<html><head><meta name="color-scheme" content="light dark"></head><body><pre style="word-wrap: break-word; white-space: pre-wrap;">From cddeab74130c3814acd49c8ac7d03041b2a7b85d Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Andreas=20M=C3=BCller?= &lt;andreas.mueller@ost.ch&gt;
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}
+\[
+\arraycolsep=1.4pt
+\renewcommand{\arraystretch}{1.2}
+\begin{array}{rcrcrcrcrcrcrcrcrcrcr}
+X^4&amp;-&amp;       X^3&amp;-&amp;         7X^2&amp;+&amp;          X&amp;+&amp;           6&amp;:&amp;2X^2&amp;+&amp;X&amp;+&amp;1&amp;=&amp;\frac12X^2&amp;-&amp;\frac34X&amp;-\frac{27}{8} = q\\
+\llap{$-($}X^4&amp;+&amp;\frac12X^3&amp;+&amp;   \frac12X^2\rlap{$)$}&amp; &amp;           &amp; &amp;            &amp; &amp;    &amp; &amp; &amp; &amp; &amp; &amp;          &amp; &amp;        &amp;             \\ \cline{1-5}
+   &amp;-&amp;\frac32X^3&amp;-&amp;\frac{15}2X^2&amp;+&amp;          X&amp; &amp;            &amp; &amp;    &amp; &amp; &amp; &amp; &amp; &amp;          &amp; &amp;        &amp;             \\
+   &amp;\llap{$-($}-&amp;\frac32X^3&amp;-&amp;\frac{ 3}4X^2&amp;-&amp;\frac{ 3}4X\rlap{$)$}&amp; &amp;            &amp; &amp;    &amp; &amp; &amp; &amp; &amp; &amp;          &amp; &amp;        &amp;             \\\cline{2-7}
+   &amp; &amp;          &amp;-&amp;\frac{27}4X^2&amp;+&amp;\frac{ 7}4X&amp;+&amp;           6&amp; &amp;    &amp; &amp; &amp; &amp; &amp; &amp;          &amp; &amp;        &amp;             \\
+   &amp; &amp;          &amp;\llap{$-($}-&amp;\frac{27}4X^2&amp;-&amp;\frac{27}8X&amp;-&amp;\frac{27}{8}\rlap{$)$}&amp; &amp;    &amp; &amp; &amp; &amp; &amp; &amp;          &amp; &amp;        &amp;             \\\cline{4-9}
+   &amp; &amp;          &amp; &amp;             &amp; &amp;\frac{41}8X&amp;+&amp;\frac{75}{8}\rlap{$\mathstrut=r$}&amp; &amp;    &amp; &amp; &amp; &amp; &amp; &amp;          &amp; &amp;        &amp;             \\
+\end{array}
+\]
+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?= &lt;andreas.mueller@ost.ch&gt;
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&lt;2-&gt;{%
 \begin{block}{Lösung}
+\vspace{-15pt}
 \[
 \arraycolsep=1.4pt
 \renewcommand{\arraystretch}{1.2}
 \begin{array}{rcrcrcrcrcrcrcrcrcrcr}
-X^4&amp;-&amp;       X^3&amp;-&amp;         7X^2&amp;+&amp;          X&amp;+&amp;           6&amp;:&amp;2X^2&amp;+&amp;X&amp;+&amp;1&amp;=&amp;\frac12X^2&amp;-&amp;\frac34X&amp;-\frac{27}{8} = q\\
-\llap{$-($}X^4&amp;+&amp;\frac12X^3&amp;+&amp;   \frac12X^2\rlap{$)$}&amp; &amp;           &amp; &amp;            &amp; &amp;    &amp; &amp; &amp; &amp; &amp; &amp;          &amp; &amp;        &amp;             \\ \cline{1-5}
-   &amp;-&amp;\frac32X^3&amp;-&amp;\frac{15}2X^2&amp;+&amp;          X&amp; &amp;            &amp; &amp;    &amp; &amp; &amp; &amp; &amp; &amp;          &amp; &amp;        &amp;             \\
