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author | LordMcFungus <mceagle117@gmail.com> | 2021-03-22 18:05:11 +0100 |
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committer | GitHub <noreply@github.com> | 2021-03-22 18:05:11 +0100 |
commit | 76d2d77ddb2bed6b7c6b8ec56648d85da4103ab7 (patch) | |
tree | 11b2d41955ee4bfa0ae5873307c143f6b4d55d26 /vorlesungen/slides/3/nichthauptideal.tex | |
parent | more chapter structure (diff) | |
parent | add title image (diff) | |
download | SeminarMatrizen-76d2d77ddb2bed6b7c6b8ec56648d85da4103ab7.tar.gz SeminarMatrizen-76d2d77ddb2bed6b7c6b8ec56648d85da4103ab7.zip |
Merge pull request #1 from AndreasFMueller/master
update
Diffstat (limited to 'vorlesungen/slides/3/nichthauptideal.tex')
-rw-r--r-- | vorlesungen/slides/3/nichthauptideal.tex | 78 |
1 files changed, 78 insertions, 0 deletions
diff --git a/vorlesungen/slides/3/nichthauptideal.tex b/vorlesungen/slides/3/nichthauptideal.tex new file mode 100644 index 0000000..46074b9 --- /dev/null +++ b/vorlesungen/slides/3/nichthauptideal.tex @@ -0,0 +1,78 @@ +% +% nichthauptideal.tex +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\bgroup +\definecolor{darkgreen}{rgb}{0,0.6,0} +\begin{frame}[t] +\setlength{\abovedisplayskip}{5pt} +\setlength{\belowdisplayskip}{5pt} +\frametitle{Nicht-Hauptideal in $\mathbb{Z}[X]$} +\vspace{-20pt} +\begin{columns}[t,onlytextwidth] +\begin{column}{0.48\textwidth} +\begin{block}{Hauptideal\uncover<2->{ = ``Gerade''}} +\vspace{-10pt} +\begin{align*} +\langle X+1\rangle&=(X+1) = {\color{red}(X+1)\cdot\mathbb{Z}[X]} +\end{align*} +\begin{center} +\begin{tikzpicture}[>=latex,thick,scale=0.4] +\draw[->] (-6.3,0) -- (6.8,0) coordinate[label={$\mathbb{Z}$}]; +\draw[->] (0,-6.2) -- (0,6.6) coordinate[label={right:$\mathbb{Z}X$}]; +\foreach \x in {-6,...,6}{ + \fill[color=red] (\x,\x) circle[radius=0.12]; +} +\end{tikzpicture} +\end{center} +\end{block} +\end{column} +\begin{column}{0.48\textwidth} +\uncover<3->{% +\begin{block}{Ideal mit zwei Erzeugenden} +\vspace{-10pt} +\begin{align*} +\uncover<6->{ +{\color{darkgreen} +\langle 2,X\rangle +} +&=} +\uncover<5->{ +{\color{red}2\cdot\mathbb{Z}[X]} +} +\uncover<6->{+} +\uncover<4->{ +{\color{blue}X\cdot\mathbb{Z}[X]} +} +\end{align*} +\begin{center} +\begin{tikzpicture}[>=latex,thick,scale=0.4] +\draw[->] (-6.3,0) -- (6.9,0) coordinate[label={$\mathbb{Z}$}]; +\draw[->] (0,-6.2) -- (0,7.0) coordinate[label={right:$\mathbb{Z}X$}]; +\uncover<6->{ + \foreach \x in {-6,-4,...,6}{ + \foreach \y in {-6,...,6}{ + \fill[color=darkgreen] (\x,\y) circle[radius=0.20]; + } + } +} +\uncover<5->{ + \foreach \x in {-6,-4,...,6}{ + \foreach \y in {-6,-4,...,6}{ + \fill[color=red] (\x,\y) circle[radius=0.16]; + } + } +} +\uncover<4->{ + \foreach \y in {-6,...,6}{ + \fill[color=blue] (0,\y) circle[radius=0.12]; + } +} +\end{tikzpicture} +\end{center} +\end{block}} +\end{column} +\end{columns} +\end{frame} +\egroup |