




"""simple docstring"""


def 	lowercase_				(			__UpperCAmelCase				)						->    bool:
      if not isinstance(__UpperCAmelCase    ,		__UpperCAmelCase				):
            lowerCAmelCase__      :			List[str]   =	f"""Input value of [number={number}] must be an integer"""
            raise TypeError(__UpperCAmelCase				)
      if number < 0:
            return False
      lowerCAmelCase__      :			List[str]   =	number * number
      while number > 0:
            if number % 10 != number_square % 10:
                  return False
            number //= 10
            number_square //= 10
      return True


if __name__ == "__main__":
  import doctest

  doctest.testmod()











"""simple docstring"""


import unittest

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


class _lowerCamelCase    (					unittest.TestCase						):






   def 	_lowerCAmelCase   (		self       :		Dict   )			->						None:

         """simple docstring"""
         lowerCAmelCase__      :			Tuple   =	Vector([1, 2, 3]   )
         self.assertEqual(x.component(0   )   ,     1   )
         self.assertEqual(x.component(2   )   ,     3   )
         lowerCAmelCase__      :			Union[str, Any]   =	Vector()






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

         """simple docstring"""
         lowerCAmelCase__      :			str   =	Vector([0, 0, 0, 0, 0, 1]   )
         self.assertEqual(str(UpperCamelCase   )   ,     """(0,0,0,0,0,1)"""   )






   def 	_lowerCAmelCase   (		self       :		Any   )			->						None:

         """simple docstring"""
         lowerCAmelCase__      :			List[Any]   =	Vector([1, 2, 3, 4]   )
         self.assertEqual(len(UpperCamelCase   )   ,     4   )






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

         """simple docstring"""
         lowerCAmelCase__      :			str   =	Vector([1, 2]   )
         lowerCAmelCase__      :			Optional[int]   =	Vector([1, 2, 3, 4, 5]   )
         lowerCAmelCase__      :			Union[str, Any]   =	Vector([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]   )
         lowerCAmelCase__      :			List[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 	_lowerCAmelCase   (		self       :		Any   )			->						None:

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

         """simple docstring"""
         lowerCAmelCase__      :			Union[str, Any]   =	Vector([1, 2, 3]   )
         lowerCAmelCase__      :			Dict   =	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 	_lowerCAmelCase   (		self       :		Optional[Any]   )			->						None:

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






   def 	_lowerCAmelCase   (		self       :		int   )			->						None:

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






   def 	_lowerCAmelCase   (		self       :		Tuple   )			->						None:

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






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

         """simple docstring"""
         lowerCAmelCase__      :			Tuple   =	Vector([1, 2, 3]   )
         lowerCAmelCase__      :			Optional[Any]   =	Vector([1, 0, 1]   )
         self.assertEqual(str(axpy(2   ,     UpperCamelCase   ,     UpperCamelCase   )   )   ,     """(3,4,7)"""   )






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

         """simple docstring"""
         lowerCAmelCase__      :			Tuple   =	Vector([1, 0, 0, 0, 0, 0]   )
         lowerCAmelCase__      :			Any   =	x.copy()
         self.assertEqual(str(UpperCamelCase   )   ,     str(UpperCamelCase   )   )






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

         """simple docstring"""
         lowerCAmelCase__      :			Tuple   =	Vector([1, 0, 0]   )
         x.change_component(0   ,     0   )
         x.change_component(1   ,     1   )
         self.assertEqual(str(UpperCamelCase   )   ,     """(0,1,0)"""   )






   def 	_lowerCAmelCase   (		self       :		int   )			->						None:

         """simple docstring"""
         lowerCAmelCase__      :			Optional[int]   =	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 	_lowerCAmelCase   (		self       :		Union[str, Any]   )			->						None:

         """simple docstring"""
         lowerCAmelCase__      :			Tuple   =	Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]   ,     3   ,     3   )
         lowerCAmelCase__      :			Dict   =	[[-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(UpperCamelCase   ,     UpperCamelCase   )   )






   def 	_lowerCAmelCase   (		self       :		List[Any]   )			->						None:

         """simple docstring"""
         lowerCAmelCase__      :			str   =	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(UpperCamelCase   ,     UpperCamelCase   )   )






   def 	_lowerCAmelCase   (		self       :		int   )			->						None:

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






   def 	_lowerCAmelCase   (		self       :		int   )			->						None:

         """simple docstring"""
         lowerCAmelCase__      :			Optional[Any]   =	Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]]   ,     3   ,     3   )
         lowerCAmelCase__      :			Tuple   =	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 	_lowerCAmelCase   (		self       :		str   )			->						None:

         """simple docstring"""
         lowerCAmelCase__      :			Dict   =	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 	_lowerCAmelCase   (		self       :		Tuple   )			->						None:

         """simple docstring"""
         lowerCAmelCase__      :			Tuple   =	Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]   ,     3   ,     3   )
         self.assertEqual(7   ,     a.component(2   ,     1   )   ,     0.01   )






   def 	_lowerCAmelCase   (		self       :		Any   )			->						None:

         """simple docstring"""
         lowerCAmelCase__      :			Tuple   =	Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]   ,     3   ,     3   )
         lowerCAmelCase__      :			List[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 	_lowerCAmelCase   (		self       :		List[Any]   )			->						None:

         """simple docstring"""
         lowerCAmelCase__      :			Optional[Any]   =	Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]   ,     3   ,     3   )
         lowerCAmelCase__      :			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 	_lowerCAmelCase   (		self       :		Union[str, 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()





