LaTeX 使用手册

2022-12-10

类别: 软件技术

标签: LaTeX MathJax

希腊字母表

	小写形式		大写形式		变形形式
\alpha	\(\alpha\)	A	\(A\)
\beta	\(\beta\)	B	\(B\)
\gamma	\(\gamma\)	\Gamma	\(\Gamma\)
\delta	\(\delta\)	\Delta	\(\Delta\)
\epsilon	\(\epsilon\)	E	\(E\)	\varepsilon	\(\varepsilon\)
\zeta	\(\zeta\)	Z	\(Z\)
\eta	\(\eta\)	H	\(H\)
\theta	\(\theta\)	\Theta	\(\Theta\)	\vartheta	\(\vartheta\)
\iota	\(\iota\)	I	\(I\)
\kappa	\(\kappa\)	K	\(K\)	\varkappa	\(\varkappa\)
\lambda	\(\lambda\)	\Lambda	\(\Lambda\)
\mu	\(\mu\)	M	\(M\)
\nu	\(\nu\)	N	\(N\)
\xi	\(\xi\)	\Xi	\(\Xi\)
o	\(o\)	O	\(O\)
\pi	\(\pi\)	\Pi	\(\Pi\)	\varpi	\(\varpi\)
\rho	\(\rho\)	P	\(P\)	\varrho	\(\varrho\)
\sigma	\(\sigma\)	\Sigma	\(\Sigma\)	\varsigma	\(\varsigma\)
\tau	\(\tau\)	T	\(T\)
\upsilon	\(\upsilon\)	\Upsilon	\(\Upsilon\)
\phi	\(\phi\)	\Phi	\(\Phi\)	\varphi	\(\varphi\)
\chi	\(\chi\)	X	\(X\)
\psi	\(\psi\)	\Psi	\(\Psi\)
\omega	\(\omega\)	\Omega	\(\Omega\)

希腊字母中有七个变形形式，它们与 LaTeX 相关的历史可以参考文章 What does the \var prefix stand for in \varphi and \varepsilon etc?

