LaTeX
1. Equation
in-line delimiter
\$a + b = c\$$a + b = c$math delimiter
\$\$a + b = c\$\$
$$a + b = c$$automatic numbering
\begin{equation}
E = mc^2 \text{, Description}
\label{eq:Sample}
\end\begin{equation}
E = mc^2 \text{, Description}
\label{eq:Sample}
\end{equation}
2. Superscript, Subscript
^表示上标, _表示下标. 如果上下标内容多余一个字符, 则需要用{}将其变成一个整体.
Superscript
\$\$ x^{y^z} = (1 + e^x)^{-2xy^w} \$\$
$$ x^{y^z} = (1 + e^x)^{-2xy^w} $$
Subscript
\$\$ x_n = y_n + 1 \$\$
$$ x_n = y_n + 1 $$
Subscript and Superscript
\$\$ x_1^2 x{_1}{^2} \$\$
$$ x_1^2 \quad x{_1}{^2} $$
3. Bracket and Delimiter
| Input | Output | Input | Output |
|---|---|---|---|
| \langle | $\langle$ | \rangle | $\rangle$ |
| \lceil | $\lceil$ | \rceil | $\rceil$ |
| \lfloor | $\lfloor$ | \rfloor | $\rfloor$ |
| \lbrace | $\lbrace$ | \rbrace | $\rbrace$ |
Sample:
\$\$ f(x,y,z) = 3y^2z \left( 3 + \frac{7x + 5}{1 + y^2} \right) \$\$ |
$$ f(x,y,z) = 3y^2z \left( 3 + \frac{7x + 5}{1 + y^2} \right) $$
4. Space
1em, em, m表示当前字体下接近字母'M'的宽度(approximately the width of an "M" in the current font)
| width | Input | Output |
|---|---|---|
| 两个m的宽度 | a \qquad b | $a \qquad b$ |
| 一个m的宽度 | a \quad b | $a \quad b$ |
| 1/3m的宽度 | a\ b | $a\ b$ |
| 2/7m的宽度 | a;b | $a;b$ |
| 1/6m的宽度 | a,b | $a,b$ |
| 无空格 | ab | $ab$ |
| 缩进1/6宽度 | a\!b | $a\!b$ |
5. Root
Sample:
\$\$ \sqrt{2} \quad and \quad \sqrt[n]{3} \$\$ |
$$ \sqrt{2} \quad and \quad \sqrt[n]{3} $$
6. Ellipsis
Sample:
\$\$ f{x_1, x_2, \underbrace{\ldots}_{\rm ldots}, x_n } = x{_1}{^2} + x{_2}{^2} + {\cdots} + x{_n}{^n} \$\$ |
$$ f(x_1, x_2, \underbrace{\ldots}_{\rm ldots}, x_n ) = x{_1}{^2} + x{_2}{^2} + \underbrace{\cdots}_{\rm cdots} + x{_n}{^n} $$
7. Vector Arrow
Sample 1
\$\$ \vec{a} \cdot \vec{b} = 0 \$\$
$$\vec{a} \cdot \vec{b} = 0$$
Sample 2
\$\$ \overleftarrow{xy} \quad and \quad \overleftrightarrow{xy} \quad and \quad \overrightarrow{xy} \$\$
$$\overleftarrow{xy} \quad and \quad \overleftrightarrow{xy} \quad and \quad \overrightarrow{xy}$$
8. Integral
\$\$ \int_0^1 {x^2} x \$\$ |
$$ \int_0^1 {x^2} dx $$
9. Limit
Sample 1
\$\$ \lim_{n \to +\infty} \frac{1}{n(n + 1)} \$\$
$$ \lim_{n \to +\infty} \frac{1}{n(n + 1)} $$
Sample 2
\$\$ \lim_{1 \leftarrow n} \frac{1}{n(n + 1)} \$\$
$$ \lim_{1 \leftarrow n} \frac{1}{n(n + 1)} $$
10. Sum and Product
Sum
\$\$ \sum_{i=1}^{n} \frac{1}{i^2} \$\$
$$ \sum_{i=1}^{n} \frac{1}{i^2} $$
Product
\$\$ \prod_{i=1}^{n} \frac{1}{i^2} \$\$
$$ \prod_{i=1}^{n} \frac{1}{i^2} $$
11. Font Styles
| Description | Input | Output |
|---|---|---|
| Normal Text | \text{abc} | $\text{abc}$ |
| Text Mode | \textrm{abc} | $\textrm{abc}$ |
| Italic Text | \textit{abc} | $\textit{abc}$ |
| Bold Text | \textbf{abc} | $\textbf{abc}$ |
12. Arrow
| Input | Output | Input | Output |
|---|---|---|---|
| \uparrow | $\uparrow$ | \Uparrow | $\Uparrow $ |
| \leftarrow | $\leftarrow$ | \Leftarrow | $\Leftarrow$ |
| \rightarrow | $\rightarrow$ | \Rightarrow | $\Rightarrow$ |
| \downarrow | $\downarrow$ | \Downarrow | $\Downarrow$ |
| \updownarrow | $\updownarrow$ | \rightrightarrows | $\rightrightarrows$ |
| \Updownarrow | $\Updownarrow$ | \rightleftarrows | $\rightleftarrows$ |
| \leftrightarrow | $\leftrightarrow$ | \Leftrightarrow | $\Leftrightarrow$ |
| \rightrightarrows | $\rightrightarrows$ | \rightleftarrows | $\rightleftarrows$ |
| \nearrow | $\nearrow$ | \swarrow | $\swarrow$ |
| \searrow | $\searrow$ | \nwarrow | $\nwarrow$ |
| \Longleftarrow | $\Longleftarrow$ | \Longrightarrow | $\Longrightarrow$ |
| \hookleftarrow | $\hookleftarrow$ | \hookrightarrow | $\hookrightarrow$ |
| \leftharpoonup | $\leftharpoonup$ | \rightharpoonup | $\rightharpoonup$ |
