diff options
Diffstat (limited to 'vorlesungen/slides/3/division.tex')
| -rw-r--r-- | vorlesungen/slides/3/division.tex | 19 |
1 files changed, 11 insertions, 8 deletions
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} |