updated langfassung

13 files changed, 369 insertions, 167 deletions

diff --git a/langfassung/docs/2_einleitung.tex b/langfassung/docs/2_einleitung.tex
index 806c214..bce9ec8 100644
--- a/langfassung/docs/2_einleitung.tex
+++ b/langfassung/docs/2_einleitung.tex
@@ -1,3 +1,4 @@
+op
 Einleitung
 
 \subsection{Themen}
@@ -16,4 +17,50 @@ Einleitung
 
 \subsection{Motivation}
 
+\paragraph{ \( \Phi \) }
+
+\begin{equation}
+  \Phi(r) = - \frac{4\pi G \rho_0 R_s^3}{r} \ln ( 1+ \frac{r}{R_s} )
+\end{equation}
+
+with the limits
+
+\begin{equation}
+  \lim_{r\to \infty} \Phi=0
+\end{equation}
+
+and
+
+\begin{equation}
+  \lim_{r\to 0} \Phi=-4\pi G\rho_0 R_s^2
+\end{equation}
+
+\paragraph{ \( \rho \) }
+
+\begin{equation}
+  \rho(r) = \frac{1}{\sqrt{2 \cdot \pi} \cdot \sigma} \cdot
+  e^{\left( - \frac{(\Phi(r)}{\sigma^{2}} \right)}
+\end{equation}
+
+\paragraph{\( \rho_{new} \rightarrow (deriviation) \) }
+
+\begin{equation}
+  \rho(r) \cdot 1-\frac{1}{(2 \cdot sigma^{2} )} \cdot
+  ( Mxx \cdot x^{2} + 2 \cdot Mxy \cdot xy + Myy \cdot y^{2} ))
+\end{equation}
+
+% def rho_new(x, y, z):
+%     a = (1 - ((1) / (2 * (sigma ** 2))) * ( Mxx * x**2 + 2 * Mxy * x * y + Myy * y**2 ) )
+%     return rho(x, y, z) * a
+%
+% # phi function
+% def phi(x):
+%     if x == 0:
+%         return -4 * pi * f_0 * G * R_s**2
+%
+%     a = - ( 4 * pi * G * f_0 * R_s ** 3 ) / x
+%     b = np.log(1. + (x / R_s) )
+%     c = a * b
+%     return c
+
 Motivations blah
diff --git a/langfassung/docs/3_hauptteil.tex b/langfassung/docs/3_hauptteil.tex
index eab3897..5174f08 100644
--- a/langfassung/docs/3_hauptteil.tex
+++ b/langfassung/docs/3_hauptteil.tex
@@ -43,14 +43,59 @@ Blender is Awesome, Python is Awesome and together they are
 
 \subsection{Making things faster}
 
-Kicking out to many Stars, 1 out of 10000 is just to much...
+\paragraph{ Kicking out to many Stars, 1 out of 10000 is just to much... }
+~\\
+
+\begin{itemize}
+  \item Use a custom Density function for each Axis
+  \begin{itemize}
+    \item \( \phi(r_x)\), \( \phi(r_y) \) and \( \phi(r_z) \)
+    \item more controll
+  \end{itemize}
+\end{itemize}
+
+\begin{tikzpicture}
+\begin{scope}
+
+    \node[draw] (H) at (0,-2)
+        {\( \phi(x_1) > rand_x \)};
+    \node[draw] (I) at (5,-2)
+        {\( \phi(y_1) > rand_y \)};
+    \node[draw] (J) at (10,-2)
+        {\( \phi(z_1) > rand_z \)};
+
+    \node[draw] (K) at (10, -4) {true};
+    \node[draw] (L) at (0, -4) {false};
+
+    \node[draw] (M) at (10, -6) {write data to data.csv};
+
+    \node[draw] (N) at (0, -6) {generate new random coordinates};
+
+\end{scope}
+
+\begin{scope} [every node/.style={fill=white,circle},
+              every edge/.style={draw=red,very thick}]
+
+    \path[->] (H) edge (K);
+    \path[->] (I) edge (K);
+    \path[->] (J) edge (K);
+    \path[->] (H) edge (L);
+    \path[->] (I) edge (L);
+    \path[->] (J) edge (L);
+
+    \path[->] (K) edge (M);
+    \path[->] (L) edge (N);
+
+\end{scope}
+
+\end{tikzpicture}
 
 \subsection{Spiral Galaxies}
 
 The previous Galaxy models where all using a completely spherical model, generating
 a spiral galaxy is just not possible using these models.
 
-\subsubsection{N-Körper problem}
+\subsubsection{N-body problem}
 
 Kurze Beschreibung des N-Körper Problems
 
diff --git a/langfassung/docs/4_ergebnisse.tex b/langfassung/docs/4_ergebnisse.tex
index abd806d..088b13e 100644
--- a/langfassung/docs/4_ergebnisse.tex
+++ b/langfassung/docs/4_ergebnisse.tex
@@ -22,6 +22,32 @@ Pro MegaByte können die Koordinaten von 10000 Sternen gespeichert werden.
 
 Die generierung von Spiralgalaxien gestaltet sich schweiriger als erwartet.
 
+\subsection{Lookup-Table Speed}
+
+\begin{tabular}{l | l | l}
+rho-values  & step  & time (in seconds) \\ \hline\hline
+1500000     & 1     & 8.07  \\
+750000      & 2     & 4.4   \\
+375000      & 4     & 2.26  \\
+187500      & 8     & 1.35  \\
+93750       & 16    & 0.76  \\
+\end{tabular}
+
+The correlation between the number of stars generated and the time needed ist
+clearly linear.
+
+\paragraph{Python script} ~\\
+\lstset{language=Python}
+\begin{lstlisting}[frame = single]
+import matplotlib.pyplot as plt
+
+list_time = [8.07, 4.4, 2.26, 1.35, 0.76]
+list_rho_values = [1500000, 750000, 375000, 187500, 93750]
+
+plt.plot(list_time, list_rho_values, '-ro')
+plt.show()
+\end{lstlisting}
+
 \subsection{Distortion of Galaxies}
 
