phases, typos

6 files changed, 28 insertions, 20 deletions

diff --git a/vorlesungen/slides/3/Makefile.inc b/vorlesungen/slides/3/Makefile.inc
index ac2c3a5..3a55274 100644
--- a/vorlesungen/slides/3/Makefile.inc
+++ b/vorlesungen/slides/3/Makefile.inc
@@ -6,6 +6,7 @@
 #
 chapter3 =								\
 	../slides/3/motivation.tex					\
+	../slides/3/inverse.tex						\
 	../slides/3/polynome.tex					\
 	../slides/3/division.tex					\
 	../slides/3/division2.tex					\
diff --git a/vorlesungen/slides/3/chapter.tex b/vorlesungen/slides/3/chapter.tex
index 672b05a..e63002c 100644
--- a/vorlesungen/slides/3/chapter.tex
+++ b/vorlesungen/slides/3/chapter.tex
@@ -4,6 +4,7 @@
 % (c) 2021 Prof Dr Andreas Müller, Hochschule Rapperswi
 %
 \folie{3/motivation.tex}
+\folie{3/inverse.tex}
 \folie{3/polynome.tex}
 \folie{3/division.tex}
 \folie{3/division2.tex}
@@ -15,6 +16,7 @@
 \folie{3/maximalergrad.tex}
 \folie{3/minimalbeispiel.tex}
 \folie{3/minimalpolynom.tex}
+\folie{3/drehmatrix.tex}
 \folie{3/drehfaktorisierung.tex}
 \folie{3/operatoren.tex}
 \folie{3/adjunktion.tex}
diff --git a/vorlesungen/slides/3/division.tex b/vorlesungen/slides/3/division.tex
index 0932f48..94df27b 100644
--- a/vorlesungen/slides/3/division.tex
+++ b/vorlesungen/slides/3/division.tex
@@ -11,19 +11,22 @@ $a= X^4- X^3-7X^2+ X+6\in\mathbb{Z}[X]$
 und
 $b= X^2+X+1\in\mathbb{Z}[X]$
 \end{block}
+\uncover<2->{%
 \begin{block}{Lösung}
 \[
 \arraycolsep=1.4pt
 \begin{array}{rcrcrcrcrcrcrcrcrcrcr}
-X^4&-& X^3&-&7X^2&+& X&+&6&:&X^2&+&X&+&1&=&X^2&-&2X&-&6=q\\
-\llap{$-($}X^4&+& X^3&+& X^2\rlap{$)$}& &  & & & &   & & & & & &   & &  & & \\ \cline{1-5}
-   &-&2X^3&-&8X^2&+& X& & & &   & & & & & &   & &  & & \\
-   &\llap{$-($}-&2X^3&-&2X^2&-&2X\rlap{$)$}& & & &   & & & & & &   & &  & & \\ \cline{2-7}
-   & &    &-&6X^2&+&3X&+&6& &   & & & & & &   & &  & & \\
-   & &    &\llap{$-($}-&6X^2&-&6X&-&6\rlap{$)$}& &   & & & & & &   & &  & & \\ \cline{4-9}
-   & &    & &    & &9X&+&12\rlap{$\mathstrut=r$}& &   & & & & & &   & &  & & \\ \cline{7-9}
+\llap{$($}X^4&-& X^3&-&7X^2&+& X&+&6\rlap{$)$}&\;\mathstrut:\mathstrut&(X^2&+&X&+&1)&=&\uncover<3->{X^2}&\uncover<7->{-&2X}&\uncover<11->{-&6}=q\\
+\uncover<4->{\llap{$-($}X^4&+& X^3&+& X^2\rlap{$)$}}& &  & & & &   & & & & & &   & &  & & \\ 
+   &\uncover<5->{-&2X^3&-&8X^2}&\uncover<6->{+& X}& & & &   & & & & & &   & &  & & \\
+   &\uncover<8->{\llap{$-($}-&2X^3&-&2X^2&-&2X\rlap{$)$}}& & & &   & & & & & &   & &  & & \\ 
+   & &    &\uncover<9->{-&6X^2&+&3X}&\uncover<10->{+&6}& &   & & & & & &   & &  & & \\
+   & &    &\uncover<12->{\llap{$-($}-&6X^2&-&6X&-&6\rlap{$)$}}& &   & & & & & &   & &  & & \\ 
+   & &    & &    & &\uncover<13->{9X&+&12\rlap{$\mathstrut=r$}}& &   & & & & & &   & &  & &
 \end{array}
 \]
+\uncover<14->{
 Funktioniert weil $b$ normiert ist!
-\end{block}
+}
+\end{block}}
 \end{frame}
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}
diff --git a/vorlesungen/slides/3/operatoren.tex b/vorlesungen/slides/3/operatoren.tex
index 20b7f3a..161c330 100644
--- a/vorlesungen/slides/3/operatoren.tex
+++ b/vorlesungen/slides/3/operatoren.tex
@@ -13,7 +13,7 @@ $a(X)=a_0+a_1X+\dots+a_nX^n$
 a(X)
 =
 \begin{pmatrix}
-a_0\\a_1\\a_2\\a_3\\\vdots\\a_nX^n
+a_0\\a_1\\a_2\\a_3\\\vdots\\a_n
 \end{pmatrix}
 \]
 \end{block}
diff --git a/vorlesungen/slides/3/polynome.tex b/vorlesungen/slides/3/polynome.tex
index 161a4ed..d7179a0 100644
--- a/vorlesungen/slides/3/polynome.tex
+++ b/vorlesungen/slides/3/polynome.tex
@@ -20,9 +20,9 @@ a(X) = a_nX^n+a_{n-1}X^{n-1} + \dots a_2X^2+a_1X + a_0, a_k\in R
 \end{definition}
 
 \begin{itemize}
-\item {\em Grad} des Polynoms: $\deg a(X) = \deg a = n$
-\item $\deg 0 = -\infty$
-\item {\em normiertes Polynom}: $a_n=1$
+\item<2-> {\em Grad} des Polynoms: $\deg a(X) = \deg a = n$
+\item<3-> $\deg 0 = -\infty$
+\item<4-> {\em normiertes Polynom}: $a_n=1$
 \end{itemize}