From f2454006fa4e2a0b4093507300fab8a29e3b5901 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Andreas=20M=C3=BCller?= <andreas.mueller@ost.ch>
Date: Mon, 8 Mar 2021 09:40:32 +0100
Subject: final preparation

---
 vorlesungen/slides/4/euklidbeispiel.tex | 66 +++++++++++++++++++++++++--------
 1 file changed, 50 insertions(+), 16 deletions(-)

(limited to 'vorlesungen/slides/4/euklidbeispiel.tex')

diff --git a/vorlesungen/slides/4/euklidbeispiel.tex b/vorlesungen/slides/4/euklidbeispiel.tex
index cbc3137..366a7a6 100644
--- a/vorlesungen/slides/4/euklidbeispiel.tex
+++ b/vorlesungen/slides/4/euklidbeispiel.tex
@@ -6,39 +6,73 @@
 \bgroup
 \definecolor{darkgreen}{rgb}{0,0.6,0}
 \begin{frame}[t]
-\frametitle{Beispiel}
+\frametitle{Euklidischer Algorithmus: Beispiel}
 \setlength{\abovedisplayskip}{0pt}
 \setlength{\belowdisplayskip}{0pt}
 \vspace{-0pt}
 \begin{block}{Finde $\operatorname{ggT}(25,15)$}
 \vspace{-12pt}
 \begin{align*}
-a_0&=25 & b_0 &= 15 &25&=15 \cdot {\color{red}      1} + 10 &q_0 &= {\color{red}1} & r_0 &= 10\\
-a_1&=15 & b_1 &= 10 &15&=10 \cdot {\color{darkgreen}1} + \phantom{0}5  &q_1 &= {\color{darkgreen}1} & r_1 &= \phantom{0}5 \\
-a_2&=10 & b_2 &= \phantom{0}5 &10&=\phantom{0}5  \cdot {\color{blue}     2} + \phantom{0}0  &q_2 &= {\color{blue}2} & r_2 &= \phantom{0}0 
+a_0&=25 & b_0 &= 15 &\uncover<2->{25&=15 \cdot {\color{orange}      1} + 10 &q_0 &= {\color{orange}1} & r_0 &= 10}\\
+\uncover<3->{a_1&=15 & b_1 &= 10}&\uncover<4->{15&=10 \cdot {\color{darkgreen}1} + \phantom{0}5  &q_1 &= {\color{darkgreen}1} & r_1 &= \phantom{0}5}\\
+\uncover<5->{a_2&=10 & b_2 &= \phantom{0}5}&\uncover<6->{10&=\phantom{0}5  \cdot {\color{blue}     2} + \phantom{0}0  &q_2 &= {\color{blue}2} & r_2 &= \phantom{0}0 }
 \end{align*}
 \end{block}
 \vspace{-5pt}
+\uncover<7->{%
 \begin{block}{Matrix-Operationen}
 \begin{align*}
 Q
 &=
-Q({\color{blue}2}) Q({\color{darkgreen}1}) Q({\color{red}1})
+\uncover<9->{Q({\color{blue}2})}
+\uncover<8->{Q({\color{darkgreen}1})}
+Q({\color{orange}1})
 =
-\begin{pmatrix}0&1\\1&-{\color{blue}2}\end{pmatrix}
-\begin{pmatrix}0&1\\1&-{\color{darkgreen}1}\end{pmatrix}
-\begin{pmatrix}0&1\\1&-{\color{red}1}\end{pmatrix}
-=\begin{pmatrix}
--1&2\\3&-5
-\end{pmatrix}
+\uncover<9->{
+\begin{pmatrix*}[r]0&1\\1&-{\color{blue}2}\end{pmatrix*}
+}
+\uncover<8->{
+\begin{pmatrix*}[r]0&1\\1&-{\color{darkgreen}1}\end{pmatrix*}
+}
+\begin{pmatrix*}[r]0&1\\1&-{\color{orange}1}\end{pmatrix*}
+=
+\ifthenelse{\boolean{presentation}}{
+\only<7>{
+\begin{pmatrix*}[r]\phantom{-}0&1\\1&-1\end{pmatrix*}
+}
+\only<8>{
+\begin{pmatrix*}[r]
+1&-1\\-1&2
+\end{pmatrix*}
+}
+}{}
+\only<9->{
+\begin{pmatrix*}[r]
+{\color{red}-1}&{\color{red}2}\\3&-5
+\end{pmatrix*}}
 \end{align*}
-\end{block}
+\end{block}}
 \vspace{-5pt}
+\uncover<10->{%
 \begin{block}{Relationen ablesen}
-\begin{align*}
-\operatorname{ggT}({\usebeamercolor[fg]{title}25},{\usebeamercolor[fg]{title}15}) &= 5 = -1\cdot {\usebeamercolor[fg]{title}25} + 2\cdot {\usebeamercolor[fg]{title}15} \\
+\[
+\begin{pmatrix}
+\operatorname{ggT}(a,b)\\0
+\end{pmatrix}
+=
+Q
+\begin{pmatrix}a\\b\end{pmatrix}
+\uncover<11->{%
+\quad
+\Rightarrow\quad
+\left\{
+\begin{aligned}
+\operatorname{ggT}({\usebeamercolor[fg]{title}25},{\usebeamercolor[fg]{title}15}) &= 5 =
+{\color{red}-1}\cdot {\usebeamercolor[fg]{title}25} + {\color{red}2}\cdot {\usebeamercolor[fg]{title}15} \\
  0                        &= \phantom{5=-}3\cdot {\usebeamercolor[fg]{title}25} -5\cdot {\usebeamercolor[fg]{title}15}
-\end{align*}
-\end{block}
+\end{aligned}
+\right.}
+\]
+\end{block}}
 
 \end{frame}
-- 
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