


def 						_snake_case(   SCREAMING_SNAKE_CASE__      :     str				)							->				bool:





    '''simple docstring'''






    return credit_card_number.startswith(('34', '35', '37', '4', '5', '6')				)
def 						_snake_case(   SCREAMING_SNAKE_CASE__      :     str				)							->				bool:





    '''simple docstring'''






    A__   				=       credit_card_number
    A__   				=       0
    A__   				=       len(SCREAMING_SNAKE_CASE__				) - 2
    for i in range(SCREAMING_SNAKE_CASE__   ,      -1   ,      -2				):
        #  double the value of every second digit
        A__   				=       int(cc_number[i]				)
        digit *= 2
        # If doubling of a number results in a two digit number
        # i.e greater than 9(e.g., 6 × 2 = 12),
        # then add the digits of the product (e.g., 12: 1 + 2 = 3, 15: 1 + 5 = 6),
        # to get a single digit number.
        if digit > 9:
            digit %= 10
            digit += 1
        A__   				=       cc_number[:i] + str(SCREAMING_SNAKE_CASE__				) + cc_number[i + 1 :]
        total += digit

    # Sum up the remaining digits
    for i in range(len(SCREAMING_SNAKE_CASE__				) - 1   ,      -1   ,      -2				):
        total += int(cc_number[i]				)

    return total % 10 == 0
def 						_snake_case(   SCREAMING_SNAKE_CASE__      :     str				)							->				bool:





    '''simple docstring'''






    A__   				=       f'{credit_card_number} is an invalid credit card number because'
    if not credit_card_number.isdigit():
        print(f'{error_message} it has nonnumerical characters.'				)
        return False

    if not 13 <= len(SCREAMING_SNAKE_CASE__				) <= 16:
        print(f'{error_message} of its length.'				)
        return False

    if not validate_initial_digits(SCREAMING_SNAKE_CASE__				):
        print(f'{error_message} of its first two digits.'				)
        return False

    if not luhn_validation(SCREAMING_SNAKE_CASE__				):
        print(f'{error_message} it fails the Luhn check.'				)
        return False

    print(f'{credit_card_number} is a valid credit card number.'				)
    return True


if __name__ == "__main__":
     import doctest

     doctest.testmod()
     validate_credit_card_number("4111111111111111")
     validate_credit_card_number("32323")




from __future__ import annotations

from scipy.special import comb  # type: ignore


class 			A						:







    """simple docstring"""





    def __init__(				self			:	Any,lowercase_			:	list[tuple[float, float]]		)->   Optional[int]:





        '''simple docstring'''







        A__   				=       list_of_points
        # Degree determines the flexibility of the curve.
        # Degree = 1 will produce a straight line.
        A__   				=       len(lowercase_		) - 1


    def 						snake_case__					(				self			:	List[Any],lowercase_			:	float		)->   list[float]:





        '''simple docstring'''







        assert 0 <= t <= 1, "Time t must be between 0 and 1."
        A__   				=       []
        for i in range(len(self.list_of_points		)		):
            # basis function for each i
            output_values.append(
                comb(self.degree,lowercase_		) * ((1 - t) ** (self.degree - i)) * (t**i)		)
        # the basis must sum up to 1 for it to produce a valid Bezier curve.
        assert round(sum(lowercase_		),5		) == 1
        return output_values


    def 						snake_case__					(				self			:	str,lowercase_			:	float		)->   tuple[float, float]:





        '''simple docstring'''







        assert 0 <= t <= 1, "Time t must be between 0 and 1."

        A__   				=       self.basis_function(lowercase_		)
        A__   				=       0.0
        A__   				=       0.0
        for i in range(len(self.list_of_points		)		):
            # For all points, sum up the product of i-th basis function and i-th point.
            x += basis_function[i] * self.list_of_points[i][0]
            y += basis_function[i] * self.list_of_points[i][1]
        return (x, y)


    def 						snake_case__					(				self			:	str,lowercase_			:	float = 0.01		)->   str:





        '''simple docstring'''







        from matplotlib import pyplot as plt  # type: ignore

        A__   				=       []  # x coordinates of points to plot
        A__   				=       []  # y coordinates of points to plot

        A__   				=       0.0
        while t <= 1:
            A__   				=       self.bezier_curve_function(lowercase_		)
            to_plot_x.append(value[0]		)
            to_plot_y.append(value[1]		)
            t += step_size

        A__   				=       [i[0] for i in self.list_of_points]
        A__   				=       [i[1] for i in self.list_of_points]

        plt.plot(
            lowercase_,lowercase_,color='blue',label='Curve of Degree ' + str(self.degree		),)
        plt.scatter(lowercase_,lowercase_,color='red',label='Control Points'		)
        plt.legend()
        plt.show()


if __name__ == "__main__":
     import doctest

     doctest.testmod()

     BezierCurve([(1, 2), (3, 5)]).plot_curve()  # degree 1
     BezierCurve([(0, 0), (5, 5), (5, 0)]).plot_curve()  # degree 2
     BezierCurve([(0, 0), (5, 5), (5, 0), (2.5, -2.5)]).plot_curve()  # degree 3

