#!/usr/bin/env python
# encoding: utf-8

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())

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