


'''simple docstring'''







def 				lowerCAmelCase__	(    lowerCamelCase					:      float  ,lowerCamelCase					:      int       ):
       if digit_amount > 0:
              return round(number - int(lowerCamelCase       )  ,lowerCamelCase       )
       return number - int(lowerCamelCase       )


if __name__ == "__main__":
   print(decimal_isolate(1.53, 0))
   print(decimal_isolate(35.3_45, 1))
   print(decimal_isolate(35.3_45, 2))
   print(decimal_isolate(35.3_45, 3))
   print(decimal_isolate(-14.7_89, 3))
   print(decimal_isolate(0, 2))
   print(decimal_isolate(-14.1_23, 1))
   print(decimal_isolate(-14.1_23, 2))
   print(decimal_isolate(-14.1_23, 3))










'''simple docstring'''







from __future__ import annotations


class 			__lowerCamelCase			:
    """simple docstring"""


    def __init__(  self      :							List[Any]				,							SCREAMING_SNAKE_CASE      :							list[list[int]]):
           _A					:     Dict     = TypeError(
               'Matrices must be formed from a list of zero or more lists containing at '
               'least one and the same number of values, each of which must be of type '
               'int or float.')
           if len(SCREAMING_SNAKE_CASE) != 0:
                  _A					:     str     = len(rows[0])
                  if cols == 0:
                         raise error
                  for row in rows:
                         if len(SCREAMING_SNAKE_CASE) != cols:
                                raise error
                         for value in row:
                                if not isinstance(SCREAMING_SNAKE_CASE				,							(int, float)):
                                       raise error
                  _A					:     str     = rows
           else:
                  _A					:     Tuple     = []


    def        A   (  self      :							Optional[Any]):
           return [[row[i] for row in self.rows] for i in range(len(self.rows[0]))]


    @property
    def        A   (  self      :							List[str]):
           return len(self.rows)


    @property
    def        A   (  self      :							Optional[int]):
           return len(self.rows[0])


    @property
    def        A   (  self      :							Optional[int]):
           return (self.num_rows, self.num_columns)


    @property
    def        A   (  self      :							Any):
           return self.order[0] == self.order[1]


    def        A   (  self      :							int):
           _A					:     Union[str, Any]     = [
               [0 if column_num != row_num else 1 for column_num in range(self.num_rows)]
               for row_num in range(self.num_rows)
           ]
           return Matrix(SCREAMING_SNAKE_CASE)


    def        A   (  self      :							List[Any]):
           if not self.is_square:
                  return 0
           if self.order == (0, 0):
                  return 1
           if self.order == (1, 1):
                  return int(self.rows[0][0])
           if self.order == (2, 2):
                  return int(
                      (self.rows[0][0] * self.rows[1][1])
                      - (self.rows[0][1] * self.rows[1][0]))
           else:
                  return sum(
                      self.rows[0][column] * self.cofactors().rows[0][column]
                      for column in range(self.num_columns))


    def        A   (  self      :							Tuple):
           return bool(self.determinant())


    def        A   (  self      :							int				,							SCREAMING_SNAKE_CASE      :							int				,							SCREAMING_SNAKE_CASE      :							int):
           _A					:     str     = [
               [
                   self.rows[other_row][other_column]
                   for other_column in range(self.num_columns)
                   if other_column != column
               ]
               for other_row in range(self.num_rows)
               if other_row != row
           ]
           return Matrix(SCREAMING_SNAKE_CASE).determinant()


    def        A   (  self      :							List[Any]				,							SCREAMING_SNAKE_CASE      :							int				,							SCREAMING_SNAKE_CASE      :							int):
           if (row + column) % 2 == 0:
                  return self.get_minor(SCREAMING_SNAKE_CASE				,							SCREAMING_SNAKE_CASE)
           return -1 * self.get_minor(SCREAMING_SNAKE_CASE				,							SCREAMING_SNAKE_CASE)


    def        A   (  self      :							Optional[int]):
           return Matrix(
               [
                   [self.get_minor(SCREAMING_SNAKE_CASE				,							SCREAMING_SNAKE_CASE) for column in range(self.num_columns)]
                   for row in range(self.num_rows)
               ])


    def        A   (  self      :							Optional[int]):
           return Matrix(
               [
                   [
                       self.minors().rows[row][column]
                       if (row + column) % 2 == 0
                       else self.minors().rows[row][column] * -1
                       for column in range(self.minors().num_columns)
                   ]
                   for row in range(self.minors().num_rows)
               ])


    def        A   (  self      :							Tuple):
           _A					:     str     = [
               [self.cofactors().rows[column][row] for column in range(self.num_columns)]
               for row in range(self.num_rows)
           ]
           return Matrix(SCREAMING_SNAKE_CASE)


    def        A   (  self      :							Tuple):
           _A					:     str     = self.determinant()
           if not determinant:
                  raise TypeError('Only matrices with a non-zero determinant have an inverse')
           return self.adjugate() * (1 / determinant)


    def __repr__(  self      :							str):
           return str(self.rows)


