UPDATE 数学符号
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%!TEX program = xelatex
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%表示用xelatex编译文件
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\documentclass[a4paper]{ctexart}
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\usepackage{array}
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\usepackage{tabularx}
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\usepackage{indentfirst}
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\setlength{\parindent}{2em}
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\usepackage{booktabs}
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\usepackage{multirow}
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\usepackage{makecell}
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\usepackage{graphicx}
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\usepackage{subfig}
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\usepackage{amsmath}
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\usepackage{amsfonts}
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\usepackage{amssymb}
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\usepackage{amsthm}
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\usepackage{latexsym}
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\begin{document}
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\title{标题页}
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\author{Ryan\thanks{注脚}%
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\and Fan\thanks{注脚}%
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}
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\date{\today}
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\maketitle
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\abstract
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一般用于紧跟\textbackslash maketitle 命令之后介绍文档的摘要\par
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中文\LaTeX{}排版。
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\section{用\LaTeX 排版文字}
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{}分段\\换行\textbackslash\textbackslash\par
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冒号``please press the `x' key.''\par
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连字符-用来组成复合词，\\%
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短破折号--用来连接数字表示范围，\\%
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长破折号---用来连接单词\par
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省略号\dots{}和\ldots\par
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波浪号～\par
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强调\underline{文字,但是无法换行，}%
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\uline{ulem 宏包解决了这一问题,它提供的 uline 命令能够轻松生成自动换行的下划线。}%
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\emph{emph 命令用来将文字变为斜体以示强调。%
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\emph{如果在本身已经用 emph 命令强调的文字内部嵌套使用 emph 命令,}%
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内部则使用直立体文字。%
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}\par
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在合适的位置插入一个不会断行的空格Fig.~1, Ryan~Fan\par
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断行\\[15pt]可以带可选参数 $\langle length\rangle$,用于在换行处向下增加垂直间距%
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\newline{}或者newline命令，不用带参数\par
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\newpage 断页，在在双栏排版中只起到另起一栏的作用\par
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断词 I think this is: supercalifragil\-isticexpialidocious. %
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And I think this is: supercalifragilisticexpialidocious.\par
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\newpage
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\tableofcontents
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\section[目录和页眉页脚]{章节}
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\subsection{子章节}
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\subsubsection{子子章节}
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\paragraph{段落}
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\subparagraph{子段落}
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\section*{标题不带编号}
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\addcontentsline{toc}{section}{标题不带编号}
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\part{分块}
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\section{交叉引用}
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A reference to this subsection\label{sec:this} looks like: %
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``see section~\ref{sec:this} on page~\pageref{sec:this}.''
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\section{脚注和边注}
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“天地玄黄,宇宙洪荒。日月盈昃,辰宿列张。”\footnote{出自《千字文》。}\par
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\begin{tabular}{l}
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\hline
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有些情况下(比如在表格环境、各种盒子\\
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内)使用 footnote 并不能正确生成脚\\
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注。我们以分两步进行,先使用 \\
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footnotemark 为脚注计数,再在合适\\
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的位置用 footnotetext 生成脚注。\footnotemark\\
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\hline
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\end{tabular}
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\footnotetext{出自《千字文》。}
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\marginpar{\footnotesize 边注较窄,不要写过多文字,最好设置较小的字号。}
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\section{特殊环境}
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\subsection{列表}
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有序列表
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\begin{enumerate}
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\item An item.
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\begin{enumerate}
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\item A nested item.\label{itref}
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\item[*] A starred item.
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\end{enumerate}
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\item Reference(\ref{itref}).
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\end{enumerate}
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无序列表
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\begin{itemize}
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\item An item.
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\begin{itemize}
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\item A nested item.
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\item[+] A `plus' item. + A ‘plus’ item.
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\item Another item. – Another item.
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\end{itemize}
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\item Go back to upper level.
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\end{itemize}
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关键字环境
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\begin{description}
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\item[Enumerate] Numbered list.
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\item[Itemize] Non-numbered list.
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\end{description}
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重定义无序列表的符号
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\renewcommand{\labelitemi}{\dag}
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\renewcommand{\labelitemii}{\ddag}
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\begin{itemize}
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\item First item
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\begin{itemize}
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\item Subitem
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\item Subitem
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\end{itemize}
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\item Second item
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\end{itemize}
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重定义有序列表的符号
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\renewcommand{\labelenumi}{\Alph{enumi}>}
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\begin{enumerate}
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\item First item
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\item Second item
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\end{enumerate}
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\subsection{对齐环境}
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center、flushleft 和 flushright 环境分别用于生成%
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居中、左对齐和右对齐的文本环境。
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\begin{center}
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Centered text using a
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\verb|center| environment.
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\end{center}
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\begin{flushleft}
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Left-aligned text using a
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\verb|flushleft| environment.
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\end{flushleft}
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\begin{flushright}
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Right-aligned text using a
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\verb|flushright| environment.
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\end{flushright}
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还可以用以下命令直接改变文字的对齐方式:
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\centering
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Centered text paragraph.\par
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\raggedright
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Left-aligned text paragraph.\par
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\raggedleft
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Right-aligned text paragraph.\par
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\begin{flushleft}
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center 等环境会在上下文产生一个额外间距,%
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而 \textbackslash centering 等命令不产生,只是改变对齐方式。%
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\end{flushleft}
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\raggedright
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比如在浮动体环境 table 或 figure 内实现居中对齐,%
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用 \textbackslash centering 命令即可,没必要再用 center 环境。
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\subsection{引用环境}
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\begin{description}
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\item[quote] 用于引用较短的文字,首行不缩进\\
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Francis Bacon says:
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\begin{quote}
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Knowledge is power.
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\end{quote}
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\item[quotation] 用于引用若干段文字,首行缩进\\