 Galaxien verformen dinge
diff --git a/langfassung/master.aux b/langfassung/master.aux
index 41ce740..65d8f03 100644
--- a/langfassung/master.aux
+++ b/langfassung/master.aux
@@ -26,6 +26,9 @@
 \newlabel{Einleitung}{{1}{2}{Einleitung}{section.1}{}}
 \@writefile{toc}{\contentsline {subsection}{\numberline {1.1}Themen}{2}{subsection.1.1}}
 \@writefile{toc}{\contentsline {subsection}{\numberline {1.2}Motivation}{2}{subsection.1.2}}
+\@writefile{toc}{\contentsline {paragraph}{\nonumberline \( \Phi \)}{2}{section*.2}}
+\@writefile{toc}{\contentsline {paragraph}{\nonumberline \( \rho \)}{2}{section*.3}}
+\@writefile{toc}{\contentsline {paragraph}{\nonumberline \( \rho _{new} \rightarrow (deriviation) \)}{2}{section*.4}}
 \@writefile{toc}{\contentsline {section}{\numberline {2}Hauptteil}{3}{section.2}}
 \newlabel{Hauptteil}{{2}{3}{Hauptteil}{section.2}{}}
 \@writefile{toc}{\contentsline {subsection}{\numberline {2.1}Notes}{3}{subsection.2.1}}
@@ -38,20 +41,23 @@
 \@writefile{toc}{\contentsline {subsection}{\numberline {2.3}Einasto profile}{4}{subsection.2.3}}
 \@writefile{toc}{\contentsline {subsection}{\numberline {2.4}Blender + Python}{4}{subsection.2.4}}
 \@writefile{toc}{\contentsline {subsection}{\numberline {2.5}Making things faster}{5}{subsection.2.5}}
+\@writefile{toc}{\contentsline {paragraph}{\nonumberline Kicking out to many Stars, 1 out of 10000 is just to much...}{5}{section*.5}}
 \@writefile{toc}{\contentsline {subsection}{\numberline {2.6}Spiral Galaxies}{5}{subsection.2.6}}
-\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.6.1}N-K\IeC {\"o}rper problem}{5}{subsubsection.2.6.1}}
+\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.6.1}N-body problem}{5}{subsubsection.2.6.1}}
 \@writefile{toc}{\contentsline {subsubsection}{\numberline {2.6.2}Hilbert Spiral}{5}{subsubsection.2.6.2}}
 \@writefile{toc}{\contentsline {subsection}{\numberline {2.7}Gr\IeC {\"o}\IeC {\ss }eneinheiten}{5}{subsection.2.7}}
 \@writefile{toc}{\contentsline {section}{\numberline {3}Ergebnisse}{6}{section.3}}
 \newlabel{ergebnisse}{{3}{6}{Ergebnisse}{section.3}{}}
 \@writefile{toc}{\contentsline {subsection}{\numberline {3.1}Simulation Speed}{6}{subsection.3.1}}
 \@writefile{toc}{\contentsline {subsection}{\numberline {3.2}Spiral Galaxies}{6}{subsection.3.2}}
-\@writefile{toc}{\contentsline {subsection}{\numberline {3.3}Distortion of Galaxies}{6}{subsection.3.3}}
-\@writefile{toc}{\contentsline {section}{\numberline {4}Quellen und Hilfen}{7}{section.4}}
-\newlabel{quellen}{{4}{7}{Quellen und Hilfen}{section.4}{}}
-\@writefile{toc}{\contentsline {paragraph}{\nonumberline Herrn J\IeC {\"o}rg Thar}{7}{section*.3}}
-\@writefile{toc}{\contentsline {paragraph}{\nonumberline Konstantin Bosbach}{7}{section*.4}}
-\@writefile{toc}{\contentsline {paragraph}{\nonumberline Tilman Hoffbauer}{7}{section*.5}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {3.3}Lookup-Table Speed}{6}{subsection.3.3}}
+\@writefile{toc}{\contentsline {paragraph}{\nonumberline Python script}{6}{section*.6}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {3.4}Distortion of Galaxies}{7}{subsection.3.4}}
+\@writefile{toc}{\contentsline {section}{\numberline {4}Quellen und Hilfen}{8}{section.4}}
+\newlabel{quellen}{{4}{8}{Quellen und Hilfen}{section.4}{}}
+\@writefile{toc}{\contentsline {paragraph}{\nonumberline Herrn J\IeC {\"o}rg Thar}{8}{section*.8}}
+\@writefile{toc}{\contentsline {paragraph}{\nonumberline Konstantin Bosbach}{8}{section*.9}}
+\@writefile{toc}{\contentsline {paragraph}{\nonumberline Tilman Hoffbauer}{8}{section*.10}}
 \global\@namedef{scr@dte@section@lastmaxnumwidth}{11.8799pt}
 \global\@namedef{scr@dte@subsection@lastmaxnumwidth}{19.71382pt}
 \global\@namedef{scr@dte@subsubsection@lastmaxnumwidth}{28.8528pt}
diff --git a/langfassung/master.fdb_latexmk b/langfassung/master.fdb_latexmk
index e83a18b..a073a11 100644
--- a/langfassung/master.fdb_latexmk
+++ b/langfassung/master.fdb_latexmk
@@ -1,5 +1,5 @@
 # Fdb version 3
-["pdflatex"] 1511362333 "master.tex" "master.pdf" "master" 1511362334
+["pdflatex"] 1512422718 "master.tex" "master.pdf" "master" 1512422719
   "/usr/share/texmf-dist/fonts/enc/dvips/lm/lm-mathex.enc" 1510784331 3486 c7eadf5dcc57b3b2d11736679f6636ba ""
   "/usr/share/texmf-dist/fonts/enc/dvips/lm/lm-mathit.enc" 1510784331 2405 5dcf2c1b967ee25cc46c58cd52244aed ""
   "/usr/share/texmf-dist/fonts/enc/dvips/lm/lm-mathsy.enc" 1510784331 2840 216e6e45ad352e2456e1149f28885bee ""
@@ -29,12 +29,15 @@
   "/usr/share/texmf-dist/fonts/type1/public/lm/lmbx12.pfb" 1510784333 116908 1fca96723793882c2e0160350c192fc8 ""
   "/usr/share/texmf-dist/fonts/type1/public/lm/lmex10.pfb" 1510784333 23055 2e5b42921de910eaa97b85df04ca4891 ""
   "/usr/share/texmf-dist/fonts/type1/public/lm/lmmi12.pfb" 1510784333 30696 2654571912f9cd384da9f7cb8a60c568 ""
+  "/usr/share/texmf-dist/fonts/type1/public/lm/lmmi6.pfb" 1510784333 31113 04b711c9a4c7f8cb4ed784c6fc4cc1c5 ""
   "/usr/share/texmf-dist/fonts/type1/public/lm/lmmi8.pfb" 1510784332 30635 833ec815d446ec453a4913fc26d24cbc ""
   "/usr/share/texmf-dist/fonts/type1/public/lm/lmr12.pfb" 1510784332 113634 f99c44d58bae0863375faf0e1d74d612 ""
   "/usr/share/texmf-dist/fonts/type1/public/lm/lmr17.pfb" 1510784332 119752 1bd8d06e4079df624bf59ce3ad7c9aa6 ""
+  "/usr/share/texmf-dist/fonts/type1/public/lm/lmr6.pfb" 1510784332 123394 d390152bb30feeb496aaaa93299ee9ba ""
   "/usr/share/texmf-dist/fonts/type1/public/lm/lmr8.pfb" 1510784332 122174 a7a08406857c9530a0320a2517f60370 ""
   "/usr/share/texmf-dist/fonts/type1/public/lm/lmssbx10.pfb" 1510784332 119663 e82fa1a58f98ccd89bdbd77311ac9cf1 ""
   "/usr/share/texmf-dist/fonts/type1/public/lm/lmsy10.pfb" 1510784332 27863 09ce3735688ffde955e72da27c95b61a ""
+  "/usr/share/texmf-dist/fonts/type1/public/lm/lmsy8.pfb" 1510784332 27802 5c876bb2c4040caaf035d60bd74a86bd ""
   "/usr/share/texmf-dist/fonts/type1/public/lm/lmtt12.pfb" 1510784332 110323 92daea7ca7b4120bd2b54b047c93be27 ""
   "/usr/share/texmf-dist/tex/context/base/mkii/supp-pdf.mkii" 1510784369 71627 94eb9990bed73c364d7f53f960cc8c5b ""
   "/usr/share/texmf-dist/tex/generic/babel-english/english.ldf" 1510784355 7008 9ff5fdcc865b01beca2b0fe4a46231d4 ""
@@ -136,6 +139,10 @@
   "/usr/share/texmf-dist/tex/latex/koma-script/typearea.sty" 1510784351 54085 f72333c4528ff9a19f74234c26dfd7a9 ""
   "/usr/share/texmf-dist/tex/latex/latexconfig/epstopdf-sys.cfg" 1510784351 678 4792914a8f45be57bb98413425e4c7af ""
   "/usr/share/texmf-dist/tex/latex/latexconfig/hyperref.cfg" 1510784351 235 6031e5765137be07eed51a510b2b8fb7 ""
+  "/usr/share/texmf-dist/tex/latex/listings/listings.cfg" 1510784350 1827 d72ad54409ca5c1068a1939c63441bd2 ""
+  "/usr/share/texmf-dist/tex/latex/listings/listings.sty" 1510784350 80336 ff90c926c3d7bfdaa3d80ca57123b0bb ""
+  "/usr/share/texmf-dist/tex/latex/listings/lstlang1.sty" 1510784350 93445 48e5be20ba2d0a2ca5c4ce7e292a4bbc ""
+  "/usr/share/texmf-dist/tex/latex/listings/lstmisc.sty" 1510784350 77028 c3eb00afb55a32bc13ca8da7f5234377 ""
