UPDATE 数学符号
This commit is contained in:
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%!TEX program = xelatex
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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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@@ -10,6 +10,13 @@
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\usepackage{makecell}
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\usepackage{graphicx}
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\usepackage{subfig}
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\usepackage{amsmath,amsfonts,amssymb,amsthm}
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\usepackage{latexsym}
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\usepackage{float}
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\DeclareMathOperator{\argh}{argh}
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\DeclareMathOperator*{\nut}{Nut}
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\usepackage{yhmath}
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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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@@ -494,8 +501,556 @@
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\end{minipage}
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}
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\caption{使用 subfig 宏包的 \textbackslash subfloat 命令排版子图。}
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\end{figure}
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\section{数学公式}
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amsmath 宏 包,对多行公式的排版提供了有力的支持,%
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amsfonts 宏包以及基于它的 amssymb 宏包提 供了丰富的数学符号,%
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amsthm 宏包扩展了 \LaTeX 定理证明格式。\par
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\subsection{公式排版基础}
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\subsubsection{行内和行间公式}
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行内公式由一对 \$ 符号包裹:\\
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The Pythagorean theorem is %
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$a^2 + b^2 = c^2$.\par
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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,%
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这个编号可以用 \textbackslash label 和 \textbackslash ref 生成交叉引用。\par
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amsmath 的 \textbackslash eqref 命令甚至为引用 自动加上圆括号;%
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还可以用 \textbackslash tag 命令手动修改公式的编号,%
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或者用 \textbackslash notag 命令取消为公式编 号。\par
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The Pythagorean theorem is:
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\begin{equation}
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a^2 + b^2 = c^2 \label{pythagorean}
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\end{equation}
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Equation \eqref{pythagorean} is called `Gougu theorem' in Chinese.\par
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It's wrong to say
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\begin{equation}
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1 + 1 = 3 \tag{dumb}
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\end{equation}
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or
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\begin{equation}
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1 + 1 = 4 \notag
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\end{equation}\par
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直接使用不带编号的行间公式:
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\begin{equation*}
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a^2 + b^2 = c^2
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\end{equation*}
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For short:
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\[a^2 + b^2 = c^2\]
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Or if you like the long one:
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\begin{displaymath}
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a^2 + b^2 = c^2
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\end{displaymath}
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行内公式和行间公式的对比:\\
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In text:
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$\lim_{n \to \infty} \sum_{k=1}^n \frac{1}{k^2} = \frac{\pi^2}{6}$\\
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In display:
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\[\lim_{n \to \infty} \sum_{k=1}^n \frac{1}{k^2} = \frac{\pi^2}{6}\]
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\subsection{数学模式}
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\renewcommand{\labelenumi}{\arabic{enumi}.}
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\begin{enumerate}
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\item 数学模式中输入的空格被忽略。
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\item 不允许有空行(分段)。
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\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,%
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可以用\textbackslash mathrm 或者 amsmath 提供的 \textbackslash text 命令。
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\end{enumerate}
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$x^2 \geq 0 \qquad
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\text{for \textbf{all} } x \in \mathbb{R}$
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\subsection{数学符号}
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\subsubsection{一般符号}
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\begin{table}[H]
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\centering
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\caption{文本/数学模式通用符号}
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\begin{tabular}{clclclcl}
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\hline
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\{ & \textbackslash\{ & \} & \textbackslash\} & \$ & \textbackslash\$ & \% & \textbackslash\% \\
