9 files changed, 299 insertions, 0 deletions
diff --git a/vorlesungen/slides/2/images/Makefile b/vorlesungen/slides/2/images/Makefile
new file mode 100644
index 0000000..8bce5c9
--- /dev/null
+++ b/vorlesungen/slides/2/images/Makefile
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+#
+# Makefile
+#
+# (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+#
+all:	quotient1.jpg quotient2.jpg quotient1.pdf quotient2.pdf
+
+quotient1.png:	quotient1.pov quotient.inc
+	povray +A0.1 +W1920 +H1080 -Oquotient1.png quotient1.pov
+
+quotient1.jpg:	quotient1.png Makefile
+	convert -extract 1360x1040+330+20 quotient1.png \
+		-density 300 -units PixelsPerInch quotient1.jpg
+
+quotient2.png:	quotient2.pov quotient.inc
+	povray +A0.1 +W1920 +H1080 -Oquotient2.png quotient2.pov
+
+quotient2.jpg:	quotient2.png Makefile
+	convert -extract 1360x1040+330+20 quotient2.png \
+		-density 300 -units PixelsPerInch quotient2.jpg
+
+quotient:	quotient.ini quotient.inc quotient.pov
+	rm -rf quotient
+	mkdir quotient
+	povray +A0.1 -Oquotient/0.png -W1920 -H1080 quotient.ini
+
+quotient1.pdf:	quotient1.tex quotient1.jpg
+	pdflatex quotient1.tex
+
+quotient2.pdf:	quotient2.tex quotient2.jpg
+	pdflatex quotient2.tex
+
diff --git a/vorlesungen/slides/2/images/quotient.inc b/vorlesungen/slides/2/images/quotient.inc
new file mode 100644
index 0000000..3fa49d1
--- /dev/null
+++ b/vorlesungen/slides/2/images/quotient.inc
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+//
+// quotient.pov
+//
+// (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+//
+#version 3.7;
+#include "colors.inc"
+
+global_settings {
+	assumed_gamma 1
+}
+
+#declare imagescale = 0.035;
+#declare O = <0, 0, 0>;
+#declare at = 0.015;
+
+camera {
+	location <8, 15, -50>
+	look_at <0.4, 0.2, 0.4>
+	right 16/9 * x * imagescale
+	up y * imagescale
+}
+
+light_source {
+	<-4, 20, -50> color White
+	area_light <1,0,0> <0,0,1>, 10, 10
+	adaptive 1
+	jitter
+}
+
+sky_sphere {
+	pigment {
+		color rgb<1,1,1>
+	}
+}
+
+#macro arrow(from, to, arrowthickness, c)
+#declare arrowdirection = vnormalize(to - from);
+#declare arrowlength = vlength(to - from);
+union { 
+	sphere {
+		from, 1.1 * arrowthickness
+	}
+	cylinder {
+		from,
+		from + (arrowlength - 5 * arrowthickness) * arrowdirection,
+		arrowthickness
+	}
+	cone {  
+		from + (arrowlength - 5 * arrowthickness) * arrowdirection,
+		2 * arrowthickness,
+		to,
+		0
+	}
+	pigment {
+		color c
+	}
+	finish {
+		specular 0.9
+		metallic
+	}
+}
+#end
+
+#macro kasten()
+	box { <-0.5,-0.5,-0.5>, <1.5,1,1.5> }
+#end
+
+
+arrow(<-0.6,0,0>, <1.6,0,0>, at, White)
+arrow(<0,0,-0.6>, <0,0,1.6>, at, White)
+arrow(<0,-0.6,0>, <0,1.2,0>, at, White)
+
+#declare U = <-1,3,-0.5>;
+#declare V1 = <1,0.2,0>;
+#declare V2 = <0,0.2,1>;
+
+#macro gerade(richtung, farbe)
+	intersection {
+		kasten()
+		cylinder { -U + richtung, U + richtung, at }
+		pigment {
+			color farbe
+		}
+		finish {
+			specular 0.9
+			metallic
+		}
+	}
+#end
+
+#declare A = <0.8, -0.2, 0>;
+#declare B = <0.2, 0.8, 0>;
+
+#macro ebene(vektor1, vektor2)
+#declare n = vcross(vektor1,vektor2);
+
+
+intersection {
+	kasten()
+	plane { n, 0.005 }
+	plane { -n, 0.005 }
+	pigment {
+		color rgbf<0.8,0.8,1,0.7>
+	}
+	finish {
+		specular 0.9
+		metallic
+	}
+}
+
+intersection {
+	kasten()
+	union {
+		#declare Xstep = 0.45;
+		#declare X = -5 * Xstep;
+		#while (X < 5.5 * Xstep)
+			cylinder { X*vektor1 - 5*vektor2, X*vektor1 + 5*vektor2, at/2 }
+			#declare X = X + Xstep;
+		#end
+		#declare Ystep = 0.45;
+		#declare Y = -5 * Ystep;
+		#while (Y < 5.5 * Ystep)
+			cylinder { -5*vektor1 + Y*vektor2, 5*vektor1 + Y*vektor2, at/2 }
+			#declare Y = Y + Ystep;
+		#end
+	}
+	pigment {
+		color rgb<0.9,0.9,1>
+	}
+	finish {
+		specular 0.9
+		metallic
+	}
+}
+#end
+
+
+gerade(O, Red)
+