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《木兰诗》:
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\begin{quotation}
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万里赴戎机,关山度若飞。
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朔气传金柝,寒光照铁衣。
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将军百战死,壮士十年归。
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归来见天子,天子坐明堂。
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策勋十二转,赏赐百千强。......
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\end{quotation}
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\end{description}
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\subsection{代码环境}
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\begin{verbatim}
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#include <iostream>
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int main()
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{
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std::cout << "Hello, world!"
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<< std::endl;
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return 0;
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}
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\end{verbatim}
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\begin{verbatim*}
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for (int i=0; i<4; ++i)
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printf("Number %d\n",i);
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\end{verbatim*}
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要排版简短的代码或关键字\textbackslash verb $\langle delim\rangle\langle code\rangle\langle delim\rangle$\par
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$\langle delim\rangle$ 标明代码的分界位置,前后必须一致,除字母、空格或星号外,%
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可任意选择使得不与代码本身冲突,习惯上使用 | 符号。\par
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\verb|\LaTeX| \\
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\verb+(a || b)+ \verb*+(a || b)+
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\subsection{表格}
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\subsubsection{列表格}
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tabular 环境使用 $\langle column-spec\rangle$ 参数指定表格的列数以及每列的格式。\par
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\begin{tabular}{lcr|p{6em}}
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\hline
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left & center & right & par box with fixed width\\
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L & C & R & P\\
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\hline
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\end{tabular}\par
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@ 格式可在单元格前后插入任意的文本,%
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但同时它也消除了单元格前后额外添加的间距。\par
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\begin{tabular}{@{} r@{:}lr @{}}
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\hline
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1 & 1 & one\\
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11 & 3 & eleven\\
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\hline
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\end{tabular}\par
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格式参数重复\par
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\begin{tabular}{|*{5}{c|}*{2}{p{3em}|}}
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\hline
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one & two & three & four & five & Hello! \LaTeX & Hello!\\
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1 & 2 & 3 & 4 & 5 & hello! & \LaTeX\\
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\hline
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\end{tabular}\par
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辅助格式 > 和 <,用于给列格式前后加上修饰命令\par
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\begin{tabular}{>{\itshape}r<{*}l}
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%需要使用array宏包
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\hline
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italic & normal \\
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column & column \\
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\hline
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\end{tabular}\par
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\begin{tabular}{>{\centering\arraybackslash}p{16em}}
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\hline
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辅助格式甚至支持插入 \textbackslash centering 等%
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命令改变 p 列格式的对齐方式,一般还要加额外的命令 %
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\textbackslash arraybackslash 以免出错。\\
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\hline
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\textbackslash centering 等对齐命令会破坏表格环境里 %
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\textbackslash\textbackslash 换行命令的定义,%
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\textbackslash arraybackslash 用来恢复之。%
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如果不加 \textbackslash arraybackslash 命令,%
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也可以用 \textbackslash tabularnewline 命令%
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代替原来的 \textbackslash\textbackslash 实现表格换行。\\
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\hline
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\end{tabular}\par
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\LaTeX 本身提供了 tabular* 环境用来排版定宽表格,但是不太方便使用,%
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比如要用到 @ 格式插入额外命令,令单元格之间的间距为 \textbackslash fill,%
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但即使这样仍然有瑕疵:\par
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\begin{tabular*}{14em}{@{\extracolsep{\fill}}|c|c|c|c|}
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\hline
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A & B & C & D \\
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\hline
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a & b & c & d \\
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\hline
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\end{tabular*}\par
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tabularx 宏包为我们提供了方便的解决方案。它引入了一个 X 列格式,%
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类似 p 列格式,不过会根据表格宽度自动计算列宽,多个X列格式平均分配列宽。%
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X列格式也可以用 array 里的辅助 格式修饰对齐方式:\par
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\begin{tabularx}{14em}{|*{4}{>{\centering\arraybackslash}X|}}
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\hline
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A & B & C & D \\
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\hline
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a & b & c & d \\
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\hline
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\end{tabularx}\par
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\subsubsection{横线}
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\textbackslash cline\{$\langle i-j\rangle$\} 用来绘制跨越部分单元格的横线:\par
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\begin{tabular}{|c|c|c|}
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\hline
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4 & 9 & 2 \\ \cline{2-3}
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3 & 5 & 7 \\ \cline{1-1}
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8 & 1 & 6 \\
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\hline
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\end{tabular}\par
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三线表由 booktabs 宏包 支持,它提供了 \textbackslash toprule、%
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\textbackslash midrule 和 \textbackslash bottomrule %
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命令用以排版三线表的三条线, 以及和 \textbackslash cline 对应的 %
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\textbackslash cmidrule。除此之外,最好不要用其它横线以及竖线:\par
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\begin{tabular}{cccc}
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\toprule
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& \multicolumn{3}{c}{Numbers} \\
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\cmidrule{2-4}
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& 1 & 2 & 3 \\
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\midrule
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Alphbet & A & B & C \\
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Roman & I & II& III \\
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\bottomrule
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\end{tabular} \par
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\subsubsection{合并单元格}
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横向合并单元格较为容易,由 \textbackslash multicolumn\{$\langle n\rangle$\}\{$\langle column-spec\rangle$\}\{$\langle item\rangle$\} %
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命令实现:\par
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其中 $\langle n\rangle$ 为要合并的列数,$\langle column-spec\rangle$ 为合并单元格后的列格式,只允许出现一个 l/c/r 或 p 格式。%
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如果合并前的单元格前后带表格线 |,合并后的列格式也要带 | 以使得表格的竖线一致。\par
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形如 \textbackslash multicolumn\{1\}\{$\langle column-spec\rangle$\}\{$\langle item\rangle$\} %
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的命令可以用来修改某一个单元格的列格式。\par
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\begin{tabular}{|c|c|c|}
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\hline
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1 & 2 & Center \\
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\hline
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\multicolumn{2}{|c|}{3} & \multicolumn{1}{r|}{Right} \\
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\hline
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4 & \multicolumn{2}{c|}{C} \\
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\hline
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\end{tabular}\par
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纵向合并单元格需要用到 multirow 宏包提供的 %
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\textbackslash multirow\{$\langle n\rangle$\}\{$\langle width\rangle$\}\{$\langle item\rangle$\} 命令:\par
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$\langle width\rangle$ 为合并后单元格的宽度,可以填 * 以使用自然宽度。\par
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\begin{tabular}{ccc}
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\hline
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\multirow{2}{*}{Item} & \multicolumn{2}{c}{Value} \\
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\cline{2-3}
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& First & Second \\
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\hline
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A & 1 & 2 \\
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\hline
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\end{tabular}
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\subsubsection{嵌套表格}
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在单元格中嵌套一个小表格可 以起到``拆分单元格''的效果。\par
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注意要用 \textbackslash multicolumn 命令配合 @\{\} %
