markdown 公式 II
多行公式
cases
\[equation\begin{cases}
eq1
\begin{cases}
equation1\\
equation2\\
\end{cases}\\
equation2
\begin{cases}
eq1\\
eq2\\
\end{cases}\\
\end{cases}
\]
$$
equation\begin{cases}
eq1
\begin{cases}
equation1\\
equation2\\
\end{cases}\\
equation2
\begin{cases}
eq1\\
eq2\\
\end{cases}\\
\end{cases}
$$
aligned
\[\left\{
\begin{aligned}
equation1
\left\{
\begin{aligned}
equation1-1\\
equation1-2\\
\end{aligned}
\right.
\\equation2\\equation3
\end{aligned}
\right.
\]
$$
\left\{
\begin{aligned}
equation1
\left\{
\begin{aligned}
equation1-1\\
equation1-2\\
\end{aligned}
\right.
\\equation2\\equation3
\end{aligned}
\right.
$$
array
\[\left\{
\begin{array}{l}
equation1
\left\{
\begin{array}{}
equation1-1\\
equation1-2\\
\end{array}
\right.
\\equation2\\equation3
\end{array}
\right.
\]
$$
\left\{
\begin{array}{lcr}
equation1
\left\{
\begin{array}{}
equation1-1\\
equation1-2\\
\end{array}
\right.
\\equation2\\equation3
\end{array}
\right.
$$
括号
\[\left(\frac{x}{y}\right) \
\left[\frac{x}{y}\right] \
\left\{\frac{x}{y}\right\} \
\left\langle\frac{x}{y}\right\rangle \
\left|\frac{x}{y}\right| \
\left\|\frac{x}{y}\right\| \
\]
$$
\left(\frac{x}{y}\right) \
\left[\frac{x}{y}\right] \
\left\{\frac{x}{y}\right\} \
\left\langle\frac{x}{y}\right\rangle \
\left|\frac{x}{y}\right| \
\left\|\frac{x}{y}\right\| \
$$
二项式
\[\binom{n}{1} \quad
{n\choose m} \quad
\left(
\begin{array}{c}
x\\y
\end{array}
\right)
\]
$$
\binom{n}{1} \quad
{n\choose m} \quad
\left(
\begin{array}{c}
x\\y
\end{array}
\right)
$$
各种关系符号
\[>\ \ge \ \geq \\
<\ \le \ \leq \\
\neq \ \approx \ \equiv\\
\geqslant \ \leqslant \ \approxeq\\
\cong \ \propto \ \subset\\
\subseteqq \ \nsubseteq \ \nsubseteqq\\
\gg \ \ll \ \perp \\
\parallel \ a\overset{eq}{=}b \ a\xlongequal[abc]{def}b
\]
$$
>\ \ge \ \geq \\
<\ \le \ \leq \\
\neq \ \approx \ \equiv\\
\geqslant \ \leqslant \ \approxeq\\
\cong \ \propto \ \subset\\
\subseteqq \ \nsubseteq \ \nsubseteqq\\
\gg \ \ll \ \perp \\
\parallel \ a\overset{eq}{=}b \ a\xlongequal[abc]{def}b
$$
希腊字母
\[\alpha \ \beta \ \zeta \ \epsilon \ \varepsilon\\
\delta \ \Delta \ \varDelta \ \phi \ \Phi \ \varphi \ \varPhi\\
\pi \ \Pi \ \varpi \ \varPi \ \psi \ \Psi \ \varPsi \\
\sigma \ \Sigma \ \varsigma \ \varSigma \ \gamma \ \Gamma \ \varGamma\\
\omega \ \Omega \ \varOmega \theta \ \Theta \ \vartheta \ \varTheta\\
\lambda\ \Lambda \ \varLambda\ \rho\ \varrho\ \nu \ \mu \\
