from math import *

# finds Greatest Common Divisor for two integers
def gcd(a,b):
    u, v = a, b

    counter2=0;
    while v != 0:
        r = u % v
        #print "The remainder is", r
        u = v
        v = r
        counter2 +=1

    return u

# Fraction class
class Fraction:
    def __init__(self,num=0,denom=1):
        if denom==0: # fraction is undefined
            self._n=0
            self._d=0
        else :
            factor = gcd(abs(num),abs(denom))
            if denom < 0:
                factor=-factor # the sign is always in numerator
            self._n=num/factor
            self._d=denom/factor

    def __str__(self):
        if self._d == 0:
            return 'Undefined'
        elif self._d == 1 :
            return str(self._n)
        else:
            return str(self._n) + '/' + str(self._d)

    def __add__(self,other): # Addition of two fractions
        return Fraction(self._n*other._d+other._n*self._d,self._d*other._d)

    def __sub__(self,other): # Subtraction of two fractions
        return Fraction(self._n*other._d-other._n*self._d,self._d*other._d)

    def __mul__(self,other): # Multiplication of two fractions
        return Fraction(self._n*other._n,self._d*other._d)

    def __div__(self,other): # division of two fractions self/other
        return Fraction(self._n*other._d,self._d*other._n)

    def __neg__(self): # negation of a fraction
        return Fraction(-self._n,self._d)

    def n_invert(self): # negative reciprocal of a fraction
        return Fraction(self._d,self._n).__neg__()
        #return -Fraction(self._d,self._n)

      # conversion of a fraction to a mixed number
      # so far if a user tries to convert a proper fraction to a mixed number,
      # the warning is displayed, but the mixed number is still created,
      # with 0 as the whole part (quotient)
      #! in a mixed number the sign is stored with the whole part
    def fraction2mixed(self):
        if abs(self._n) < self._d: # used abs to take into account negative fractions
            print "Warning: you tried to convert a proper fraction to a mixed number!"
            print "The mixed number was created, but its whole part (quotient) is 0"
            return MixedNumber(0,self._n,self._d)
        else:
            if self._n < 0: # if the fraction's numerator is negative,
                # the sign will be stored in the whole part of the mixed number
                return MixedNumber(-(abs(self._n)//self._d),abs(self._n)%self._d,self._d)
            else:
                return MixedNumber(self._n//self._d,self._n%self._d,self._d)

# Mixed Numbers Class
class MixedNumber(Fraction):
    def __init__(self,w=0,num=0,denom=1): # initially, by default, we have 0 0/1 
        self._w=w
        if num >= denom: # if fractional part is improper fraction, fix it
            if self._w < 0:
                self._w = -(abs(self._w) + num//denom)
            else:
                self._w += num//denom
            num = num%denom
        self._f=Fraction(num,denom)
      

    def __str__(self):
        if self._w == 0:
            return str(self._f)
        else:
            return str(self._w) + '  ' + str(self._f)

      # conversion of a mixed number to improper fraction
    def mixed2fraction(self):
        if self._w < 0: # if the mixed number is negative
            return -(Fraction(abs(self._w),1) + self._f)
        else: # if the mixed number is positive
            return Fraction(self._w,1) + self._f

    def __add__(self,other): # Addition of two mixed numbers or
                             #a mixed number and a fraction, or ...
        a=self.mixed2fraction() # first mixed number is converted to a fraction
        if isinstance(other,MixedNumber):
            b=other.mixed2fraction() # second mixed number is covnerted to a fraction
            c=a+b
        elif isinstance(other,Fraction): # if second number is a fraction
            c=a+other
        elif isinstance(other,int): # if second number is integer
            b=Fraction(other,1)
            c=a+b
        else:
            print 'Tried to perform the following operation:',self,' + ',other
            raiseTypeError('These items cannot be added')

        return c.fraction2mixed()

    def __sub__(self,other): # Subtraction of two mixed numbers
        a=self.mixed2fraction() # first mixed number is converted to a fraction
        if isinstance(other,MixedNumber):
            b=other.mixed2fraction() # second mixed number is covnerted to a fraction
            c=a-b
        elif isinstance(other,Fraction): # if second number is a fraction
            c=a-other
        elif isinstance(other,int): # if second number is integer
            b=Fraction(other,1)
            c=a-b
        else:
            print 'Tried to perform the following operation:',self,' - ',other
            raiseTypeError('subtraction cannot be done')

        return c.fraction2mixed()

    def __mul__(self,other): # Multiplication of two mixed numbers
        a=self.mixed2fraction()
        if isinstance(other,MixedNumber):
            b=other.mixed2fraction()
            c=a*b
        elif isinstance(other,Fraction):
            c=a*other
        elif isinstance(other,int):
            b=Fraction(other,1)
            c=a*b
        else:
            print 'Tried to perform the following operation:',self,' * ',other
            raiseTypeError('Cannot find the product of these items')

        return c.fraction2mixed()

    def __div__(self,other): # division of two mixed numbers
        a=self.mixed2fraction()
        if isinstance(other,MixedNumber):
            b=other.mixed2fraction()
            c=a/b
        elif isinstance(other,Fraction):
            c=a/other
        elif isinstance(other,int):
            b=Fraction(other,1)
            c=a/b
        else:
            print 'Tried to perform the following operation:',self,' / ',other
            raiseTypeError('Division cannot be performed')

        return c.fraction2mixed()

    def __neg__(self): # negation of a mixed number
        return MixedNumber(-self._w, self._f._n,self._f._d)

    # not needed
    #def n_invert(self): # negative reciprocal of a fraction
    #    pass

def main():
    print "Adding a negative mixed number and a positive mixed number"
    m1=MixedNumber(-2,5,4)
    m2=MixedNumber(1,2,3)
    print m1, '+', m2, "  is  ",(m1+m2)

    tt=raw_input('Press Enter to continue')

    print "Converting a negative fraction to a negative mixed number"

    f=Fraction(-14,12)
    m=f.fraction2mixed()
    print f, " is ", m

    tt=raw_input('Press Enter to continue')

    print "Adding a negative mixed number and a fraction"

    f1=Fraction(2,3)
    m3=m1+f1
    print m1, " + ", f1, " is ",m3

    tt=raw_input('Press Enter to continue')

    print "Negating a mixed number"

    print '-(',m1,") is ", -m1

    tt=raw_input('Press Enter to continue')

    print "Multiplying two mixed numbers"

    m4 = m1*m2
    print m1,"  *  ", m2, "  is",m4

    tt=raw_input('Press Enter to continue')

    print "Dividing a mixed number by a mixed number"

    m5=m1/m2
    print m1,' / ',m2,' is ', m5

    tt=raw_input('Press Enter to continue')

    print "Subtracting two mixed numbers"

    m6=m1-m2
    print m1,' - ',m2,' is ', m6
    
main()