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/Makefile.inc     | 10 ++++++
 vorlesungen/slides/4/chapter.tex      |  6 ++++
 vorlesungen/slides/4/euklidmatrix.tex |  9 +++++
 vorlesungen/slides/4/ggt.tex          | 62 +++++++++++++++++++++++++++++++++++
 vorlesungen/slides/Makefile.inc       |  3 +-
 vorlesungen/slides/test.tex           |  2 +-
 6 files changed, 90 insertions(+), 2 deletions(-)
 create mode 100644 vorlesungen/slides/4/Makefile.inc
 create mode 100644 vorlesungen/slides/4/chapter.tex
 create mode 100644 vorlesungen/slides/4/euklidmatrix.tex
 create mode 100644 vorlesungen/slides/4/ggt.tex

diff --git a/vorlesungen/slides/4/Makefile.inc b/vorlesungen/slides/4/Makefile.inc
new file mode 100644
index 0000000..dabdb7c
--- /dev/null
+++ b/vorlesungen/slides/4/Makefile.inc
@@ -0,0 +1,10 @@
+
+#
+# Makefile.inc -- additional depencencies
+#
+# (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+#
+chapter4 =								\
+	../slides/4/ggt.tex						\
+	../slides/4/chapter.tex
+
diff --git a/vorlesungen/slides/4/chapter.tex b/vorlesungen/slides/4/chapter.tex
new file mode 100644
index 0000000..1e04e9f
--- /dev/null
+++ b/vorlesungen/slides/4/chapter.tex
@@ -0,0 +1,6 @@
+%
+% chapter.tex
+%
+% (c) 2021 Prof Dr Andreas Müller, Hochschule Rapperswi
+%
+\folie{4/ggt.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}
diff --git a/vorlesungen/slides/4/ggt.tex b/vorlesungen/slides/4/ggt.tex
new file mode 100644
index 0000000..77b2a1d
--- /dev/null
+++ b/vorlesungen/slides/4/ggt.tex
@@ -0,0 +1,62 @@
+%
+% ggt.tex -- GGT, Definition und Algorithmus
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschuöe
+%
+\begin{frame}[t]
+\frametitle{Grösster gemeinsamer Teiler}
+\vspace{-15pt}
+\setlength{\abovedisplayskip}{5pt}
+\setlength{\belowdisplayskip}{5pt}
+\begin{columns}[t,onlytextwidth]
+\begin{column}{0.48\textwidth}
+\begin{block}{Definition}
+Gegeben: $a,b\in\mathbb Z$
+\\
+Gesucht: grösster gemeinsamer Teiler $\operatorname{ggT}(a,b)$
+\end{block}
+\begin{block}{Euklidischer Algorithmus}
+$a_0 = a$, $b_0=b$
+\begin{align*}
+a_0&=b_0q_0 + r_0 & a_1 &=b_0 & b_1&=r_0 \\
+a_1&=b_1q_1 + r_1 & a_2 &=b_1 & b_2&=r_1 \\
+a_2&=b_2q_2 + r_2 & a_3 &=b_2 & b_3&=r_2 \\
+   &\;\vdots      &     &     &    &     \\
+a_n&=b_nq_n + r_n & r_n &= 0  & r_{n-1}&)=\operatorname{ggT}(a,b)
+\end{align*}
+\end{block}
+\end{column}
+\begin{column}{0.48\textwidth}
+\begin{block}{$\operatorname{ggT}(15,25) = 5$}
+\begin{center}
+\begin{tikzpicture}[>=latex,thick,scale=0.09]
+\draw[->] (-1,0) -- (65,0) coordinate[label={$a$}];
+\draw[->] (0,-1) -- (0,65) coordinate[label={right:$b$}];
+\begin{scope}
+\clip (-1,-1) rectangle (65,65);
+\foreach \x in {0,...,4}{
+	\draw[line width=0.2pt] ({\x*15},-2) -- ({\x*15},65);
+}
+\foreach \y in {0,...,2}{
+	\draw[line width=0.2pt] (-2,{\y*25}) -- (65,{\y*25});
+}
+\foreach \x in {0,5,...,120}{
+	\draw[color=blue] ({\x+2},-2) -- ({\x+2-70},{-2+70});
+	\node[color=blue] at ({0.5*\x-0.5},{0.5*\x-0.5}) [rotate=-45,above] {\tiny $\x$};
+}
+\foreach \x in {0,...,4}{
+	\foreach \y in {0,...,2}{
+		\fill[color=red] ({\x*15},{\y*25}) circle[radius=0.8];
+	}
+}
+\foreach \x in {0,5,...,60}{
+	\fill[color=blue] (\x,0) circle[radius=0.5];
+	\node at (\x,0) [below] {\tiny $\x$};
+}
+\end{scope}
+\end{tikzpicture}
+\end{center}
+\end{block}
+\end{column}
+\end{columns}
+\end{frame}
diff --git a/vorlesungen/slides/Makefile.inc b/vorlesungen/slides/Makefile.inc
index 910f87e..61dc3c6 100644
--- a/vorlesungen/slides/Makefile.inc
+++ b/vorlesungen/slides/Makefile.inc
@@ -6,6 +6,7 @@
 include ../slides/0/Makefile.inc
 include ../slides/1/Makefile.inc
 include ../slides/3/Makefile.inc
+include ../slides/4/Makefile.inc
 
 slides = 								\
-	$(chapter0) $(chapter1) $(chapter3)
+	$(chapter0) $(chapter1) $(chapter3) $(chapter4)
diff --git a/vorlesungen/slides/test.tex b/vorlesungen/slides/test.tex
index 7e97995..2faf3b3 100644
--- a/vorlesungen/slides/test.tex
+++ b/vorlesungen/slides/test.tex
@@ -29,7 +29,7 @@
 % Adjunktion von \cos(\pi/1291) und \cos(\pi/1291)
 % XXX \folie{3/adj1291.tex}
 
-% XXX \folie{4/ggt.tex}
+\folie{4/ggt.tex}
 % XXX \folie{4/euklidmatrix.tex}
 
 % XXX \folie{4/fp.tex}
-- 
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