\eta\ \tau\ \iota\ \kappa\ \varkappa\ \xi \ \Xi\ \varXi\\
\upsilon \ \Upsilon\ \varUpsilon \ \chi\ \varnothing\ \oiint
\]
$$
\alpha \ \beta \ \zeta \ \epsilon \ \varepsilon\\
\delta \ \Delta \ \varDelta \ \phi \ \Phi \ \varphi \ \varPhi\\
\pi \ \Pi \ \varpi \ \varPi \ \psi \ \Psi \ \varPsi \\
\sigma \ \Sigma \ \varsigma \ \varSigma \ \gamma \ \Gamma \ \varGamma\\
\omega \ \Omega \ \varOmega \theta \ \Theta \ \vartheta \ \varTheta\\
\lambda\ \Lambda \ \varLambda\ \rho\ \varrho\ \nu \ \mu \\
\eta\ \tau\ \iota\ \kappa\ \varkappa\ \xi \ \Xi\ \varXi\\
\upsilon \ \Upsilon\ \varUpsilon \ \chi\ \varnothing\ \oiint
$$
上标
\[\hat{x}\ \widehat{x}\ \tilde{x}\ \widetilde{x}\\
\dot{x}\ \ddot{x}\ \dddot{x}\ \ \ddddot{x}\\
\vec{x}\ \overrightarrow{x}\ \mathop{x}\limits^{\rightarrow}\ \bar{x}\\
\overline{x}\ \check{x}\ \breve{x}\ \acute{x}\\
\grave{x}\ \mathring{x}
\]
$$
\hat{x}\ \widehat{x}\ \tilde{x}\ \widetilde{x}\\
\dot{x}\ \ddot{x}\ \dddot{x}\ \ \ddddot{x}\\
\vec{x}\ \overrightarrow{x}\ \mathop{x}\limits^{\rightarrow}\ \bar{x}\\
\overline{x}\ \check{x}\ \breve{x}\ \acute{x}\\
\grave{x}\ \mathring{x}
$$
矩阵
\[\begin{aligned}
\begin{matrix}1 & 2 \\ 3 &4\\ \end{matrix}\quad
\begin{pmatrix}1 & 2 \\ 3 &4\\ \end{pmatrix}\quad
\begin{bmatrix}1 & 2 \\ 3 & 4\\ \end{bmatrix}\\
\begin{Bmatrix}1 &2 \\ 3 & 4\\ \end{Bmatrix}\quad
\begin{vmatrix}1 &2 \\ 3 &4\\ \end{vmatrix}\quad
\begin{Vmatrix}1 & 2 \\ 3 & 4\\ \end{Vmatrix}\\
\begin{pmatrix}1&a_1&a_1^2&\cdots&a_1^n\\1&a_2&a_2^2&\cdots&a_2^n\\\vdots&\vdots&\vdots&\ddots&\vdots\\1&a_m&a_m^2&\cdots&a_m^n\\\end{pmatrix}
\end{aligned}
\]
$$
\begin{aligned}
\begin{matrix}1 & 2 \\ 3 &4\\ \end{matrix}\quad
\begin{pmatrix}1 & 2 \\ 3 &4\\ \end{pmatrix}\quad
\begin{bmatrix}1 & 2 \\ 3 & 4\\ \end{bmatrix}\\
\begin{Bmatrix}1 &2 \\ 3 & 4\\ \end{Bmatrix}\quad
\begin{vmatrix}1 &2 \\ 3 &4\\ \end{vmatrix}\quad
\begin{Vmatrix}1 & 2 \\ 3 & 4\\ \end{Vmatrix}\\
\begin{pmatrix}1&a_1&a_1^2&\cdots&a_1^n\\1&a_2&a_2^2&\cdots&a_2^n\\\vdots&\vdots&\vdots&\ddots&\vdots\\1&a_m&a_m^2&\cdots&a_m^n\\\end{pmatrix}
\end{aligned}
$$
积分
\[\int_V \ \iint_V \ \iiint_V \ \iiiint_V\\
\idotsint_V\ \oint_V \ \oiint_V \\
\int\limits_V\ \iint\limits_V\ \iiint\limits_V\ \iiiint\limits_V\\
\oint\limits_V\ \oiint\limits_V \ \idotsint\limits_V
\]
$$
\int_V \ \iint_V \ \iiint_V \ \iiiint_V\\
\idotsint_V\ \oint_V \ \oiint_V \\
\int\limits_V\ \iint\limits_V\ \iiint\limits_V\ \iiiint\limits_V\\