常用符号

比较符号	<	\(<\)	>	\(>\)	=	\(=\)
	\leq	\(\leq\)	\geq	\(\geq\)	\equiv	\(\equiv\)
	\gg	\(\gg\)	\ggg	\(\ggg\)	\ll	\(\ll\)
	\subset	\(\subset\)	\supset	\(\supset\)	\sim	\(\sim\)
	\subseteq	\(\subseteq\)	\supseteq	\(\supseteq\)	\simeq	\(\simeq\)
	\in	\(\in\)	\ni	\(\ni\)	\approx	\(\approx\)
	\mid	\(\mid\)	\parallel	\(\parallel\)	\cong	\(\cong\)
	\neq	\(\neq\)	\propto	\(\propto\)	\doteq	\(\doteq\)
箭头	\leftarrow	\(\leftarrow\)	\rightarrow	\(\rightarrow\)	\uparrow	\(\uparrow\)
	\longleftarrow	\(\longleftarrow\)	\longrightarrow	\(\longrightarrow\)	\downarrow	\(\downarrow\)
	\Leftarrow	\(\Leftarrow\)	\Rightarrow	\(\Rightarrow\)	\Uparrow	\(\Uparrow\)
	\Longleftarrow	\(\Longleftarrow\)	\Longrightarrow	\(\Longrightarrow\)	\Downarrow	\(\Downarrow\)
	\leftrightarrow	\(\leftrightarrow\)	\Leftrigtarrow	\(\Leftrightarrow\)	\updownarrow	\(\updownarrow\)
	\longleftrightarrow	\(\longleftrightarrow\)	\Longleftrigtarrow	\(\Longleftrightarrow\)	\Updownarrow	\(\Updownarrow\)
	\mapsto	\(\mapsto\)	\longmapsto	\(\longmapsto\)	\nearrow	\(\nearrow\)
	\searrow	\(\searrow\)	\swarrow	\(\swarrow\)	\nwarrow	\(\nwarrow\)
结构符号	\frac{abc}{xyz}	\(\frac{abc}{xyz}\)	\overline{abc}	\(\overline{abc}\)	\overrightarrow{abc}	\(\overrightarrow{abc}\)
	f’	\(f'\)	\underline{abc}	\(\underline{abc}\)	\overleftarrow{abc}	\(\overleftarrow{abc}\)
	\sqrt{abc}	\(\sqrt{abc}\)	\widehat{abc}	\(\widehat{abc}\)	\overbrace{abc}	\(\overbrace{abc}\)
	\sqrt[n]{abc}	\(\sqrt[n]{abc}\)	\widetilde{abc}	\(\widetilde{abc}\)	\underbrace{abc}	\(\underbrace{abc}\)
	\acute{a}	\(\acute{a}\)	\bar{a}	\(\bar{a}\)	\hat{a}	\(\hat{a}\)
	\dot{a}	\(\dot{a}\)	\ddot{a}	\(\ddot{a}\)	\grave{a}	\(\grave{a}\)
	\breve{a}	\(\breve{a}\)	\vec{a}	\(\vec{a}\)	\tilde{a}	\(\tilde{a}\)
	\binom{a}{b}	\(\binom{a}{b}\)
函数名	\lim_{h\to 0}	\(\lim_{h\to 0}\)	\ln	\(\ln\)	\sin	\(\sin\)
	\exp	\(\exp\)	\max	\(\max\)	\inf	\(\inf\)
	\limsup	\(\limsup\)	\liminf	\(\liminf\)	\gcd	\(\gcd\)
其他符号	\cdots	\(\cdots\)	\vdots	\(\vdots\)	\ldots	\(\ldots\)
	\infty	\(\infty\)	\forall	\(\forall\)	\exists	\(\exists\)
	\nabla	\(\nabla\)	\partial	\(\partial\)	\nexists	\(\nexists\)
	\emptyset	\(\emptyset\)	\varnothing	\(\varnothing\)	\square	\(\square\)
	\clubsuit	\(\clubsuit\)	\diamondsuit	\(\diamondsuit\)	\heartsuit	\(\heartsuit\)
	\spadesuit	\(\spadesuit\)	\triangle	\(\triangle\)	\triangledown	\(\triangledown\)
	\int	\(\int\)	\iint	\(\iint\)	\oint	\(\oint\)
	\cdot	\(\cdot\)	\ast	\(\ast\)	\star	\(\star\)
	\circ	\(\circ\)	\bullet	\(\bullet\)	\bigcirc	\(\bigcirc\)
	\times	\(\times\)	\div	\(\div\)	\odot	\(\odot\)
	\ominus	\(\ominus\)	\oplus	\(\oplus\)	\otimes	\(\otimes\)
	\sum	\(\sum\)	\prod	\(\prod\)	\coprod	\(\coprod\)
	\bigcap	\(\bigcap\)	\bigcup	\(\bigcup\)	\bigotimes	\(\bigotimes\)

数学字体

Caligraphic letters：\mathcal{A}

\[\mathcal{A B C D E F G H I J K L M N O P Q R S T U V W X Y Z}\] \[\mathcal{a b c d e f g h i j k l m n o p q r s t u v w x y z}\] \[\mathcal{1 2 3 4 5 6 7 8 9 0}\]

Mathbb letters：\mathbb{A}

\[\mathbb{A B C D E F G H I J K L M N O P Q R S T U V W X Y Z}\] \[\mathbb{a b c d e f g h i j k l m n o p q r s t u v w x y z}\] \[\mathbb{1 2 3 4 5 6 7 8 9 0}\]

Mathfrak letters：\mathfrak{A}

\[\mathfrak{A B C D E F G H I J K L M N O P Q R S T U V W X Y Z}\] \[\mathfrak{a b c d e f g h i j k l m n o p q r s t u v w x y z}\] \[\mathfrak{1 2 3 4 5 6 7 8 9 0}\]

Math Sans serif letters：\mathsf{A}

\[\mathsf{A B C D E F G H I J K L M N O P Q R S T U V W X Y Z}\] \[\mathsf{a b c d e f g h i j k l m n o p q r s t u v w x y z}\] \[\mathsf{1 2 3 4 5 6 7 8 9 0}\]

Math bold letters：\mathbf{A}

\[\mathbf{A B C D E F G H I J K L M N O P Q R S T U V W X Y Z}\] \[\mathbf{a b c d e f g h i j k l m n o p q r s t u v w x y z}\] \[\mathbf{1 2 3 4 5 6 7 8 9 0}\]

矩阵和方程组

用 array 环境生成公式，基本语法如下，其中的 cols 对每一列取 [lrc] 中的一个字符表示相应列的对齐方式，还可以加上 | 来加上竖线，每一行的 \(row_j\) 用 & 做列分隔符。用 \hline 可以在行中间加上横线。

