Legendre-Symbol

source-code/Pseudocode/Calculate-Legendre/Calculate-Legendre.tex

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+\documentclass{article}
+\usepackage[pdftex,active,tightpage]{preview}
+\setlength\PreviewBorder{2mm}
+
+\usepackage[utf8]{inputenc} % this is needed for umlauts
+\usepackage[ngerman]{babel} % this is needed for umlauts
+\usepackage[T1]{fontenc}    % this is needed for correct output of umlauts in pdf
+\usepackage{amssymb,amsmath,amsfonts} % nice math rendering
+\usepackage{braket} % needed for \Set
+\usepackage{algorithm,algpseudocode}
+
+\usepackage{tikz}
+\usetikzlibrary{decorations.pathreplacing,calc}
+\newcommand{\tikzmark}[1]{\tikz[overlay,remember picture] \node (#1) {};}
+\newcommand*{\AddNote}[4]{%
+    \begin{tikzpicture}[overlay, remember picture]
+        \draw [decoration={brace,amplitude=0.5em},decorate,very thick]
+            ($(#3)!(#1.north)!($(#3)-(0,1)$)$) --  
+            ($(#3)!(#2.south)!($(#3)-(0,1)$)$)
+                node [align=center, text width=2.5cm, pos=0.5, anchor=west] {#4};
+    \end{tikzpicture}
+}%
+
+\begin{document}
+\begin{preview}
+    \begin{algorithm}[H]
+        \begin{algorithmic}
+            \Require $p \in \mathbb{P}, a \in \mathbb{Z}, p \geq 3$
+            \If{$a \geq p$}\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 $\prod_{i=1}^n \Call{CalculateLegendre}{p_i, a}$
+			\ElsIf{$p == 3$} \Comment{Regel (IV)}
+				\State $t \gets p \mod 3$
+				\If{$t == 2$}
+					\State $t \gets -1$
+				\EndIf
+				\State \Return $t$
+			\Else
+				\State \Return $a^\frac{p-1}{2} \mod p$
+			\EndIf
+        \end{algorithmic}
+    \caption{Calculate Legendre-Symbol}
+    %\AddNote{top}{bottom}{right}{calclulate $p$ such that: $b^p \leq Z < b^{p+1}$}  %\tikzmark{top},\tikzmark{right},\tikzmark{bottom}
+    \label{alg:euclidBaseTransformation}
+    \end{algorithm}
+\end{preview}
+\end{document}