如何在 Latex 中输入方程和等价关系

Question

我试图在 Latex 中输入以下方程和等价关系，但却遇到了奇怪的输出，请您帮我解决这个问题：

\begin{document}
\begin{flalign*}
    (f_{uvw},f_{u_{1}v_{1}w_{1}})_{[u]([v][w])} & =f_{uvw}-f_{u_{1}v_{1}w_{1}} &\\
    &= [u]([v]([v_{1}][w_{1}]))-([u][v])([v_{1}][w_{1}])+([u]([v_{1}][w_{1}]))[v]\\
    &-[u]([v]([v_{1}][w_{1}]))+[u](([v][v_{1}])[w_{1}])-[u](([v][w_{1}])[v_{1}])&\\
    \equiv -(([u][v])[v_{1}])[w_{1}] + (([u][v])[w_{1}])[v_{1}] +(([u][v_{1}])[w_{1}])[v_{1}] \\
    & -(([u][w_{1}])[v_{1}])[v] + (([u][v])[v_{1}])[w_{1}] -(([u][v_{1}])[v])[w_{1}] \\
    &-(([u][w_{1}])[v])[v_{1}] + (([u][w_{1}])[v_{1}])[v]-(([u][v])[w_{1}])[v_{1}]  \\
    &+(([u][w_{1}])[v])[v_{1}] +(([u][v_{1}])[v])[w_{1}] _(([u][v_{1}])[w_{1}])[v_{1}] 
 \end{flalign*}
\end{document}

Answer 1

你没有说出你想要什么输出，但我猜你错过了一个&

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{flalign*}
    (f_{uvw},f_{u_{1}v_{1}w_{1}})_{[u]([v][w])} & =f_{uvw}-f_{u_{1}v_{1}w_{1}} &\\
    &= [u]([v]([v_{1}][w_{1}]))-([u][v])([v_{1}][w_{1}])+([u]([v_{1}][w_{1}]))[v]\\
    &-[u]([v]([v_{1}][w_{1}]))+[u](([v][v_{1}])[w_{1}])-[u](([v][w_{1}])[v_{1}])&\\
    \equiv
& 
-(([u][v])[v_{1}])[w_{1}] + (([u][v])[w_{1}])[v_{1}] +(([u][v_{1}])[w_{1}])[v_{1}] \\
    & -(([u][w_{1}])[v_{1}])[v] + (([u][v])[v_{1}])[w_{1}] -(([u][v_{1}])[v])[w_{1}] \\
    &-(([u][w_{1}])[v])[v_{1}] + (([u][w_{1}])[v_{1}])[v]-(([u][v])[w_{1}])[v_{1}]  \\
    &+(([u][w_{1}])[v])[v_{1}] +(([u][v_{1}])[v])[w_{1}] _(([u][v_{1}])[w_{1}])[v_{1}] 
 \end{flalign*}
\end{document}

Answer 2

只是为了好玩 [!?]，这是 David 方法的改进。它在第 1 行和第 3 行后添加了一些额外的垂直空白，它为第 3、5、6 和 7 行中的材料提供了缩进，并且它修复了最后一行中最后一个加法项中应该放在下标中的材料的问题。

\documentclass{article}
\usepackage{amsmath} % for 'flalign*' env.
\begin{document}
\begin{flalign*}
    (f_{uvw},f_{u_1 v_1 w_1})_{[u]([v][w])} 
    &= f_{uvw}-f_{u_1v_1w_1} \\[0.5ex]
    &=      [u]([v]([v_1][w_1]))-([u][v])([v_1][w_1])+([u]([v_1][w_1]))[v]\\
    &\quad -[u]([v]([v_1][w_1])) + [u](([v][v_1])[w_1]) -[u](([v][w_1])[v_1])\\[0.5ex]
    &\equiv-(([u][v])[v_1])[w_1] + (([u][v])[w_1])[v_1] +(([u][v_1])[w_1])[v_1] \\
    &\quad -(([u][w_1])[v_1])[v] + (([u][v])[v_1])[w_1] -(([u][v_1])[v])[w_1] \\
    &\quad -(([u][w_1])[v])[v_1] + (([u][w_1])[v_1])[v] -(([u][v])[w_1])[v_1]  \\
    &\quad +(([u][w_1])[v])[v_1] + (([u][v_1])[v])[w_1]_{(([u][v_1])[w_1])[v_1]}
 \end{flalign*}
\end{document}

Answer 3

fleqnfromnccmath和multlinedfrom还有一些有趣的内容mathtools。我对最后一行末尾的代码做了不同的解释：

\documentclass{article}
\usepackage{showframe}
\renewcommand\ShowFrameLinethickness{0.3pt}
\usepackage{mathtools, nccmath}

\begin{document}

\begin{fleqn}
  \begin{align*}
 & \mathrlap{ (f_{uvw},f_{u_{1}v_{1}w_{1}})_{[u]([v][w])} =f_{uvw}-f_{u_{1}v_{1}w_{1}}} \\
      & & & =\begin{multlined}[t] [u]([v]([v_{1}][w_{1}]))-([u][v])([v_{1}][w_{1}])+([u]([v_{1}][w_{1}]))[v]\\
    -[u]([v]([v_{1}][w_{1}]))+[u](([v][v_{1}])[w_{1}])-[u](([v][w_{1}])[v_{1}])\end{multlined}\\
   & & & \equiv
\begin{multlined}[t]
-(([u][v])[v_{1}])[w_{1}] + (([u][v])[w_{1}])[v_{1}] +(([u][v_{1}])[w_{1}])[v_{1}] \\
 -(([u][w_{1}])[v_{1}])[v] + (([u][v])[v_{1}])[w_{1}] -(([u][v_{1}])[v])[w_{1}] \\
-(([u][w_{1}])[v])[v_{1}] + (([u][w_{1}])[v_{1}])[v]-(([u][v])[w_{1}])[v_{1}] \\
+(([u][w_{1}])[v])[v_{1}] +(([u][v_{1}])[v])[w_{1}]-(([u][v_{1}])[w_{1}])[v_{1}]
\end{multlined}
 \end{align*}
\end{fleqn}

\end{document}