diff options
Diffstat (limited to 'vorlesungen/slides/3/division2.tex')
| -rw-r--r-- | vorlesungen/slides/3/division2.tex | 18 |
1 files changed, 10 insertions, 8 deletions
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} |