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格式把单元格的额外边距去掉,使得嵌套的表格线能和外层的表格线正确相连:\par
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\begin{tabular}{|c|c|c|}
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\hline
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a & b & c \\
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\hline
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a & \multicolumn{1}{@{}c@{}|}
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{\begin{tabular}{c|c}
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e & f \\
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\hline
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e & f \\
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\end{tabular}} & c \\
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\hline
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a & b & c \\
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\hline
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\end{tabular}\par
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如果不需要为“拆分的单元格”画线,并且只在垂直方向“拆分”的话,makecell 宏包%
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提供 的 \textbackslash makecell 命令是一个简单的解决方案:\par
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\begin{tabular}{|c|c|}
|
||||||
|
\hline
|
||||||
|
a & \makecell{d1 \\ d2} \\
|
||||||
|
\hline
|
||||||
|
b & c \\
|
||||||
|
\hline
|
||||||
|
\end{tabular}
|
||||||
|
\subsubsection{行距控制}
|
||||||
|
\LaTeX 生成的表格看起来通常比较紧凑。%
|
||||||
|
修改参数 \textbackslash arraystretch 可以得到行距更加宽松 的表格:\par
|
||||||
|
\renewcommand\arraystretch{1.8}
|
||||||
|
\begin{tabular}{|c|}
|
||||||
|
\hline
|
||||||
|
Really loose \\
|
||||||
|
\hline
|
||||||
|
tabular rows. \\
|
||||||
|
\hline
|
||||||
|
\end{tabular}\par
|
||||||
|
另一种增加间距的办法是给换行命令 \textbackslash\textbackslash 添加可选参数,%
|
||||||
|
在这一行下面加额外的间距,适合用于在行间不加横线的表格:\par
|
||||||
|
\renewcommand\arraystretch{1}
|
||||||
|
\begin{tabular}{c}
|
||||||
|
\hline
|
||||||
|
Head lines \\[6pt]
|
||||||
|
tabular lines \\
|
||||||
|
tabular lines \\
|
||||||
|
\hline
|
||||||
|
\end{tabular}
|
||||||
|
\subsection{图片}
|
||||||
|
\LaTeX 本身不支持插图功能,需要由 graphicx 宏包辅助支持。\par
|
||||||
|
使用 \textbackslash includegraphics[$\langle options\rangle$]\{$\langle filename\rangle$\} 命令加载图片了:\par
|
||||||
|
其中 $\langle filename\rangle$ 为图片文件名,文件名有时需要使用相对路径或绝对路径。\par
|
||||||
|
\textbackslash graphicspath 命令,用于声明一个或多个图片文件存放的目录,%
|
||||||
|
使用这些目录里的图片时可不用写路径:\par
|
||||||
|
\textbackslash includegraphics 命令的可选参数 $\langle options\rangle$ 支持 %
|
||||||
|
$\langle key\rangle$=$\langle value\rangle$ 形式赋值,常用的参数如下:\par
|
||||||
|
\begin{tabular}{ll}
|
||||||
|
\hline
|
||||||
|
参数 & 含义 \\
|
||||||
|
\hline
|
||||||
|
width=$\langle width\rangle$ & 将图片缩放到宽度为$\langle width\rangle$ \\
|
||||||
|
height=$\langle height\rangle$ & 将图片缩放到高度为$\langle height\rangle$ \\
|
||||||
|
scale=$\langle scale\rangle$ & 将图片相对于原尺寸缩放$\langle scale\rangle$倍 \\
|
||||||
|
angle=$\langle angle\rangle$ & 令图片逆时针旋转$\langle angle\rangle$度 \\
|
||||||
|
\hline
|
||||||
|
\end{tabular}
|
||||||
|
\includegraphics[scale=0.05]{/home/ryan/Pictures/wallpaper/heic2007a}
|
||||||
|
\graphicspath{{/home/ryan/Pictures/wallpaper/}}
|
||||||
|
\includegraphics[scale=0.05]{heic1501a}
|
||||||
|
\subsection{盒子}
|
||||||
|
\subsubsection{水平盒子}
|
||||||
|
\textbackslash mbox\{\ldots \}\par
|
||||||
|
\textbackslash makebox$[\langle width\rangle][\langle align\rangle]\{\ldots \}$\par
|
||||||
|
\textbackslash mbox 生成一个基本的水平盒子,内容只有一行,不允许分段(除非嵌套其它盒子)
|
||||||
|
\textbackslash makebox 更进一步,可以加上可选参数用于控制盒子的宽度 $\langle width\rangle$,%
|
||||||
|
以及内容的对齐方式$\langle align\rangle$,可选居中 c(默认值) 、左对齐 l、右对齐 r 和分散对齐 s\par
|
||||||
|
|\mbox{Test some words.}|\\
|
||||||
|
|\makebox[10em]{Test some words.}|\\
|
||||||
|
|\makebox[10em][l]{Test some words.}|\\
|
||||||
|
|\makebox[10em][r]{Test some words.}|\\
|
||||||
|
|\makebox[10em][s]{Test some words.}|\par
|
||||||
|
\subsubsection{带框的水平盒子}
|
||||||
|
\textbackslash fbox 和 \textbackslash framebox 让我们可以为水平盒子添加边框。\par
|
||||||
|
\fbox{Test some words.}\\
|
||||||
|
\framebox[10em][r]{Test some words.}\par
|
||||||
|
可以通过 \textbackslash setlength 命令调节边框的宽度 \textbackslash fboxrule %
|
||||||
|
和内边距 \textbackslash fboxsep:\par
|
||||||
|
\framebox[10em][r]{Test box.}\\
|
||||||
|
\setlength{\fboxrule}{1.6pt}
|
||||||
|
\setlength{\fboxsep}{1em}
|
||||||
|
\framebox[10em][r]{Test box.}\par
|
||||||
|
\subsubsection{垂直盒子}
|
||||||
|
排版一个文字可以换行的盒子:\par
|
||||||
|
\textbackslash parbox$[\langle align\rangle][\langle height\rangle][\langle inner-align\rangle]\{\langle width\rangle\}\{\ldots \}$
|
||||||
|
\textbackslash begin\{minipage\}$[\langle align\rangle][\langle height\rangle][\langle inner-align\rangle]\{\langle width\rangle\}$\\
|
||||||
|
\ldots\\
|
||||||
|
\textbackslash end\{minipage\}\par
|
||||||
|
其中 $[\langle align\rangle]$ 为盒子和周围文字的对齐情况(类似 tabular 环境); %
|
||||||
|
$\langle height\rangle$ 和 $\langle inner-align\rangle$设置盒子的高度和内容的对齐方式,%
|
||||||
|
类似水平盒子 \textbackslash makebox 的设置,不过 $\langle inner-align\rangle$ 接受的%
|
||||||
|
参数是顶部 t、底部 b、居中 c 和分散对齐 s。\par
|
||||||
|
三字经：\parbox[t]{3em}{人之初 性本善 性相近 习相远}
|
||||||
|
\quad
|
||||||
|
千字文：
|
||||||
|
\begin{minipage}[b][8ex][t]{4em}
|
||||||
|
天地玄黄 宇宙洪荒
|
||||||
|
\end{minipage}\par
|
||||||
|
如果在 minipage 里使用 \textbackslash footnote 命令,生成的脚注会出现在盒子底部,编号是独立的, %
|
||||||
|
并且使用小写字母编号。而在 \textbackslash parbox 里无法正常使用 \textbackslash footnote 命令,%
|
||||||
|
只能在盒子里使用\textbackslash footnotemark,在盒子外使用\textbackslash footnotetext。\par
|
||||||
|
\fbox{这是一个垂直盒子的测试。\footnotemark}
|
||||||
|
\footnotetext{注脚来自fbox}
|
||||||
|
\fbox{\begin{minipage}{15em}%
|
||||||
|
这是一个垂直盒子的测试。
|
||||||
|
\footnote{注脚来自minipage.}
|
||||||
|
\end{minipage}
|
||||||
|
}\par
|
||||||
|
\subsubsection{标尺盒子}
|
||||||
|
\textbackslash rule $[\langle raise\rangle]\{\langle width\rangle\}\{\langle height\rangle\}$%
|
||||||
|
命令用来画一个实心的矩形盒子,也可适当调整以用来画线(标尺):\par
|
||||||
|
Black \rule{12pt}{4pt} box.\\
|
||||||
|
Upper \rule[4pt]{6pt}{8pt} and lower \rule[-4pt]{6pt}{8pt} box.\\
|
||||||
|
A \rule[-.4pt]{6pt}{.4pt} line.\par
|
||||||
|
\subsection{浮动体}
|
||||||
|
\LaTeX 预定义了两类浮动体环境 figure 和 table。习惯上 figure 里放图片,table 里放表格,但并没有严格限制,%
|
||||||
|
可以在任何一个浮动体里放置文字、公式、表格、图片等等任意内容。\par
|
||||||
|
\textbackslash begin\{table\}$[\langle placement\rangle]$\\
|
||||||
|
\ldots\\
|
||||||
|
\textbackslash end\{table\}\par
|
||||||
|
$[\langle placement\rangle]$ 参数提供了一些符号用来表示浮动体允许排版的位置,%
|
||||||
|
如 hbp 允许浮动体排版在当前位置、底部或者单独成页。table 和 figure 浮动体的默认设置为 tbp。\par
|
||||||
|
双栏排版环境下,\LaTeX 提供了 table* 和 figure* 环境用来排版跨栏的浮动体。它们的用%
|
||||||
|
法与 table 和 figure 一样,不同之处为双栏的 $[\langle placement\rangle]$ 参数只能用 tp 两个位置。\par
|
||||||
|
\begin{tabular}{ll}
|
||||||
|
\toprule
|
||||||
|
参数 & 含义\\
|
||||||
|
\midrule
|
||||||
|
h & 当前位置(代码所处的上下文)\\
|
||||||
|
t & 顶部\\
|
||||||
|
b & 底部\\
|
||||||
|
p & 单独成页\\
|
||||||
|
! & 在决定位置时忽视限制\\
|
||||||
|
\bottomrule
|
||||||
|
\end{tabular}\par
|
||||||
|
\textbackslash clearpage 命令 会在另起一页之前,先将所有推迟处理的浮动体排版成页,%
|
||||||
|
此时 htbp 等位置限制被完全忽略。\par
|
||||||
|
float 宏包为浮动体提供了 H 位置参数,不与 htbp 及 ! 混用。使用 H 位置参数时,%
|
||||||
|
会取消浮 动机制,将浮动体视为一般的盒子插入当前位置。\par
|
||||||
|
\subsubsection{浮动体的标题}
|
||||||
|
图表等浮动体提供了 \textbackslash caption\{\ldots\} 命令加标题,并且自动给浮动体编号:\par
|
||||||
|
可以用带星号的命令 \textbackslash caption* 生成不带编号 的标题,%
|
||||||
|
也可以使用带可选参数的形式 \textbackslash caption[\ldots]\{\ldots\},
|
||||||
|
使得在目录里使用短标题。\textbackslash caption 命令之后还可以紧跟 %
|
||||||
|
\textbackslash label 命令标记交叉引用。\par
|
||||||
|
可通过修改 \textbackslash figurename 和 \textbackslash tablename %
|
||||||
|
的内容来修改标题的前缀。标题样式的 定制功能由 caption 宏包提供.\par
|
||||||
|
table 和 figure 两种浮动体分别有各自的生成目录的命令:\\
|
||||||
|
\textbackslash listoftables\\
|
||||||
|
\textbackslash listoffigures\par
|
||||||
|
\subsubsection{并排和子图表}
|
||||||
|
\begin{figure}[htbp]
|
||||||
|
\centering
|
||||||
|
\includegraphics[scale=0.015]{heic1501a}
|
||||||
|
\qquad
|
||||||
|
\includegraphics[scale=0.015]{heic2007a}\\
|
||||||
|
\includegraphics[scale=0.02]{opo0501a}
|
||||||
|
\caption{图片标题}
|
||||||
|
\label{}
|
||||||
|
\end{figure}
|
||||||
|
由于标题是横跨一行的,用 \textbackslash caption 命令为每个图片单独生成标题%
|
||||||
|
就需要借助前文提到的\textbackslash parbox 或者 minipage 环境,将标题限制在盒子内。\par
|
||||||
|
\begin{figure}[htbp]
|
||||||
|
\centering
|
||||||
|
\begin{minipage}[b][120pt][t]{0.45\linewidth}
|
||||||
|
\centering
|
||||||
|
\includegraphics[scale=0.025]{heic1501a}
|
||||||
|
\caption{并排图1}
|
||||||
|
\end{minipage}
|
||||||
|
\qquad
|
||||||
|
\begin{minipage}[b][120pt][t]{0.45\linewidth}
|
||||||
|
\centering
|
||||||
|
\includegraphics[scale=0.025]{heic2007a}
|
||||||
|
\caption{并排图2}
|
||||||
|
\end{minipage}
|
||||||
|
\end{figure}
|
||||||
|
给每个图片定义小标题时,就要用到 subfig 宏包的功能
|
||||||
|
\begin{figure}[htbp]
|
||||||
|
\centering
|
||||||
|
\subfloat[]{%
|
||||||
|
\begin{minipage}[b][100pt][t]{0.45\linewidth}
|
||||||
|
\centering
|
||||||
|
\includegraphics[scale=0.025]{heic2007a}
|
||||||
|
\end{minipage}
|
||||||
|
}
|
||||||
|
\qquad
|
||||||
|
\subfloat[]{%
|
||||||
|
\begin{minipage}[b][100pt][t]{0.45\linewidth}
|
||||||
|
\centering
|
||||||
|
\includegraphics[scale=0.025]{heic1501a}
|
||||||
|
\end{minipage}
|
||||||
|
}
|
||||||
|
\caption{使用 subfig 宏包的 \textbackslash subfloat 命令排版子图。}
|
||||||
|
\end{figure}
|
||||||
|
\section{数学公式}
|
||||||
|
amsmath 宏 包,对多行公式的排版提供了有力的支持,%
|
||||||
|
amsfonts 宏包以及基于它的 amssymb 宏包提 供了丰富的数学符号,%
|
||||||
|
amsthm 宏包扩展了 \LaTeX 定理证明格式。\par
|
||||||
|
\subsection{公式排版基础}
|
||||||
|
\subsubsection{行内和行间公式}
|
||||||
|
行内公式由一对 \$ 符号包裹:\\
|
||||||
|
The Pythagorean theorem is %
|
||||||
|
$a^2 + b^2 = c^2$.\par
|
||||||
|
行间公式在 \LaTeX 里由 equation 环境包裹,equation 环境为公式自动生成一 个编号,%
|
||||||
|
这个编号可以用 \textbackslash label 和 \textbackslash ref 生成交叉引用。\par
|
||||||
|
amsmath 的 \textbackslash eqref 命令甚至为引用 自动加上圆括号;%
|
||||||
|
还可以用 \textbackslash tag 命令手动修改公式的编号,%
|
||||||
|
或者用 \textbackslash notag 命令取消为公式编 号。\par
|
||||||
|
The Pythagorean theorem is:
|
||||||
|
\begin{equation}
|
||||||
|
a^2 + b^2 = c^2 \label{pythagorean}
|
||||||
|
\end{equation}
|
||||||
|
Equation \eqref{pythagorean} is called `Gougu theorem' in Chinese.\par
|
||||||
|
It's wrong to say
|
||||||
|
\begin{equation}
|
||||||
|
1 + 1 = 3 \tag{dumb}
|
||||||
|
\end{equation}
|
||||||
|
or
|
||||||
|
\begin{equation}
|
||||||
|
1 + 1 = 4 \notag
|
||||||
|
\end{equation}\par
|
||||||
|
直接使用不带编号的行间公式:
|
||||||
|
\begin{equation*}
|
||||||
|
a^2 + b^2 = c^2
|
||||||
|
\end{equation*}
|
||||||
|
For short:
|
||||||
|
\[a^2 + b^2 = c^2\]
|
||||||
|
Or if you like the long one:
|
||||||
|
\begin{displaymath}
|
||||||
|
a^2 + b^2 = c^2
|
||||||
|
\end{displaymath}
|
||||||
|
行内公式和行间公式的对比:\\
|
||||||
|
In text:
|
||||||
|
$\lim_{n \to \infty} \sum_{k=1}^n \frac{1}{k^2} = \frac{\pi^2}{6}$\\
|
||||||
|
In display:
|
||||||
|
\[\lim_{n \to \infty} \sum_{k=1}^n \frac{1}{k^2} = \frac{\pi^2}{6}\]
|
||||||
|
\subsection{数学模式}
|
||||||
|
\renewcommand{\labelenumi}{\arabic{enumi}.}
|
||||||
|
\begin{enumerate}
|
||||||
|
\item 数学模式中输入的空格被忽略。
|
||||||
|
\item 不允许有空行(分段)。
|
||||||
|
\item 所有的字母被当作数学公式中的变量处理,想在数学公式中输入正体的文本,%
|
||||||
|
可以用\textbackslash mathrm 或者 amsmath 提供的 \textbackslash text 命令。
|
||||||
|
\end{enumerate}
|
||||||
|
$x^2 \geq 0 \qquad
|
||||||
|
\text{for \textbf{all} } x \in \mathbb{R}$
|
||||||
|
\subsection{数学符号}
|
||||||
|
\subsubsection{一般符号}
|
||||||
|
\centering
|
||||||
|
文本/数学模式通用符号\\
|
||||||
|
\begin{tabular}{clclclcl}
|
||||||
|
\hline
|
||||||
|
\{ & \textbackslash\{ & \} & \textbackslash\} & \$ & \textbackslash\$ & \% & \textbackslash\% \\
|
||||||
|
\dag & \textbackslash dag & \S & \textbackslash S & \copyright & \textbackslash copyright & \dots & \textbackslash dots \\
