poles and zeros

8 files changed, 64 insertions, 25 deletions

diff --git a/buch/chapters/110-elliptisch/images/ellall.pdf b/buch/chapters/110-elliptisch/images/ellall.pdf
index a57be97..fd0a5dd 100644
--- a/buch/chapters/110-elliptisch/images/ellall.pdf
+++ b/buch/chapters/110-elliptisch/images/ellall.pdf
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}
 
 
diff --git a/buch/chapters/110-elliptisch/images/ellcommon.tex b/buch/chapters/110-elliptisch/images/ellcommon.tex
index 90bc486..cd3245d 100644
--- a/buch/chapters/110-elliptisch/images/ellcommon.tex
+++ b/buch/chapters/110-elliptisch/images/ellcommon.tex
@@ -10,15 +10,15 @@
 \def\l{0.2}
 
 \def\pol#1#2{
-	\draw[color=#2!40,line width=2.4pt]
+	\draw[color=#2!50,line width=3.0pt]
 		($#1+(-\l,-\l)$) -- ($#1+(\l,\l)$);
-	\draw[color=#2!40,line width=2.4pt]
+	\draw[color=#2!50,line width=3.0pt]
 		($#1+(-\l,\l)$) -- ($#1+(\l,-\l)$);
 }
 \def\nullstelle#1#2{
-	\draw[color=#2!40,line width=2.4pt] #1 circle[radius=\l];
+	\draw[color=#2!50,line width=3.0pt] #1 circle[radius=\l];
 }
 \def\rechteck#1#2{
 	\fill[color=#1!20] (-1,-1) rectangle (1,1);
-	\node[color=#1] at (0,0) {$#2$};
+	\node[color=#1] at (0,0) {$#2\mathstrut$};
 }
diff --git a/buch/chapters/110-elliptisch/images/ellpolnul.pdf b/buch/chapters/110-elliptisch/images/ellpolnul.pdf
index d6549c4..9143d2d 100644
--- a/buch/chapters/110-elliptisch/images/ellpolnul.pdf
+++ b/buch/chapters/110-elliptisch/images/ellpolnul.pdf
diff --git a/buch/chapters/110-elliptisch/images/ellpolnul.tex b/buch/chapters/110-elliptisch/images/ellpolnul.tex
index 1ed6b22..16730f9 100644
--- a/buch/chapters/110-elliptisch/images/ellpolnul.tex
+++ b/buch/chapters/110-elliptisch/images/ellpolnul.tex
@@ -38,7 +38,7 @@
 \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}
 
diff --git a/buch/chapters/110-elliptisch/images/jacobiplots.pdf b/buch/chapters/110-elliptisch/images/jacobiplots.pdf
index 49bfeb2..331270e 100644
--- a/buch/chapters/110-elliptisch/images/jacobiplots.pdf
+++ b/buch/chapters/110-elliptisch/images/jacobiplots.pdf
diff --git a/buch/chapters/110-elliptisch/images/kegelpara.pdf b/buch/chapters/110-elliptisch/images/kegelpara.pdf
index 65a5b45..b23654c 100644
--- a/buch/chapters/110-elliptisch/images/kegelpara.pdf
+++ b/buch/chapters/110-elliptisch/images/kegelpara.pdf
diff --git a/buch/chapters/110-elliptisch/images/torusschnitt.pdf b/buch/chapters/110-elliptisch/images/torusschnitt.pdf
index 519a5a3..f70f362 100644
--- a/buch/chapters/110-elliptisch/images/torusschnitt.pdf
+++ b/buch/chapters/110-elliptisch/images/torusschnitt.pdf