   "/usr/share/texmf-dist/tex/latex/lm/lmodern.sty" 1510784350 1606 c17281c7cff2bbd7ff0173e1433487ec ""
   "/usr/share/texmf-dist/tex/latex/lm/omllmm.fd" 1510784350 888 44447a3a3af84a22454ef89500942d93 ""
   "/usr/share/texmf-dist/tex/latex/lm/omslmsy.fd" 1510784350 805 af340a8260c447aa315cfc740ff0152f ""
@@ -165,20 +172,21 @@
   "/usr/share/texmf-dist/tex/latex/url/url.sty" 1510784349 12796 8edb7d69a20b857904dd0ea757c14ec9 ""
   "/usr/share/texmf-dist/tex/latex/xcolor/xcolor.sty" 1510784348 55589 34128738f682d033422ca125f82e5d62 ""
   "/usr/share/texmf-dist/web2c/texmf.cnf" 1510784374 32585 d82bbcf7626b7842c87671687479e852 ""
-  "/var/lib/texmf/fonts/map/pdftex/updmap/pdftex.map" 1511090916 336252 084fb726fd87e45c0944c78793f2bb29 ""
-  "/var/lib/texmf/web2c/pdftex/pdflatex.fmt" 1511090907 7736839 eb24867d9acdaababaab39123dc79039 ""
-  "docs/1_kurzfassung.tex" 1510759687 12 ed7507f8f11464d9cabafe708c0da627 ""
-  "docs/2_einleitung.tex" 1511362025 322 20a22b40f27387abc3c406de06a95e1d ""
-  "docs/3_hauptteil.tex" 1511362318 2271 31097f2a9e492a43ccfd8c5e1168bd17 ""
-  "docs/4_ergebnisse.tex" 1510763342 666 5133b4af1584bbbc7efc3cb2fc4ea797 ""
-  "docs/5_quellen.tex" 1510760778 1431 30d35adc0566f6440733273e181037f4 ""
-  "master.aux" 1511362334 3922 88094869bdb4659b0c121910ff08a38d ""
-  "master.out" 1511362334 1514 a9ac8a29ff5c871c66620ea7a44d1d7c ""
-  "master.tex" 1510851639 3642 c3afecf1a4fd747ed72e69ca07b7ce80 ""
-  "master.toc" 1511362334 2189 b6355552f443f37cbfbc5c393d80a9fb ""
+  "/var/lib/texmf/fonts/map/pdftex/updmap/pdftex.map" 1512287864 2354178 d796f0af48448ed886bee26a94683716 ""
+  "/var/lib/texmf/web2c/pdftex/pdflatex.fmt" 1512287847 7736838 e293961f0b0b637126843b81f4a20c68 ""
+  "docs/1_kurzfassung.tex" 1510756086 12 ed7507f8f11464d9cabafe708c0da627 ""
+  "docs/2_einleitung.tex" 1512332654 1345 0f7d1076186de68b807f1efaaa8fae7f ""
+  "docs/3_hauptteil.tex" 1512418786 3312 27548267e878c726f48026b96e26ab7b ""
+  "docs/4_ergebnisse.tex" 1512422716 1345 9c8be2dc26aaf15827e19bac1e1f3511 ""
+  "docs/5_quellen.tex" 1510757178 1431 30d35adc0566f6440733273e181037f4 ""
+  "master.aux" 1512422719 4524 5afa24661157ff445acc1c12f6ab488d ""
+  "master.out" 1512422719 1577 8c8b082a5766a6f5c8d790f742d2e884 ""
+  "master.tex" 1512422442 3663 b961f57a5a4485630e57a2739768cc2e ""
+  "master.toc" 1512422719 2683 045b72e788ef0486ae97695d968a0345 ""
   (generated)
-  "master.out"
   "master.aux"
-  "master.pdf"
   "master.toc"
+  "master.x.gnuplot"
   "master.log"
+  "master.out"
+  "master.pdf"
diff --git a/langfassung/master.fls b/langfassung/master.fls
index 250f4b2..e3a6179 100644
--- a/langfassung/master.fls
+++ b/langfassung/master.fls
@@ -1,4 +1,4 @@
-PWD /home/hanemile/Nextcloud/JUFO/Langfassung
+PWD /home/hanemile/Documents/github/JUFO18_GalaxyGeneration/langfassung
 INPUT /usr/share/texmf-dist/web2c/texmf.cnf
 INPUT /var/lib/texmf/web2c/pdftex/pdflatex.fmt
 INPUT master.tex
@@ -197,6 +197,12 @@ INPUT /usr/share/texmf-dist/tex/generic/pgf/libraries/pgflibraryplothandlers.cod
 INPUT /usr/share/texmf-dist/tex/generic/pgf/modules/pgfmodulematrix.code.tex
 INPUT /usr/share/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarytopaths.code.tex
 INPUT /usr/share/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarytopaths.code.tex
+INPUT /usr/share/texmf-dist/tex/latex/listings/listings.sty
+INPUT /usr/share/texmf-dist/tex/latex/listings/listings.sty
+INPUT /usr/share/texmf-dist/tex/latex/listings/lstmisc.sty
+INPUT /usr/share/texmf-dist/tex/latex/listings/lstmisc.sty
+INPUT /usr/share/texmf-dist/tex/latex/listings/listings.cfg
+INPUT /usr/share/texmf-dist/tex/latex/listings/listings.cfg
 INPUT master.aux
 INPUT master.aux
 OUTPUT master.aux
@@ -272,24 +278,29 @@ INPUT docs/3_hauptteil.tex
 INPUT docs/3_hauptteil.tex
 INPUT docs/4_ergebnisse.tex
 INPUT docs/4_ergebnisse.tex
+INPUT /usr/share/texmf-dist/tex/latex/listings/lstlang1.sty
+INPUT /usr/share/texmf-dist/tex/latex/listings/lstlang1.sty
 INPUT docs/5_quellen.tex
 INPUT docs/5_quellen.tex
 INPUT master.aux
 INPUT ./master.out
 INPUT ./master.out
+INPUT /usr/share/texmf-dist/fonts/enc/dvips/lm/lm-mathex.enc
 INPUT /usr/share/texmf-dist/fonts/enc/dvips/lm/lm-mathit.enc
 INPUT /usr/share/texmf-dist/fonts/enc/dvips/lm/lm-rm.enc
-INPUT /usr/share/texmf-dist/fonts/enc/dvips/lm/lm-mathex.enc
 INPUT /usr/share/texmf-dist/fonts/enc/dvips/lm/lm-mathsy.enc
 INPUT /usr/share/texmf-dist/fonts/enc/dvips/lm/lm-ts1.enc
 INPUT /usr/share/texmf-dist/fonts/enc/dvips/lm/lm-rmtt.enc
 INPUT /usr/share/texmf-dist/fonts/type1/public/lm/lmbx12.pfb
 INPUT /usr/share/texmf-dist/fonts/type1/public/lm/lmex10.pfb
 INPUT /usr/share/texmf-dist/fonts/type1/public/lm/lmmi12.pfb
+INPUT /usr/share/texmf-dist/fonts/type1/public/lm/lmmi6.pfb
 INPUT /usr/share/texmf-dist/fonts/type1/public/lm/lmmi8.pfb
 INPUT /usr/share/texmf-dist/fonts/type1/public/lm/lmr12.pfb
 INPUT /usr/share/texmf-dist/fonts/type1/public/lm/lmr17.pfb
+INPUT /usr/share/texmf-dist/fonts/type1/public/lm/lmr6.pfb
 INPUT /usr/share/texmf-dist/fonts/type1/public/lm/lmr8.pfb
 INPUT /usr/share/texmf-dist/fonts/type1/public/lm/lmssbx10.pfb
 INPUT /usr/share/texmf-dist/fonts/type1/public/lm/lmsy10.pfb
+INPUT /usr/share/texmf-dist/fonts/type1/public/lm/lmsy8.pfb
 INPUT /usr/share/texmf-dist/fonts/type1/public/lm/lmtt12.pfb
diff --git a/langfassung/master.log b/langfassung/master.log
index fd0e2dd..0199ddf 100644
--- a/langfassung/master.log
+++ b/langfassung/master.log
@@ -1,4 +1,4 @@
-This is pdfTeX, Version 3.14159265-2.6-1.40.18 (TeX Live 2017/Arch Linux) (preloaded format=pdflatex 2017.11.19)  22 NOV 2017 15:52
+This is pdfTeX, Version 3.14159265-2.6-1.40.18 (TeX Live 2017/Arch Linux) (preloaded format=pdflatex 2017.12.3)  4 DEC 2017 22:25
 entering extended mode
  restricted \write18 enabled.
  file:line:error style messages enabled.
@@ -1030,32 +1030,53 @@ File: pgfmodulematrix.code.tex 2013/09/17  (rcs-revision 1.8)
 \tikz@expandcount=\count134
  (/usr/share/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarytopaths.code.tex
 File: tikzlibrarytopaths.code.tex 2008/06/17 v3.0.1a (rcs-revision 1.2)
-)))
-Package hyperref Info: Option `colorlinks' set `true' on input line 23.
+))) (/usr/share/texmf-dist/tex/latex/listings/listings.sty
+\lst@mode=\count135
+\lst@gtempboxa=\box41
+\lst@token=\toks37
+\lst@length=\count136
+\lst@currlwidth=\dimen187
+\lst@column=\count137
+\lst@pos=\count138
+\lst@lostspace=\dimen188
+\lst@width=\dimen189
+\lst@newlines=\count139
+\lst@lineno=\count140
+\lst@maxwidth=\dimen190
+ (/usr/share/texmf-dist/tex/latex/listings/lstmisc.sty
+File: lstmisc.sty 2015/06/04 1.6 (Carsten Heinz)
+\c@lstnumber=\count141
+\lst@skipnumbers=\count142
+\lst@framebox=\box42
+) (/usr/share/texmf-dist/tex/latex/listings/listings.cfg
+File: listings.cfg 2015/06/04 1.6 listings configuration
+))
+Package: listings 2015/06/04 1.6 (Carsten Heinz)
+Package hyperref Info: Option `colorlinks' set `true' on input line 24.
  (./master.aux)
 \openout1 = `master.aux'.
 
