



import unittest

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

class        snake_case__    (unittest.TestCase		):







						"""simple docstring"""




						def 							SCREAMING_SNAKE_CASE__(       self  ) ->				None:
									"""simple docstring"""




									a__       :						Union[str, Any]							=  Vector([1, 2, 3]  )
									self.assertEqual(x.component(0  ) ,       1  )
									self.assertEqual(x.component(2  ) ,       3  )
									a__       :						List[str]							=  Vector()

						def 							SCREAMING_SNAKE_CASE__(       self  ) ->				None:
									"""simple docstring"""




									a__       :						Optional[Any]							=  Vector([0, 0, 0, 0, 0, 1]  )
									self.assertEqual(str(UpperCamelCase__  ) ,       """(0,0,0,0,0,1)"""  )

						def 							SCREAMING_SNAKE_CASE__(       self  ) ->				None:
									"""simple docstring"""




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

						def 							SCREAMING_SNAKE_CASE__(       self  ) ->				None:
									"""simple docstring"""




									a__       :						str							=  Vector([1, 2]  )
									a__       :						Optional[Any]							=  Vector([1, 2, 3, 4, 5]  )
									a__       :						int							=  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() ,       2.2_3_6 ,       3  )
									self.assertAlmostEqual(y.euclidean_length() ,       7.4_1_6 ,       3  )
									self.assertEqual(z.euclidean_length() ,       0  )
									self.assertAlmostEqual(w.euclidean_length() ,       7.6_1_6 ,       3  )

						def 							SCREAMING_SNAKE_CASE__(       self  ) ->				None:
									"""simple docstring"""




									a__       :						Optional[Any]							=  Vector([1, 2, 3]  )
									a__       :						Optional[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 							SCREAMING_SNAKE_CASE__(       self  ) ->				None:
									"""simple docstring"""




									a__       :						Any							=  Vector([1, 2, 3]  )
									a__       :						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 							SCREAMING_SNAKE_CASE__(       self  ) ->				None:
									"""simple docstring"""




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

						def 							SCREAMING_SNAKE_CASE__(       self  ) ->				None:
									"""simple docstring"""




									self.assertEqual(str(zero_vector(1_0  )  ).count("""0"""  ) ,       1_0  )

						def 							SCREAMING_SNAKE_CASE__(       self  ) ->				None:
									"""simple docstring"""




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

						def 							SCREAMING_SNAKE_CASE__(       self  ) ->				None:
									"""simple docstring"""




									a__       :						Optional[Any]							=  Vector([1, 2, 3]  )
									a__       :						List[str]							=  Vector([1, 0, 1]  )
									self.assertEqual(str(axpy(2 ,       UpperCamelCase__ ,       UpperCamelCase__  )  ) ,       """(3,4,7)"""  )

						def 							SCREAMING_SNAKE_CASE__(       self  ) ->				None:
									"""simple docstring"""




									a__       :						Tuple							=  Vector([1, 0, 0, 0, 0, 0]  )
									a__       :						Dict							=  x.copy()
									self.assertEqual(str(UpperCamelCase__  ) ,       str(UpperCamelCase__  )  )

						def 							SCREAMING_SNAKE_CASE__(       self  ) ->				None:
									"""simple docstring"""




									a__       :						Optional[int]							=  Vector([1, 0, 0]  )
									x.change_component(0 ,       0  )
									x.change_component(1 ,       1  )
									self.assertEqual(str(UpperCamelCase__  ) ,       """(0,1,0)"""  )

						def 							SCREAMING_SNAKE_CASE__(       self  ) ->				None:
									"""simple docstring"""




									a__       :						Tuple							=  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(UpperCamelCase__  )  )

						def 							SCREAMING_SNAKE_CASE__(       self  ) ->				None:
									"""simple docstring"""