\oint\limits_V\ \oiint\limits_V \ \idotsint\limits_V
$$
求和求积
\[\sum_{i=1}^n \quad \prod_{i=1}^n
\]
$$
\sum_{i=1}^n \quad \prod_{i=1}^n
$$
极限
\[\lim_{n \to \infty}
\]
$$
\lim_{n \to \infty}
$$
箭头
\[\rightarrow \quad \longrightarrow \ \Rightarrow \ \Longrightarrow \\
\leftarrow \quad \longleftarrow \ \Leftarrow \ \Longleftarrow \\
\nrightarrow \quad \nleftarrow \ \nRightarrow \ \nLeftrightarrow \ \nleftrightarrow\\
\]
$$
\rightarrow \quad \longrightarrow \ \Rightarrow \ \Longrightarrow \\
\leftarrow \quad \longleftarrow \ \Leftarrow \ \Longleftarrow \\
\nrightarrow \quad \nleftarrow \ \nRightarrow \ \nLeftrightarrow \ \nleftrightarrow\\
$$
根式
\[\sqrt{a}\quad
\sqrt[n]{a}\quad
\sqrt[\leftroot{1}\uproot{3}n]{a}\quad
\sqrt[\leftroot{2}\uproot{4}n]{a}\quad
\]
在\sqrt命令的可选参数中可以指定根指数的位置，以改善根指数与根号过于紧凑的情况。
$$
\sqrt{a}\quad
\sqrt[n]{a}\quad
\sqrt[\leftroot{1}\uproot{3}n]{a}\quad
\sqrt[\leftroot{2}\uproot{4}n]{a}\quad
$$
数学字体
\[X \quad \textbf{X}\quad \mathbf{X}\quad \mathsf{X}\quad \mathit{X}\quad \mathcal{X}\quad \mathbb{X}\quad \mathfrak{X}
\]
$$
X \quad \textbf{X}\quad \mathbf{X}\quad \mathsf{X}\quad \mathit{X}\quad \mathcal{X}\quad \mathbb{X}\quad \mathfrak{X}
$$
三种矩阵排版的效果比较
vmatrix
\[\begin{vmatrix}
\frac{\partial x}{\partial y}&\frac{\partial G}{\partial \mu}\\
\frac{\partial H}{\partial \tau}&\frac{\partial F}{\partial t}
\end{vmatrix}
\]
$$
\begin{vmatrix}
\frac{\partial x}{\partial y}&\frac{\partial G}{\partial \mu}\\
\frac{\partial H}{\partial \tau}&\frac{\partial F}{\partial t}
\end{vmatrix}
$$
aligned
\[\left|
\begin{aligned}
\frac{\partial x}{\partial y}&\frac{\partial G}{\partial \mu}\\
\frac{\partial H}{\partial \tau}&\frac{\partial F}{\partial t}
\end{aligned}
\right|
\]
$$
\left|
\begin{aligned}
\frac{\partial x}{\partial y}&\frac{\partial G}{\partial \mu}\\
\frac{\partial H}{\partial \tau}&\frac{\partial F}{\partial t}
\end{aligned}
\right|
$$
array
\[\left|
\begin{array}{}
\frac{\partial x}{\partial y}&\frac{\partial G}{\partial \mu}\\
\frac{\partial H}{\partial \tau}&\frac{\partial F}{\partial t}
\end{array}
\right|
\]
$$
\left|
\begin{array}{}
\frac{\partial x}{\partial y}&\frac{\partial G}{\partial \mu}\\
\frac{\partial H}{\partial \tau}&\frac{\partial F}{\partial t}
\end{array}
\right|
$$
逻辑运算符
\[\because \ \therefore \ \forall \ \exists \ \not= \ \not> \ \not\subset
\]
$$
\because \ \therefore \ \forall \ \exists \ \not= \ \not> \ \not\subset
$$