-LaTeX Font Info:    Checking defaults for OML/cmm/m/it on input line 36.
-LaTeX Font Info:    ... okay on input line 36.
-LaTeX Font Info:    Checking defaults for T1/cmr/m/n on input line 36.
-LaTeX Font Info:    ... okay on input line 36.
-LaTeX Font Info:    Checking defaults for OT1/cmr/m/n on input line 36.
-LaTeX Font Info:    ... okay on input line 36.
-LaTeX Font Info:    Checking defaults for OMS/cmsy/m/n on input line 36.
-LaTeX Font Info:    ... okay on input line 36.
-LaTeX Font Info:    Checking defaults for OMX/cmex/m/n on input line 36.
-LaTeX Font Info:    ... okay on input line 36.
-LaTeX Font Info:    Checking defaults for U/cmr/m/n on input line 36.
-LaTeX Font Info:    ... okay on input line 36.
-LaTeX Font Info:    Checking defaults for PD1/pdf/m/n on input line 36.
-LaTeX Font Info:    ... okay on input line 36.
-LaTeX Font Info:    Checking defaults for TS1/cmr/m/n on input line 36.
-LaTeX Font Info:    Try loading font information for TS1+cmr on input line 36.
+LaTeX Font Info:    Checking defaults for OML/cmm/m/it on input line 37.
+LaTeX Font Info:    ... okay on input line 37.
+LaTeX Font Info:    Checking defaults for T1/cmr/m/n on input line 37.
+LaTeX Font Info:    ... okay on input line 37.
+LaTeX Font Info:    Checking defaults for OT1/cmr/m/n on input line 37.
+LaTeX Font Info:    ... okay on input line 37.
+LaTeX Font Info:    Checking defaults for OMS/cmsy/m/n on input line 37.
+LaTeX Font Info:    ... okay on input line 37.
+LaTeX Font Info:    Checking defaults for OMX/cmex/m/n on input line 37.
+LaTeX Font Info:    ... okay on input line 37.
+LaTeX Font Info:    Checking defaults for U/cmr/m/n on input line 37.
+LaTeX Font Info:    ... okay on input line 37.
+LaTeX Font Info:    Checking defaults for PD1/pdf/m/n on input line 37.
+LaTeX Font Info:    ... okay on input line 37.
+LaTeX Font Info:    Checking defaults for TS1/cmr/m/n on input line 37.
+LaTeX Font Info:    Try loading font information for TS1+cmr on input line 37.
  (/usr/share/texmf-dist/tex/latex/base/ts1cmr.fd
 File: ts1cmr.fd 2014/09/29 v2.5h Standard LaTeX font definitions
 )
-LaTeX Font Info:    ... okay on input line 36.
-LaTeX Font Info:    Try loading font information for OT1+lmr on input line 36.
+LaTeX Font Info:    ... okay on input line 37.
+LaTeX Font Info:    Try loading font information for OT1+lmr on input line 37.
  (/usr/share/texmf-dist/tex/latex/lm/ot1lmr.fd
 File: ot1lmr.fd 2009/10/30 v1.6 Font defs for Latin Modern
 )
@@ -1093,35 +1114,35 @@ File: ot1lmr.fd 2009/10/30 v1.6 Font defs for Latin Modern
 * \@reversemarginfalse
 * (1in=72.27pt=25.4mm, 1cm=28.453pt)
 
