From cddeab74130c3814acd49c8ac7d03041b2a7b85d Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Andreas=20M=C3=BCller?= <andreas.mueller@ost.ch>
Date: Sun, 28 Feb 2021 22:37:26 +0100
Subject: add new slides
---
vorlesungen/slides/3/division2.tex | 32 ++++++++++++++++++++++++++++++++
1 file changed, 32 insertions(+)
create mode 100644 vorlesungen/slides/3/division2.tex
(limited to 'vorlesungen/slides/3/division2.tex')
diff --git a/vorlesungen/slides/3/division2.tex b/vorlesungen/slides/3/division2.tex
new file mode 100644
index 0000000..80d6a75
--- /dev/null
+++ b/vorlesungen/slides/3/division2.tex
@@ -0,0 +1,32 @@
+%
+% division2.tex
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\begin{frame}[t]
+\frametitle{Division in $\Bbbk[X]$}
+\vspace{-5pt}
+\begin{block}{Aufgabe}
+Finde Quotienten und Rest der Polynome
+$a(X) = X^4-X^3-7X^2+X+6$
+und
+$b(X) = 2X^2+X+1$
+\end{block}
+\begin{block}{Lösung}
+\[
+\arraycolsep=1.4pt
+\renewcommand{\arraystretch}{1.2}
+\begin{array}{rcrcrcrcrcrcrcrcrcrcr}
+X^4&-& X^3&-& 7X^2&+& X&+& 6&:&2X^2&+&X&+&1&=&\frac12X^2&-&\frac34X&-\frac{27}{8} = q\\
+\llap{$-($}X^4&+&\frac12X^3&+& \frac12X^2\rlap{$)$}& & & & & & & & & & & & & & & \\ \cline{1-5}
+ &-&\frac32X^3&-&\frac{15}2X^2&+& X& & & & & & & & & & & & & \\
+ &\llap{$-($}-&\frac32X^3&-&\frac{ 3}4X^2&-&\frac{ 3}4X\rlap{$)$}& & & & & & & & & & & & & \\\cline{2-7}
+ & & &-&\frac{27}4X^2&+&\frac{ 7}4X&+& 6& & & & & & & & & & & \\
+ & & &\llap{$-($}-&\frac{27}4X^2&-&\frac{27}8X&-&\frac{27}{8}\rlap{$)$}& & & & & & & & & & & \\\cline{4-9}
+ & & & & & &\frac{41}8X&+&\frac{75}{8}\rlap{$\mathstrut=r$}& & & & & & & & & & & \\
+\end{array}
+\]
+Funktioniert, weil man in $\Bbbk[X]$ immer normieren kann
+\end{block}
+
+\end{frame}
--
cgit v1.2.1
From 67addea9bf154558ca3bbc14703c2b0fef8fc60c Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Andreas=20M=C3=BCller?= <andreas.mueller@ost.ch>
Date: Mon, 1 Mar 2021 08:18:59 +0100
Subject: phases, typos
---
vorlesungen/slides/3/division2.tex | 18 ++++++++++--------
1 file changed, 10 insertions(+), 8 deletions(-)
(limited to 'vorlesungen/slides/3/division2.tex')
diff --git a/vorlesungen/slides/3/division2.tex b/vorlesungen/slides/3/division2.tex
index 80d6a75..0602598 100644
--- a/vorlesungen/slides/3/division2.tex
+++ b/vorlesungen/slides/3/division2.tex
@@ -12,21 +12,23 @@ $a(X) = X^4-X^3-7X^2+X+6$
und
$b(X) = 2X^2+X+1$
\end{block}
+\uncover<2->{%
\begin{block}{Lösung}
+\vspace{-15pt}
\[
\arraycolsep=1.4pt
\renewcommand{\arraystretch}{1.2}
\begin{array}{rcrcrcrcrcrcrcrcrcrcr}
-X^4&-& X^3&-& 7X^2&+& X&+& 6&:&2X^2&+&X&+&1&=&\frac12X^2&-&\frac34X&-\frac{27}{8} = q\\
-\llap{$-($}X^4&+&\frac12X^3&+& \frac12X^2\rlap{$)$}& & & & & & & & & & & & & & & \\ \cline{1-5}
- &-&\frac32X^3&-&\frac{15}2X^2&+& X& & & & & & & & & & & & & \\
- &\llap{$-($}-&\frac32X^3&-&\frac{ 3}4X^2&-&\frac{ 3}4X\rlap{$)$}& & & & & & & & & & & & & \\\cline{2-7}
- & & &-&\frac{27}4X^2&+&\frac{ 7}4X&+& 6& & & & & & & & & & & \\
- & & &\llap{$-($}-&\frac{27}4X^2&-&\frac{27}8X&-&\frac{27}{8}\rlap{$)$}& & & & & & & & & & & \\\cline{4-9}
- & & & & & &\frac{41}8X&+&\frac{75}{8}\rlap{$\mathstrut=r$}& & & & & & & & & & & \\
+\llap{$($}X^4&-& X^3&-& 7X^2&+& X&+& 6\rlap{$)$}&\mathstrut\;:\mathstrut&(2X^2&+&X&+&1)&=&\uncover<3->{\frac12X^2}&\uncover<7->{-&\frac34X}&\uncover<11->{-\frac{27}{8}} = q\\
+\uncover<4->{\llap{$-($}X^4&+&\frac12X^3&+& \frac12X^2\rlap{$)$}}& & & & & & & & & & & & & & & \\
+ &\uncover<5->{-&\frac32X^3&-&\frac{15}2X^2}&\uncover<6->{+& X}& & & & & & & & & & & & & \\
+ &\uncover<8->{\llap{$-($}-&\frac32X^3&-&\frac{ 3}4X^2&-&\frac{ 3}4X\rlap{$)$}}& & & & & & & & & & & & & \\
+ & & &\uncover<9->{-&\frac{27}4X^2&+&\frac{ 7}4X}&\uncover<10->{+& 6}& & & & & & & & & & & \\
+ & & &\uncover<12->{\llap{$-($}-&\frac{27}4X^2&-&\frac{27}8X&-&\frac{27}{8}\rlap{$)$}}& & & & & & & & & & & \\
+ & & & & & &\uncover<13->{\frac{41}8X&+&\frac{75}{8}\rlap{$\mathstrut=r$}}& & & & & & & & & & & \\
\end{array}
\]
Funktioniert, weil man in $\Bbbk[X]$ immer normieren kann
-\end{block}
+\end{block}}
\end{frame}
--
cgit v1.2.1