


import unittest

from .lib import (
    Matrix,
    Vector,
    axpy,
    square_zero_matrix,
    unit_basis_vector,
    zero_vector,
)
class 	UpperCAmelCase_					(					unittest.TestCase    ):

   '''simple docstring'''




   def _snake_case    (		self ):






     """simple docstring"""





     lowerCamelCase :					List[str]    =				Vector([1, 2, 3] )
     self.assertEqual(x.component(0 )						,				1 )
     self.assertEqual(x.component(2 )						,				3 )
     lowerCamelCase :					int    =				Vector()






   def _snake_case    (		self ):






     """simple docstring"""





     lowerCamelCase :					Dict    =				Vector([0, 0, 0, 0, 0, 1] )
     self.assertEqual(str(__A )						,				"(0,0,0,0,0,1)" )






   def _snake_case    (		self ):






     """simple docstring"""





     lowerCamelCase :					Dict    =				Vector([1, 2, 3, 4] )
     self.assertEqual(len(__A )						,				4 )






   def _snake_case    (		self ):






     """simple docstring"""





     lowerCamelCase :					Union[str, Any]    =				Vector([1, 2] )
     lowerCamelCase :					Dict    =				Vector([1, 2, 3, 4, 5] )
     lowerCamelCase :					str    =				Vector([0, 0, 0, 0, 0, 0, 0, 0, 0, 0] )
     lowerCamelCase :					List[str]    =				Vector([1, -1, 1, -1, 2, -3, 4, -5] )
     self.assertAlmostEqual(x.euclidean_length()						,				2.236						,				3 )
     self.assertAlmostEqual(y.euclidean_length()						,				7.416						,				3 )
     self.assertEqual(z.euclidean_length()						,				0 )
     self.assertAlmostEqual(w.euclidean_length()						,				7.616						,				3 )






   def _snake_case    (		self ):






     """simple docstring"""





     lowerCamelCase :					Tuple    =				Vector([1, 2, 3] )
     lowerCamelCase :					Dict    =				Vector([1, 1, 1] )
     self.assertEqual((x + y).component(0 )						,				2 )
     self.assertEqual((x + y).component(1 )						,				3 )
     self.assertEqual((x + y).component(2 )						,				4 )






   def _snake_case    (		self ):






     """simple docstring"""





     lowerCamelCase :					Dict    =				Vector([1, 2, 3] )
     lowerCamelCase :					Optional[int]    =				Vector([1, 1, 1] )
     self.assertEqual((x - y).component(0 )						,				0 )
     self.assertEqual((x - y).component(1 )						,				1 )
     self.assertEqual((x - y).component(2 )						,				2 )






   def _snake_case    (		self ):






     """simple docstring"""





     lowerCamelCase :					int    =				Vector([1, 2, 3] )
     lowerCamelCase :					Union[str, Any]    =				Vector([2, -1, 4] )  # for test of dot product
     lowerCamelCase :					Optional[Any]    =				Vector([1, -2, -1] )
     self.assertEqual(str(x * 3.0 )						,				"(3.0,6.0,9.0)" )
     self.assertEqual((a * b)						,				0 )






   def _snake_case    (		self ):






     """simple docstring"""





     self.assertEqual(str(zero_vector(10 ) ).count("0" )						,				10 )






   def _snake_case    (		self ):






     """simple docstring"""





     self.assertEqual(str(unit_basis_vector(3						,				1 ) )						,				"(0,1,0)" )






   def _snake_case    (		self ):






     """simple docstring"""





     lowerCamelCase :					Dict    =				Vector([1, 2, 3] )
     lowerCamelCase :					List[str]    =				Vector([1, 0, 1] )
     self.assertEqual(str(axpy(2						,				__A						,				__A ) )						,				"(3,4,7)" )






   def _snake_case    (		self ):






     """simple docstring"""





     lowerCamelCase :					Tuple    =				Vector([1, 0, 0, 0, 0, 0] )
     lowerCamelCase :					List[str]    =				x.copy()
     self.assertEqual(str(__A )						,				str(__A ) )






   def _snake_case    (		self ):






     """simple docstring"""





     lowerCamelCase :					int    =				Vector([1, 0, 0] )
     x.change_component(0						,				0 )
     x.change_component(1						,				1 )
     self.assertEqual(str(__A )						,				"(0,1,0)" )






   def _snake_case    (		self ):