    def __str__(  self      :							Optional[int]):
           if self.num_rows == 0:
                  return "[]"
           if self.num_rows == 1:
                  return "[[" + ". ".join(str(self.rows[0])) + "]]"
           return (
               "["
               + "\n ".join(
                   [
                       '[' + '. '.join([str(SCREAMING_SNAKE_CASE) for value in row]) + '.]'
                       for row in self.rows
                   ])
               + "]"
           )


    def        A   (  self      :							List[Any]				,							SCREAMING_SNAKE_CASE      :							list[int]				,							SCREAMING_SNAKE_CASE      :							int | None = None):
           _A					:     Tuple     = TypeError('Row must be a list containing all ints and/or floats')
           if not isinstance(SCREAMING_SNAKE_CASE				,							SCREAMING_SNAKE_CASE):
                  raise type_error
           for value in row:
                  if not isinstance(SCREAMING_SNAKE_CASE				,							(int, float)):
                         raise type_error
           if len(SCREAMING_SNAKE_CASE) != self.num_columns:
                  raise ValueError(
                      'Row must be equal in length to the other rows in the matrix')
           if position is None:
                  self.rows.append(SCREAMING_SNAKE_CASE)
           else:
                  _A					:     List[str]     = self.rows[0:position] + [row] + self.rows[position:]


    def        A   (  self      :							List[Any]				,							SCREAMING_SNAKE_CASE      :							list[int]				,							SCREAMING_SNAKE_CASE      :							int | None = None):
           _A					:     int     = TypeError(
               'Column must be a list containing all ints and/or floats')
           if not isinstance(SCREAMING_SNAKE_CASE				,							SCREAMING_SNAKE_CASE):
                  raise type_error
           for value in column:
                  if not isinstance(SCREAMING_SNAKE_CASE				,							(int, float)):
                         raise type_error
           if len(SCREAMING_SNAKE_CASE) != self.num_rows:
                  raise ValueError(
                      'Column must be equal in length to the other columns in the matrix')
           if position is None:
                  _A					:     str     = [self.rows[i] + [column[i]] for i in range(self.num_rows)]
           else:
                  _A					:     Dict     = [
                      self.rows[i][0:position] + [column[i]] + self.rows[i][position:]
                      for i in range(self.num_rows)
                  ]


    def __eq__(  self      :							List[str]				,							SCREAMING_SNAKE_CASE      :							object):
           if not isinstance(SCREAMING_SNAKE_CASE				,							SCREAMING_SNAKE_CASE):
                  return NotImplemented
           return self.rows == other.rows


    def __ne__(  self      :							Any				,							SCREAMING_SNAKE_CASE      :							object):
           return not self == other


    def __neg__(  self      :							Optional[Any]):
           return self * -1


    def __add__(  self      :							Any				,							SCREAMING_SNAKE_CASE      :							Matrix):
           if self.order != other.order:
                  raise ValueError('Addition requires matrices of the same order')
           return Matrix(
               [
                   [self.rows[i][j] + other.rows[i][j] for j in range(self.num_columns)]
                   for i in range(self.num_rows)
               ])


    def __sub__(  self      :							List[str]				,							SCREAMING_SNAKE_CASE      :							Matrix):
           if self.order != other.order:
                  raise ValueError('Subtraction requires matrices of the same order')
           return Matrix(
               [
                   [self.rows[i][j] - other.rows[i][j] for j in range(self.num_columns)]
                   for i in range(self.num_rows)
               ])


    def __mul__(  self      :							Dict				,							SCREAMING_SNAKE_CASE      :							Matrix | int | float):
           if isinstance(SCREAMING_SNAKE_CASE				,							(int, float)):
                  return Matrix(
                      [[int(element * other) for element in row] for row in self.rows])
           elif isinstance(SCREAMING_SNAKE_CASE				,							SCREAMING_SNAKE_CASE):
                  if self.num_columns != other.num_rows:
                         raise ValueError(
                             'The number of columns in the first matrix must '
                             'be equal to the number of rows in the second')
                  return Matrix(
                      [
                          [Matrix.dot_product(SCREAMING_SNAKE_CASE				,							SCREAMING_SNAKE_CASE) for column in other.columns()]
                          for row in self.rows
                      ])
           else:
                  raise TypeError(
                      'A Matrix can only be multiplied by an int, float, or another matrix')


    def __pow__(  self      :							Any				,							SCREAMING_SNAKE_CASE      :							int):
           if not isinstance(SCREAMING_SNAKE_CASE				,							SCREAMING_SNAKE_CASE):
                  raise TypeError('A Matrix can only be raised to the power of an int')
           if not self.is_square:
                  raise ValueError('Only square matrices can be raised to a power')
           if other == 0:
                  return self.identity()
           if other < 0:
                  if self.is_invertable():
                         return self.inverse() ** (-other)
                  raise ValueError(
                      'Only invertable matrices can be raised to a negative power')
           _A					:     Union[str, Any]     = self
           for _ in range(other - 1):
                  result *= self
           return result


    @classmethod
    def        A   (  cls      :							List[str]				,							SCREAMING_SNAKE_CASE      :							list[int]				,							SCREAMING_SNAKE_CASE      :							list[int]):
           return sum(row[i] * column[i] for i in range(len(SCREAMING_SNAKE_CASE)))


if __name__ == "__main__":
   import doctest

   doctest.testmod()






