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Simplified pseudocode

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Martin Thoma 2013-09-01 11:29:01 +02:00
parent f111747eb1
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source-code/Pseudocode/Calculate-Legendre/Calculate-Legendre.tex
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@ -28,31 +28,25 @@
\Require $p \in \mathbb{P}, a \in \mathbb{Z}, p \geq 3$
\If{$a \geq p$ or $a < 0$}\Comment{Regel (III)}
\State \Return $\Call{CalculateLegendre}{a \mod p, p}$ \Comment{nun: $a \in [0, \dots, p-1]$}
\ElsIf{$a \equiv 0 \mod p$} \Comment{Null-Fall}
\State \Return 0
\ElsIf{$a \equiv 1 \mod p$} \Comment{Eins-Fall}
\State \Return 1
\ElsIf{$a \equiv -1 \mod p$} \Comment{Regel (VI)}
\If{$p \equiv 1 \mod 4$}
\State \Return 1
\Else
\State \Return -1
\EndIf
\ElsIf{!$\Call{isPrime}{|a|}$} \Comment{Regel (II)}
\State $p_1, p_2, \dots, p_n \gets \Call{Faktorisiere}{a}$
\State \Return $\prod_{i=1}^n \Call{CalculateLegendre}{p_i, a}$ \Comment{nun: $a \in \mathbb{P}$}
\ElsIf{$a == 0$} \Comment{Null-Fall}
\State \Return 0 \Comment{nun: $a \in [1, \dots, p-1]$}
\ElsIf{$a == 1$} \Comment{Eins-Fall}
\State \Return 1 \Comment{nun: $a \in [2, \dots, p-1]$}
\ElsIf{$a == 2$} \Comment{Regel (VII)}
\If{$a \equiv \pm 1 \mod 8$}
\State \Return 1
\Else
\State \Return -1
\EndIf \Comment{nun: $a \in \mathbb{P}, a \geq 3$}
\ElsIf{$p == 3$} \Comment{Regel (IV)}
\State $t \gets p \mod 3$
\If{$t == 2$}
\State $t \gets -1$
\EndIf
\State \Return $t$
\EndIf \Comment{nun: $a \in [3, \dots, p-1]$}
\ElsIf{$a == p-1$} \Comment{Regel (VI)}
\If{$p \equiv 1 \mod 4$}
\State \Return 1
\Else
\State \Return -1
\EndIf \Comment{nun: $a \in [3, \dots, p-2]$}
\ElsIf{!$\Call{isPrime}{a}$} \Comment{Regel (II)}
\State $p_1, p_2, \dots, p_n \gets \Call{Faktorisiere}{a}$
\State \Return $\prod_{i=1}^n \Call{CalculateLegendre}{p_i, p}$ \Comment{nun: $a \in \mathbb{P}, a \geq 3$}
\Else
\State \Return $(-1) \cdot \Call{CalculateLegendre}{p, a}$
\EndIf