# Latex模板

$$\mathop{\arg\min}\_{h}$$、

$$\sim$$、

### 希腊字母

| Latex | 效果                |   | 效果           |
| ----- | ----------------- | - | ------------ |
|       | $$\alpha$$        |   | $$\mu$$      |
|       | $$\beta$$         |   | $$\xi$$      |
|       | $$\gamma$$        |   | $$\delta$$   |
|       | $$\pi$$           |   | $$\epsilon$$ |
|       | $$\zeta$$         |   | $$\rho$$     |
|       | $$\sigma$$        |   | $$\eta$$     |
|       | $$\tau$$          |   | $$\theta$$   |
|       | $$\upsilon$$      |   | $$\phi$$     |
|       | $$\lambda$$       |   | $$\psi$$     |
|       | $$\omega \Omega$$ |   |              |

### 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}  | $$\tilde{\iota}$$  |

### 函数

| 语法                                                             | 效果                                                                 | 语法                 | 效果                     | 语法                 | 效果                     |
| -------------------------------------------------------------- | ------------------------------------------------------------------ | ------------------ | ---------------------- | ------------------ | ---------------------- |
| \sin\theta                                                     | $$\sin\theta$$                                                     | \cos\theta         | $$\cos\theta$$         | \tan\theta         | $$\tan\theta$$         |
| \arcsin\frac{L}{r}                                             | $$\arcsin\frac{L}{r}$$                                             | \arccos\frac{T}{r} | $$\arccos\frac{T}{r}$$ | \arctan\frac{L}{T} | $$\arctan\frac{L}{T}$$ |
| \sinh g                                                        | $$\sinh g$$                                                        | \cosh h            | $$\cosh h$$            | \tanh i            | $$\tanh i$$            |
| k'(x)=\lim\_{\Delta x\to 0}\frac{k(x)-k(x-\Delta x)}{\Delta x} | $$k'(x)=\lim\_{\Delta x\to 0}\frac{k(x)-k(x-\Delta x)}{\Delta x}$$ | \limsup S          | $$\limsup S$$          | \liminf I          | $$\liminf I$$          |
| \max H                                                         | $$\max H$$                                                         | \min L             | $$\min L$$             | \inf s             | $$\inf s$$             |
| \sup t                                                         | $$\sup t$$                                                         | \exp!t             | $$\exp!t$$             | \ln X              | $$\ln X$$              |
| \lg X                                                          | $$\lg X$$                                                          | \log X             | $$\log X$$             | \log\_\alpha X     | $$\log\_\alpha X$$     |
| \ker x                                                         | $$\ker x$$                                                         | \deg x             | $$\deg x$$             | \gcd(T,U,V,W,X)    | $$\gcd(T,U,V,W,X)$$    |
| \Pr x                                                          | $$\Pr x$$                                                          | \det x             | $$\det x$$             | \hom x             | $$\hom x$$             |
| \arg x                                                         | $$\arg x$$                                                         | \dim x             | $$\dim x$$             | \lim\_{t\to n}T    | $$\lim\_{t\to n}T$$    |

### 同余

| 语法       | 效果           | 语法        | 效果            |
| -------- | ------------ | --------- | ------------- |
| \pmod{m} | $$\pmod{m}$$ | a \bmod b | $$a \bmod b$$ |

### 微分

| 语法     | 效果         | 语法         | 效果             | 语法          | 效果              |
| ------ | ---------- | ---------- | -------------- | ----------- | --------------- |
| \nabla | $$\nabla$$ | \partial x | $$\partial x$$ | \mathrm{d}x | $$\mathrm{d}x$$ |
| \dot x | $$\dot x$$ | \ddot y    | $$\ddot y$$    |             |                 |

