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

$$\because \ \therefore \ \forall \ \exists \ \not= \ \not> \ \not\subset$$

$$
\because \ \therefore \ \forall \ \exists \ \not= \ \not> \ \not\subset
$$