define a \LaTeX{} command to print one
%letter from that font as a math symbol:
新しい数学記号を定義する適切な方法は,
\emph{\LaTeXe{}フォントの選択}で説明されています\cite{fntguide}.
フォントの仕様の影響を最初に理解する必要があるため,
ここでは有用な概要を与えることは実際には不可能です.
しかし,\fn{wncyr10}という名前のキリル文字フォントが利用できることを知っているとて,
そのフォントの1文字を数学記号としてプリントするための\LaTeX{}コマンドでの定義方法について
最小の例を示します:
\begin{verbatim}
% Declare that the combination of font attributes OT2/wncyr/m/n
% should select the wncyr font.
\DeclareFontShape{OT2}{wncyr}{m}{n}{<->wncyr10}{}
% Declare that the symbolic math font name "cyr" should resolve to
% OT2/wncyr/m/n.
\DeclareSymbolFont{cyr}{OT2}{wncyr}{m}{n}
% Declare that the command \Sh should print symbol 88 from the math font
% "cyr", and that the symbol class is 0 (= alphabetic = Ord).
\DeclareMathSymbol{\Sh}{\mathalpha}{cyr}{88}
\end{verbatim}
%\subsection{Some symbols intentionally omitted here}
\subsection{意図的にここで省略された記号}
%The following math symbols that are mentioned in the \LaTeX{} book
%\cite{lamport} are intentionally omitted from this discussion because
%they are superseded by equivalent symbols when the \pkg{amssymb} package
%is loaded. If you are using the \pkg{amssymb} package anyway, the only
%thing that you are likely to gain by using the alternate name is an
%unnecessary increase in the number of fonts used by your document.
次に示す数学記号は\LaTeX{} book\cite{lamport}に記載されていますが,
\pkg{amssymb}パッケージがロードされたときに同等の記号に置き換えらるため,
意図的に省略しています.
\pkg{amssymb}パッケージを使用している場合は,代替名を使用することは
たんにドキュメントで使用されるフォントの数を不必要に増やしだけです.
\begin{center}
\def\jdo#1{\cn{#1} \ $\csname #1\endcsname$}
%\begin{tabular}{r@{\,, see \ }l}
\begin{tabular}{r@{\,, 右のコマンドを使う \ }l}
\cn{Box}&\jdo{square}\\
\cn{Diamond}&\jdo{lozenge}\\
\cn{leadsto}&\jdo{rightsquigarrow}\\
\cn{Join}&\jdo{bowtie}\\
\cn{lhd}&\jdo{vartriangleleft}\\
\cn{unlhd}&\jdo{trianglelefteq}\\
\cn{rhd}&\jdo{vartriangleright}\\
\cn{unrhd}&\jdo{trianglerighteq}
\end{tabular}
\end{center}
%Furthermore, there are \strong{many, many additional symbols} available
%for \lat/ use above and beyond the ones included here. This list is not
%intended to be comprehensive. For a much more comprehensive list of
%symbols, including nonmathematically oriented ones, such as phonetic
%alphabetic or dingbats, see \emph{The Comprehensive \LaTeX{} Symbol
%List}~\cite{comprehensive}. (Full font tables, ordered by font name,
%for all the fonts covered by the comprehensive list are included in
%the documentation provided by \TeX~Live: \texttt{texdoc rawtables}.
%These tables do not include symbol names.) Another source of symbol
%information is the \pkg{unicode-math} package; see~\cite{uc-math}.
さらに,\lat/ には,ここに含まれているものよりも\strong{強力なものがたくさん}あります.
このリストは包括的なものではありません.
音標アルファベットや記号のような数学では必要ない記号も含まれた包括的なリストについては,
\emph{The Comprehensive \LaTeX{} Symbol List}~\cite{comprehensive}を参照してください.
(すべてのフォントの一覧は,フォント名順に\TeX~Live:\texttt{texdoc rawtables}が
提供するドキュメントに含まれています.
これらの表には記号名は含まれません.)
この他の記号についての情報については\pkg{unicode-math}パッケージにあります;
\cite{uc-math}を参照してください.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\newpage
%\subsection{Alphabets and digits\nopunct}\label{alpha-digit}
\subsection{アルファベットと数}\label{alpha-digit}
%\subsubsection{Latin letters and Arabic numerals}
%The Latin letters are simple symbols, class~0. The default font for them
%in math formulas is italic.
\subsubsection{ラテン文字とアラビア数字}
ラテン文字は,クラス0の単純な記号です.
数式内のラテン文字のデフォルトのフォントはイタリックです.
\begin{center}
\begin{tabular}{c}
$A\,B\,C\,D\,E\,F\,G\,H\,I\,J\,K\,L\,M%
\,N\,O\,P\,Q\,R\,S\,T\,U\,V\,W\,X\,Y\,Z$\\
$a\,b\,c\,d\,e\,f\,g\,h\,i\,j\,k\,l\,m%
\,n\,o\,p\,q\,r\,s\,t\,u\,v\,w\,x\,y\,z$
\end{tabular}
\end{center}
%When adding an accent to an $i$ or $j$ in math, dotless variants can be
%obtained with \cn{imath} and \cn{jmath}:
数式で$i$や$j$にアクセントを加えるときには,ドットのない$i$や$j$は\cn{imath}や\cn{jmath}
を使います:
\begin{symlist}
\dosymbol{Var}{imath}{kernel}
\dosymbol{Var}{jmath}{kernel}
\symbox{\hat{\jmath}}{\string\hat\string{\string\jmath\string}}
\end{symlist}
%Arabic numerals 0\ndash 9 are also of class~0. Their default font is
%upright/roman.
アラビア数字0\ndash 9もクラス0です.デフォルトのフォントは立体/ローマン体です.
\[0\,1\,2\,3\,4\,5\,6\,7\,8\,9\]
%\subsubsection{Greek letters}
\subsubsection{ギリシア文字}
%Like the Latin letters, the Greek letters are simple symbols, class~0.
%For obscure historical reasons, the default font for lowercase Greek
%letters in math formulas is italic while the default font for capital
%Greek letters is upright/roman. (In other fields such as physics and
%chemistry, however, the typographical traditions are somewhat
%different.) The capital Greek letters not present in this list are the
%letters that have the same appearance as some Latin letter: A for Alpha,
%B for Beta, and so on. In the list of lowercase letters there is no
%omicron because it would be identical in appearance to Latin $o$. In
%practice, the Greek letters that have Latin look-alikes are seldom used
%in math formulas, to avoid confusion.
ラテン文字のように,ギリシャ文字は簡単な記号,クラス0です.
あいまいな歴史的な理由から,数式の小文字のギリシャ文字のデフォルトフォントはイタリックで,
大文字のギリシャ文字のデフォルトフォントは立体/ローマン体です.
しかし,物理学や化学などの他の分野と,伝統的な数学の文字の使い方は多少異なります.
このリストにはないギリシャ語の文字は,アルファの場合はA,ベータの場合はB,等々.
小文字のリストには,外観がラテン文字の$o$と同じであるため,オミクロンはありません.
実際には,混乱を避けるために,ラテン語と似ているギリシャ文字は,
数式にほとんど使われていません.
\begin{symlist}[adjustheight=12pt]
\dosymbol{Var}{Gamma}{kernel}
\dosymbol{Var}{Delta}{kernel}
\dosymbol{Var}{Lambda}{kernel}
\dosymbol{Var}{Phi}{kernel}
\dosymbol{Var}{Pi}{kernel}
\dosymbol{Var}{Psi}{kernel}
\dosymbol{Var}{Sigma}{kernel}
\dosymbol{Var}{Theta}{kernel}
\dosymbol{Var}{Upsilon}{kernel}
\dosymbol{Var}{Xi}{kernel}
\dosymbol{Var}{Omega}{kernel}
\newcolumn
\dosymbol{Var}{alpha}{kernel}
\dosymbol{Var}{beta}{kernel}
\dosymbol{Var}{gamma}{kernel}
\dosymbol{Var}{delta}{kernel}
\dosymbol{Var}{epsilon}{kernel}
\dosymbol{Var}{zeta}{kernel}
\dosymbol{Var}{eta}{kernel}
\dosymbol{Var}{theta}{kernel}
\dosymbol{Var}{iota}{kernel}
\dosymbol{Var}{kappa}{kernel}
\dosymbol{Var}{lambda}{kernel}
\dosymbol{Var}{mu}{kernel}
\newcolumn
\dosymbol{Var}{nu}{kernel}
\dosymbol{Var}{xi}{kernel}
%\dosymbol{Var}{omicron}{??}
\dosymbol{Var}{pi}{kernel}
\dosymbol{Var}{rho}{kernel}
\dosymbol{Var}{sigma}{kernel}
\dosymbol{Var}{tau}{kernel}
\dosymbol{Var}{upsilon}{kernel}
\dosymbol{Var}{phi}{kernel}
\dosymbol{Var}{chi}{kernel}
\dosymbol{Var}{psi}{kernel}
\dosymbol{Var}{omega}{kernel}
\newcolumn
\dosymbol{Ord}{digamma}{amssymb}
\dosymbol{Var}{varepsilon}{kernel}
\dosymbol{Ord}{varkappa}{amssymb}
\dosymbol{Var}{varphi}{kernel}
\dosymbol{Var}{varpi}{kernel}
\dosymbol{Var}{varrho}{kernel}
\dosymbol{Var}{varsigma}{kernel}
\dosymbol{Var}{vartheta}{kernel}
\end{symlist}
%\subsubsection{Other ``basic'' alphabetic symbols}
\subsubsection{その他の``基本''アルファベット記号}
これらもクラス0です.
\begin{symlist}
\dosymbol{Ord}{aleph}{kernel}
\dosymbol{Ord}{beth}{amssymb}
\dosymbol{Ord}{daleth}{amssymb}
\dosymbol{Ord}{gimel}{amssymb}
\dosymbol{Ord}{complement}{amssymb}
\dosymbol{Ord}{ell}{kernel}
\dosymbol{Ord}{eth}{amssymb}
\dosymbol{Ord}{hbar}{amssymb}
\dosymbol{Ord}{hslash}{amssymb}
\dosymbol{Ord}{mho}{amssymb}
\dosymbol{Ord}{partial}{kernel}
\dosymbol{Ord}{wp}{kernel}
\dosymbol{Ord}{circledS}{amssymb}
\dosymbol{Ord}{Bbbk}{amssymb}
\dosymbol{Ord}{Finv}{amssymb}
\dosymbol{Ord}{Game}{amssymb}
\dosymbol{Ord}{Im}{kernel}
\dosymbol{Ord}{Re}{kernel}
\vfil
\end{symlist}
\begin{notes}
\end{notes}
%\subsubsection{Math font switches}\label{mathfonts}
\subsubsection{数式フォントの変更}\label{mathfonts}
%Not all of the fonts necessary to support comprehensive math font
%switching are commonly available in a typical \LaTeX{} setup. Here are
%the results of applying various font switches to a wide range of math
%symbols when the standard set of Computer Modern fonts is in use. It can
%be seen that the only symbols that respond correctly to all of the font
%switches are the uppercase Latin letters. In fact, \emph{nearly all}
%math symbols apart from Latin letters remain unaffected by font
%switches; and although the lowercase Latin letters, capital Greek
%letters, and numerals do respond properly to some font switches, they
%produce bizarre results for other font switches. (Use of alternative
%math font sets such as Lucida New Math may ameliorate the situation
%somewhat.)
包括的な数学フォントの変更をサポートするために必要なフォントのすべてが,
通常の\LaTeX{}設定で一般的に利用できるわけではありません.
ここには,Computer Modernフォントの標準セットが使用されているときに,
幅広い数学記号にさまざまなフォント変換を適用した結果があります.
すべてのフォント変更に正しく応答する唯一の記号は大文字のラテン文字であることがわかります.
実際,ラテン文字とは別に\emph{ほぼすべての}数学記号はフォントの変更に影響されません.