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\dag & \textbackslash dag & \S & \textbackslash S & \copyright & \textbackslash copyright & \dots & \textbackslash dots \\
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\ddag & \textbackslash ddag & \P & \textbackslash P & \pounds & \textbackslash pounds \\
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\hline
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\end{tabular}
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\end{table}
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\begin{table}[H]
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\centering
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\caption{希腊字母}
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\begin{tabular}{clclclcl}
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\toprule
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$\alpha$ & \textbackslash alpha & $\theta$ & \textbackslash theta &
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$o$ & o & $\upsilon$ & \textbackslash upsilon \\
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$\beta$ & \textbackslash beta & $\vartheta$ & \textbackslash vartheta &
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$\pi$ & \textbackslash pi & $\phi$ & \textbackslash phi \\
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$\gamma$ & \textbackslash gamma & $\iota$ & \textbackslash iota &
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$\varpi$ & \textbackslash varpi & $\varphi$ & \textbackslash varphi \\
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$\delta$ & \textbackslash delta & $\kappa$ & \textbackslash kappa &
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$\rho$ & \textbackslash rho & $\chi$ & \textbackslash chi \\
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$\epsilon$ & \textbackslash epsilon & $\lambda$ & \textbackslash lambda &
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$\varrho$ & \textbackslash varrho & $\psi$ & \textbackslash psi \\
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$\varepsilon$ & \textbackslash varepsilon & $\mu$ & \textbackslash mu &
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$\sigma$ & \textbackslash sigma & $\omega$ & \textbackslash omega \\
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$\zeta$ & \textbackslash zeta & $\nu$ & \textbackslash nu &
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$\varsigma$ & \textbackslash varsigma \\
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$\eta$ & \textbackslash eta & $\xi$ & \textbackslash xi &
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$\tau$ & \textbackslash tau \\
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\midrule
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$\Gamma$ & \textbackslash Gamma & $\Lambda$ & \textbackslash Lambda &
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$\Sigma$ & \textbackslash Sigma & $\Psi$ & \textbackslash Psi \\
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$\Delta$ & \textbackslash Delta & $\Xi$ & \textbackslash Xi &
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$\Upsilon$ & \textbackslash Upsilon & $\Omega$ & \textbackslash Omega \\
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$\Theta$ & \textbackslash Theta & $\Pi$ & \textbackslash Pi &
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$\Phi$ & \textbackslash Phi \\
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\midrule
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\multicolumn{4}{l}{以下命令依赖 amsmath 宏包}\\
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$\varGamma$ & \textbackslash varGamma & $\varLambda$ & \textbackslash varLambda &
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$\varSigma$ & \textbackslash varSigma & $\varPsi$ & \textbackslash varPsi \\
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$\varDelta$ & \textbackslash varDelta & $\varXi$ & \textbackslash varXi &
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$\varUpsilon$ & \textbackslash varUpsilon & $\varOmega$ & \textbackslash varOmega \\
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$\varTheta$ & \textbackslash varTheta & $\varPi$ & \textbackslash varPi &
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$\varPhi$ & \textbackslash varPhi \\
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\midrule
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\multicolumn{4}{l}{依赖 amssymb 宏包}\\
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$\digamma$ & \textbackslash digamma & $\varkappa$ & \textbackslash varkappa &
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$\beth$ & \textbackslash beth & $\gimel$ & \textbackslash gimel \\
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$\daleth$ & \textbackslash daleth \\
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\bottomrule
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\end{tabular}
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\end{table}
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\begin{table}[H]
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\centering
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\caption{其它符号}
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\begin{tabular}{clclclcl}
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\toprule
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$\dots$ & \textbackslash dots & $\cdots$ & \textbackslash cdots &
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$\vdots$ & \textbackslash vdots & $\ddots$ & \textbackslash ddots \\
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$\hbar$ & \textbackslash hbar & $\imath$ & \textbackslash imath &
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$\jmath$ & \textbackslash jmath & $\ell$ & \textbackslash ell \\
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$\Re$ & \textbackslash Re & $\Im$ & \textbackslash Im &
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$\aleph$ & \textbackslash aleph & $\wp$ & \textbackslash wp \\
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$\forall$ & \textbackslash forall & $\exists$ & \textbackslash exists &
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$\partial$ & \textbackslash partial & $'$ & ' \\
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$\prime$ & \textbackslash prime & $\emptyset$ & \textbackslash emptyset &
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$\infty$ & \textbackslash infty & $\nabla$ & \textbackslash nabla \\
