mirror of
https://github.com/MartinThoma/LaTeX-examples.git
synced 2025-04-19 11:38:05 +02:00
Remove trailing spaces
The commands
find . -type f -name '*.md' -exec sed --in-place 's/[[:space:]]\+$//' {} \+
and
find . -type f -name '*.tex' -exec sed --in-place 's/[[:space:]]\+$//' {} \+
were used to do so.
This commit is contained in:
Martin Thoma
parent
c578b25d2f
commit
7740f0147f
538 changed files with 3496 additions and 3496 deletions
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@ -33,7 +33,7 @@
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\EndIf \Comment{now: $a \in [3, \dots, p-2]$}
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\ElsIf{!$\Call{isPrime}{a}$} \Comment{rule (II)}
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\State $p_1, p_2, \dots, p_n \gets \Call{Factorize}{a}$
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\State \Return $\prod_{i=1}^n \Call{CalculateLegendre}{p_i, p}$
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\State \Return $\prod_{i=1}^n \Call{CalculateLegendre}{p_i, p}$
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\Else \Comment{now: $a \in \mathbb{P}, \sqrt{p-2} \geq a \geq 3$}
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\If{$\frac{p-1}{2} \equiv 0 \mod 2$ or $\frac{a-1}{2} \equiv 0 \mod 2$}
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\State \Return $\Call{CalculateLegendre}{p, a}$
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@ -1,6 +1,6 @@
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\documentclass[aspectratio=169,hyperref={pdfpagelabels=false}]{beamer}
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\usepackage{lmodern}
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\usepackage[utf8]{inputenc} % this is needed for german umlauts
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\usepackage[ngerman]{babel} % this is needed for german umlauts
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\usepackage[T1]{fontenc} % this is needed for correct output of umlauts in pdf
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@ -11,7 +11,7 @@
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\usepackage{verbatim}
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\usepackage{tikz}
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\usetikzlibrary{arrows,shapes}
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% Define some styles for graphs
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\tikzstyle{vertex}=[circle,fill=black!25,minimum size=20pt,inner sep=0pt]
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\tikzstyle{selected vertex} = [vertex, fill=red!24]
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@ -20,14 +20,14 @@
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\tikzstyle{weight} = [font=\small]
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\tikzstyle{selected edge} = [draw,line width=5pt,-,red!50]
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\tikzstyle{ignored edge} = [draw,line width=5pt,-,black!20]
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% see http://deic.uab.es/~iblanes/beamer_gallery/index_by_theme.html
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%\usetheme{Frankfurt}
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\usefonttheme{professionalfonts}
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% disables bottom navigation bar
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\beamertemplatenavigationsymbolsempty
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% http://tex.stackexchange.com/questions/23727/converting-beamer-slides-to-animated-images
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\setbeamertemplate{navigation symbols}{}%
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@ -41,7 +41,7 @@
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\pgfsetlayers{background,main}
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\newcommand\hlight[1]{\tikz[overlay, remember picture,baseline=-\the\dimexpr\fontdimen22\textfont2\relax]\node[rectangle,fill=blue!50,rounded corners,fill opacity = 0.2,draw,thick,text opacity =1] {$#1$};}
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\newcommand\tocalculate[1]{\tikz[overlay, remember picture,baseline=-\the\dimexpr\fontdimen22\textfont2\relax]\node[rectangle,fill=green!50,rounded corners,fill opacity = 0.2,draw,thick,text opacity =1] {$#1$};}
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\begin{frame}
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\begin{minipage}[b]{0.30\linewidth}
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\centering
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@ -11,11 +11,11 @@
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\begin{document}
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\begin{preview}
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Sei $n \in \mathbb{N}_{\geq 1}$, $A \in \mathbb{R}^{n \times n}$ und
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Sei $n \in \mathbb{N}_{\geq 1}$, $A \in \mathbb{R}^{n \times n}$ und
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positiv definit sowie symmetrisch.