小文字のラテン文字,大文字のギリシャ文字,数字は一部のフォント変更に正しく対応しますが,
他のフォント変更では奇妙な結果が生じます.(Lucida New Mathなどの数学フォントセットを
使用すると,状況が多少改善される可能性があります).
\[\renewcommand{\arraystretch}{1.3}
\begin{array}{cccccccc}
%\text{default}& \cn{mathbf}& \cn{mathsf}& \cn{mathit}& \cn{mathcal}&
% \cn{mathscr}& \cn{mathbb}& \cn{mathfrak}\\
\text{default}& \cn{mathbf}& \cn{mathrm}& \cn{mathsf}& \cn{mathit}&
\cn{mathcal}& \cn{mathbb}& \cn{mathfrak}\\
\hline
\symrow{X} \\
\symrow{x} \\
\symrow{0} \\
\symrow{[\,]} \\
\symrow{+} \\
\symrow{-} \\
\symrow{=} \\
\symrow{\Xi} \\
\symrow{\xi} \\
\symrow{\infty} \\
\symrow{\aleph} \\
\symrow{\sum}\\
\symrow{\amalg} \\
\symrow{\Re} \\
\end{array}\]
%A common desire is to get a bold version of a particular math symbol.
%For those symbols where \cn{mathbf} is not applicable, the
%\cn{boldsymbol} or \cn{pmb} commands can be used.
一般的な望みは,特定の数学記号の太字のバージョンを得ることです.
\cn{mathbf}が適用されない記号については,\cn{boldsymbol}または\cn{pmb}コマンドを使用できます.
\begin{equation}
A_\infty + \pi A_0
\sim \mathbf{A}_{\boldsymbol{\infty}} \boldsymbol{+}
\boldsymbol{\pi} \mathbf{A}_{\boldsymbol{0}}
\sim\pmb{A}_{\pmb{\infty}} \pmb{+}\pmb{\pi} \pmb{A}_{\pmb{0}}
\end{equation}
\begin{verbatim}
A_\infty + \pi A_0
\sim \mathbf{A}_{\boldsymbol{\infty}} \boldsymbol{+}
\boldsymbol{\pi} \mathbf{A}_{\boldsymbol{0}}
\sim\pmb{A}_{\pmb{\infty}} \pmb{+}\pmb{\pi} \pmb{A}_{\pmb{0}}
\end{verbatim}
%The \cn{boldsymbol} command is obtained preferably by using
%the \pkg{bm} package, which provides a newer, more powerful version than
%the one provided by the \pkg{amsmath} package. It is usually
%ill-advised to apply \cn{boldsymbol} to more than one symbol at a time;
%if such a need seems to arise, it more likely means that there is
%another, better way of going about it.
\cn{boldsymbol}コマンドは,\pkg{amsmath}パッケージよりも新しい,
強力なバージョンである\pkg{bm}パッケージを読み込んで使うのが望ましいです.
一度に複数の記号に\cn{boldsymbol}を適用することは通常はお勧めできません.
もしそのような必要性が生じているようであれば,別のより良い方法があることを意味します.
%\subsubsection{Blackboard Bold letters (\fn{msbm}; no lowercase)}
\subsubsection{黒板太字 (\fn{msbm}; ただし小文字はありません)}
% Usage: \verb'\mathbb{R}'. Requires \pkg{amsfonts}.
使い方は\verb'\mathbb{R}'です.\pkg{amsfonts}が必要です.
\[
\mathbb{A}\,\mathbb{B}\,\mathbb{C}\,\mathbb{D}\,\mathbb{E}\,\mathbb{F}
\,\mathbb{G}\,\mathbb{H}\,\mathbb{I}\,\mathbb{J}\,\mathbb{K}\,\mathbb{L}
\,\mathbb{M}\,\mathbb{N}\,\mathbb{O}\,\mathbb{P}\,\mathbb{Q}\,\mathbb{R}
\,\mathbb{S}\,\mathbb{T}\,\mathbb{U}\,\mathbb{V}\,\mathbb{W}\,\mathbb{X}
\,\mathbb{Y}\,\mathbb{Z}
\]
%One lowercase letter is available with a distinct name:\qquad
一つだけ小文字が用意されています:\qquad
$\Bbbk$\quad \cn{Bbbk}
%\newpage
%\subsubsection{Calligraphic letters (\fn{cmsy}; no lowercase)} Usage:
%\verb'\mathcal{M}'.
\subsubsection{飾り文字(\fn{cmsy}; 小文字はありません)}
使い方:
\verb'\mathcal{M}'.
\[
\mathcal{A}\,\mathcal{B}\,\mathcal{C}\,\mathcal{D}\,\mathcal{E}
\,\mathcal{F}\,\mathcal{G}\,\mathcal{H}\,\mathcal{I}\,\mathcal{J}
\,\mathcal{K}\,\mathcal{L}\,\mathcal{M}\,\mathcal{N}\,\mathcal{O}
\,\mathcal{P}\,\mathcal{Q}\,\mathcal{R}\,\mathcal{S}\,\mathcal{T}
\,\mathcal{U}\,\mathcal{V}\,\mathcal{W}\,\mathcal{X}\,\mathcal{Y}
\,\mathcal{Z}
\]
%\subsubsection{Non-CM calligraphic and script letters}
\subsubsection{CMフォントではない飾り文字と手書き文字}
%(\fn{rsfs}; no lowercase) Usage: \verb'\usepackage{mathrsfs}' \verb'\mathscr{B}'.
(\fn{rsfs}; 小文字はありません) 使い方:\verb'\usepackage{mathrsfs}' \verb'\mathscr{B}'.
\[
\mathscr{A}\,\mathscr{B}\,\mathscr{C}\,\mathscr{D}\,\mathscr{E}
\,\mathscr{F}\,\mathscr{G}\,\mathscr{H}\,\mathscr{I}\,\mathscr{J}
\,\mathscr{K}\,\mathscr{L}\,\mathscr{M}\,\mathscr{N}\,\mathscr{O}
\,\mathscr{P}\,\mathscr{Q}\,\mathscr{R}\,\mathscr{S}\,\mathscr{T}
\,\mathscr{U}\,\mathscr{V}\,\mathscr{W}\,\mathscr{X}\,\mathscr{Y}
\,\mathscr{Z}
\]
\begingroup
\noindent
%(\fn{eusm}; no lowercase) Usage: \verb'\usepackage{euscript}' \verb'\mathscr{E}'.
(\fn{eusm}; 小文字はありません)使い方: \verb'\usepackage{euscript}' \verb'\mathscr{E}'.
\renewcommand{\mathscr}{\EuScript}
\[
\mathscr{A}\,\mathscr{B}\,\mathscr{C}\,\mathscr{D}\,\mathscr{E}
\,\mathscr{F}\,\mathscr{G}\,\mathscr{H}\,\mathscr{I}\,\mathscr{J}
\,\mathscr{K}\,\mathscr{L}\,\mathscr{M}\,\mathscr{N}\,\mathscr{O}
\,\mathscr{P}\,\mathscr{Q}\,\mathscr{R}\,\mathscr{S}\,\mathscr{T}
\,\mathscr{U}\,\mathscr{V}\,\mathscr{W}\,\mathscr{X}\,\mathscr{Y}
\,\mathscr{Z}
\]
\endgroup
%\subsubsection{Fraktur letters (\fn{eufm})}
\subsubsection{フラクトゥール文字 (\fn{eufm})}
使い方 \verb'\mathfrak{S}'. \pkg{amsfonts}が必要です.
\[
\mathfrak{A}\,\mathfrak{B}\,\mathfrak{C}\,\mathfrak{D}\,\mathfrak{E}
\,\mathfrak{F}\,\mathfrak{G}\,\mathfrak{H}\,\mathfrak{I}\,\mathfrak{J}
\,\mathfrak{K}\,\mathfrak{L}\,\mathfrak{M}\,\mathfrak{N}\,\mathfrak{O}
\,\mathfrak{P}\,\mathfrak{Q}\,\mathfrak{R}\,\mathfrak{S}\,\mathfrak{T}
\,\mathfrak{U}\,\mathfrak{V}\,\mathfrak{W}\,\mathfrak{X}\,\mathfrak{Y}
\,\mathfrak{Z}
\]
\[
\mathfrak{a}\,\mathfrak{b}\,\mathfrak{c}\,\mathfrak{d}\,\mathfrak{e}
\,\mathfrak{f}\,\mathfrak{g}\,\mathfrak{h}\,\mathfrak{i}\,\mathfrak{j}
\,\mathfrak{k}\,\mathfrak{l}\,\mathfrak{m}\,\mathfrak{n}\,\mathfrak{o}
\,\mathfrak{p}\,\mathfrak{q}\,\mathfrak{r}\,\mathfrak{s}\,\mathfrak{t}
\,\mathfrak{u}\,\mathfrak{v}\,\mathfrak{w}\,\mathfrak{x}\,\mathfrak{y}
\,\mathfrak{z}
\]
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\subsection{Miscellaneous simple symbols}
\subsection{いくつかの単純な記号}
%These symbols are also of class~0 (ordinary) which means
%they do not have any built-in spacing.%
これらの文字もクラス0(通常)です.
つまり組み込みの空白がありません.%
\begin{symlist}
\dosymbol{Ordx}{\#}{kernel}
\dosymbol{Ordx}{\&}{kernel}
\dosymbol{Ord}{angle}{amssymb}
\dosymbol{Ord}{backprime}{amssymb}
\dosymbol{Ord}{bigstar}{amssymb}
\dosymbol{Ord}{blacklozenge}{amssymb}
\dosymbol{Ord}{blacksquare}{amssymb}
\dosymbol{Ord}{blacktriangle}{amssymb}
\dosymbol{Ord}{blacktriangledown}{amssymb}
\dosymbol{Ord}{bot}{kernel}
\dosymbol{Ord}{clubsuit}{kernel}
\dosymbol{Ord}{diagdown}{amssymb}
\dosymbol{Ord}{diagup}{amssymb}
\dosymbol{Ord}{diamondsuit}{kernel}
\dosymbol{Ord}{emptyset}{kernel}
\dosymbol{Ord}{exists}{kernel}
\dosymbol{Ord}{flat}{kernel}
\dosymbol{Ord}{forall}{kernel}
\dosymbol{Ord}{heartsuit}{kernel}
\dosymbol{Ord}{infty}{kernel}
\dosymbol{Ord}{lozenge}{amssymb}
\dosymbol{Ord}{measuredangle}{amssymb}
\dosymbol{Ord}{nabla}{kernel}
\dosymbol{Ord}{natural}{kernel}
\dosymbol{Ord}{neg}{kernel}
\dosymbol{Ord}{nexists}{amssymb}
\dosymbol{Ord}{prime}{kernel}
\dosymbol{Ord}{sharp}{kernel}
\dosymbol{Ord}{spadesuit}{kernel}
\dosymbol{Ord}{sphericalangle}{amssymb}
\dosymbol{Ord}{square}{amssymb}
\dosymbol{Ord}{surd}{kernel}
\dosymbol{Ord}{top}{kernel}
\dosymbol{Ord}{triangle}{kernel}
\dosymbol{Ord}{triangledown}{amssymb}
\dosymbol{Ord}{varnothing}{amssymb}
\end{symlist}
\begin{notes}
%\item A common mistake in the use of the symbols $\square$ and $\#$
% is to try to make them serve as binary operators or relation symbols
% without using a properly defined math symbol command. If you merely
% use the existing commands \cn{square} or \cn{\#} the intersymbol
% spacing will be incorrect because those commands produce a class-0
% symbol.
\item
記号$\square$と$\#$を使用する際のよくある間違いは,適切に定義された数学記号コマンドを使用せずに,2項演算子または関係記号として用いることです.単に既存のコマンド\cn{square}または\cn{\#}を使用すると,これらのコマンドがクラス0記号を生成するため,記号間の間隔が正しくありません.