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$\triangle$ & \textbackslash triangle & $\bot$ & \textbackslash bot &
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$\top$ & \textbackslash top & $\angle$ & \textbackslash angle \\
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$\surd$ & \textbackslash surd & $\diamondsuit$ & \textbackslash diamondsuit &
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$\heartsuit$ & \textbackslash heartsuit & $\clubsuit$ & \textbackslash clubsuit \\
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$\spadesuit$ & \textbackslash spadesuit & $\neg$ & \textbackslash neg or \textbackslash lnot &
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$\flat$ & \textbackslash flat & $\natural$ & \textbackslash natural \\
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$\sharp$ & \textbackslash sharp \\
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\midrule
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\multicolumn{3}{l}{以下命令依赖 latexsym 宏包}\\
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$\mho$ & \textbackslash mho & $\Box$ & \textbackslash Box &
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$\Diamond$ & \textbackslash Diamond \\
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\bottomrule
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\end{tabular}
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\end{table}
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$a_1,a_2,\dots,a_n$\\
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$a_1 + a_2 + \cdots + a_n$\par
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\subsubsection{指数、上下标和导数}
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\textasciicircum 和 \_ 标明上下标。%
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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
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$p^3_{ij} \qquad
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m_\mathrm{Kunth} \qquad
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\sum_{k=1}^3 k$\\
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$a^x +y \neq a^{x+y} \qquad
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e^{x^2} \neq {e^x}^2$ \par
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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
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$f(x) = x^2 \quad
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f'(x) = 2x \quad
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f''^{2}(x) = 4$ \par
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\subsubsection{分式和根式}
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分式使用 \textbackslash frac\{分子\}\{分母\} 来书写。%
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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。%
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amsmath 提供了方便的命令 \textbackslash dfrac 和 \textbackslash tfrac,%
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令用户能够在行内使用正常大小的 分式，或是反过来。\par
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In display style:
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\[
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3/8 \qquad
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\frac{3}{8} \qquad
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\tfrac{3}{8}
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\]
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In text style:
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$1\frac{1}{2}$~hours \qquad
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$1\dfrac{1}{2}$~hours\par
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一般的根式使用 \textbackslash sqrt\{\dots\};%
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表示 n 次方根时写成 \textbackslash sqrt[n]\{\dots\}。\par
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$\sqrt{x} \Leftrightarrow x^{1/2} \quad
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\sqrt[3]{2} \quad
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\sqrt{x^{2} + \sqrt{y}}$ \par
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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
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Pascal's rule is
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\[
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\binom{n}{k} = \binom{n - 1}{k} + \binom{n - 1}{k}
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\]
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\subsubsection{关系符}
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\begin{table}[H]
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\centering
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\caption{二元关系符}
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\begin{tabular}{clclcl}
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\toprule
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$<$ & < & $>$ & > &
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$=$ & = \\
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$\equiv$ & \textbackslash equiv & $\leq$ & \textbackslash leq or \textbackslash le &
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$\geq$ & \textbackslash geq or \textbackslash ge \\
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$\ll$ & \textbackslash ll & $\gg$ & \textbackslash gg &
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$\doteq$ & \textbackslash doteq \\
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$\prec$ & \textbackslash prec & $\succ$ & \textbackslash succ &
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$\sim$ & \textbackslash sim \\
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$\preceq$ & \textbackslash preceq & $\succeq$ & \textbackslash succeq &
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$\simeq$ & \textbackslash simeq \\
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$\subset$ & \textbackslash subset & $\supset$ & \textbackslash supset &
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$\approx$ & \textbackslash approx \\
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$\subseteq$ & \textbackslash subseteq & $\supseteq$ & \textbackslash supseteq &
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$\cong$ & \textbackslash cong \\
