From f7987f342c3f9153a0f05c2f940f370aa61960ee Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Andreas=20M=C3=BCller?= <andreas.mueller@ost.ch>
Date: Sun, 7 Mar 2021 22:34:49 +0100
Subject: euklidslide

---
 vorlesungen/slides/4/Makefile.inc   |  1 +
 vorlesungen/slides/4/chapter.tex    |  1 +
 vorlesungen/slides/4/euklidpoly.tex | 47 +++++++++++++++++++++++++++++++++++++
 vorlesungen/slides/test.tex         |  9 ++++---
 4 files changed, 53 insertions(+), 5 deletions(-)
 create mode 100644 vorlesungen/slides/4/euklidpoly.tex

diff --git a/vorlesungen/slides/4/Makefile.inc b/vorlesungen/slides/4/Makefile.inc
index 13de58c..2329e4a 100644
--- a/vorlesungen/slides/4/Makefile.inc
+++ b/vorlesungen/slides/4/Makefile.inc
@@ -14,6 +14,7 @@ chapter4 =								\
 	../slides/4/gauss.tex						\
 	../slides/4/dh.tex						\
 	../slides/4/divisionpoly.tex					\
+	../slides/4/euklidpoly.tex					\
 	../slides/4/polynomefp.tex					\
 	../slides/4/chapter.tex
 
diff --git a/vorlesungen/slides/4/chapter.tex b/vorlesungen/slides/4/chapter.tex
index 84b1f8f..830537e 100644
--- a/vorlesungen/slides/4/chapter.tex
+++ b/vorlesungen/slides/4/chapter.tex
@@ -12,4 +12,5 @@
 \folie{4/gauss.tex}
 \folie{4/dh.tex}
 \folie{4/divisionpoly.tex}
+\folie{4/euklidpoly.tex}
 \folie{4/polynomefp.tex}
diff --git a/vorlesungen/slides/4/euklidpoly.tex b/vorlesungen/slides/4/euklidpoly.tex
new file mode 100644
index 0000000..432b6b4
--- /dev/null
+++ b/vorlesungen/slides/4/euklidpoly.tex
@@ -0,0 +1,47 @@
+%
+% euklidpoly.tex
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\begin{frame}[t]
+\setlength{\abovedisplayskip}{5pt}
+\setlength{\belowdisplayskip}{5pt}
+\frametitle{Euklidischer Algorithmus in $\mathbb{F}_2[X]$}
+Gegeben: $m(X)=X^4+X+1$, $b(X) = {\color{blue}X^2+1}$
+\\
+\uncover<2->{Berechne $s,t\in\mathbb{F}_2[X]$ derart, dass $sm+tb=1$}
+\uncover<3->{%
+\begin{center}
+\begin{tabular}{|>{$}c<{$}|>{$}c<{$}>{$}c<{$}|>{$}c<{$}|>{$}c<{$}|>{$}c<{$}>{$}c<{$}|}
+\hline
+k&    a_k&  b_k&  q_k&r_k&  c_k&    d_k\\
+\hline
+ &       &     &     &   &    1&      0\\
+0&X^4+X+1&{\color{blue}X^2+1}&\uncover<4->{X^2+1}&\uncover<4->{X}&    0&      1\\
+1&\uncover<5->{X^2+1 }&\uncover<5->{X}&\uncover<5->{X}&\uncover<5->{1}&\uncover<5->{1}&\uncover<5->{X^2+1}\\
+2&\uncover<6->{X     }&\uncover<6->{1}&\uncover<6->{X}&\uncover<6->{0}&\uncover<6->{{\color{red}X}}&\uncover<6->{{\color{red}X^3+X+1}}\\
+3&\uncover<7->{1     }&\uncover<7->{0}&&&\uncover<7->{X^2+1}&\uncover<7->{X^4+X+1} \\
+\hline
+\end{tabular}
+\end{center}}
+\ifthenelse{\boolean{presentation}}{
+\only<8->{%
+\begin{block}{Kontrolle}
+\vspace{-10pt}
+\begin{align*}
+{\color{red}X}\cdot (X^4+X+1) + ({\color{red}X^3+X+1})({\color{blue}X^2+1})
+&\uncover<9->{=
+(X^5+X^2+X)}\\
+&\qquad \uncover<10->{+ (X^5+X^3+X^2+X^3+X+1)}
+\\
+&\uncover<11->{=(X^5+X^2+X) + (X^5+X^2+X+1)}
+\\
+&\uncover<12->{=1}
+\end{align*}
+\end{block}}}{}
+\begin{block}{Rechenregeln in $\mathbb{F}_2$}
+$1+1=0$,
+$2=0$, $+1=-1$.
+\end{block}
+
+\end{frame}
diff --git a/vorlesungen/slides/test.tex b/vorlesungen/slides/test.tex
index 2df5421..b7b696a 100644
--- a/vorlesungen/slides/test.tex
+++ b/vorlesungen/slides/test.tex
@@ -26,17 +26,16 @@
 
 %\folie{4/ggt.tex}
 %\folie{4/euklidmatrix.tex}
-%\folie{4/euklidbeispiel.tex}
-%\folie{4/euklidtabelle.tex}
+\folie{4/euklidbeispiel.tex}
+\folie{4/euklidtabelle.tex}
 %\folie{4/fp.tex}
 %\folie{4/division.tex}
 %\folie{4/gauss.tex}
 % \folie{4/dh.tex}
 % XXX \folie{4/frobenius.tex}
 
-\folie{4/divisionpoly.tex}
-% XXX \folie{4/ggtpoly.tex}
-% XXX \folie{4/euklidpoly.tex}
+%\folie{4/divisionpoly.tex}
+\folie{4/euklidpoly.tex}
 %\folie{4/polynomefp.tex}
 
 % XXX \folie{4/f2.tex}
-- 
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