
"""simple docstring"""







from math import sqrt

import numpy as np
from sympy import symbols

# Coefficient
# Speed of light (m/s)
_SCREAMING_SNAKE_CASE	       =      299_792_458

# Symbols
_SCREAMING_SNAKE_CASE       ,							_SCREAMING_SNAKE_CASE       ,							_SCREAMING_SNAKE_CASE       ,							_SCREAMING_SNAKE_CASE	       =      symbols("""ct x y z""")
def   __UpperCamelCase   (					SCREAMING_SNAKE_CASE )  ->     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   (					SCREAMING_SNAKE_CASE )  ->     float:







							"""simple docstring"""


							return 1 / sqrt(1 - beta(SCREAMING_SNAKE_CASE ) ** 2 )
def   __UpperCamelCase   (					SCREAMING_SNAKE_CASE )  ->     np.ndarray:







							"""simple docstring"""


							return np.array(
							    [
							        [gamma(SCREAMING_SNAKE_CASE ), -gamma(SCREAMING_SNAKE_CASE ) * beta(SCREAMING_SNAKE_CASE ), 0, 0],
							        [-gamma(SCREAMING_SNAKE_CASE ) * beta(SCREAMING_SNAKE_CASE ), gamma(SCREAMING_SNAKE_CASE ), 0, 0],
							        [0, 0, 1, 0],
							        [0, 0, 0, 1],
							    ] )
def   __UpperCamelCase   (					SCREAMING_SNAKE_CASE							,    SCREAMING_SNAKE_CASE = None )  ->     np.ndarray:







							"""simple docstring"""


							if event is None:
														__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(SCREAMING_SNAKE_CASE ) @ event


if __name__ == "__main__":
		import doctest

		doctest.testmod()

		# Example of symbolic vector:
		_SCREAMING_SNAKE_CASE	       =      transform(29_979_245)
		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	       =      {ct: c, x: 1, y: 1, z: 1}
		_SCREAMING_SNAKE_CASE	       =      [four_vector[i].subs(sub_dict) for i in range(4)]

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


"""simple docstring"""







from __future__ import annotations

from dataclasses import dataclass







@dataclass
class 							__magic_name__     :
					_SCREAMING_SNAKE_CASE       :					float
					_SCREAMING_SNAKE_CASE       :					TreeNode | None     							=   None
					_SCREAMING_SNAKE_CASE       :					TreeNode | None     							=   None




def   __UpperCamelCase   (					SCREAMING_SNAKE_CASE )  ->     bool:







							"""simple docstring"""


							def is_valid_tree(SCREAMING_SNAKE_CASE ) -> bool:
														if node is None:
																					return True

														if not isinstance(SCREAMING_SNAKE_CASE							,    SCREAMING_SNAKE_CASE ):
																					return False

														try:
																					float(node.data )
														except (TypeError, ValueError):
																					return False

														return is_valid_tree(node.left ) and is_valid_tree(node.right )

							if not is_valid_tree(SCREAMING_SNAKE_CASE ):
														raise ValueError(
														    "Each node should be type of TreeNode and data should be float." )

							def is_binary_search_tree_recursive_check(
							    SCREAMING_SNAKE_CASE							,    SCREAMING_SNAKE_CASE							,    SCREAMING_SNAKE_CASE ) -> bool:

														if node is None:
																					return True

														return (
														    left_bound < node.data < right_bound
														    and is_binary_search_tree_recursive_check(node.left							,    SCREAMING_SNAKE_CASE							,    node.data )
														    and is_binary_search_tree_recursive_check(
														        node.right							,    node.data							,    SCREAMING_SNAKE_CASE )
														)

							return is_binary_search_tree_recursive_check(SCREAMING_SNAKE_CASE							,    -float("inf" )							,    float("inf" ) )


if __name__ == "__main__":
		import doctest

		doctest.testmod()