13. Greek Letters
| Input | Output | Input | Output | Input | Output | Input | Output |
|---|---|---|---|---|---|---|---|
| \alpha | $\alpha$ | \beta | $\beta$ | \gamma | $\gamma$ | \delta | $\delta$ |
| \epsilon | $\epsilon$ | \zeta | $\zeta$ | \eta | $\eta$ | \theta | $\theta$ |
| \iota | $\iota$ | \kappa | $\kappa$ | \lambda | $\lambda$ | \mu | $\mu$ |
| \nu | $\nu$ | \xi | $\xi$ | o | $o$ | \pi | $\pi$ |
| \rho | $\rho$ | \sigma | $\sigma$ | \tau | $\tau$ | \upsilon | $\upsilon$ |
| \phi | $\phi$ | \chi | $\chi$ | \psi | $\psi$ | \omega | $\omega$ |
14. Set Symbols
| Input | Output | Input | Output | Input | Output | Input | Output |
|---|---|---|---|---|---|---|---|
| \emptyset | $\emptyset$ | \in | $\in$ | \notin | $\notin$ | \subset | $\subset$ |
| \supset | $\supset$ | \subseteq | $\subseteq$ | \supseteq | $\supseteq$ | \bigcap | $\bigcap$ |
| \bigcup | $\bigcup$ | \bigvee | $\bigvee$ | \bigwedge | $\bigwedge$ | \biguplus | $\biguplus$ |
15. Relation Symbols
| Input | Output | Input | Output | Input | Output | Input | Output |
|---|---|---|---|---|---|---|---|
| \pm | $\pm$ | \times | $\times$ | \div | $\div$ | \mid | $\mid$ |
| \nmid | $\nmid$ | \cdot | $\cdot$ | \circ | $\circ$ | \ast | $\ast$ |
| \bigodot | $\bigodot$ | \bigotimes | $\bigotimes$ | \bigoplus | $\bigoplus$ | \leq | $\leq$ |
| \geq | $\geq$ | \neq | $\neq$ | \approx | $\approx$ | \equiv | $\equiv$ |
| \sum | $\sum$ | \prod | $\prod$ | \coprod | $\coprod$ | \backslash | $\backslash$ |
16. Integral Signs
| Input | Output | Input | Output | Input | Output |
|---|---|---|---|---|---|
| \int | $\int$ | \iint | $\iint$ | \iiint | $\iiint$ |
| \iiiint | $\iiiint$ | \oint | $\oint$ | \prime | $\prime$ |
| \lim | $\lim$ | \infty | $\infty$ | \nabla | $\nabla$ |
17. Logic Notations
| Input | Output | Input | Output |
|---|---|---|---|
| \because | $\because$ | \therefore | $\therefore$ |
| \forall | $\forall$ | \exists | $\exists$ |
| \not\subset | $\not\subset$ | \not< | $\not<$ |
| \not> | $\not>$ | \not= | $\not=$ |
18. Dots
| Input | Output | Input | Output |
|---|---|---|---|
| \cdots | $\cdots$ | \ddots | $\ddots$ |
| \ldots | $\ldots$ | \vdots | $\vdots$ |
19. Matrix
matrix
\begin{matrix}
1 & 2 \\ 3 & 4
\end{matrix}\begin{matrix} 1 & 2 \\ 3 & 4 \\ \end{matrix}
pmatrix
\begin{pmatrix}
1 & 2 \\ 3 & 4
\end{pmatrix}$$ \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} $$
bmatrix
\begin{bmatrix}
1 & 2 \\ 3 & 4
\end{bmatrix}\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}
Bmatrix
\begin{Bmatrix}
1 & 2 \\ 3 & 4
\end{Bmatrix}\begin{Bmatrix} 1 & 2 \\ 3 & 4 \end{Bmatrix}
vmatrix
\begin{vmatrix}
1 & 2 \\ 3 & 4
\end{vmatrix}\begin{vmatrix} 1 & 2 \\ 3 & 4 \end{vmatrix}
Vmatrix
\begin{Vmatrix}
1 & 2 \\\\ 3 & 4 \\\\
\end{Vmatrix}\begin{Vmatrix} 1 & 2 \\ 3 & 4 \end{Vmatrix}
20. Equation
20.1 Equation Numbering
方程式序列无需声明公式符号$和$$, {align}包括的语句自动编号, 序列的每一行都需要用\\分行
Sample:
\begin{align} |
\begin{align}
\sqrt{37} = \sqrt{\frac{73^2 - 1}{12^2}} \\
= \sqrt{\frac{73^2}{12^2} \cdot \frac{73^2 - 1}{73 ^ 2}} \\
= \sqrt{\frac{73^2}{12^2}} \sqrt{\frac{73^2 - 1}{73^2}} \\
= \frac{73}{12} \sqrt{1 - \frac{1}{73^2}} \\
\approx \frac{73}{12} \left( 1 - \frac{1}{2 \cdot 73^2} \right)
\end{align}
20.2 Comment
在{align}中灵活组合\text和\tag语句可实现添加注解和手动编号
Sample:
\begin{align} |
\begin{align}
v + w = 0 && \text{Given} \tag 1 \\
-w = -w + 0 && \text{additive identity} \tag 2 \\
-w + 0 = -w + (v + w) && \text{equations $(1)$ and $(2)$} \tag 3
\end{align}
21. Conditional Expression
$$ |
$$
f(n) =
\begin{cases}
\frac{n}{2}, & \text{if $n$ is even} \\[2ex]
3n + 1, & \text{if $n$ is odd}
\end{cases}
$$