diff --git a/__latexindent_temp.tex b/__latexindent_temp.tex index 2b03806..307ff5b 100644 --- a/__latexindent_temp.tex +++ b/__latexindent_temp.tex @@ -1 +1,769 @@ -⟨ \ No newline at end of file +%!TEX program = xelatex +%表示用xelatex编译文件 +\documentclass[a4paper]{ctexart} +\usepackage{array} +\usepackage{tabularx} +\usepackage{indentfirst} +\setlength{\parindent}{2em} +\usepackage{booktabs} +\usepackage{multirow} +\usepackage{makecell} +\usepackage{graphicx} +\usepackage{subfig} +\usepackage{amsmath} +\usepackage{amsfonts} +\usepackage{amssymb} +\usepackage{amsthm} +\usepackage{latexsym} +\begin{document} + \title{标题页} + \author{Ryan\thanks{注脚}% + \and Fan\thanks{注脚}% + } + \date{\today} + \maketitle + \abstract + 一般用于紧跟\textbackslash maketitle 命令之后介绍文档的摘要\par + 中文\LaTeX{}排版。 + \section{用\LaTeX 排版文字} + {}分段\\换行\textbackslash\textbackslash\par + 冒号``please press the `x' key.''\par + 连字符-用来组成复合词，\\% + 短破折号--用来连接数字表示范围，\\% + 长破折号---用来连接单词\par + 省略号\dots{}和\ldots\par + 波浪号～\par + 强调\underline{文字,但是无法换行，}% + \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。}% + \emph{emph 命令用来将文字变为斜体以示强调。% + \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,}% + 内部则使用直立体文字。% + }\par + 在合适的位置插入一个不会断行的空格Fig.~1, Ryan~Fan\par + 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% + \newline{}或者newline命令，不用带参数\par + \newpage 断页，在在双栏排版中只起到另起一栏的作用\par + 断词　I think this is: supercalifragil\-isticexpialidocious. % + And I think this is: supercalifragilisticexpialidocious.\par + \newpage + \tableofcontents + \section[目录和页眉页脚]{章节} + \subsection{子章节} + \subsubsection{子子章节} + \paragraph{段落} + \subparagraph{子段落} + \section*{标题不带编号} + \addcontentsline{toc}{section}{标题不带编号} + \part{分块} + \section{交叉引用} + A reference to this subsection\label{sec:this} looks like: % + ``see section~\ref{sec:this} on page~\pageref{sec:this}.'' + \section{脚注和边注} + “天地玄黄,宇宙洪荒。日月盈昃,辰宿列张。”\footnote{出自《千字文》。}\par + \begin{tabular}{l} + \hline + 有些情况下(比如在表格环境、各种盒子\\ + 内)使用 footnote 并不能正确生成脚\\ + 注。我们以分两步进行,先使用 \\ + footnotemark 为脚注计数,再在合适\\ + 的位置用 footnotetext 生成脚注。\footnotemark\\ + \hline + \end{tabular} + \footnotetext{出自《千字文》。} + \marginpar{\footnotesize 边注较窄,不要写过多文字,最好设置较小的字号。} + \section{特殊环境} + \subsection{列表} + 有序列表 + \begin{enumerate} + \item An item. + \begin{enumerate} + \item A nested item.\label{itref} + \item[*] A starred item. + \end{enumerate} + \item Reference(\ref{itref}). + \end{enumerate} + 无序列表 + \begin{itemize} + \item An item. + \begin{itemize} + \item A nested item. + \item[+] A `plus' item. + A ‘plus’ item. + \item Another item. – Another item. + \end{itemize} + \item Go back to upper level. + \end{itemize} + 关键字环境 + \begin{description} + \item[Enumerate] Numbered list. + \item[Itemize] Non-numbered list. + \end{description} + 重定义无序列表的符号 + \renewcommand{\labelitemi}{\dag} + \renewcommand{\labelitemii}{\ddag} + \begin{itemize} + \item First item + \begin{itemize} + \item Subitem + \item Subitem + \end{itemize} + \item Second item + \end{itemize} + 重定义有序列表的符号 + \renewcommand{\labelenumi}{\Alph{enumi}>} + \begin{enumerate} + \item First item + \item Second item + \end{enumerate} + \subsection{对齐环境} + center、flushleft 和 flushright 环境分别用于生成% + 居中、左对齐和右对齐的文本环境。 + \begin{center} + Centered text using a + \verb|center| environment. + \end{center} + \begin{flushleft} + Left-aligned text using a + \verb|flushleft| environment. + \end{flushleft} + \begin{flushright} + Right-aligned text using a + \verb|flushright| environment. + \end{flushright} + 还可以用以下命令直接改变文字的对齐方式: + \centering + Centered text paragraph.\par + \raggedright + Left-aligned text paragraph.\par + \raggedleft + Right-aligned text paragraph.\par + \begin{flushleft} + center 等环境会在上下文产生一个额外间距,% + 而 \textbackslash centering 等命令不产生,只是改变对齐方式。% + \end{flushleft} + \raggedright + 比如在浮动体环境 table 或 figure 内实现居中对齐,% + 用 \textbackslash centering 命令即可,没必要再用 center 环境。 + \subsection{引用环境} + \begin{description} + \item[quote] 用于引用较短的文字,首行不缩进\\ + Francis Bacon says: + \begin{quote} + Knowledge is power. + \end{quote} + \item[quotation] 用于引用若干段文字,首行缩进\\ + 《木兰诗》: + \begin{quotation} + 万里赴戎机,关山度若飞。 + 朔气传金柝,寒光照铁衣。 + 将军百战死,壮士十年归。 + + 归来见天子,天子坐明堂。 + 策勋十二转,赏赐百千强。...... + \end{quotation} + \end{description} + \subsection{代码环境} + \begin{verbatim} + #include + int main() + { + std::cout << "Hello, world!" + << std::endl; + return 0; + } + \end{verbatim} + \begin{verbatim*} + for (int i=0; i<4; ++i) + printf("Number %d\n",i); + \end{verbatim*} + 要排版简短的代码或关键字\textbackslash verb $\langle delim\rangle\langle code\rangle\langle delim\rangle$\par + $\langle delim\rangle$ 标明代码的分界位置,前后必须一致,除字母、空格或星号外,% + 可任意选择使得不与代码本身冲突,习惯上使用 | 符号。\par + \verb|\LaTeX| \\ + \verb+(a || b)+ \verb*+(a || b)+ + \subsection{表格} + \subsubsection{列表格} + 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 + \begin{tabular}{lcr|p{6em}} + \hline + left & center & right & par box with fixed width\\ + L & C & R & P\\ + \hline + \end{tabular}\par + @ 格式可在单元格前后插入任意的文本,% + 但同时它也消除了单元格前后额外添加的间距。\par + \begin{tabular}{@{} r@{:}lr @{}} + \hline + 1 & 1 &　one\\ + 11 & 3 & eleven\\ + \hline + \end{tabular}\par + 格式参数重复\par + \begin{tabular}{|*{5}{c|}*{2}{p{3em}|}} + \hline + one & two & three & four & five & Hello! \LaTeX & Hello!\\ + 1 & 2 & 3 & 4 & 5 & hello! & \LaTeX\\ + \hline + \end{tabular}\par + 辅助格式 > 和 <,用于给列格式前后加上修饰命令\par + \begin{tabular}{>{\itshape}r<{*}l} + %需要使用array宏包 + \hline + italic & normal \\ + column & column \\ + \hline + \end{tabular}\par + \begin{tabular}{>{\centering\arraybackslash}p{16em}} + \hline + 辅助格式甚至支持插入 \textbackslash centering 等% + 命令改变 p 列格式的对齐方式,一般还要加额外的命令 % + \textbackslash arraybackslash 以免出错。\\ + \hline + \textbackslash centering 等对齐命令会破坏表格环境里 % + \textbackslash\textbackslash 换行命令的定义,% + \textbackslash arraybackslash 用来恢复之。% + 如果不加 \textbackslash arraybackslash 命令,% + 也可以用 \textbackslash tabularnewline 命令% + 代替原来的 \textbackslash\textbackslash 实现表格换行。\\ + \hline + \end{tabular}\par + \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,% + 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,% + 但即使这样仍然有瑕疵:\par + \begin{tabular*}{14em}{@{\extracolsep{\fill}}|c|c|c|c|} + \hline + A & B & C & D \\ + \hline + a & b & c & d \\ + \hline + \end{tabular*}\par + 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,% + 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。