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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/polynome.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/polynome.tex | 22 |
1 files changed, 21 insertions, 1 deletions
diff --git a/vorlesungen/slides/3/polynome.tex b/vorlesungen/slides/3/polynome.tex index 6ca0009..161a4ed 100644 --- a/vorlesungen/slides/3/polynome.tex +++ b/vorlesungen/slides/3/polynome.tex @@ -3,7 +3,27 @@ % % (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule % -\begin{frame} +\begin{frame}[t] \frametitle{Polynome} +$R$ ein Ring, z.~B.~$\mathbb{Z}$, $\mathbb{Q}$, $\mathbb{R}$ + +\begin{definition} +Polynome in $X$ mit Koeffizienten in $R$: +\[ +R[X] += +\{ +a(X)\;|\; +a(X) = a_nX^n+a_{n-1}X^{n-1} + \dots a_2X^2+a_1X + a_0, a_k\in R +\} +\] +\end{definition} + +\begin{itemize} +\item {\em Grad} des Polynoms: $\deg a(X) = \deg a = n$ +\item $\deg 0 = -\infty$ +\item {\em normiertes Polynom}: $a_n=1$ +\end{itemize} + \end{frame} |