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Diffstat (limited to 'buch/chapters/110-elliptisch/images/ellall.tex')
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diff --git a/buch/chapters/110-elliptisch/images/ellall.tex b/buch/chapters/110-elliptisch/images/ellall.tex new file mode 100644 index 0000000..b37fe12 --- /dev/null +++ b/buch/chapters/110-elliptisch/images/ellall.tex @@ -0,0 +1,215 @@ +% +% ellpolnul.tex -- template for standalon tikz images +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{amsmath} +\usepackage{times} +\usepackage{txfonts} +\usepackage{pgfplots} +\usepackage{csvsimple} +\usetikzlibrary{arrows,intersections,math,calc} +\begin{document} +\input{ellcommon.tex} +\def\skala{1} +\begin{tikzpicture}[>=latex,thick,scale=\skala] + +%\draw (-1,-1) rectangle (1,1); +%\node at (-1,-1) [below left] {$0$}; +%\node at (1,-1) [below right] {$K$}; +%\node at (1,1) [above right] {$K+iK'$}; +%\node at (-1,1) [above left] {$iK'$}; +%\node at (0,0) {$u$}; + +\fill[color=rot!10,opacity=0.5] (-5.5,-4.3) rectangle (7.3,-1.7); +\fill[color=blau!10,opacity=0.5] (-5.5,-7.3) rectangle (7.3,-4.7); +\fill[color=gruen!10,opacity=0.5] (-5.5,-10.3) rectangle (7.3,-7.7); + +\fill[color=rot!10,opacity=0.5] (-1.3,-10.5) rectangle (1.3,2.5); +\fill[color=blau!10,opacity=0.5] (1.7,-10.5) rectangle (4.3,2.5); +\fill[color=gruen!10,opacity=0.5] (4.7,-10.5) rectangle (7.3,2.5); + +\begin{scope}[xshift=1.5cm,yshift=2cm] +\node at (0,0) {Zähler}; +\draw[<-] (-4.5,0) -- (-1,0); +\draw[->] (1,0) -- (4.5,0); +\node[color=black] at (-4.5,-0.4) {\Large n}; +\node[color=rot] at (-1.5,-0.4) {\Large s}; +\node[color=blau] at (1.5,-0.4) {\Large c}; +\node[color=gruen] at (4.5,-0.4) {\Large d}; +\end{scope} + +\begin{scope}[xshift=-5.1cm,yshift=-4.5cm] +\node at (0,0) [rotate=90] {Nenner}; +\draw[<-] (0,-4.5) -- (0,-1); +\draw[->] (0,1) -- (0,4.5); +\node[color=gruen] at (0.4,-4.5) [rotate=90] {\Large d}; +\node[color=blau] at (0.4,-1.5) [rotate=90] {\Large c}; +\node[color=rot] at (0.4,1.5) [rotate=90] {\Large s}; +\node[color=black] at (0.4,4.5) [rotate=90] {\Large n}; +\end{scope} + +\begin{scope}[xshift=-3cm,yshift=0cm] +\node at (0,0) {$1$}; +\draw[color=gray!20] (-1,-1) rectangle (1,1); +\end{scope} + +\definecolor{sccolor}{rgb}{0.8,0.0,1.0} +\definecolor{sdcolor}{rgb}{0.6,0.6,0.0} +\definecolor{cdcolor}{rgb}{0.0,0.6,1.0} + +\begin{scope}[xshift=0cm] +\rechteck{rot}{\operatorname{sn}(u,k)} +\nullstelle{(-1,-1)}{rot} +\pol{(-1,1)}{rot} +\node at (-1,-1) {$0$}; +\node at (1,-1) {$1$}; +\node at (1,1) {$\frac1k$}; +\node at (-1,1) {$\infty$}; +\end{scope} + +\begin{scope}[xshift=3cm] +\rechteck{blau}{\operatorname{cn}(u,k)} +\nullstelle{(1,-1)}{blau} +\pol{(-1,1)}{blau} +\node at (-1,-1) {$1$}; +\node at (1,-1) {$0$}; +\node at (1,1) {$\frac{k'}{ik}$}; +\node at (-1,1) {$\infty$}; +\end{scope} + +\begin{scope}[xshift=6cm] +\rechteck{gruen}{\operatorname{dn}(u,k)} +\nullstelle{(1,1)}{gruen} +\pol{(-1,1)}{gruen} +\node at (-1,-1) {$1$}; +\node at (1,-1) {$k'$}; +\node