使用格点表示群的子群

Question

我想利用类似于格点的图来显示大阶子群的元素。

有什么建议么？

Answer 1

\documentclass[border = 5pt]{standalone}

\usepackage{tikz}


\begin{document}

\begin{tikzpicture}

  \newdimen\radius
  \dimen0=0.5pt
  \dimen1=1.2pt

  \foreach \x in {0 ,..., 11} {
    \foreach \y in {0 ,..., 17} {

      \pgfmathsetmacro{\xmod}{(mod(\x,2) == 0)}
      \pgfmathsetmacro{\ymod}{(mod(\y + \x,3) == 0)}
      \ifnum\ymod=1 \ifnum\xmod=1 \radius=\dimen1 \else \radius=\dimen0 \fi
      \else \radius=\dimen0
      \fi
      \draw[fill] (0.5 * \x, 0.4 * \y) circle (\radius);

      \ifnum\x=0
      \node[yshift = 0.4 * \y cm, xshift = -0.5cm] (0, 0) {\small\y};
      \fi
    }

    \node[xshift = 0.5 * \x cm, yshift = -0.5cm] (0, 0) {\small\x};
  }
\end{tikzpicture}
\end{document}

Answer 2

这应该可以让你开始。我相信会有其他人为你输入整个表格。

\documentclass{article}
\usepackage{amsmath}
\begin{document}

\begin{figure}
  \centering
  $
  \begin{array}{cccc}
    2 & \cdot   & \cdot & \cdot   \\
    1 & \cdot   & \cdot & \bullet \\
    0 & \bullet & \cdot & \cdot   \\
      & 0       & 1     & 2       \\
  \end{array}
  $
  \caption{}
\end{figure}

\end{document}

Answer 3

picture这里介绍一种图片环境方法。它展示了如何在 LaTeX2e 图片环境中独立缩放 x 轴和 y 轴的技术（得益于包的使用，但还有一些额外的技巧）。

随附的图片\multiput大概可以（或应该）替代\xintFor。

该方法可以轻松扩展到生成器给出的任何子群：您不必计算属于子群的“方程”。

\documentclass[]{article}
%\usepackage{babel}
\usepackage{picture}
\usepackage{caption}
\usepackage{xinttools}
\begin{document}

% \setlength\unitlength{2em}

\edef\xs{\dimexpr\number\dimexpr2em\relax sp\relax}
\edef\ys{\dimexpr\number\dimexpr1em\relax sp\relax}%

\begin{figure}[htbp]
\centering
% use xshift to get "Figure 1" positioned as in OP
\begin{picture}(14\xs,19\ys)(-2\xs,-\ys)
% use \multiput ?
% never read its doc
  \xintFor* #1 in {\xintSeq{0}{11}}\do
  {
    \put(#1\xs, -\ys){\makebox(0,0){#1}}
  }
  \xintFor* #1 in {\xintSeq{0}{17}}\do
  {
    \put(-\xs, #1\ys){\makebox(0,0)[r]{#1}}
  } 
  \xintFor* #1 in {\xintSeq{0}{11}}\do
  {
    \xintFor* #2 in {\xintSeq{0}{17}}\do
    {
      \put(#1\xs, #2\ys){\makebox(0,0){.}}
    }
  }
  \def\x {0}
  \def\y {0}
  \xintFor* #1 in {\xintSeq{0}{18}}\do
  {
    \put(\x\xs, \y\ys){\circle*{.25\xs}}
    % weird formulas but that's what we need to do 
    % with \numexpr to achieve remainder in integer division
    % \x <- \x + 2  modulo 12
    % \y <- \y + 1  modulo 18
    \edef\x {\the\numexpr \x + 2 - 12 * ((\x + 2 + 6)/12 - 1)}
    \edef\y {\the\numexpr \y + 1 - 18 * ((\y + 1 + 9)/18 - 1)}
  }
  \def\x {6}
  \def\y {0}
  \xintFor* #1 in {\xintSeq{0}{18}}\do
  {
    \put(\x\xs, \y\ys){\circle*{.25\xs}}
    \edef\x {\the\numexpr \x + 2 - 12 * ((\x + 2 + 6)/12 - 1)}
    \edef\y {\the\numexpr \y + 1 - 18 * ((\y + 1 + 9)/18 - 1)}
  }
\end{picture}
\caption{}
\end{figure}
\end{document}