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