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author | Andreas Müller <andreas.mueller@ost.ch> | 2021-02-28 22:37:26 +0100 |
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committer | Andreas Müller <andreas.mueller@ost.ch> | 2021-02-28 22:37:26 +0100 |
commit | cddeab74130c3814acd49c8ac7d03041b2a7b85d (patch) | |
tree | b7fe6247083774badfd63e54467d2db340d23462 /vorlesungen/slides/3/division.tex | |
parent | typos (diff) | |
download | SeminarMatrizen-cddeab74130c3814acd49c8ac7d03041b2a7b85d.tar.gz SeminarMatrizen-cddeab74130c3814acd49c8ac7d03041b2a7b85d.zip |
add new slides
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-rw-r--r-- | vorlesungen/slides/3/division.tex | 29 |
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diff --git a/vorlesungen/slides/3/division.tex b/vorlesungen/slides/3/division.tex new file mode 100644 index 0000000..0932f48 --- /dev/null +++ b/vorlesungen/slides/3/division.tex @@ -0,0 +1,29 @@ +% +% division.tex +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\begin{frame}[t] +\frametitle{Polynomdivision} +\begin{block}{Aufgabe} +Finde Quotient und Rest für +$a= X^4- X^3-7X^2+ X+6\in\mathbb{Z}[X]$ +und +$b= X^2+X+1\in\mathbb{Z}[X]$ +\end{block} +\begin{block}{Lösung} +\[ +\arraycolsep=1.4pt +\begin{array}{rcrcrcrcrcrcrcrcrcrcr} +X^4&-& X^3&-&7X^2&+& X&+&6&:&X^2&+&X&+&1&=&X^2&-&2X&-&6=q\\ +\llap{$-($}X^4&+& X^3&+& X^2\rlap{$)$}& & & & & & & & & & & & & & & & \\ \cline{1-5} + &-&2X^3&-&8X^2&+& X& & & & & & & & & & & & & & \\ + &\llap{$-($}-&2X^3&-&2X^2&-&2X\rlap{$)$}& & & & & & & & & & & & & & \\ \cline{2-7} + & & &-&6X^2&+&3X&+&6& & & & & & & & & & & & \\ + & & &\llap{$-($}-&6X^2&-&6X&-&6\rlap{$)$}& & & & & & & & & & & & \\ \cline{4-9} + & & & & & &9X&+&12\rlap{$\mathstrut=r$}& & & & & & & & & & & & \\ \cline{7-9} +\end{array} +\] +Funktioniert weil $b$ normiert ist! +\end{block} +\end{frame} |