如何获得一个二维方程矩阵，其中列的子方程自动添加后缀 a)、b) 等，并且每行的数字自动递增？

Question 1

下面的代码实现了equationgrid允许对这些类型的方程使用以下语法的环境：

\begin{equationgrid}[Reference case,   Modified Case]{one}%
  a &= kb,  a' &= 3b\\
  x &= y^k, y' &= y^{0.5} \\
  z &= e^k, z' &= e^{1.1}
\end{equationgrid}

equation使用计数器和“列”计数器对方程式进行编号a，，，，...：bc

环境equationgrid接受两个参数：

一个选修的标题行是用逗号分隔的列标题列表。
方程式需要 A —— 因为我坚信你不应该给方程式贴标签，label除非你打算以后引用它。在上面的例子中，可以使用、和来引用\ref{one-1a}子\ref{one-1b}方程式。\ref{one-2a}\ref{one-2b}

请注意，方程式本身用逗号分隔，用于\\标记方程行的结尾。列数原则上是任意的。例如，您可以使用

\begin{equationgrid}{two}%
  a &= kb,  a' &= 3 b,     a &= k b, a' &= 3 b\\
  x &= y^k, y' &= y^{0.5}, x &= y^k, y' &= y^{0.5} \\
  z &= e^k, z' &= e^{1.1}, z &= e^k, z' &= e^{1.1}
\end{equationgrid}

生产

（这些方程的方程参考是two-1a，，two-1b...，two-3d。）这些方程是在align*环境中排版的，因此这个环境和页面宽度限制了实际可以使用的列数。

代码使用LaTex3本质上是序列。首先，gridequation使用换行符将环境的内容拆分成行\\，然后使用逗号将行进一步拆分成列。完成后，方程式将重新组合，同时添加方程式编号和标签。

以下是代码：

\documentclass{article}
\usepackage{amsmath}
\usepackage{xparse}
% two counters for the keeping track of grid rows and columns
\newcounter{GridEqnCol}[equation]
\newcounter{GridEqnRow}
\renewcommand\theGridEqnCol{(\theequation\alph{GridEqnCol})}
\renewcommand\theGridEqnRow{\arabic{GridEqnRow}\alph{GridEqnCol}}
\ExplSyntaxOn
\int_new:N \l_grid_row_int   % grid row number
\seq_new:N \l_grid_col_seq   % the column entries in one row
\seq_new:N \l_grid_head_seq  % the optional column headers
\seq_new:N \l_grid_row_seq   % the rows of the equation
\tl_new:N  \l_grid_hline_tl  % a hack to adjust the columns
\tl_new:N  \l_grid_label_tl  % for construction equation labels
% \begin{equationgrid}[column headers as csv]{label}...\end{equationgrid}
\NewDocumentEnvironment{equationgrid}{ o m b }{
    % split the environment body into rows using the \\
    \tl_clear:N \l_grid_hline_tl
    \int_zero:N \l_grid_row_int
    \setcounter{GridEqnRow}{0}
    \tl_set:Nn \l_grid_label_tl {#2-}
    \seq_set_split:Nnn \l_grid_row_seq { \\ } { #3 }
    \IfNoValueTF{#1}{ \seq_clear:N \l_grid_head_seq }
    {
      \seq_set_split:Nnn \l_grid_head_seq {,} {#1}
      \tl_put_right:Nx \l_grid_hline_tl {
          \noexpand\cline{1-\int_eval:n{2+4*\seq_count:N \l_grid_head_seq} }
      }
    }
    \begin{align*}
      \seq_if_empty:NF \l_grid_head_seq {
         \seq_map_function:NN \l_grid_head_seq \__grid_head:n
         \\\tl_use:N \l_grid_hline_tl
      }
      \seq_map_inline:Nn \l_grid_row_seq { \__grid_row:n {##1} }
    \end{align*}
}{}
% typeset an entry of the header row
\cs_new:Npn \__grid_head:n #1 { \multispan{2}{\textbf{#1}} &&& }
% typeset an equation row, adding equation numbers and references
\cs_new:Npn \__grid_row:n #1 {
  \refstepcounter{equation}
  \refstepcounter{GridEqnRow}
  % split #1 into column entries using the ,
  \seq_set_split:Nnn \l_grid_col_seq { , } {#1}
  \seq_map_inline:Nn \l_grid_col_seq {
      \refstepcounter{GridEqnCol}
      \tl_set:No \l_tmpa_tl {\tl_use:N \l_grid_label_tl \theGridEqnRow}
      % align* disables equation numbers so need \ltx@label instead of \label
      \use:c{ltx@label}{ \tl_use:N \l_tmpa_tl }
      ##1 & \theGridEqnCol &&
   }
   \\
}
\ExplSyntaxOff
\begin{document}

  \begin{equationgrid}[Reference case,   Modified Case]{one}%
    a &= kb,  a' &= 3b\\
    x &= y^k, y' &= y^{0.5} \\
    z &= e^k, z' &= e^{1.1}
  \end{equationgrid}

  \begin{equationgrid}{two}%
    a &= kb,  a' &= 3 b,     a &= k b, a' &= 3 b\\
    x &= y^k, y' &= y^{0.5}, x &= y^k, y' &= y^{0.5} \\
    z &= e^k, z' &= e^{1.1}, z &= e^k, z' &= e^{1.1}
  \end{equationgrid}

  As you see, equations \ref{one-1a} and \ref{two-1a} are similar.

