


from math import sqrt

import numpy as np
from sympy import symbols

# Coefficient
# Speed of light (m/s)
UpperCAmelCase_				:			Optional[Any]   =	2_9979_2458

# Symbols
UpperCAmelCase_ ,       UpperCAmelCase_ ,       UpperCAmelCase_ ,       UpperCAmelCase_				:			Dict   =	symbols('ct x y z')







def 	SCREAMING_SNAKE_CASE_						(      __A			:      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 	SCREAMING_SNAKE_CASE_						(      __A			:      float    )     ->		float:

       """simple docstring"""

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







def 	SCREAMING_SNAKE_CASE_						(      __A			:      float    )     ->		np.ndarray:

       """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 	SCREAMING_SNAKE_CASE_						(      __A			:      float  ,   __A			:      np.ndarray | None = None    )     ->		np.ndarray:

       """simple docstring"""

       if event is None:
              a_ :		List[Any]							=  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:
   UpperCAmelCase_				:			List[Any]   =	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
   UpperCAmelCase_				:			Dict   =	{ct: c, x: 1, y: 1, z: 1}
   UpperCAmelCase_				:			Any   =	[four_vector[i].subs(sub_dict) for i in range(4)]

   print(F'\n{numerical_vector}')






from __future__ import annotations

from math import pi

# Define the Reduced Planck Constant ℏ (H bar), speed of light C, value of
# Pi and the function
UpperCAmelCase_				:			str   =	1.054571817e-34  # unit of ℏ : J * s

UpperCAmelCase_				:			Dict   =	3e8  # unit of c : m * s^-1







def 	SCREAMING_SNAKE_CASE_						(      __A			:      float  ,   __A			:      float  ,   __A			:      float    )     ->		dict[str, float]:

       """simple docstring"""

       if (force, area, distance).count(0    ) != 1:
              raise ValueError('One and only one argument must be 0'    )
       if force < 0:
              raise ValueError('Magnitude of force can not be negative'    )
       if distance < 0:
              raise ValueError('Distance can not be negative'    )
       if area < 0:
              raise ValueError('Area can not be negative'    )
       if force == 0:
              a_ :		Optional[Any]							=  (REDUCED_PLANCK_CONSTANT * SPEED_OF_LIGHT * pi**2 * area) / (
                  2_40 * (distance) ** 4
              )
              return {"force": force}
       elif area == 0:
              a_ :		List[str]							=  (2_40 * force * (distance) ** 4) / (
                  REDUCED_PLANCK_CONSTANT * SPEED_OF_LIGHT * pi**2
              )
              return {"area": area}
       elif distance == 0:
              a_ :		Tuple							=  (
                  (REDUCED_PLANCK_CONSTANT * SPEED_OF_LIGHT * pi**2 * area) / (2_40 * force)
              ) ** (1 / 4)
              return {"distance": distance}
       raise ValueError('One and only one argument must be 0'    )


# Run doctest
if __name__ == "__main__":
   import doctest

   doctest.testmod()


