将公式与方程对齐

Question

使用方程式环境，我将各种公式列在一起。但是，变量没有对齐：

\begin{equation}
  \begin{aligned}
    V = \{ & w_{v}^{V}\mid v\in \{1,2,\dots,|V|\};\\
           & w_{v}^{V} \neq w_{v'}, \forall v,v' \in \{1,2,\dots,|V|\} \}.
  \end{aligned}
\end{equation}

\begin{equation}
  \begin{aligned}
    T = \{w_{n,k}^{T}\mid  w_{n,k}^{T} \in V ; n\in\{1,2,\dots,N\}; \\
    k\in\{1,2,\dots,K\}\}. \\
  \end{aligned}
\end{equation}

\begin{equation}
  \begin{aligned}
    C = \{f_{v}\mid f_{v} \in  \mathbb{Z_{+}}; \forall v \in \{1,2, \dots , |V|\}  \}.
  \end{aligned}
\end{equation}

\begin{equation}
  \begin{aligned}
    C'= \{f_{v'}^{'}\mid f_{v'}^{'}\geq c_{v'+1}^{'} \forall v' \in \{1,2,...|V|-1\} \}.
  \end{aligned}
\end{equation}

\begin{equation}
  \begin{aligned}
    IC_{v'}= \{v'|f_{v'} = c_{k} \forall v',k \in \{1,2,...,|V|\}  \}.
  \end{aligned}
\end{equation}
\\
Additionally, the function $M(w_{v}^{V})$ maps a word $w_{v}^{V}$ to the set $IC_{v'}$.
\begin{equation}
  \begin{aligned}
    M(w_{v}^{V}): w_{v}^{V} \rightarrow IC_{v'}
  \end{aligned}
\end{equation}

我怎样才能使它们对齐？

Answer 1

你想split筑巢align。

我假设您使用的是双列格式，所以我添加了一个负空间（经过调整以便适合方程式）。

1. 我将末尾的句号改为逗号，除了最后一个
2. 我删除了aligned最后一个等式中无用的部分
3. 不要\\在等式后使用
4. ...应该\dots
5. 外支架已变成\big
6. 修复|了一个\mid
7. 全部^{'}改成'

\documentclass[twocolumn]{article}
\usepackage{amsmath,amssymb}

\newcommand{\antiquad}{\hspace{-0.8em}}

\begin{document}

\begin{align}
  \begin{split}
  \antiquad
    V = \bigl\{ & w_{v}^{V}\mid v\in \{1,2,\dots,|V|\};\\
                & w_{v}^{V} \neq w_{v'}, \forall v,v' \in \{1,2,\dots,|V|\}
        \bigr\},
  \end{split}
\\
  \begin{split}
  \antiquad
    T = \bigl\{ & w_{n,k}^{T}\mid  w_{n,k}^{T} \in V ; n\in\{1,2,\dots,N\}; \\
                & k\in\{1,2,\dots,K\}
        \bigr\},
  \end{split}
\\
  \antiquad
    C = \bigl\{ & f_{v}\mid f_{v} \in  \mathbb{Z_{+}}; \forall v \in \{1,2, \dots , |V|\}
        \bigr\},
\\
  \antiquad
    C'= \bigl\{ & f_{v'}'\mid f_{v'}'\geq c_{v'+1}' \forall v' \in \{1,2,\dots,|V|-1\}
        \bigr\},
\\
  \antiquad
    IC_{v'}= \bigl\{ & v' \mid f_{v'} = c_{k} \forall v',k \in \{1,2,\dots,|V|\}
             \bigr\}.
\end{align}
Additionally, the function $M(w_{v}^{V})$ maps a word $w_{v}^{V}$ to the set $IC_{v'}$.
\begin{equation}
    M(w_{v}^{V})\colon w_{v}^{V} \rightarrow IC_{v'}
\end{equation}

\end{document}

另一方面，我看到图片中的方程式数字以“Times”为单位，因此我建议使用newtx。

\documentclass[twocolumn]{article}
\usepackage{amsmath}
\usepackage{newtxtext,newtxmath}

\begin{document}

\begin{align}
  \begin{split}
    V = \bigl\{ & w_{v}^{V}\mid v\in \{1,2,\dots,|V|\};\\
                & w_{v}^{V} \neq w_{v'}, \forall v,v' \in \{1,2,\dots,|V|\}
        \bigr\},
  \end{split}
\\
  \begin{split}
    T = \bigl\{ & w_{n,k}^{T}\mid  w_{n,k}^{T} \in V ; n\in\{1,2,\dots,N\}; \\
                & k\in\{1,2,\dots,K\}
        \bigr\},
  \end{split}
\\
    C = \bigl\{ & f_{v}\mid f_{v} \in  \mathbb{Z_{+}}; \forall v \in \{1,2, \dots , |V|\}
        \bigr\},
\\
    C'= \bigl\{ & f_{v'}'\mid f_{v'}'\geq c_{v'+1}' \forall v' \in \{1,2,\dots,|V|-1\}
        \bigr\},
\\
    IC_{v'}= \bigl\{ & v' \mid f_{v'} = c_{k} \forall v',k \in \{1,2,\dots,|V|\}
             \bigr\}.
\end{align}
Additionally, the function $M(w_{v}^{V})$ maps a word $w_{v}^{V}$ to the set $IC_{v'}$.
\begin{equation}
    M(w_{v}^{V})\colon w_{v}^{V} \rightarrow IC_{v'}
\end{equation}

\end{document}

不需要负间距，因为 Times 比 Computer Modern 窄。