at (1,1) {$0$}; +\node at (-1,1) {$\infty$}; +\end{scope} + +% +% start row with denominator sn(u,k) +% + +\begin{scope}[xshift=-3cm,yshift=-3cm] +\rechteck{rot}{\operatorname{ns}(u,k)} +\pol{(-1,-1)}{rot} +\nullstelle{(-1,1)}{rot} +\node at (-1,-1) {$\infty$}; +\node at (1,-1) {$1$}; +\node at (1,1) {$k$}; +\node at (-1,1) {$0$}; +\end{scope} + +\begin{scope}[xshift=0cm,yshift=-3cm] +%\rechteck{gray}{1} +\fill[color=white] (-1,-1) rectangle (1,1); +\node[color=gray] at (0,0) {$1$}; +\end{scope} + +\begin{scope}[xshift=3cm,yshift=-3cm] +\rechteck{sccolor}{\operatorname{cs}(u,k)} +\pol{(-1,-1)}{sccolor} +\nullstelle{(1,-1)}{sccolor} +\node at (-1,-1) {$\infty$}; +\node at (1,-1) {$0$}; +\node at (1,1) {$\frac{k'}{i}$}; +\node at (-1,1) {$ $}; +\end{scope} + +\begin{scope}[xshift=6cm,yshift=-3cm] +\rechteck{sdcolor}{\operatorname{ds}(u,k)} +\pol{(-1,-1)}{sdcolor} +\nullstelle{(1,1)}{sdcolor} +\node at (-1,-1) {$\infty$}; +\node at (1,-1) {$k'$}; +\node at (1,1) {$0$}; +\node at (-1,1) {$ $}; +\end{scope} + +% +% start row with denominator cn(u,k) +% + +\begin{scope}[xshift=-3cm,yshift=-6cm] +\rechteck{blau}{\operatorname{nc}(u,k)} +\pol{(1,-1)}{blau} +\nullstelle{(-1,1)}{blau} +\node at (-1,-1) {$1$}; +\node at (-1,1) {$0$}; +\node at (1,-1) {$\infty$}; +\node at (1,1) {$\frac{ik}{k'}$}; +\end{scope} + +\begin{scope}[xshift=0cm,yshift=-6cm] +\rechteck{sccolor}{\operatorname{sc}(u,k)} +\nullstelle{(-1,-1)}{sccolor} +\pol{(1,-1)}{sccolor} +\node at (-1,-1) {$0$}; +\node at (1,-1) {$\infty$}; +\node at (-1,1) {$ $}; +\node at (1,1) {$\frac{i}{k'}$}; +\end{scope} + +\begin{scope}[xshift=3cm,yshift=-6cm] +%\rechteck{gray}{1} +\fill[color=white] (-1,-1) rectangle (1,1); +\node[color=gray] at (0,0) {$1$}; +\end{scope} + +\begin{scope}[xshift=6cm,yshift=-6cm] +\rechteck{cdcolor}{\operatorname{dc}(u,k)} +\nullstelle{(1,1)}{cdcolor} +\pol{(1,-1)}{cdcolor} +\node at (-1,-1) {$1$}; +\node at (1,-1) {$\infty$}; +\node at (-1,1) {$k$}; +\node at (1,1) {$0$}; +\end{scope} + +% +% start row with denominator dn(u,k) +% + +\begin{scope}[xshift=-3cm,yshift=-9cm] +\rechteck{gruen}{\operatorname{nd}(u,k)} +\pol{(1,1)}{gruen} +\nullstelle{(-1,1)}{gruen} +\node at (-1,-1) {$1$}; +\node at (-1,1) {$0$}; +\node at (1,-1) {$\frac{1}{k'}$}; +\node at (1,1) {$\infty$}; +\end{scope} + +\begin{scope}[xshift=0cm,yshift=-9cm] +\rechteck{sdcolor}{\operatorname{sd}(u,k)} +\nullstelle{(-1,-1)}{sdcolor} +\pol{(1,1)}{sdcolor} +\node at (-1,-1) {$0$}; +\node at (1,-1) {$\frac{1}{k'}$}; +\node at (-1,1) {$ $}; +\node at (1,1) {$\infty$}; +\end{scope} + +\begin{scope}[xshift=3cm,yshift=-9cm] +\rechteck{cdcolor}{\operatorname{cd}(u,k)} +\pol{(1,1)}{cdcolor} +\nullstelle{(1,-1)}{cdcolor} +\node at (-1,-1) {$1$}; +\node at (-1,1) {$\frac1k $}; +\node at (1,-1) {$0$}; +\node at (1,1) {$\infty$}; +\end{scope} + +\begin{scope}[xshift=6cm,yshift=-9cm] +%\rechteck{gray}{1} +\fill[color=white] (-1,-1) rectangle (1,1); +\node[color=gray] at (0,0) {$1$}; +\end{scope} + + +\end{tikzpicture} +\end{document} + |