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Markdown Cheat Sheet

[TOC]

数学相关LaTeX表达

表 1: 数学模式重音符

示例 代码 示例 代码 示例 代码 示例 代码
$\hat {a}$ \hat{a} $\check{a}$ \check{a} $\tilde{a}$ \tilde{a} $\acute{a}$ \acute{a}
**$\grave{a}$ ** \grave{a} **$\dot {a}$ ** \dot{a} **$\bar{a}$ ** \bar{a} $\ddot a$ \ddot{a}
**$\vec {a}$ ** \vec{a} **$\widehat{A}$ ** \widehat{A} $\widetilde{A}$ \widetilde{A} $\breve a$ \breve{a}
$\hat{A}$ \hat{A} $\tilde{A}$ \tilde{A}

表2: 小写希腊字母

示例 代码 示例 代码 示例 代码 示例 代码
$\alpha$ \alpha $\theta$ \theta $\upsilon$ \upsilon $o $ o
$\beta$ \beta $\vartheta$ \vartheta $\pi$ \pi $\phi$ \phi
$\gamma$ \gamma $\iota$ \iota $\varpi$ \varpi $\varphi$ \varphi
$\delta$ \delta $\kappa$ \kappa $\rho$ \rho $\chi$ \chi
$\epsilon$ \epsilon $\lambda$ \lambda $\varrho$ \varrho $\psi$ \psi
$\varepsilon$ \varepsilon $\mu$ \mu $\sigma$ \sigma $\omega$ \omega
$\zeta$ \zeta $\nu$ \nu $\varsigma$ \varsigma $\nabla$ \nabla
$\eta$ \eta $\xi$ \xi $\tau$ \tau

表 3: 大写希腊字母

示例 代码 示例 代码 示例 代码 示例 代码
$\Gamma$ \Gamma $\Lambda$ \Lambda $\Sigma$ \Sigma $\Psi$ \Psi
$\Delta$ \Delta $\Xi$ \Xi $\Upsilon$ \Upsilon $\Omega$ \Omega
$\Theta$ \Theta $\Pi$ \Pi $\Phi$ \Phi

表 4: 数学字母

示例 代码
$\mathrm {ABCdef}$ \mathrm{ABCdef}
$\mathit {ABCdef}$ \mathit{ABCdef}
$\mathcal {ABCdef}$ \mathcal{ABCdef}
$\mathscr {ABCdef}$ \mathscr{ABCdef}
$\mathfrak {ABCdef}$ \mathfrak{ABCdef}
$\mathbb{ABCdef}$ \mathbb{ABCdef}

表 5: 运算符

示例 代码 示例 代码 示例 代码
$\sum$ \sum $\prod$ \prod $x\cdot{y}$ x\cdot{y}
$\bigcup$ \bigcup $\bigoplus$ \bigoplus $x\times {y}$ x\times {y}
$\bigvee$ \bigvee $\bigcap$ \bigcap $\left|w\right|$ \left|w\right|
$\bigwedge$ \bigwedge $\biguplus$ \biguplus $\iiint$ \iiint
$\bigotimes$ \bigotimes $\oint$ \oint $\iint$ \iint
$\int x,{\rm d}x$ \int x,{\rm d}x $\bigsqcup$ \bigsqcup $\lgroup \rgroup$ \lgroup \rgroup
$\coprod$ \coprod $\bigodot$ \bigodot $\partial$ \partial

表 6: 常用箭头

示例 代码 示例 代码 示例 代码
$\leftarrow$ \leftarrow $\rightarrow$ \rightarrow $\leftrightarrow$ \leftrightarrow
$\longleftarrow$ \longleftarrow $\longrightarrow$ \longrightarrow $\longleftrightarrow$ \longleftrightarrow
$\Leftarrow$ \Leftarrow $\Rightarrow$ \Rightarrow $\Leftrightarrow$ \Leftrightarrow
$\Longleftarrow$ \Longleftarrow $\Longrightarrow$ \Longrightarrow $\Longleftrightarrow$ \Longleftrightarrow
$\uparrow$ \uparrow $\downarrow$ \downarrow $\updownarrow$ \updownarrow

