



from __future__ import annotations

UpperCAmelCase							 =					8.988E9  # units = N * m^s * C^-2

def 			A_      (	__a     :				float ,		__a     :				float ,		__a     :				float ,		__a     :				float		):

				"""simple docstring"""
				a__				      =		abs(chargea * chargea		)

				if (force, chargea, chargea, distance).count(0		) != 1:
								raise ValueError("""One and only one argument must be 0"""		)
				if distance < 0:
								raise ValueError("""Distance cannot be negative"""		)
				if force == 0:
								a__				      =		COULOMBS_CONSTANT * charge_product / (distance**2)
								return {"force": force}
				elif chargea == 0:
								a__				      =		abs(__a		) * (distance**2) / (COULOMBS_CONSTANT * chargea)
								return {"charge1": chargea}
				elif chargea == 0:
								a__				      =		abs(__a		) * (distance**2) / (COULOMBS_CONSTANT * chargea)
								return {"charge2": chargea}
				elif distance == 0:
								a__				      =		(COULOMBS_CONSTANT * charge_product / abs(__a		)) ** 0.5
								return {"distance": distance}
				raise ValueError("""Exactly one argument must be 0"""		)


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)
UpperCAmelCase							 =					299_792_458

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

def 			A_      (	__a     :				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 			A_      (	__a     :				float		):

				"""simple docstring"""
				return 1 / sqrt(1 - beta(__a		) ** 2		)

def 			A_      (	__a     :				float		):

				"""simple docstring"""
				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 			A_      (	__a     :				float ,		__a     :				np.ndarray | None = None		):

				"""simple docstring"""
				# Ensure event is not empty
				if event is None:
								a__				      =		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:
	UpperCAmelCase							 =					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
	UpperCAmelCase							 =					{ct: c, x: 1, y: 1, z: 1}
	UpperCAmelCase							 =					[four_vector[i].subs(sub_dict) for i in range(4)]

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