%\item Synonyms: \alias{lnot}
\item 同義語\alias{lnot}
\end{notes}
%\subsection{Binary operator symbols\nopunct}
\subsection{二項演算の記号\nopunct}
\begin{symlist}
\dosymbol{Binc}{*}{kernel}
\dosymbol{Binc}{+}{kernel}
\dosymbol{Binc}{-}{kernel}
\dosymbol{Bin}{amalg}{kernel}
\dosymbol{Bin}{ast}{kernel}
\dosymbol{Bin}{barwedge}{amssymb}
\dosymbol{Bin}{bigcirc}{kernel}
\dosymbol{Bin}{bigtriangledown}{kernel}
\dosymbol{Bin}{bigtriangleup}{kernel}
\dosymbol{Bin}{boxdot}{amssymb}
\dosymbol{Bin}{boxminus}{amssymb}
\dosymbol{Bin}{boxplus}{amssymb}
\dosymbol{Bin}{boxtimes}{amssymb}
\dosymbol{Bin}{bullet}{kernel}
\dosymbol{Bin}{cap}{kernel}
\dosymbol{Bin}{Cap}{amssymb}
\dosymbol{Bin}{cdot}{kernel}
\dosymbol{Bin}{centerdot}{amssymb}
\dosymbol{Bin}{circ}{kernel}
\dosymbol{Bin}{circledast}{amssymb}
\dosymbol{Bin}{circledcirc}{amssymb}
\dosymbol{Bin}{circleddash}{amssymb}
\dosymbol{Bin}{cup}{kernel}
\dosymbol{Bin}{Cup}{amssymb}
\dosymbol{Bin}{curlyvee}{amssymb}
\dosymbol{Bin}{curlywedge}{amssymb}
\dosymbol{Bin}{dagger}{kernel}
\dosymbol{Bin}{ddagger}{kernel}
\dosymbol{Bin}{diamond}{kernel}
\dosymbol{Bin}{div}{kernel}
\dosymbol{Bin}{divideontimes}{amssymb}
\dosymbol{Bin}{dotplus}{amssymb}
\dosymbol{Bin}{doublebarwedge}{amssymb}
\dosymbol{Bin}{gtrdot}{amssymb}
\dosymbol{Bin}{intercal}{amssymb}
\dosymbol{Bin}{leftthreetimes}{amssymb}
\dosymbol{Bin}{lessdot}{amssymb}
\dosymbol{Bin}{ltimes}{amssymb}
\dosymbol{Bin}{mp}{kernel}
\dosymbol{Bin}{odot}{kernel}
\dosymbol{Bin}{ominus}{kernel}
\dosymbol{Bin}{oplus}{kernel}
\dosymbol{Bin}{oslash}{kernel}
\dosymbol{Bin}{otimes}{kernel}
\dosymbol{Bin}{pm}{kernel}
\dosymbol{Bin}{rightthreetimes}{amssymb}
\dosymbol{Bin}{rtimes}{amssymb}
\dosymbol{Bin}{setminus}{kernel}
\dosymbol{Bin}{smallsetminus}{amssymb}
\dosymbol{Bin}{sqcap}{kernel}
\dosymbol{Bin}{sqcup}{kernel}
\dosymbol{Bin}{star}{kernel}
\dosymbol{Bin}{times}{kernel}
\dosymbol{Bin}{triangleleft}{kernel}
\dosymbol{Bin}{triangleright}{kernel}
\dosymbol{Bin}{uplus}{kernel}
\dosymbol{Bin}{vee}{kernel}
\dosymbol{Bin}{veebar}{amssymb}
\dosymbol{Bin}{wedge}{kernel}
\dosymbol{Bin}{wr}{kernel}
\end{symlist}
\begin{notes}
\synonyms \alias{land}, \alias{lor}, \alias{doublecup}, \alias{doublecap}
\end{notes}
%\subsection{Relation symbols:
% \texorpdfstring{$<$ $=$ $>$ $\succ$ $\sim$}{< + > succeed ~}
% and variants\nopunct}
\subsection{関係記号:
\texorpdfstring{$<$ $=$ $>$ $\succ$ $\sim$}{< + > succeed ~}
および,それらの変種\nopunct}
\begin{symlist}[adjustheight=10pt]
\dosymbol{Relc}{<}{kernel}
\dosymbol{Relc}{=}{kernel}
\dosymbol{Relc}{>}{kernel}
\dosymbol{Rel}{approx}{kernel}
\dosymbol{Rel}{approxeq}{amssymb}
\dosymbol{Rel}{asymp}{kernel}
\dosymbol{Rel}{backsim}{amssymb}
\dosymbol{Rel}{backsimeq}{amssymb}
\dosymbol{Rel}{bumpeq}{amssymb}
\dosymbol{Rel}{Bumpeq}{amssymb}
\dosymbol{Rel}{circeq}{amssymb}
\dosymbol{Rel}{cong}{kernel}
\dosymbol{Rel}{curlyeqprec}{amssymb}
\dosymbol{Rel}{curlyeqsucc}{amssymb}
\dosymbol{Rel}{doteq}{kernel}
\dosymbol{Rel}{doteqdot}{amssymb}
\dosymbol{Rel}{eqcirc}{amssymb}
\dosymbol{Rel}{eqsim}{amssymb}
\dosymbol{Rel}{eqslantgtr}{amssymb}
\dosymbol{Rel}{eqslantless}{amssymb}
\dosymbol{Rel}{equiv}{kernel}
\dosymbol{Rel}{fallingdotseq}{amssymb}
\dosymbol{Rel}{geq}{kernel}
\dosymbol{Rel}{geqq}{amssymb}
\dosymbol{Rel}{geqslant}{amssymb}
\dosymbol{Rel}{gg}{kernel}
\dosymbol{Rel}{ggg}{amssymb}
\dosymbol{Rel}{gnapprox}{amssymb}
\dosymbol{Rel}{gneq}{amssymb}
\dosymbol{Rel}{gneqq}{amssymb}
\dosymbol{Rel}{gnsim}{amssymb}
\dosymbol{Rel}{gtrapprox}{amssymb}
\dosymbol{Rel}{gtreqless}{amssymb}
\dosymbol{Rel}{gtreqqless}{amssymb}
\dosymbol{Rel}{gtrless}{amssymb}
\dosymbol{Rel}{gtrsim}{amssymb}
\dosymbol{Rel}{gvertneqq}{amssymb}
\dosymbol{Rel}{leq}{kernel}
\dosymbol{Rel}{leqq}{amssymb}
\dosymbol{Rel}{leqslant}{amssymb}
\dosymbol{Rel}{lessapprox}{amssymb}
\dosymbol{Rel}{lesseqgtr}{amssymb}
\dosymbol{Rel}{lesseqqgtr}{amssymb}
\dosymbol{Rel}{lessgtr}{amssymb}
\dosymbol{Rel}{lesssim}{amssymb}
\dosymbol{Rel}{ll}{kernel}
\dosymbol{Rel}{lll}{amssymb}
\dosymbol{Rel}{lnapprox}{amssymb}
\dosymbol{Rel}{lneq}{amssymb}
\dosymbol{Rel}{lneqq}{amssymb}
\dosymbol{Rel}{lnsim}{amssymb}
\dosymbol{Rel}{lvertneqq}{amssymb}
\dosymbol{Rel}{ncong}{amssymb}
\dosymbol{Rel}{neq}{kernel}
\dosymbol{Rel}{ngeq}{amssymb}
\dosymbol{Rel}{ngeqq}{amssymb}
\dosymbol{Rel}{ngeqslant}{amssymb}
\dosymbol{Rel}{ngtr}{amssymb}
\dosymbol{Rel}{nleq}{amssymb}
\dosymbol{Rel}{nleqq}{amssymb}
\dosymbol{Rel}{nleqslant}{amssymb}
\dosymbol{Rel}{nless}{amssymb}
\dosymbol{Rel}{nprec}{amssymb}
\dosymbol{Rel}{npreceq}{amssymb}
\dosymbol{Rel}{nsim}{amssymb}
\dosymbol{Rel}{nsucc}{amssymb}
\dosymbol{Rel}{nsucceq}{amssymb}
\dosymbol{Rel}{prec}{kernel}
\dosymbol{Rel}{precapprox}{amssymb}
\dosymbol{Rel}{preccurlyeq}{amssymb}
\dosymbol{Rel}{preceq}{kernel}
\dosymbol{Rel}{precnapprox}{amssymb}
\dosymbol{Rel}{precneqq}{amssymb}
\dosymbol{Rel}{precnsim}{amssymb}
\dosymbol{Rel}{precsim}{amssymb}
\dosymbol{Rel}{risingdotseq}{amssymb}
\dosymbol{Rel}{sim}{kernel}
\dosymbol{Rel}{simeq}{kernel}
\dosymbol{Rel}{succ}{kernel}
\dosymbol{Rel}{succapprox}{amssymb}
\dosymbol{Rel}{succcurlyeq}{amssymb}
\dosymbol{Rel}{succeq}{kernel}
\dosymbol{Rel}{succnapprox}{amssymb}
\dosymbol{Rel}{succneqq}{amssymb}
\dosymbol{Rel}{succnsim}{amssymb}
\dosymbol{Rel}{succsim}{amssymb}
\dosymbol{Rel}{thickapprox}{amssymb}
\dosymbol{Rel}{thicksim}{amssymb}
\dosymbol{Rel}{triangleq}{amssymb}
\end{symlist}
\begin{notes}
\synonyms \alias{ne}, \alias{le}, \alias{ge}, \alias{Doteq}, \alias{llless}, \alias{gggtr}
\end{notes}
%\subsection{Relation symbols: arrows}
\subsection{関係記号:矢印}
%See also \secref{notations}.
次も参照\secref{notations}.
