misc

source-code/Pseudocode/SolveLinearCongruences/solveLinearCongruences.py

@@ -0,0 +1,49 @@
+#!/usr/bin/env python
+# -*- coding: utf-8 -*-
+
+def ExtendedEuclideanAlgorithm(a, b):
+	"""
+		Calculates gcd(a,b) and a linear combination such that
+		gcd(a,b) = a*x + b*y
+
+		As a side effect:
+		If gcd(a,b) = 1 = a*x + b*y
+		Then x is multiplicative inverse of a modulo b.
+	"""
+	aO, bO = a, b
+
+	x=lasty=0
+	y=lastx=1
+	while (b!=0):
+		q= a/b
+		a, b = b, a%b
+		x, lastx = lastx-q*x, x
+		y, lasty = lasty-q*y, y
+
+	return {
+		"x": lastx,
+		"y": lasty,
+		"gcd": aO * lastx + bO * lasty
+	}
+
+def solveLinearCongruenceEquations(rests, modulos):
+	"""
+	Solve a system of linear congruences.
+
+	>>> solveLinearCongruenceEquations([4, 12, 14], [19, 37, 43])
+	{'congruence class': 22804, 'modulo': 30229}
+	"""
+	assert len(rests) == len(modulos)
+	x = 0
+	M = reduce(lambda x, y: x*y, modulos)
+
+	for mi, resti in zip(modulos, rests):
+		Mi = M / mi
+		s = ExtendedEuclideanAlgorithm(Mi, mi)["x"]
+		e = s * Mi
+		x += resti * e
+	return {"congruence class": ((x % M) + M) % M, "modulo": M}
+
+if __name__ == "__main__":
+	import doctest
+	doctest.testmod()