



import unittest

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



class       UpperCAmelCase__(							unittest.TestCase	):

   '''simple docstring'''




   def 			UpperCAmelCase		(						self  :			Any)	->				None:




         """simple docstring"""

         lowercase__     =  Vector([1, 2, 3])
         self.assertEqual(x.component(0)			,				1)
         self.assertEqual(x.component(2)			,				3)
         lowercase__     =  Vector()


   def 			UpperCAmelCase		(						self  :			Optional[Any])	->				None:




         """simple docstring"""

         lowercase__     =  Vector([0, 0, 0, 0, 0, 1])
         self.assertEqual(str(lowerCAmelCase)			,				'(0,0,0,0,0,1)')


   def 			UpperCAmelCase		(						self  :			Any)	->				None:




         """simple docstring"""

         lowercase__     =  Vector([1, 2, 3, 4])
         self.assertEqual(len(lowerCAmelCase)			,				4)


   def 			UpperCAmelCase		(						self  :			Optional[int])	->				None:




         """simple docstring"""

         lowercase__     =  Vector([1, 2])
         lowercase__     =  Vector([1, 2, 3, 4, 5])
         lowercase__     =  Vector([0, 0, 0, 0, 0, 0, 0, 0, 0, 0])
         lowercase__     =  Vector([1, -1, 1, -1, 2, -3, 4, -5])
         self.assertAlmostEqual(x.euclidean_length()			,				2.2_36			,				3)
         self.assertAlmostEqual(y.euclidean_length()			,				7.4_16			,				3)
         self.assertEqual(z.euclidean_length()			,				0)
         self.assertAlmostEqual(w.euclidean_length()			,				7.6_16			,				3)


   def 			UpperCAmelCase		(						self  :			List[str])	->				None:




         """simple docstring"""

         lowercase__     =  Vector([1, 2, 3])
         lowercase__     =  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 			UpperCAmelCase		(						self  :			List[Any])	->				None:




         """simple docstring"""

         lowercase__     =  Vector([1, 2, 3])
         lowercase__     =  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 			UpperCAmelCase		(						self  :			List[str])	->				None:




         """simple docstring"""

         lowercase__     =  Vector([1, 2, 3])
         lowercase__     =  Vector([2, -1, 4])  # for test of dot product
         lowercase__     =  Vector([1, -2, -1])
         self.assertEqual(str(x * 3.0)			,				'(3.0,6.0,9.0)')
         self.assertEqual((a * b)			,				0)


   def 			UpperCAmelCase		(						self  :			Optional[int])	->				None:




         """simple docstring"""

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


   def 			UpperCAmelCase		(						self  :			Dict)	->				None:




         """simple docstring"""

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


   def 			UpperCAmelCase		(						self  :			Optional[Any])	->				None:




         """simple docstring"""

         lowercase__     =  Vector([1, 2, 3])
         lowercase__     =  Vector([1, 0, 1])
         self.assertEqual(str(axpy(2			,				lowerCAmelCase			,				lowerCAmelCase))			,				'(3,4,7)')


   def 			UpperCAmelCase		(						self  :			Tuple)	->				None:




         """simple docstring"""

         lowercase__     =  Vector([1, 0, 0, 0, 0, 0])
         lowercase__     =  x.copy()
         self.assertEqual(str(lowerCAmelCase)			,				str(lowerCAmelCase))


   def 			UpperCAmelCase		(						self  :			Any)	->				None:




         """simple docstring"""

         lowercase__     =  Vector([1, 0, 0])
         x.change_component(0			,				0)
         x.change_component(1			,				1)
         self.assertEqual(str(lowerCAmelCase)			,				'(0,1,0)')


   def 			UpperCAmelCase		(						self  :			Any)	->				None:




         """simple docstring"""

         lowercase__     =  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(lowerCAmelCase))


   def 			UpperCAmelCase		(						self  :			Union[str, Any])	->				None:




         """simple docstring"""

         lowercase__     =  Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]			,				3			,				3)
         lowercase__     =  [[-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(lowerCAmelCase			,				lowerCAmelCase))


   def 			UpperCAmelCase		(						self  :			Any)	->				None:




         """simple docstring"""

         lowercase__     =  Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]			,				3			,				3)
         lowercase__     =  [[-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(lowerCAmelCase			,				lowerCAmelCase))


   def 			UpperCAmelCase		(						self  :			Any)	->				None:




         """simple docstring"""

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


   def 			UpperCAmelCase		(						self  :			Dict)	->				None:




         """simple docstring"""

         lowercase__     =  Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]]			,				3			,				3)
         lowercase__     =  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 			UpperCAmelCase		(						self  :			Any)	->				None:




         """simple docstring"""

         lowercase__     =  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(lowerCAmelCase))


   def 			UpperCAmelCase		(						self  :			Any)	->				None:




         """simple docstring"""

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


   def 			UpperCAmelCase		(						self  :			Tuple)	->				None:




         """simple docstring"""

         lowercase__     =  Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]			,				3			,				3)
         lowercase__     =  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 			UpperCAmelCase		(						self  :			str)	->				None:




         """simple docstring"""

         lowercase__     =  Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]			,				3			,				3)
         lowercase__     =  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 			UpperCAmelCase		(						self  :			Any)	->				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()





from maths.is_square_free import is_square_free
from maths.prime_factors import prime_factors

def   _lowerCAmelCase   (						A__	):
      lowercase__     =  prime_factors(A__	)
      if is_square_free(A__	):
            return -1 if len(A__	) % 2 else 1
      return 0


if __name__ == "__main__":
       import doctest

       doctest.testmod()