|
||||||
|
\ddag & \textbackslash ddag & \P & \textbackslash P & \pounds & \textbackslash pounds \\
|
||||||
|
\hline
|
||||||
|
\end{tabular}
|
||||||
|
\newpage
|
||||||
|
希腊字母\par
|
||||||
|
\begin{tabular}{clclclcl}
|
||||||
|
\toprule
|
||||||
|
$\alpha$ & \textbackslash alpha & $\theta$ & \textbackslash theta &
|
||||||
|
$o$ & o & $\upsilon$ & \textbackslash upsilon \\
|
||||||
|
$\beta$ & \textbackslash beta & $\vartheta$ & \textbackslash vartheta &
|
||||||
|
$\pi$ & \textbackslash pi & $\phi$ & \textbackslash phi \\
|
||||||
|
$\gamma$ & \textbackslash gamma & $\iota$ & \textbackslash iota &
|
||||||
|
$\varpi$ & \textbackslash varpi & $\varphi$ & \textbackslash varphi \\
|
||||||
|
$\delta$ & \textbackslash delta & $\kappa$ & \textbackslash kappa &
|
||||||
|
$\rho$ & \textbackslash rho & $\chi$ & \textbackslash chi \\
|
||||||
|
$\epsilon$ & \textbackslash epsilon & $\lambda$ & \textbackslash lambda &
|
||||||
|
$\varrho$ & \textbackslash varrho & $\psi$ & \textbackslash psi \\
|
||||||
|
$\varepsilon$ & \textbackslash varepsilon & $\mu$ & \textbackslash mu &
|
||||||
|
$\sigma$ & \textbackslash sigma & $\omega$ & \textbackslash omega \\
|
||||||
|
$\zeta$ & \textbackslash zeta & $\nu$ & \textbackslash nu &
|
||||||
|
$\varsigma$ & \textbackslash varsigma \\
|
||||||
|
$\eta$ & \textbackslash eta & $\xi$ & \textbackslash xi &
|
||||||
|
$\tau$ & \textbackslash tau \\
|
||||||
|
\midrule
|
||||||
|
$\Gamma$ & \textbackslash Gamma & $\Lambda$ & \textbackslash Lambda &
|
||||||
|
$\Sigma$ & \textbackslash Sigma & $\Psi$ & \textbackslash Psi \\
|
||||||
|
$\Delta$ & \textbackslash Delta & $\Xi$ & \textbackslash Xi &
|
||||||
|
$\Upsilon$ & \textbackslash Upsilon & $\Omega$ & \textbackslash Omega \\
|
||||||
|
$\Theta$ & \textbackslash Theta & $\Pi$ & \textbackslash Pi &
|
||||||
|
$\Phi$ & \textbackslash Phi \\
|
||||||
|
\midrule
|
||||||
|
\multicolumn{4}{l}{以下命令依赖 amsmath 宏包}\\
|
||||||
|
$\varGamma$ & \textbackslash varGamma & $\varLambda$ & \textbackslash varLambda &
|
||||||
|
$\varSigma$ & \textbackslash varSigma & $\varPsi$ & \textbackslash varPsi \\
|
||||||
|
$\varDelta$ & \textbackslash varDelta & $\varXi$ & \textbackslash varXi &
|
||||||
|
$\varUpsilon$ & \textbackslash varUpsilon & $\varOmega$ & \textbackslash varOmega \\
|
||||||
|
$\varTheta$ & \textbackslash varTheta & $\varPi$ & \textbackslash varPi &
|
||||||
|
$\varPhi$ & \textbackslash varPhi \\
|
||||||
|
\midrule
|
||||||
|
\multicolumn{4}{l}{依赖 amssymb 宏包}\\
|
||||||
|
$\digamma$ & \textbackslash digamma & $\varkappa$ & \textbackslash varkappa &
|
||||||
|
$\beth$ & \textbackslash beth & $\gimel$ & \textbackslash gimel \\
|
||||||
|
$\daleth$ & \textbackslash daleth \\
|
||||||
|
\bottomrule
|
||||||
|
\end{tabular}\par
|
||||||
|
其它符号\par
|
||||||
|
\begin{tabular}{clclclcl}
|
||||||
|
\toprule
|
||||||
|
$\dots$ & \textbackslash dots & $\cdots$ & \textbackslash cdots &
|
||||||
|
$\vdots$ & \textbackslash vdots & $\ddots$ & \textbackslash ddots \\
|
||||||
|
$\hbar$ & \textbackslash hbar & $\imath$ & \textbackslash imath &
|
||||||
|
$\jmath$ & \textbackslash jmath & $\ell$ & \textbackslash ell \\
|
||||||
|
$\Re$ & \textbackslash Re & $\Im$ & \textbackslash Im &
|
||||||
|
$\aleph$ & \textbackslash aleph & $\wp$ & \textbackslash wp \\
|
||||||
|
$\forall$ & \textbackslash forall & $\exists$ & \textbackslash exists &
|
||||||
|
$\partial$ & \textbackslash partial & $'$ & ' \\
|
||||||
|
$\prime$ & \textbackslash prime & $\emptyset$ & \textbackslash emptyset &
|
||||||
|
$\infty$ & \textbackslash infty & $\nabla$ & \textbackslash nabla \\
|
||||||
|
$\triangle$ & \textbackslash triangle & $\bot$ & \textbackslash bot &
|
||||||
|
$\top$ & \textbackslash top & $\angle$ & \textbackslash angle \\
|
||||||
|
$\surd$ & \textbackslash surd & $\diamondsuit$ & \textbackslash diamondsuit &
|
||||||
|
$\heartsuit$ & \textbackslash heartsuit & $\clubsuit$ & \textbackslash clubsuit \\
|
||||||
|
$\spadesuit$ & \textbackslash spadesuit & $\neg$ & \textbackslash neg or \textbackslash lnot &
|
||||||
|
$\flat$ & \textbackslash flat & $\natural$ & \textbackslash natural \\
|
||||||
|
$\sharp$ & \textbackslash sharp \\
|
||||||
|
\midrule
|
||||||
|
\multicolumn{4}{l}{以下命令依赖 latexsym 宏包}\\
|
||||||
|
$\mho$ & \textbackslash mho & $\Box$ & \textbackslash Box &
|
||||||
|
$\Diamond$ & \textbackslash Diamond \\
|
||||||
|
\bottomrule
|
||||||
|
\end{tabular}
|
||||||
|
\flushleft
|
||||||
|
$a_1,a_2,\dots,a_n$\\
|
||||||
|
$a_1 + a_2 + \cdots + a_n$\par
|
||||||
|
\subsubsection{指数、上下标和导数}
|
||||||
|
\textasciicircum 和 \_ 标明上下标。%
|
||||||
|
注意上下标的内容(子公式)一般需要用花括号包裹，否 则上下标只对后面的一个符号起作用:\par
|
||||||
|
$p^3_{ij} \qquad
|
||||||
|
m_\mathrm{Kunth} \qquad
|
||||||
|
\sum_{k=1}^3 k$\\
|
||||||
|
$a^x +y \neq a^{x+y} \qquad
|
||||||
|
e^{x^2} \neq {e^x}^2$ \par
|
||||||
|
导数符号$'$ 是一类特殊的上标,可以适当连用表示多阶导数,也可以在其后连用上标:\par
|
||||||
|
$f(x) = x^2 \quad
|
||||||
|
f'(x) = 2x \quad
|
||||||
|
f''^{2}(x) = 4$ \par
|
||||||
|
\subsubsection{分式和根式}
|
||||||
|
分式使用 \textbackslash frac\{分子\}\{分母\} 来书写。%
|
||||||
|
分式的大小在行间公式中是正常大小,而在行内被 极度压缩。%
|
||||||
|
amsmath 提供了方便的命令 \textbackslash dfrac 和 \textbackslash tfrac,%
|
||||||
|
令用户能够在行内使用正常大小的 分式，或是反过来。\par
|
||||||
|
In display style:
|
||||||
|
\[
|
||||||
|
3/8 \qquad
|
||||||
|
\frac{3}{8} \qquad
|
||||||
|
\tfrac{3}{8}
|
||||||
|
\]
|
||||||
|
In text style:
|
||||||
|
$1\frac{1}{2}$~hours \qquad
|
||||||
|
$1\dfrac{1}{2}$~hours\par
|
||||||
|
一般的根式使用 \textbackslash sqrt\{\dots\};%
|
||||||
|
表示 n 次方根时写成 \textbackslash sqrt[n]\{\dots\}。\par
|
||||||
|
$\sqrt{x} \Leftrightarrow x^{1/2} \quad
|
||||||
|
\sqrt[3]{2} \quad
|
||||||
|
\sqrt{x^{2} + \sqrt{y}}$ \par
|
||||||
|
特殊的分式形式,如二项式结构,由 amsmath 宏包的 \textbackslash binom 命令生成:\par
|
||||||
|
Pascal's rule is
|
||||||
|
\[
|
||||||
|
\binom{n}{k} = \binom{n - 1}{k} + \binom{n - 1}{k}
|
||||||
|
\]
|
||||||
|
\newpage
|
||||||
|
\subsubsection{关系符}
|
||||||
|
\centering
|
||||||
|
二元关系符\par
|
||||||
|
\begin{table}
|
||||||
|
\caption{二元关系符}
|
||||||
|
\begin{tabular}{clclcl}
|
||||||
|
\toprule
|
||||||
|
$<$ & < & $>$ & > &
|
||||||
|
$=$ & = \\
|
||||||
|
$\equiv$ & \textbackslash equiv & $\leq$ & \textbackslash leq or \textbackslash le &
|
||||||
|
$\geq$ & \textbackslash geq or \textbackslash ge \\
|
||||||
|
$\ll$ & \textbackslash ll & $\gg$ & \textbackslash gg &
|
||||||
|
$\doteq$ & \textbackslash doteq \\
|
||||||
|
$\prec$ & \textbackslash prec & $\succ$ & \textbackslash succ &
|
||||||
|
$\sim$ & \textbackslash sim \\
|
||||||
|
$\preceq$ & \textbackslash preceq & $\succeq$ & \textbackslash succeq &
|
||||||
|
$\simeq$ & \textbackslash simeq \\
|
||||||
|
$\subset$ & \textbackslash subset & $\supset$ & \textbackslash supset &
|
||||||
|
$\approx$ & \textbackslash approx \\
|
||||||
|
$\subseteq$ & \textbackslash subseteq & $\supseteq$ & \textbackslash supseteq &
|
||||||
|
$\cong$ & \textbackslash cong \\
|
||||||
|
$\sqsubseteq$ & \textbackslash sqsubseteq & $\sqsupseteq$ & \textbackslash sqsupseteq &
|
||||||
|
$\bowtie$ & \textbackslash bowtie \\
|
||||||
|
$\in$ & \textbackslash in & $\ni$ & \textbackslash ni ,\textbackslash owns &
|
||||||
|
$\propto$ & \textbackslash propto \\
|
||||||
|
$\vdash$ & \textbackslash vdash & $\dashv$ & \textbackslash dashv &
|
||||||
|
$\models$ & \textbackslash models \\
|
||||||
|
$\mid$ & \textbackslash mid & $\parallel$ & \textbackslash parallel &
|
||||||
|
$\perp$ & \textbackslash perp \\
|
||||||
|
$\smile$ & \textbackslash smile & $\frown$ & \textbackslash frown &
|
||||||
|
$\asymp$ & \textbackslash asymp \\
|
||||||
|
$:$ & : & $\notin$ & \textbackslash notin &
|
||||||
|
$\neq$ & \textbackslash neq or \textbackslash ne \\
|
||||||
|
\midrule
|
||||||
|
\multicolumn{4}{l}{以下命令依赖 latexsym 宏包}\\
|
||||||
|
$\sqsubset$ & \textbackslash sqsubset & $\sqsupset$ & \textbackslash sqsupset &
|
||||||
|
$\Join$ & \textbackslash Join \\
|
||||||
|
\midrule
|
||||||
|
\multicolumn{4}{l}{以下命令依赖 amssymb 宏包}\\
|
||||||
|
$\lessdot$ & \textbackslash lessdot & $\gtrdot$ & \textbackslash gtrdot &
|
||||||
|
$\doteqdot$ & \textbackslash doteqdot \\
|
||||||
|
$\leqslant$ & \textbackslash leqslant & $\geqslant$ & \textbackslash geqslant &
|
||||||
|
$\risingdotseq$ & \textbackslash risingdotseq \\
|
||||||
|
$\eqslantless$ & \textbackslash eqslantless & $\eqslantgtr$ & \textbackslash eqslantgtr &
|
||||||
|
$\fallingdotseq$ & \textbackslash fallingdotseq \\
|
||||||
|
$\leqq$ & \textbackslash leqq & $\geqq$ & \textbackslash geqq &
|
||||||
|
$\eqcirc$ & \textbackslash eqcirc \\
|
||||||
|
$\circeq$ & \textbackslash circeq & $\ggg$ & \textbackslash ggg &
|
||||||
|
$\lll$ & \textbackslash lll or \textbackslash llless \\
|
||||||
|
$\lesssim$ & \textbackslash lesssim & $\gtrsim$ & \textbackslash gtrsim &
|
||||||
|
$\triangleq$ & \textbackslash triangle \\
|
||||||
|
$\lessapprox$ & \textbackslash lessapprox & $\gtrapprox$ & \textbackslash gtrapprox &
|
||||||
|
$\bumpeq$ & \textbackslash bumpeq \\
|
||||||
|
$\lessgtr$ & \textbackslash lessgtr & $\gtrless$ & \textbackslash gtrless &
|
||||||
|
$\Bumpeq$ & \textbackslash Bumpeq \\
|
||||||
|
$\lesseqgtr$ & \textbackslash lesseqgtr & $\gtreqless$ & \textbackslash gtreqless &
|
||||||
|
$\thicksim$ & \textbackslash thicksim \\
|
||||||
|
$\lesseqqgtr$ & \textbackslash lesseqqgtr & $\gtreqqless$ & \textbackslash gtreqqless &
|
||||||
|
$\thickapprox$ & \textbackslash thickapprox \\
|
||||||
|
$\preccurlyeq$ & \textbackslash preccurlyeq & $\succcurlyeq$ & \textbackslash succcurlyeq &
|
||||||
|
$\approxeq$ & \textbackslash approxeq \\
|
||||||
|
$\curlyeqprec$ & \textbackslash curlyeqprec & $\curlyeqsucc$ & \textbackslash curlyeqsucc &
|
||||||
|
$\backsim$ & \textbackslash backsim \\
|
||||||
|
$\precsim$ & \textbackslash precsim & $\succsim$ & \textbackslash succsim &
|
||||||
|
$\backsimeq$ & \textbackslash backsimeq \\
|
||||||
|
$\precapprox$ & \textbackslash precapprox & $\succapprox$ & \textbackslash succapprox &
|
||||||
|
$\vDash$ & \textbackslash vDash \\
|
||||||
|
$\subseteqq$ & \textbackslash subseteqq & $\supseteqq$ & \textbackslash supseteqq &
|
||||||
|
$\Vdash$ & \textbackslash Vdash \\
|
||||||
|
$\shortparallel$ & \textbackslash shortparallel & $\Supset$ & \textbackslash Supset &
|
||||||
|
$\Vvdash$ & \textbackslash Vvdash \\
|
||||||
|
$\blacktriangleleft$ & \textbackslash blacktriangleleft & $\sqsupset$ & \textbackslash sqsupset &
|
||||||
|
$\backepsilon$ & \textbackslash backepsilon \\
|
||||||
|
$\vartriangleright$ & \textbackslash vartriangleright & $\because$ & \textbackslash because &
|
||||||
|
$\varpropto$ & \textbackslash varpropto \\
|
||||||
|
$\blacktriangleright$ & \textbackslash blacktriangleright & $\Subset$ & \textbackslash Subset &
|
||||||
|
$\between$ & \textbackslash between \\
|
||||||
|
$\trianglerighteq$ & \textbackslash trianglerighteq & $\smallfrown$ & \textbackslash smallfrown &
|
||||||
|
$\pitchfork$ & \textbackslash pitchfork \\
|
||||||
|
$\vartriangleleft$ & \textbackslash vartriangleleft & $\shortmid$ & \textbackslash shortmid &
|
||||||
|
$\smallsmile$ & \textbackslash smallsmile \\
|
||||||
|
$\trianglelefteq$ & \textbackslash trianglelefteq & $\therefore$ & \textbackslash therefore &
|
||||||
|
$\sqsubset$ & \textbackslash sqsubset \\
|
||||||
|
\bottomrule
|
||||||
|
\end{tabular}
|
||||||
|
\end{table}
|
||||||
|
\flushleft
|
||||||
|
\LaTeX 还提供了自定义二元关系符的命令 \textbackslash stackrel,用于将一个符号叠加在原有的二元关 系符之上:\par
|
||||||
|
\[
|
||||||
|
f_n(x) \stackrel{*}{\approx} 1
|
||||||
|
\]
|
||||||
|
|
||||||
|
\newpage
|
||||||
|
\appendix
|
||||||
|
\section{附录}
|
||||||
|
\end{document}
|
||||||
|
|||||||
Binary file not shown.
