使用Latex错误集

1、写公式的函数——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}

%红色代码是给每行公式标号，超高级，好用！

（2）align中公式的两行之间不能有空行，会报错；

（3）align前后不能有空行，要不然pdf会有大片空白；

（4）如果是公式代码写错了，latex会说是align出错了，千万别信！！！抓紧检查公式代码（latex报错：Paragraph ended before \align was complete）

（5）align不能和\begin{equation}\end{equation}互相套用，各用个的。

2、写公式的函数——aligned(是个奶娃娃，没有独立性，必须在数学环境下使用，$$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，按理说不应该呀，可是刚才确实报错了，说：Package amsmath Error: \tag not allowed here

latex报错：Paragraph ended before \align was complete