


'''simple docstring'''







from math import sqrt

import numpy as np
from sympy import symbols

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

# Symbols
A						, A						, A						, A				:					Optional[Any]    						=			symbols('''ct x y z''')






def 				lowerCAmelCase__	(    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 				lowerCAmelCase__	(    lowerCamelCase					:      float       ):
       return 1 / sqrt(1 - beta(lowerCamelCase       ) ** 2       )






def 				lowerCAmelCase__	(    lowerCamelCase					:      float       ):
       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 				lowerCAmelCase__	(    lowerCamelCase					:      float  ,lowerCamelCase					:      np.ndarray | None = None       ):
       # Ensure event is not empty
       if event is None:
              _A					:     int     = 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:
   A				:					List[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				:					Union[str, Any]    						=			{ct: c, x: 1, y: 1, z: 1}
   A				:					Optional[int]    						=			[four_vector[i].subs(sub_dict) for i in range(4)]

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










'''simple docstring'''







from __future__ import annotations


class 			__lowerCamelCase			:
    """simple docstring"""


    def __init__(  self      :							Optional[Any]				,							SCREAMING_SNAKE_CASE      :							Tuple=None):
           _A					:     Any     = data
           _A					:     Optional[Any]     = None


    def __repr__(  self      :							List[str]):
           _A					:     List[Any]     = []
           _A					:     Any     = self
           while temp:
                  string_rep.append(F'{temp.data}')
                  _A					:     List[Any]     = temp.next
           return "->".join(SCREAMING_SNAKE_CASE)






def 				lowerCAmelCase__	(    lowerCamelCase					:      list       ):
       if not elements_list:
              raise Exception('The Elements List is empty'       )

       _A					:     Union[str, Any]     = Node(elements_list[0]       )
       for i in range(1  ,len(lowerCamelCase       )       ):
              _A					:     Dict     = Node(elements_list[i]       )
              _A					:     int     = current.next
       return head






def 				lowerCAmelCase__	(    lowerCamelCase					:      Node       ):
       if head_node is not None and isinstance(lowerCamelCase  ,lowerCamelCase       ):
              print_reverse(head_node.next       )
              print(head_node.data       )






def 				lowerCAmelCase__	(    ):
       from doctest import testmod

       testmod()

       _A					:     List[str]     = make_linked_list([14, 52, 14, 12, 43]       )
       print('Linked List:'       )
       print(lowerCamelCase       )
       print('Elements in Reverse:'       )
       print_reverse(lowerCamelCase       )


if __name__ == "__main__":
   main()






