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Diffstat (limited to 'vorlesungen/slides/5/folgerungen.tex')
| -rw-r--r-- | vorlesungen/slides/5/folgerungen.tex | 62 |
1 files changed, 57 insertions, 5 deletions
diff --git a/vorlesungen/slides/5/folgerungen.tex b/vorlesungen/slides/5/folgerungen.tex index a1fa6bf..4a8dbe6 100644 --- a/vorlesungen/slides/5/folgerungen.tex +++ b/vorlesungen/slides/5/folgerungen.tex @@ -3,10 +3,14 @@ % % (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule % +\bgroup +\def\sx{1} +\definecolor{darkgreen}{rgb}{0,0.6,0} \begin{frame}[t] \frametitle{Folgerungen} +\vspace{-10pt} \begin{columns}[t] -\begin{column}{0.48\textwidth} +\begin{column}{0.30\textwidth} \begin{block}{Zunahme} Für alle $k<l$ gilt \begin{align*} @@ -23,10 +27,58 @@ Für $k\ge l$ gilt Ausserdem ist $l\le n$ \end{block} \end{column} -\begin{column}{0.48\textwidth} -\begin{proof}[Beweis] -XXX -\end{proof} +\begin{column}{0.66\textwidth} +\begin{center} +\begin{tikzpicture}[>=latex,thick] +\def\pfad{ + ({0*\sx},6) -- + ({1*\sx},4.5) -- + ({2*\sx},3.5) -- + ({3*\sx},2.9) -- + ({4*\sx},2.6) -- + ({5*\sx},2.4) -- + ({6*\sx},2.4) +} + +\fill[color=orange!20] \pfad -- ({6*\sx},0) -- (0,0) -- cycle; +\fill[color=darkgreen!20] \pfad -- ({6*\sx},6) -- cycle; +\fill[color=orange!40] ({5*\sx},0) rectangle ({6*\sx},2.4); +\fill[color=darkgreen!40] ({5*\sx},6) rectangle ({6*\sx},2.4); + +\draw[color=darkgreen,line width=2pt] ({3*\sx},6) -- ({3*\sx},2.9); +\node[color=darkgreen] at ({3*\sx},4.45) [rotate=90,above] {$\dim\mathcal{K}^k(A)$}; +\draw[color=orange,line width=2pt] ({3*\sx},0) -- ({3*\sx},2.9); +\node[color=orange] at ({3*\sx},1.45) [rotate=90,above] {$\dim\mathcal{J}^k(A)$}; + +\node[color=orange] at ({5.5*\sx},1.2) [rotate=90] {bijektiv}; +\node[color=darkgreen] at ({5.5*\sx},4.2) [rotate=90] {konstant}; + +\fill ({0*\sx},6) circle[radius=0.08]; +\fill ({1*\sx},4.5) circle[radius=0.08]; +\fill ({2*\sx},3.5) circle[radius=0.08]; +\fill ({3*\sx},2.9) circle[radius=0.08]; +\fill ({4*\sx},2.6) circle[radius=0.08]; +\fill ({5*\sx},2.4) circle[radius=0.08]; +\fill ({6*\sx},2.4) circle[radius=0.08]; + +\draw \pfad; + +\draw[->] (-0.1,0) -- ({6*\sx+0.5},0) coordinate[label={$k$}]; +\draw[->] (-0.1,6) -- ({6*\sx+0.5},6); + +\foreach \x in {0,...,6}{ + \draw (\x,-0.05) -- (\x,0.05); +} +\foreach \x in {0,...,3}{ + \node at ({\x*\sx},-0.05) [below] {$\x$}; +} +\node at ({4*\sx},-0.05) [below] {$\dots\mathstrut$}; +\node at ({5*\sx},-0.05) [below] {$l$}; +\node at ({6*\sx},-0.05) [below] {$l+1$}; + +\end{tikzpicture} +\end{center} \end{column} \end{columns} \end{frame} +\egroup |