''' 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.
    '''
    # You can use functions within other functions.
    # If you defined is_factor() you can use it in the function definition
    # of is_prime()

    # 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 ( y is a factor of x)
    else: 
        result = False  # if it is not, return value is False
                            # y is not a factor of x
    # return determination
    return result

# Parameter and Argument is different!
    # Parameter is in the function definition.
    # def functionname( parameters ):
    # Parameters are going to be replaced by arguments.

    # Arguments are in the function call.
    # x = functionname( arguments )
    # Arguments are the explicit values that are passed in to start up the function so it can run.
    # SO PARAMETER IS IN FUNCTION DEFINITION ARGUMENT IS IN FUNCTION CALL

#


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.
    '''

    for f in range( 2, x ):         # We only want to check values 2 to x - 1 because 1 and x are already factors!
         check = is_factor( x, f )          # Let's go through each potential factor f (number from 2 to x - 1) and see if it's a factor
         if ( check == True ):              # or if ( check ) - THIS CHECKS OTHER FACTORS TO SEE IF F IS A FACTOR OF X
             return False                   # If I find another factor then we want to return False because then it's not prime
         else:
             pass
    return True                             # We return True outside the for loop because we're done checking all factors
                                            # so we can return True (the number is prime)
                                            # If the loop finishes, none of the other factors were factors so that means
                                            # the number is prime (only had factors 1 and itself aka x)!

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.
    '''
    if ( is_factor( x , y ) == False and is_factor( y, x ) == False):
        return True
    else:
        return False


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 )