mirror of
https://github.com/MartinThoma/LaTeX-examples.git
synced 2025-04-26 06:48:04 +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.
50 lines
1.8 KiB
TeX
50 lines
1.8 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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\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 $p \in \mathbb{P}, a \in \mathbb{Z}, p \geq 3$
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\Procedure{CalculateLegendre}{$a$, $p$}
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\If{$a \geq p$ or $a < 0$}\Comment{rule (III)}
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\State \Return $\Call{CalculateLegendre}{a \mod p, p}$ \Comment{now: $a \in [0, \dots, p-1]$}
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\ElsIf{$a == 0$ or $a == 1$}
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\State \Return $a$ \Comment{now: $a \in [2, \dots, p-1]$}
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\ElsIf{$a == 2$} \Comment{rule (VII)}
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\If{$p \equiv \pm 1 \mod 8$}
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\State \Return 1
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\Else
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\State \Return -1
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\EndIf \Comment{now: $a \in [3, \dots, p-1]$}
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\ElsIf{$a == p-1$} \Comment{rule (VI)}
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\If{$p \equiv 1 \mod 4$}
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\State \Return 1
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\Else
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\State \Return -1
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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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\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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\Else
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\State \Return $(-1) \cdot \Call{CalculateLegendre}{p, a}$
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\EndIf
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\EndIf
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\EndProcedure
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\end{algorithmic}
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\caption{Calculate Legendre symbol}
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\label{alg:calculateLegendreSymbol}
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\end{algorithm}
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\end{preview}
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\end{document}
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