diff options
| -rw-r--r-- | vorlesungen/slides/4/Makefile.inc | 10 | ||||
| -rw-r--r-- | vorlesungen/slides/4/chapter.tex | 6 | ||||
| -rw-r--r-- | vorlesungen/slides/4/euklidmatrix.tex | 9 | ||||
| -rw-r--r-- | vorlesungen/slides/4/ggt.tex | 62 | ||||
| -rw-r--r-- | vorlesungen/slides/Makefile.inc | 3 | ||||
| -rw-r--r-- | vorlesungen/slides/test.tex | 2 |
6 files changed, 90 insertions, 2 deletions
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} |