dummy

参考1

参考2

在线编辑

0.1 行内行间应用方式

$ equation $  (正文)
$$ eqauation $$ (单独)

0.2 常用希腊字母

\alpha \(\alpha\) \varTheta \(\varTheta\)
\beta \(\beta\) \varGamma \(\varGamma\)
\gamma \(\gamma\) \Gamma \(\Gamma\)
\theta \(\theta\) \Theta \(\Theta\)
\delta \(\delta\) \Delta \(\Delta\)
\epsilon \(\epsilon\) \varDelta \(\varDelta\)
\zeta \(\zeta\) \varLambda \(\varLambda\)
\eta \(\eta\)
\iota \(\iota\)
\kappa \(\kappa\) \varLambda \(\varLambda\)
\lambda \(\lambda\) \Lambda \(\Lambda\)
\mu \(\mu\) \varOmega \(\varOmega\)
\nu \(\nu\) \varPi \(\varPi\)
\pi \(\pi\) \Pi \(\Pi\)
\rho \(\rho\) \varSigma \(\varSigma\)
\sigma \(\sigma\) \Sigma \(\Sigma\)
\tau \(\tau\) \varPhi \(\varPhi\)
\phi \(\phi\) \Phi \(\Phi\)
\omega \(\omega\) \Omega \(\Omega\)
\tau \(\tau\) \Tau \(\Tau\)
\chi \(\chi\)
\upsilon \(\upsilon\)
\iota \(\iota\)

0.3 常用求和符号和积分号

\sum \(\sum\)
\int \(\int\)
\sum_{i=1}^{N} \(\sum_{i=1}^{N}\)
\int_{a}^{b} \(\int_{a}^{b}\)
\prod \(\prod\)
\iint \(\iint\)
\prod_{i=1}^{N} \(\prod_{i=1}^{N}\)
\iint_{a}^{b} \(\iint_{a}^{b}\)
\bigcup \(\bigcup\)
\bigcap \(\bigcap\)
\bigcup_{i=1}^{N} \(\bigcup_{i=1}^{N}\)
\bigcap_{i=1}^{N} \(\bigcap_{i=1}^{N}\)

0.4 其他常用符号

\sqrt[3]{2} \(\sqrt[3]{2}\)
\sqrt{2} \(\sqrt{2}\)
\sqrt{a} \(\sqrt{a}\)
\vec{a} \(\vec{a}\)
\tilde{a} \(\tilde{a}\)
\sqrt[3]{2} \(\sqrt[3]{2}\)
x_{3} \(x_{3}\)
\lim_{x \to 0} \(\lim_{x \to 0}\)
\frac{1}{2} \(\frac{1}{2}\)
\infty \(\infty\)
\cdotp \(\cdotp\)
\cdots \(\cdots\)
\vdots \(\vdots\)
\ddots \(\ddots\)
\bot \(\bot\)
\partial \(\partial\)
\hat{a} \(\hat{a}\)
\dot{a} \(\dot{a}\)
\bar{a} \(\bar{a}\)
a^{3} \(a^{3}\)
\frac{1}{a} \(\frac{1}{a}\)

0.5 运算符

语法 效果 语法 效果
\pm \(\pm\) \propto \(\propto\)
\times \(\times\) \leq \(\leq\)
\circ \(\circ\) \subseteq \(\subseteq\)
\cdot \(\cdot\) \subset \(\subset\)
\cap \(\cap\) \cup \(\cup\)
\supset \(\supset\) \bullet \(\bullet\)
\supseteq \(\supseteq\) \div \(\div\)
\geq \(\geq\) \mp \(\mp\)
\in \(\in\)

0.6 声调

语法 效果 语法 效果 语法 效果
\bar{x} \(\bar{x}\) \acute{\eta} \(\acute{\eta}\) \check{\alpha} \(\check{\alpha}\)
\grave{\eta} \(\grave{\eta}\) \breve{a} \(\breve{a}\) \ddot{y} \(\ddot{y}\)
\dot{x} \(\dot{x}\) \hat{\alpha} \(\hat{\alpha}\) \tilde{\iota} \(\tilde{\iota}\)

0.7 根号

语法 效果 语法 效果
\sqrt{3} \(\sqrt{3}\) \sqrt[n]{3} \(\sqrt[n]{3}\)

