在方程式内居中对齐块

Question

如何将一组对齐的块水平居中，所有块都位于单个编号的块内？

下面，我想将第一行和包含第二行和第三行的块居中。

\documentclass[10pt]{report}
\usepackage{amsthm,amsmath,amssymb,showframe}

\begin{document}
\begin{equation}
    \begin{split}
        \begin{aligned}
        e_{0}^{2} &=  e_{0}, &
        e_{1}^{2} &= -e_{0}, &
        e_{2}^{2} &= -e_{0}, &
        e_{3}^{2} &= -e_{0},
        \end{aligned}\\
        \begin{aligned}
        e_{0}\cdot e_{1}=  e_{1}\cdot e_{0} &= e_{1}, &
        e_{0}\cdot e_{2}=  e_{2}\cdot e_{0} &= e_{2}, &
        e_{0}\cdot e_{3}=  e_{3}\cdot e_{0} &= e_{3},  \\
        e_{1}\cdot e_{2}= -e_{2}\cdot e_{1} &= e_{3}, &
        e_{2}\cdot e_{3}= -e_{3}\cdot e_{2} &= e_{1}, &
        e_{3}\cdot e_{1}= -e_{1}\cdot e_{3} &= e_{2}.
        \end{aligned}
    \end{split}
\end{equation}
\end{document}

Answer 1

我会使用gathered嵌套的aligned；在后一种环境中，我会使用第一个=来设置对齐方式，而不是最后一个。

\documentclass[10pt]{report}
\usepackage{amsthm,amsmath,amssymb,showframe}

\begin{document}

\begin{equation}
\begin{gathered}
  e_{0}^{2} = e_{0},\quad
  e_{1}^{2} = -e_{0},\quad
  e_{2}^{2} = -e_{0},\quad
  e_{3}^{2} = -e_{0},
\\
\begin{aligned}
  e_{0}\cdot e_{1} &=  e_{1}\cdot e_{0} = e_{1}, &
  e_{0}\cdot e_{2} &=  e_{2}\cdot e_{0} = e_{2}, &
  e_{0}\cdot e_{3} &=  e_{3}\cdot e_{0} = e_{3},  \\
  e_{1}\cdot e_{2} &= -e_{2}\cdot e_{1} = e_{3}, &
  e_{2}\cdot e_{3} &= -e_{3}\cdot e_{2} = e_{1}, &
  e_{3}\cdot e_{1} &= -e_{1}\cdot e_{3} = e_{2}.
\end{aligned}
\end{gathered}
\end{equation}    
\end{document}

但这个\cdot符号似乎是多余的。

\documentclass[10pt]{report}
\usepackage{amsthm,amsmath,amssymb,showframe}

\begin{document}

\begin{equation}
\begin{gathered}
  e_{0}^{2} = e_{0},\quad
  e_{1}^{2} = -e_{0},\quad
  e_{2}^{2} = -e_{0},\quad
  e_{3}^{2} = -e_{0},
\\
\begin{aligned}
  e_{0} e_{1} &=  e_{1} e_{0} = e_{1}, &
  e_{0} e_{2} &=  e_{2} e_{0} = e_{2}, &
  e_{0} e_{3} &=  e_{3} e_{0} = e_{3},  \\
  e_{1} e_{2} &= -e_{2} e_{1} = e_{3}, &
  e_{2} e_{3} &= -e_{3} e_{2} = e_{1}, &
  e_{3} e_{1} &= -e_{1} e_{3} = e_{2}.
\end{aligned}
\end{gathered}
\end{equation}

\end{document}

Answer 2

不完全符合要求（没有对齐），但这可以令人满意吗？

\documentclass[10pt]{report}
%\usepackage{amsthm,amsmath,amssymb,showframe}
\usepackage{amsthm,mathtools,amssymb}

\begin{document}
\begin{equation}
    \begin{gathered}
        e_{0}^{2} =  e_{0}, \quad
        e_{1}^{2} = -e_{0}, \quad
        e_{2}^{2} = -e_{0}, \quad
        e_{3}^{2} = -e_{0}, \\
        e_{0}\cdot e_{1}=  e_{1}\cdot e_{0} = e_{1}, \quad
        e_{0}\cdot e_{2}=  e_{2}\cdot e_{0} = e_{2}, \quad
        e_{0}\cdot e_{3}=  e_{3}\cdot e_{0} = e_{3},  \\
        e_{1}\cdot e_{2}= -e_{2}\cdot e_{1} = e_{3}, \quad
        e_{2}\cdot e_{3}= -e_{3}\cdot e_{2} = e_{1}, \quad
        e_{3}\cdot e_{1}= -e_{1}\cdot e_{3} = e_{2}.
    \end{gathered}
\end{equation}
\end{document}

需要mathtools（对于gathered环境），它会加载amsmath。