使用模运算绘制图形

Question

我有一张由 Z/11 中的 x 和 y 组成的图表。是否可以以编程方式绘制斜率为 2 的线？

例如从 (0,0) 到 (5,10) 并且 (6,12) 将因为模 11 而变成 (6,1)。就像下面的图一样。

对于该图表，我使用以下代码。但我必须手动计算起点和终点。

    \begin{tikzpicture}
    \coordinate (Origin)   at (0,0);
    \coordinate (XAxisMin) at (0,0);
    \coordinate (XAxisMax) at (11,0);
    \coordinate (YAxisMin) at (0,0);
    \coordinate (YAxisMax) at (0,11);

    \draw [thick, gray,-latex] (XAxisMin) -- (XAxisMax);% Draw x axis
    \draw [thick, gray,-latex] (YAxisMin) -- (YAxisMax);% Draw y axis

    \foreach \x in {0,1,...,10}{% Two indices running over each
      \foreach \y in {0,1,...,10}{% node on the grid we have drawn 
        \node[draw,circle,inner sep=1pt,fill] at (\x,\y) {};
            % Places a dot at those points
      }
    }

    \draw [thin, blue,-latex] (Origin) -- (5,10);
      \draw [thin, blue,-latex] (6,1) -- (10,9);
\end{tikzpicture}

Answer 1

您可以使用Mod(<num>,<base>)函数来获取模数，但我不明白您是否希望在每个循环中使用它，所以这里是循环

\documentclass{article}
\usepackage{tikz}

\begin{document}
\begin{tikzpicture}
    \coordinate (Origin)   at (0,0);
    \coordinate (XAxisMin) at (0,0);
    \coordinate (XAxisMax) at (11,0);
    \coordinate (YAxisMin) at (0,0);
    \coordinate (YAxisMax) at (0,11);

    \draw [thick, gray,-latex] (XAxisMin) -- (XAxisMax);% Draw x axis
    \draw [thick, gray,-latex] (YAxisMin) -- (YAxisMax);% Draw y axis

    \foreach \x in {0,1,...,10}{% Two indices running over each
      \foreach \y[evaluate=\y as \yi using {Mod(\y,11)}] in {0,1,...,15}{
        \node[draw,circle,inner sep=1pt,fill] at (\x,\y) {};
        \draw (0,0) -- (\x,\yi);
            % Places a dot at those points
      }
    }
\end{tikzpicture}
\end{document}

我希望我理解正确，

\documentclass{article}
\usepackage{tikz}

\begin{document}
\begin{tikzpicture}
    \coordinate (Origin)   at (0,0);
    \coordinate (XAxisMin) at (0,0);
    \coordinate (XAxisMax) at (11,0);
    \coordinate (YAxisMin) at (0,0);
    \coordinate (YAxisMax) at (0,11);

    \draw [thick, gray,-latex] (XAxisMin) -- (XAxisMax);% Draw x axis
    \draw [thick, gray,-latex] (YAxisMin) -- (YAxisMax);% Draw y axis

\draw  (0,0)  \foreach \x in {1,...,11}{
                \foreach \y in {1,...,11}{
                  node[draw,circle,inner sep=1pt,fill] at (\x-1,\y-1) {}
                  -- ({Mod(\x,11)},{Mod(2*\x,11)})
                }
              };
\end{tikzpicture}
\end{document}