+#declare gruen = rgb<0.2,0.4,0.2>;
+#declare blau = rgb<0,0.4,0.8>;
+#declare rot = rgb<1,0.4,0.0>;
+
+#macro repraesentanten(vektor1, vektor2) 
+
+#declare d1 = A.x*vektor1 + A.y*vektor2;
+#declare d2 = B.x*vektor1 + B.y*vektor2;
+
+arrow(0, d1 + d2, at, rot)
+gerade(d1 + d2, rot)
+
+gerade(d1, blau)
+arrow(O, d1, at, blau)
+cylinder { d1, d1 + d2, 0.6 * at
+	pigment {
+		color gruen
+	}
+	finish {
+		specular 0.9
+		metallic
+	}
+}
+
+gerade(d2, gruen)
+arrow(O, d2, at, gruen)
+cylinder { d2, d1 + d2, 0.6 * at
+	pigment {
+		color blau
+	}
+	finish {
+		specular 0.9
+		metallic
+	}
+}
+
+#end
+
+#macro vektorraum(s)
+#declare b1 = V1 + s * 0.03 * U;
+#declare b2 = V2 + s * 0.03 * U;
+
+ebene(b1, b2)
+repraesentanten(b1, b2)
+#end
+
diff --git a/vorlesungen/slides/2/images/quotient.ini b/vorlesungen/slides/2/images/quotient.ini
new file mode 100644
index 0000000..f62b21a
--- /dev/null
+++ b/vorlesungen/slides/2/images/quotient.ini
@@ -0,0 +1,7 @@
+Input_File_Name="quotient.pov"
+Initial_Frame=0
+Final_Frame=100
+Initial_Clock=-1
+Final_Clock=1
+Cyclic_Animation=off
+Pause_when_Done=off
diff --git a/vorlesungen/slides/2/images/quotient1.jpg b/vorlesungen/slides/2/images/quotient1.jpg
new file mode 100644
index 0000000..aeb713e
--- /dev/null
+++ b/vorlesungen/slides/2/images/quotient1.jpg
diff --git a/vorlesungen/slides/2/images/quotient1.pov b/vorlesungen/slides/2/images/quotient1.pov
new file mode 100644
index 0000000..60bab7f
--- /dev/null
+++ b/vorlesungen/slides/2/images/quotient1.pov
@@ -0,0 +1,8 @@
+//
+// quotient1.pov
+//
+// (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+//
+#include "quotient.inc"
+
+vektorraum(-1)
diff --git a/vorlesungen/slides/2/images/quotient1.tex b/vorlesungen/slides/2/images/quotient1.tex
new file mode 100644
index 0000000..30d82d2
--- /dev/null
+++ b/vorlesungen/slides/2/images/quotient1.tex
@@ -0,0 +1,29 @@
+%
+% quotient1.tex -- Vektorraumquotient
+%
+% (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}
+\definecolor{darkgreen}{rgb}{0,0.6,0}
+\definecolor{darkred}{rgb}{0.7,0,0}
+\def\skala{1}
+\begin{tikzpicture}[>=latex,thick,scale=\skala]
+
+\node at (0,0) {\includegraphics[width=8cm]{quotient1.jpg}};
+
+\node[color=blue] at (0.7,-1.3) {$v$};
+\node[color=darkgreen] at (-1.0,0.1) {$w$};
+\node[color=orange] at (2.5,0.1) {$v+w$};
+\node[color=darkred] at (-2.1,-0.9) {$0$};
+\node[color=darkred] at (-3.1,2.4) {$U$};
+
+\end{tikzpicture}
+\end{document}
+
diff --git a/vorlesungen/slides/2/images/quotient2.jpg b/vorlesungen/slides/2/images/quotient2.jpg
new file mode 100644
index 0000000..345cf22
--- /dev/null
+++ b/vorlesungen/slides/2/images/quotient2.jpg
diff --git a/vorlesungen/slides/2/images/quotient2.pov b/vorlesungen/slides/2/images/quotient2.pov
new file mode 100644
index 0000000..771425d
--- /dev/null
+++ b/vorlesungen/slides/2/images/quotient2.pov
@@ -0,0 +1,8 @@
+//
+// quotient2.pov
+//
+// (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+//
+#include "quotient.inc"
+
+vektorraum(1)
diff --git a/vorlesungen/slides/2/images/quotient2.tex b/vorlesungen/slides/2/images/quotient2.tex
new file mode 100644
index 0000000..607fd03
--- /dev/null
+++ b/vorlesungen/slides/2/images/quotient2.tex
@@ -0,0 +1,29 @@
+%
+% quotient2.tex -- Vektorraumquotient
+%
+% (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}
+\definecolor{darkgreen}{rgb}{0,0.6,0}
+\definecolor{darkred}{rgb}{0.7,0,0}
+\def\skala{1}
+\begin{tikzpicture}[>=latex,thick,scale=\skala]
+
+\node at (0,0) {\includegraphics[width=8cm]{quotient2.jpg}};
+
+\node[color=blue] at (0.57,-0.94) {$v$};
+\node[color=darkgreen] at (-1.15,0.65) {$w$};
+\node[color=orange] at (2.15,1) {$v+w$};
+\node[color=darkred] at (-2.1,-0.9) {$0$};
+\node[color=darkred] at (-3.1,2.4) {$U$};
+
+\end{tikzpicture}
+\end{document}
+