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$\sqsubseteq$ & \textbackslash sqsubseteq & $\sqsupseteq$ & \textbackslash sqsupseteq &
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$\bowtie$ & \textbackslash bowtie \\
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$\in$ & \textbackslash in & $\ni$ & \textbackslash ni ,\textbackslash owns &
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$\propto$ & \textbackslash propto \\
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$\vdash$ & \textbackslash vdash & $\dashv$ & \textbackslash dashv &
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$\models$ & \textbackslash models \\
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$\mid$ & \textbackslash mid & $\parallel$ & \textbackslash parallel &
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$\perp$ & \textbackslash perp \\
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$\smile$ & \textbackslash smile & $\frown$ & \textbackslash frown &
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$\asymp$ & \textbackslash asymp \\
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$:$ & : & $\notin$ & \textbackslash notin &
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$\neq$ & \textbackslash neq or \textbackslash ne \\
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\midrule
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\multicolumn{3}{l}{以下命令依赖 latexsym 宏包}\\
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$\sqsubset$ & \textbackslash sqsubset & $\sqsupset$ & \textbackslash sqsupset &
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$\Join$ & \textbackslash Join \\
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\midrule
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\multicolumn{3}{l}{以下命令依赖 amssymb 宏包}\\
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$\lessdot$ & \textbackslash lessdot & $\gtrdot$ & \textbackslash gtrdot &
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$\doteqdot$ & \textbackslash doteqdot \\
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$\leqslant$ & \textbackslash leqslant & $\geqslant$ & \textbackslash geqslant &
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$\risingdotseq$ & \textbackslash risingdotseq \\
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$\eqslantless$ & \textbackslash eqslantless & $\eqslantgtr$ & \textbackslash eqslantgtr &
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$\fallingdotseq$ & \textbackslash fallingdotseq \\
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$\leqq$ & \textbackslash leqq & $\geqq$ & \textbackslash geqq &
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$\eqcirc$ & \textbackslash eqcirc \\
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$\circeq$ & \textbackslash circeq & $\ggg$ & \textbackslash ggg &
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$\lll$ & \textbackslash lll or \textbackslash llless \\
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$\lesssim$ & \textbackslash lesssim & $\gtrsim$ & \textbackslash gtrsim &
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$\triangleq$ & \textbackslash triangle \\
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$\lessapprox$ & \textbackslash lessapprox & $\gtrapprox$ & \textbackslash gtrapprox &
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$\bumpeq$ & \textbackslash bumpeq \\
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$\lessgtr$ & \textbackslash lessgtr & $\gtrless$ & \textbackslash gtrless &
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$\Bumpeq$ & \textbackslash Bumpeq \\
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$\lesseqgtr$ & \textbackslash lesseqgtr & $\gtreqless$ & \textbackslash gtreqless &
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$\thicksim$ & \textbackslash thicksim \\
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$\lesseqqgtr$ & \textbackslash lesseqqgtr & $\gtreqqless$ & \textbackslash gtreqqless &
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$\thickapprox$ & \textbackslash thickapprox \\
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$\preccurlyeq$ & \textbackslash preccurlyeq & $\succcurlyeq$ & \textbackslash succcurlyeq &
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$\approxeq$ & \textbackslash approxeq \\
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$\curlyeqprec$ & \textbackslash curlyeqprec & $\curlyeqsucc$ & \textbackslash curlyeqsucc &
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$\backsim$ & \textbackslash backsim \\
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$\precsim$ & \textbackslash precsim & $\succsim$ & \textbackslash succsim &
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$\backsimeq$ & \textbackslash backsimeq \\
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$\precapprox$ & \textbackslash precapprox & $\succapprox$ & \textbackslash succapprox &
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$\vDash$ & \textbackslash vDash \\
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$\subseteqq$ & \textbackslash subseteqq & $\supseteqq$ & \textbackslash supseteqq &
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$\Vdash$ & \textbackslash Vdash \\
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$\shortparallel$ & \textbackslash shortparallel & $\Supset$ & \textbackslash Supset &
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$\Vvdash$ & \textbackslash Vvdash \\
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$\blacktriangleleft$ & \textbackslash blacktriangleleft & $\sqsupset$ & \textbackslash sqsupset &
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$\backepsilon$ & \textbackslash backepsilon \\
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$\vartriangleright$ & \textbackslash vartriangleright & $\because$ & \textbackslash because &
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$\varpropto$ & \textbackslash varpropto \\
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$\blacktriangleright$ & \textbackslash blacktriangleright & $\Subset$ & \textbackslash Subset &
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$\between$ & \textbackslash between \\
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$\trianglerighteq$ & \textbackslash trianglerighteq & $\smallfrown$ & \textbackslash smallfrown &
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$\pitchfork$ & \textbackslash pitchfork \\