0.8 上标下标

功能 语法 效果
上标 a^2 \(a^2\)
下标 a_2 \(a_2\)
组合 a^{2+2} \(a^{2+2}\)
组合 a_{i,j} \(a_{i,j}\)
结合 x_2^3 \(x_2^3\)
前置 {}_1^2!X_3^4 \({}_1^2\!X_3^4\)
向量 \vec{c} \(\vec{c}\)
向量 \overleftarrow{a b} \(\overleftarrow{a b}\)
向量 \overrightarrow{c d} \(\overrightarrow{c d}\)
导数 x' \(x'\)
导数 x^\prime \(x^\prime\)
导数 \dot{x} \(\dot{x}\)
导数 \ddot{y} \(\ddot{y}\)
上划线 \overline{h i j} \(\overline{h i j}\)
下划线 \underline{k l m} \(\underline{k l m}\)
上面 \overset{P}{\longrightarrow} \(\overset{P}{\longrightarrow}\)
下面 \underset{P}{\Longrightarrow} \(\underset{P}{\Longrightarrow}\)
  • 默认行内公式$\sum_{k=1}^n{x_k}$上下标: \(\sum_{k=1}^n{x_k}\)
  • 默认行间公式$$\sum_{k=1}^n{x_k}$$上下标: \[\sum_{k=1}^n{x_k}\]

  • 强制行内公式$\sum\limits_{k=1}^n{x_k}$上下标: \(\sum\limits_{k=1}^n{x_k}\)
  • 强制行间公式$$\sum\nolimits_{k=1}^n{x_k}$$上下标: \[\sum\nolimits_{k=1}^n{x_k}\]

0.9 空白类型列举

功能 语法 效果 描述
两个空格 a \qquad b \(a \qquad b\) 两个m的宽度
一个空格 a \quad b \(a \quad b\) 一个m的宽度
大空格 a\ b \(a\ b\) 1/3m宽度
中等空格 a\;b \(a\;b\) 2/7m宽度
小空格 a,b \(a,b\) 1/6m宽度
没有空格 ab \(ab\) 正常宽度
紧贴 a!b \(a!b\) 缩进1/6m宽度

0.10 公式锚点

$\int_{-\infty}^\infty e^{-\pi x^2}\,\mathrm{d}x=1\label{a}\tag{1}$

这里引用$\ref{a}$

\(\int_{-\infty}^\infty e^{-\pi x^2}\,\mathrm{d}x=1\label{a}\tag{1}\) 这里引用\(\ref{a}\)

0.11 矩阵

0.11.1 简单的矩阵

$$
\begin{matrix}
    1 & 2 & 3 \\
    4 & 5 & 6 \\
    7 & 8 & 9
\end{matrix}  \tag{3}
$$

\[ \begin{matrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{matrix} \tag{3} \]

0.11.2 带括号的矩阵

$$
\left \{
    \begin{matrix}
        1 & 2 & 3 \\
        4 & 5 & 6 \\
        7 & 8 & 9
    \end{matrix}
\right \} \tag{4}
$$

\[ \left \{ \begin{matrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{matrix} \right \} \tag{4} \]

$$
\left [
    \begin{matrix}
        1 & 2 & 3 \\
        4 & 5 & 6 \\
        7 & 8 & 9
    \end{matrix}
\right ] \tag{5}
$$

\[ \left[ \begin{matrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{matrix} \right] \tag{5} \]

$$
\begin{bmatrix}
    1 & 2 & 3 \\
    4 & 5 & 6 \\
    7 & 8 & 9
\end{bmatrix} \tag{6}
$$

\[ \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{bmatrix} \tag{6} \]

$$
\begin{Bmatrix}
    1 & 2 & 3 \\
    4 & 5 & 6 \\
    7 & 8 & 9
\end{Bmatrix} \tag{7}
$$

\[ \begin{Bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{Bmatrix} \tag{7} \]

$$
\begin{vmatrix}
    1 & 2 & 3 \\
    4 & 5 & 6 \\
    7 & 8 & 9
\end{vmatrix} \tag{8}
$$

\[ \begin{vmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{vmatrix} \tag{8} \]

$$
\begin{Vmatrix}
    1 & 2 & 3 \\
    4 & 5 & 6 \\
    7 & 8 & 9
\end{Vmatrix} \tag{9}
$$

\[ \begin{Vmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{Vmatrix} \tag{9} \]

