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 | $g^\prime$ | g^\prime | | |
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 \(f(x,y) = \begin{cases} 1 & x与y满足某一事实\\ 0 & 否则 \end{cases}\)
1
2
3
4
5
| # 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
1
2
3
4
5
6
7
| # 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
1
2
3
4
5
| \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
1
2
3
4
5
| \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：
- align
- \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
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
| \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}
|
\[\overbrace{abcde}\underbrace{fghij}\overline{klmn}\underline{opqr}\overleftarrow{stuv}\overrightarrow{wxyz}\]
1
| \overbrace{abcde}\underbrace{fghij}\overline{klmn}\underline{opqr}\overleftarrow{stuv}\overrightarrow{wxyz}
|
Emoji
表XI: Emoji
| :smirk: smirk | :smile:smile | :laughing:laughing | :blush:blush | :smiley:smiley | :heart_eyes:heart_eyes |
|---|
| 😘kissing_heart | :wink:wink | :kissing:kissing | :confused:confused | :sweat:sweat | :joy:joy |
| :sob:sob | :cry:cry | :angry:angry | :yum:yum | :mask:mask | :sunglasses:sunglasses |
| :heartpulse:heartpulse | :alien:alien | :cupid:cupid | :+1:+1 | :cn:cn | :shit:shit |
Refs
- Markdown 数学符号速查
- Cmd Markdown公式指导手册
- Equals_Sign
- Emoji
- Short Math Guide for LaTeX
- List of Mathematical Symbols
- Matplotlib Math Text
