"""simple docstring"""



from abc import ABC, abstractmethod
from argparse import ArgumentParser



class   _A						(    SCREAMING_SNAKE_CASE__       ):




    """simple docstring"""




    @staticmethod
    @abstractmethod
    def 			lowercase       (		A_				:  ArgumentParser     )     ->							Optional[Any]:
         raise NotImplementedError()







    @abstractmethod
    def 			lowercase       (		self				:  List[Any]     )     ->							List[Any]:
         raise NotImplementedError()





from math import sqrt

import numpy as np
from sympy import symbols

# Coefficient
# Speed of light (m/s)
SCREAMING_SNAKE_CASE:     Optional[int]									= 2_9_9_7_9_2_4_5_8

# Symbols
SCREAMING_SNAKE_CASE				,					SCREAMING_SNAKE_CASE				,					SCREAMING_SNAKE_CASE				,					SCREAMING_SNAKE_CASE:     Tuple									= symbols('''ct x y z''')


def 					_a							(					lowerCAmelCase )->	float:
		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							(					lowerCAmelCase )->	float:
		return 1 / sqrt(1 - beta(lowerCAmelCase ) ** 2 )


def 					_a							(					lowerCAmelCase )->	np.ndarray:
		return np.array(
		    [
		        [gamma(lowerCAmelCase ), -gamma(lowerCAmelCase ) * beta(lowerCAmelCase ), 0, 0],
		        [-gamma(lowerCAmelCase ) * beta(lowerCAmelCase ), gamma(lowerCAmelCase ), 0, 0],
		        [0, 0, 1, 0],
		        [0, 0, 0, 1],
		    ] )


def 					_a							(					lowerCAmelCase    ,						lowerCAmelCase = None )->	np.ndarray:
		# Ensure event is not empty
		if event is None:
				SCREAMING_SNAKE_CASE_					      =							np.array([ct, x, y, z] )  # Symbolic four vector
		else:
				event[0] *= c  # x0 is ct (speed of light * time)

		return transformation_matrix(lowerCAmelCase ) @ event


if __name__ == "__main__":
						import doctest

						doctest.testmod()

						# Example of symbolic vector:
						SCREAMING_SNAKE_CASE:     int									= transform(2_9_9_7_9_2_4_5)
						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
						SCREAMING_SNAKE_CASE:     List[Any]									= {ct: c, x: 1, y: 1, z: 1}
						SCREAMING_SNAKE_CASE:     Optional[Any]									= [four_vector[i].subs(sub_dict) for i in range(4)]

						print(f"""\n{numerical_vector}""")