\begin{symlist}[adjustheight=10pt]
\dosymbol{Rel}{circlearrowleft}{amssymb}
\dosymbol{Rel}{circlearrowright}{amssymb}
\dosymbol{Rel}{curvearrowleft}{amssymb}
\dosymbol{Rel}{curvearrowright}{amssymb}
\dosymbol{Rel}{downdownarrows}{amssymb}
\dosymbol{Rel}{downharpoonleft}{amssymb}
\dosymbol{Rel}{downharpoonright}{amssymb}
\dosymbol{Rel}{hookleftarrow}{kernel}
\dosymbol{Rel}{hookrightarrow}{kernel}
\dosymbol{Rel}{leftarrow}{kernel}
\dosymbol{Rel}{Leftarrow}{kernel}
\dosymbol{Rel}{leftarrowtail}{amssymb}
\dosymbol{Rel}{leftharpoondown}{kernel}
\dosymbol{Rel}{leftharpoonup}{kernel}
\dosymbol{Rel}{leftleftarrows}{amssymb}
\dosymbol{Rel}{leftrightarrow}{kernel}
\dosymbol{Rel}{Leftrightarrow}{kernel}
\dosymbol{Rel}{leftrightarrows}{amssymb}
\dosymbol{Rel}{leftrightharpoons}{amssymb}
\dosymbol{Rel}{leftrightsquigarrow}{amssymb}
\dosymbol{Rel}{Lleftarrow}{amssymb}
\dosymbol{Rel}{longleftarrow}{kernel}
\dosymbol{Rel}{Longleftarrow}{kernel}
\dosymbol{Rel}{longleftrightarrow}{kernel}
\dosymbol{Rel}{Longleftrightarrow}{kernel}
\dosymbol{Rel}{longmapsto}{kernel}
\dosymbol{Rel}{longrightarrow}{kernel}
\dosymbol{Rel}{Longrightarrow}{kernel}
\dosymbol{Rel}{looparrowleft}{amssymb}
\dosymbol{Rel}{looparrowright}{amssymb}
\dosymbol{Rel}{Lsh}{amssymb}
\dosymbol{Rel}{mapsto}{kernel}
\dosymbol{Rel}{multimap}{amssymb}
\dosymbol{Rel}{nLeftarrow}{amssymb}
\dosymbol{Rel}{nLeftrightarrow}{amssymb}
\dosymbol{Rel}{nRightarrow}{amssymb}
\dosymbol{Rel}{nearrow}{kernel}
\dosymbol{Rel}{nleftarrow}{amssymb}
\dosymbol{Rel}{nleftrightarrow}{amssymb}
\dosymbol{Rel}{nrightarrow}{amssymb}
\dosymbol{Rel}{nwarrow}{kernel}
\dosymbol{Rel}{rightarrow}{kernel}
\dosymbol{Rel}{Rightarrow}{kernel}
\dosymbol{Rel}{rightarrowtail}{amssymb}
\dosymbol{Rel}{rightharpoondown}{kernel}
\dosymbol{Rel}{rightharpoonup}{kernel}
\dosymbol{Rel}{rightleftarrows}{amssymb}
\dosymbol{Rel}{rightleftharpoons}{amssymb}
\dosymbol{Rel}{rightrightarrows}{amssymb}
\dosymbol{Rel}{rightsquigarrow}{amssymb}
\dosymbol{Rel}{Rrightarrow}{amssymb}
\dosymbol{Rel}{Rsh}{amssymb}
\dosymbol{Rel}{searrow}{kernel}
\dosymbol{Rel}{swarrow}{kernel}
\dosymbol{Rel}{twoheadleftarrow}{amssymb}
\dosymbol{Rel}{twoheadrightarrow}{amssymb}
\dosymbol{Rel}{upharpoonleft}{amssymb}
\dosymbol{Rel}{upharpoonright}{amssymb}
\dosymbol{Rel}{upuparrows}{amssymb}
\end{symlist}
\begin{notes}
\synonyms \alias{gets}, \alias{to}, \alias{restriction}
\end{notes}
%\subsection{Relation symbols: miscellaneous\nopunct}
\subsection{関係記号:その他\nopunct}
\begin{symlist}[adjustheight=10pt]
\dosymbol{Rel}{backepsilon}{amssymb}
\dosymbol{Rel}{because}{amssymb}
\dosymbol{Rel}{between}{amssymb}
\dosymbol{Rel}{blacktriangleleft}{amssymb}
\dosymbol{Rel}{blacktriangleright}{amssymb}
\dosymbol{Rel}{bowtie}{kernel}
\dosymbol{Rel}{dashv}{kernel}
\dosymbol{Rel}{frown}{kernel}
\dosymbol{Rel}{in}{kernel}
\dosymbol{Rel}{mid}{kernel}
\dosymbol{Rel}{models}{kernel}
\dosymbol{Rel}{ni}{kernel}
\dosymbol{Rel}{nmid}{amssymb}
\dosymbol{Rel}{notin}{kernel}
\dosymbol{Rel}{nparallel}{amssymb}
\dosymbol{Rel}{nshortmid}{amssymb}
\dosymbol{Rel}{nshortparallel}{amssymb}
\dosymbol{Rel}{nsubseteq}{amssymb}
\dosymbol{Rel}{nsubseteqq}{amssymb}
\dosymbol{Rel}{nsupseteq}{amssymb}
\dosymbol{Rel}{nsupseteqq}{amssymb}
\dosymbol{Rel}{ntriangleleft}{amssymb}
\dosymbol{Rel}{ntrianglelefteq}{amssymb}
\dosymbol{Rel}{ntriangleright}{amssymb}
\dosymbol{Rel}{ntrianglerighteq}{amssymb}
\dosymbol{Rel}{nvdash}{amssymb}
\dosymbol{Rel}{nVdash}{amssymb}
\dosymbol{Rel}{nvDash}{amssymb}
\dosymbol{Rel}{nVDash}{amssymb}
\dosymbol{Rel}{parallel}{kernel}
\dosymbol{Rel}{perp}{kernel}
\dosymbol{Rel}{pitchfork}{amssymb}
\dosymbol{Rel}{propto}{kernel}
\dosymbol{Rel}{shortmid}{amssymb}
\dosymbol{Rel}{shortparallel}{amssymb}
\dosymbol{Rel}{smallfrown}{amssymb}
\dosymbol{Rel}{smallsmile}{amssymb}
\dosymbol{Rel}{smile}{kernel}
\dosymbol{Rel}{sqsubset}{amssymb}
\dosymbol{Rel}{sqsubseteq}{kernel}
\dosymbol{Rel}{sqsupset}{amssymb}
\dosymbol{Rel}{sqsupseteq}{kernel}
\dosymbol{Rel}{subset}{kernel}
\dosymbol{Rel}{Subset}{amssymb}
\dosymbol{Rel}{subseteq}{kernel}
\dosymbol{Rel}{subseteqq}{amssymb}
\dosymbol{Rel}{subsetneq}{amssymb}
\dosymbol{Rel}{subsetneqq}{amssymb}
\dosymbol{Rel}{supset}{kernel}
\dosymbol{Rel}{Supset}{amssymb}
\dosymbol{Rel}{supseteq}{kernel}
\dosymbol{Rel}{supseteqq}{amssymb}
\dosymbol{Rel}{supsetneq}{amssymb}
\dosymbol{Rel}{supsetneqq}{amssymb}
\dosymbol{Rel}{therefore}{amssymb}
\dosymbol{Rel}{trianglelefteq}{amssymb}
\dosymbol{Rel}{trianglerighteq}{amssymb}
\dosymbol{Rel}{varpropto}{amssymb}
\dosymbol{Rel}{varsubsetneq}{amssymb}
\dosymbol{Rel}{varsubsetneqq}{amssymb}
\dosymbol{Rel}{varsupsetneq}{amssymb}
\dosymbol{Rel}{varsupsetneqq}{amssymb}
\dosymbol{Rel}{vartriangle}{amssymb}
\dosymbol{Rel}{vartriangleleft}{amssymb}
\dosymbol{Rel}{vartriangleright}{amssymb}
\dosymbol{Rel}{vdash}{kernel}
\dosymbol{Rel}{Vdash}{amssymb}
\dosymbol{Rel}{vDash}{amssymb}
\dosymbol{Rel}{Vvdash}{amssymb}
\end{symlist}
\begin{notes}
\synonyms \alias{owns}
\end{notes}
%\subsection{Cumulative (variable-size) operators\nopunct}
\subsection{大きさの変わる作用素 \nopunct}
\begin{symlist}[adjustcols=-1]
\openup3pt
\dosymbol{COi}{int}{kernel}
\dosymbol{COi}{oint}{kernel}
\dosymbol{COs}{bigcap}{kernel}
\dosymbol{COs}{bigcup}{kernel}
\dosymbol{COs}{bigodot}{kernel}
\dosymbol{COs}{bigoplus}{kernel}
\dosymbol{COs}{bigotimes}{kernel}
\dosymbol{COs}{bigsqcup}{kernel}
\dosymbol{COs}{biguplus}{kernel}
\dosymbol{COs}{bigvee}{kernel}
\dosymbol{COs}{bigwedge}{kernel}
\dosymbol{COs}{coprod}{kernel}
\dosymbol{COs}{prod}{kernel}
\dosymbol{COs}{smallint}{kernel}
\dosymbol{COs}{sum}{kernel}
\end{symlist}
%\subsection{Punctuation\nopunct}
\subsection{句読点\nopunct}
\begin{symlist}[adjustcols=-4]
\openup2pt
\dosymbol{Ordc}{.}{kernel}
\dosymbol{Ordc}{/}{kernel}
\dosymbol{Ordc}{|}{kernel}
\dosymbol{Punc}{,}{kernel}
\dosymbol{Punc}{;}{kernel}
\dosymbol{Pun}{colon}{kernel}
\dosymbol{Relc}{:}{kernel}
%\dosymbol{DeR}{!}{kernel}
%\dosymbol{DeR}{?}{kernel}
\dosymbol{Punc}{!}{kernel}
\dosymbol{Punc}{?}{kernel}
\dosymbol{Inn}{dotsb}{kernel}
\dosymbol{Inn}{dotsc}{kernel}
\dosymbol{Inn}{dotsi}{kernel}
\dosymbol{Inn}{dotsm}{kernel}
\dosymbol{Inn}{dotso}{kernel}
\dosymbol{Inn}{ddots}{kernel}
\dosymbol{Ord}{vdots}{kernel}
\end{symlist}
\begin{notes}
%\item The \verb':' by itself produces a colon with
% class-3 (relation) spacing. The command \cn{colon} produces special
% spacing for use in constructions such as \verb'f\colon A\to B'
% $f\colon A\to B$.
\item \verb':'はそれ自身でクラス3(関係)の空白をもつコロンを生成します.
\cn{コロン}コマンドは,\verb'f\colon A\to B'では$f\colon A\to B$のように特別な空白を作成します.
%\item Although the commands \cn{cdots} and \cn{ldots} are frequently
% used, we recommend the more semantically oriented commands
% \cn{dotsb} \cn{dotsc} \cn{dotsi} \cn{dotsm} \cn{dotso} for most
% purposes\dotsref.
\item コマンド\cn{cdots}と\cn{ldots}は頻繁に使用されますが,意味に応じたコマンド\cn{dotsb} \cn{dotsc} \cn{dotsi} \cn{dotsm} \cn{dotso}の使用をお勧めします.\dotsref.
\end{notes}
%\subsection{Pairing delimiters (extensible)}\label{pair-delims}
\subsection{ペアになる(大きさの変わる)記号)}\label{pair-delims}
%See Section~\ref{delim} for more information.
詳しくは\ref{delim}節を参照のこと.
\begin{symlist}
\openup7pt
\dosymbol{DeLRc}{(}{)}{kernel}
\dosymbol{DeLRc}{[}{]}{kernel}
\dosymbol{DeLR}{lbrace}{rbrace}{kernel}
\dosymbol{DeLR}{lvert}{rvert}{kernel}
\dosymbol{DeLR}{lVert}{rVert}{kernel}
\dosymbol{DeLR}{langle}{rangle}{kernel}
\dosymbol{DeLR}{lceil}{rceil}{kernel}
\dosymbol{DeLR}{lfloor}{rfloor}{kernel}
\dosymbol{DeLR}{lgroup}{rgroup}{kernel}
\dosymbol{DeLR}{lmoustache}{rmoustache}{kernel}
\end{symlist}
%\subsection{Nonpairing extensible symbols\nopunct}
\subsection{ペアでは使われないが大きさの変わる記号\nopunct}
\begin{symlist}
\dosymbol{DeB}{vert}{kernel}
\dosymbol{DeB}{Vert}{kernel}
\dosymbol{DeBc}{/}{kernel}
\dosymbol{DeB}{backslash}{kernel}
\dosymbol{DeB}{arrowvert}{kernel}
\dosymbol{DeB}{Arrowvert}{kernel}
\dosymbol{DeB}{bracevert}{kernel}
\end{symlist}
\begin{notes}
%\item Using \cn{vert}, \verb'|', \cn{Vert}, or \cn{|} for paired
%delimiters is not recommended\vertref. Instead, use delimiters from
%the list in Section~\ref{pair-delims}.
\item \cn{vert},\verb'|',\cn{Vert},\cn{|}をペアのデリミタ(語の前後を区切る,あるいは行列や絶対値など要素を囲む記号)として使うのは勧めません.\vertref
代わりに,\ref{pair-delims}節にある一覧表にあるデリミタを使用します.
\synonyms \alias{|}
\end{notes}
%\subsection{Extensible vertical arrows\nopunct}
\subsection{大きさの変わる垂直の矢印\nopunct}
\begin{symlist}
\dosymbol{DeA}{uparrow}{kernel}
\dosymbol{DeA}{Uparrow}{kernel}
\dosymbol{DeA}{downarrow}{kernel}
\dosymbol{DeA}{Downarrow}{kernel}
\dosymbol{DeA}{updownarrow}{kernel}
\dosymbol{DeA}{Updownarrow}{kernel}
\end{symlist}
%\subsection{Math accents\nopunct}\label{accents}
\subsection{数式で使われるアクセント\nopunct}\label{accents}
\begin{symlist}[adjustcols=1]
\dosymbol{Acc}{acute}{kernel}
\dosymbol{Acc}{grave}{kernel}
\dosymbol{Acc}{ddot}{kernel}
\dosymbol{Acc}{tilde}{kernel}
\dosymbol{Acc}{bar}{kernel}
\dosymbol{Acc}{breve}{kernel}
\dosymbol{Acc}{check}{kernel}
\dosymbol{Acc}{hat}{kernel}
\dosymbol{Acc}{vec}{kernel}
\dosymbol{Acc}{dot}{kernel}
\dosymbol{Acc}{ddot}{amsmath}
\dosymbol{Acc}{dddot}{amsmath}
\dosymbol{Acc}{mathring}{amsmath}
\dosymbol{Accw}{widetilde}{kernel}
\dosymbol{Accw}{widehat}{kernel}
\end{symlist}
%\subsection{Named operators}
\subsection{名前付き作用素}
%These operators are represented by a multiletter abbreviation.
これらの作用素は複数の文字による省略形で表されています.
\shiftlistright40pt
\begin{symlist}[adjustcols=-1]
\dosymbol{Opn}{arccos}{kernel}
\dosymbol{Opn}{arcsin}{kernel}
\dosymbol{Opn}{arctan}{kernel}
\dosymbol{Opn}{arg}{kernel}
\dosymbol{Opn}{cos}{kernel}
\dosymbol{Opn}{cosh}{kernel}
\dosymbol{Opn}{cot}{kernel}
\dosymbol{Opn}{coth}{kernel}
\dosymbol{Opn}{csc}{kernel}
\dosymbol{Opn}{deg}{kernel}
\dosymbol{Opn}{det}{kernel}
\dosymbol{Opn}{dim}{kernel}
\dosymbol{Opn}{exp}{kernel}
\dosymbol{Opn}{gcd}{kernel}
\dosymbol{Opn}{hom}{kernel}
\dosymbol{Opn}{inf}{kernel}
\dosymbol{Opn}{injlim}{kernel}
\dosymbol{Opn}{ker}{kernel}
\dosymbol{Opn}{lg}{kernel}
\dosymbol{Opn}{lim}{kernel}
\dosymbol{Opn}{liminf}{kernel}
\dosymbol{Opn}{limsup}{kernel}
\dosymbol{Opn}{ln}{kernel}
\dosymbol{Opn}{log}{kernel}
\dosymbol{Opn}{max}{kernel}
\dosymbol{Opn}{min}{kernel}
\dosymbol{Opn}{Pr}{kernel}
\dosymbol{Opn}{projlim}{kernel}
\dosymbol{Opn}{sec}{kernel}
\dosymbol{Opn}{sin}{kernel}
\dosymbol{Opn}{sinh}{kernel}
\dosymbol{Opn}{sup}{kernel}
\dosymbol{Opn}{tan}{kernel}
\dosymbol{Opn}{tanh}{kernel}
\dosymbol{Opn}{varinjlim}{kernel}
\dosymbol{Opn}{varprojlim}{kernel}
\dosymbol{Opn}{varliminf}{kernel}
\dosymbol{Opn}{varlimsup}{kernel}
\end{symlist}
%To define additional named operators outside the above list, use the
%\cn{DeclareMathOperator} command; for example, after
上記のリストにない追加の名前付き作用素を定義するには,\cn{DeclareMathOperator}コマンドを使用します.たとえば,
\begin{verbatim}
\DeclareMathOperator{\rank}{rank}
\DeclareMathOperator{\esssup}{ess\,sup}
\end{verbatim}
%one could write
このようにできます.
\begin{center}
\begin{tabular}{rl}
\verb'\rank(x)'& $\rank(x)$\\
\verb'\esssup(y,z)'& $\esssup(y,z)$
\end{tabular}
\end{center}
%The star form \cn{DeclareMathOperator*} creates an operator that takes
%limits in a displayed formula, such as $\sup$ or $\max$.
\cn{DeclareMathOperator*}にある星印は,ディスプレイ数式,
$\sup$や$\max$などにある範囲を示す式を使う作用素を作成します.
%When predefining such a named operator is problematic (e.g., when using
%one in the title or abstract of an article), there is an alternative
%form that can be used directly:
このようなすでに定義されている名前付き作用素で問題がある場合(たとえば,論文の表題や要約に1つ使用する場合など),
直接使用できる別の形式があります.
\[\verb'\operatorname{rank}(x)'\quad
\rightarrow\quad\operatorname{rank}(x)\]
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\section{Notations}
\section{記法}
\label{notations}
%\subsection{Top and bottom embellishments}
\subsection{上側と下側を飾る}
%These are visually similar to accents but generally span multiple
%symbols rather than being applied to a single base symbol. For ease of
%reference, \cn{widetilde} and \cn{widehat} are redundantly included here
%and in the table of math accents.
これらは視覚的にはアクセントと似ていますが,
1つの基になる記号だけに適用されるのではなく,
複数の記号にまたがります.
参照を便利にするために,ここでは\cn{widetilde}と\cn{widehat}を重複して,
数式アクセントの表に含めています.
\begin{symlist}
\dosymbol{Accw}{widetilde}{kernel}
\dosymbol{Accw}{widehat}{kernel}
\dosymbol{Accw}{overline}{kernel}
\dosymbol{Accw}{underline}{kernel}
\dosymbol{Accw}{overbrace}{kernel}
\dosymbol{Accw}{underbrace}{kernel}
\dosymbol{Accw}{overleftarrow}{kernel}
\dosymbol{Accw}{underleftarrow}{amsmath}
\dosymbol{Accw}{overrightarrow}{kernel}
\dosymbol{Accw}{underrightarrow}{amsmath}
\dosymbol{Accw}{overleftrightarrow}{amsmath}
\dosymbol{Accw}{underleftrightarrow}{amsmath}
\end{symlist}
%\subsection{Extensible arrows}
\subsection{長さが伸びる矢印}
%\cn{xleftarrow} and \cn{xrightarrow} produce
%arrows\index{arrows!extensible} that extend automatically to accommodate
%unusually wide subscripts or superscripts. These commands take one
%optional argument (the subscript) and one mandatory argument (the
%superscript, possibly empty):
\cn{xleftarrow}と\cn{xrightarrow}は,普通より広い下付き文字や上付き文字に対応するために自動的に拡張される矢印\index{arrows!extensible}を生成します.
これらのコマンドは,1つのオプションの引数(添え字)と1つの必須の引数(上付き文字,空の場合もある)を取ります:
\begin{equation}
A\xleftarrow{n+\mu-1}B \xrightarrow[T]{n\pm i-1}C
\end{equation}
\begin{verbatim}
\xleftarrow{n+\mu-1}\quad \xrightarrow[T]{n\pm i-1}
\end{verbatim}
%\subsection{Affixing symbols to other symbols}
\subsection{記号に別の記号を重ねる}
%In addition to the standard accents (Section~\ref{accents}), other
%symbols can be placed above or below a base symbol with the \cn{overset}
%and \cn{underset} commands. For example, writing \verb|\overset{*}{X}|
%will place a superscript-size $*$ above the $X$, thus: $\overset{*}{X}$.
%See also the description of \cn{sideset} in \secref{sideset}.
標準のアクセント(\ref{accents}節)に加えて,\cn{overset}と\cn{underset}コマンドで,基礎におく記号の上または下に他の記号を配置することができます.
たとえば,\verb|\overset{*}{X}|とすれば,$X$の上に上付き小文字の$*$を置くので,$\overset{*}{X}$になります.
\secref{sideset}の\cn{sideset}の説明も参照してください.
%\subsection{Matrices}\label{ss:matrix}
\subsection{行列}\label{ss:matrix}
%The environments \env{pmatrix}, \env{bmatrix}, \env{Bmatrix},
%\env{vmatrix}, and \env{Vmatrix} have (respectively) $(\,)$, $[\,]$,
%$\lbrace\,\rbrace$, $\lvert\,\rvert$, and $\lVert\,\rVert$ delimiters
%built in. There is also a \env{matrix} environment without delimiters
%and an \env{array} environment that can be used to obtain left alignment
%or other variations in the column specs.
\env{pmatrix},\env{bmatrix},\env{Bmatrix},\env{vmatrix},\env{Vmatrix}の環境はそれぞれ適切なデリミタ$(\,)$, $[\,]$,$\lbrace\, \rbrace$,$\lvert\,\rvert $,$\lVert\,\rVert $が組み込まれています.
また,デリミタをもたない\env{matrix}環境と,左揃えまたは列指定の他のバリエーションを取得するために使用できる\env{array}環境があります.
\begin{center}
\begin{minipage}{.4\columnwidth}
\begin{verbatim}
\begin{pmatrix}
\alpha& \beta^{*}\\
\gamma^{*}& \delta
\end{pmatrix}
\end{verbatim}
\end{minipage}
\qquad
\begin{minipage}{.4\columnwidth}
\[
\begin{pmatrix}
\alpha& \beta^{*}\\
\gamma^{*}& \delta
\end{pmatrix}
\]
\end{minipage}
\end{center}
%To produce a small matrix suitable for use in text, there is a
%\env{smallmatrix} environment (e.g.,
本文中での使用に適した小さな行列を生成するには,\env{smallmatrix}環境(たとえば,
\begin{math}
\bigl( \begin{smallmatrix}
a&b\\ c&d
\end{smallmatrix} \bigr)
\end{math})
%that comes closer to fitting within a single text line than a normal
%matrix. This example was produced by
とします.そうすると通常の行列よりも小さくなるので,文章の行の大きさにあいます.この例は,
\begin{verbatim}
\bigl( \begin{smallmatrix}
a&b\\ c&d
\end{smallmatrix} \bigr)
\end{verbatim}
としたものです.
%By default, all elements in a matrix are centered horizontally.
%The \pkg{mathtools} package provides starred versions of all the matrix
%environments that facilitate other alignments. That package also provides
%fenced versions of \env{smallmatrix} with parallel names in both starred
%and nonstarred versions.
デフォルトでは,行列内のすべての要素は水平方向に中央揃えされます.
\pkg{mathtools}パッケージは,これ以外の位置揃えを容易にするすべての行列環境の星印バージョンを提供します.
このパッケージはまた,星印バージョンと星印なしバージョンの両方で並列名をもつ\env{smallmatrix}の囲まれた版を提供します.
%To produce a row of dots in a matrix\index{matrices!ellipsis
% dots}\index{ellipsis dots!in matrices}\index{dots|see{ellipsis dots}}
%spanning a given number of columns, use \cn{hdotsfor}. For example,
%\verb'\hdotsfor{3}' in the second column of a four-column matrix will
%print a row of dots across the final three columns.
行列の中に指定された数の列にまたがるドットの行を生成するには\index{matrices!ellipsis dots}\index{ellipsis dots!in matrices}\index{dots|see{ellipsis dots}}\cn{hdotsfor} を使います.
たとえば,4列の行列の2番目の列の\verb'\hdotsfor{3}'は,最後の3つの列にドットだけの行がプリントされます
%For piecewise function definitions there is a \env{cases} environment:
区分関数の定義には,\env{cases}環境があります:
\begin{verbatim}
P_{r-j}=\begin{cases}
0& \text{if $r-j$ is odd},\\
r!\,(-1)^{(r-j)/2}& \text{if $r-j$ is even}.
\end{cases}
\end{verbatim}
%Notice the use of \cn{text} and the embedded math.
\cn{text}と埋め込み数式の使用に注意してください.
\begin{notes}
% \singlenote The plain \TeX{} form \verb'\matrix{...\cr...\cr}' and the
% related commands \cn{pmatrix}, \cn{cases} should be avoided in
% \LaTeX{} (and when the \pkg{amsmath} package is loaded they are
% disabled).
\singlenote plain\,\TeX{}形式の\verb'\matrix{...\cr...\cr}'と関連コマンド\cn{pmatrix},\cn{cases}は\LaTeX{}では避けるべきです(これらは\pkg{amsmath}パッケージがロードされると無効になります).
\end{notes}
%\subsection{Math spacing commands}
\subsection{数学用の空白コマンド}
%When the \pkg{amsmath} package is used, all of these math spacing
%commands can be used both in and out of math mode.
\pkg{amsmath}パッケージが使われていると,これらの数学用の空白コマンドはすべて,
数学モードの内側でも外側でも使用できます.
\begin{center}\begin{tabular}{llllll}
%Abbrev.& Spelled out& Example & Abbrev.& Spelled out& Example\\
省略形 & コマンド & 例 & 省略形 & コマンド & 例\\
\hline
\strut & no space& \spx{}& & no space& \spx{}\\
\cn{\,}& \cn{thinspace}& \spx{\,}&
\cn{!}& \cn{negthinspace}& \spx{\!}\\
\cn{\:}& \cn{medspace}& \spx{\:}&
& \cn{negmedspace}& \spx{\negmedspace}\\
\cn{\;}& \cn{thickspace}& \spx{\;}&
& \cn{negthickspace}& \spx{\negthickspace}\\
& \cn{quad}& \spx{\quad}\\
& \cn{qquad}& \spx{\qquad}
\end{tabular}\end{center}
%For finer control over math spacing, use \cn{mspace}
%and `math units'. One math unit, or \verb|mu|, is equal to \verb|mu|. Thus to
%get a negative half \cn{quad} write \verb|\mspace{-9.0mu}|.
数式での間隔をより細かく制御するには,\cn{mspace}と`数学単位(math units)'を使用します.
1つの数学単位,すなわち\verb|mu|は\verb|mu|に等しい.
したがって,負の半分\cn{quad}を得るには,\verb|\mspace{-9.0mu}|と書きます.
%There are also three commands that leave a space equal to the height
%and/or width of a given fragment of \lat/ material:
これ以外に\lat/ では,与えらた断片の高さまたは幅に等しい空白を入れる3つのコマンドもあります:
\begin{center}\begin{tabular}{ll}
%\colhead{Example}& \colhead{Result}\\
\colhead{例}& \colhead{結果}\\
\hline
%\verb'\phantom{XXX}'& space as wide and high as three X's\strut \\
%\verb'\hphantom{XXX}'& space as wide as three X's; height 0\\
%\verb'\vphantom{X}'& space of width 0, height = height of X
\verb'\phantom{XXX}' & 3つのXに等しい空白.高さは\strut{}.\\
\verb'\hphantom{XXX}' & 3つのXのに等しい空白高さは0\\
\verb'\vphantom{X}' & 0に等しい幅,高さ= Xの高さ
\end{tabular}\end{center}
%\subsection{Dots}\label{dots}
\subsection{ドット}\label{dots}
%For preferred placement of ellipsis dots (raised or on-line) in various
%contexts there is no general consensus. It may therefore be considered a
%matter of taste. In most situations, the generic \cn{dots} can be used,
%and \pkg{amsmath} will interpret it in the manner preferred by the AMS,
%namely low dots (\cn{ldots}) between commas or raised dots (\cn{cdots})
%between binary operators and relations, etc. If what follows the dots is
%ambiguous as to the choice, the specific form of the command can be used.
%However, by using the semantically oriented commands
種々の状況において優先される省略記号(斜めまたは水平オンライン)については一般的な合意がありません.
そのため好み問題と考えられるかもしれません.ほとんどの場合,一般的な\cn{dots}を使用することができ,\pkg{amsmath}はAMSの規則に従った斜めドット(\cn{ldots})の間の中心ドット(\cn{cdots})を指定することができます.ドットの後に続くものがあいまいである場合,コマンドにより特定の形式が使用できます.
しかし,\cn{ldots}や\cn{cdots}の代わりに,次に示すような意味に応じたコマンドを使うべきです.
\begin{itemize}
\setlength{\itemsep}{0pt}
%\item \cn{dotsc} for \qq{dots with commas}
%\item \cn{dotsb} for \qq{dots with binary operators/relations}
%\item \cn{dotsm} for \qq{multiplication dots}
%\item \cn{dotsi} for \qq{dots with integrals}
%\item \cn{dotso} for \qq{other dots} (none of the above)
\item \cn{dotsc} は \qq{コンマに続くドット}
\item \cn{dotsb} は \qq{に黄砂要素あるいは二項関係の後のドット}
\item \cn{dotsm} は \qq{たくさんのドット}
\item \cn{dotsi} は \qq{積分の後のドット}
\item \cn{dotso} は \qq{それ以外} (上の例に該当しない場合)
\end{itemize}
%instead of \cn{ldots} and \cn{cdots}, you make it possible for your
%document to be adapted to different conventions on the fly, in case (for
%example) you have to submit it to a publisher who insists on following
%house tradition in this respect. The default treatment for the various
%kinds follows American Mathematical Society conventions:
著者は,その場に応じた規約に適合させるべきである.
たとえば,出版社の規則に応じた規則に従って提出する必要があります
ここではアメリカの数学会の慣習に従います:
\begin{center}
\vspace{-\topsep}
\begin{tabular}{@{}ll@{}}
\begin{minipage}[t]{.50\textwidth}
\small
\begin{verbatim}
We have the series $A_1,A_2,\dotsc$,
the regional sum $A_1+A_2+\dotsb$,
the orthogonal product $A_1A_2\dotsm$,
and the infinite integral
\[\int_{A_1}\int_{A_2}\dotsi\].
\end{verbatim}
\end{minipage}
&
\begin{minipage}[t]{.48\textwidth}
\noindent
We have the series $A_1,A_2,\dotsc$,
the regional sum $A_1+A_2+\dotsb$,
the orthogonal product $A_1A_2\dotsm$,
and the infinite integral
\[\int_{A_1}\int_{A_2}\dotsi.\]
\end{minipage}
\end{tabular}
\end{center}
%\subsection{Nonbreaking dashes}
\subsection{分割させないダッシュ}
%The command \cn{nobreakdash} suppresses the possibility
%of a linebreak after the following hyphen or dash. For example, if you
%write `pages 1\ndash 9' as \verb|pages 1\nobreakdash--9| then a linebreak will
%never occur between the dash and the 9. You can also use
%\cn{nobreakdash} to prevent undesirable hyphenations in combinations
%like \verb|$p$-adic|. For frequent use, it's advisable to make abbreviations,
%e.g.,
\cn{nobreakdash}コマンドはハイフンまたはダッシュの後の改行を抑制します.
たとえば,`pages 1\ndash 9'とするためには\verb|pages 1\nobreakdash--9|と書くことで,
ハイフンと9のあいだで改行は起こりません.
\cn{nobreakdash}を使用すれば,\verb|$p$-adic|のような組み合わせのときの望ましくないハイフネーションを防ぐこともできます.頻繁に使用する場合は,略語を使用することを勧めます.
たとえば
\begin{verbatim}
\newcommand{\p}{$p$\nobreakdash}% for "\p adic" ("p-adic")
\newcommand{\Ndash}{\nobreakdash\textendash}% for "pages 1\Ndash 9"
% For "\n dimensional" ("n-dimensional"):
\newcommand{\n}{$n$\nobreakdash-\hspace{0pt}}
\end{verbatim}
%The last example shows how to prohibit a linebreak after the hyphen but
%allow normal hyphenation in the following word. (Add a zero-width space
%after the hyphen.)
最後の例は,ハイフンの後で改行を禁止する方法を示していますが,次の語には通常のハイフネーションを許可しています.ハイフンの後ろにゼロ幅の空白を追加します.
%\subsection{Roots}
\subsection{根号}
%The command \cn{sqrt} produces a square root. To specify an explicit
%radix, give it as an optional argument.
\cn{sqrt}コマンドは平方根を生成します.
基数を指定するには,オプション引数を1つ与えます.
\[
\verb'\sqrt{\frac{n}{n-1} S}'\quad\sqrt{\frac{n}{n-1} S}, \qquad
\verb'\sqrt[3]{2}'\quad
\sqrt[3]{2}
\]
%\subsection{Boxed formulas}
\subsection{数式の枠囲み}
%The command \cn{boxed} puts a box around its
%argument, like \cn{fbox} except that the contents are in math mode:
\cn{boxed}コマンドは,引数の周りを枠で囲みます.
\cn{fbox}は引数が数式にのみ適用できます:
\begin{equation}
\boxed{\eta \leq C(\delta(\eta) +\Lambda_M(0,\delta))}
\end{equation}
\begin{verbatim}
\boxed{\eta \leq C(\delta(\eta) +\Lambda_M(0,\delta))}
\end{verbatim}
%If you need to box an equation including the equation number, it may be
%difficult, depending on the context; there are some suggestions in the
%AMS author FAQ; see the entry outlined in red on the page
%\url{https://www.ams.org/faq?faq_id=290}.
数式番号を含む方程式を囲む必要がある場合は,状況に応じて難しい場合があります.
AMSの著者のためのFAQにいくつかの提案があります.ページの赤で概説されている項目を参照してください
\url{https://www.ams.org/faq?faq_id=290}.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\section{Fractions and related constructions}
\section{分数とそれに関連する話題}
%\subsection{The \hycn{frac}, \hycn{dfrac}, and
% \hycn{tfrac} commands}
\subsection{\hycn{frac}, \hycn{dfrac}, および
\hycn{tfrac}コマンド}
%The \cn{frac} command\index{fractions} takes two arguments\mdash
%numerator and denominator\mdash and typesets them in normal fraction
%form. Use \cn{dfrac} or \cn{tfrac} to overrule \LaTeX{}'s guess about
%the proper size to use for the fraction's contents (t = text style, d =
%display style).
\cn{frac}コマンド\index{fractions}は,2つの引数\mdash{}分子と分母\mdash{}を取り,それらを通常の分数の形式にタイプセットします.
\cn{dfrac}や\cn{tfrac}を使えば\LaTeX{}が想定する大きさの代わりに
(t =テキストスタイル,d =ディスプレイスタイル)適切な大きさになります.
\begin{equation}
\frac{1}{k}\log_2 c(f),\quad\dfrac{1}{k}\log_2 c(f),\quad\tfrac{1}{k}\log_2 c(f)
\end{equation}
\begin{verbatim}
\begin{equation}
\frac{1}{k}\log_2 c(f),\quad\dfrac{1}{k}\log_2 c(f),
\quad\tfrac{1}{k}\log_2 c(f)
\end{equation}
\end{verbatim}
\begin{equation}
\Re{z} =\frac{n\pi \dfrac{\theta +\psi}{2}}{
\left(\dfrac{\theta +\psi}{2}\right)^2 + \left( \dfrac{1}{2}
\log \left\lvert\dfrac{B}{A}\right\rvert\right)^2}.
\end{equation}
\begin{verbatim}
\begin{equation}
\Re{z} =\frac{n\pi \dfrac{\theta +\psi}{2}}{
\left(\dfrac{\theta +\psi}{2}\right)^2 + \left( \dfrac{1}{2}
\log \left\lvert\dfrac{B}{A}\right\rvert\right)^2}.
\end{equation}
\end{verbatim}
%\subsection{The \hycn{binom}, \hycn{dbinom}, and
% \hycn{tbinom} commands}
\subsection{\hycn{binom}, \hycn{dbinom},および
\hycn{tbinom}コマンド}
%For binomial expressions\index{binomials} such as $\binom{n}{k}$
%there are \cn{binom}, \cn{dbinom} and \cn{tbinom} commands:
$\binom{n}{k}$\index{binomials}のような2項式の場合には,\cn{binom},\cn{dbinom},\cn{tbinom}というコマンドを使います:
\begin{equation}
2^k-\binom{k}{1}2^{k-1}+\binom{k}{2}2^{k-2}
\end{equation}
\begin{verbatim}
2^k-\binom{k}{1}2^{k-1}+\binom{k}{2}2^{k-2}
\end{verbatim}
%\subsection{The \hycn{genfrac} command}
\subsection{\hycn{genfrac}コマンド}
%The capabilities of \cn{frac}, \cn{binom}, and their variants are
%subsumed by a generalized fraction command \cn{genfrac} with six
%arguments. The last two correspond to \cn{frac}'s numerator and
%denominator; the first two are optional delimiters (as seen in
%\cn{binom}); the third is a line thickness override (\cn{binom} uses
%this to set the fraction line thickness to 0 pt\mdash i.e., invisible);
%and the fourth argument is a mathstyle override: integer values
%0\ndash 3 select, respectively, \cn{displaystyle}, \cn{textstyle},
%\cn{scriptstyle}, and \cn{scriptscriptstyle}. If the third argument is
%left empty, the line thickness defaults to ``normal''.
\cn{frac},\cn{binom}の機能とその変種は次のとおりです.
一般化された分数コマンド\cn{genfrac}は6つの引数をとります.
最後の2つは,`\cn{frac}'の分子と分母に対応します.
最初の2つはオプションのデリミタです(\cn{binom}参照).
3番目は分母分子の間の線の太さを決めます(\cn{binom}はこれを使って分母分子の間の線の太さを0ptに設定,つまり表示しません).
4番目の引数は数式のスタイルを決めます:整数値0\ndash 3は,それぞれ\cn{displaystyle},\cn{textstyle},\cn{scriptstyle},\cn{scriptscriptstyle}を選択します.
3番目の引数が空の場合,線の太さはデフォルトで``normal''になります.
\begin{cmdspec}[25em]
\string\genfrac \ma{left-delim} \ma{right-delim} \ma{thickness}
\ma{mathstyle} \ma{numerator} \ma{denominator}
\end{cmdspec}
%To illustrate, here is how \cn{frac}, \cn{tfrac}, and
%\cn{binom} might be defined.