\end{document}

最后一点需要注意：由于行\\和列之间用逗号分隔,，因此您不能在方程式中使用逗号。如果您想插入逗号，最简单的方法是使用\newcommand\comma{,}。我遵循了 OP 的语法，但我可能会在每个方程式的末尾放一个逗号。

编辑

这是代码的更新版本，其中equationgrid环境现在接受一个额外的可选参数，因为<...>它给出了一个以逗号分隔的列索引列表，其中应省略方程编号。此外，您可以\notag在任何单元格中放置命令以隐藏该单元格的方程编号（请注意，命令\notag必须位于逗号之前！）。例如，

\begin{equationgrid}<1,3>{three}%
  a &= kb,  a' &= 3 b,     a &= k b, a' &= 3 b\\
  x &= y^k, y' &= y^{0.5}, x &= y^k, y' &= y^{0.5} \\
  z &= e^k, z' &= e^{1.1}\notag, z &= e^k, z' &= e^{1.1}
\end{equationgrid}

抑制第 1 列和第 3 列以及第 3 行第 2 列的方程编号以产生：

以下是更新后的代码：

\documentclass{article}
\usepackage{amsmath}
\usepackage{xparse}
% two counters for the keeping track of grid rows and columns
\newcounter{GridEqnCol}[equation]
\newcounter{GridEqnRow}
\renewcommand\theGridEqnCol{(\theequation\alph{GridEqnCol})}
\ExplSyntaxOn
\bool_new:N \g_print_eq_bool  % suppress equation numbers in this column
\int_new:N \l_grid_row_int    % grid row number
\seq_new:N \l_grid_col_seq    % the column entries in one row
\seq_new:N \l_grid_head_seq   % the optional column headers
\seq_new:N \l_grid_row_seq    % the rows of the equation
\seq_new:N \l_suppress_eq_seq % suppress equation numbers in these columns
\tl_new:N  \l_grid_hline_tl   % a hack to adjust the columns
\tl_new:N  \l_grid_label_tl   % for construction equation labels
\renewcommand\theGridEqnRow{ \tl_use:N \l_grid_label_tl-\arabic{GridEqnRow}\alph{GridEqnCol} }
% \begin{equationgrid}<suppress column equation numbers>[column headers as csv]{label}...\end{equationgrid}
\NewDocumentEnvironment{equationgrid}{ D<>{} o m b }{
    % split the environment body into rows using the \\
    \tl_clear:N \l_grid_hline_tl
    \int_zero:N \l_grid_row_int
    \let\notag\relax % for completeness but not strictly necessary
    \setcounter{GridEqnRow}{0}
    \seq_set_split:Nnn \l_suppress_eq_seq { , } { #1 }
    \tl_set:Nn \l_grid_label_tl {#3}
    \seq_set_split:Nnn \l_grid_row_seq { \\ } { #4 }
    \IfNoValueTF{#2}{ \seq_clear:N \l_grid_head_seq }
    {
      \seq_set_split:Nnn \l_grid_head_seq {,} {#2}
      \tl_put_right:Nx \l_grid_hline_tl {
          \noexpand\cline{1-\int_eval:n{2+4*\seq_count:N \l_grid_head_seq} }
      }
    }
    \begin{align*}
      \seq_if_empty:NF \l_grid_head_seq {
         \seq_map_function:NN \l_grid_head_seq \__grid_head:n
         \\\tl_use:N \l_grid_hline_tl
      }
      \seq_map_inline:Nn \l_grid_row_seq { \__grid_row:n {##1} }
    \end{align*}
}{}
% typeset an entry of the header row
\cs_new:Npn \__grid_head:n #1 { \multispan{2}{\textbf{#1}} &&& }
% typeset an equation row, adding equation numbers and references
\cs_new:Npn \__grid_row:n #1 {
  \refstepcounter{equation}
  \refstepcounter{GridEqnRow}
  % split #1 into column entries using the ,
  \seq_set_split:Nnn \l_grid_col_seq { , } {#1}
  \seq_map_inline:Nn \l_grid_col_seq {
      \refstepcounter{GridEqnCol}
      \bool_gset_true:N \g_print_eq_bool
      \seq_if_in:NxT \l_suppress_eq_seq {\arabic{GridEqnCol}} { \bool_gset_false:N \g_print_eq_bool }
      \str_if_in:nnT { ##1 } { \notag } { \bool_gset_false:N \g_print_eq_bool }
      \bool_if:NT \g_print_eq_bool
      {
        % align* disables equation numbers so need \ltx@label instead of \label
        \use:c{ltx@label}{ \theGridEqnRow }
      }
      ##1 & \bool_if:NT \g_print_eq_bool {\theGridEqnCol} &&
   }
   \\
}
\cs_generate_variant:Nn \seq_if_in:NnF {NxF}
\ExplSyntaxOff
\begin{document}

  \begin{equationgrid}[Reference case,   Modified Case]{one}%
    a &= kb,  a' &= 3b\\
    x &= y^k, y' &= y^{0.5} \\
    z &= e^k, z' &= e^{1.1}
  \end{equationgrid}

  \begin{equationgrid}{two}%
    a &= kb,  a' &= 3 b,     a &= k b, a' &= 3 b\\
    x &= y^k, y' &= y^{0.5}, x &= y^k, y' &= y^{0.5} \\
    z &= e^k, z' &= e^{1.1}, z &= e^k, z' &= e^{1.1}
  \end{equationgrid}

  As you see, equations \ref{one-1a} and \ref{two-1a} are similar.

  \begin{equationgrid}<1,3>{three}%
    a &= kb,  a' &= 3 b,     a &= k b, a' &= 3 b\\
    x &= y^k, y' &= y^{0.5}, x &= y^k, y' &= y^{0.5} \\
    z &= e^k, z' &= e^{1.1}\notag, z &= e^k, z' &= e^{1.1}
  \end{equationgrid}

\end{document}

Answer