     """simple docstring"""





     lowerCamelCase :					Any    =				Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]						,				3						,				3 )
     self.assertEqual("|1,2,3|\n|2,4,5|\n|6,7,8|\n"						,				str(__A ) )






   def _snake_case    (		self ):






     """simple docstring"""





     lowerCamelCase :					Dict    =				Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]						,				3						,				3 )
     lowerCamelCase :					int    =				[[-3, -14, -10], [-5, -10, -5], [-2, -1, 0]]
     for x in range(a.height() ):
       for y in range(a.width() ):
         self.assertEqual(minors[x][y]						,				a.minor(__A						,				__A ) )






   def _snake_case    (		self ):






     """simple docstring"""





     lowerCamelCase :					List[Any]    =				Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]						,				3						,				3 )
     lowerCamelCase :					int    =				[[-3, 14, -10], [5, -10, 5], [-2, 1, 0]]
     for x in range(a.height() ):
       for y in range(a.width() ):
         self.assertEqual(cofactors[x][y]						,				a.cofactor(__A						,				__A ) )






   def _snake_case    (		self ):






     """simple docstring"""





     lowerCamelCase :					Union[str, Any]    =				Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]						,				3						,				3 )
     self.assertEqual(-5						,				a.determinant() )






   def _snake_case    (		self ):






     """simple docstring"""





     lowerCamelCase :					int    =				Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]]						,				3						,				3 )
     lowerCamelCase :					int    =				Vector([1, 2, 3] )
     self.assertEqual("(14,32,50)"						,				str(a * x ) )
     self.assertEqual("|2,4,6|\n|8,10,12|\n|14,16,18|\n"						,				str(a * 2 ) )






   def _snake_case    (		self ):






     """simple docstring"""





     lowerCamelCase :					str    =				Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]						,				3						,				3 )
     a.change_component(0						,				2						,				5 )
     self.assertEqual("|1,2,5|\n|2,4,5|\n|6,7,8|\n"						,				str(__A ) )






   def _snake_case    (		self ):






     """simple docstring"""





     lowerCamelCase :					Optional[Any]    =				Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]						,				3						,				3 )
     self.assertEqual(7						,				a.component(2						,				1 )						,				0.01 )






   def _snake_case    (		self ):






     """simple docstring"""





     lowerCamelCase :					int    =				Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]						,				3						,				3 )
     lowerCamelCase :					Any    =				Matrix([[1, 2, 7], [2, 4, 5], [6, 7, 10]]						,				3						,				3 )
     self.assertEqual("|2,4,10|\n|4,8,10|\n|12,14,18|\n"						,				str(a + b ) )






   def _snake_case    (		self ):






     """simple docstring"""





     lowerCamelCase :					List[Any]    =				Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]						,				3						,				3 )
     lowerCamelCase :					Optional[int]    =				Matrix([[1, 2, 7], [2, 4, 5], [6, 7, 10]]						,				3						,				3 )
     self.assertEqual("|0,0,-4|\n|0,0,0|\n|0,0,-2|\n"						,				str(a - b ) )






   def _snake_case    (		self ):






     """simple docstring"""





     self.assertEqual(
         "|0,0,0,0,0|\n|0,0,0,0,0|\n|0,0,0,0,0|\n|0,0,0,0,0|\n|0,0,0,0,0|\n"						,				str(square_zero_matrix(5 ) )						,				)


if __name__ == "__main__":
   unittest.main()







from math import sqrt

import numpy as np
from sympy import symbols

# Coefficient
# Speed of light (m/s)
_snake_case             =     2_99_79_24_58

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






def 		lowercase_(  SCREAMING_SNAKE_CASE_	):


  '''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 		lowercase_(  SCREAMING_SNAKE_CASE_	):


  '''simple docstring'''

  return 1 / sqrt(1 - beta(SCREAMING_SNAKE_CASE_	) ** 2	)






def 		lowercase_(  SCREAMING_SNAKE_CASE_	):


  '''simple docstring'''

  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 		lowercase_(  SCREAMING_SNAKE_CASE_      ,						SCREAMING_SNAKE_CASE_ = None	):


  '''simple docstring'''

  if event is None:
    lowerCamelCase :					Tuple    =				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:
   _snake_case             =     transform(29_97_92_45)
   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
   _snake_case             =     {ct: c, x: 1, y: 1, z: 1}
   _snake_case             =     [four_vector[i].subs(sub_dict) for i in range(4)]

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