### 集合

| 语法        | 效果            | 语法          | 效果              | 语法        | 效果            | 语法        | 效果            | 语法          | 效果              |
| --------- | ------------- | ----------- | --------------- | --------- | ------------- | --------- | ------------- | ----------- | --------------- |
| \in       | $$\in$$       | \ni         | $$\ni$$         |           |               | \notin    | $$\notin$$    | \subset     | $$\subset$$     |
| \subseteq | $$\subseteq$$ | \supset     | $$\supset$$     | \supseteq | $$\supseteq$$ | \cap      | $$\cap$$      | \bigcap     | $$\bigcap$$     |
| \cup      | $$\cup$$      | \bigcup     | $$\bigcup$$     | \biguplus | $$\biguplus$$ | \sqsubset | $$\sqsubset$$ | \sqsubseteq | $$\sqsubseteq$$ |
| \sqsupset | $$\sqsupset$$ | \sqsupseteq | $$\sqsupseteq$$ | \sqcap    | $$\sqcap$$    | \sqcup    | $$\sqcup$$    | \bigsqcup   | $$\bigsqcup$$   |

### 逻辑

| 语法            | 效果                | 语法     | 效果         | 语法        | 效果            | 语法             | 效果                 |
| ------------- | ----------------- | ------ | ---------- | --------- | ------------- | -------------- | ------------------ |
| p             | $$p$$             | \land  | $$\land$$  | \wedge    | $$\wedge$$    | \bigwedge      | $$\bigwedge$$      |
| \bar{q} \to p | $$\bar{q} \to p$$ | \lor   | $$\lor$$   | \vee      | $$\vee$$      | \bigvee        | $$\bigvee$$        |
| \lnot         | $$\lnot$$         | \neg q | $$\neg q$$ | \setminus | $$\setminus$$ | \smallsetminus | $$\smallsetminus$$ |

### 根号

| 语法       | 效果           | 语法           | 效果               |
| -------- | ------------ | ------------ | ---------------- |
| \sqrt{3} | $$\sqrt{3}$$ | \sqrt\[n]{3} | $$\sqrt\[n]{3}$$ |

### 关系符号

| 语法                                      | 效果                                          |
| --------------------------------------- | ------------------------------------------- |
| \Delta ABC\sim\Delta XYZ                | $$\Delta ABC\sim\Delta XYZ$$                |
| \sqrt{3}\approx1.732050808\ldots        | $$\sqrt{3}\approx1.732050808\ldots$$        |
| \simeq                                  | $$\simeq$$                                  |
| \cong                                   | $$\cong$$                                   |
| \dot=                                   | $$\dot=$$                                   |
| \ggg                                    | $$\ggg$$                                    |
| \gg                                     | $$\gg$$                                     |
|                                         |                                             |
| \ge                                     | $$\ge$$                                     |
| \geqq                                   | $$\geqq$$                                   |
| =                                       | $$=$$                                       |
| \leq                                    | $$\leq$$                                    |
| \leqq                                   | $$\leqq$$                                   |
| <                                       | $$<$$                                       |
| \ll                                     | $$\ll$$                                     |
| \lll                                    | $$\lll$$                                    |
| (x-y)^2\equiv(-x+y)^2\equiv x^2-2xy+y^2 | $$(x-y)^2\equiv(-x+y)^2\equiv x^2-2xy+y^2$$ |
| x\ne A                                  | $$x\ne A$$                                  |
| x\neq C                                 | $$x\neq C$$                                 |
| t\propto v                              | $$t\propto v$$                              |
| \pm                                     | $$\pm$$                                     |
| \mp                                     | $$\mp$$                                     |

### 箭头符号

| 语法              | 效果                  | 语法              | 效果                  | 语法             | 效果                 |
| --------------- | ------------------- | --------------- | ------------------- | -------------- | ------------------ |
| \leftarrow      | $$\leftarrow$$      | \gets           | $$\gets$$           | \rightarrow    | $$\rightarrow$$    |
| \to             | $$\to$$             | \leftrightarrow | $$\leftrightarrow$$ | \longleftarrow | $$\longleftarrow$$ |
| \longrightarrow | $$\longrightarrow$$ | \mapsto         | $$\mapsto$$         | \longmapsto    | $$\longmapsto$$    |
| \hookrightarrow | $$\hookrightarrow$$ | \hookleftarrow  | $$\hookleftarrow$$  | \nearrow       | $$\nearrow$$       |
| \searrow        | $$\searrow$$        | \swarrow        | $$\swarrow$$        | \nwarrow       | $$\nwarrow$$       |
| \uparrow        | $$\uparrow$$        | \downarrow      | $$\downarrow$$      | \updownarrow   | $$\updownarrow$$   |