Binary file not shown.
@@ -1,4 +1,4 @@
|
|||||||
%!TEX program = xelatex
|
%TEX program = xelatex
|
||||||
%表示用xelatex编译文件
|
%表示用xelatex编译文件
|
||||||
\documentclass[a4paper]{ctexart}
|
\documentclass[a4paper]{ctexart}
|
||||||
\usepackage{array}
|
\usepackage{array}
|
||||||
@@ -10,6 +10,13 @@
|
|||||||
\usepackage{makecell}
|
\usepackage{makecell}
|
||||||
\usepackage{graphicx}
|
\usepackage{graphicx}
|
||||||
\usepackage{subfig}
|
\usepackage{subfig}
|
||||||
|
\usepackage{amsmath,amsfonts,amssymb,amsthm}
|
||||||
|
\usepackage{latexsym}
|
||||||
|
\usepackage{float}
|
||||||
|
\DeclareMathOperator{\argh}{argh}
|
||||||
|
\DeclareMathOperator*{\nut}{Nut}
|
||||||
|
\usepackage{yhmath}
|
||||||
|
|
||||||
\begin{document}
|
\begin{document}
|
||||||
\title{标题页}
|
\title{标题页}
|
||||||
\author{Ryan\thanks{注脚}%
|
\author{Ryan\thanks{注脚}%
|
||||||
@@ -494,8 +501,556 @@
|
|||||||
\end{minipage}
|
\end{minipage}
|
||||||
}
|
}
|
||||||
\caption{使用 subfig 宏包的 \textbackslash subfloat 命令排版子图。}
|
\caption{使用 subfig 宏包的 \textbackslash subfloat 命令排版子图。}
|
||||||
|
|
||||||
\end{figure}
|
\end{figure}
|
||||||
|
\section{数学公式}
|
||||||
|
amsmath 宏 包,对多行公式的排版提供了有力的支持,%
|
||||||
|
amsfonts 宏包以及基于它的 amssymb 宏包提 供了丰富的数学符号,%
|
||||||
|
amsthm 宏包扩展了 \LaTeX 定理证明格式。\par
|
||||||
|
\subsection{公式排版基础}
|
||||||
|
\subsubsection{行内和行间公式}
|
||||||
|
行内公式由一对 \$ 符号包裹:\\
|
||||||
|
The Pythagorean theorem is %
|
||||||
|
$a^2 + b^2 = c^2$.\par
|
||||||
|
行间公式在 \LaTeX 里由 equation 环境包裹,equation 环境为公式自动生成一 个编号,%
|
||||||
|
这个编号可以用 \textbackslash label 和 \textbackslash ref 生成交叉引用。\par
|
||||||
|
amsmath 的 \textbackslash eqref 命令甚至为引用 自动加上圆括号;%
|
||||||
|
还可以用 \textbackslash tag 命令手动修改公式的编号,%
|
||||||
|
或者用 \textbackslash notag 命令取消为公式编 号。\par
|
||||||
|
The Pythagorean theorem is:
|
||||||
|
\begin{equation}
|
||||||
|
a^2 + b^2 = c^2 \label{pythagorean}
|
||||||
|
\end{equation}
|
||||||
|
Equation \eqref{pythagorean} is called `Gougu theorem' in Chinese.\par
|
||||||
|
It's wrong to say
|
||||||
|
\begin{equation}
|
||||||
|
1 + 1 = 3 \tag{dumb}
|
||||||
|
\end{equation}
|
||||||
|
or
|
||||||
|
\begin{equation}
|
||||||
|
1 + 1 = 4 \notag
|
||||||
|
\end{equation}\par
|
||||||
|
直接使用不带编号的行间公式:
|
||||||
|
\begin{equation*}
|
||||||
|
a^2 + b^2 = c^2
|
||||||
|
\end{equation*}
|
||||||
|
For short:
|
||||||
|
\[a^2 + b^2 = c^2\]
|
||||||
|
Or if you like the long one:
|
||||||
|
\begin{displaymath}
|
||||||
|
a^2 + b^2 = c^2
|
||||||
|
\end{displaymath}
|
||||||
|
行内公式和行间公式的对比:\\
|
||||||
|
In text:
|
||||||
|
$\lim_{n \to \infty} \sum_{k=1}^n \frac{1}{k^2} = \frac{\pi^2}{6}$\\
|
||||||
|
In display:
|
||||||
|
\[\lim_{n \to \infty} \sum_{k=1}^n \frac{1}{k^2} = \frac{\pi^2}{6}\]
|
||||||
|
\subsection{数学模式}
|
||||||
|
\renewcommand{\labelenumi}{\arabic{enumi}.}
|
||||||
|
\begin{enumerate}
|
||||||
|
\item 数学模式中输入的空格被忽略。
|
||||||
|
\item 不允许有空行(分段)。
|
||||||
|
\item 所有的字母被当作数学公式中的变量处理,想在数学公式中输入正体的文本,%
|
||||||
|
可以用\textbackslash mathrm 或者 amsmath 提供的 \textbackslash text 命令。
|
||||||
|
\end{enumerate}
|
||||||
|
$x^2 \geq 0 \qquad
|
||||||
|
\text{for \textbf{all} } x \in \mathbb{R}$
|
||||||
|
\subsection{数学符号}
|
||||||
|
\subsubsection{一般符号}
|
||||||
|
\begin{table}[H]
|
||||||
|
\centering
|
||||||
|
\caption{文本/数学模式通用符号}
|
||||||
|
\begin{tabular}{clclclcl}
|
||||||
|
\hline
|
||||||
|
\{ & \textbackslash\{ & \} & \textbackslash\} & \$ & \textbackslash\$ & \% & \textbackslash\% \\
|
||||||
|
\dag & \textbackslash dag & \S & \textbackslash S & \copyright & \textbackslash copyright & \dots & \textbackslash dots \\
|
||||||
|
\ddag & \textbackslash ddag & \P & \textbackslash P & \pounds & \textbackslash pounds \\
|
||||||
|
\hline
|
||||||
|
\end{tabular}
|
||||||
|
\end{table}
|
||||||
|
\begin{table}[H]
|
||||||
|
\centering
|
||||||
|
\caption{希腊字母}
|
||||||
|
\begin{tabular}{clclclcl}
|
||||||
|
\toprule
|
||||||
|
$\alpha$ & \textbackslash alpha & $\theta$ & \textbackslash theta &
|
||||||
|
$o$ & o & $\upsilon$ & \textbackslash upsilon \\
|
||||||
|
$\beta$ & \textbackslash beta & $\vartheta$ & \textbackslash vartheta &
|
||||||
|
$\pi$ & \textbackslash pi & $\phi$ & \textbackslash phi \\
|
||||||
|
$\gamma$ & \textbackslash gamma & $\iota$ & \textbackslash iota &
|
||||||
|
$\varpi$ & \textbackslash varpi & $\varphi$ & \textbackslash varphi \\
|
||||||
|
$\delta$ & \textbackslash delta & $\kappa$ & \textbackslash kappa &
|
||||||
|
$\rho$ & \textbackslash rho & $\chi$ & \textbackslash chi \\
|
||||||
|
$\epsilon$ & \textbackslash epsilon & $\lambda$ & \textbackslash lambda &
|
||||||
|
$\varrho$ & \textbackslash varrho & $\psi$ & \textbackslash psi \\
|
||||||
|
$\varepsilon$ & \textbackslash varepsilon & $\mu$ & \textbackslash mu &
|
||||||
|
$\sigma$ & \textbackslash sigma & $\omega$ & \textbackslash omega \\
|
||||||
|
$\zeta$ & \textbackslash zeta & $\nu$ & \textbackslash nu &
|
||||||
|
$\varsigma$ & \textbackslash varsigma \\
|
||||||
|
$\eta$ & \textbackslash eta & $\xi$ & \textbackslash xi &
|
||||||
|
$\tau$ & \textbackslash tau \\
|
||||||
|
\midrule
|
||||||
|
$\Gamma$ & \textbackslash Gamma & $\Lambda$ & \textbackslash Lambda &
|
||||||
|
$\Sigma$ & \textbackslash Sigma & $\Psi$ & \textbackslash Psi \\
|
||||||
|
$\Delta$ & \textbackslash Delta & $\Xi$ & \textbackslash Xi &
|
||||||
|
$\Upsilon$ & \textbackslash Upsilon & $\Omega$ & \textbackslash Omega \\
|
||||||
|
$\Theta$ & \textbackslash Theta & $\Pi$ & \textbackslash Pi &
|
||||||
|
$\Phi$ & \textbackslash Phi \\
|
||||||
|
\midrule
|
||||||
|
\multicolumn{4}{l}{以下命令依赖 amsmath 宏包}\\
|
||||||
|
$\varGamma$ & \textbackslash varGamma & $\varLambda$ & \textbackslash varLambda &
|
||||||
|
$\varSigma$ & \textbackslash varSigma & $\varPsi$ & \textbackslash varPsi \\
|
||||||
|
$\varDelta$ & \textbackslash varDelta & $\varXi$ & \textbackslash varXi &
|
||||||
|
$\varUpsilon$ & \textbackslash varUpsilon & $\varOmega$ & \textbackslash varOmega \\
|
||||||
|
$\varTheta$ & \textbackslash varTheta & $\varPi$ & \textbackslash varPi &
|
||||||
|
$\varPhi$ & \textbackslash varPhi \\
|
||||||
|
\midrule
|
||||||
|
\multicolumn{4}{l}{依赖 amssymb 宏包}\\
|
||||||
|
$\digamma$ & \textbackslash digamma & $\varkappa$ & \textbackslash varkappa &
|
||||||
|
$\beth$ & \textbackslash beth & $\gimel$ & \textbackslash gimel \\
|
||||||
|
$\daleth$ & \textbackslash daleth \\
|
||||||
|
\bottomrule
|
||||||
|
\end{tabular}
|
||||||
|
\end{table}
|
||||||
|
\begin{table}[H]
|
||||||
|
\centering
|
||||||
|
\caption{其它符号}
|
||||||
|
\begin{tabular}{clclclcl}
|
||||||
|
\toprule
|
||||||
|
$\dots$ & \textbackslash dots & $\cdots$ & \textbackslash cdots &
|
||||||
|
$\vdots$ & \textbackslash vdots & $\ddots$ & \textbackslash ddots \\
|
||||||
|
$\hbar$ & \textbackslash hbar & $\imath$ & \textbackslash imath &
|
||||||
|
$\jmath$ & \textbackslash jmath & $\ell$ & \textbackslash ell \\
|
||||||
|
$\Re$ & \textbackslash Re & $\Im$ & \textbackslash Im &
|
||||||
|
$\aleph$ & \textbackslash aleph & $\wp$ & \textbackslash wp \\
|
||||||
|
$\forall$ & \textbackslash forall & $\exists$ & \textbackslash exists &
|
||||||
|
$\partial$ & \textbackslash partial & $'$ & ' \\
|
||||||
|
$\prime$ & \textbackslash prime & $\emptyset$ & \textbackslash emptyset &
|
||||||
|
$\infty$ & \textbackslash infty & $\nabla$ & \textbackslash nabla \\
|
||||||
|
$\triangle$ & \textbackslash triangle & $\bot$ & \textbackslash bot &
|
||||||
|
$\top$ & \textbackslash top & $\angle$ & \textbackslash angle \\
