1、寫公式的函數——align（最怕空行）
（1）align用法示例
\begin{align}
& \left\{
\begin{array}{ll} \sup\limits_{\tilde{\mu}} & \sum\limits_{i = 1}^N \mu_i \cdot ( \eta_i + (1-\alpha_i)^{-1}\mathbb{E}[(F-\eta_i)_+] )\\ s.t. & \mu \in \mathbb{B}_r(\mu_0) \end{array}
\right. \label{4.1}\\
=& \left\{
\begin{array}{ll} \sup\limits_{\tilde{\mu},\Pi} &\sum\limits_{i = 1}^N \mu_i \cdot ( \eta_i + (1-\alpha_i)^{-1}\mathbb{E}[(F-\eta_i)_+] ) \\
s.t. &\int_{[0,1]^2}|\alpha-\alpha_0|\Pi(d\alpha,d\alpha_0) \leq r\\
& \mu_i = \int_{\alpha_{i-1}}^{\alpha_i}\mu(d \alpha),i = 1,\dots,N \\ \end{array}
\right. \tag{\ref{4.1}{a}}\label{4.1a}
\end{align}
%紅色代碼是給每行公式標號，超高級，好用！
（2）align中公式的兩行之間不能有空行，會報錯；
（3）align前后不能有空行，要不然pdf會有大片空白；
（4）如果是公式代碼寫錯了，latex會說是align出錯了，千萬別信！！！抓緊檢查公式代碼（latex報錯：Paragraph ended before \align was complete）
（5）align不能和\begin{equation}\end{equation}互相套用，各用個的。
2、寫公式的函數——aligned(是個奶娃娃，沒有獨立性，必須在數學環境下使用，$$或\begin{equation}\end{equation}都行)
（1）aligned示例
$$
\begin{aligned}
& \left\{
\begin{array}{lll}
\inf\limits_{\lambda \geq 0} & \lambda r + \frac{1}{M}\sum\limits_{k=1}{M}\sum\limits_{i=1}{N}(\eta_i + \frac{1}{1-\alpha_i}s_i - \lambda t_k)& \\
s.t.& s_i \geq (F-\eta_i)_+ & 1 \leq i \leq N \\
& t_k \geq \sup\limits_{\alpha \in [0,1]} |\alpha-\mu_0^k| & 1 \leq k \leq M
\end{array}
\right.\\ %\tag{\ref{4.1}{h}}\label{4.1h}\\
=& \left\{
\begin{array}{lll}
\inf\limits_{\lambda,s_i,t_k} & \lambda r + \frac{1}{M}\sum\limits_{k=1}{M}\sum\limits_{i=1}{N}(\eta_i + \frac{1}{1-\alpha_i}s_i - \lambda t_k)& \\
s.t.& \lambda \geq 0 & \\
& s_i \geq F-\eta_i & 1 \leq i \leq N \\
& s_i \geq 0 & 1 \leq i \leq N \\
& t_k + \mu_0^k \geq 1 & 1 \leq k \leq M\\
&\mu_0^k - t_k \leq 0 & 1 \leq k \leq M
\end{array}
\right.%\tag{\ref{4.1}{i}}\label{4.1i}
\end{aligned}
$$
（2）aligned不能用\tag，按理說不應該呀，可是剛才確實報錯了，說：Package amsmath Error: \tag not allowed here
latex報錯：Paragraph ended before \align was complete