diff options
Diffstat (limited to 'vorlesungen/slides')
| -rw-r--r-- | vorlesungen/slides/3/Makefile.inc | 1 | ||||
| -rw-r--r-- | vorlesungen/slides/3/chapter.tex | 2 | ||||
| -rw-r--r-- | vorlesungen/slides/3/division.tex | 19 | ||||
| -rw-r--r-- | vorlesungen/slides/3/division2.tex | 18 | ||||
| -rw-r--r-- | vorlesungen/slides/3/operatoren.tex | 2 | ||||
| -rw-r--r-- | vorlesungen/slides/3/polynome.tex | 6 | ||||
| -rw-r--r-- | vorlesungen/slides/test.tex | 25 |
7 files changed, 41 insertions, 32 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} diff --git a/vorlesungen/slides/test.tex b/vorlesungen/slides/test.tex index 24d9ffa..3c0348f 100644 --- a/vorlesungen/slides/test.tex +++ b/vorlesungen/slides/test.tex @@ -4,18 +4,19 @@ % (c) 2019 Prof Dr Andreas Müller, Hochschule Rapperswil % -%\folie{3/motivation.tex} -%\folie{3/polynome.tex} -%\folie{3/division.tex} -%\folie{3/division2.tex} -%\folie{3/ringstruktur.tex} -%\folie{3/teilbarkeit.tex} -%\folie{3/faktorisierung.tex} -%\folie{3/faktorzerlegung.tex} -%\folie{3/einsetzen.tex} -%\folie{3/maximalergrad.tex} -%\folie{3/minimalbeispiel.tex} -%\folie{3/minimalpolynom.tex} +\folie{3/motivation.tex} +\folie{3/inverse.tex} +\folie{3/polynome.tex} +\folie{3/division.tex} +\folie{3/division2.tex} +\folie{3/ringstruktur.tex} +\folie{3/teilbarkeit.tex} +\folie{3/faktorisierung.tex} +\folie{3/faktorzerlegung.tex} +\folie{3/einsetzen.tex} +\folie{3/maximalergrad.tex} +\folie{3/minimalbeispiel.tex} +\folie{3/minimalpolynom.tex} \folie{3/drehmatrix.tex} \folie{3/drehfaktorisierung.tex} \folie{3/operatoren.tex} |