''' Purpose: continue introduction to functions

    Name:

    Email id:

    Who checked your code: 

    Whose code did you check: 
'''

def is_factor( x, y ) :
    ''' Parameters x and y are integers. The function returns whether y is a
        factor of x.
    '''

    # compute remainder of x divided by y
    rem = x % y

    # check it out
    if ( rem == 0 ) :   # check whether remainder is 0
        result = True   # if it is, return value is True
    else: 
        result = False  # if it is not, return value is False

    # return determination
    return result

def are_relative_primes( x, y ) :
    ''' Parameters x and y are integers. The function returns whether x and y
        are relatively prime; i.e., whether y is not a factor of x and
        vice-versa.
    '''

    # We can use is_factor() to determine whether y is a factor of x and vise versa!

    is_x_a_factor_of_y = is_factor( y , x ) # tells us if x is a factor of y
    is_y_a_factor_of_x = is_factor( x , y ) # tells us if y is a factor of x

    if ( is_x_a_factor_of_y == True ) : # if x is a factor of y then they are not relatively prime!
        result = False # Since they're not relatively prime, we would have the result be false
    elif ( is_y_a_factor_of_x == True ) : # if y is a factor of x then they are not relatively prime
        result = False # Since they're not relatively prime, we would have the result be false
    else: # This is the final condition where x and y are relatively prime given
        # that x is not a factor of y and y is not a factor of x
        # this means that is_x_a_factor_of_x is False and is_y_a_factor_of_x is False (satisfying the problem conditions!)
        result = True # result is true since they are relatively prime

    return result # return the final result after testing the conditions in the if, elif, and else statements

def is_prime( x ) :
    ''' Parameter x is am integer. The function returns whether x is prime;
        i.e., its only factors are 1 and itself.
    '''

    # We need to check out all other possible factors such as 2,3,4 all the way to n-1
    # This is why we would want to use a range!
    # We're assuming the number is prime until we have a check to see if it's not
    result = True # We assumed the result is true ( x is prime )
    for y in range( 2 , x ) :
        is_y_a_factor_of_x = is_factor( x , y ) # this checks if y is a factor of x
        if ( is_y_a_factor_of_x == True ): # if y is a factor of x then x has a factor other than 1 that is a factor of itself
            result = False # result is False given that x has another factor other than 1
            break # Python keyword break gets you out of a loop!
        else:
            pass # We want to keep our existing result since we did not find another factor of x

    return result # return the final result whether x is prime or not






if __name__ == "__main__":

    import primal

    a1, b1 = 6, 2
    a2, b2 = 7, 3
    a3, b3 = 4, 5

    f1 = primal.is_factor( a1, b1 )
    f2 = primal.is_factor( a2, b2 )
    f3 = primal.is_factor( a3, b3 )

    print( 'is_factor(', a1, ',' , b1, ') = ', f1 )
    print( 'is_factor(', a2, ',' , b2, ') = ', f2 )
    print( 'is_factor(', a3, ',' , b3, ') = ', f3 )