mirror of
https://github.com/2martens/uni.git
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92 lines
3.2 KiB
TeX
92 lines
3.2 KiB
TeX
\documentclass[10pt,a4paper,oneside,ngerman,numbers=noenddot]{scrartcl}
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\usepackage[T1]{fontenc}
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\usepackage[utf8x]{inputenc}
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\usepackage[ngerman]{babel}
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\usepackage{amsmath}
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\usepackage{amsfonts}
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\usepackage{amssymb}
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\usepackage{paralist}
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\usepackage{gauss}
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\usepackage{pgfplots}
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\usepackage[locale=DE,exponent-product=\cdot,detect-all]{siunitx}
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\usepackage{tikz}
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\usetikzlibrary{automata,matrix,fadings,calc,positioning,decorations.pathreplacing,arrows,decorations.markings}
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\usepackage{polynom}
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\usepackage{multirow}
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\usepackage[german]{fancyref}
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\polyset{style=C, div=:,vars=x}
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\pgfplotsset{compat=1.8}
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\pagenumbering{arabic}
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% ensures that paragraphs are separated by empty lines
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\parskip 12pt plus 1pt minus 1pt
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\parindent 0pt
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% define how the sections are rendered
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\def\thesection{7.\arabic{section})}
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\def\thesubsection{\arabic{subsection}.}
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\def\thesubsubsection{(\alph{subsubsection})}
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% some matrix magic
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\makeatletter
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\renewcommand*\env@matrix[1][*\c@MaxMatrixCols c]{%
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\hskip -\arraycolsep
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\let\@ifnextchar\new@ifnextchar
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\array{#1}}
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\makeatother
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\begin{document}
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\author{Benjamin Kuffel, Jim Martens\\Gruppe 6}
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\title{Hausaufgaben zum 1. Dezember}
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\maketitle
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\setcounter{section}{2}
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\section{} %7.3
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\setcounter{subsection}{1}
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\subsection{}
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Das Netz \(N_{1}\) ist nicht lebendig, beschränkt oder reversibel. Die Transitionen gta, rz, s und f sind lebendig. Alle Plätze außer "`Bauteile"' und "`fertige Bauteile"' sind beschränkt.
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\section{} %7.4
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\subsection{}
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Der Erreichbarkeitsgraph für das Netz \(N_{7.4a}\) befindet sich auf \fref{fig:1}. Der Erreichbarkeitsgraph für das Netz \(N_{7.4b}\) befindet sich auf \fref{fig:2} und der Algorithmus hätte in der Markierung \((3,0,0,3)^T\) abgebrochen.
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\begin{figure}
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\begin{tikzpicture}[node distance=2cm]
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\node (m0) {\((0,0,2,4)^T\)};
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\node (m1) [right=of m0] {\((1,0,1,3)^T\)};
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\node (m2) [right=of m1] {\((2,0,0,2)^T\)};
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\node (m3) [below=of m2] {\((0,1,1,2)^T\)};
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\node (m4) [right=of m3] {\((1,1,0,1)^T\)};
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\path[->] (m0) edge node[above] {v} (m1)
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(m1) edge node[above] {v} (m2)
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(m2) edge node[right] {u} (m3)
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(m3) edge node[above right] {t} (m1)
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(m3) edge node[above] {v} (m4)
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(m4) edge node[above right] {t} (m2);
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\end{tikzpicture}
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\caption{Erreichbarkeitsgraph für Netz \(N_{7.4a}\)}
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\label{fig:1}
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\end{figure}
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\begin{figure}
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\begin{tikzpicture}[node distance=2cm]
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\node (m0) {\((0,0,1,4)^T\)};
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\node (m1) [right=of m0] {\((3,0,0,3)^T\)};
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\node (m2) [right=of m1] {\((1,2,1,3)^T\)};
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\node (m3) [below=of m2] {\((3,0,1,4)^T\)};
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\node (m4) [left=of m3] {\((3,2,0,2)^T\)};
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\node (m5) [below=of m3] {\((6,0,0,3)^T\)};
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\node (m6) [below=of m5] {\((4,2,1,3)^T\)};
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\node (m7) [left=of m5] {\((1,2,2,4)^T\)};
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\node (m8) [left=of m7] {\((1,4,1,2)^T\)};
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\node (m9) [left=of m4] {\((5,0,0,3)^T\)};
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\path[->] (m0) edge node[above] {v} (m1)
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(m1) edge node[above] {u} (m2)
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(m2) edge node[right] {t} (m3)
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(m2) edge node[below right] {v} (m4)
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(m3) edge node[right] {v} (m5)
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(m4) edge node[below right] {u} (m8)
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(m4) edge node[above] {t} (m9)
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(m5) edge node[right] {u} (m6)
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(m3) edge node[below right] {u} (m7);
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\end{tikzpicture}
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\caption{Erreichbarkeitsgraph für Netz \(N_{7.4b}\)}
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\label{fig:2}
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\end{figure}
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\end{document}
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