0.12 排版

0.12.1 多行方程组对齐

$$ 
\begin{cases} 
    a_{11}x_1&+&a_{12}x_2&+&\cdots&+a_{1n}x_n&=&b_1\\
    &&&&\vdots\\
    a_{n1}x_1&+&a_{n2}x_2&+&\cdots&+a_{nn}x_n&=&b_n&
\end{cases}
$$

\[ \begin{cases} a_{11}x_1&+&a_{12}x_2&+&\cdots&+a_{1n}x_n&=&b_1\\ &&&&\vdots\\ a_{n1}x_1&+&a_{n2}x_2&+&\cdots&+a_{nn}x_n&=&b_n& \end{cases} \]

$$ 
\begin{align*} 
  &a_1 x + b_1 y + c_1 z = d_1\tag{$3.11$}  \\ 
  &aa_2 x + b_2 y + c_2 z = d_2\tag{$3.12$}  \\
  &aaa_3 x + b_3 y + c_3 z = d_3\tag{$3.13$}
\end{align*}
$$

\[ \begin{align*}   &a_1 x + b_1 y + c_1 z = d_1\tag{$3.11$} \\   &aa_2 x + b_2 y + c_2 z = d_2\tag{$3.12$} \\   &aaa_3 x + b_3 y + c_3 z = d_3\tag{$3.13$} \end{align*} \]

0.12.2 多行公式等号对齐

eqnarray(built-in) is similar to align(amsmath package) below

$$
\begin{eqnarray}
    f(x,y) &=& 2xy+(x-y)^2\\
           &=& x^2+y^2
\end{eqnarray}
$$

\[ \begin{eqnarray} f(x,y) &=& 2xy+(x-y)^2\\ &=& x^2+y^2 \end{eqnarray} \]

$$
\begin{align*}
    f(x,y) &= 2xy+(x-y)^2 \\
           &= x^2+y^2
\end{align*}
$$

\[ \begin{align*} f(x,y) &= 2xy+(x-y)^2 \\ &= x^2+y^2 \end{align*} \]

指定第几列对齐

$$
\begin{alignat}{2} 
    \sigma_1 &= x + y &\qquad \sigma_2 &= \frac{x}{y} \\
    \sigma_1' &= \frac{\partial x + y}{\partial x} & \sigma_2' &= \frac{\partial \frac{x}{y}}{\partial x}
\end{alignat}
$$

\[ \begin{alignat}{2} \sigma_1 &= x + y &\quad \sigma_2 &= \frac{x}{y} \\ \sigma_1' &= \frac{\partial x + y}{\partial x} & \sigma_2' &= \frac{\partial \frac{x}{y}}{\partial x} \end{alignat} \]

0.12.3 大括号右多行赋值

$$
\left\{\begin{array}{cc} 
        1, & x=f(Pa_{x})\\ 
        0, & other\ values 
\end{array}\right.
$$

\[ \left\{\begin{array}{cc} 1, & x=f(Pa_{x})\\ 0, & other\ values \end{array}\right. \]

$$
P(x|Pa_x)=\begin{cases} 
        1, & x=f(Pa_{x})\\ 
        0, & other\ values 
\end{cases}
$$

\[ P(x|Pa_x)=\begin{cases} 1, & x=f(Pa_{x})\\ 0, & other\ values \end{cases} \]

$$
\begin{equation}
    \left.\begin{aligned}
            B'&=-\partial \times E,\\
            E'&=\partial \times B - 4\pi j,
           \end{aligned}
    \right\}
    \qquad \text{Maxwell's equations}
\end{equation}
$$

\[ \begin{equation} \left.\begin{aligned} B'&=-\partial \times E,\\ E'&=\partial \times B - 4\pi j, \end{aligned} \right\} \qquad \text{Maxwell's equations} \end{equation} \]

0.13 字体

  • 黑板粗体$\mathbb{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$: \(\mathbb{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\)
  • 正粗体$\mathbf{012abcABC}$: \(\mathbf{012abcABC}\)
  • 罗马体$\mathrm{012abcABC}$: \(\mathrm{012abcABC}\)
  • 斜体数字$\mathit{0123456789}$: \(\mathit{0123456789}\)
  • 手写体 $\mathcal{012abcABC}$: \(\mathcal{012abcABC}\)

0.14 括号

\Bigg ( \bigg [ \Big \{ \big \langle \left | \| \frac{a}{b} \| \right | \big\rangle \Big \} \bigg ] \Bigg ):

\[ \Bigg ( \bigg [ \Big \{ \big \langle \left | \| \frac{a}{b} \| \right | \big\rangle \Big \} \bigg ] \Bigg ) \]

