From 17f90bd131bdf24110d8933fd804413d53e17bc5 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Andreas=20M=C3=BCller?= <andreas.mueller@othello.ch>
Date: Wed, 22 Jun 2022 13:07:36 +0200
Subject: add graph for all functions

---
 buch/chapters/110-elliptisch/images/ellall.tex | 148 +++++++++++++++++++++++++
 1 file changed, 148 insertions(+)
 create mode 100644 buch/chapters/110-elliptisch/images/ellall.tex

(limited to 'buch/chapters/110-elliptisch/images/ellall.tex')

diff --git a/buch/chapters/110-elliptisch/images/ellall.tex b/buch/chapters/110-elliptisch/images/ellall.tex
new file mode 100644
index 0000000..5d63322
--- /dev/null
+++ b/buch/chapters/110-elliptisch/images/ellall.tex
@@ -0,0 +1,148 @@
+%
+% 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) {$u$};
+
+\begin{scope}[xshift=-3cm,yshift=0cm]
+\rechteck{gray}{1}
+\end{scope}
+
+\definecolor{sccolor}{rgb}{0.8,0.2,0.8}
+\definecolor{sdcolor}{rgb}{0.8,0.8,0.2}
+\definecolor{cdcolor}{rgb}{0.2,0.8,0.8}
+
+\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) {$\frac{ik'}k$};
+\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}
+\end{scope}
+
+\begin{scope}[xshift=0cm,yshift=-3cm]
+\rechteck{gray}{1}
+\end{scope}
+
+\begin{scope}[xshift=3cm,yshift=-3cm]
+\rechteck{sccolor}{\operatorname{cs}(u,k)}
+\pol{(1,-1)}{sccolor}
+\nullstelle{(-1,-1)}{sccolor}
+\end{scope}
+
+\begin{scope}[xshift=6cm,yshift=-3cm]
+\rechteck{sdcolor}{\operatorname{ds}(u,k)}
+\pol{(-1,1)}{sdcolor}
+\nullstelle{(-1,-1)}{sdcolor}
+\nullstelle{(1,1)}{sdcolor}
+\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}
+\end{scope}
+
+\begin{scope}[xshift=0cm,yshift=-6cm]
+\rechteck{sccolor}{\operatorname{sc}(u,k)}
+\nullstelle{(1,-1)}{sccolor}
+\pol{(-1,-1)}{sccolor}
+\end{scope}
+
+\begin{scope}[xshift=3cm,yshift=-6cm]
+\rechteck{gray}{1}
+\end{scope}
+
+\begin{scope}[xshift=6cm,yshift=-6cm]
+\rechteck{cdcolor}{\operatorname{dc}(u,k)}
+\nullstelle{(1,1)}{cdcolor}
+\nullstelle{(1,-1)}{cdcolor}
+\pol{(-1,1)}{cdcolor}
+\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}
+\end{scope}
+
+\begin{scope}[xshift=0cm,yshift=-9cm]
+\rechteck{sdcolor}{\operatorname{sd}(u,k)}
+\nullstelle{(-1,1)}{sdcolor}
+\pol{(-1,-1)}{sdcolor}
+\pol{(1,1)}{sdcolor}
+\end{scope}
+
+\begin{scope}[xshift=3cm,yshift=-9cm]
+\rechteck{cdcolor}{\operatorname{cd}(u,k)}
+\pol{(1,1)}{cdcolor}
+\pol{(1,-1)}{cdcolor}
+\nullstelle{(-1,1)}{cdcolor}
+\end{scope}
+
+\begin{scope}[xshift=6cm,yshift=-9cm]
+\rechteck{gray}{1}
+\end{scope}
+
+
+\end{tikzpicture}
+\end{document}
+
-- 
cgit v1.2.1


From 43a21e525fe5f9f2e81113ed84742c42178c7114 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Andreas=20M=C3=BCller?= <andreas.mueller@othello.ch>
Date: Wed, 22 Jun 2022 16:02:19 +0200
Subject: new images

---
 buch/chapters/110-elliptisch/images/ellall.tex | 28 ++++++++++++++++++++++++++
 1 file changed, 28 insertions(+)

(limited to 'buch/chapters/110-elliptisch/images/ellall.tex')

diff --git a/buch/chapters/110-elliptisch/images/ellall.tex b/buch/chapters/110-elliptisch/images/ellall.tex
index 5d63322..b694441 100644
--- a/buch/chapters/110-elliptisch/images/ellall.tex
+++ b/buch/chapters/110-elliptisch/images/ellall.tex
@@ -22,6 +22,34 @@
 %\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]
 \rechteck{gray}{1}
 \end{scope}
-- 
cgit v1.2.1


From 0a0f36f71e9dff9b9c87a66a669e0d2f388d21c6 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Andreas=20M=C3=BCller?= <andreas.mueller@ost.ch>
Date: Thu, 23 Jun 2022 19:23:58 +0200
Subject: poles and zeros

---
 buch/chapters/110-elliptisch/images/ellall.tex | 79 +++++++++++++++++++-------
 1 file changed, 59 insertions(+), 20 deletions(-)

(limited to 'buch/chapters/110-elliptisch/images/ellall.tex')

diff --git a/buch/chapters/110-elliptisch/images/ellall.tex b/buch/chapters/110-elliptisch/images/ellall.tex
index b694441..b37fe12 100644
--- a/buch/chapters/110-elliptisch/images/ellall.tex
+++ b/buch/chapters/110-elliptisch/images/ellall.tex
@@ -51,12 +51,13 @@
 \end{scope}
 
 \begin{scope}[xshift=-3cm,yshift=0cm]
-\rechteck{gray}{1}
+\node at (0,0) {$1$};
+\draw[color=gray!20] (-1,-1) rectangle (1,1);
 \end{scope}
 
-\definecolor{sccolor}{rgb}{0.8,0.2,0.8}
-\definecolor{sdcolor}{rgb}{0.8,0.8,0.2}
-\definecolor{cdcolor}{rgb}{0.2,0.8,0.8}
+\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)}
@@ -74,7 +75,7 @@
 \pol{(-1,1)}{blau}
 \node at (-1,-1) {$1$};
 \node at (1,-1) {$0$};
-\node at (1,1) {$\frac{ik'}k$};
+\node at (1,1) {$\frac{k'}{ik}$};
 \node at (-1,1) {$\infty$};
 \end{scope}
 
@@ -96,23 +97,36 @@
 \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}
+%\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}
+\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}
+\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}
 
 %
@@ -123,23 +137,36 @@
 \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}
+\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}
+%\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}
-\nullstelle{(1,-1)}{cdcolor}
-\pol{(-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}
 
 %
@@ -150,24 +177,36 @@
 \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}
+\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}
-\pol{(1,-1)}{cdcolor}
-\nullstelle{(-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}
+%\rechteck{gray}{1}
+\fill[color=white] (-1,-1) rectangle (1,1);
+\node[color=gray] at (0,0) {$1$};
 \end{scope}
 
 
-- 
cgit v1.2.1

