



from math import sqrt

import numpy as np
from sympy import symbols

# Coefficient
# Speed of light (m/s)
lowercase_						=       2_9979_2458

# Symbols
lowercase_			,      lowercase_			,      lowercase_			,      lowercase_						=       symbols("""ct x y z""")



def __lowerCAmelCase	(       SCREAMING_SNAKE_CASE_					):
			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	(       SCREAMING_SNAKE_CASE_					):
			return 1 / sqrt(1 - beta(SCREAMING_SNAKE_CASE_					) ** 2					)



def __lowerCAmelCase	(       SCREAMING_SNAKE_CASE_					):
			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 __lowerCAmelCase	(       SCREAMING_SNAKE_CASE_  ,					SCREAMING_SNAKE_CASE_ = None					):
			# Ensure event is not empty
			if event is None:
						lowercase__   					=			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:
							lowercase_						=       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
							lowercase_						=       {ct: c, x: 1, y: 1, z: 1}
							lowercase_						=       [four_vector[i].subs(sub_dict) for i in range(4)]

							print(F'\n{numerical_vector}')









from graphs.minimum_spanning_tree_kruskal import kruskal



def __lowerCAmelCase	(       ):
			lowercase__   					=			9
			lowercase__   					=			[
			    [0, 1, 4],
			    [0, 7, 8],
			    [1, 2, 8],
			    [7, 8, 7],
			    [7, 6, 1],
			    [2, 8, 2],
			    [8, 6, 6],
			    [2, 3, 7],
			    [2, 5, 4],
			    [6, 5, 2],
			    [3, 5, 14],
			    [3, 4, 9],
			    [5, 4, 10],
			    [1, 7, 11],
			]

			lowercase__   					=			kruskal(SCREAMING_SNAKE_CASE_  ,					SCREAMING_SNAKE_CASE_					)

			lowercase__   					=			[
			    [7, 6, 1],
			    [2, 8, 2],
			    [6, 5, 2],
			    [0, 1, 4],
			    [2, 5, 4],
			    [2, 3, 7],
			    [0, 7, 8],
			    [3, 4, 9],
			]

			assert sorted(SCREAMING_SNAKE_CASE_					) == sorted(SCREAMING_SNAKE_CASE_					)