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Dann existiert eine Zerlegung $A = L \cdot L^T$, wobei $L$ eine
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untere Dreiecksmatrix ist. Diese wird von folgendem Algorithmus
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untere Dreiecksmatrix ist. Diese wird von folgendem Algorithmus
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berechnet:
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\begin{algorithm}[H]
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@ -9,8 +9,8 @@
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\usepackage{braket} % needed for \Set
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\usepackage{algorithm,algpseudocode}
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\algnewcommand\True{\textbf{true}\space}
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\algnewcommand\False{\textbf{false}\space}
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\algnewcommand\True{\textbf{true}\space}
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\algnewcommand\False{\textbf{false}\space}
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\algnewcommand{\LineComment}[1]{\State \(\triangleright\) #1}
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\begin{document}
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\begin{preview}
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@ -15,7 +15,7 @@
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\newcommand*{\AddNote}[4]{%
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\begin{tikzpicture}[overlay, remember picture]
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\draw [decoration={brace,amplitude=0.5em},decorate,very thick]
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($(#3)!(#1.north)!($(#3)-(0,1)$)$) --
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($(#3)!(#1.north)!($(#3)-(0,1)$)$) --
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($(#3)!(#2.south)!($(#3)-(0,1)$)$)
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node [align=center, text width=2.5cm, pos=0.5, anchor=west] {#4};
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\end{tikzpicture}
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@ -28,7 +28,7 @@
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\Require $Z \in \mathbb{R}_{\geq 0}, b \in \mathbb{N}_{\geq 2}$
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\State $p\gets 0$\tikzmark{top}
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\While{$b^p > Z$}\tikzmark{right}
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\State $p\gets p+1$
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\State $p\gets p+1$
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\EndWhile
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\State $i\gets p-1$\tikzmark{bottom}
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\\
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@ -11,7 +11,7 @@
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\begin{itemize}
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\item $c:E \rightarrow \mathbb{R}_0^+$: capacity of an edge
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\item $e: V \rightarrow \mathbb{R}_0^+$: excess (too much flow in one node)
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\item $r_f: V \times V \rightarrow \mathbb{R}, \; r_f(u,v) := c(u,v) - f(u,v) $: remaining capacity
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\item $r_f: V \times V \rightarrow \mathbb{R}, \; r_f(u,v) := c(u,v) - f(u,v) $: remaining capacity
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\item $dist: V \rightarrow \mathbb{N}$: the label (imagine this as height)
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\end{itemize}
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@ -15,7 +15,7 @@
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\newcommand*{\AddNote}[4]{%
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\begin{tikzpicture}[overlay, remember picture]
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\draw [decoration={brace,amplitude=0.5em},decorate,very thick]
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($(#3)!(#1.north)!($(#3)-(0,1)$)$) --
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($(#3)!(#1.north)!($(#3)-(0,1)$)$) --
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($(#3)!(#2.south)!($(#3)-(0,1)$)$)
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node [align=center, text width=2.5cm, pos=0.5, anchor=west] {#4};
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\end{tikzpicture}
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@ -9,8 +9,8 @@
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\usepackage{braket} % needed for \Set
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\usepackage{algorithm,algpseudocode}
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\algnewcommand\True{\textbf{true}\space}
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\algnewcommand\False{\textbf{false}\space}
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\algnewcommand\True{\textbf{true}\space}
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\algnewcommand\False{\textbf{false}\space}
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\algnewcommand{\LineComment}[1]{\State \(\triangleright\) #1}
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\begin{document}
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\begin{preview}
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@ -15,7 +15,7 @@
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\newcommand*{\AddNote}[4]{%
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\begin{tikzpicture}[overlay, remember picture]
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\draw [decoration={brace,amplitude=0.5em},decorate,very thick]
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($(#3)!(#1.north)!($(#3)-(0,1)$)$) --
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($(#3)!(#1.north)!($(#3)-(0,1)$)$) --
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($(#3)!(#2.south)!($(#3)-(0,1)$)$)
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node [align=center, text width=2.5cm, pos=0.5, anchor=west] {#4};
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\end{tikzpicture}
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@ -11,7 +11,7 @@
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\begin{document}
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\begin{preview}
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Sei $S \subseteq V$ und $c:E\rightarrow\mathbb{R}_0^+$ die
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Sei $S \subseteq V$ und $c:E\rightarrow\mathbb{R}_0^+$ die
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Kantengewichtsfunktion.
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Für $v \in V \setminus S$ sei:
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@ -20,8 +20,8 @@
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c(S,v) &:= \sum_{\substack{\Set{u,v} \in E\\ u \in S}} c(\Set{u,v})
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\end{align*}
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Sei nun $d: \mathcal{P}(V) \rightarrow V$ die Funktion, die den
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Knoten liefert, der am stärksten mit $S \in \mathcal{P}(V)$
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Sei nun $d: \mathcal{P}(V) \rightarrow V$ die Funktion, die den
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Knoten liefert, der am stärksten mit $S \in \mathcal{P}(V)$
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verbunden ist:
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\[d(S) := v \in V \setminus S: c(S, v) = \max(\Set{c(S,v) | v \in V \setminus S})\]
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@ -16,7 +16,7 @@
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\Require $G = (V, E)$ an undirected graph
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\State $n \gets |V|$
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\State Give all vertices an index $1 \leq i \leq n$ that defines an order
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\For{$i \in 1, \dots, n$}
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\State $v_i$.color $\gets 1$
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\EndFor
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@ -17,7 +17,7 @@
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\Require $G = (V, E)$ an undirected graph
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\State $n \gets |V|$
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\State Give all vertices an index $1 \leq i \leq n$ that defines an order
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\For{$i \in 1, \dots, n$}
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\State $v_i$.color $\gets 1$
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\EndFor
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@ -39,7 +39,7 @@
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\EndFor
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\EndFor
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\State
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\State
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\State \Return $D[|r|][|h|]$
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\EndFunction
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\end{algorithmic}
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