表 7: 其他常用符号

示例 代码 示例 代码 示例 代码
$\therefore$ \therefore $\because$ \because $\min \limits_{f \in {H}}$ \min \limits_{f \in {H}}
$\leqslant$ \leqslant $\geqslant$ \geqslant $\cal {C} \equiv 1$ \equiv
$\thickapprox$ \thickapprox $\thicksim \sim$ \thicksim \sim $\left(\frac{A}{B}\right)$ \left(\frac{A}{B}\right)
$\neq$ \neq $\in$ \in $\hat{=}$ \hat{=}
$\pm$ \pm $\sqrt{a}$ \sqrt{a} $\geq \leq$ \geq \leq
$\bot $ \bot $\angle$ \angle $\varpropto$ \varpropto
$\infty$ \infty

表8: 使用字体

{\rm text}

示例 代码 备注
$\rm {ABCdefxyzXYZ123}$ \rm {ABCdefXYZ123} 罗马体
$\it{ABCdefxyzXYZ123}$ \it{ABCdefXYZ123} 意大利体
$\bf{ABCdefxyzXYZ123}$ \bf{ABCdefXYZ123} 黑体
$\cal {ABCdefxyzXYZ123}$ \cal {ABCdefXYZ123} 花体
$\sf{ABCdefXYZ123}$ \sf{ABCdefXYZ123} 等线体
$\mit{ABCdefxyzXYZ123}$ \mit{ABCdefXYZ123} 数字斜体
$\tt{ABCdefxyzXYZ123}$ \tt{ABCdefXYZ123} 打印机字体

表9: 分段函数与公式对齐

分段函数

示例 $$ f(x,y) = \begin{cases} 1 & x与y满足某一事实\ 0 & 否则 \end{cases} $$

# 代码
f(x,y) = \begin{cases}
1 & x与y满足某一事实\\
0 & 否则
\end{cases}

$$ \begin{aligned} L(w)&=\sum\limits^{N}{i=1}[y_i\log\pi(x_i)+(1-y_i)\log(1-\pi(x_i))]\&=\sum\limits^{N}{i=1}[y_i\log{\frac{\pi(x_i)}{1-\pi(x_i)}}+\log(1-\pi(x_i))]\&=\sum\limits^{N}_{i=1}[y_i(w\cdot x_i)-\log(1+\exp(w\cdot{x_i})] \end{aligned} $$

对齐控制

# 代码
# 通过\begin{aligned}\end{aligned}控制对齐, 使用&表示对齐点.
\begin{aligned}
L(w)&=\sum\limits^{N}_{i=1}[y_i\log\pi(x_i)+(1-y_i)\log(1-\pi(x_i))]\\
&=\sum\limits^{N}_{i=1}[y_i\log{\frac{\pi(x_i)}{1-\pi(x_i)}}+\log(1-\pi(x_i))]\\
&=\sum\limits^{N}_{i=1}[y_i(w\cdot x_i)-\log(1+\exp(w\cdot{x_i})]
\end{aligned}

另外注意到前面的分段函数自动变好了, 但是上面多行对齐的公式没有自动编号, 如果需要自动编号, 外面嵌入equation $$ \begin{equation} \begin{aligned} L(w)&=\sum\limits^{N}{i=1}[y_i\log\pi(x_i)+(1-y_i)\log(1-\pi(x_i))]\ &=\sum\limits^{N}{i=1}[y_i\log{\frac{\pi(x_i)}{1-\pi(x_i)}}+\log(1-\pi(x_i))]\ &=\sum\limits^{N}_{i=1}[y_i(w\cdot x_i)-\log(1+\exp(w\cdot{x_i})] \end{aligned} \end{equation} $$ 代码如下