これを説明するために,ここで\cn{frac},\cn{tfrac},そして
\cn{binom}が,どのように定義されているかをみます.
\begin{verbatim}
\newcommand{\frac}[2]{\genfrac{}{}{}{}{#1}{#2}}
\newcommand{\tfrac}[2]{\genfrac{}{}{}{1}{#1}{#2}}
\newcommand{\binom}[2]{\genfrac{(}{)}{0pt}{}{#1}{#2}}
\end{verbatim}
\begin{notes}
% \singlenote For technical reasons, using the primitive fraction
% commands \cn{over}, \cn{atop}, \cn{above} in a \LaTeX{} document is
% not recommended (see, e.g., \url{https://www.ams.org/faq?faq\_id=288},
% the entry outlined in red).
\singlenote 技術的な理由から,\LaTeX{}ドキュメントでプリミティブ分数コマンド\cn{over},\cn{atop},\cn{above}を使用することは推奨されません
(例:\url{https://www.ams.org/faq?faq\_id=288},赤で囲まれたエントリ).
\end{notes}
%\subsection{Continued fractions}
\subsection{連分数}
%The continued fraction\index{continued fractions}
連分数\index{continued fractions}
\begin{equation}
\cfrac{1}{\sqrt{2}+
\cfrac{1}{\sqrt{2}+
\cfrac{1}{\sqrt{2}+\cdots
}}}
\end{equation}
%can be obtained by typing
は,次のようにします.
{\samepage
\begin{verbatim}
\cfrac{1}{\sqrt{2}+
\cfrac{1}{\sqrt{2}+
\cfrac{1}{\sqrt{2}+\dotsb
}}}
\end{verbatim}
}% End of \samepage
%This produces better-looking results than straightforward use of
%\cn{frac}. Left or right placement of any of the numerators is
%accomplished by using \cn{cfrac}\verb|[l]| or \cn{cfrac}\verb|[r]| instead of
%\cn{cfrac}.
こうすれば,\cn{frac}をそのまま使うよりは綺麗に作成されます.
任意の分子の左または右の配置は,\cn{cfrac}の代わりに\cn{cfrac}\verb|[l]|または\cn{cfrac}\verb|[r]|を使用して行います.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\section{Delimiters}\label{delim}
\section{デリミタ}\label{delim}
%\subsection{Delimiter sizes}\label{bigdel}
\subsection{デリミタの大きさ}\label{bigdel}
%Unless you indicate otherwise, delimiters in math formulas will remain
%at the standard size regardless of the height of the enclosed material.
%To get larger sizes, you can either select a particular size using a
%\cn{big...} prefix (see below), or you can use \cn{left} and \cn{right}
%prefixes for autosizing.
指定しない限り,数式のデリミタは,含まれる数式の標準の高さのままです.
より大きなサイズを得るには,接頭辞\cn{big ...}(下記参照)を使用して特定のサイズを選択するか,
または自動サイズ設定のために接頭辞\cn{left}と\cn{right}を使用できます.
%The automatic delimiter sizing done by \cn{left} and \cn{right} has two
%limitations: first, it is applied mechanically to produce delimiters
%large enough to encompass the largest contained item, and second, the
%range of sizes has fairly large quantum jumps. This means that an
%expression that is infinitesimally too large for a given delimiter size
%will get the next larger size, a jump of 6pt or so (3pt top and bottom)
%in normal-sized text. There are two or three situations where the
%delimiter size is commonly adjusted. These adjustments are
%done using the following commands:
\cn{left}と\cn{right}で行われるデリミタの自動的な大きさ調整には2つの制限があります:
第1に,最大の数式を包むのに十分な大きさのでリミタを機械的に適用し,
その次がかなり大きいデリミタへと一足飛びに拡大したものになります.
これは,指定されたデリミタのサイズが極端に大きすぎる式は,
全体のサイズが大きくなることを意味します.
通常のサイズのテキストでは,6pt(3ptの上端と下端)へ飛びます.
デリミタのサイズを調整すべき状況が2つまたは3つあります.
これらの調整は,次のコマンドを使用して行われます:
\begin{center}\begin{tabular}{l|llllll}
%Delimiter&
% no size& \ncn{left}& \ncn{bigl}& \ncn{Bigl}& \ncn{biggl}& \ncn{Biggl}\\
%size&
% specified& \ncn{right}& \ncn{bigr}& \ncn{Bigr}& \ncn{biggr}& \ncn{Biggr}\\[4pt]
デリミタ &
サイズを& \ncn{left}& \ncn{bigl}& \ncn{Bigl}& \ncn{biggl}& \ncn{Biggl}\\
サイズ &
指定しない & \ncn{right}& \ncn{bigr}& \ncn{Bigr}& \ncn{biggr}& \ncn{Biggr}\\[4pt]
%\hline\omit\rule{0pt}{1ex}\\
\hline\omit\rule{0pt}{1ex}\\[-1ex]
Result $\vphantom{\Bigg|^{\frac{1}{2}}}$ & % force height to avoid gap in vertical
$\displaystyle(b)(\frac{c}{d})$&
$\displaystyle\left(b\right)\left(\frac{c}{d}\right)$&
$\displaystyle\bigl(b\bigr)\bigl(\frac{c}{d}\bigr)$&
$\displaystyle\Bigl(b\Bigr)\Bigl(\frac{c}{d}\Bigr)$&
$\displaystyle\biggl(b\biggr)\biggl(\frac{c}{d}\biggr)$&
$\displaystyle\Biggl(b\Biggr)\Biggl(\frac{c}{d}\Biggr)$
\end{tabular}\end{center}
%The first kind of adjustment is done for cumulative operators with
%limits, such as summation signs. With \cn{left} and \cn{right} the
%delimiters usually turn out larger than necessary, and using the
%\verb|Big| or \verb|bigg| sizes\index{big@\cn{big}, \cn{Big}, \cn{bigg},
% \dots\ delimiters} instead gives better results:
第1の種類の調整は,総和記号などの値の範囲を示す累積作用素に対して行われます.
\cn{left}と\cn{right}を使うとデリミタは通常は必要なものより大きくなるので,\verb|Big|または\verb|bigg|を使用する方が良い結果が得られます:\index{big@\cn{big}, \cn{Big}, \cn{bigg},\dots\ delimiters}
\begin{equation*}
\left[\sum_i a_i\left\lvert\sum_j x_{ij}\right\rvert^p\right]^{1/p}
%\quad\text{versus}\quad
\quad\text{見比べましょう}\quad
\biggl[\sum_i a_i\Bigl\lvert\sum_j x_{ij}\Bigr\rvert^p\biggr]^{1/p}
\end{equation*}
\begin{verbatim}
\biggl[\sum_i a_i\Bigl\lvert\sum_j x_{ij}\Bigr\rvert^p\biggr]^{1/p}
\end{verbatim}
%The second kind of situation is clustered pairs of delimiters, where
%\cn{left} and \cn{right} make them all the same size (because that is
%adequate to cover the encompassed material), but what you really want
%is to make some of the delimiters slightly larger to make the nesting
%easier to see.
2番目の種類の状況はペアと成っているデリミタをいくつか入れ子にして使う場合です.
ここでは,\cn{left}と\cn{right}はすべて同じサイズになります(包含されたマテリアルをカバーするのに十分です).デリミタを少し大きくして入れ子の要素を見やすくします.
\begin{equation*}
\left((a_1 b_1) - (a_2 b_2)\right)
\left((a_2 b_1) + (a_1 b_2)\right)
%\quad\text{versus}\quad
\quad\text{見比べましょう}\quad
\bigl((a_1 b_1) - (a_2 b_2)\bigr)
\bigl((a_2 b_1) + (a_1 b_2)\bigr)
\end{equation*}
\begin{verbatim}
\left((a_1 b_1) - (a_2 b_2)\right)
\left((a_2 b_1) + (a_1 b_2)\right)
%\quad\text{versus}\quad
\quad\text{見比べましょう}\quad
\bigl((a_1 b_1) - (a_2 b_2)\bigr)
\bigl((a_2 b_1) + (a_1 b_2)\bigr)
\end{verbatim}
%The third kind of situation is a slightly oversize object in running
%text, such as $\left\lvert\frac{b'}{d'}\right\rvert$ where the
%delimiters produced by \cn{left} and \cn{right} cause too much line
%spreading. In that case \ncn{bigl} and \ncn{bigr}\index{big@\cn{big},
%\cn{Big}, \cn{bigg}, \dots\ delimiters} can be used to produce
%delimiters that are larger than the base size but still able to
%fit within the normal line spacing:
%$\bigl\lvert\frac{b'}{d'}\bigr\rvert$.
3番目の状況は,$\left\lvert\frac{b'}{d'}\right\rvert$のように,\cn{left}と\cn{right}は広すぎる行間を引き起こします.その場合,\ncn{bigl}と\ncn{bigr}を使用してデリミタを生成できます.\index{big@\cn{big},\cn{Big}, \cn{bigg}, \dots\ delimiters}
基本となるサイズよりも大きいが,通常の行間にくらべて違和感が少ないようにできます:$\bigl\lvert\frac{b '}{d'}\bigr\rvert $.
%The \pkg{mathtools} package provides a feature \cn{DeclarePairedDelimiter}
%that can simplify sizing; see the package documentation for details.
\pkg{mathtools}パッケージにはサイジングを簡素化できる\cn{DeclarePairedDelimiter}機能があります.
詳細については,パッケージのドキュメントを参照してください.
%\subsection{Vertical bar notations}\label{verts}
\subsection{縦棒の記法}\label{verts}
%The use of the \verb'|' character to produce paired delimiters is not
%recommended. There is an ambiguity about the directionality of the
%symbol that will in rare cases produce incorrect spacing\mdash e.g.,
%\verb'|k|=|-k|' produces $|k|=|-k|$, and \verb'|\sin x|' produces $|\sin x|$
%instead of the correct $\lvert\sin x\rvert$. Using \cn{lvert} for a \qq{left
%vert bar} and \cn{rvert} for a \qq{right vert bar} whenever they are
%used in pairs will prevent this problem; compare $\lvert -k\rvert$,
%produced by \verb'\lvert -k\rvert'. For double bars there are analogous
%\cn{lVert}, \cn{rVert} commands. Recommended practice is to define
%suitable commands in the document preamble for any paired-delimiter use
%of vert bar symbols:
\verb'|'を用いて(絶対値のような)ペアになったデリミタを生成することは推奨されません.
記号の向きについてあいまいさがあり,まれに間違った間隔が生じます.
たとえば,\verb'|k|=|-k|'は$|k|=|-k|$を生成し,\verb'|\sin x|'は正しい$\lvert\sin x\rvert $の代わりに$|\sin x|$を生成します.
\cn{lvert}を\qq{left vert bar}に\cn{rvert}を\qq{right vert bar}に使うと,この問題が回避されます.
\verb'\lvert -k\rvert'によって生成された$\lvert -k\rvert$と比べてみましょう.
二重バーの場合は,\cn{lVert}, \cn{rVert}という似た方法があります.
推奨されるプラクティスは,ドキュメントのプリアンブルに,縦棒の記号のペアを使うさいの適切なコマンドを定義しておくことです:
\begin{verbatim}
\providecommand{\abs}[1]{\lvert#1\rvert}
\providecommand{\norm}[1]{\lVert#1\rVert}
\end{verbatim}
%whereupon \verb|\abs{z}| would produce $\lvert z\rvert$ and
%\verb|\norm{v}| would produce $\lVert v\rVert$.
こうすれば\verb|\abs{z}|は$\lvert z\rvert$を生成し,
\verb|\norm{v}|は$\lVert v\rVert$を生成します.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\section{The \hycn{text} command}
\section{\hycn{text}コマンド}
%The main use of the command \cn{text} is for words or phrases\index{text
% fragments inside math} in a display. It is similar to \cn{mbox} in its
%effects but, unlike \cn{mbox}, automatically produces subscript-size
%text if used in a subscript.
\cn{text}コマンドの主な用途は,ディスプレイ内に単語または短い文を入れることです.\index{text fragments inside math}
これは\cn{mbox}と似ていますが,\cn{mbox}と異なり,添え字を使用しても自動的に添字の大きさでテキストが生成されます.
\begin{equation}
f_{[x_{i-1},x_i]} \text{ is monotonic,}
\quad i = 1,\dots,c+1
\end{equation}
\begin{verbatim}
f_{[x_{i-1},x_i]} \text{ is monotonic,}
\quad i = 1,\dots,c+1
\end{verbatim}
%\subsection{\hycn{mod} and its relatives}
\subsection{\hycn{mod} と,その仲間}
%Commands \cn{mod}, \cn{bmod}, \cn{pmod}, \cn{pod} deal with the special
%spacing conventions of \qq{mod} notation. \cn{mod} and \cn{pod} are
%variants of \cn{pmod} preferred by some authors; \cn{mod} omits the
%parentheses, whereas \cn{pod} omits the \qq{mod} and retains the
%parentheses.