|
||||||
|
$\surd$ & \textbackslash surd & $\diamondsuit$ & \textbackslash diamondsuit &
|
||||||
|
$\heartsuit$ & \textbackslash heartsuit & $\clubsuit$ & \textbackslash clubsuit \\
|
||||||
|
$\spadesuit$ & \textbackslash spadesuit & $\neg$ & \textbackslash neg or \textbackslash lnot &
|
||||||
|
$\flat$ & \textbackslash flat & $\natural$ & \textbackslash natural \\
|
||||||
|
$\sharp$ & \textbackslash sharp \\
|
||||||
|
\midrule
|
||||||
|
\multicolumn{3}{l}{以下命令依赖 latexsym 宏包}\\
|
||||||
|
$\mho$ & \textbackslash mho & $\Box$ & \textbackslash Box &
|
||||||
|
$\Diamond$ & \textbackslash Diamond \\
|
||||||
|
\bottomrule
|
||||||
|
\end{tabular}
|
||||||
|
\end{table}
|
||||||
|
$a_1,a_2,\dots,a_n$\\
|
||||||
|
$a_1 + a_2 + \cdots + a_n$\par
|
||||||
|
\subsubsection{指数、上下标和导数}
|
||||||
|
\textasciicircum 和 \_ 标明上下标。%
|
||||||
|
注意上下标的内容(子公式)一般需要用花括号包裹，否 则上下标只对后面的一个符号起作用:\par
|
||||||
|
$p^3_{ij} \qquad
|
||||||
|
m_\mathrm{Kunth} \qquad
|
||||||
|
\sum_{k=1}^3 k$\\
|
||||||
|
$a^x +y \neq a^{x+y} \qquad
|
||||||
|
e^{x^2} \neq {e^x}^2$ \par
|
||||||
|
导数符号$'$ 是一类特殊的上标,可以适当连用表示多阶导数,也可以在其后连用上标:\par
|
||||||
|
$f(x) = x^2 \quad
|
||||||
|
f'(x) = 2x \quad
|
||||||
|
f''^{2}(x) = 4$ \par
|
||||||
|
\subsubsection{分式和根式}
|
||||||
|
分式使用 \textbackslash frac\{分子\}\{分母\} 来书写。%
|
||||||
|
分式的大小在行间公式中是正常大小,而在行内被 极度压缩。%
|
||||||
|
amsmath 提供了方便的命令 \textbackslash dfrac 和 \textbackslash tfrac,%
|
||||||
|
令用户能够在行内使用正常大小的 分式，或是反过来。\par
|
||||||
|
In display style:
|
||||||
|
\[
|
||||||
|
3/8 \qquad
|
||||||
|
\frac{3}{8} \qquad
|
||||||
|
\tfrac{3}{8}
|
||||||
|
\]
|
||||||
|
In text style:
|
||||||
|
$1\frac{1}{2}$~hours \qquad
|
||||||
|
$1\dfrac{1}{2}$~hours\par
|
||||||
|
一般的根式使用 \textbackslash sqrt\{\dots\};%
|
||||||
|
表示 n 次方根时写成 \textbackslash sqrt[n]\{\dots\}。\par
|
||||||
|
$\sqrt{x} \Leftrightarrow x^{1/2} \quad
|
||||||
|
\sqrt[3]{2} \quad
|
||||||
|
\sqrt{x^{2} + \sqrt{y}}$ \par
|
||||||
|
特殊的分式形式,如二项式结构,由 amsmath 宏包的 \textbackslash binom 命令生成:\par
|
||||||
|
Pascal's rule is
|
||||||
|
\[
|
||||||
|
\binom{n}{k} = \binom{n - 1}{k} + \binom{n - 1}{k}
|
||||||
|
\]
|
||||||
|
\subsubsection{关系符}
|
||||||
|
\begin{table}[H]
|
||||||
|
\centering
|
||||||
|
\caption{二元关系符}
|
||||||
|
\begin{tabular}{clclcl}
|
||||||
|
\toprule
|
||||||
|
$<$ & < & $>$ & > &
|
||||||
|
$=$ & = \\
|
||||||
|
$\equiv$ & \textbackslash equiv & $\leq$ & \textbackslash leq or \textbackslash le &
|
||||||
|
$\geq$ & \textbackslash geq or \textbackslash ge \\
|
||||||
|
$\ll$ & \textbackslash ll & $\gg$ & \textbackslash gg &
|
||||||
|
$\doteq$ & \textbackslash doteq \\
|
||||||
|
$\prec$ & \textbackslash prec & $\succ$ & \textbackslash succ &
|
||||||
|
$\sim$ & \textbackslash sim \\
|
||||||
|
$\preceq$ & \textbackslash preceq & $\succeq$ & \textbackslash succeq &
|
||||||
|
$\simeq$ & \textbackslash simeq \\
|
||||||
|
$\subset$ & \textbackslash subset & $\supset$ & \textbackslash supset &
|
||||||
|
$\approx$ & \textbackslash approx \\
|
||||||
|
$\subseteq$ & \textbackslash subseteq & $\supseteq$ & \textbackslash supseteq &
|
||||||
|
$\cong$ & \textbackslash cong \\
|
||||||
|
$\sqsubseteq$ & \textbackslash sqsubseteq & $\sqsupseteq$ & \textbackslash sqsupseteq &
|
||||||
|
$\bowtie$ & \textbackslash bowtie \\
|
||||||
|
$\in$ & \textbackslash in & $\ni$ & \textbackslash ni ,\textbackslash owns &
|
||||||
|
$\propto$ & \textbackslash propto \\
|
||||||
|
$\vdash$ & \textbackslash vdash & $\dashv$ & \textbackslash dashv &
|
||||||
|
$\models$ & \textbackslash models \\
|
||||||
|
$\mid$ & \textbackslash mid & $\parallel$ & \textbackslash parallel &
|
||||||
|
$\perp$ & \textbackslash perp \\
|
||||||
|
$\smile$ & \textbackslash smile & $\frown$ & \textbackslash frown &
|
||||||
|
$\asymp$ & \textbackslash asymp \\
|
||||||
|
$:$ & : & $\notin$ & \textbackslash notin &
|
||||||
|
$\neq$ & \textbackslash neq or \textbackslash ne \\
|
||||||
|
\midrule
|
||||||
|
\multicolumn{3}{l}{以下命令依赖 latexsym 宏包}\\
|
||||||
|
$\sqsubset$ & \textbackslash sqsubset & $\sqsupset$ & \textbackslash sqsupset &
|
||||||
|
$\Join$ & \textbackslash Join \\
|
||||||
|
\midrule
|
||||||
|
\multicolumn{3}{l}{以下命令依赖 amssymb 宏包}\\
|
||||||
|
$\lessdot$ & \textbackslash lessdot & $\gtrdot$ & \textbackslash gtrdot &
|
||||||
|
$\doteqdot$ & \textbackslash doteqdot \\
|
||||||
|
$\leqslant$ & \textbackslash leqslant & $\geqslant$ & \textbackslash geqslant &
|
||||||
|
$\risingdotseq$ & \textbackslash risingdotseq \\
|
||||||
|
$\eqslantless$ & \textbackslash eqslantless & $\eqslantgtr$ & \textbackslash eqslantgtr &
|
||||||
|
$\fallingdotseq$ & \textbackslash fallingdotseq \\
|
||||||
|
$\leqq$ & \textbackslash leqq & $\geqq$ & \textbackslash geqq &
|
||||||
|
$\eqcirc$ & \textbackslash eqcirc \\
|
||||||
|
$\circeq$ & \textbackslash circeq & $\ggg$ & \textbackslash ggg &
|
||||||
|
$\lll$ & \textbackslash lll or \textbackslash llless \\
|
||||||
|
$\lesssim$ & \textbackslash lesssim & $\gtrsim$ & \textbackslash gtrsim &
|
||||||
|
$\triangleq$ & \textbackslash triangle \\
|
||||||
|
$\lessapprox$ & \textbackslash lessapprox & $\gtrapprox$ & \textbackslash gtrapprox &
|
||||||
|
$\bumpeq$ & \textbackslash bumpeq \\
|
||||||
|
$\lessgtr$ & \textbackslash lessgtr & $\gtrless$ & \textbackslash gtrless &
|
||||||
|
$\Bumpeq$ & \textbackslash Bumpeq \\
|
||||||
|
$\lesseqgtr$ & \textbackslash lesseqgtr & $\gtreqless$ & \textbackslash gtreqless &
|
||||||
|
$\thicksim$ & \textbackslash thicksim \\
|
||||||
|
$\lesseqqgtr$ & \textbackslash lesseqqgtr & $\gtreqqless$ & \textbackslash gtreqqless &
|
||||||
|
$\thickapprox$ & \textbackslash thickapprox \\
|
||||||
|
$\preccurlyeq$ & \textbackslash preccurlyeq & $\succcurlyeq$ & \textbackslash succcurlyeq &
|
||||||
|
$\approxeq$ & \textbackslash approxeq \\
|
||||||
|
$\curlyeqprec$ & \textbackslash curlyeqprec & $\curlyeqsucc$ & \textbackslash curlyeqsucc &
|
||||||
|
$\backsim$ & \textbackslash backsim \\
|
||||||
|
$\precsim$ & \textbackslash precsim & $\succsim$ & \textbackslash succsim &
|
||||||
|
$\backsimeq$ & \textbackslash backsimeq \\
|
||||||
|
$\precapprox$ & \textbackslash precapprox & $\succapprox$ & \textbackslash succapprox &
|
||||||
|
$\vDash$ & \textbackslash vDash \\
|
||||||
|
$\subseteqq$ & \textbackslash subseteqq & $\supseteqq$ & \textbackslash supseteqq &
|
||||||
|
$\Vdash$ & \textbackslash Vdash \\
|
||||||
|
$\shortparallel$ & \textbackslash shortparallel & $\Supset$ & \textbackslash Supset &
|
||||||
|
$\Vvdash$ & \textbackslash Vvdash \\
|
||||||
|
$\blacktriangleleft$ & \textbackslash blacktriangleleft & $\sqsupset$ & \textbackslash sqsupset &
|
||||||
|
$\backepsilon$ & \textbackslash backepsilon \\
|
||||||
|
$\vartriangleright$ & \textbackslash vartriangleright & $\because$ & \textbackslash because &
|
||||||
|
$\varpropto$ & \textbackslash varpropto \\
|
||||||
|
$\blacktriangleright$ & \textbackslash blacktriangleright & $\Subset$ & \textbackslash Subset &
|
||||||
|
$\between$ & \textbackslash between \\
|
||||||
|
$\trianglerighteq$ & \textbackslash trianglerighteq & $\smallfrown$ & \textbackslash smallfrown &
|
||||||
|
$\pitchfork$ & \textbackslash pitchfork \\
|
||||||
|
$\vartriangleleft$ & \textbackslash vartriangleleft & $\shortmid$ & \textbackslash shortmid &
|
||||||
|
$\smallsmile$ & \textbackslash smallsmile \\
|
||||||
|
$\trianglelefteq$ & \textbackslash trianglelefteq & $\therefore$ & \textbackslash therefore &
