From a3413288381b9a85b7545631b08d07801cfbe200 Mon Sep 17 00:00:00 2001
From: Lafrite <lafrite@poneyworld.net>
Date: Fri, 19 Jul 2013 15:11:40 +0200
Subject: [PATCH] Fraction more or less done. Need to think about what to
 return

---
 arithmetic.py |  31 ++++++++
 fraction.py   | 190 ++++++++++++++++++++++++++++++++++++++++++++++++++
 2 files changed, 221 insertions(+)
 create mode 100644 arithmetic.py
 create mode 100644 fraction.py

diff --git a/arithmetic.py b/arithmetic.py
new file mode 100644
index 0000000..f99054e
--- /dev/null
+++ b/arithmetic.py
@@ -0,0 +1,31 @@
+#!/usr/bin/env python
+# encoding: utf-8
+
+
+def gcd(a, b):
+		"""Compute gcd(a,b)
+
+		:param a: first number
+		:param b: second number
+		:returns: the gcd
+
+		"""
+		if a > b:
+			c = a % b
+		else:
+			c = b % a
+
+		if c == 0:
+			return min(a,b)
+		elif a == 1:
+			return b
+		elif b == 1:
+			return a
+		else:
+			return gcd(min(a,b), c)
+
+
+# -----------------------------
+# Reglages pour 'vim'
+# vim:set autoindent expandtab tabstop=4 shiftwidth=4:
+# cursor: 16 del 
diff --git a/fraction.py b/fraction.py
new file mode 100644
index 0000000..c3b173c
--- /dev/null
+++ b/fraction.py
@@ -0,0 +1,190 @@
+#!/usr/bin/env python
+# encoding: utf-8
+
+from calculus import isNumber
+from arithmetic import gcd
+
+class Fraction(object):
+	"""Fractions!"""
+
+	def __init__(self, num, denom = 1):
+		"""To initiate a fraction we need a numerator and a denominator
+
+		:param num: the numerator
+		:param denom: the denominator
+
+		"""
+		self._num = num
+		self._denom = denom
+
+	def simplify(self):
+		"""Simplify the fraction 
+
+		:returns: steps to simplify the fraction or the fraction if there is nothing to do
+		"""
+		steps = [str(self)]
+
+		if self._denom < 0:
+			self._num = - self._num
+			self._denom = - self._denom
+			steps += [str(self)]
+
+		gcd_ = gcd(abs(self._num), abs(self._denom))
+		if self._num == self._denom:
+			self._num = 1
+			self._denom = 1
+			steps += [str(self)]
+		elif gcd_ != 1:
+
+			self._num, self._denom = self._num // gcd_ , self._denom // gcd_
+			steps += ["( {reste1} * {gcd} ) / ( {reste2} * {gcd} )".format(reste1 = self._num, reste2 = self._denom, gcd = gcd_)]
+			steps += [str(self)]
+		return steps
+
+	def __str__(self):
+		if self._denom == 1:
+			return str(self._num)
+		else:
+			return str(self._num) + " / " + str(self._denom)
+	
+	def __add__(self, other):
+		if type(other) == Fraction:
+			#cool
+			number = other
+		else:
+			number = Fraction(other)
+
+		steps = ["{frac1} + {frac2}".format(frac1 = self, frac2 = number)]
+
+		if self._denom == number._denom:
+			com_denom = self._denom
+			num1 = self._num
+			num2 = number._num
+
+		else:
+			gcd_denom = gcd(self._denom, number._denom)
+			coef1 = number._denom // gcd_denom
+			coef2 = self._denom // gcd_denom
+
+			steps += ["( {num1} * {coef1} ) / ( {den1} * {coef1} ) + ( {num2} * {coef2} ) / ( {den2} * {coef2} )".format(num1 = self._num, den1 = self._denom, coef1 = coef1, num2 = number._num, den2 = number._denom, coef2 = coef2)] 
+
+			com_denom = self._denom * coef1
+			num1 = self._num * coef1
+			num2 = number._num * coef2
+
+		steps += ["( {num1} + {num2} ) / {denom}".format(num1 = num1, num2 = num2, denom = com_denom)]
+
+		num = num1 + num2
+
+		ans_frac = Fraction(num, com_denom)
+		steps += ans_frac.simplify()
+
+		return steps
+
+	def __sub__(self, other):
+		if type(other) == Fraction:
+			#cool
+			number = other
+		else:
+			number = Fraction(other)
+
+		steps = ["{frac1} - {frac2}".format(frac1 = self, frac2 = number)]
+
+		if self._denom == number._denom:
+			com_denom = self._denom
+			num1 = self._num
+			num2 = number._num
+
+		else:
+			gcd_denom = gcd(self._denom, number._denom)
+			coef1 = number._denom // gcd_denom
+			coef2 = self._denom // gcd_denom
+
+			steps += ["( {num1} * {coef1} ) / ( {den1} * {coef1} ) - ( {num2} * {coef2} ) / ( {den2} * {coef2} )".format(num1 = self._num, den1 = self._denom, coef1 = coef1, num2 = number._num, den2 = number._denom, coef2 = coef2)] 
+
+			com_denom = self._denom * coef1
+			num1 = self._num * coef1
+			num2 = number._num * coef2
+
+		steps += ["( {num1} - {num2} ) / {denom}".format(num1 = num1, num2 = num2, denom = com_denom)]
+
+		num = num1 - num2
+
+		ans_frac = Fraction(num, com_denom)
+		steps += ans_frac.simplify()
+
+		return steps
+	
+	def __mul__(self, other):
+		if type(other) == Fraction:
+			#cool
+			number = other
+		else:
+			number = Fraction(other)
+
+		steps = ["( {frac1} ) * ( {frac2} )".format(frac1 = self, frac2 = number)]
+		steps += ["( {num1} * {num2} ) / ( {denom1} * {denom2} )".format(num1 = self._num, num2 = number._num, denom1 = self._denom, denom2 = number._denom)]
+
+		num = self._num * number._num
+		denom = self._denom * number._denom
+
+		ans_frac = Fraction(num, denom)
+		steps += ans_frac.simplify()
+
+		return steps
+
+	def __truediv__(self, other):
+		if type(other) == Fraction:
+			#cool
+			number = other
+		else:
+			number = Fraction(other)
+
+		steps = ["( {frac1} ) / ( {frac2} )".format(frac1 = self, frac2 = number)]
+		number = Fraction(number._denom, number._num)
+		steps += self * number
+
+		return steps
+
+
+
+
+if __name__ == '__main__':
+	f = Fraction(34, 12)
+	g = Fraction(1,5)
+	h = Fraction(-1,5)
+	t = Fraction(-4,5)
+	print("---------")
+	for i in (f - 1):
+		print(i)
+	print("---------")
+	for i in (f + 1):
+		print(i)
+	print("---------")
+	for i in (f + g):
+		print(i)
+	print("---------")
+	for i in (f - g):
+		print(i)
+	print("---------")
+	for i in (f * g):
+		print(i)
+	print("---------")
+	for i in (h + t):
+		print(i)
+	print("---------")
+	for i in (h - t):
+		print(i)
+	print("---------")
+	for i in (h * t):
+		print(i)
+	print("---------")
+	for i in (h / t):
+		print(i)
+
+	#print(f.simplify())
+
+# -----------------------------
+# Reglages pour 'vim'
+# vim:set autoindent expandtab tabstop=4 shiftwidth=4:
+# cursor: 16 del