From 385db80750dce2b87fb49784814ee660123ca7ff Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Andreas=20M=C3=BCller?= <andreas.mueller@ost.ch>
Date: Thu, 18 Mar 2021 13:21:18 +0100
Subject: =?UTF-8?q?slides=20=C3=BCber=20Ideale?=
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 vorlesungen/slides/3/nichthauptideal2.tex | 92 +++++++++++++++++++++++++++++++
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 create mode 100644 vorlesungen/slides/3/nichthauptideal2.tex

(limited to 'vorlesungen/slides/3/nichthauptideal2.tex')

diff --git a/vorlesungen/slides/3/nichthauptideal2.tex b/vorlesungen/slides/3/nichthauptideal2.tex
new file mode 100644
index 0000000..f362a4a
--- /dev/null
+++ b/vorlesungen/slides/3/nichthauptideal2.tex
@@ -0,0 +1,92 @@
+%
+% nichthauptideal2.tex
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\bgroup
+\definecolor{darkgreen}{rgb}{0,0.6,0}
+\begin{frame}[t]
+\frametitle{Das Ideal $\langle 2,X\rangle \subset \mathbb{Z}[X]$}
+\vspace{-12pt}
+\begin{center}
+\begin{tikzpicture}[>=latex,thick]
+
+\def\c{\clip (-2.8,-2.0) rectangle (2.8,2.0);}
+
+\def\labels{
+	\fill[color=white,opacity=0.5] (1.5,-0.1) circle[radius=0.2];
+	\node at (1.5,-0.1) {$1$};
+	\fill[color=white,opacity=0.5] (-0.9,1.7) circle[radius=0.2];
+	\node at (-0.9,1.7) {$X$};
+	\fill[color=white,opacity=0.5] (0.8,0.7) circle[radius=0.2];
+	\node at (0.8,0.7) {$X^2$};
+}
+
+\only<-3>{
+\begin{scope}[xshift=3.0cm,yshift=1.9cm]
+	\begin{scope}
+	\c
+	\node at (0,0)
+	{\includegraphics[width=7cm]{../slides/3/images/ring.jpg}};
+	\end{scope}
+	\node[color=orange] at (1.9,0.1) [right] {$\mathbb{Z}[X]$};
+	\fill[color=white,opacity=0.5] (1.5,-0.6) circle[radius=0.2];
+	\node at (1.5,-0.6) {$1$};
+	\fill[color=white,opacity=0.5] (-0.4,1.7) circle[radius=0.2];
+	\node at (-0.4,1.7) {$X$};
+\end{scope}
+}
+
+\uncover<2->{
+\begin{scope}[xshift=-3.0cm,yshift=1.9cm]
+	\begin{scope}
+	\c
+	\node at (0,0)
+	{\includegraphics[width=7cm]{../slides/3/images/hauptideal.jpg}};
+	\end{scope}
+	\node[color=blue] at (-0.2,-1.2) {$(X+1)\cdot\mathbb{Z}[X]$};
+	\labels
+\end{scope}
+}
+
+\uncover<3->{
+\begin{scope}[xshift=-3.0cm,yshift=-1.9cm]
+	\begin{scope}
+	\c
+	\node at (0,0)
+	{\includegraphics[width=7cm]{../slides/3/images/hauptideal2.jpg}};
+	\end{scope}
+	\node[color=darkgreen] at (-3.0,-0.8) {$2\cdot\mathbb{Z}[X]$};
+\end{scope}
+
+\begin{scope}[xshift=3.0cm,yshift=-1.9cm]
+	\begin{scope}
+	\c
+	\node at (0,0)
+	{\includegraphics[width=7cm]{../slides/3/images/hauptidealX.jpg}};
+	\end{scope}
+	\node[color=darkgreen] at (2.5,-0.8) {$X\cdot\mathbb{Z}[X]$};
+	\labels
+\end{scope}
+}
+
+\uncover<4->{
+\begin{scope}[xshift=3.0cm,yshift=1.9cm]
+	\begin{scope}
+	\c
+	\node at (0,0)
+	{\includegraphics[width=7cm]{../slides/3/images/nichthauptideal.jpg}};
+	\end{scope}
+	\node[color=orange] at (1.9,0.1) [right] {$\mathbb{Z}[X]$};
+	\node[color=darkgreen] at (1.9,-0.4) [right] {$\langle 2,X\rangle$};
+\end{scope}
+}
+
+\draw[color=gray!50] (-6.6,0) -- (6.4,0);
+\draw[color=gray!50] (0,-3.8) -- (0,3.8);
+
+\end{tikzpicture}
+\end{center}
+
+\end{frame}
+\egroup
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