-\AtBeginShipoutBox=\box41
-Package hyperref Info: Link coloring ON on input line 36.
+\AtBeginShipoutBox=\box43
+Package hyperref Info: Link coloring ON on input line 37.
 (/usr/share/texmf-dist/tex/latex/hyperref/nameref.sty
 Package: nameref 2016/05/21 v2.44 Cross-referencing by name of section
  (/usr/share/texmf-dist/tex/generic/oberdiek/gettitlestring.sty
 Package: gettitlestring 2016/05/16 v1.5 Cleanup title references (HO)
 )
-\c@section@level=\count135
+\c@section@level=\count143
 )
-LaTeX Info: Redefining \ref on input line 36.
-LaTeX Info: Redefining \pageref on input line 36.
-LaTeX Info: Redefining \nameref on input line 36.
+LaTeX Info: Redefining \ref on input line 37.
+LaTeX Info: Redefining \pageref on input line 37.
+LaTeX Info: Redefining \nameref on input line 37.
  (./master.out) (./master.out)
 \@outlinefile=\write4
 \openout4 = `master.out'.
 
  (/usr/share/texmf-dist/tex/context/base/mkii/supp-pdf.mkii
 [Loading MPS to PDF converter (version 2006.09.02).]
-\scratchcounter=\count136
-\scratchdimen=\dimen187
-\scratchbox=\box42
-\nofMPsegments=\count137
-\nofMParguments=\count138
-\everyMPshowfont=\toks37
-\MPscratchCnt=\count139
-\MPscratchDim=\dimen188
-\MPnumerator=\count140
-\makeMPintoPDFobject=\count141
-\everyMPtoPDFconversion=\toks38
+\scratchcounter=\count144
+\scratchdimen=\dimen191
+\scratchbox=\box44
+\nofMPsegments=\count145
+\nofMParguments=\count146
+\everyMPshowfont=\toks38
+\MPscratchCnt=\count147
+\MPscratchDim=\dimen192
+\MPnumerator=\count148
+\makeMPintoPDFobject=\count149
+\everyMPtoPDFconversion=\toks39
 ) (/usr/share/texmf-dist/tex/latex/oberdiek/epstopdf-base.sty
 Package: epstopdf-base 2016/05/15 v2.6 Base part for package epstopdf
  (/usr/share/texmf-dist/tex/latex/oberdiek/grfext.sty
@@ -1135,42 +1156,44 @@ Package grfext Info: Graphics extension search list:
 File: epstopdf-sys.cfg 2010/07/13 v1.3 Configuration of (r)epstopdf for TeX Live
 ))
 Package caption Info: Begin \AtBeginDocument code.
+Package caption Info: listings package is loaded.
 Package caption Info: End \AtBeginDocument code.
  ABD: EveryShipout initializing macros
-LaTeX Font Info:    Try loading font information for OT1+lmss on input line 44.
+\c@lstlisting=\count150
+LaTeX Font Info:    Try loading font information for OT1+lmss on input line 45.
  (/usr/share/texmf-dist/tex/latex/lm/ot1lmss.fd
 File: ot1lmss.fd 2009/10/30 v1.6 Font defs for Latin Modern
 )
-LaTeX Font Info:    Try loading font information for OML+lmm on input line 44.
+LaTeX Font Info:    Try loading font information for OML+lmm on input line 45.
  (/usr/share/texmf-dist/tex/latex/lm/omllmm.fd
 File: omllmm.fd 2009/10/30 v1.6 Font defs for Latin Modern
 )
-LaTeX Font Info:    Try loading font information for OMS+lmsy on input line 44.
+LaTeX Font Info:    Try loading font information for OMS+lmsy on input line 45.
  (/usr/share/texmf-dist/tex/latex/lm/omslmsy.fd
 File: omslmsy.fd 2009/10/30 v1.6 Font defs for Latin Modern
 )
-LaTeX Font Info:    Try loading font information for OMX+lmex on input line 44.
+LaTeX Font Info:    Try loading font information for OMX+lmex on input line 45.
  (/usr/share/texmf-dist/tex/latex/lm/omxlmex.fd
 File: omxlmex.fd 2009/10/30 v1.6 Font defs for Latin Modern
 )
 LaTeX Font Info:    External font `lmex10' loaded for size
-(Font)              <17.28> on input line 44.
+(Font)              <17.28> on input line 45.
 LaTeX Font Info:    External font `lmex10' loaded for size
-(Font)              <12> on input line 44.
+(Font)              <12> on input line 45.
 LaTeX Font Info:    External font `lmex10' loaded for size
-(Font)              <10> on input line 44.
-LaTeX Font Info:    Try loading font information for OT1+lmtt on input line 44.
+(Font)              <10> on input line 45.
+LaTeX Font Info:    Try loading font information for OT1+lmtt on input line 45.
  (/usr/share/texmf-dist/tex/latex/lm/ot1lmtt.fd
 File: ot1lmtt.fd 2009/10/30 v1.6 Font defs for Latin Modern
 ) (./docs/1_kurzfassung.tex)
 Package babel Info: Redefining ngerman shorthand "|
-(babel)             in language append on input line 48.
+(babel)             in language append on input line 49.
 Package babel Info: Redefining ngerman shorthand "~
-(babel)             in language append on input line 48.
+(babel)             in language append on input line 49.
 Package babel Info: Redefining ngerman shorthand "|
-(babel)             in language append on input line 48.
+(babel)             in language append on input line 49.
 Package babel Info: Redefining ngerman shorthand "~
-(babel)             in language append on input line 48.
+(babel)             in language append on input line 49.
  [1
 
 
@@ -1184,84 +1207,84 @@ LaTeX Font Info:    External font `lmex10' loaded for size
 \openout5 = `master.toc'.
 
 Package babel Info: Redefining ngerman shorthand "|
-(babel)             in language append on input line 53.
+(babel)             in language append on input line 54.
 Package babel Info: Redefining ngerman shorthand "~
-(babel)             in language append on input line 53.
+(babel)             in language append on input line 54.
 Package babel Info: Redefining ngerman shorthand "|
-(babel)             in language append on input line 53.
+(babel)             in language append on input line 54.
 Package babel Info: Redefining ngerman shorthand "~
-(babel)             in language append on input line 53.
+(babel)             in language append on input line 54.
 pdfTeX warning (ext4): destination with the same identifier (name{page.1}) has been already used, duplicate ignored
 <to be read again> 
                    \relax 
-l.53 \newpage
+l.54 \newpage
               [1
 
