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如何对齐多行方程？

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如何对齐多行方程？

我正在处理需要分成多行的方程式。我编写的代码如下：

\begin{equation}
\begin{aligned}
     O_{max} = w_1 \Sigma_{a=1}^{m} \Sigma_{b=a+1}^{n} (-\left|CPT_a 
     - CPT_b\right|)\\ 
     & + w_2 \Sigma_{j=1}^{m} (DIF_j) + w_3 \Sigma_{j=1}^{m} 
    (INT_j/\Sigma_{x=1}^{n} x_{ij})
\end{aligned}
\label{equ:ho}
\end{equation}

另一个是

 \begin{align} 
    \begin{split}
     nr(G_i,r) = 
     \begin{cases}
         1 &  \text{r is naturally played by one member of $G_i$}\\
         -2 &  \text{r is not naturally played in $G_i$} \\
         -p & \text{r is naturally played by p members in $G_i$}\\
     \end{cases}
   \end{split} \nonumber \\ 
   \begin{split}
      nb(G_i) = \Sigma_{r=1}^{9} nr(G_i,r)\\ 
      & max_{\forall G\in C} \left( b(G) = 
      \frac{\Sigma_{i=1}^{g}nb(G_i)}{g}\right)
   \end{split}
   \label{equ:yannibelli}       
 \end{align}

每个方程的对齐方式都不一样（第二部分向右并超出了页面边缘）。请问我该如何修复它们？

答案1

编辑：2020/01/01，针对用户@Mico 的评论. 首次与用户的重要建议对齐@Sigur是：

在此处输入图片描述

\documentclass[a4paper,12pt]{article}
    \usepackage{amsmath,amssymb}
    \begin{document}
    \begin{equation}
    \begin{aligned}
     O_{\max}& = w_1 \sum_{a=1}^{m} \sum_{b=a+1}^{n} (-\lvert\text{CPT}_a 
         -\text{CPT}_b\rvert)\\ 
         &\quad + w_2 \sum_{j=1}^{m} (\text{DIF}_j) + w_3 \sum_{j=1}^{m} 
        (\text{INT}_j/\sum_{x=1}^{n} x_{ij})
    \end{aligned}
    \label{equ:ho}
    \end{equation}
    \end{document}

对于第二段代码我建议的对齐方式是：

在此处输入图片描述

    \documentclass[a4paper,12pt]{article}
    \usepackage{amsmath,amssymb}
    \begin{document}
    \[\begin{aligned} 
         \mathrm{nr}(G_i,r) & = 
         \begin{cases}
             1 &  \text{$r$ is naturally played by one member of $G_i$}\\
             -2 &  \text{$r$ is not naturally played in $G_i$} \\
             -p & \text{$r$ is naturally played by $p$ members in $G_i$}\\
         \end{cases}\\[3pt]
        \mathrm{nb}(G_i) & = \sum_{r=1}^{9} \mathrm{nr}(G_i,r)\\ 
          & = \max_{\forall G\in C} \left( b(G) = \frac{\sum\limits_{r=1}^{9}\mathrm{nb}(G_i)}{g}\right)
          \label{equ:yannibel}
       \end{aligned} 
       \]
    \end{document}

答案2

对齐要求使用对齐符号 - &- 正确指示用于对齐目的的连续行内的水平位置。在第一个构造中，您没有使用任何对齐符号。它应该是这样的：

在此处输入图片描述

\begin{equation}
  \begin{aligned}
     O_{\max} &= w_1 \sum_{a = 1}^m \sum_{b = a + 1}^n (-\lvert CPT_a 
      - CPT_b \rvert) \\ 
     &\phantom{{}={}} + w_2 \sum_{j = 1}^m (DIF_j) + w_3 \sum_{j = 1}^m 
      (INT_j / \sum_{x = 1}^n x_{ij})
  \end{aligned}
\end{equation}

请注意使用\maxand\sum代替maxand \Sigma。您也可以考虑将\CPTand定义\DIF为数学运算符。

然后，对于第二个构造，这里似乎没有必要split。您可以使用嵌套equation-aligned就像第一个一样：

在此处输入图片描述

\begin{equation}
  \begin{aligned}
    nr(G_i, r) &=
      \begin{cases}
         1 & \text{$r$ is naturally played by one member of $G_i$}\\
        -2 & \text{$r$ is not naturally played in $G_i$} \\
        -p & \text{$r$ is naturally played by $p$ members in $G_i$}\\
      \end{cases} \\
    nb(G_i) &= \sum_{r = 1}^9 nr(G_i, r) \\
      & \max_{\forall G \in C} \left( b(G) = \frac{\sum_{i = 1}^g nb(G_i)}{g} \right)
  \end{aligned}
\end{equation}

这实际上取决于您希望如何对齐以及编号。我在此的假设是基于每个构造的单一编号。

答案3

我会这样做（使用\sum而不是\Sigma）：

在此处输入图片描述

\documentclass{article}
\usepackage{amsmath,amssymb}

\begin{document}
\begin{equation}
\begin{aligned}
O_{\max} &= w_1 \sum_{a=1}^{m} \sum_{b=a+1}^{n} (-|CPT_a - CPT_b|) \\
&\quad + w_2 \sum_{j=1}^{m} DIF_j + w_3 \sum_{j=1}^{m}  \Bigl(INT_j/\sum_{i=1}^{n} x_{ij}\Bigr)
\end{aligned}
\label{equ:ho}
\end{equation}

or another version with \verb|\mathrm{}|:

\begin{equation}
\begin{aligned}
O_{\max} &= w_1 \sum_{a=1}^{m} \sum_{b=a+1}^{n} (-|\mathrm{CPT}_a - \mathrm{CPT}_b|) \\
&\quad + w_2 \sum_{j=1}^{m} \mathrm{DIF}_j + w_3 \sum_{j=1}^{m}  \Bigl(\mathrm{INT}_j/\sum_{i=1}^{n} x_{ij}\Bigr)
\end{aligned}
\label{equ:ho}
\end{equation}
\end{document}

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