diff options
Diffstat (limited to 'buch/chapters/30-endlichekoerper/images/fermat.tex')
| -rw-r--r-- | buch/chapters/30-endlichekoerper/images/fermat.tex | 138 |
1 files changed, 138 insertions, 0 deletions
diff --git a/buch/chapters/30-endlichekoerper/images/fermat.tex b/buch/chapters/30-endlichekoerper/images/fermat.tex new file mode 100644 index 0000000..6cdafaa --- /dev/null +++ b/buch/chapters/30-endlichekoerper/images/fermat.tex @@ -0,0 +1,138 @@ +% +% fermat.tex -- Illustration zum kleinen Satz von Fermat +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{amsmath} +\usepackage{times} +\usepackage{txfonts} +\usepackage{pgfplots} +\usepackage{csvsimple} +\usetikzlibrary{arrows,intersections,math,calc} +\begin{document} +\def\skala{1} +\begin{tikzpicture}[>=latex,thick,scale=\skala] + +\def\s{34} + +\definecolor{farbe1}{rgb}{0.0,0.4,0.0} +\definecolor{farbe2}{rgb}{0.0,1.0,1.0} +\definecolor{farbe3}{rgb}{0.0,0.4,0.6} +\definecolor{farbe4}{rgb}{0.0,0.0,0.8} +\definecolor{farbe5}{rgb}{0.4,0.0,1.0} +\definecolor{farbe6}{rgb}{0.8,0.0,0.0} +\definecolor{farbe7}{rgb}{0.8,0.4,0.4} +\definecolor{farbe8}{rgb}{1.0,0.8,0.0} + +\def\perle#1#2#3{ + \fill[color=#3] ($#1+({#2*0.15},0)$) circle[radius=0.075]; +} + +\def\perlena#1#2#3#4#5#6{ + \draw #1 -- ($#1+({0.15*9},0)$); + \perle{#1}{0}{#2} + \perle{#1}{1}{#3} + \perle{#1}{2}{#4} + \perle{#1}{3}{#5} + \perle{#1}{4}{#6} +} +\def\perlenb#1#2#3#4#5#6{ + \perle{#1}{5}{#2} + \perle{#1}{6}{#3} + \perle{#1}{7}{#4} + \perle{#1}{8}{#5} + \perle{#1}{9}{#6} +} + +\begin{scope}[xshift=3cm] +\draw (0,0) circle[radius=4]; +\foreach \k in {-1,...,8}{ + \draw (0,0) -- ({90+\k*\s}:4); +} +\foreach \k in {1,...,8}{ + \node at ({90+\s*(\k-0.5)}:3.7) {$A_{\k\mathstrut}$}; +} + +\pgfmathparse{90-(360-9*\s)/2-\s} +\xdef\b{\pgfmathresult} +\foreach \d in {-10,-5,...,10}{ + \fill ({\b+\d}:2.8) circle[radius=0.04]; +} +\node at ({90-(\s/2)}:3.7) {$A_{p\mathstrut}$}; + +\node at (-4,4) {$s_1$}; +\node at (-3.8,2.6) {$s_2$}; +\node at (-4.8,0.6) {$s_3$}; +\node at (-4.2,-2) {$s_4$}; +\node at (-4,-4) {$s_5$}; + +\perlena{({-3*sin(-0.5*\s)-0.54},{3*cos(-0.5*\s)})}{farbe8}{farbe1}{farbe2}{farbe3}{farbe4} +\perlenb{({-3*sin(-0.5*\s)-0.54},{3*cos(-0.5*\s)})}{farbe5}{farbe6}{farbe7}{black,opacity=0}{black,opacity=0} + +\perlena{({-3*sin(0.5*\s)-0.74},{3*cos(0.5*\s)})}{farbe1}{farbe2}{farbe3}{farbe4}{farbe5} +\perlenb{({-3*sin(0.5*\s)-0.74},{3*cos(0.5*\s)})}{farbe6}{farbe7}{black,opacity=