'''simple docstring'''

import math
from collections.abc import Callable







def      UpperCamelCase_						(					snake_case_       :       Callable[[float], float]						,		snake_case_       :       float						,		snake_case_       :       float      )					->     float:






 '''simple docstring'''

 __lowerCAmelCase											=						xa
 __lowerCAmelCase											=						xa
 while True:
  if x_n == x_na or function(snake_case_      ) == function(snake_case_      ):
   raise ZeroDivisionError("""float division by zero, could not find root"""      )
  __lowerCAmelCase											=						x_na - (
      function(snake_case_      ) / ((function(snake_case_      ) - function(snake_case_      )) / (x_na - x_n))
  )
  if abs(x_na - x_na      ) < 10**-5:
   return x_na
  __lowerCAmelCase											=						x_na
  __lowerCAmelCase											=						x_na







def      UpperCamelCase_						(					snake_case_       :       float      )					->     float:






 '''simple docstring'''

 return math.pow(snake_case_						,		3      ) - (2 * x) - 5


if __name__ == "__main__":
 print(intersection(f, 3, 3.5))







'''simple docstring'''

from math import sqrt

import numpy as np
from sympy import symbols

# Coefficient
# Speed of light (m/s)
_A			:      List[Any]					      =				299792458

# Symbols
_A      ,     _A      ,     _A      ,     _A			:      Union[str, Any]					      =				symbols('''ct x y z''')







def      UpperCamelCase_						(					snake_case_       :       float      )					->     float:






 '''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      UpperCamelCase_						(					snake_case_       :       float      )					->     float:






 '''simple docstring'''

 return 1 / sqrt(1 - beta(snake_case_      ) ** 2      )







def      UpperCamelCase_						(					snake_case_       :       float      )					->     np.ndarray:






 '''simple docstring'''

 return np.array(
     [
         [gamma(snake_case_      ), -gamma(snake_case_      ) * beta(snake_case_      ), 0, 0],
         [-gamma(snake_case_      ) * beta(snake_case_      ), gamma(snake_case_      ), 0, 0],
         [0, 0, 1, 0],
         [0, 0, 0, 1],
     ]      )







def      UpperCamelCase_						(					snake_case_       :       float						,		snake_case_       :       np.ndarray | None = None      )					->     np.ndarray:






 '''simple docstring'''

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

 return transformation_matrix(snake_case_      ) @ event


if __name__ == "__main__":
 import doctest

 doctest.testmod()

 # Example of symbolic vector:
 _A			:      str					      =				transform(29979245)
 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			:      int					      =				{ct: c, x: 1, y: 1, z: 1}
 _A			:      Any					      =				[four_vector[i].subs(sub_dict) for i in range(4)]

 print(f'\n{numerical_vector}')