Array 环境是 LaTeX 中数学模式下的表格对齐环境，tabular 是文本模式下表格环境。

\begin{array}{cols}
row1 \\
row2 \\
... \\
rowm
\end{array}

代码 1：

\left(
    \begin{array}{cc}
     2\tau & 7\phi-\frac5{12} \\
        3\psi & \frac{\pi}8
    \end{array}
\right)
\left( \begin{array}{c} x \\ y \end{array} \right)
~\mbox{and}~
\left[
    \begin{array}{cc|r}
    3 & 4 & 5 \\
    1 & 3 & 729
    \end{array}
\right]

效果 1： \(\left( \begin{array}{cc} 2\tau & 7\phi-\frac5{12} \\ 3\psi & \frac{\pi}8 \end{array} \right) \left( \begin{array}{c} x \\ y \end{array} \right) ~\mbox{and}~ \left[ \begin{array}{cc|r} 3 & 4 & 5 \\ 1 & 3 & 729 \end{array} \right]\)

代码 2：

f(z) =
\left\{
    \begin{array}{rcl}
        \overline{\overline{z^2}+\cos z} & \mbox{for} & |z|<3 \\
        0 & \mbox{for} & 3\leq|z|\leq5 \\
        \sin\overline{z} & \mbox{for} & |z|>5
    \end{array}
\right.

效果 2： \(f(z) = \left\{ \begin{array}{rcl} \overline{\overline{z^2}+\cos z} & \mbox{for} & |z|<3 \\ 0 & \mbox{for} & 3\leq|z|\leq5 \\ \sin\overline{z} & \mbox{for} & |z|>5 \end{array} \right.\)

下面是使用 align 环境来对齐公式。align 是 AMS-LaTeX 项目提供的环境。

代码 1：

$$
\begin{align}
  \frac{d}{dx} \ln x &= \lim_{h\to 0} \frac{\ln(x+h) - \ln x}{h} \\
  &= \ln e^{1/x} &&\text{How this follows is left as an exercise.}\\
  &= \frac{1}{x} &&\text{Using the definition of ln as inverse function}
 \end{align}
$$

效果 1：

\[\begin{align} \frac{d}{dx} \ln x &= \lim_{h\to 0} \frac{\ln(x+h) - \ln x}{h} \\ &= \ln e^{1/x} &&\text{How this follows is left as an exercise.}\\ &= \frac{1}{x} &&\text{Using the definition of ln as inverse function} \end{align}\]

代码 2：

$$
\left\{
\begin{matrix}
\begin{align}
& l_0(x_0) = 1, l_0(x_1) = 0, ..., l_0(x_n) = 0, \\
& l_1(x_0) = 0, l_1(x_1) = 1, ..., l_1(x_n) = 0, \\
& \cdots \cdots \\
& l_n(x_0) = 0, l_n(x_1) = 0, ..., l_n(x_n) = 1. \\
\end{align}
\end{matrix}
\right. \qquad (6)
$$

效果 2：

\[\left\{ \begin{matrix} \begin{align} & l_0(x_0) = 1, l_0(x_1) = 0, ..., l_0(x_n) = 0, \\ & l_1(x_0) = 0, l_1(x_1) = 1, ..., l_1(x_n) = 0, \\ & \cdots \cdots \\ & l_n(x_0) = 0, l_n(x_1) = 0, ..., l_n(x_n) = 1. \\ \end{align} \end{matrix} \right. \qquad (6)\]

代码 3：

$$
c[i, j] =
\left\{
\begin{matrix}
\begin{align}
& {0} && {if \quad i = 0 \; or \; j = 0,} \\
& {c[i - 1, j - 1] + 1} && {if \quad i, j > 0 \; and \; x_i = y_j,} \\
& {max(c[i, j - 1], c[i - 1, j])} && {if \quad i, j > 0 \; and \; x_i \neq y_j.} \\
\end{align}
\end{matrix}
\right.
$$

效果 3：

\[c[i, j] = \left\{ \begin{matrix} \begin{align} & {0} && {if \quad i = 0 \; or \; j = 0,} \\ & {c[i - 1, j - 1] + 1} && {if \quad i, j > 0 \; and \; x_i = y_j,} \\ & {max(c[i, j - 1], c[i - 1, j])} && {if \quad i, j > 0 \; and \; x_i \neq y_j.} \\ \end{align} \end{matrix} \right.\]