									a__       :						List[str]							=  Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]] ,       3 ,       3  )
									a__       :						List[Any]							=  [[-3, -1_4, -1_0], [-5, -1_0, -5], [-2, -1, 0]]
									for x in range(a.height()  ):
												for y in range(a.width()  ):
															self.assertEqual(minors[x][y] ,       a.minor(UpperCamelCase__ ,       UpperCamelCase__  )  )

						def 							SCREAMING_SNAKE_CASE__(       self  ) ->				None:
									"""simple docstring"""




									a__       :						int							=  Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]] ,       3 ,       3  )
									a__       :						Tuple							=  [[-3, 1_4, -1_0], [5, -1_0, 5], [-2, 1, 0]]
									for x in range(a.height()  ):
												for y in range(a.width()  ):
															self.assertEqual(cofactors[x][y] ,       a.cofactor(UpperCamelCase__ ,       UpperCamelCase__  )  )

						def 							SCREAMING_SNAKE_CASE__(       self  ) ->				None:
									"""simple docstring"""




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

						def 							SCREAMING_SNAKE_CASE__(       self  ) ->				None:
									"""simple docstring"""




									a__       :						List[str]							=  Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]] ,       3 ,       3  )
									a__       :						str							=  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 							SCREAMING_SNAKE_CASE__(       self  ) ->				None:
									"""simple docstring"""




									a__       :						Tuple							=  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(UpperCamelCase__  )  )

						def 							SCREAMING_SNAKE_CASE__(       self  ) ->				None:
									"""simple docstring"""




									a__       :						Dict							=  Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]] ,       3 ,       3  )
									self.assertEqual(7 ,       a.component(2 ,       1  ) ,       0.0_1  )

						def 							SCREAMING_SNAKE_CASE__(       self  ) ->				None:
									"""simple docstring"""




									a__       :						Optional[int]							=  Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]] ,       3 ,       3  )
									a__       :						Tuple							=  Matrix([[1, 2, 7], [2, 4, 5], [6, 7, 1_0]] ,       3 ,       3  )
									self.assertEqual("""|2,4,10|\n|4,8,10|\n|12,14,18|\n""" ,       str(a + b  )  )

						def 							SCREAMING_SNAKE_CASE__(       self  ) ->				None:
									"""simple docstring"""




									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, 1_0]] ,       3 ,       3  )
									self.assertEqual("""|0,0,-4|\n|0,0,0|\n|0,0,-2|\n""" ,       str(a - b  )  )

						def 							SCREAMING_SNAKE_CASE__(       self  ) ->				None:
									"""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()











_lowercase		:				Optional[int]      		=[
    (1000, "M"),
    (900, "CM"),
    (500, "D"),
    (400, "CD"),
    (100, "C"),
    (90, "XC"),
    (50, "L"),
    (40, "XL"),
    (10, "X"),
    (9, "IX"),
    (5, "V"),
    (4, "IV"),
    (1, "I"),
]

def      lowerCAmelCase_					(  _lowercase    :       str)							->	int:







			"""simple docstring"""
			a__       :						Union[str, Any]							=  {"""I""": 1, """V""": 5, """X""": 10, """L""": 50, """C""": 100, """D""": 500, """M""": 1000}
			a__       :						List[Any]							=  0
			a__       :						Dict							=  0
			while place < len(_lowercase):
						if (place + 1 < len(_lowercase)) and (vals[roman[place]] < vals[roman[place + 1]]):
									total += vals[roman[place + 1]] - vals[roman[place]]
									place += 2
						else:
									total += vals[roman[place]]
									place += 1
			return total

def      lowerCAmelCase_					(  _lowercase    :       int)							->	str:







			"""simple docstring"""
			a__       :						Optional[Any]							=  []
			for arabic, roman in ROMAN:
						((a__)	,						(a__))       :						Optional[Any]							=  divmod(_lowercase						,       _lowercase)
						result.append(roman * factor)
						if number == 0:
									break
			return "".join(_lowercase)


if __name__ == "__main__":
		import doctest

		doctest.testmod()




