flalign 和 cases 环境中行向量的水平对齐

Question

我写了这段代码

\begin{flalign*}
    t\hphantom{^{\prime}}&=
        \begin{cases}
            \begin{pmatrix} 1 & 2 & ... & \frac{p}{2} & \frac{p}{2}+1 & ... & p \end{pmatrix} & \text{if $p$ even,} \\
            \begin{pmatrix} 1 & 2 & ... & \frac{p-1}{2} & \frac{p-1}{2}+1 & ... & p \end{pmatrix} & \text{if $p$ odd,}
        \end{cases}&&\\ 
    t^{\prime}&=
        \begin{cases}
            \begin{pmatrix} \frac{p}{2}+1 & \frac{p}{2}+2 & ... & p & 1 & ... & \frac{p}{2} \end{pmatrix} & \text{if $p$ even,} \\
            \begin{pmatrix} \frac{p-1}{2}+1 & \frac{p-1}{2}+2 & ... & p & 1 & ... & \frac{p-1}{2} \end{pmatrix} & \text{if $p$ odd.}
        \end{cases}&&
\end{flalign*}

得出以下方程

如何让所有行向量的相应元素水平对齐？

Answer 1

以下解决方案将每一列元素设置在 内，并对每一列\eqmathbox[<tag>]使用相同的元素。<tag>eqparbox然后找出哪个元素的<tag>宽度最大，并将它们全部放在这个最大宽度的框中。这样就可以水平排列。

\documentclass{article}

\usepackage{amsmath,eqparbox}

% https://tex.stackexchange.com/a/34412/5764
\makeatletter
\NewDocumentCommand{\eqmathbox}{o O{c} m}{%
  \IfValueTF{#1}
    {\def\eqmathbox@##1##2{\eqmakebox[#1][#2]{$##1##2$}}}
    {\def\eqmathbox@##1##2{\eqmakebox{$##1##2$}}}
  \mathpalette\eqmathbox@{#3}
}
\makeatother

\begin{document}

Original nonalignment:
\begin{flalign*}
  t\hphantom{^{\prime}}&=
    \begin{cases}
      \begin{pmatrix} 1 & 2 & \cdots & \frac{p}{2} & \frac{p}{2} + 1 & \cdots & p \end{pmatrix} & \text{if $p$ even,} \\
      \begin{pmatrix} 1 & 2 & \cdots & \frac{p - 1}{2} & \frac{p - 1}{2} + 1 & \cdots & p \end{pmatrix} & \text{if $p$ odd,}
    \end{cases}&&\\ 
  t^{\prime}&=
    \begin{cases}
      \begin{pmatrix} \frac{p}{2} + 1 & \frac{p}{2} + 2 & \cdots & p & 1 & \cdots & \frac{p}{2} \end{pmatrix} & \text{if $p$ even,} \\
      \begin{pmatrix} \frac{p-1}{2} + 1 & \frac{p - 1}{2} + 2 & \cdots & p & 1 & \cdots & \frac{p - 1}{2} \end{pmatrix} & \text{if $p$ odd.}
    \end{cases}&&
\end{flalign*}

