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实际上我尝试太多了,但运行后无法修复错误:如能提供任何帮助,我们将不胜感激:
\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{align*}
(f_{xy},f_{yz}) _{[w]}&=[f_{xy},z] - [x, f_{yz}]\\
&=[[x,y]- \sum \alpha_{xy}^v v ,z ] - [x ,[y,z] -\sum\alpha_{yz}^v v ]\\
&=[[x,y,z]]- \sum \alpha_{xy}^v [v,z] - [x,[y,z]] + \sum \alpha_{yz}^v [x,v]\\
\text{Using Jacobi's identity this equals}
&=[[x,z],y] - \sum\alpha_{xy}^v ([v,z] - \sum \alpha_{vz}^u u)\\
&+ \sum \alpha_{yz}^v ( [x,v] - \sum \alpha_{xv}^u u ) - \sum \alpha_{xy}^v \alpha_{vz}^u u + \sum \alpha_{yz}^v \alpha_{xv}^u u\\
&= [[x,z] - \sum \alpha_{xz}^v v , y ] + \sum \alpha_{xz}^v ([v,y] - \sum \alpha_{vy}^u u)\\
&-\sum \alpha_{xy}^v f_{vz} + \sum \alpha_{yz}^v f_{xv}\\
& -\sum_{u} (\sum \alpha_{xy}^v \alpha_{vz}^u + \sum \alpha_{yz}^v \alpha_{vx}^u + \sum \alpha_{zx}^v \alpha_{vy}^u) u
\end{align*}
\end{document}
答案1
您的代码运行良好,但您似乎正在intertext
寻找海科·奥伯迪克在他的评论中建议:
\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{align*}
(f_{xy},f_{yz}) _{[w]}&=[f_{xy},z] - [x, f_{yz}]\\
&=[[x,y]- \sum \alpha_{xy}^v v ,z ] - [x ,[y,z] -\sum\alpha_{yz}^v v ]\\
&=[[x,y,z]]- \sum \alpha_{xy}^v [v,z] - [x,[y,z]] + \sum \alpha_{yz}^v [x,v]
\intertext{Using Jacobi's identity this equals:}
&=[[x,z],y] - \sum\alpha_{xy}^v ([v,z] - \sum \alpha_{vz}^u u)\\
&+ \sum \alpha_{yz}^v ( [x,v] - \sum \alpha_{xv}^u u ) - \sum \alpha_{xy}^v \alpha_{vz}^u u + \sum \alpha_{yz}^v \alpha_{xv}^u u\\
&= [[x,z] - \sum \alpha_{xz}^v v , y ] + \sum \alpha_{xz}^v ([v,y] - \sum \alpha_{vy}^u u)\\
&-\sum \alpha_{xy}^v f_{vz} + \sum \alpha_{yz}^v f_{xv}\\
& -\sum_{u} (\sum \alpha_{xy}^v \alpha_{vz}^u + \sum \alpha_{yz}^v \alpha_{vx}^u + \sum \alpha_{zx}^v \alpha_{vy}^u) u
\end{align*}
\end{document}
然而,我会把这个方程写如下:
(红线表示文本边框)
\documentclass{article}
\usepackage{mathtools} % <--- instead of `amsmath`, it define `multlined` environment
\begin{document}
\begin{align*}
(f_{xy},f_{yz}) _{[w]}&=[f_{xy},z] - [x, f_{yz}]\\
& = \Bigl[[x,y]- \sum \alpha_{xy}^v v ,z \Bigr]
- \Bigl[x ,[y,z] -\sum\alpha_{yz}^v v \Bigr]\\
& = [x,y,z] - \sum \alpha_{xy}^v [v,z] - \bigl[x,[y,z]\bigr] + \sum \alpha_{yz}^v [x,v]
\intertext{Using Jacobi's identity this equals:}
(f_{xy},f_{yz})_{[w]}
& = \begin{multlined}[t][0.7\linewidth]
\bigl[[x,z],y\bigr] - \sum\alpha_{xy}^v \Bigl([v,z] - \sum \alpha_{vz}^u u\Bigr)\\
+ \sum \alpha_{yz}^v
\Bigl( [x,v] - \sum \alpha_{xv}^u u \Bigr) - \sum \alpha_{xy}^v \alpha_{vz}^u u + \sum \alpha_{yz}^v \alpha_{xv}^u u
\end{multlined} \\
& = \begin{multlined}[t][0.7\linewidth]
\Bigl[[x,z] - \sum \alpha_{xz}^v v , y \Bigr] \\
+ \sum \alpha_{xz}^v \left([v,y] - \sum \alpha_{vy}^u u\right) %\\
-\sum \alpha_{xy}^v f_{vz} + \sum \alpha_{yz}^v f_{xv} \\
-\sum_{u} \Bigl(\sum \alpha_{xy}^v \alpha_{vz}^u + \sum \alpha_{yz}^v \alpha_{vx}^u + \sum \alpha_{zx}^v \alpha_{vy}^u\Bigr) u
\end{multlined}
\end{align*}
\end{document}
答案2
一种变体,具有multlined
来自的环境mathtools
和可选的间距参数\intertext
(在中定义nccmath
),以及一些分隔符大小改进:
\documentclass{article}
\usepackage{mathtools, nccmath}
\begin{document}
\begin{align*}
(f_{xy},f_{yz}) _{[w]}&=[f_{xy},z] - [x, f_{yz}]\\
&=\bigl[[x,y]- \sum \alpha_{xy}^v v ,z \bigr] - \bigl[x ,[y,z] -\sum\alpha_{yz}^v v \bigr]\\
&=\bigl[[x,y,z]\bigr]- \sum \alpha_{xy}^v [v,z] - \bigl[x,[y,z]\bigr] + \sum \alpha_{yz}^v [x,v]
\intertext[0.5ex]{Using Jacobi's identity this equals:}
&=\begin{multlined}[t]{}
\bigl[[x,z],y\bigr] - \sum\alpha_{xy}^v ([v,z] - \sum \alpha_{vz}^u u)\\
+ \sum \alpha_{yz}^v\bigl( [x,v] - \sum \alpha_{xv}^u u \bigr) - \sum \alpha_{xy}^v \alpha_{vz}^u u + \sum \alpha_{yz}^v \alpha_{xv}^u u
\end{multlined}\\
&= \begin{multlined}[t]{}%
\bigl[[x,z] - \sum \alpha_{xz}^v v , y \bigr] + \sum \alpha_{xz}^v \bigl([v,y] - \sum \alpha_{vy}^u u\bigr)\\
-\sum \alpha_{xy}^v f_{vz} + \sum \alpha_{yz}^v f_{xv}\\
-\sum_{u} \Bigl(\sum \alpha_{xy}^v \alpha_{vz}^u + \sum \alpha_{yz}^v \alpha_{vx}^u + \sum \alpha_{zx}^v \alpha_{vy}^u\Bigr) u
\end{multlined}
\end{align*}
\end{document}