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使用 Tikz 自动从列表中获取具有关系的线性箭筒

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使用 Tikz 自动从列表中获取具有关系的线性箭筒

我有一个列表 L，其示例如下：

L=[ 5, [ (1)*a2*a3, (1)*a3*a4 ], [ (1)*a1*a2, (1)*a3*a4 ], [ (1)*a1*a2*a3, (1)*a3*a4 ], [ (1)*a3*a4 ], [ (1)*a1*a2, (1)*a2*a3 ], [ (1)*a2*a3 ], [ (1)*a1*a2, (1)*a2*a3*a4 ], 
  [ (1)*a1*a2*a3, (1)*a2*a3*a4 ], [ (1)*a2*a3*a4 ], [ (1)*a1*a2 ], [ (1)*a1*a2*a3 ], [ (1)*a1*a2*a3*a4 ] ]

第一个条目是一个数字，这里是 5。其他条目是形式为的列表，例如 [ (1)*a2*a3, (1)*a3*a4 ]。

从这个包含 n 个条目的列表中，我们可以生成 n-1 张图片，其中每张图片如下所示，对应于以下形式的列表[ (1)*a2*a3, (1)*a3*a4 ]：

绘制一个有 z 个顶点（z 是列表 L 中的第一个数字）的箭筒（=有向图），它是一条线性定向线，带有以 命名的箭头a_1 to a_{z-1}。

现在输入关系，例如[ (1)*a2*a3, (1)*a3*a4 ]输入到这个箭筒中。

该示例[ (1)*a2*a3, (1)*a3*a4 ]应提供以下 tikz 图片（我使用 tikz 的 quiver 应用程序生成，您可以复制粘贴链接以在 quiverapp 编辑器中获取图片）：

％https://q.uiver.app/#q=WzAsNSxbMCwwLCIxIl0sWzEsMCwiMiJdLFsyLDAsIjMiXSxbMywwLCI0Il0sWzQsMCwiNSJdLFswLDEsImFfMSJdLFsxLDIsImFfMiJdLFsyLDMsImFfMyJdLFszLDQsImFfNCJdLFsxLDMsIiIsMSx7ImN1cnZlIjozLCJzdHlsZSI6eyJib2R5Ijp7Im5hbWUiOiJkYXNoZWQifX19XSxbMiw0LCIiLDEseyJjdXJ2ZSI6Mywic3R5bGUiOnsiYm9keSI6eyJuYW1lIjoiZGFzaGVkIn19fV1d

\[\begin{tikzcd}
    1 & 2 & 3 & 4 & 5
    \arrow["{a_1}", from=1-1, to=1-2]
    \arrow["{a_2}", from=1-2, to=1-3]
    \arrow["{a_3}", from=1-3, to=1-4]
    \arrow["{a_4}", from=1-4, to=1-5]
    \arrow[curve={height=18pt}, dashed, from=1-2, to=1-4]
    \arrow[curve={height=18pt}, dashed, from=1-3, to=1-5]
\end{tikzcd}\]

因此输入应该是列表 L，输出应该是 n-1 个这样的颤动，其关系按给定的顺序与列表 L 的条目相对应。

问题 1：有没有一种简单的方法可以使用 Tikz 自动完成此操作？

这里是具有编译关系的线性箭筒图片的最小示例：

\documentclass{article}
\usepackage{amsmath}
\usepackage{xcolor}
\usepackage{pgfplots}
\usepackage{tikz-cd}
\usetikzlibrary{calc}

\begin{document}

{\tikzset{curve/.style={settings={#1},to path={(\tikztostart)
    .. controls ($(\tikztostart)!\pv{pos}!(\tikztotarget)!\pv{height}!270:(\tikztotarget)$)
    and ($(\tikztostart)!1-\pv{pos}!(\tikztotarget)!\pv{height}!270:(\tikztotarget)$)
    .. (\tikztotarget)\tikztonodes}},
    settings/.code={\tikzset{quiver/.cd,#1}
        \def\pv##1{\pgfkeysvalueof{/tikz/quiver/##1}}},
    quiver/.cd,pos/.initial=0.35,height/.initial=0}
    
