






'''simple docstring'''


import unittest

from .lib import (
    Matrix,
    Vector,
    axpy,
    square_zero_matrix,
    unit_basis_vector,
    zero_vector,
)




class 				lowerCAmelCase       (				unittest.TestCase ):







   """simple docstring"""







   def  __magic_name__     (			self      )     -> None:
    __a     :						Any          =    Vector([1, 2, 3]      )
    self.assertEqual(x.component(0      ) , 1      )
    self.assertEqual(x.component(2      ) , 3      )
    __a     :						str          =    Vector()



   def  __magic_name__     (			self      )     -> None:
    __a     :						Tuple          =    Vector([0, 0, 0, 0, 0, 1]      )
    self.assertEqual(str(_A      ) , '(0,0,0,0,0,1)'      )



   def  __magic_name__     (			self      )     -> None:
    __a     :						Union[str, Any]          =    Vector([1, 2, 3, 4]      )
    self.assertEqual(len(_A      ) , 4      )



   def  __magic_name__     (			self      )     -> None:
    __a     :						List[Any]          =    Vector([1, 2]      )
    __a     :						Tuple          =    Vector([1, 2, 3, 4, 5]      )
    __a     :						Dict          =    Vector([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]      )
    __a     :						Any          =    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  __magic_name__     (			self      )     -> None:
    __a     :						Any          =    Vector([1, 2, 3]      )
    __a     :						List[Any]          =    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  __magic_name__     (			self      )     -> None:
    __a     :						Any          =    Vector([1, 2, 3]      )
    __a     :						Union[str, Any]          =    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  __magic_name__     (			self      )     -> None:
    __a     :						List[Any]          =    Vector([1, 2, 3]      )
    __a     :						Union[str, Any]          =    Vector([2, -1, 4]      )  # for test of dot product
    __a     :						Any          =    Vector([1, -2, -1]      )
    self.assertEqual(str(x * 3.0      ) , '(3.0,6.0,9.0)'      )
    self.assertEqual((a * b) , 0      )



   def  __magic_name__     (			self      )     -> None:
    self.assertEqual(str(zero_vector(10      )      ).count('0'      ) , 10      )



   def  __magic_name__     (			self      )     -> None:
    self.assertEqual(str(unit_basis_vector(3 , 1      )      ) , '(0,1,0)'      )



   def  __magic_name__     (			self      )     -> None:
    __a     :						int          =    Vector([1, 2, 3]      )
    __a     :						List[Any]          =    Vector([1, 0, 1]      )
    self.assertEqual(str(axpy(2 , _A , _A      )      ) , '(3,4,7)'      )



   def  __magic_name__     (			self      )     -> None:
    __a     :						List[Any]          =    Vector([1, 0, 0, 0, 0, 0]      )
    __a     :						List[str]          =    x.copy()
    self.assertEqual(str(_A      ) , str(_A      )      )



   def  __magic_name__     (			self      )     -> None:
    __a     :						int          =    Vector([1, 0, 0]      )
    x.change_component(0 , 0      )
    x.change_component(1 , 1      )
    self.assertEqual(str(_A      ) , '(0,1,0)'      )



   def  __magic_name__     (			self      )     -> None:
    __a     :						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  __magic_name__     (			self      )     -> None:
    __a     :						Tuple          =    Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]] , 3 , 3      )
    __a     :						List[str]          =    [[-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  __magic_name__     (			self      )     -> None:
    __a     :						Tuple          =    Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]] , 3 , 3      )
    __a     :						Optional[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  __magic_name__     (			self      )     -> None:
    __a     :						Dict          =    Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]] , 3 , 3      )
    self.assertEqual(-5 , a.determinant()      )



   def  __magic_name__     (			self      )     -> None:
    __a     :						int          =    Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]] , 3 , 3      )
    __a     :						List[Any]          =    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  __magic_name__     (			self      )     -> None:
    __a     :						Any          =    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  __magic_name__     (			self      )     -> None:
    __a     :						str          =    Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]] , 3 , 3      )
    self.assertEqual(7 , a.component(2 , 1      ) , 0.01      )



   def  __magic_name__     (			self      )     -> None:
    __a     :						Tuple          =    Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]] , 3 , 3      )
    __a     :						Union[str, 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  __magic_name__     (			self      )     -> None:
    __a     :						Optional[Any]          =    Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]] , 3 , 3      )
    __a     :						Dict          =    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  __magic_name__     (			self      )     -> None:
    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()






import math





def      lowerCamelCase_					(							lowerCamelCase__       ):

				if 1 < number < 4:
								# 2 and 3 are primes
								return True
				elif number < 2 or number % 2 == 0 or number % 3 == 0:
								# Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
								return False

				# All primes number are in format of 6k +/- 1
				for i in range(5      ,					int(math.sqrt(lowerCamelCase__       ) + 1       )      ,					6       ):
								if number % i == 0 or number % (i + 2) == 0:
												return False
				return True





def      lowerCamelCase_					(							lowerCamelCase__ = 1_0_0_0_1       ):

				try:
								lowerCamelCase_         =     int(lowerCamelCase__       )
				except (TypeError, ValueError):
								raise TypeError("Parameter nth must be int or castable to int."       ) from None
				if nth <= 0:
								raise ValueError("Parameter nth must be greater than or equal to one."       )
				lowerCamelCase_         =     []
				lowerCamelCase_         =     2
				while len(lowerCamelCase__       ) < nth:
								if is_prime(lowerCamelCase__       ):
												primes.append(lowerCamelCase__       )
												num += 1
								else:
												num += 1
				return primes[len(lowerCamelCase__       ) - 1]


if __name__ == "__main__":
			print(F"""{solution() = }""")


