fixed bug and added implementation

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

@@ -35,7 +35,11 @@
 				\State $p_1, p_2, \dots, p_n \gets \Call{Factorize}{a}$
 				\State \Return $\prod_{i=1}^n \Call{CalculateLegendre}{p_i, p}$ 
 			\Else \Comment{now: $a \in \mathbb{P}, \sqrt{p-2} \geq a \geq 3$}
-				\State \Return $(-1) \cdot \Call{CalculateLegendre}{p, a}$
+				\If{$\frac{p-1}{2} \equiv 0 \mod 2$}
+					\State \Return $(-1) \cdot \Call{CalculateLegendre}{p, a}$
+				\Else
+					\State \Return $(-1) \cdot \Call{CalculateLegendre}{p, a}$
+				\EndIf
 			\EndIf
 		\EndProcedure
         \end{algorithmic}

source-code/Pseudocode/Calculate-Legendre/calculateLegendre.py

@@ -0,0 +1,63 @@
+#!/usr/bin/env python
+# -*- coding: utf-8 -*-
+
+def isPrime(a):
+    return all(a % i for i in xrange(2, a))
+
+# http://stackoverflow.com/a/14793082/562769
+def factorize(n):
+    factors = []
+
+    p = 2
+    while True:
+        while(n % p == 0 and n > 0): #while we can divide by smaller number, do so
+            factors.append(p)
+            n = n / p
+        p += 1  #p is not necessary prime, but n%p == 0 only for prime numbers
+        if p > n / p:
+            break
+    if n > 1:
+        factors.append(n)
+    return factors
+
+def calculateLegendre(a, p):
+	"""
+	Calculate the legendre symbol (a, p) with p is prime.
+	The result is either -1, 0 or 1
+
+	>>> calculateLegendre(3, 29)
+	-1
+	>>> calculateLegendre(111, 41)
+	-1
+	>>> calculateLegendre(113, 41)
+	1
+	"""
+	if a >= p or a < 0:
+		return calculateLegendre(a % p, p)
+	elif a == 0 or a == 1:
+		return a
+	elif a == 2:
+		if a%8 == 1 or a%8 == 7:
+			return 1
+		else:
+			return -1
+	elif a == p-1:
+		if p%4 == 1:
+			return 1
+		else:
+			return -1
+	elif not isPrime(a):
+		factors = factorize(a)
+		product = 1
+		for pi in factors:
+			product *= calculateLegendre(pi, p)
+		return product
+	else:
+		if ((p-1)/2)%2==0:
+			return calculateLegendre(p, a)
+		else:
+			return (-1)*calculateLegendre(p, a)
+
+if __name__ == "__main__":
+	import doctest
+	doctest.testmod()