% https://q.uiver.app/#q=WzAsNSxbMCwwLCIxIl0sWzEsMCwiMiJdLFsyLDAsIjMiXSxbMywwLCI0Il0sWzQsMCwiNSJdLFswLDEsImFfMSJdLFsxLDIsImFfMiJdLFsyLDMsImFfMyJdLFszLDQsImFfNCJdLFsxLDMsIiIsMSx7ImN1cnZlIjozLCJzdHlsZSI6eyJib2R5Ijp7Im5hbWUiOiJkYXNoZWQifX19XSxbMiw0LCIiLDEseyJjdXJ2ZSI6Mywic3R5bGUiOnsiYm9keSI6eyJuYW1lIjoiZGFzaGVkIn19fV1d
\[\begin{tikzcd}
    1 & 2 & 3 & 4 & 5
    \arrow["{a_1}", from=1-1, to=1-2]
    \arrow["{a_2}", from=1-2, to=1-3]
    \arrow["{a_3}", from=1-3, to=1-4]
    \arrow["{a_4}", from=1-4, to=1-5]
    \arrow[curve={height=18pt}, dashed, from=1-2, to=1-4]
    \arrow[curve={height=18pt}, dashed, from=1-3, to=1-5]
\end{tikzcd}\]



\end{document}

感谢您的任何帮助！

编辑：

这是一个完整的例子：

该列表[ 4, [ (1)*a1*a2, (1)*a2*a3 ], [ (1)*a2*a3 ], [ (1)*a1*a2 ], [ (1)*a1*a2*a3 ] ]应给出以下 4 个线性定向箭筒及其对应关系的 tikz 图片：

\documentclass{article}
\usepackage{amsmath}
\usepackage{xcolor}
\usepackage{pgfplots}
\usepackage{tikz-cd}
\usetikzlibrary{calc}

\begin{document}

{\tikzset{curve/.style={settings={#1},to path={(\tikztostart)
    .. controls ($(\tikztostart)!\pv{pos}!(\tikztotarget)!\pv{height}!270:(\tikztotarget)$)
    and ($(\tikztostart)!1-\pv{pos}!(\tikztotarget)!\pv{height}!270:(\tikztotarget)$)
    .. (\tikztotarget)\tikztonodes}},
    settings/.code={\tikzset{quiver/.cd,#1}
        \def\pv##1{\pgfkeysvalueof{/tikz/quiver/##1}}},
    quiver/.cd,pos/.initial=0.35,height/.initial=0}
    
      % https://q.uiver.app/#q=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

  

    \[\begin{tikzcd}
        1 & 2 & 3 & 4 \\
        1 & 2 & 3 & 4 \\
        1 & 2 & 3 & 4 \\
        1 & 2 & 3 & 4
        \arrow["{a_1}", from=1-1, to=1-2]
        \arrow["{a_2}", from=1-2, to=1-3]
        \arrow["{a_3}", from=1-3, to=1-4]
        \arrow["{a_1}", from=2-1, to=2-2]
        \arrow["{a_2}", from=2-2, to=2-3]
        \arrow["{a_3}", from=2-3, to=2-4]
        \arrow["{a_1}", from=3-1, to=3-2]
        \arrow["{a_2}", from=3-2, to=3-3]
        \arrow["{a_3}", from=3-3, to=3-4]
        \arrow["{a_1}", from=4-1, to=4-2]
        \arrow["{a_2}", from=4-2, to=4-3]
        \arrow["{a_3}", from=4-3, to=4-4]
        \arrow[curve={height=18pt}, dashed, from=1-1, to=1-3]
        \arrow[curve={height=18pt}, dashed, from=1-2, to=1-4]
        \arrow[curve={height=18pt}, dashed, from=2-2, to=2-4]
        \arrow[curve={height=18pt}, dashed, from=3-1, to=3-3]
        \arrow[curve={height=18pt}, dashed, from=4-1, to=4-4]
    \end{tikzcd}\]



