




from __future__ import annotations

from decimal import Decimal

from numpy import array


def   lowerCamelCase__			(     lowercase				):

  """simple docstring"""






  SCREAMING_SNAKE_CASE       :      List[str]							=    Decimal

  # Check if the provided matrix has 2 rows and 2 columns
  # since this implementation only works for 2x2 matrices
  if len(lowercase				) == 2 and len(matrix[0]				) == 2 and len(matrix[1]				) == 2:
    # Calculate the determinant of the matrix
    SCREAMING_SNAKE_CASE       :      Union[str, Any]							=    float(
        d(matrix[0][0]				) * d(matrix[1][1]				) - d(matrix[1][0]				) * d(matrix[0][1]				)				)
    if determinant == 0:
      raise ValueError("This matrix has no inverse."				)

    # Creates a copy of the matrix with swapped positions of the elements
    SCREAMING_SNAKE_CASE       :      Any							=    [[0.0, 0.0], [0.0, 0.0]]
    SCREAMING_SNAKE_CASE       :      str							=    matrix[1][1], matrix[0][0]
    SCREAMING_SNAKE_CASE       :      Tuple							=    -matrix[1][0], -matrix[0][1]

    # Calculate the inverse of the matrix
    return [
        [(float(d(lowercase				)				) / determinant) or 0.0 for n in row] for row in swapped_matrix
    ]
  elif (
      len(lowercase				) == 3
      and len(matrix[0]				) == 3
      and len(matrix[1]				) == 3
      and len(matrix[2]				) == 3
  ):
    # Calculate the determinant of the matrix using Sarrus rule
    SCREAMING_SNAKE_CASE       :      Optional[int]							=    float(
        (
            (d(matrix[0][0]				) * d(matrix[1][1]				) * d(matrix[2][2]				))
            + (d(matrix[0][1]				) * d(matrix[1][2]				) * d(matrix[2][0]				))
            + (d(matrix[0][2]				) * d(matrix[1][0]				) * d(matrix[2][1]				))
        )
        - (
            (d(matrix[0][2]				) * d(matrix[1][1]				) * d(matrix[2][0]				))
            + (d(matrix[0][1]				) * d(matrix[1][0]				) * d(matrix[2][2]				))
            + (d(matrix[0][0]				) * d(matrix[1][2]				) * d(matrix[2][1]				))
        )				)
    if determinant == 0:
      raise ValueError("This matrix has no inverse."				)

    # Creating cofactor matrix
    SCREAMING_SNAKE_CASE       :      Optional[Any]							=    [
        [d(0.0				), d(0.0				), d(0.0				)],
        [d(0.0				), d(0.0				), d(0.0				)],
        [d(0.0				), d(0.0				), d(0.0				)],
    ]
    SCREAMING_SNAKE_CASE       :      str							=    (d(matrix[1][1]				) * d(matrix[2][2]				)) - (
        d(matrix[1][2]				) * d(matrix[2][1]				)
    )
    SCREAMING_SNAKE_CASE       :      List[Any]							=    -(
        (d(matrix[1][0]				) * d(matrix[2][2]				)) - (d(matrix[1][2]				) * d(matrix[2][0]				))
    )
    SCREAMING_SNAKE_CASE       :      Optional[int]							=    (d(matrix[1][0]				) * d(matrix[2][1]				)) - (
        d(matrix[1][1]				) * d(matrix[2][0]				)
    )
    SCREAMING_SNAKE_CASE       :      Any							=    -(
        (d(matrix[0][1]				) * d(matrix[2][2]				)) - (d(matrix[0][2]				) * d(matrix[2][1]				))
    )
    SCREAMING_SNAKE_CASE       :      Optional[int]							=    (d(matrix[0][0]				) * d(matrix[2][2]				)) - (
        d(matrix[0][2]				) * d(matrix[2][0]				)
    )
    SCREAMING_SNAKE_CASE       :      str							=    -(
        (d(matrix[0][0]				) * d(matrix[2][1]				)) - (d(matrix[0][1]				) * d(matrix[2][0]				))
    )
    SCREAMING_SNAKE_CASE       :      Dict							=    (d(matrix[0][1]				) * d(matrix[1][2]				)) - (
        d(matrix[0][2]				) * d(matrix[1][1]				)
    )
    SCREAMING_SNAKE_CASE       :      List[Any]							=    -(
        (d(matrix[0][0]				) * d(matrix[1][2]				)) - (d(matrix[0][2]				) * d(matrix[1][0]				))
    )
    SCREAMING_SNAKE_CASE       :      int							=    (d(matrix[0][0]				) * d(matrix[1][1]				)) - (
        d(matrix[0][1]				) * d(matrix[1][0]				)
    )

    # Transpose the cofactor matrix (Adjoint matrix)
    SCREAMING_SNAKE_CASE       :      int							=    array(lowercase				)
    for i in range(3				):
      for j in range(3				):
        SCREAMING_SNAKE_CASE       :      List[str]							=    cofactor_matrix[j][i]

        # Inverse of the matrix using the formula (1/determinant) * adjoint matrix
    SCREAMING_SNAKE_CASE       :      int							=    array(lowercase				)
    for i in range(3				):
      for j in range(3				):
        inverse_matrix[i][j] /= d(lowercase				)

        # Calculate the inverse of the matrix
    return [[float(d(lowercase				)				) or 0.0 for n in row] for row in inverse_matrix]
  raise ValueError("Please provide a matrix of size 2x2 or 3x3."				)














from __future__ import annotations

from cmath import sqrt


def   lowerCamelCase__			(     lowercase						,     lowercase						,     lowercase				):

  """simple docstring"""






  if a == 0:
    raise ValueError("Coefficient 'a' must not be zero."				)
  SCREAMING_SNAKE_CASE       :      List[str]							=    b * b - 4 * a * c

  SCREAMING_SNAKE_CASE       :      str							=    (-b + sqrt(lowercase				)) / (2 * a)
  SCREAMING_SNAKE_CASE       :      Any							=    (-b - sqrt(lowercase				)) / (2 * a)

  return (
      root_a.real if not root_a.imag else root_a,
      root_a.real if not root_a.imag else root_a,
  )


def   lowerCamelCase__			(     ):

  """simple docstring"""






  SCREAMING_SNAKE_CASE						,  SCREAMING_SNAKE_CASE       :      Dict							=    quadratic_roots(a=5						,     b=6						,     c=1				)
  print(F'''The solutions are: {solutiona} and {solutiona}'''				)


if __name__ == "__main__":
   main()