\begin{equation}
\begin{aligned}
L(w)&=\sum\limits^{N}_{i=1}[y_i\log\pi(x_i)+(1-y_i)\log(1-\pi(x_i))]\\&=\sum\limits^{N}_{i=1}[y_i\log{\frac{\pi(x_i)}{1-\pi(x_i)}}+\log(1-\pi(x_i))]\\&=\sum\limits^{N}_{i=1}[y_i(w\cdot x_i)-\log(1+\exp(w\cdot{x_i})]
\end{aligned}
\end{equation}

公式编号

关于编号也可以通过行间公式做如下表达 $$ \begin{align} L(w)&=\sum\limits^{N}{i=1}[y_i\log\pi(x_i)+(1-y_i)\log(1-\pi(x_i))]\ &=\sum\limits^{N}{i=1}[y_i\log{\frac{\pi(x_i)}{1-\pi(x_i)}}+\log(1-\pi(x_i))]\nonumber\ &=\sum\limits^{N}_{i=1}[y_i(w\cdot x_i)-\log(1+\exp(w\cdot{x_i})] \end{align} $$ 代码如下

\begin{align}
L(w)&=\sum\limits^{N}_{i=1}[y_i\log\pi(x_i)+(1-y_i)\log(1-\pi(x_i))]\\
&=\sum\limits^{N}_{i=1}[y_i\log{\frac{\pi(x_i)}{1-\pi(x_i)}}+\log(1-\pi(x_i))]\nonumber\\
&=\sum\limits^{N}_{i=1}[y_i(w\cdot x_i)-\log(1+\exp(w\cdot{x_i})]
\end{align}

以上代码有两点需要注意体会：

  1. align
  2. \nonumber的使用

表X: 矩阵

$$ \begin{aligned} M_1(x)= \begin{bmatrix} &a_{01}&a_{02}\\ &0&0 \end{bmatrix} &,M_2(x)= \begin{bmatrix} &b_{11}&b_{12}\\ &b_{21}&b_{22} \end{bmatrix} \\ M_3(x)= \begin{bmatrix} &c_{11}&c_{12}\\ &c_{21}&c_{22} \end{bmatrix} &,M_4(x)= \begin{bmatrix} &1&0\\ &1&0 \end{bmatrix} \end{aligned} $$

代码

\begin{aligned}
M_1(x)=
\begin{bmatrix}
&a_{01}&a_{02}\\
&0&0
\end{bmatrix}
&,M_2(x)=
\begin{bmatrix}
&b_{11}&b_{12}\\
&b_{21}&b_{22}
\end{bmatrix}
\\
M_3(x)=
\begin{bmatrix}
&c_{11}&c_{12}\\
&c_{21}&c_{22}
\end{bmatrix}
&,M_4(x)=
\begin{bmatrix}
&1&0\\
&1&0
\end{bmatrix}
\end{aligned}

$$ \overbrace{abcde}\underbrace{fghij}\overline{klmn}\underline{opqr}\overleftarrow{stuv}\overrightarrow{wxyz} $$

\overbrace{abcde}\underbrace{fghij}\overline{klmn}\underline{opqr}\overleftarrow{stuv}\overrightarrow{wxyz}

Emoji

表XI: Emoji

😏 smirk 😄smile 😆laughing 😊blush 😃smiley 😍heart_eyes
😘kissing_heart 😉wink 😗kissing 😕confused 😓sweat 😂joy
😭sob 😢cry 😠angry 😋yum 😷mask 😎sunglasses
💗heartpulse 👽alien 💘cupid 👍+1 🇨🇳cn 💩shit

Refs

  1. Markdown 数学符号速查
  2. Cmd Markdown公式指导手册
  3. Equals_Sign
  4. Emoji
  5. Short Math Guide for LaTeX
  6. List of Mathematical Symbols
  7. Matplotlib Math Text