





"""simple docstring"""





from math import sqrt

import numpy as np
from sympy import symbols

# Coefficient
# Speed of light (m/s)
__A											=		2_9979_2458

# Symbols
__A											=		symbols("""ct x y z""")
def  __A   (_SCREAMING_SNAKE_CASE			)					->Optional[Any]:





  """simple docstring"""


  if velocity > c:
    raise ValueError('Speed must not exceed light speed 299,792,458 [m/s]!'			)
  elif velocity < 1:
    # Usually the speed should be much higher than 1 (c order of magnitude)
    raise ValueError('Speed must be greater than or equal to 1!'			)

  return velocity / c
def  __A   (_SCREAMING_SNAKE_CASE			)					->Any:





  """simple docstring"""


  return 1 / sqrt(1 - beta(_A			) ** 2			)
def  __A   (_SCREAMING_SNAKE_CASE			)					->Union[str, Any]:





  """simple docstring"""


  return np.array(
      [
          [gamma(_A			), -gamma(_A			) * beta(_A			), 0, 0],
          [-gamma(_A			) * beta(_A			), gamma(_A			), 0, 0],
          [0, 0, 1, 0],
          [0, 0, 0, 1],
      ]			)
def  __A   (_SCREAMING_SNAKE_CASE     ,   _SCREAMING_SNAKE_CASE = None			)					->List[Any]:





  """simple docstring"""


  if event is None:
    lowerCAmelCase__			:Optional[int]											=							np.array([ct, x, y, z]			)  # Symbolic four vector
  else:
    event[0] *= c  # x0 is ct (speed of light * time)

  return transformation_matrix(_A			) @ event


if __name__ == "__main__":
  import doctest

  doctest.testmod()

  # Example of symbolic vector:
  __A											=		transform(2997_9245)
  print("""Example of four vector: """)
  print(F'''ct\' = {four_vector[0]}''')
  print(F'''x\' = {four_vector[1]}''')
  print(F'''y\' = {four_vector[2]}''')
  print(F'''z\' = {four_vector[3]}''')

  # Substitute symbols with numerical values
  __A											=		{ct: c, x: 1, y: 1, z: 1}
  __A											=		[four_vector[i].subs(sub_dict) for i in range(4)]

  print(F'''\n{numerical_vector}''')






def 						lowerCamelCase__    (		_A							):







	'''simple docstring'''





	if num <= 0:
		raise ValueError("Input must be a positive integer"							)

	snake_case_		    =     [True] * (num + 1)

	snake_case_		    =     2
	while p * p <= num:
		if primes[p]:
			for i in range(p * p     ,	num + 1     ,	_A							):
				snake_case_		    =     False
		p += 1

	return [prime for prime in range(2     ,	num + 1							) if primes[prime]]


if __name__ == "__main__":
		import doctest

		doctest.testmod()

		lowercase__				:     Tuple 		=						int(input("Enter a positive integer: ").strip())
		print(prime_sieve_eratosthenes(user_num))
