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-rw-r--r--buch/chapters/60-gruppen/images/Makefile5
-rw-r--r--buch/chapters/60-gruppen/images/scherungen.pdfbin0 -> 24544 bytes
-rw-r--r--buch/chapters/60-gruppen/images/scherungen.tex157
3 files changed, 161 insertions, 1 deletions
diff --git a/buch/chapters/60-gruppen/images/Makefile b/buch/chapters/60-gruppen/images/Makefile
index 8824d75..3ed39e5 100644
--- a/buch/chapters/60-gruppen/images/Makefile
+++ b/buch/chapters/60-gruppen/images/Makefile
@@ -3,7 +3,7 @@
#
# (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
#
-all: phasenraum.pdf kartenkreis.pdf karten.pdf sl2.pdf
+all: phasenraum.pdf kartenkreis.pdf karten.pdf sl2.pdf scherungen.pdf
phasenraum.pdf: phasenraum.tex
pdflatex phasenraum.tex
@@ -20,3 +20,6 @@ karten.pdf: karten.tex torus.png
sl2.pdf: sl2.tex
pdflatex sl2.tex
+scherungen.pdf: scherungen.tex
+ pdflatex scherungen.tex
+
diff --git a/buch/chapters/60-gruppen/images/scherungen.pdf b/buch/chapters/60-gruppen/images/scherungen.pdf
new file mode 100644
index 0000000..c7f4988
--- /dev/null
+++ b/buch/chapters/60-gruppen/images/scherungen.pdf
Binary files differ
diff --git a/buch/chapters/60-gruppen/images/scherungen.tex b/buch/chapters/60-gruppen/images/scherungen.tex
new file mode 100644
index 0000000..893bd12
--- /dev/null
+++ b/buch/chapters/60-gruppen/images/scherungen.tex
@@ -0,0 +1,157 @@
+%
+% scherungen.tex -- template for standalon tikz images
+%
+% (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}
+\begin{document}
+\def\skala{1}
+\begin{tikzpicture}[>=latex,thick,scale=\skala]
+
+\definecolor{blau}{rgb}{0,0.8,1}
+\definecolor{blau}{rgb}{0,0.6,0}
+\def\s{1.1}
+
+\begin{scope}[xshift=-4.6cm]
+
+ \fill[color=blue!20] (0,0) rectangle (2,2);
+ \fill[color=red!40,opacity=0.5] (0,0) -- (2,\s) -- (2,{2+\s}) -- (0,2)
+ -- cycle;
+
+ \foreach \x in {-1,...,3}{
+ \draw[color=blau] (\x,-1) -- (\x,3);
+ \draw[color=blau] (-1,\x) -- (3,\x);
+ }
+
+ \begin{scope}
+ \clip (-1,-1) rectangle (3,3);
+ \foreach \x in {-1,...,3}{
+ \draw[color=orange] (\x,-1) -- (\x,3);
+ \draw[color=orange] (-1,{\x-0.5*\s}) -- (3,{\x+1.5*\s});
+ }
+ \end{scope}
+
+ \draw[->] (-1.1,0) -- (3.3,0) coordinate[label={$x$}];
+ \draw[->] (0,-1.1) -- (0,3.5) coordinate[label={right:$y$}];
+
+ \node[color=blue] at (0,2) [above left] {$1$};
+ \node[color=blue] at (2,0) [below right] {$1$};
+ \draw[->,color=blue] (0,0) -- (2,0);
+ \draw[->,color=blue] (0,0) -- (0,2);
+
+ \draw[->,color=red] (0,0) -- (2,\s);
+ \draw[->,color=red] (0,0) -- (0,2);
+
+ \node[color=red] at (2,\s) [below right] {$(1,t)$};
+
+ \node at (0,0) [below right] {$O$};