 ]
 Package babel Info: Redefining ngerman shorthand "|
-(babel)             in language append on input line 55.
+(babel)             in language append on input line 56.
 Package babel Info: Redefining ngerman shorthand "~
-(babel)             in language append on input line 55.
+(babel)             in language append on input line 56.
  (./docs/2_einleitung.tex
 Package babel Info: Redefining ngerman shorthand "|
-(babel)             in language append on input line 3.
+(babel)             in language append on input line 4.
 Package babel Info: Redefining ngerman shorthand "~
-(babel)             in language append on input line 3.
-LaTeX Font Info:    Try loading font information for TS1+lmr on input line 6.
+(babel)             in language append on input line 4.
+LaTeX Font Info:    Try loading font information for TS1+lmr on input line 7.
  (/usr/share/texmf-dist/tex/latex/lm/ts1lmr.fd
 File: ts1lmr.fd 2009/10/30 v1.6 Font defs for Latin Modern
 )
 Package babel Info: Redefining ngerman shorthand "|
-(babel)             in language append on input line 17.
+(babel)             in language append on input line 18.
 Package babel Info: Redefining ngerman shorthand "~
-(babel)             in language append on input line 17.
+(babel)             in language append on input line 18.
 )
 Package babel Info: Redefining ngerman shorthand "|
-(babel)             in language append on input line 57.
+(babel)             in language append on input line 58.
 Package babel Info: Redefining ngerman shorthand "~
-(babel)             in language append on input line 57.
+(babel)             in language append on input line 58.
 Package babel Info: Redefining ngerman shorthand "|
-(babel)             in language append on input line 57.
+(babel)             in language append on input line 58.
 Package babel Info: Redefining ngerman shorthand "~
-(babel)             in language append on input line 57.
+(babel)             in language append on input line 58.
  [2]
 Package babel Info: Redefining ngerman shorthand "|
-(babel)             in language append on input line 59.
-Package babel Info: Redefining ngerman shorthand "~
-(babel)             in language append on input line 59.
-Package babel Info: Redefining ngerman shorthand "|
 (babel)             in language append on input line 60.
 Package babel Info: Redefining ngerman shorthand "~
 (babel)             in language append on input line 60.
 Package babel Info: Redefining ngerman shorthand "|
-(babel)             in language append on input line 62.
+(babel)             in language append on input line 61.
 Package babel Info: Redefining ngerman shorthand "~
-(babel)             in language append on input line 62.
+(babel)             in language append on input line 61.
 Package babel Info: Redefining ngerman shorthand "|
-(babel)             in language append on input line 73.
+(babel)             in language append on input line 63.
 Package babel Info: Redefining ngerman shorthand "~
-(babel)             in language append on input line 73.
+(babel)             in language append on input line 63.
 Package babel Info: Redefining ngerman shorthand "|
-(babel)             in language append on input line 82.
+(babel)             in language append on input line 74.
 Package babel Info: Redefining ngerman shorthand "~
-(babel)             in language append on input line 82.
+(babel)             in language append on input line 74.
 Package babel Info: Redefining ngerman shorthand "|
-(babel)             in language append on input line 98.
+(babel)             in language append on input line 83.
 Package babel Info: Redefining ngerman shorthand "~
-(babel)             in language append on input line 98.
+(babel)             in language append on input line 83.
+Package babel Info: Redefining ngerman shorthand "|
+(babel)             in language append on input line 99.
+Package babel Info: Redefining ngerman shorthand "~
+(babel)             in language append on input line 99.
 Package babel Info: Redefining ngerman shorthand "|
-(babel)             in language append on input line 111.
+(babel)             in language append on input line 112.
 Package babel Info: Redefining ngerman shorthand "~
-(babel)             in language append on input line 111.
+(babel)             in language append on input line 112.
 Package babel Info: Redefining ngerman shorthand "|
-(babel)             in language append on input line 111.
+(babel)             in language append on input line 112.
 Package babel Info: Redefining ngerman shorthand "~
-(babel)             in language append on input line 111.
+(babel)             in language append on input line 112.
  [3]
 Package babel Info: Redefining ngerman shorthand "|
-(babel)             in language append on input line 115.
+(babel)             in language append on input line 116.
 Package babel Info: Redefining ngerman shorthand "~
-(babel)             in language append on input line 115.
+(babel)             in language append on input line 116.
  (./docs/3_hauptteil.tex
 Package babel Info: Redefining ngerman shorthand "|
 (babel)             in language append on input line 1.
@@ -1279,45 +1302,50 @@ Package babel Info: Redefining ngerman shorthand "|
 (babel)             in language append on input line 44.
 Package babel Info: Redefining ngerman shorthand "~
 (babel)             in language append on input line 44.
+
+Underfull \hbox (badness 10000) in paragraph at lines 47--48
+
+ []
+
 Package babel Info: Redefining ngerman shorthand "|
-(babel)             in language append on input line 48.
+(babel)             in language append on input line 50.
 Package babel Info: Redefining ngerman shorthand "~
-(babel)             in language append on input line 48.
+(babel)             in language append on input line 50.
 Package babel Info: Redefining ngerman shorthand "|
-(babel)             in language append on input line 48.
+(babel)             in language append on input line 50.
 Package babel Info: Redefining ngerman shorthand "~
-(babel)             in language append on input line 48.
- [4]
+(babel)             in language append on input line 50.
+[4]
 Package babel Info: Redefining ngerman shorthand "|
-(babel)             in language append on input line 48.
+(babel)             in language append on input line 93.
 Package babel Info: Redefining ngerman shorthand "~
-(babel)             in language append on input line 48.
+(babel)             in language append on input line 93.
 Package babel Info: Redefining ngerman shorthand "|
-(babel)             in language append on input line 53.
+(babel)             in language append on input line 98.
 Package babel Info: Redefining ngerman shorthand "~
-(babel)             in language append on input line 53.
+(babel)             in language append on input line 98.
 Package babel Info: Redefining ngerman shorthand "|
-(babel)             in language append on input line 57.
+(babel)             in language append on input line 102.
 Package babel Info: Redefining ngerman shorthand "~
-(babel)             in language append on input line 57.
+(babel)             in language append on input line 102.
 Package babel Info: Redefining ngerman shorthand "|
-(babel)             in language append on input line 61.
+(babel)             in language append on input line 106.
 Package babel Info: Redefining ngerman shorthand "~
-(babel)             in language append on input line 61.
+(babel)             in language append on input line 106.
 )
 Package babel Info: Redefining ngerman shorthand "|
-(babel)             in language append on input line 130.
+(babel)             in language append on input line 131.
 Package babel Info: Redefining ngerman shorthand "~
-(babel)             in language append on input line 130.
+(babel)             in language append on input line 131.
 Package babel Info: Redefining ngerman shorthand "|
-(babel)             in language append on input line 130.
+(babel)             in language append on input line 131.
 Package babel Info: Redefining ngerman shorthand "~
-(babel)             in language append on input line 130.
+(babel)             in language append on input line 131.
  [5]
 Package babel Info: Redefining ngerman shorthand "|
-(babel)             in language append on input line 132.
+(babel)             in language append on input line 133.
 Package babel Info: Redefining ngerman shorthand "~
-(babel)             in language append on input line 132.
+(babel)             in language append on input line 133.
  (./docs/4_ergebnisse.tex
 Package babel Info: Redefining ngerman shorthand "|
 (babel)             in language append on input line 3.
@@ -1331,52 +1359,73 @@ Package babel Info: Redefining ngerman shorthand "|
 (babel)             in language append on input line 25.
 Package babel Info: Redefining ngerman shorthand "~
 (babel)             in language append on input line 25.
+ (/usr/share/texmf-dist/tex/latex/listings/lstlang1.sty
+File: lstlang1.sty 2015/06/04 1.6 listings language file
 )
+Underfull \hbox (badness 10000) in paragraph at lines 39--41
+
+ []
+
 Package babel Info: Redefining ngerman shorthand "|
-(babel)             in language append on input line 134.
+(babel)             in language append on input line 49.
 Package babel Info: Redefining ngerman shorthand "~
-(babel)             in language append on input line 134.
+(babel)             in language append on input line 49.
 Package babel Info: Redefining ngerman shorthand "|
-(babel)             in language append on input line 134.
+(babel)             in language append on input line 49.
 Package babel Info: Redefining ngerman shorthand "~
-(babel)             in language append on input line 134.
- [6]
+(babel)             in language append on input line 49.
+[6]
 Package babel Info: Redefining ngerman shorthand "|
-(babel)             in language append on input line 136.
+(babel)             in language append on input line 51.
 Package babel Info: Redefining ngerman shorthand "~
-(babel)             in language append on input line 136.
- (./docs/5_quellen.tex)
+(babel)             in language append on input line 51.
+)
 Package babel Info: Redefining ngerman shorthand "|
-(babel)             in language append on input line 139.
+(babel)             in language append on input line 135.
 Package babel Info: Redefining ngerman shorthand "~
-(babel)             in language append on input line 139.
+(babel)             in language append on input line 135.
 Package babel Info: Redefining ngerman shorthand "|
-(babel)             in language append on input line 139.
+(babel)             in language append on input line 135.
 Package babel Info: Redefining ngerman shorthand "~
-(babel)             in language append on input line 139.
+(babel)             in language append on input line 135.
  [7]
-Package atveryend Info: Empty hook `BeforeClearDocument' on input line 139.
-Package atveryend Info: Empty hook `AfterLastShipout' on input line 139.
+Package babel Info: Redefining ngerman shorthand "|
+(babel)             in language append on input line 137.
+Package babel Info: Redefining ngerman shorthand "~
+(babel)             in language append on input line 137.
+ (./docs/5_quellen.tex)
+Package babel Info: Redefining ngerman shorthand "|
+(babel)             in language append on input line 140.
+Package babel Info: Redefining ngerman shorthand "~
+(babel)             in language append on input line 140.
+Package babel Info: Redefining ngerman shorthand "|
+(babel)             in language append on input line 140.
+Package babel Info: Redefining ngerman shorthand "~
+(babel)             in language append on input line 140.
+ [8]
+Package atveryend Info: Empty hook `BeforeClearDocument' on input line 140.
+Package atveryend Info: Empty hook `AfterLastShipout' on input line 140.
  (./master.aux)
-Package atveryend Info: Executing hook `AtVeryEndDocument' on input line 139.
-Package atveryend Info: Executing hook `AtEndAfterFileList' on input line 139.
+Package atveryend Info: Executing hook `AtVeryEndDocument' on input line 140.
+Package atveryend Info: Executing hook `AtEndAfterFileList' on input line 140.
 Package rerunfilecheck Info: File `master.out' has not changed.
-(rerunfilecheck)             Checksum: A9AC8A29FF5C871C66620EA7A44D1D7C;1514.
-Package atveryend Info: Empty hook `AtVeryVeryEnd' on input line 139.
+(rerunfilecheck)             Checksum: 8C8B082A5766A6F5C8D790F742D2E884;1577.
+Package atveryend Info: Empty hook `AtVeryVeryEnd' on input line 140.
  ) 
 Here is how much of TeX's memory you used:
- 20681 strings out of 492985
- 380647 string characters out of 6138637
- 539003 words of memory out of 5000000
- 23829 multiletter control sequences out of 15000+600000
+ 22596 strings out of 492985
+ 406085 string characters out of 6138638
+ 571919 words of memory out of 5000000
+ 25708 multiletter control sequences out of 15000+600000
  39415 words of font info for 39 fonts, out of 8000000 for 9000
  1141 hyphenation exceptions out of 8191
- 64i,7n,60p,8882b,458s stack positions out of 5000i,500n,10000p,200000b,80000s
-{/usr/share/texmf-dist/fonts/enc/dvips/lm/lm-mathit.enc}{/usr/share/texmf-dist/fonts/enc/dvips/lm/lm-rm.enc}{/usr/share/texmf-dist/fonts/enc/dvips/lm/lm-mathex.enc}{/usr/share/texmf-dist/fonts/enc/dvips/lm/lm-mathsy.enc}{/usr/share/texmf-dist/fonts/enc/dvips/lm/lm-ts1.enc}{/usr/share/texmf-dist/fonts/enc/dvips/lm/lm-rmtt.enc}</usr/share/texmf-dist/fonts/type1/public/lm/lmbx12.pfb></usr/share/texmf-dist/fonts/type1/public/lm/lmex10.pfb></usr/share/texmf-dist/fonts/type1/public/lm/lmmi12.pfb></usr/share/texmf-dist/fonts/type1/public/lm/lmmi8.pfb></usr/share/texmf-dist/fonts/type1/public/lm/lmr12.pfb></usr/share/texmf-dist/fonts/type1/public/lm/lmr17.pfb></usr/share/texmf-dist/fonts/type1/public/lm/lmr8.pfb></usr/share/texmf-dist/fonts/type1/public/lm/lmssbx10.pfb></usr/share/texmf-dist/fonts/type1/public/lm/lmsy10.pfb></usr/share/texmf-dist/fonts/type1/public/lm/lmtt12.pfb>
-Output written on master.pdf (8 pages, 189951 bytes).
+ 64i,8n,60p,8882b,1233s stack positions out of 5000i,500n,10000p,200000b,80000s
+{/usr/share/texmf-dist/fonts/enc/dvips/lm/lm-mathex.enc}{/usr/share/texmf-dist/fonts/enc/dvips/lm/lm-mathit.enc}{/usr/share/texmf-dist/fonts/enc/dvips/lm/lm-rm.enc}{/usr/share/texmf-dist/fonts/enc/dvips/lm/lm-mathsy.enc}{/usr/share/texmf-dist/fonts/enc/dvips/lm/lm-ts1.enc}{/usr/share/texmf-dist/fonts/enc/dvips/lm/lm-rmtt.enc}</usr/share/texmf-dist/fonts/type1/public/lm/lmbx12.pfb></usr/share/texmf-dist/fonts/type1/public/lm/lmex10.pfb></usr/share/texmf-dist/fonts/type1/public/lm/lmmi12.pfb></usr/share/texmf-dist/fonts/type1/public/lm/lmmi6.pfb></usr/share/texmf-dist/fonts/type1/public/lm/lmmi8.pfb></usr/share/texmf-dist/fonts/type1/public/lm/lmr12.pfb></usr/share/texmf-dist/fonts/type1/public/lm/lmr17.pfb></usr/share/texmf-dist/fonts/type1/public/lm/lmr6.pfb></usr/share/texmf-dist/fonts/type1/public/lm/lmr8.pfb></usr/share/texmf-dist/fonts/type1/public/lm/lmssbx10.pfb></usr/share/texmf-dist/fonts/type1/public/lm/lmsy10.pfb></usr/share/texmf-dist/fonts/type1/public/lm/lmsy8.pfb></usr/
+share/texmf-dist/fonts/type1/public/lm/lmtt12.pfb>
+Output written on master.pdf (9 pages, 223308 bytes).
 PDF statistics:
- 234 PDF objects out of 1000 (max. 8388607)
- 211 compressed objects within 3 object streams
- 44 named destinations out of 1000 (max. 500000)
- 197 words of extra memory for PDF output out of 10000 (max. 10000000)
+ 276 PDF objects out of 1000 (max. 8388607)
+ 249 compressed objects within 3 object streams
+ 64 named destinations out of 1000 (max. 500000)
+ 205 words of extra memory for PDF output out of 10000 (max. 10000000)
 
