update to current state of book

1 files changed, 157 insertions, 157 deletions

diff --git a/buch/chapters/60-gruppen/images/scherungen.tex b/buch/chapters/60-gruppen/images/scherungen.tex
index 893bd12..f6df172 100644
--- a/buch/chapters/60-gruppen/images/scherungen.tex
+++ b/buch/chapters/60-gruppen/images/scherungen.tex
@@ -1,157 +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}
-
+%

+% 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}

+