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$\vartriangleleft$ & \textbackslash vartriangleleft & $\shortmid$ & \textbackslash shortmid &
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$\smallsmile$ & \textbackslash smallsmile \\
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$\trianglelefteq$ & \textbackslash trianglelefteq & $\therefore$ & \textbackslash therefore &
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$\sqsubset$ & \textbackslash sqsubset \\
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\bottomrule
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\end{tabular}
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\end{table}
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\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
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\[
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f_n(x) \stackrel{*}{\approx} 1
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\]
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\subsubsection{算符}
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\begin{table}[H]
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\centering
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\caption{二元运算符}
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\begin{tabular}{clclcl}
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\toprule
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$+$ & + &$-$ & - &
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$\pm$ & \textbackslash pm \\
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$\mp$ & \textbackslash mp & $\triangleleft$ & \textbackslash triangleleft &
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$\cdot$ & \textbackslash cdot \\
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$\div$ & \textbackslash div & $\triangleright$ & \textbackslash triangleright &
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$\times$ & \textbackslash times \\
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$\setminus$ & \textbackslash setminus & $\star$ & \textbackslash star &
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$\cup$ & \textbackslash cup \\
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$\cap$ & \textbackslash cap & $\ast$ & \textbackslash ast &
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$\sqcup$ & \textbackslash sqcup \\
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$\sqcap$ & \textbackslash sqcap & $\circ$ & \textbackslash circ &
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$\vee$ & \textbackslash vee \\
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$\lor$ & \textbackslash lor & $\wedge$ & \textbackslash wedge &
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$\land$ & \textbackslash land \\
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$\bullet$ & \textbackslash bullet & $\oplus$ & \textbackslash oplus &
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$\ominus$ & \textbackslash ominus \\
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$\diamond$ & \textbackslash diamond & $\odot$ & \textbackslash odot &
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$\oslash$ & \textbackslash oslash \\
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$\uplus$ & \textbackslash uplus & $\otimes$ & \textbackslash otimes &
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$\bigcirc$ & \textbackslash bigcirc \\
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$\amalg$ & \textbackslash amalg & $\bigtriangleup$ & \textbackslash bigtriangleup &
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$\bigtriangledown$ & \textbackslash bigtriangledown \\
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$\dagger$ & \textbackslash dagger & $\ddagger$ & \textbackslash ddagger &
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$\wr$ & \textbackslash wr \\
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\midrule
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\multicolumn{3}{l}{以下命令依赖 latexsym 宏包} \\
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$\lhd$ & \textbackslash lhd & $\rhd$ & \textbackslash rhd \\
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$\unlhd$ & \textbackslash unlhd & $\unrhd$ & \textbackslash unrhd \\
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\midrule
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\multicolumn{3}{l}{以下命令依赖 amssymb 宏包} \\
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$\dotplus$ & \textbackslash dotplus & $\centerdot$ & \textbackslash centerdot \\
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$\ltimes$ & \textbackslash ltimes & $\rtimes$ & \textbackslash rtimes &
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$\divideontimes$ & \textbackslash divideontimes \\
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$\doublecup$ & \textbackslash doublecup & $\doublecap$ & \textbackslash doublecap &
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$\smallsetminus$ & \textbackslash smallsetminus \\
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$\veebar$ & \textbackslash veebar & $\barwedge$ & \textbackslash barwedge &
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$\doublebarwedge$ & \textbackslash doublebarwedge \\
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$\boxplus$ & \textbackslash boxplus & $\boxminus$ & \textbackslash boxminus &
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$\circleddash$ & \textbackslash circleddash \\
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$\boxtimes$ & \textbackslash boxtimes & $\boxdot$ & \textbackslash boxdot &
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$\circledcirc$ & \textbackslash circledcirc \\
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$\intercal$ & \textbackslash intercal & $\circledast$ & \textbackslash circledast &
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$\rightthreetimes$ & \textbackslash rightthreetimes \\
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$\curlyvee$ & \textbackslash curlyvee & $\curlywedge$ & \textbackslash curlywedge &
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$\leftthreetimes$ & \textbackslash listoffigures \\
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||||
\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}
|
||||
|
||||
Reference in New Issue
Block a user