
from math import sqrt

import numpy as np
from sympy import symbols

# Coefficient
# Speed of light (m/s)
__A							=2_9_9_7_9_2_4_5_8

# Symbols
__A,		__A,		__A,		__A							=symbols('''ct x y z''')





def      lowerCamelCase_					(							lowerCamelCase__       ):
				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__       ):
				return 1 / sqrt(1 - beta(lowerCamelCase__       ) ** 2       )





def      lowerCamelCase_					(							lowerCamelCase__       ):
				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__      ,					lowerCamelCase__ = None       ):
				# Ensure event is not empty
				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(lowerCamelCase__       ) @ event


if __name__ == "__main__":
			import doctest

			doctest.testmod()

			# Example of symbolic vector:
			__A							=transform(2_9_9_7_9_2_4_5)
			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							={ct: c, x: 1, y: 1, z: 1}
			__A							=[four_vector[i].subs(sub_dict) for i in range(4)]

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




class        _SCREAMING_SNAKE_CASE	:



	def __init__(       self		,    lowercase		,    lowercase=None		,    lowercase=None					)							->			List[Any]:
					lowerCamelCase_         =     data
					lowerCamelCase_         =     previous
					lowerCamelCase_         =     next_node



	def __str__(       self					)							->			str:
					return f'{self.data}'



	def        SCREAMING_SNAKE_CASE_(       self					)							->			int:
					return self.data



	def        SCREAMING_SNAKE_CASE_(       self					)							->			Union[str, Any]:
					return self.next



	def        SCREAMING_SNAKE_CASE_(       self					)							->			int:
					return self.previous




class        _SCREAMING_SNAKE_CASE	:



	def __init__(       self		,    lowercase					)							->			Optional[int]:
					lowerCamelCase_         =     head



	def __iter__(       self					)							->			int:
					return self



	def        SCREAMING_SNAKE_CASE_(       self					)							->			Optional[Any]:
					if not self.current:
									raise StopIteration
					else:
									lowerCamelCase_         =     self.current.get_data()
									lowerCamelCase_         =     self.current.get_next()
									return value




class        _SCREAMING_SNAKE_CASE	:



	def __init__(       self					)							->			Union[str, Any]:
					lowerCamelCase_         =     None  # First node in list
					lowerCamelCase_         =     None  # Last node in list



	def __str__(       self					)							->			Optional[Any]:
					lowerCamelCase_         =     self.head
					lowerCamelCase_         =     []
					while current is not None:
									nodes.append(current.get_data()					)
									lowerCamelCase_         =     current.get_next()
					return " ".join(str(lowercase					) for node in nodes					)



	def __contains__(       self		,    lowercase					)							->			Optional[int]:
					lowerCamelCase_         =     self.head
					while current:
									if current.get_data() == value:
													return True
									lowerCamelCase_         =     current.get_next()
					return False



	def __iter__(       self					)							->			List[str]:
					return LinkedListIterator(self.head					)



	def        SCREAMING_SNAKE_CASE_(       self					)							->			List[str]:
					if self.head:
									return self.head.get_data()
					return None



	def        SCREAMING_SNAKE_CASE_(       self					)							->			Any:
					if self.tail:
									return self.tail.get_data()
					return None



	def        SCREAMING_SNAKE_CASE_(       self		,    lowercase					)							->			None:
					if self.head is None:
									lowerCamelCase_         =     node
									lowerCamelCase_         =     node
					else:
									self.insert_before_node(self.head		,    lowercase					)



	def        SCREAMING_SNAKE_CASE_(       self		,    lowercase					)							->			None:
					if self.head is None:
									self.set_head(lowercase					)
					else:
									self.insert_after_node(self.tail		,    lowercase					)



	def        SCREAMING_SNAKE_CASE_(       self		,    lowercase					)							->			None:
					lowerCamelCase_         =     Node(lowercase					)
					if self.head is None:
									self.set_head(lowercase					)
					else:
									self.set_tail(lowercase					)



	def        SCREAMING_SNAKE_CASE_(       self		,    lowercase		,    lowercase					)							->			None:
					lowerCamelCase_         =     node
					lowerCamelCase_         =     node.previous

					if node.get_previous() is None:
									lowerCamelCase_         =     node_to_insert
					else:
									lowerCamelCase_         =     node_to_insert

					lowerCamelCase_         =     node_to_insert



	def        SCREAMING_SNAKE_CASE_(       self		,    lowercase		,    lowercase					)							->			None:
					lowerCamelCase_         =     node
					lowerCamelCase_         =     node.next

					if node.get_next() is None:
									lowerCamelCase_         =     node_to_insert
					else:
									lowerCamelCase_         =     node_to_insert

					lowerCamelCase_         =     node_to_insert



	def        SCREAMING_SNAKE_CASE_(       self		,    lowercase		,    lowercase					)							->			None:
					lowerCamelCase_         =     1
					lowerCamelCase_         =     Node(lowercase					)
					lowerCamelCase_         =     self.head
					while node:
									if current_position == position:
													self.insert_before_node(lowercase		,    lowercase					)
													return
									current_position += 1
									lowerCamelCase_         =     node.next
					self.insert_after_node(self.tail		,    lowercase					)



	def        SCREAMING_SNAKE_CASE_(       self		,    lowercase					)							->			Node:
					lowerCamelCase_         =     self.head
					while node:
									if node.get_data() == item:
													return node
									lowerCamelCase_         =     node.get_next()
					raise Exception("Node not found"					)



	def        SCREAMING_SNAKE_CASE_(       self		,    lowercase					)							->			Union[str, Any]:
					if (node := self.get_node(lowercase					)) is not None:
									if node == self.head:
													lowerCamelCase_         =     self.head.get_next()

									if node == self.tail:
													lowerCamelCase_         =     self.tail.get_previous()

									self.remove_node_pointers(lowercase					)



	@staticmethod
	def        SCREAMING_SNAKE_CASE_(       lowercase					)							->			None:
					if node.get_next():
									lowerCamelCase_         =     node.previous

					if node.get_previous():
									lowerCamelCase_         =     node.next

					lowerCamelCase_         =     None
					lowerCamelCase_         =     None



	def        SCREAMING_SNAKE_CASE_(       self					)							->			int:
					return self.head is None





def      lowerCamelCase_					(							):
				pass


if __name__ == "__main__":
			import doctest

			doctest.testmod()


