




from __future__ import annotations







class  UpperCAmelCase:



	"""simple docstring"""






	def __init__(	self			, lowerCamelCase							)   ->     str:





								"""simple docstring"""


								lowercase__    :			Tuple     =				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(a__							) != 0:
															lowercase__    :			Optional[Any]     =				len(rows[0]							)
															if cols == 0:
																						raise error
															for row in rows:
																						if len(a__							) != cols:
																													raise error
																						for value in row:
																													if not isinstance(a__			, (int, float)							):
																																				raise error
															lowercase__    :			int     =				rows
								else:
															lowercase__    :			Any     =				[]

	def        __a      (	self							)   ->     list[list[int]]:





								"""simple docstring"""


								return [[row[i] for row in self.rows] for i in range(len(self.rows[0]							)							)]

	@property
	def        __a      (	self							)   ->     int:





								"""simple docstring"""


								return len(self.rows							)

	@property
	def        __a      (	self							)   ->     int:





								"""simple docstring"""


								return len(self.rows[0]							)

	@property
	def        __a      (	self							)   ->     tuple[int, int]:





								"""simple docstring"""


								return (self.num_rows, self.num_columns)

	@property
	def        __a      (	self							)   ->     bool:





								"""simple docstring"""


								return self.order[0] == self.order[1]

	def        __a      (	self							)   ->     Matrix:





								"""simple docstring"""


								lowercase__    :			Dict     =				[
								    [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(a__							)

	def        __a      (	self							)   ->     int:





								"""simple docstring"""


								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							)   ->     bool:





								"""simple docstring"""


								return bool(self.determinant()							)

	def        __a      (	self			, lowerCamelCase			, lowerCamelCase							)   ->     int:





								"""simple docstring"""


								lowercase__    :			List[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(a__							).determinant()

	def        __a      (	self			, lowerCamelCase			, lowerCamelCase							)   ->     int:





								"""simple docstring"""


								if (row + column) % 2 == 0:
															return self.get_minor(a__			, a__							)
								return -1 * self.get_minor(a__			, a__							)

	def        __a      (	self							)   ->     Matrix:





								"""simple docstring"""


								return Matrix(
								    [
								        [self.get_minor(a__			, a__							) for column in range(self.num_columns							)]
								        for row in range(self.num_rows							)
								    ]							)

	def        __a      (	self							)   ->     Matrix:





								"""simple docstring"""


								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							)   ->     Matrix:





								"""simple docstring"""


								lowercase__    :			int     =				[
								    [self.cofactors().rows[column][row] for column in range(self.num_columns							)]
								    for row in range(self.num_rows							)
								]
								return Matrix(a__							)

	def        __a      (	self							)   ->     Matrix:





								"""simple docstring"""


								lowercase__    :			Optional[int]     =				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:





								"""simple docstring"""


								return str(self.rows							)

	def __str__(	self							)   ->     str:





								"""simple docstring"""


								if self.num_rows == 0:
															return "[]"
								if self.num_rows == 1:
															return "[[" + ". ".join(str(self.rows[0]							)							) + "]]"
								return (
								    "["
								    + "\n ".join(
								        [
								            "[" + ". ".join([str(a__							) for value in row]							) + ".]"
								            for row in self.rows
								        ]							)
								    + "]"
								)

	def        __a      (	self			, lowerCamelCase			, lowerCamelCase = None							)   ->     None:





								"""simple docstring"""


								lowercase__    :			int     =				TypeError("Row must be a list containing all ints and/or floats"							)
								if not isinstance(a__			, a__							):
															raise type_error
								for value in row:
															if not isinstance(a__			, (int, float)							):
																						raise type_error
								if len(a__							) != 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(a__							)
								else:
															lowercase__    :			int     =				self.rows[0:position] + [row] + self.rows[position:]

	def        __a      (	self			, lowerCamelCase			, lowerCamelCase = None							)   ->     None:





								"""simple docstring"""


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

	def __eq__(	self			, lowerCamelCase							)   ->     bool:





								"""simple docstring"""


								if not isinstance(a__			, a__							):
															return NotImplemented
								return self.rows == other.rows

	def __ne__(	self			, lowerCamelCase							)   ->     bool:





								"""simple docstring"""


								return not self == other

	def __neg__(	self							)   ->     Matrix:





								"""simple docstring"""


								return self * -1

	def __add__(	self			, lowerCamelCase							)   ->     Matrix:





								"""simple docstring"""


								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			, lowerCamelCase							)   ->     Matrix:





								"""simple docstring"""


								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			, lowerCamelCase							)   ->     Matrix:





								"""simple docstring"""


								if isinstance(a__			, (int, float)							):
															return Matrix(
															    [[int(element * other							) for element in row] for row in self.rows]							)
								elif isinstance(a__			, a__							):
															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(a__			, a__							) 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			, lowerCamelCase							)   ->     Matrix:





								"""simple docstring"""


								if not isinstance(a__			, a__							):
															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"							)
								lowercase__    :			int     =				self
								for _ in range(other - 1							):
															result *= self
								return result







	@classmethod
	def        __a      (	cls			, lowerCamelCase			, lowerCamelCase							)   ->     int:





								"""simple docstring"""


								return sum(row[i] * column[i] for i in range(len(a__							)							)							)


if __name__ == "__main__":
						import doctest

						doctest.testmod()







def 	UpperCamelCase	(							snake_case__  : float						,snake_case__  : int	):




     '''simple docstring'''






     if digit_amount > 0:
          return round(number - int(snake_case__	)						,snake_case__	)
     return number - int(snake_case__	)


if __name__ == "__main__":
     print(decimal_isolate(1.5_3, 0))
     print(decimal_isolate(3_5.3_4_5, 1))
     print(decimal_isolate(3_5.3_4_5, 2))
     print(decimal_isolate(3_5.3_4_5, 3))
     print(decimal_isolate(-1_4.7_8_9, 3))
     print(decimal_isolate(0, 2))
     print(decimal_isolate(-1_4.1_2_3, 1))
     print(decimal_isolate(-1_4.1_2_3, 2))
     print(decimal_isolate(-1_4.1_2_3, 3))


