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author | LordMcFungus <mceagle117@gmail.com> | 2021-03-22 18:05:11 +0100 |
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committer | GitHub <noreply@github.com> | 2021-03-22 18:05:11 +0100 |
commit | 76d2d77ddb2bed6b7c6b8ec56648d85da4103ab7 (patch) | |
tree | 11b2d41955ee4bfa0ae5873307c143f6b4d55d26 /vorlesungen/slides/4/euklidtabelle.tex | |
parent | more chapter structure (diff) | |
parent | add title image (diff) | |
download | SeminarMatrizen-76d2d77ddb2bed6b7c6b8ec56648d85da4103ab7.tar.gz SeminarMatrizen-76d2d77ddb2bed6b7c6b8ec56648d85da4103ab7.zip |
Merge pull request #1 from AndreasFMueller/master
update
Diffstat (limited to '')
-rw-r--r-- | vorlesungen/slides/4/euklidtabelle.tex | 73 |
1 files changed, 73 insertions, 0 deletions
diff --git a/vorlesungen/slides/4/euklidtabelle.tex b/vorlesungen/slides/4/euklidtabelle.tex new file mode 100644 index 0000000..3f1b8d7 --- /dev/null +++ b/vorlesungen/slides/4/euklidtabelle.tex @@ -0,0 +1,73 @@ +% +% 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} |