

from math import sqrt

import numpy as np
from sympy import symbols

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

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

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

def  lowerCamelCase__ (					_a):
	return np.array(
	    [
	        [gamma(_a), -gamma(_a) * beta(_a), 0, 0],
	        [-gamma(_a) * beta(_a), gamma(_a), 0, 0],
	        [0, 0, 1, 0],
	        [0, 0, 0, 1],
	    ])

def  lowerCamelCase__ (					_a							,			_a = None):
	# Ensure event is not empty
	if event is None:
		SCREAMING_SNAKE_CASE   :      Optional[Any]				     =       np.array([ct, x, y, z])  # Symbolic four vector
	else:
		event[0] *= c  # x0 is ct (speed of light * time)

	return transformation_matrix(_a) @ event


if __name__ == "__main__":
			import doctest

			doctest.testmod()

			# Example of symbolic vector:
			a_						     =    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
			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}''')



from __future__ import annotations

def  lowerCamelCase__ (					_a							,			_a):
	if b == 0:
		return (1, 0)
	((SCREAMING_SNAKE_CASE)     ,(SCREAMING_SNAKE_CASE))   :      Tuple				     =       extended_euclid(_a							,			a % b)
	SCREAMING_SNAKE_CASE   :      Dict				     =       a // b
	return (y, x - k * y)

def  lowerCamelCase__ (					_a							,			_a							,			_a							,			_a):
	((SCREAMING_SNAKE_CASE)     ,(SCREAMING_SNAKE_CASE))   :      str				     =       extended_euclid(_a							,			_a)
	SCREAMING_SNAKE_CASE   :      str				     =       na * na
	SCREAMING_SNAKE_CASE   :      int				     =       ra * x * na + ra * y * na
	return (n % m + m) % m

def  lowerCamelCase__ (					_a							,			_a):
	((SCREAMING_SNAKE_CASE)     ,(SCREAMING_SNAKE_CASE))   :      List[str]				     =       extended_euclid(_a							,			_a)
	if b < 0:
		SCREAMING_SNAKE_CASE   :      int				     =       (b % n + n) % n
	return b

def  lowerCamelCase__ (					_a							,			_a							,			_a							,			_a):
	SCREAMING_SNAKE_CASE     ,SCREAMING_SNAKE_CASE   :      Dict				     =       invert_modulo(_a							,			_a), invert_modulo(_a							,			_a)
	SCREAMING_SNAKE_CASE   :      Optional[int]				     =       na * na
	SCREAMING_SNAKE_CASE   :      Optional[Any]				     =       ra * x * na + ra * y * na
	return (n % m + m) % m


if __name__ == "__main__":
			from doctest import testmod

			testmod(name='chinese_remainder_theorem', verbose=True)
			testmod(name='chinese_remainder_theorem2', verbose=True)
			testmod(name='invert_modulo', verbose=True)
			testmod(name='extended_euclid', verbose=True)