add more algebra stuff

5 files changed, 132 insertions, 0 deletions

diff --git a/buch/chapters/10-vektorenmatrizen/images/Makefile b/buch/chapters/10-vektorenmatrizen/images/Makefile
new file mode 100644
index 0000000..779d571
--- /dev/null
+++ b/buch/chapters/10-vektorenmatrizen/images/Makefile
@@ -0,0 +1,12 @@
+#
+# Makefile -- build images
+#
+# (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+#
+all:	ideale.pdf gausszahlen.pdf
+
+ideale.pdf:	ideale.tex
+	pdflatex ideale.tex
+
+gausszahlen.pdf:	gausszahlen.tex
+	pdflatex gausszahlen.tex
diff --git a/buch/chapters/10-vektorenmatrizen/images/gausszahlen.pdf b/buch/chapters/10-vektorenmatrizen/images/gausszahlen.pdf
new file mode 100644
index 0000000..b717fa6
--- /dev/null
+++ b/buch/chapters/10-vektorenmatrizen/images/gausszahlen.pdf
diff --git a/buch/chapters/10-vektorenmatrizen/images/gausszahlen.tex b/buch/chapters/10-vektorenmatrizen/images/gausszahlen.tex
new file mode 100644
index 0000000..6786f05
--- /dev/null
+++ b/buch/chapters/10-vektorenmatrizen/images/gausszahlen.tex
@@ -0,0 +1,48 @@
+%
+% gausszahlen.tex -- Ganze Gausssche Zahlen
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\documentclass[tikz]{standalone}
+\usepackage{amsmath}
+\usepackage{times}
+\usepackage{txfonts}
+\usepackage{pgfplots}
+\usepackage{csvsimple}
+\usepackage{color}
+\usetikzlibrary{arrows,intersections,math}
+\begin{document}
+\definecolor{darkgreen}{rgb}{0,0.6,0}
+\begin{tikzpicture}[>=latex,thick,scale=0.8]
+\draw[->] (-8.5,0) -- (8.5,0) coordinate[label={$\Re z$}];
+\draw[->] (0,-4.5) -- (0,4.5) coordinate[label={right:$\Im z$}];
+\foreach \x in {-8,...,8}{
+	\foreach \y in {-4,...,4}{
+		\fill (\x,\y) circle[radius=0.05];
+	}
+}
+
+
+\coordinate (O) at (0,0);
+\coordinate (A) at (2,2);
+\coordinate (B) at (-3,1);
+\coordinate (C) at (-8,-4);
+\coordinate (D) at (-1,3);
+\draw[line width=0.5pt] (A)--(D)--(B);
+\draw[->,color=red] (O) -- (A);
+\draw[->,color=red] (O) -- (B);
+\draw[->,color=blue] (O) -- (C);
+\draw[->,color=darkgreen] (O) -- (D);
+\fill[color=red] (A) circle[radius=0.08];
+\fill[color=red] (B) circle[radius=0.08];
+\fill[color=blue] (C) circle[radius=0.08];
+\fill[color=darkgreen] (D) circle[radius=0.08];
+\fill[color=black] (O) circle[radius=0.08];
+\node[color=red] at (A) [above right] {$z$};
+\node[color=red] at (B) [above left] {$w$};
+\node[color=darkgreen] at (D) [above] {$z+w$};
+\node[color=blue] at (C) [below right] {$z\cdot w$};
+
+\end{tikzpicture}
+\end{document}
+
diff --git a/buch/chapters/10-vektorenmatrizen/images/ideale.pdf b/buch/chapters/10-vektorenmatrizen/images/ideale.pdf
new file mode 100644
index 0000000..439afcc
--- /dev/null
+++ b/buch/chapters/10-vektorenmatrizen/images/ideale.pdf
diff --git a/buch/chapters/10-vektorenmatrizen/images/ideale.tex b/buch/chapters/10-vektorenmatrizen/images/ideale.tex
new file mode 100644
index 0000000..9793c8e
--- /dev/null
+++ b/buch/chapters/10-vektorenmatrizen/images/ideale.tex
@@ -0,0 +1,72 @@
+%
+% ideale.tex -- Ideale in den ganzen Gaussschen Zahlen
+%
+% (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}
+\begin{tikzpicture}[>=latex,thick,scale=0.35]
+\begin{scope}[xshift=-9.5cm]
+\begin{scope}
+\clip (-8.3,-8.3) rectangle (8.3,8.3);
+	\foreach \x in {-8,...,8}{
+		\foreach \y in {-8,...,8}{
+			\fill (\x,\y) circle[radius=0.08];
+		}
+	}
+	\foreach \x in {-8,...,8}{
+		\foreach \y in {-8,...,8}{
+			\fill[color=blue]
+				({\x-2*\y},{2*\x+\y}) circle[radius=0.12];
+		}
+	}
+	\foreach \x in {-8,...,8}{
+		\draw[color=blue,line width=0.5pt]
+			({\x-2*(-8)},{2*\x+(-8)}) 
+			--
+			({\x-2*8},{2*\x+8});
+	}
+	\foreach \y in {-8,...,8}{
+		\draw[color=blue,line width=0.5pt]
+			({(-8)-2*\y},{2*(-8)+\y}) 
+			--
+			({8-2*\y},{2*8+\y});
+	}
+\end{scope}
+	\draw[->] (-8.3,0) -- (9.1,0) coordinate[label={$\Re z$}];
+	\draw[->] (0,-8.3) -- (0,8.9) coordinate[label={right:$\Im z$}];
+\end{scope}
+
+\begin{scope}[xshift=9.5cm]
+\begin{scope}
+\clip (-8.3,-8.3) rectangle (8.3,8.3);
+	\foreach \x in {-8,...,8}{
+		\foreach \y in {-8,...,8}{
+			\fill[color=red] ({\x-\y},{\x+\y}) circle[radius=0.12];
+		}
+	}
+	\foreach \x in {-8,...,8}{
+		\foreach \y in {-8,...,8}{
+			\fill (\x,\y) circle[radius=0.08];
+		}
+	}
+	\foreach \x in {-8,...,8}{
+		\draw[color=red,line width=0.5pt]
+			({\x+8},{\x-8}) -- ({\x-8},{\x+8});
+		\draw[color=red,line width=0.5pt]
+			({-8-\x},{-8+\x}) -- ({8-\x},{8+\x});
+	}
+\end{scope}
+	\draw[->] (-8.3,0) -- (9.1,0) coordinate[label={$\Re z$}];
+	\draw[->] (0,-8.3) -- (0,8.9) coordinate[label={right:$\Im z$}];
+\end{scope}
+
+\end{tikzpicture}
+\end{document}
+