+ \node at (1,-1.1) [below] {$\displaystyle
+ \begin{aligned}
+ M &= \begin{pmatrix}0&0\\1&0 \end{pmatrix}
+ \\
+ e^{Mt}
+ &=
+ \begin{pmatrix}1&0\\t&1 \end{pmatrix}
+ \end{aligned}
+ $};
+\end{scope}
+
+\begin{scope}
+ \fill[color=blue!20] (0,0) rectangle (2,2);
+ \fill[color=red!40,opacity=0.5] (0,0) -- (2,0) -- ({2+\s},2) -- (\s,2)
+ -- cycle;
+
+ \foreach \x in {-1,...,3}{
+ \draw[color=blau] (\x,-1) -- (\x,3);
+ \draw[color=blau] (-1,\x) -- (3,\x);
+ }
+
+ \begin{scope}
+ \clip (-1,-1) rectangle (3,3);
+ \foreach \x in {-1,...,3}{
+ \draw[color=orange] (-1,\x) -- (3,\x);
+ \draw[color=orange] ({\x-0.5*\s},-1) -- ({\x+1.5*\s},3);
+ }
+ \end{scope}
+
+ \draw[->] (-1.1,0) -- (3.3,0) coordinate[label={$x$}];
+ \draw[->] (0,-1.1) -- (0,3.5) coordinate[label={right:$y$}];
+
+ \node[color=blue] at (0,2) [above left] {$1$};
+ \node[color=blue] at (2,0) [below right] {$1$};
+ \draw[->,color=blue] (0,0) -- (2,0);
+ \draw[->,color=blue] (0,0) -- (0,2);
+
+ \draw[->,color=red] (0,0) -- (2,0);
+ \draw[->,color=red] (0,0) -- (\s,2);
+
+ \node[color=red] at (\s,2) [above left] {$(t,1)$};
+
+ \node at (0,0) [below right] {$O$};
+
+ \node at (1,-1.1) [below] {$\displaystyle
+ \begin{aligned} N &= \begin{pmatrix}0&1\\0&0 \end{pmatrix}
+ \\
+ e^{Nt}
+ &=
+ \begin{pmatrix}1&t\\0&1 \end{pmatrix}
+ \end{aligned}
+ $};
+\end{scope}
+
+\begin{scope}[xshift=3.6cm,yshift=0cm]
+ \def\punkt#1#2{({1.6005*(#1)+0.4114*(#2)},{-0.2057*(#1)+0.5719*(#2)})}
+ \fill[color=blue!20] (0,0) rectangle (2,2);
+ \fill[color=red!40,opacity=0.5]
+ (0,0) -- \punkt{2}{0} -- \punkt{2}{2} -- \punkt{0}{2} -- cycle;
+
+ \foreach \x in {0,...,4}{
+ \draw[color=blau] (\x,-1) -- (\x,3);
+ }
+ \foreach \y in {-1,...,3}{
+ \draw[color=blau] (0,\y) -- (4,\y);
+ }
+
+ \begin{scope}
+ \clip (-0,-1) rectangle (4,3);
+ \foreach \x in {-1,...,6}{
+ \draw[color=orange] \punkt{\x}{-3} -- \punkt{\x}{6};
+ \draw[color=orange] \punkt{-3}{\x} -- \punkt{6}{\x};
+ }
+ \end{scope}
+
+ \draw[->] (-0.1,0) -- (4.3,0) coordinate[label={$x$}];
+ \draw[->] (0,-1.1) -- (0,3.5) coordinate[label={right:$y$}];
+
+ \node[color=blue] at (0,2) [above left] {$1$};
+ \node[color=blue] at (2,0) [below right] {$1$};
+ \draw[->,color=blue] (0,0) -- (2,0);
+ \draw[->,color=blue] (0,0) -- (0,2);
+
+ \draw[->,color=red] (0,0) -- \punkt{2}{0};
+ \draw[->,color=red] (0,0) -- \punkt{0}{2};
+
+ \node at (0,0) [below right] {$O$};
+
+ \node at (2,-1.1) [below] {$\displaystyle
+ \begin{aligned} D &= \begin{pmatrix}0.5&0.4\\-0.2&-0.5 \end{pmatrix}
+ \\
+ e^{D\cdot 1}
+ &=
+ \begin{pmatrix}
+ 1.6005 & 0.4114\\
+ -0.2057 & 0.5719
+ \end{pmatrix}
+ \end{aligned}
+ $};
+\end{scope}
+
+\end{tikzpicture}
+\end{document}
+