



from maths.prime_check import is_prime



def __lowerCAmelCase	(       SCREAMING_SNAKE_CASE_					):
			if not isinstance(SCREAMING_SNAKE_CASE_  ,					SCREAMING_SNAKE_CASE_					):
						lowercase__   					=			f'''Input value of [number={number}] must be an integer'''
						raise TypeError(SCREAMING_SNAKE_CASE_					)
			if is_prime(SCREAMING_SNAKE_CASE_					) and is_prime(number + 2					):
						return number + 2
			else:
						return -1


if __name__ == "__main__":
							import doctest

							doctest.testmod()









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}')