|
||||||
|
$\sqsubset$ & \textbackslash sqsubset \\
|
||||||
|
\bottomrule
|
||||||
|
\end{tabular}
|
||||||
|
\end{table}
|
||||||
|
\LaTeX 还提供了自定义二元关系符的命令 \textbackslash stackrel,用于将一个符号叠加在原有的二元关 系符之上:\par
|
||||||
|
\[
|
||||||
|
f_n(x) \stackrel{*}{\approx} 1
|
||||||
|
\]
|
||||||
|
\subsubsection{算符}
|
||||||
|
\begin{table}[H]
|
||||||
|
\centering
|
||||||
|
\caption{二元运算符}
|
||||||
|
\begin{tabular}{clclcl}
|
||||||
|
\toprule
|
||||||
|
$+$ & + &$-$ & - &
|
||||||
|
$\pm$ & \textbackslash pm \\
|
||||||
|
$\mp$ & \textbackslash mp & $\triangleleft$ & \textbackslash triangleleft &
|
||||||
|
$\cdot$ & \textbackslash cdot \\
|
||||||
|
$\div$ & \textbackslash div & $\triangleright$ & \textbackslash triangleright &
|
||||||
|
$\times$ & \textbackslash times \\
|
||||||
|
$\setminus$ & \textbackslash setminus & $\star$ & \textbackslash star &
|
||||||
|
$\cup$ & \textbackslash cup \\
|
||||||
|
$\cap$ & \textbackslash cap & $\ast$ & \textbackslash ast &
|
||||||
|
$\sqcup$ & \textbackslash sqcup \\
|
||||||
|
$\sqcap$ & \textbackslash sqcap & $\circ$ & \textbackslash circ &
|
||||||
|
$\vee$ & \textbackslash vee \\
|
||||||
|
$\lor$ & \textbackslash lor & $\wedge$ & \textbackslash wedge &
|
||||||
|
$\land$ & \textbackslash land \\
|
||||||
|
$\bullet$ & \textbackslash bullet & $\oplus$ & \textbackslash oplus &
|
||||||
|
$\ominus$ & \textbackslash ominus \\
|
||||||
|
$\diamond$ & \textbackslash diamond & $\odot$ & \textbackslash odot &
|
||||||
|
$\oslash$ & \textbackslash oslash \\
|
||||||
|
$\uplus$ & \textbackslash uplus & $\otimes$ & \textbackslash otimes &
|
||||||
|
$\bigcirc$ & \textbackslash bigcirc \\
|
||||||
|
$\amalg$ & \textbackslash amalg & $\bigtriangleup$ & \textbackslash bigtriangleup &
|
||||||
|
$\bigtriangledown$ & \textbackslash bigtriangledown \\
|
||||||
|
$\dagger$ & \textbackslash dagger & $\ddagger$ & \textbackslash ddagger &
|
||||||
|
$\wr$ & \textbackslash wr \\
|
||||||
|
\midrule
|
||||||
|
\multicolumn{3}{l}{以下命令依赖 latexsym 宏包} \\
|
||||||
|
$\lhd$ & \textbackslash lhd & $\rhd$ & \textbackslash rhd \\
|
||||||
|
$\unlhd$ & \textbackslash unlhd & $\unrhd$ & \textbackslash unrhd \\
|
||||||
|
\midrule
|
||||||
|
\multicolumn{3}{l}{以下命令依赖 amssymb 宏包} \\
|
||||||
|
$\dotplus$ & \textbackslash dotplus & $\centerdot$ & \textbackslash centerdot \\
|
||||||
|
$\ltimes$ & \textbackslash ltimes & $\rtimes$ & \textbackslash rtimes &
|
||||||
|
$\divideontimes$ & \textbackslash divideontimes \\
|
||||||
|
$\doublecup$ & \textbackslash doublecup & $\doublecap$ & \textbackslash doublecap &
|
||||||
|
$\smallsetminus$ & \textbackslash smallsetminus \\
|
||||||
|
$\veebar$ & \textbackslash veebar & $\barwedge$ & \textbackslash barwedge &
|
||||||
|
$\doublebarwedge$ & \textbackslash doublebarwedge \\
|
||||||
|
$\boxplus$ & \textbackslash boxplus & $\boxminus$ & \textbackslash boxminus &
|
||||||
|
$\circleddash$ & \textbackslash circleddash \\
|
||||||
|
$\boxtimes$ & \textbackslash boxtimes & $\boxdot$ & \textbackslash boxdot &
|
||||||
|
$\circledcirc$ & \textbackslash circledcirc \\
|
||||||
|
$\intercal$ & \textbackslash intercal & $\circledast$ & \textbackslash circledast &
|
||||||
|
$\rightthreetimes$ & \textbackslash rightthreetimes \\
|
||||||
|
$\curlyvee$ & \textbackslash curlyvee & $\curlywedge$ & \textbackslash curlywedge &
|
||||||
|
$\leftthreetimes$ & \textbackslash listoffigures \\
|
||||||
|
\bottomrule
|
||||||
|
\end{tabular}
|
||||||
|
\end{table}
|
||||||
|
\begin{table}[H]
|
||||||
|
\centering
|
||||||
|
\caption{\LaTeX 作为算符的函数名称}
|
||||||
|
\begin{tabular}{clclclcl}
|
||||||
|
\toprule
|
||||||
|
\multicolumn{8}{l}{不带上下限的算符}\\
|
||||||
|
$\sin$ & \textbackslash sin & $\arcsin$ & \textbackslash arcsin &
|
||||||
|
$\sinh$ & \textbackslash sinh & $\exp$ & \textbackslash exp \\
|
||||||
|
$\dim$ & \textbackslash dim & $\cos$ & \textbackslash cos &
|
||||||
|
$\arccos$ & \textbackslash arccos &$\cosh$ & \textbackslash cosh \\
|
||||||
|
$\log$ & \textbackslash log & $\ker$ & \textbackslash ker &
|
||||||
|
$\tan$ & \textbackslash tan & $\arctan$ & \textbackslash arctan \\
|
||||||
|
$\tanh$ & \textbackslash tanh & $\lg$ & \textbackslash lg &
|
||||||
|
$\hom$ & \textbackslash hom & $\cot$ & \textbackslash cot \\
|
||||||
|
$\arg$ & \textbackslash arg & $\coth$ & \textbackslash coth &
|
||||||
|
$\ln$ & \textbackslash ln & $\deg$ & \textbackslash deg \\
|
||||||
|
$\sec$ & \textbackslash sec & $\csc$ & \textbackslash csc \\
|
||||||
|
\midrule
|
||||||
|
\multicolumn{8}{l}{带上下限的算符}\\
|
||||||
|
$\lim$ & \textbackslash lim & $\limsup$ & \textbackslash limsup &
|
||||||
|
$\liminf$ & \textbackslash liminf & $\sup$ & \textbackslash sup \\
|
||||||
|
$\inf$ & \textbackslash inf & $\min$ & \textbackslash min &
|
||||||
|
$\max$ & \textbackslash max & $\det$ & \textbackslash det \\
|
||||||
|
$\Pr$ & \textbackslash Pr & $\gcd$ & \textbackslash gcd \\
|
||||||
|
\bottomrule
|
||||||
|
\end{tabular}
|
||||||
|
\end{table}
|
||||||
|
\[
|
||||||
|
\lim_{x \rightarrow 0} \frac{\sin x}{s} = 1
|
||||||
|
\]
|
||||||
|
对于求模表达式,\LaTeX 提供了 \textbackslash pmod 和 \textbackslash bmod 命令:\par
|
||||||
|
\[
|
||||||
|
a \bmod b \qquad
|
||||||
|
x \equiv a \pmod{b}
|
||||||
|
\]
|
||||||
|
amsmath 允许用户在\emph{导言区}用 \textbackslash DeclareMathOperator 在定义自己 的算符,%
|
||||||
|
其中带星号的命令定义带上下限的算符:\\
|
||||||
|
\[ \argh 3 = \nut_{x = 1} 4x \]
|
||||||
|
\subsubsection{巨算符}
|
||||||
|
In text:
|
||||||
|
$
|
||||||
|
\sum_{i=1}^n \quad
|
||||||
|
\int_0^{\frac{\pi}{2}} \quad
|
||||||
|
\oint_0^{\frac{\pi}{2}} \quad
|
||||||
|
\prod_{\epsilon}
|
||||||
|
$\\
|
||||||
|
In display:
|
||||||
|
\[
|
||||||
|
\sum_{i=1}^n \quad
|
||||||
|
\int_0^{\frac{\pi}{2}}\quad
|
||||||
|
\oint_0^{\frac{\pi}{2}} \quad
|
||||||
|
\prod_{\epsilon}
|
||||||
|
\]\par
|
||||||
|
巨算符的上下标位置可由 \textbackslash limits 和 \textbackslash nolimits 控制\par
|
||||||
|
In text:
|
||||||
|
$
|
||||||
|
\sum\limits_{i=1}^n \quad
|
||||||
|
\int\limits_0^{\frac{\pi}{2}} \quad
|
||||||
|
\oint\limits_0^{\frac{\pi}{2}} \quad
|
||||||
|
\prod\limits_{\epsilon}
|
||||||
|
$\\
|
||||||
|
In display:
|
||||||
|
\[
|
||||||
|
\sum\nolimits_{i = 1}^n \quad
|
||||||
|
\int\limits_0^{\frac{\pi}{2}} \quad
|
||||||
|
\oint\limits_0^{\frac{\pi}{2}} \quad
|
||||||
|
\prod\nolimits_{\epsilon}
|
||||||
|
\]\par
|
||||||
|
amsmath 宏包还提供了 \textbackslash substack,能够在下限位置书写多行表达式:
|
||||||
|
\[
|
||||||
|
\sum_{\substack{0\le i\le n\\
|
||||||
|
j\in\mathbb{R}}} P(i,j) = Q(n)
|
||||||
|
\]
|
||||||
|
subarray 环境更进 一步,令多行表达式可选择居中 (c) 或左对齐 (l):
|
||||||
|
\[
|
||||||
|
\sum_{\begin{subarray}{l}
|
||||||
|
0\le i\le n\\
|
||||||
|
j\in\mathbb{R}
|
||||||
|
\end{subarray}} P(i,j) =
|
||||||
|
Q(n)
|
||||||
|
\]
|
||||||
|
\subsubsection{数学重音和上下括号}
|
||||||
|
\begin{table}[H]
|
||||||
|
\centering
|
||||||
|
\caption{数学重音符号}
|
||||||
|
\begin{tabular}{clclcl}
|
||||||
|
\toprule
|
||||||
|
$\hat{a}$ & \textbackslash hat\{a\} & $\check{a}$ & \textbackslash check\{a\} &
|
||||||
|
$\tilde{a}$ & \textbackslash tilde\{a\} \\
|
||||||
|
$\acute{a}$ & \textbackslash acute\{a\} & $\grave{a}$ & \textbackslash grave\{a\} &
|
||||||
|
$\breve{a}$ & \textbackslash breve\{a\} \\
|
||||||
|
$\bar{a}$ & \textbackslash bar\{a\} & $\vec{a}$ & \textbackslash vec\{a\} &
|
||||||
|
$\mathring{a}$ & \textbackslash mathring\{a\} \\
|
||||||
|
$\dot{a}$ & \textbackslash dot\{a\} & $\ddot{a}$ & \textbackslash ddot\{a\} \\
|
||||||
|
