''' Purpose: continue introduction to functions
'''

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 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 want to check all possible factors from 2 to n - 1 because
    # for a number to be prime, its only factors are 1 and n!
    for i in range( 2, x ): # range(2,x) will go from 2 to x - 1!
        if ( is_factor(x, i) == True ): # check if i is a factor of x
            # is factor(x,i) is a function that returns True/False so we can
            # either do if (is_factor(x,i)) or if (is_factor(x,i) == True)
            return False # The minute we find another factor besides 1 and n,
                        # we know x is not prime! Just return False right here!
        else: 
            continue # go onto the next value of the for loop

    return True  # This says we checked all the numbers in the for loop and
    # if we never returned False (none were a factor), then we know
    # that x is prime! - indented into the function but outside the for loop

            # else: (indented into for loop)
            #     return True # We can't return True right off the bat because
                            # once you hit a return statement, the function is done!
                            # it doesn't check the rest of the numbers in the for loop!
                            # It only checked 2 as a factor and either returned True/False


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.
    '''

    # You can use functions within other functions!
    x_is_factor_y = is_factor( y , x ) # tells you if x is a factor of y
    y_is_factor_x = is_factor( x , y ) # tells you if y is a factor of x

    if ( x_is_factor_y == True ):
        result = False
    elif ( y_is_factor_x == True ):
        result = False
    else:   # x is not a factor of y and y is not a factor of X (both are False)
        result = True
    return result

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 )