0.15 颜色

  • 字体颜色︰$\color{色调}表达式$
  • 背景颜色︰$\pagecolor{色调}表达式$
\(\color{Apricot}Apricot\) \(\color{Aquamarine}Aquamarine\) \(\color{Bittersweet}Bittersweet\) \(\color{Black}Black\)
\(\color{Blue}Blue\) \(\color{BlueGreen}BlueGreen\) \(\color{BlueViolet}BlueViolet\) \(\color{BrickRed}BrickRed\)
\(\color{Brown}Brown\) \(\color{BurntOrange}BurntOrange\) \(\color{CadetBlue}CadetBlue\) \(\color{CarnationPink}CarnationPink\)
\(\color{Cerulean}Cerulean\) \(\color{CornflowerBlue}CornflowerBlue\) \(\color{Cyan}Cyan\) \(\color{Dandelion}Dandelion\)
\(\color{DarkOrchid}DarkOrchid\) \(\color{Emerald}Emerald\) \(\color{ForestGreen}ForestGreen\) \(\color{Fuchsia}Fuchsia\)
\(\color{Goldenrod}Goldenrod\) \(\color{Gray}Gray\) \(\color{Green}Green\) \(\color{GreenYellow}GreenYellow\)
\(\color{JungleGreen}JungleGreen\) \(\color{Lavender}Lavender\) \(\color{LimeGreen}LimeGreen\) \(\color{Magenta}Magenta\)
\(\color{Mahogany}Mahogany\) \(\color{Maroon}Maroon\) \(\color{Melon}Melon\) \(\color{MidnightBlue}MidnightBlue\)
\(\color{Mulberry}Mulberry\) \(\color{NavyBlue}NavyBlue\) \(\color{OliveGreen}OliveGreen\) \(\color{Orange}Orange\)
\(\color{OrangeRed}OrangeRed\) \(\color{Orchid}Orchid\) \(\color{Peach}Peach\) \(\color{Periwinkle}Periwinkle\)
\(\color{PineGreen}PineGreen\) \(\color{Plum}Plum\) \(\color{ProcessBlue}ProcessBlue\) \(\color{Purple}Purple\)
\(\color{RawSienna}RawSienna\) \(\color{Red}Red\) \(\color{RedOrange}RedOrange\) \(\color{RedViolet}RedViolet\)
\(\color{Rhodamine}Rhodamine\) \(\color{RoyalBlue}RoyalBlue\) \(\color{RoyalPurple}RoyalPurple\) \(\color{RubineRed}RubineRed\)
\(\color{Salmon}Salmon\) \(\color{SeaGreen}SeaGreen\) \(\color{Sepia}Sepia\) \(\color{SkyBlue}SkyBlue\)
\(\color{SpringGreen}SpringGreen\) \(\color{Tan}Tan\) \(\color{TealBlue}TealBlue\) \(\color{Thistle}Thistle\)
\(\color{Turquoise}Turquoise\) \(\color{Violet}Violet\) \(\color{VioletRed}VioletRed\) \(\color{White}White\)
\(\color{WildStrawberry}WildStrawberry\) \(\color{Yellow}Yellow\) \(\color{YellowGreen}YellowGreen\) \(\color{YellowOrange}YellowOrange\)

0.16 特殊例子

0.16.1 分子分母

$$
x_1^*=\dfrac{a_{22}r_1-a_{12}r_2}{a_{11}a_{22}-a_{12}a_{21}}
$$

\[ x_1^*=\dfrac{a_{22}r_1-a_{12}r_2}{a_{11}a_{22}-a_{12}a_{21}} \]

语法 效果 语法 效果 语法 效果
\frac{a}{b} \(\frac{a}{b}\) \dfrac{c}{d} \(\dfrac{c}{d}\) e/f \(e/f\)

0.16.2 分布

分布名 语法 效果 例子
二项分布 \binom{n}{k} \(\binom{n}{k}\) \(f(k) = \binom{n}{k} p^k (1-p)^{n-k}\)

0.16.3 在线使用

只能行间

![](http://latex.codecogs.com/gif.latex?F%28x%29%20%3D%20%5Cint_%7Ba%7D%5E%7Bb%7Df%28x%29dx "latextest")

输出: