From 6a56afa0e79fb4ac6f04c1d3c3a8e6314331989b Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Andreas=20M=C3=BCller?= <andreas.mueller@ost.ch>
Date: Mon, 1 Mar 2021 16:04:13 +0100
Subject: new slides

---
 vorlesungen/slides/4/euklidmatrix.tex | 9 +++++++++
 1 file changed, 9 insertions(+)
 create mode 100644 vorlesungen/slides/4/euklidmatrix.tex

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

diff --git a/vorlesungen/slides/4/euklidmatrix.tex b/vorlesungen/slides/4/euklidmatrix.tex
new file mode 100644
index 0000000..2090c0a
--- /dev/null
+++ b/vorlesungen/slides/4/euklidmatrix.tex
@@ -0,0 +1,9 @@
+%
+% euklidmatrix.tex
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostscheizer Fachhochschule
+%
+\begin{frame}[t]
+\frametitle{Matrixform}
+
+\end{frame}
-- 
cgit v1.2.1


From ca12778acdf6f2da84aec311c5ab63cde5d847cd Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Andreas=20M=C3=BCller?= <andreas.mueller@ost.ch>
Date: Mon, 1 Mar 2021 21:20:36 +0100
Subject: add slides

---
 vorlesungen/slides/4/euklidmatrix.tex | 86 ++++++++++++++++++++++++++++++++++-
 1 file changed, 85 insertions(+), 1 deletion(-)

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

diff --git a/vorlesungen/slides/4/euklidmatrix.tex b/vorlesungen/slides/4/euklidmatrix.tex
index 2090c0a..6ffa4c2 100644
--- a/vorlesungen/slides/4/euklidmatrix.tex
+++ b/vorlesungen/slides/4/euklidmatrix.tex
@@ -4,6 +4,90 @@
 % (c) 2021 Prof Dr Andreas Müller, OST Ostscheizer Fachhochschule
 %
 \begin{frame}[t]
-\frametitle{Matrixform}
+\frametitle{Matrixform des euklidischen Algorithmus}
+\setlength{\abovedisplayskip}{5pt}
+\setlength{\belowdisplayskip}{5pt}
+\vspace{-20pt}
+\begin{columns}[t,onlytextwidth]
+\begin{column}{0.52\textwidth}
+\begin{block}{Einzelschritt}
+\vspace{-10pt}
+\[
+a_k = b_kq_k + r_k
+\;\Rightarrow\;
+\left\{
+\begin{aligned}
+a_{k+1} &= b_k = \phantom{a_k-q_k}\llap{$-\mathstrut$}b_k \\
+b_{k+1} &= \phantom{b_k}\llap{$r_k$} = a_k - q_kb_k 
+\end{aligned}
+\right.
+\]
+\end{block}
+\end{column}
+\begin{column}{0.44\textwidth}
+\begin{block}{Matrixschreibweise}
+\vspace{-10pt}
+\begin{align*}
+\begin{pmatrix}
+a_{k+1}\\
+b_{k+1}
+\end{pmatrix}
+&=
+\begin{pmatrix}
+b_k\\r_k
+\end{pmatrix}
+=
+\underbrace{\begin{pmatrix}0&1\\1&-q_k\end{pmatrix}}_{\displaystyle =Q(q_k)}
+\begin{pmatrix}
+a_k\\b_k
+\end{pmatrix}
+\end{align*}
+\end{block}
+\end{column}
+\end{columns}
+\vspace{-10pt}
+\begin{block}{Ende des Algorithmus}
+\vspace{-10pt}
+\begin{align*}
+\begin{pmatrix}
+a_{n+1}\\
+b_{n+1}\\
+\end{pmatrix}
+&=
+\begin{pmatrix}
+r_{n-1}\\
+r_{n}
+\end{pmatrix}
+=
+\begin{pmatrix}
+\operatorname{ggT}(a,b) \\
+0
+\end{pmatrix}
+=
+\underbrace{Q(q_n)
+\dots
+Q(q_1)
+Q(q_0)}_{\displaystyle =Q}
+\begin{pmatrix} a_0\\ b_0\end{pmatrix}
+=
+Q\begin{pmatrix}a\\b\end{pmatrix}
+\end{align*}
+\end{block}
+\begin{block}{Konsequenzen}
+\[
+Q=\begin{pmatrix}
+q_{11}&q_{12}\\
+a_{21}&q_{22}
+\end{pmatrix}
+\quad\Rightarrow\quad
+\left\{
+\quad
+\begin{aligned}
+\operatorname{ggT}(a,b) &= q_{11}a + q_{12}b \\
+                      0 &= q_{21}a + q_{22}b
+\end{aligned}
+\right.
+\]
+\end{block}
 
 \end{frame}
-- 
cgit v1.2.1


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/euklidmatrix.tex | 39 ++++++++++++++++++++++++-----------
 1 file changed, 27 insertions(+), 12 deletions(-)

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

diff --git a/vorlesungen/slides/4/euklidmatrix.tex b/vorlesungen/slides/4/euklidmatrix.tex
index 6ffa4c2..be5b3ca 100644
--- a/vorlesungen/slides/4/euklidmatrix.tex
+++ b/vorlesungen/slides/4/euklidmatrix.tex
@@ -14,17 +14,19 @@
 \vspace{-10pt}
 \[
 a_k = b_kq_k + r_k
+\uncover<2->{
 \;\Rightarrow\;
 \left\{
 \begin{aligned}
 a_{k+1} &= b_k = \phantom{a_k-q_k}\llap{$-\mathstrut$}b_k \\
 b_{k+1} &= \phantom{b_k}\llap{$r_k$} = a_k - q_kb_k 
 \end{aligned}
-\right.
+\right.}
 \]
 \end{block}
 \end{column}
 \begin{column}{0.44\textwidth}
+\uncover<3->{%
 \begin{block}{Matrixschreibweise}
 \vspace{-10pt}
 \begin{align*}
@@ -37,23 +39,30 @@ b_{k+1}
 b_k\\r_k
 \end{pmatrix}
 =
-\underbrace{\begin{pmatrix}0&1\\1&-q_k\end{pmatrix}}_{\displaystyle =Q(q_k)}
+\uncover<4->{
+\underbrace{\begin{pmatrix}
+\uncover<5->{0&1}\\
+\uncover<6->{1&-q_k}
+\end{pmatrix}}_{\uncover<7->{\displaystyle =Q(q_k)}}
+}
 \begin{pmatrix}
 a_k\\b_k
 \end{pmatrix}
 \end{align*}
-\end{block}
+\end{block}}
 \end{column}
 \end{columns}
 \vspace{-10pt}
+\uncover<8->{%
 \begin{block}{Ende des Algorithmus}
 \vspace{-10pt}
 \begin{align*}
+\uncover<9->{
 \begin{pmatrix}
 a_{n+1}\\
 b_{n+1}\\
 \end{pmatrix}
-&=
+&=}
 \begin{pmatrix}
 r_{n-1}\\
 r_{n}
@@ -63,31 +72,37 @@ r_{n}
 \operatorname{ggT}(a,b) \\
 0
 \end{pmatrix}
+\uncover<11->{
 =
-\underbrace{Q(q_n)
-\dots
-Q(q_1)
-Q(q_0)}_{\displaystyle =Q}
+\underbrace{\uncover<15->{Q(q_n)}
+\uncover<14->{\dots}
+\uncover<13->{Q(q_1)}
+\uncover<12->{Q(q_0)}}_{\displaystyle =Q}}
+\uncover<10->{
 \begin{pmatrix} a_0\\ b_0\end{pmatrix}
+\uncover<6->{
 =
 Q\begin{pmatrix}a\\b\end{pmatrix}
+}
+}
 \end{align*}
-\end{block}
+\end{block}}
+\uncover<16->{%
 \begin{block}{Konsequenzen}
 \[
 Q=\begin{pmatrix}
 q_{11}&q_{12}\\
-a_{21}&q_{22}
+q_{21}&q_{22}
 \end{pmatrix}
 \quad\Rightarrow\quad
 \left\{
 \quad
 \begin{aligned}
-\operatorname{ggT}(a,b) &= q_{11}a + q_{12}b \\
+\operatorname{ggT}(a,b) &= q_{11}a + q_{12}b = {\color{red}s}a+{\color{red}t}b\\
                       0 &= q_{21}a + q_{22}b
 \end{aligned}
 \right.
 \]
-\end{block}
+\end{block}}
 
 \end{frame}
-- 
cgit v1.2.1