# -*- coding: utf-8 -*- """ Created on Mon Jan 26 13:56:26 2015 @author: Sam """ def gcd(m,n): while m%n != 0: oldm = m oldn = n m = oldn n = oldm%oldn return n def reduce(fraction): GcD = gcd(fraction.num, fraction.den) if GcD == 1 or GcD == -1: if fraction.sign == 1: return Fraction(-fraction.num,fraction.den) else: return Fraction(fraction.num,fraction.den) else: if fraction.sign == 1: return Fraction(-fraction.num/GcD,fraction.den/GcD) else: return Fraction(fraction.num/GcD,fraction.den/GcD) def posneg(fraction): if fraction.sign == 0 or fraction.sign == 2: if fraction.num < 0 or fraction.den < 0: if fraction.den < 0 and fraction.num < 0: fraction.num = -fraction.num fraction.den = -fraction.den fraction.sign = 2 return fraction # The returned fraction is made of positive integers # and has no .sign else: if fraction.den < 0: fraction.num = fraction.num fraction.den = -fraction.den fraction.sign = 1 return fraction # The returned fraction is made of positive integers # and has a sign if fraction.num < 0: fraction.num = -fraction.num fraction.den = fraction.den fraction.sign = 1 return fraction # The returned fraction is made of positive integers # and has a sign else: fraction.sign = 2 return fraction else: if fraction.num < 0 or fraction.den < 0: if fraction.den < 0 and fraction.num < 0: fraction.num = -fraction.num fraction.den = -fraction.den fraction.sign = 1 return fraction # The returned fraction is made of positive integers # and has no .sign else: if fraction.den < 0: fraction.num = fraction.num fraction.den = -fraction.den fraction.sign = 2 return fraction # The returned fraction is made of positive integers # and has a sign if fraction.num < 0: fraction.num = -fraction.num fraction.den = fraction.den fraction.sign = 2 return fraction # The returned fraction is made of positive integers # and has a sign else: fraction.sign = 1 return fraction class Fraction: def __init__(self,top,bottom): self.num = top self.den = bottom self.sign = 0 #0 is none 1 is on 2 is off #Just to start out with something # Sort out the sign on the fraction and simplify self = posneg(self) def __str__(self): if self.sign == 1: return "-" + str(self.num)+"/"+ str(self.den) else: return str(self.num)+"/"+ str(self.den) def __add__(self,otherfraction): newfrac1 = Fraction(1,1) newfrac2 = Fraction (1,1) if self.sign == 1: newfrac1.sign = 1 if self.sign == 2: newfrac1.sign = 2 if otherfraction.sign == 2: newfrac2.sign = 2 if otherfraction.sign == 1: newfrac2.sign = 1 newfrac1.den = self.den * otherfraction.den newfrac1.num = self.num * otherfraction.den newfrac2.den = otherfraction.den * self.den newfrac2.num = otherfraction.num * self.den # Temporarily declare a new fraction newfrac3 = Fraction(1,1) newfrac3.den = newfrac1.den newfrac3.sign = 0 if newfrac1.sign == 2 and newfrac2.sign == 1: newfrac3.num = newfrac1.num - newfrac2.num newfrac3 = posneg(reduce(newfrac3)) return newfrac3 if newfrac1.sign == 1 and newfrac2.sign == 2: newfrac3.num = newfrac2.num - newfrac1.num newfrac3 = posneg(reduce(newfrac3)) return newfrac3 if newfrac1.sign == 1 and newfrac2.sign == 1: newfrac3.num = newfrac1.num + newfrac2.num newfrac3.sign = 1 newfrac3 = reduce(newfrac3) newfrac3 = posneg(newfrac3) return newfrac3 if newfrac1.sign == 2 and newfrac2.sign == 2: newfrac3.num = newfrac2.num + newfrac1.num newfrac3.sign = 2 newfrac3 = posneg(reduce(newfrac3)) return newfrac3 def __mul__ (self,otherfraction): newfraction = Fraction(1,1) newfraction.num = otherfraction.num * self.num newfraction.den = otherfraction.den * self.den if self.sign == 1 and otherfraction.sign == 1: newfraction.sign = 2 if self.sign == 2 and otherfraction.sign == 1: newfraction.sign = 1 if self.sign == 1 and otherfraction.sign == 2: newfraction.sign = 1 if self.sign == 2 and otherfraction.sign == 2: newfraction.sign = 2 return newfraction def __sub__(self,otherfraction): newfraction = Fraction (1,1) negativeone = Fraction(1,1) negativeone.sign = 1 newfraction = self + (negativeone * otherfraction) return newfraction def __div__ (self,otherfraction): newfraction = Fraction (1,1) #Initializing New Fraciton inverseotherfraction = Fraction(otherfraction.num,otherfraction.den) inverseotherfraction.sign = otherfraction.sign newfraction = self*newfraction return newfraction print('Fraction') x1 = Fraction(1,3) #1/2 x2 = Fraction(1,-4) #-1/2 x3 = Fraction(-1,-5) #1/2 x4 = Fraction(-1,6) #-1/2 print(x1) print(x2) print(x3) print(x4) s1 = x1+x2 # 0 s2 = x1+x3 # 1 s3 = x1+x4 # 0 s4 = s1+x3 # 1/2 print('Sum') print(s1) print(s2) print(s3) print(s4) m1= x1*x2 m2= x1*x3 m3= x1*x4 print('multiplication') print(m1) print(m2) print(m3) sub1= x2-x1 sub2= x2-x3 sub3= x1-x4 print('Subtraction') print(sub1) print(sub2) print(sub3) d1= x2/x1 d2= x2/x3 d3= x1/x4 print('Division') print(d1) print(d2) print(d3)
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