




'''simple docstring'''


from typing import List

from .keymap import KEYMAP, get_character



def  _SCREAMING_SNAKE_CASE     (      UpperCamelCase__    :					str				):




     """simple docstring"""


     def decorator(UpperCamelCase__    :					int				):
          a_     :							Optional[int]     						=  getattr(UpperCamelCase__ ,    """handle_key""" ,    []				)
          handle += [key]
          setattr(UpperCamelCase__ ,    """handle_key""" ,    UpperCamelCase__				)
          return func

     return decorator



def  _SCREAMING_SNAKE_CASE     (      *UpperCamelCase__    :					List[str]				):




     """simple docstring"""


     def decorator(UpperCamelCase__    :					List[str]				):
          a_     :							Optional[int]     						=  getattr(UpperCamelCase__ ,    """handle_key""" ,    []				)
          handle += keys
          setattr(UpperCamelCase__ ,    """handle_key""" ,    UpperCamelCase__				)
          return func

     return decorator







class      SCREAMING_SNAKE_CASE    (						snake_case_				):






      def __new__( cls   :  Tuple						,						lowercase__   :  Optional[Any]						,						lowercase__   :  str						,						lowercase__   :  Tuple       ):


           '''simple docstring'''

           a_     :							Optional[Any]     						=  super().__new__(cls						,						lowercase__						,						lowercase__						,						lowercase__       )
           if not hasattr(lowercase__						,						"""key_handler"""       ):
                setattr(lowercase__						,						"""key_handler"""						,						{}       )
           setattr(lowercase__						,						"""handle_input"""						,						KeyHandler.handle_input       )

           for value in attrs.values():
                a_     :							str     						=  getattr(lowercase__						,						"""handle_key"""						,						[]       )
                for key in handled_keys:
                     a_     :							Tuple     						=  value
           return new_cls






      @staticmethod
      def 							lowercase_						( cls   :  Tuple       ):


           '''simple docstring'''

           a_     :							int     						=  get_character()
           if char != KEYMAP["undefined"]:
                a_     :							List[str]     						=  ord(lowercase__       )
           a_     :							Union[str, Any]     						=  cls.key_handler.get(lowercase__       )
           if handler:
                a_     :							int     						=  char
                return handler(cls       )
           else:
                return None



def  _SCREAMING_SNAKE_CASE     (      cls    :					List[str]				):




     """simple docstring"""


     return KeyHandler(cls.__name__ ,    cls.__bases__ ,    cls.__dict__.copy()				)






'''simple docstring'''


from math import sqrt

import numpy as np
from sympy import symbols

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

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



def  _SCREAMING_SNAKE_CASE     (      UpperCamelCase__    :					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     (      UpperCamelCase__    :					float				):




     """simple docstring"""


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



def  _SCREAMING_SNAKE_CASE     (      UpperCamelCase__    :					float				):




     """simple docstring"""


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



def  _SCREAMING_SNAKE_CASE     (      UpperCamelCase__    :					float ,    UpperCamelCase__    :					np.ndarray | None = None				):




     """simple docstring"""


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

     return transformation_matrix(UpperCamelCase__				) @ event


if __name__ == "__main__":
 import doctest

 doctest.testmod()

 # Example of symbolic vector:
 lowerCAmelCase_      :  Union[str, 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
 lowerCAmelCase_      :  Tuple				     =  {ct: c, x: 1, y: 1, z: 1}
 lowerCAmelCase_      :  Optional[int]				     =  [four_vector[i].subs(sub_dict) for i in range(4)]

 print(f"\n{numerical_vector}")