$\widehat{AAA}$ & \textbackslash widehat\{AAA\} & $\widetilde{AAA}$ & \textbackslash widetilde\{AAA\} \\
|
||||||
|
\midrule
|
||||||
|
\multicolumn{6}{l}{以下命令依赖 amsmath 宏包}\\
|
||||||
|
$\dddot{a}$ & \textbackslash dddot\{a\} & $\ddddot{a}$ & \textbackslash ddddot\{a\} \\
|
||||||
|
\midrule
|
||||||
|
\multicolumn{6}{l}{以下命令依赖 yhmath 宏包}\\
|
||||||
|
$\wideparen{AAA}$ & \textbackslash wideparen\{AAA\} \\
|
||||||
|
\bottomrule
|
||||||
|
\end{tabular}
|
||||||
|
\end{table}
|
||||||
|
使用时要注意 重音符号的作用区域,一般应当对某个符号而不是``符号加下标''使用重音:
|
||||||
|
\[\bar{x_0} \quad \bar{x}_0 \]
|
||||||
|
\[\vec{x_0} \quad \vec{x}_0 \]
|
||||||
|
\[\hat{\mathbf{e}_x} \quad \hat{\mathbf{e}}_x \]
|
||||||
|
\LaTeX 也能为多个字符加重音,包括直接画线的 \textbackslash overline 和 %
|
||||||
|
\textbackslash underline 命令(可叠加使 用)、宽重音符号 \textbackslash widehat、%
|
||||||
|
表示向量的箭头 \textbackslash overrightarrow 等。\par
|
||||||
|
\begin{table}[H]
|
||||||
|
\centering
|
||||||
|
\caption{作为重音的箭头符号}
|
||||||
|
\begin{tabular}{clcl}
|
||||||
|
\toprule
|
||||||
|
$\overrightarrow{AB}$ & \textbackslash overrightarrow\{AB\} &
|
||||||
|
$\overleftarrow{AB}$ & \textbackslash overleftarrow\{AB\} \\
|
||||||
|
\midrule
|
||||||
|
\multicolumn{4}{l}{以下命令依赖 amsmath 宏包}\\
|
||||||
|
$\underleftarrow{AB}$ & \textbackslash underleftarrow\{AB\} &
|
||||||
|
$\underrightarrow{AB}$ & \textbackslash underrightarrow\{AB\} \\
|
||||||
|
$\overleftrightarrow{AB}$ & \textbackslash overleftrightarrow\{AB\} &
|
||||||
|
$\underleftrightarrow{AB}$ & \textbackslash underleftrightarrow\{AB\} \\
|
||||||
|
\bottomrule
|
||||||
|
\end{tabular}
|
||||||
|
\end{table}
|
||||||
|
\[0.\overline{3} = \underline{\underline{1/3}} \]
|
||||||
|
\[\hat{XY} \qquad \widehat{XY} \]
|
||||||
|
\[\vec{AB} \qquad \overrightarrow{AB} \]
|
||||||
|
\textbackslash overbrace 和 \textbackslash underbrace 命令用来生成上/下括号,各自可带一个上/下标公式:
|
||||||
|
\[
|
||||||
|
\underbrace{\overbrace{a + b + c}^6 \cdot
|
||||||
|
\overbrace{d + e + f}^7
|
||||||
|
}_\text{meaning of life} =
|
||||||
|
42
|
||||||
|
\]
|
||||||
|
\subsubsection{箭头}
|
||||||
|
\begin{table}[H]
|
||||||
|
\centering
|
||||||
|
\caption{箭头}
|
||||||
|
\begin{tabular}{clcl}
|
||||||
|
$\leftarrow$ & \textbackslash leftarrow or \textbackslash gets & $\longleftarrow$ & \textbackslash longleftarrow \\
|
||||||
|
$\rightarrow$ & \textbackslash rightarrow or \textbackslash to & $\longrightarrow$ & \textbackslash longrightarrow \\
|
||||||
|
$\leftrightarrow$ & \textbackslash leftrightarrow & $\longleftrightarrow$ & \textbackslash longleftrightarrow \\
|
||||||
|
$\Leftarrow$ & \textbackslash Leftarrow & $\Longleftarrow$ & \textbackslash Longleftarrow \\
|
||||||
|
$\Rightarrow$ & \textbackslash Rightarrow & $\Longrightarrow$ & \textbackslash Longrightarrow \\
|
||||||
|
$\Leftrightarrow$ & \textbackslash Leftrightarrow & $\Longleftrightarrow$ & \textbackslash Longleftrightarrow \\
|
||||||
|
$\mapsto$ & \textbackslash mapsto & $\longmapsto$ & \textbackslash longmapsto \\
|
||||||
|
$\hookleftarrow$ & \textbackslash hookleftarrow & $\hookrightarrow$ & \textbackslash hookrightarrow \\
|
||||||
|
$\leftharpoonup$ & \textbackslash leftharpoonup & $\rightharpoonup$ & \textbackslash rightharpoonup \\
|
||||||
|
$\leftharpoondown$ & \textbackslash leftharpoondown & $\rightharpoondown$ & \textbackslash rightharpoondown \\
|
||||||
|
$\rightleftharpoons$ & \textbackslash rightleftharpoons & $\iff$ & \textbackslash iff \\
|
||||||
|
$\uparrow$ & \textbackslash uparrow & $\downarrow$ & \textbackslash downarrow \\
|
||||||
|
$\updownarrow$ & \textbackslash updownarrow & $\Uparrow$ & \textbackslash Uparrow \\
|
||||||
|
$\Downarrow$ & \textbackslash Downarrow & $\Updownarrow$ & \textbackslash Updownarrow \\
|
||||||
|
$\nearrow$ & \textbackslash nearrow & $\searrow$ & \textbackslash searrow \\
|
||||||
|
$\swarrow$ & \textbackslash swarrow & $\nwarrow$ & \textbackslash nwarrow \\
|
||||||
|
\midrule
|
||||||
|
\multicolumn{4}{l}{以下命令依赖 latexsym 宏包} \\
|
||||||
|
$\leadsto$ & \textbackslash leadsto \\
|
||||||
|
\bottomrule
|
||||||
|
\end{tabular}
|
||||||
|
\end{table}
|
||||||
|
amsmath 的 \textbackslash xleftarrow 和 \textbackslash xrightarrow 命令%
|
||||||
|
提供了长度可以伸展的箭头,并且可以为 箭头增加上下标:
|
||||||
|
\[ a\xleftarrow{x + y + z} b \]
|
||||||
|
\[ c\xrightarrow[x < y]{a*b*c} d \]
|
||||||
|
\subsubsection{括号和定界符}
|
||||||
|
\begin{table}[H]
|
||||||
|
\centering
|
||||||
|
\caption{定界符}
|
||||||
|
\begin{tabular}{clclcl}
|
||||||
|
\toprule
|
||||||
|
$($ & ( & $)$ & ) &
|
||||||
|
$\uparrow$ & \textbackslash uparrow \\
|
||||||
|
$[$ & \textbackslash lbrack or [ & $]$ & \textbackslash rbrack or ] &
|
||||||
|
$\downarrow$ & \textbackslash downarrow \\
|
||||||
|
$\{$ & \textbackslash lbrace or \textbackslash\{ &
|
||||||
|
$\}$ & \textbackslash rbrace or \textbackslash\} &
|
||||||
|
$\updownarrow$ & \textbackslash updownarrow \\
|
||||||
|
$\langle$ & \textbackslash langle & $\rangle$ & \textbackslash rangle &
|
||||||
|
$\Uparrow$ & \textbackslash Uparrow \\
|
||||||
|
$\vert$ & \textbackslash or | & $\Downarrow$ & \textbackslash Downarrow &
|
||||||
|
$\|$ & \textbackslash Vert or \textbackslash| \\
|
||||||
|
$/$ & / & $\backslash$ & \textbackslash backslash &
|
||||||
|
$\Updownarrow$ & \textbackslash Updownarrow \\
|
||||||
|
$\lfloor$ & \textbackslash lfloor & $\rfloor$ & \textbackslash rfloor &
|
||||||
|
$\rceil$ & \textbackslash rceil \\
|
||||||
|
$\lceil$ & \textbackslash lceil \\
|
||||||
|
\bottomrule
|
||||||
|
\end{tabular}
|
||||||
|
\end{table}
|
||||||
|
\begin{table}[H]
|
||||||
|
\centering
|
||||||
|
\caption{用于行间公式的大定界符}
|
||||||
|
\begin{tabular}{clcl}
|
||||||
|
\toprule
|
||||||
|
$\left\lgroup\right.$ & \textbackslash lgroup &
|
||||||
|
$\left\arrowvert\right.$ & \textbackslash arrowvert \\
|
||||||
|
$\left\rgroup\right.$ & \textbackslash rgroup &
|
||||||
|
$\left\Arrowvert\right.$ & \textbackslash Arrowvert \\
|
||||||
|
$\left\lmoustache\right.$ & \textbackslash lmoustache &
|
||||||
|
$\left\bracevert\right.$ & \textbackslash bracevert \\
|
||||||
|
$\left\rmoustache\right.$ & \textbackslash rmoustache \\
|
||||||
|
\bottomrule
|
||||||
|
\end{tabular}
|
||||||
|
\end{table}
|
||||||
|
\[ {a,b,c} \neq \{a,b,c\} \]
|
||||||
|
使用 \textbackslash left 和 \textbackslash right 命令可令括号(定界符)的大小可变,在行间公式中常用。%
|
||||||
|
\LaTeX 会自动根据括号内的公式大小决定定界符大小。\\
|
||||||
|
\textbackslash left 和 \textbackslash right 必须成对使用。需要使用单个定 界符时,另一个定界符写成%
|
||||||
|
\textbackslash left. 或 \textbackslash right.\par
|
||||||
|
\[
|
||||||
|
1 + \left( \frac{1}{1 - x^2} \right)^3 \qquad
|
||||||
|
\left.\frac{\partial f}{\partial t} \right|_{t = 0}
|
||||||
|
\]
|
||||||
|
还可以用 \textbackslash big、\textbackslash bigg 等命令生成固定大小的定界符。\\
|
||||||
|
更常用的形式是类似 \textbackslash left 的 \textbackslash bigl、\textbackslash biggl 等,%
|
||||||
|
以及类似 \textbackslash right 的 \textbackslash bigr、\textbackslash biggr 等%
|
||||||
|
(\textbackslash bigl 和 \textbackslash bigr 不必成对出现)。\par
|
||||||
|
\[ \Bigl((x + 1)(x - 1)\Bigr)^2 \]
|
||||||
|
\[ \bigl( \Bigl( \biggl( \Biggl( \quad
|
||||||
|
\bigr\} \Bigr\} \biggr\} \Biggr\} \quad
|
||||||
|
\big\| \Big\| \bigg\| \Bigg\| \quad
|
||||||
|
\big\Downarrow \Big\Downarrow
|
||||||
|
\bigg\Downarrow \Bigg\Downarrow
|
||||||
|
\]
|
||||||
|
\subsection{多行公式}
|
||||||
|
|
||||||
\newpage
|
\newpage
|
||||||
\appendix
|
\appendix
|
||||||
\section{附录}
|
\section{附录}
|
||||||
|
|||||||
Reference in New Issue
Block a user