diff --git a/langfassung/master.out b/langfassung/master.out
index ebce7ca..c2573b4 100644
--- a/langfassung/master.out
+++ b/langfassung/master.out
@@ -13,11 +13,12 @@
 \BOOKMARK [2][-]{subsection.2.4}{Blender + Python}{section.2}% 13
 \BOOKMARK [2][-]{subsection.2.5}{Making things faster}{section.2}% 14
 \BOOKMARK [2][-]{subsection.2.6}{Spiral Galaxies}{section.2}% 15
-\BOOKMARK [3][-]{subsubsection.2.6.1}{N-K\366rper problem}{subsection.2.6}% 16
+\BOOKMARK [3][-]{subsubsection.2.6.1}{N-body problem}{subsection.2.6}% 16
 \BOOKMARK [3][-]{subsubsection.2.6.2}{Hilbert Spiral}{subsection.2.6}% 17
 \BOOKMARK [2][-]{subsection.2.7}{Gr\366\337eneinheiten}{section.2}% 18
 \BOOKMARK [1][-]{section.3}{Ergebnisse}{}% 19
 \BOOKMARK [2][-]{subsection.3.1}{Simulation Speed}{section.3}% 20
 \BOOKMARK [2][-]{subsection.3.2}{Spiral Galaxies}{section.3}% 21
-\BOOKMARK [2][-]{subsection.3.3}{Distortion of Galaxies}{section.3}% 22
-\BOOKMARK [1][-]{section.4}{Quellen und Hilfen}{}% 23
+\BOOKMARK [2][-]{subsection.3.3}{Lookup-Table Speed}{section.3}% 22
+\BOOKMARK [2][-]{subsection.3.4}{Distortion of Galaxies}{section.3}% 23
+\BOOKMARK [1][-]{section.4}{Quellen und Hilfen}{}% 24
diff --git a/langfassung/master.pdf b/langfassung/master.pdf
index c39170c..d61dfc8 100644
--- a/langfassung/master.pdf
+++ b/langfassung/master.pdf
Binary files differdiff --git a/langfassung/master.synctex.gz b/langfassung/master.synctex.gz
index 2d05754..f9ed4ad 100644
--- a/langfassung/master.synctex.gz
+++ b/langfassung/master.synctex.gz
Binary files differdiff --git a/langfassung/master.tex b/langfassung/master.tex
index aa34893..b248c7e 100644
--- a/langfassung/master.tex
+++ b/langfassung/master.tex
@@ -12,6 +12,7 @@
 \usepackage{textcomp}
 
