Merge pull request #1 from AndreasFMueller/master

update

1 files changed, 93 insertions, 0 deletions

diff --git a/vorlesungen/slides/1/algebrastruktur.tex b/vorlesungen/slides/1/algebrastruktur.tex
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+++ b/vorlesungen/slides/1/algebrastruktur.tex
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+%
+% algebrastruktur.tex
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\bgroup
+
+\definecolor{darkgreen}{rgb}{0,0.6,0}
+
+\begin{frame}[t]
+\frametitle{Algebra über $\Bbbk$}
+\begin{center}
+\begin{tikzpicture}[>=latex,thick]
+\pgfmathparse{atan(7/4)}
+\xdef\a{\pgfmathresult}
+\uncover<2->{
+	\fill[color=red!40,opacity=0.5]
+		({-4-2.5},{2+1.0})
+		--
+		({-2.5},{-3-1.0})
+		--
+		({2.5},{-3-1.0})
+		--
+		({-4+2.5},{2+1.0})
+		-- cycle;
+}
+
+\uncover<4->{
+	\fill[color=blue!40,opacity=0.5]
+		({4-2.5},{2+1.0})
+		--
+		({-2.5},{-3-1.0})
+		--
+		({2.5},{-3-1.0})
+		--
+		({4+2.5},{2+1.0})
+		-- cycle;
+}
+
+\uncover<6->{
+	\fill[color=darkgreen!40,opacity=0.5]
+		({-4-2.5},{2+1.0})
+		-- 
+		({-4-2.5+2*(4/7)},{2-1})
+		-- 
+		({+4+2.5-2*(4/7)},{2-1})
+		-- 
+		({+4+2.5},{2+1})
+		--
+		cycle;
+}
+
+\node at ({-3-0.5},2) {Skalarmultiplikation};
+
+\node at (3.5,2.2) {Multiplikation};
+\node at (3.5,1.8) {\tiny Monoid};
+
+\node at (0,-2.8) {Addition};
+\node at (0,-3.2) {\tiny Gruppe};
+
+\uncover<4->{
+	\node[color=blue] at (4.8,-0.5) [rotate=\a] {Ring\strut};
+}
+
+\uncover<2->{
+	\node[color=red] at (-4.8,-0.5) [rotate=-\a] {Vektorraum\strut};
+}
+
+\uncover<6->{
+	\node[color=darkgreen] at (0,2.6) {$(\lambda a)b=\lambda(ab)$};
+}
+
+\uncover<3->{
+	\node[color=red] at (-2.5,-0.5) {$\displaystyle
+	\begin{aligned}
+	\lambda(a+b)&=\lambda a + \lambda b\\
+	(\lambda+\mu)a&=\lambda a +\mu a
+	\end{aligned}$};
+}
+
+\uncover<5->{
+	\node[color=blue] at (2.5,-0.5) {$\displaystyle
+	\begin{aligned}
+	a(b+c)&=ab+ac\\
+	(a+b)c&=ac+bc
+	\end{aligned}$};
+}
+
+\end{tikzpicture}
+\end{center}
+\end{frame}
+
+\egroup