mirror of
https://github.com/MartinThoma/LaTeX-examples.git
synced 2025-04-25 22:38:04 +02:00
7740f0147f
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.
46 lines
1.7 KiB
TeX
46 lines
1.7 KiB
TeX
\documentclass{article}
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\usepackage[pdftex,active,tightpage]{preview}
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\setlength\PreviewBorder{2mm}
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\usepackage[utf8]{inputenc} % this is needed for umlauts
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\usepackage[ngerman]{babel} % this is needed for umlauts
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\usepackage[T1]{fontenc} % this is needed for correct output of umlauts in pdf
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\usepackage{amssymb,amsmath,amsfonts} % nice math rendering
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\usepackage{braket} % needed for \Set
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\usepackage{algorithm,algpseudocode}
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\usepackage{tikz}
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\usetikzlibrary{decorations.pathreplacing,calc}
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\newcommand{\tikzmark}[1]{\tikz[overlay,remember picture] \node (#1) {};}
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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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($(#3)!(#2.south)!($(#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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}%
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\begin{document}
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\begin{preview}
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\begin{algorithm}[H]
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\begin{algorithmic}
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\Require $R \in \mathbb{Z}^n, P \in (\mathbb{N}_{\geq 1})^n, n \in \mathbb{N}_{\geq 1}$, where \\
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$R$ is a vector with all rests $r_i$ and\\
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$P$ is a vector with all modulos $p_i$ such that\\
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($x \equiv r_i \mod p_i$) and $\left(i \neq j \Rightarrow \Call{gcd}{p_i, p_j} = 1 \right)$
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\\
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\State $M \gets \prod_{p \in P} p$
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\For{$i \in \{1, \dots, n\}$}
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\State $M_i \gets \frac{M}{p_i} $
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\State $y_i \gets \Call{getMultiplicativeInverse}{M_i, R_i}$
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\EndFor
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\\
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\State \Return $(\sum_{i=1}^n R_i y_i M_i, M)$
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\end{algorithmic}
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\caption{Solve a system of linear congruences}
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\label{alg:solveCongruences}
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\end{algorithm}
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\end{preview}
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\end{document}
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