 \usepackage{tikz}
+\usepackage{listings}
 
 \usepackage{hyperref}
 \hypersetup{
@@ -67,7 +68,7 @@ urlcolor=black
   \item Compare the generated galaxies with real galaxies to find out if they
   are legit
   \item Generate the dark-matter, link the galaxies to the dark matter and watch
-  how the dark matter affects the galaxy while deforming the dark matter. 
+  how the dark matter affects the galaxy while deforming the dark matter.
 \end{itemize}
 
 \subsubsection{Generally building a galaxy}
diff --git a/langfassung/master.toc b/langfassung/master.toc
index 11af2a8..dce2f87 100644
--- a/langfassung/master.toc
+++ b/langfassung/master.toc
@@ -2,6 +2,9 @@
 \contentsline {section}{\numberline {1}Einleitung}{2}{section.1}
 \contentsline {subsection}{\numberline {1.1}Themen}{2}{subsection.1.1}
 \contentsline {subsection}{\numberline {1.2}Motivation}{2}{subsection.1.2}
+\contentsline {paragraph}{\nonumberline \( \Phi \)}{2}{section*.2}
+\contentsline {paragraph}{\nonumberline \( \rho \)}{2}{section*.3}
+\contentsline {paragraph}{\nonumberline \( \rho _{new} \rightarrow (deriviation) \)}{2}{section*.4}
 \contentsline {section}{\numberline {2}Hauptteil}{3}{section.2}
 \contentsline {subsection}{\numberline {2.1}Notes}{3}{subsection.2.1}
 \contentsline {subsubsection}{\numberline {2.1.1}Todo}{3}{subsubsection.2.1.1}
@@ -13,15 +16,18 @@
 \contentsline {subsection}{\numberline {2.3}Einasto profile}{4}{subsection.2.3}
 \contentsline {subsection}{\numberline {2.4}Blender + Python}{4}{subsection.2.4}
 \contentsline {subsection}{\numberline {2.5}Making things faster}{5}{subsection.2.5}
+\contentsline {paragraph}{\nonumberline Kicking out to many Stars, 1 out of 10000 is just to much...}{5}{section*.5}
 \contentsline {subsection}{\numberline {2.6}Spiral Galaxies}{5}{subsection.2.6}
-\contentsline {subsubsection}{\numberline {2.6.1}N-K\IeC {\"o}rper problem}{5}{subsubsection.2.6.1}
+\contentsline {subsubsection}{\numberline {2.6.1}N-body problem}{5}{subsubsection.2.6.1}
 \contentsline {subsubsection}{\numberline {2.6.2}Hilbert Spiral}{5}{subsubsection.2.6.2}
 \contentsline {subsection}{\numberline {2.7}Gr\IeC {\"o}\IeC {\ss }eneinheiten}{5}{subsection.2.7}
 \contentsline {section}{\numberline {3}Ergebnisse}{6}{section.3}
 \contentsline {subsection}{\numberline {3.1}Simulation Speed}{6}{subsection.3.1}
 \contentsline {subsection}{\numberline {3.2}Spiral Galaxies}{6}{subsection.3.2}
-\contentsline {subsection}{\numberline {3.3}Distortion of Galaxies}{6}{subsection.3.3}
-\contentsline {section}{\numberline {4}Quellen und Hilfen}{7}{section.4}
-\contentsline {paragraph}{\nonumberline Herrn J\IeC {\"o}rg Thar}{7}{section*.3}
-\contentsline {paragraph}{\nonumberline Konstantin Bosbach}{7}{section*.4}
-\contentsline {paragraph}{\nonumberline Tilman Hoffbauer}{7}{section*.5}
+\contentsline {subsection}{\numberline {3.3}Lookup-Table Speed}{6}{subsection.3.3}
+\contentsline {paragraph}{\nonumberline Python script}{6}{section*.6}
+\contentsline {subsection}{\numberline {3.4}Distortion of Galaxies}{7}{subsection.3.4}
+\contentsline {section}{\numberline {4}Quellen und Hilfen}{8}{section.4}
+\contentsline {paragraph}{\nonumberline Herrn J\IeC {\"o}rg Thar}{8}{section*.8}
+\contentsline {paragraph}{\nonumberline Konstantin Bosbach}{8}{section*.9}
+\contentsline {paragraph}{\nonumberline Tilman Hoffbauer}{8}{section*.10}
diff --git a/langfassung/master.x.gnuplot b/langfassung/master.x.gnuplot
new file mode 100644
index 0000000..84fcd41
--- /dev/null
+++ b/langfassung/master.x.gnuplot
@@ -0,0 +1,2 @@
+set table "master.x.table"; set format "%.5f"
+set samples 25; plot [x=-5:5] x*x