### 特殊符号

| 语法            | 效果                | 语法             | 效果                 | 语法     | 效果         | 语法     | 效果         |
| ------------- | ----------------- | -------------- | ------------------ | ------ | ---------- | ------ | ---------- |
| \triangleleft | $$\triangleleft$$ | \triangleright | $$\triangleright$$ | \infty | $$\infty$$ | \bot   | $$\bot$$   |
| \top          | $$\top$$          | \vdash         | $$\vdash$$         | \vDash | $$\vDash$$ | \Vdash | $$\Vdash$$ |
| \models       | $$\models$$       | \lVert         | $$\lVert$$         | \rVert | $$\rVert$$ |        |            |

## 上标、下标及积分

| 功能                                                  | 语法                                                  | 效果                                                      |
| --------------------------------------------------- | --------------------------------------------------- | ------------------------------------------------------- |
| 上标                                                  | a^2                                                 | $$a^2$$                                                 |
| 下标                                                  | a\_2                                                | $$a\_2$$                                                |
| 组合                                                  | a^{2+2}                                             | $$a^{2+2}$$                                             |
| a\_{i,j}                                            | $$a\_{i,j}$$                                        | $$a\_{i,j}$$                                            |
| 结合上下标                                               | x\_2^3                                              | $$x\_2^3$$                                              |
| 前置上下标                                               | {}\_1^2!X\_3^4                                      | $${}\_1^2!X\_3^4$$                                      |
| 导数                                                  | x'                                                  | $$x'$$                                                  |
| 导数 （PNG）                                            | x^\prime                                            | $$x^\prime$$                                            |
| 导数 （错误）                                             | x\prime                                             | $$x\prime$$                                             |
| 导数点                                                 | \dot{x}                                             | $$\dot{x}$$                                             |
| \ddot{y}                                            | \ddot{y}                                            | $$\ddot{y}$$                                            |
| 向量                                                  | \vec{c}                                             | $$\vec{c}$$                                             |
| 求和                                                  | \sum\_{k=1}^N k^2                                   | $$\sum\_{k=1}^N k^2$$                                   |
| \begin{matrix} \sum\_{k=1}^N k^2 \end{matrix}       | \begin{matrix} \sum\_{k=1}^N k^2 \end{matrix}       | $$\begin{matrix} \sum\_{k=1}^N k^2 \end{matrix}$$       |
| 求积                                                  | \prod\_{i=1}^N x\_i                                 | $$\prod\_{i=1}^N x\_i$$                                 |
| \begin{matrix} \prod\_{i=1}^N x\_i \end{matrix}     | \begin{matrix} \prod\_{i=1}^N x\_i \end{matrix}     | $$\begin{matrix} \prod\_{i=1}^N x\_i \end{matrix}$$     |
| 上积                                                  | \coprod\_{i=1}^N x\_i                               | $$\coprod\_{i=1}^N x\_i$$                               |
| \begin{matrix} \coprod\_{i=1}^N x\_i\end{matrix}    | \begin{matrix} \coprod\_{i=1}^N x\_i\end{matrix}    | $$\begin{matrix} \coprod\_{i=1}^N x\_i\end{matrix}$$    |
| 极限                                                  | \lim\_{n \to \infty}x\_n                            | $$\lim\_{n \to \infty}x\_n$$                            |
| \begin{matrix} \lim\_{n \to \infty}x\_n\end{matrix} | \begin{matrix} \lim\_{n \to \infty}x\_n\end{matrix} | $$\begin{matrix} \lim\_{n \to \infty}x\_n\end{matrix}$$ |


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