0}{black,opacity=0}{farbe8} + +\perlena{({-3*sin(1.5*\s)-0.74},{3*cos(1.5*\s)-0.2})}{farbe2}{farbe3}{farbe4}{farbe5}{farbe6} +\perlenb{({-3*sin(1.5*\s)-0.74},{3*cos(1.5*\s)-0.2})}{farbe7}{black,opacity=0}{black,opacity=0}{farbe8}{farbe1} + +\perlena{({-3*sin(2.5*\s)-0.0},{3*cos(2.5*\s)-0.0})}{farbe3}{farbe4}{farbe5}{farbe6}{farbe7} +\perlenb{({-3*sin(2.5*\s)-0.0},{3*cos(2.5*\s)-0.0})}{black,opacity=0}{black,opacity=0}{farbe8}{farbe1}{farbe2} + +\perlena{({-3*sin(3.5*\s)-0.74},{3*cos(3.5*\s)+0.2})}{farbe4}{farbe5}{farbe6}{farbe7}{black,opacity=0} +\perlenb{({-3*sin(3.5*\s)-0.74},{3*cos(3.5*\s)+0.2})}{black,opacity=0}{farbe8}{farbe1}{farbe2}{farbe3} + +\perlena{({-3*sin(4.5*\s)-0.74},{3*cos(4.5*\s)})}{farbe5}{farbe6}{farbe7}{black,opacity=0}{black,opacity=0} +\perlenb{({-3*sin(4.5*\s)-0.74},{3*cos(4.5*\s)})}{farbe8}{farbe1}{farbe2}{farbe3}{farbe4} + +\perlena{({-3*sin(5.5*\s)-0.64},{3*cos(5.5*\s)})}{farbe6}{farbe7}{black,opacity=0}{black,opacity=0}{farbe8} +\perlenb{({-3*sin(5.5*\s)-0.64},{3*cos(5.5*\s)})}{farbe1}{farbe2}{farbe3}{farbe4}{farbe5} + +\perlena{({-3*sin(6.5*\s)-0.64},{3*cos(6.5*\s)})}{farbe7}{black,opacity=0}{black,opacity=0}{farbe8}{farbe1} +\perlenb{({-3*sin(6.5*\s)-0.64},{3*cos(6.5*\s)})}{farbe2}{farbe3}{farbe4}{farbe5}{farbe6} + +\perlena{({-3*sin(7.5*\s)-1.14},{3*cos(7.5*\s)+0.1})}{black,opacity=0}{black,opacity=0}{farbe8}{farbe1}{farbe2} +\perlenb{({-3*sin(7.5*\s)-1.14},{3*cos(7.5*\s)+0.1})}{farbe3}{farbe4}{farbe5}{farbe6}{farbe7} + +\node at (45:4) [above right] {$A$}; + +\clip (-7,-4.4) rectangle (0,4.8); +\foreach \k in {1,...,5}{ + \pgfmathparse{20*(3-\k)} + \xdef\c{\pgfmathresult} + \pgfmathparse{90+(\k-0.5)*\s} + \xdef\a{\pgfmathresult} + \pgfmathparse{\a-180} + \xdef\b{\pgfmathresult} + \draw[->] (-7.5,0) to[out={\c},in={180+\b}] (\a:4); + %\node at (\a:4) [left] {$\b$}; +} +\end{scope} + +\def\pearl#1#2{ + \fill[color=#2] ($({90+(#1-0.5)*\s}:0.6)$) circle[radius=0.12]; + \draw[line width=0.1pt] ($({90+(#1-0.5)*\s}:0.6)$) circle[radius=0.12]; +} + +\def\kette{ + \draw (0,0) circle[radius=0.6]; + \pearl{1}{farbe1} + \pearl{2}{farbe2} + \pearl{3}{farbe3} + \pearl{4}{farbe4} + \pearl{5}{farbe5} + \pearl{6}{farbe6} + \pearl{7}{farbe7} + \pearl{0}{farbe8} +} + +\begin{scope}[xshift=-4.5cm] +\fill[color=white] (-1.5,-2.5) rectangle (1.5,2.5); +\draw (-1.5,-2.5) rectangle (1.5,2.5); +\kette +\node at (-1.5,2.5) [below right] {$G$}; +\end{scope} + +\end{tikzpicture} +\end{document} + |