% + X列格式也可以用 array 里的辅助 格式修饰对齐方式:\par + \begin{tabularx}{14em}{|*{4}{>{\centering\arraybackslash}X|}} + \hline + A & B & C & D \\ + \hline + a & b & c & d \\ + \hline + \end{tabularx}\par + \subsubsection{横线} + \textbackslash cline\{$\langle i-j\rangle$\} 用来绘制跨越部分单元格的横线:\par + \begin{tabular}{|c|c|c|} + \hline + 4 & 9 & 2 \\ \cline{2-3} + 3 & 5 & 7 \\ \cline{1-1} + 8 & 1 & 6 \\ + \hline + \end{tabular}\par + 三线表由 booktabs 宏包 支持,它提供了 \textbackslash toprule、% + \textbackslash midrule 和 \textbackslash bottomrule % + 命令用以排版三线表的三条线, 以及和 \textbackslash cline 对应的 % + \textbackslash cmidrule。除此之外,最好不要用其它横线以及竖线:\par + \begin{tabular}{cccc} + \toprule + & \multicolumn{3}{c}{Numbers} \\ + \cmidrule{2-4} + & 1 & 2 & 3 \\ + \midrule + Alphbet & A & B & C \\ + Roman & I & II& III \\ + \bottomrule + \end{tabular} \par + \subsubsection{合并单元格} + 横向合并单元格较为容易,由 \textbackslash multicolumn\{$\langle n\rangle$\}\{$\langle column-spec\rangle$\}\{$\langle item\rangle$\} % + 命令实现:\par + 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。% + 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 + 形如 \textbackslash multicolumn\{1\}\{$\langle column-spec\rangle$\}\{$\langle item\rangle$\} % + 的命令可以用来修改某一个单元格的列格式。\par + \begin{tabular}{|c|c|c|} + \hline + 1 & 2 & Center \\ + \hline + \multicolumn{2}{|c|}{3} & \multicolumn{1}{r|}{Right} \\ + \hline + 4 & \multicolumn{2}{c|}{C} \\ + \hline + \end{tabular}\par + 纵向合并单元格需要用到 multirow 宏包提供的 % + \textbackslash multirow\{$\langle n\rangle$\}\{$\langle width\rangle$\}\{$\langle item\rangle$\} 命令:\par + $\langle width\rangle$ 为合并后单元格的宽度,可以填 * 以使用自然宽度。\par + \begin{tabular}{ccc} + \hline + \multirow{2}{*}{Item} & \multicolumn{2}{c}{Value} \\ + \cline{2-3} + & First & Second \\ + \hline + A & 1 & 2 \\ + \hline + \end{tabular} + \subsubsection{嵌套表格} + 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 + 注意要用 \textbackslash multicolumn 命令配合 @\{\} % + 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 + \begin{tabular}{|c|c|c|} + \hline + a & b & c \\ + \hline + a & \multicolumn{1}{@{}c@{}|} + {\begin{tabular}{c|c} + e & f \\ + \hline + e & f \\ + \end{tabular}} & c \\ + \hline + a & b & c \\ + \hline + \end{tabular}\par + 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% + 提供 的 \textbackslash makecell 命令是一个简单的解决方案:\par + \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} diff --git a/learning_LaTeX.pdf b/learning_LaTeX.pdf index d9cd200..b0e614b 100644 Binary files a/learning_LaTeX.pdf and b/learning_LaTeX.pdf differ diff --git a/learning_LaTeX.synctex.gz b/learning_LaTeX.synctex.gz index c792dfb..1f838d4 100644 Binary files a/learning_LaTeX.synctex.gz and b/learning_LaTeX.synctex.gz differ diff --git a/learning_LaTeX.tex b/learning_LaTeX.tex index d7cee8b..687a080 100644 --- a/learning_LaTeX.tex +++ b/learning_LaTeX.tex @@ -1,4 +1,4 @@ -%!TEX program = xelatex +%TEX program = xelatex %表示用xelatex编译文件 \documentclass[a4paper]{ctexart} \usepackage{array} @@ -10,6 +10,13 @@ \usepackage{makecell} \usepackage{graphicx} \usepackage{subfig} +\usepackage{amsmath,amsfonts,amssymb,amsthm} +\usepackage{latexsym} +\usepackage{float} +\DeclareMathOperator{\argh}{argh} +\DeclareMathOperator*{\nut}{Nut} +\usepackage{yhmath} + \begin{document} \title{标题页} \author{Ryan\thanks{注脚}% @@ -494,8 +501,556 @@ \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} + \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 \appendix \section{附录}