\end{document}

答案1

首先\regex_extract_all:nnN用于获取带括号的列表。这些列表存储在中\l__Mare_arrows_seq。然后用形成一个循环\seq_map_indexed_inline:Nn。\arrow命令由\tl_build_put_right:Nn和构成\tl_build_put_right:Ne。这些命令用插入到tikzcd环境中\l__Mare_arrows_tl。

在此处输入图片描述

\documentclass[border=6pt]{standalone}
\usepackage{tikz-cd}
\ExplSyntaxOn
\cs_generate_variant:Nn \clist_map_inline:nn { en }
\cs_generate_variant:Nn \tl_set:Nn { Ne }
\cs_generate_variant:Nn \tl_build_put_right:Nn { Ne }
\seq_new:N \l__Mare_arrows_seq
\seq_new:N \l__Mare_indices_seq
\tl_new:N \l__Mare_arrow_tl
\tl_new:N \l__Mare_arrows_tl
\NewDocumentCommand { \quiver } { r[] }
  {
    \regex_extract_all:nnN { \[[^\[\]]+\] } {#1} \l__Mare_arrows_seq
    \tl_build_begin:N \l__Mare_arrows_tl
      \seq_map_indexed_inline:Nn \l__Mare_arrows_seq
        {
          \tl_set:Ne \l__Mare_arrow_tl {##2}
          \tl_remove_all:Nn \l__Mare_arrow_tl { [ }
          \tl_remove_all:Nn \l__Mare_arrow_tl { ] }
          \tl_remove_all:Nn \l__Mare_arrow_tl { a }
          \clist_map_inline:en { \l__Mare_arrow_tl }
            {
              \seq_set_split:Nnn \l__Mare_indices_seq { * } {####1}
              \tl_build_put_right:Nn \l__Mare_arrows_tl { \arrow }
              \tl_build_put_right:Ne \l__Mare_arrows_tl
                {
                  [
                    bend~right ,
                    dashed ,
                    from = ##1 - \seq_item:Nn \l__Mare_indices_seq { 2 } ,
                    to = ##1 - \int_eval:n { \seq_item:Nn \l__Mare_indices_seq { -1 } + 1 }
                  ]
                }
            }
        }
    \tl_build_end:N \l__Mare_arrows_tl
    \begin { tikzcd } [ ampersand~replacement = \& ]
      \int_step_inline:nn { \seq_count:N \l__Mare_arrows_seq }
        {
          \int_step_inline:nn { \clist_item:nn {#1} { 1 } - 1 }
            { ####1 \arrow [ r , " { a \c_math_subscript_token {####1} } " ] \& }
          \clist_item:nn {#1} { 1 }
          \int_compare:nNnF {##1} = { \seq_count:N \l__Mare_arrows_seq }
            { \\ }%no \\ for the last row
        }
      \l__Mare_arrows_tl
    \end { tikzcd }
  }
\ExplSyntaxOff
\begin{document}
$\quiver[ 5, [ (1)*a2*a3, (1)*a3*a4 ], [ (1)*a1*a2, (1)*a3*a4 ], [ (1)*a1*a2*a3, (1)*a3*a4 ], [ (1)*a3*a4 ], [ (1)*a1*a2, (1)*a2*a3 ], [ (1)*a2*a3 ], [ (1)*a1*a2, (1)*a2*a3*a4 ], 
  [ (1)*a1*a2*a3, (1)*a2*a3*a4 ], [ (1)*a2*a3*a4 ], [ (1)*a1*a2 ], [ (1)*a1*a2*a3 ], [ (1)*a1*a2*a3*a4 ] ]$
\end{document}

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