Updated horizontal alignment:
\begingroup
\setlength{\arraycolsep}{0.5\arraycolsep}%
\begin{flalign*}
  t\hphantom{^{\prime}} &=
    \begin{cases}
      \begin{pmatrix} 
        \eqmathbox[c1]{1} & \eqmathbox[c2]{2} & \eqmathbox[c3]{\cdots} & \eqmathbox[c4]{\frac{p}{2}} & 
          \eqmathbox[c5]{\frac{p}{2} + 1} & \eqmathbox[c6]{\cdots} & \eqmathbox[c7]{p} 
      \end{pmatrix} & \text{if $p$ even,} \\
      \begin{pmatrix}
        \eqmathbox[c1]{1} & \eqmathbox[c2]{2} & \eqmathbox[c3]{\cdots} & \eqmathbox[c4]{\frac{p - 1}{2}} & 
          \eqmathbox[c5]{\frac{p - 1}{2} + 1} & \eqmathbox[c6]{\cdots} & \eqmathbox[c7]{p}
      \end{pmatrix} & \text{if $p$ odd,}
    \end{cases}&& \\ 
  t^{\prime} &=
    \begin{cases}
      \begin{pmatrix}
        \eqmathbox[c1]{\frac{p}{2} + 1} & \eqmathbox[c2]{\frac{p}{2} + 2} & \eqmathbox[c3]{\cdots} & \eqmathbox[c4]{p} & 
          \eqmathbox[c5]{1} & \eqmathbox[c6]{\cdots} & \eqmathbox[c7]{\frac{p}{2}}
      \end{pmatrix} & \text{if $p$ even,} \\
      \begin{pmatrix}
        \eqmathbox[c1]{\frac{p - 1}{2} + 1} & \eqmathbox[c2]{\frac{p -1}{2} + 2} & \eqmathbox[c3]{\cdots} & \eqmathbox[c4]{p} & 
          \eqmathbox[c5]{1} & \eqmathbox[c6]{\cdots} & \eqmathbox[c7]{\frac{p - 1}{2}}
      \end{pmatrix} & \text{if $p$ odd.}
    \end{cases}&&
\end{flalign*}
\endgroup

\end{document}

另一种方法是将元素设置为固定宽度的列array。这样可以让 TeX 计算出每列的宽度，从而更加方便。

Answer 2

您可以使用nicematrix：

\documentclass{article}
\usepackage{amsmath}
\usepackage{nicematrix}

\begin{document}

\[
\begin{NiceArray}{@{} l @{\quad} l @{\qquad} l @{}}
  \Block{2-1}{t\hphantom{'} = {}} &
  \bigl(\begin{matrix}
    1 & 2 & \dots & \frac{p}{2} & \frac{p}{2}+1 & \dots & p
  \end{matrix}\bigr) &
  \text{$p$ even,}
  \\[1ex]
  &
  \bigl(\begin{matrix}
    1 & 2 & \dots & \frac{p-1}{2} & \frac{p-1}{2}+1 & \dots & p
  \end{matrix}\bigr) & \text{$p$ odd,}
  \\ \\
  \Block{2-1}{t' = {}} &
  \bigl(\begin{matrix}
    \frac{p}{2}+1 & \frac{p}{2}+2 & \dots & p & 1 & \dots & \frac{p}{2}
  \end{matrix}\bigr) & \text{$p$ even,}
  \\[1ex]
  &
  \bigl(\begin{matrix}
    \frac{p-1}{2}+1 & \frac{p-1}{2}+2 & \dots & p & 1 & \dots & \frac{p-1}{2}
  \end{matrix}\bigr) &
  \text{$p$ odd.}
\CodeAfter\SubMatrix\{{1-2}{2-2}.\SubMatrix\{{4-2}{5-2}.
\end{NiceArray}
\]

\end{document}

如果你确实希望行向量条目对齐，

\documentclass{article}
\usepackage{amsmath}
\usepackage{nicematrix}

\begin{document}

\[
\begin{NiceArray}{
  @{}
  l
  @{\quad}
  r
  @{}
  ccccccc
  @{}
  l
  @{\qquad}
  l
  @{}
}
  \Block{2-1}{t\hphantom{'} = {}} &
  \big( & 1 & 2 & \dots & \frac{p}{2} & \frac{p}{2}+1 & \dots & p & \big) &
  \text{$p$ even,}
  \\[1ex]
  &
  \big( & 1 & 2 & \dots & \frac{p-1}{2} & \frac{p-1}{2}+1 & \dots & p & \big) &
  \text{$p$ odd,}
  \\ \\
  \Block{2-1}{t' = {}} &
  \big( & \frac{p}{2}+1 & \frac{p}{2}+2 & \dots & p & 1 & \dots & \frac{p}{2} & \big) &
  \text{$p$ even,}
  \\[1ex]
  &
  \big( & \frac{p-1}{2}+1 & \frac{p-1}{2}+2 & \dots & p & 1 & \dots & \frac{p-1}{2} & \big) &
  \text{$p$ odd.}
\CodeAfter\SubMatrix\{{1-2}{2-2}.\SubMatrix\{{4-2}{5-2}.
\end{NiceArray}
\]

\end{document}