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+%
+% euklidtabelle.tex
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\begin{frame}[t]
+\setlength{\abovedisplayskip}{5pt}
+\setlength{\belowdisplayskip}{5pt}
+\frametitle{Durchführung des euklidischen Algorithmus}
+Problem: Berechnung der Produkte $Q(q_k)\cdots Q(q_1)Q(q_0)$ für $k=0,1,\dots,n$
+\uncover<2->{%
+\begin{block}{Multiplikation mit $Q(q_k)$}
+\vspace{-12pt}
+\begin{align*}
+Q(q_k)
+\ifthenelse{\boolean{presentation}}{
+\only<-3>{
+\begin{pmatrix}
+u&v\\c&d
+\end{pmatrix}
+=\begin{pmatrix}
+0&1\\1&-q_k
+\end{pmatrix}
+}}{}
+\begin{pmatrix}
+u&v\\c&d
+\end{pmatrix}
+&\uncover<3->{=
+\begin{pmatrix}
+c&d\\
+u-q_kc&v-q_kd
+\end{pmatrix}}
+&&\uncover<5->{\Rightarrow&
+\begin{pmatrix}
+c_k&d_k\\c_{k+1}&d_{k+1}
+\end{pmatrix}
+&=
+Q(q_k)
+%\begin{pmatrix}
+%0&1\\1&-q_k
+%\end{pmatrix}
+\begin{pmatrix}
+c_{k-1}&d_{k-1}\\c_{k}&d_{k}
+\end{pmatrix}}
+\end{align*}
+\end{block}}
+\vspace{-10pt}
+\uncover<6->{%
+\begin{equation*}
+\begin{tabular}{|>{\tiny$}r<{$}|>{$}c<{$}|>{$}c<{$}>{$}c<{$}|}
+\hline
+k  &q_k    &                     c_k    &                     d_k    \\
+\hline
+-1 &       &                     1      &                     0      \\
+ 0 &\uncover<7->{q_0    }&                     0      &                     1      \\
+ 1 &\uncover<9->{q_1    }&\uncover<8->{c_{-1} -q_0    \cdot c_0    &d_{-1} -q_0    \cdot d_0    }\\
+ 2 &\uncover<11->{q_2    }&\uncover<10->{c_0    -q_1    \cdot c_1    &d_0    -q_1    \cdot d_1    }\\
+\vdots&\uncover<12->{\vdots}&\uncover<12->{\vdots                    &\vdots                      }\\
+ n &\uncover<14->{q_n    }&\uncover<13->{{\color{red}c_{n-2}-q_{n-1}\cdot c_{n-1}}&{\color{red}d_{n-2}-q_{n-1}\cdot d_{n-1}}}\\
+n+1&       &\uncover<15->{c_{n-1}-q_{n}  \cdot c_{n}  &d_{n-1}-q_{n}  \cdot d_{n}  }\\
+\hline
+\end{tabular}
+\uncover<16->{
+\Rightarrow
+\left\{
+\begin{aligned}
+\rlap{${\color{red}c_{n}}$}\phantom{c_{n+1}} a + \rlap{${\color{red}d_n}$}\phantom{d_{n+1}}b &= \operatorname{ggT}(a,b)
+\\
+c_{n+1} a + d_{n+1} b &= 0
+\end{aligned}
+\right.}
+\end{equation*}}
+\end{frame}