コマンド\cn{mod},\cn{bmod},\cn{pmod},\cn{pod}は,\qq{mod}表記についての特別な空白規則を扱います.
\cn{mod}と\cn{pod}は,\cn{pmod}の変わった仲間ですが,これらのほうを好む人がいるので用意されています.
\cn{mod}はカッコを省略し,\cn{pod}は\qq{mod}を省略してカッコを保持します.
\begin{equation}
\gcd(n,m\bmod n) ;\quad x\equiv y\pmod b
;\quad x\equiv y\mod c ;\quad x\equiv y\pod d
\end{equation}
\begin{verbatim}
\gcd(n,m\bmod n) ;\quad x\equiv y\pmod b
;\quad x\equiv y\mod c ;\quad x\equiv y\pod d
\end{verbatim}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\section{Integrals and sums}
\section{積分と和}
%\subsection{Altering the placement of limits}
\subsection{範囲指定の配置}
%The limits on integrals, sums, and similar symbols are placed either to
%the side of or above and below the base symbol, depending on convention
%and context. \lat/ has rules for automatically choosing one or the
%other, and most of the time the results are satisfactory. In the event
%they are not, there are three \lat/ commands that can be used to
%influence the placement of the limits: \cn{limits}, \cn{nolimits},
%\cn{displaylimits}. Compare
積分,合計,および類似の記号で変数のとる範囲を示す式は,規則と文脈に応じて,
基礎記号の側面またはその上下に配置されます.
\lat/は自動的にどちらか一方を選択するための規則をもち,ほとんどの場合結果は問題ありません.
そうでない場合,範囲を示す式の配置に影響を与えるために使用できる3つコマンドが\lat/にはあります:\cn{limits},\cn{nolimits},\cn{displaylimits}です.
\begin{center}
\begin{minipage}{.4\columnwidth}
\[\int_{\abs{x-x_z(t)} 0} z^n}{\prod_{1\leq k\leq n} (1-q^k)}
\qquad\begin{minipage}{.5\columnwidth}
\begin{verbatim}
\frac{\sum_{n > 0} z^n}
{\prod_{1\leq k\leq n} (1-q^k)}
\end{verbatim}
\end{minipage}
\]
%Using \cn{dfrac} instead of \cn{frac} wouldn't change anything in this
%case; if you want the sum and product symbols to appear full size, you
%need the \cn{displaystyle} command:
\cn{frac}の代わりに\cn{dfrac}を使用しても,この場合は何も変更されません.
総和と総乗の記号をフルサイズで表示するには,\cn{displaystyle}コマンドが必要です:
\[
\frac{{\displaystyle\sum_{n > 0} z^n}}
{{\displaystyle\prod_{1\leq k\leq n} (1-q^k)}}
\qquad\begin{minipage}{.7\columnwidth}
\begin{verbatim}
\frac{{\displaystyle\sum_{n > 0} z^n}}
{{\displaystyle\prod_{1\leq k\leq n} (1-q^k)}}
\end{verbatim}
\end{minipage}
\]
%And if you want full-size symbols but with limits on the side, use
%the \cn{nolimits} command also:
フルサイズの記号を使用したいが範囲指定を横に置きたい場合は,
\cn{nolimits}コマンドを使用します:
\[
\frac{{\displaystyle\sum\nolimits_{n> 0} z^n}}
{{\displaystyle\prod\nolimits_{1\leq k\leq n} (1-q^k)}}
\qquad\begin{minipage}{.76\columnwidth}
\begin{verbatim}
\frac{{\displaystyle\sum\nolimits_{n> 0} z^n}}
{{\displaystyle\prod\nolimits_{1\leq k\leq n} (1-q^k)}}
\end{verbatim}
\end{minipage}
\]
%There are similar commands \cn{textstyle}, \cn{scriptstyle}, and
%\cn{scriptscriptstyle}, to force \lat/ to use the symbol size and
%spacing that would be applied in (respectively) inline math, first-order
%subscript, or second-order subscript, even when the current context
%would normally yield some other size.
同じような機能コマンド\cn{textstyle},\cn{scriptstyle},および\cn{scriptscriptstyle}があります.
これらは\lat/ に記号のサイズと空白について,現在の文脈上は他のサイズを生成する場合でも,
(それぞれ)インライン数式,一次添字,または二次添字のサイズを適用します.
%\textbf{Note:} These commands belong to a special class of
%commands referred to in the \lat/ book as ``declarations''. In
%particular, notice where the braces fall that delimit the effect of the
%command:
\textbf{注意:} これらのコマンドは,\lat/ で``宣言(declaration)''と呼ばれる特別なクラスのコマンドに属します.
特に,コマンドの有効範囲を指定する中カッコの位置に注意してください:
\begin{center}
%\textbf{Right: } \verb'{\displaystyle ...}'
%\qquad\qquad\textbf{Wrong: } \verb'\displaystyle{...}'
\textbf{正しい: } \verb'{\displaystyle ...}'
\qquad\qquad\textbf{間違い:} \verb'\displaystyle{...}'
\end{center}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\section{Other packages of interest}
\section{このほかのパッケージ}
\label{other-packages}
%Many other \LaTeX{} packages that address some aspect of mathematical
%formulas are available from CTAN (the Comprehensive \TeX{} Archive
%Network). To recommend a few examples:
数式のためドキュメントの組版に便利な他の多くの\LaTeX{}パッケージがCTAN(Comprehensive \TeX{}アーカイブネットワーク)から利用できます.
いくつかのお勧めを紹介します:
\begin{description}
%\raggedright
%\item[mathtools] Additional features extending \pkg{amsmath}; loads
% \pkg{amsmath}.
%\item[amsthm] General theorem and proof setup.
%\item[amsfonts] Defines \cn{mathbb} and \cn{mathfrak}, and provides access
% to many additional symbols (without names; \pkg{amssymb} provides the
% names).
%\item[accents] Under accents and accents using arbitrary symbols.
%\item[bm] Bold math package, provides a more general and more robust
% implementation of \cn{boldsymbol}.
%\item[mathrsfs] Ralph Smith's Formal Script, font setup.
%\item[cases] Apply a large brace to two or more equations without
% losing the individual equation numbers.
%\item[delarray] Delimiters spanning multiple rows of an array.
%%%\item[kuvio] Commutative diagrams and other diagrams. % not in TeX Live
%\item[xypic] Commutative diagrams and other diagrams.
%\item[TikZ] Comprehensive graphical facilities, including features for
% drawing diagrams.
\item[mathtools] \pkg{amsmath}に,さらに機能を追加したもの:\pkg{amsmath}を読み込みます.
\item[amsthm] 定理と証明を作成するためのもの.
\item[amsfonts] \cn{mathbb}と\cn{mathfrak}を定義し,多くの記号を使うことができるようにします(\pkg{amssymb}に含まれています).
\item[accents] アクセントと任意の記号を使ったアクセントの作成.
\item[bm] 太字のための数学パッケージで,\cn{boldsymbol}より一般的でより堅牢な実装を提供します.
\item[mathrsfs] Ralph Smithの筆記体です.
\item[cases] 2つ以上の方程式のそれぞれに式番号を降らずに,大きなブレースカッコでまとめます.
\item[delarray] 配列の複数の行にまたがるデリミタです.
%%\item[kuvio] Commutative diagrams and other diagrams. % not in TeX Live
\item[xypic] 可換図式とそれ以外の図のため.
\item[TikZ] ダイアグラムをはじめ,多くのグラフ作成のため.
\end{description}
%The \TeX{} Catalogue,\\
\TeX{}カタログの\\
\null\hspace{2\parindent}
\url{http://mirror.ctan.org/help/Catalogue/alpha.html},\\
%is a good place to look if you know a package's name.
は,パッケージ名を知っている場合には適しています.
\medskip
%Questions and answers on specific \TeX-related topics are the
%\emph{raison d'\^etre} of this forum:\\
\TeX{}に関係する質問や答えを調べる場合は,
次のフォーラムがあります:\\
\null\hspace{2\parindent}
\url{https://tex.stackexchange.com/questions}\\
%Check the archives for existing answers; pointers to selected topics
%may expedite your search:\\
すでに,誰かによって答えが示されている場合があるので,まずアーカイブを調べます.
整理された話題をもとに,そこから探すと答えを素早く得られます:\\
\null\hspace{2\parindent}
\url{https://tex.meta.stackexchange.com/a/2425#2425}\\
%If nothing useful turns up, ask your own question.
探しても見つからない場合には,あなたが初めての質問者となります.
%\newpage
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\section{Other documentation of interest}
\section{その他の役に立つドキュメント}
\begin{thebibliography}{AMUG}
\raggedright
\bibitem[AMUG]{amsldoc} American Mathematical Society and the \LaTeX3 Project:
\emph{User's Guide for the \textnormal{\ttfamily amsmath} package},
Version~2.$+$,
\url{http://mirror.ctan.org/macros/latex/required/amsmath/amsldoc.tex} and
\url{http://mirror.ctan.org/macros/latex/required/amsmath/amsldoc.pdf},
2017.
\bibitem[AFUG]{amsfndoc} American Mathematical Society:
\emph{User's Guide, AMSFonts},
\url{http://mirror.ctan.org/fonts/amsfonts/amsfndoc.pdf}, 2002.
\bibitem[CLSL]{comprehensive} Scott Pakin:
\emph{The Comprehensive \LaTeX{} Symbol List},
\url{http://mirror.ctan.org/tex-archive/info/symbols/comprehensive/},
January 2017. Raw font tables, without symbol names, are shown
alphabetically by font name in the \fn{rawtables*.pdf} files in the
same area of CTAN and from \TeX\,Live with \texttt{texdoc rawtables}.
\bibitem[Lam]{lamport} Leslie Lamport: \emph{\LaTeX{}: A document
preparation system}, 2nd edition, Addison-Wesley, 1994.
\bibitem[LC]{companion} Frank Mittelbach and Michel Goossens,
with Johannes Braams, David Carlisle, and Chris Rowley:
\emph{The \LaTeX{} Companion}, 2nd edition, Addison-Wesley, 2004.
\bibitem[LFG]{fntguide} \LaTeX3 Project Team: \emph{\LaTeXe{} font
selection}, % \fn{fntguide.tex}, November 2005.
\url{http://mirror.ctan.org/macros/latex/doc/fntguide.pdf}, 2005.
\bibitem[LGC]{graphics-companion} Michel Goossens, Frank Mittelbach,
Sebastian Rahtz, Denis Roegel, and Herbert~Vo\ss:
\emph{The \LaTeX{} Graphics Companion}, 2nd edition, Addison-Wesley, 2008.
\bibitem[LGG]{grfguide} D.~P. Carlisle, \LaTeX3 Project:
\emph{Packages in the `graphics' bundle}, %\fn{grfguide.tex}, 2017.
\url{http://mirror.ctan.org/macros/latex/required/graphics/grfguide.pdf},
2017.
\bibitem[LUG]{usrguide} \LaTeX3 Project Team: \emph{\LaTeXe~for
authors}, % \fn{usrguide.tex}, 2015.
\url{http://mirror.ctan.org/macros/latex/doc/usrguide.pdf}, 2015.
\bibitem[MML]{gratzer} George Gr\"atzer: \textit{More Math into \LaTeX},
5th edition, Springer, New York, 2016.
\bibitem[UCM]{uc-math} Will Robertson: \emph{Every symbol
\textup{(}most symbols\textup{)} defined by \pkg{unicode-math}},
\url{http://mirror.ctan.org/macros/latex/contrib/unicode-math/unimath-symbols.pdf}, 2017; and\\
Will Robertson, Philipp Stephani, Joseph Wright, and Khaled Hosny:
\emph{Experimental Unicode mathematical typesetting: The \pkg{unicode-math}
package},
\url{http://mirror.ctan.org/macros/latex/contrib/unicode-math/unicode-math.pdf}, 2017.
\end{thebibliography}
\end{document}