-   &amp;\llap{$-($}-&amp;\frac32X^3&amp;-&amp;\frac{ 3}4X^2&amp;-&amp;\frac{ 3}4X\rlap{$)$}&amp; &amp;            &amp; &amp;    &amp; &amp; &amp; &amp; &amp; &amp;          &amp; &amp;        &amp;             \\\cline{2-7}
-   &amp; &amp;          &amp;-&amp;\frac{27}4X^2&amp;+&amp;\frac{ 7}4X&amp;+&amp;           6&amp; &amp;    &amp; &amp; &amp; &amp; &amp; &amp;          &amp; &amp;        &amp;             \\
-   &amp; &amp;          &amp;\llap{$-($}-&amp;\frac{27}4X^2&amp;-&amp;\frac{27}8X&amp;-&amp;\frac{27}{8}\rlap{$)$}&amp; &amp;    &amp; &amp; &amp; &amp; &amp; &amp;          &amp; &amp;        &amp;             \\\cline{4-9}
-   &amp; &amp;          &amp; &amp;             &amp; &amp;\frac{41}8X&amp;+&amp;\frac{75}{8}\rlap{$\mathstrut=r$}&amp; &amp;    &amp; &amp; &amp; &amp; &amp; &amp;          &amp; &amp;        &amp;             \\
+\llap{$($}X^4&amp;-&amp;       X^3&amp;-&amp;         7X^2&amp;+&amp;          X&amp;+&amp;           6\rlap{$)$}&amp;\mathstrut\;:\mathstrut&amp;(2X^2&amp;+&amp;X&amp;+&amp;1)&amp;=&amp;\uncover&lt;3-&gt;{\frac12X^2}&amp;\uncover&lt;7-&gt;{-&amp;\frac34X}&amp;\uncover&lt;11-&gt;{-\frac{27}{8}} = q\\
+\uncover&lt;4-&gt;{\llap{$-($}X^4&amp;+&amp;\frac12X^3&amp;+&amp;   \frac12X^2\rlap{$)$}}&amp; &amp;           &amp; &amp;            &amp; &amp;    &amp; &amp; &amp; &amp; &amp; &amp;          &amp; &amp;        &amp;             \\
+   &amp;\uncover&lt;5-&gt;{-&amp;\frac32X^3&amp;-&amp;\frac{15}2X^2}&amp;\uncover&lt;6-&gt;{+&amp;          X}&amp; &amp;            &amp; &amp;    &amp; &amp; &amp; &amp; &amp; &amp;          &amp; &amp;        &amp;             \\
+   &amp;\uncover&lt;8-&gt;{\llap{$-($}-&amp;\frac32X^3&amp;-&amp;\frac{ 3}4X^2&amp;-&amp;\frac{ 3}4X\rlap{$)$}}&amp; &amp;            &amp; &amp;    &amp; &amp; &amp; &amp; &amp; &amp;          &amp; &amp;        &amp;             \\
+   &amp; &amp;          &amp;\uncover&lt;9-&gt;{-&amp;\frac{27}4X^2&amp;+&amp;\frac{ 7}4X}&amp;\uncover&lt;10-&gt;{+&amp;           6}&amp; &amp;    &amp; &amp; &amp; &amp; &amp; &amp;          &amp; &amp;        &amp;             \\
+   &amp; &amp;          &amp;\uncover&lt;12-&gt;{\llap{$-($}-&amp;\frac{27}4X^2&amp;-&amp;\frac{27}8X&amp;-&amp;\frac{27}{8}\rlap{$)$}}&amp; &amp;    &amp; &amp; &amp; &amp; &amp; &amp;          &amp; &amp;        &amp;             \\
+   &amp; &amp;          &amp; &amp;             &amp; &amp;\uncover&lt;13-&gt;{\frac{41}8X&amp;+&amp;\frac{75}{8}\rlap{$\mathstrut=r$}}&amp; &amp;    &amp; &amp; &amp; &amp; &amp; &amp;          &amp; &amp;        &amp;             \\
 \end{array}
 \]
 Funktioniert, weil man in $\Bbbk[X]$ immer normieren kann
-\end{block}
+\end{block}}
 
 \end{frame}
-- 
cgit v1.2.1

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