


from __future__ import annotations

from typing import Any
def 			__SCREAMING_SNAKE_CASE							(					*lowercase__	:List[str]					)							->	list[list[int]]:
						if all(_check_not_integer(lowerCAmelCase_					) for m in matrix_s					):
												for i in matrix_s[1:]:
																		_verify_matrix_sizes(matrix_s[0]   ,    lowerCAmelCase_					)
												return [[sum(lowerCAmelCase_					) for t in zip(*lowerCAmelCase_					)] for m in zip(*lowerCAmelCase_					)]
						raise TypeError('Expected a matrix, got int/list instead'					)
def 			__SCREAMING_SNAKE_CASE							(					lowercase__	:List[str]   ,    lowercase__	:str					)							->	list[list[int]]:
						if (
						    _check_not_integer(lowerCAmelCase_					)
						    and _check_not_integer(lowerCAmelCase_					)
						    and _verify_matrix_sizes(lowerCAmelCase_   ,    lowerCAmelCase_					)
						):
												return [[i - j for i, j in zip(*lowerCAmelCase_					)] for m in zip(lowerCAmelCase_   ,    lowerCAmelCase_					)]
						raise TypeError('Expected a matrix, got int/list instead'					)
def 			__SCREAMING_SNAKE_CASE							(					lowercase__	:Any   ,    lowercase__	:str					)							->	list[list[float]]:
						return [[x * n for x in row] for row in matrix]
def 			__SCREAMING_SNAKE_CASE							(					lowercase__	:List[str]   ,    lowercase__	:Any					)							->	list[list[int]]:
						if _check_not_integer(lowerCAmelCase_					) and _check_not_integer(lowerCAmelCase_					):
												__magic_name__					:				Tuple				=   _verify_matrix_sizes(lowerCAmelCase_   ,    lowerCAmelCase_					)

						if cols[0] != rows[1]:
												__magic_name__					:				str				=   (
												    '''Cannot multiply matrix of dimensions '''
												    f"({rows[0]},{cols[0]}) and ({rows[1]},{cols[1]})"
												)
												raise ValueError(lowerCAmelCase_					)
						return [
						    [sum(m * n for m, n in zip(lowerCAmelCase_   ,    lowerCAmelCase_					)					) for j in zip(*lowerCAmelCase_					)] for i in matrix_a
						]
def 			__SCREAMING_SNAKE_CASE							(					lowercase__	:Dict					)							->	list[list[int]]:
						__magic_name__					:				Optional[Any]				=   int(lowerCAmelCase_					)
						return [[int(row == column					) for column in range(lowerCAmelCase_					)] for row in range(lowerCAmelCase_					)]
def 			__SCREAMING_SNAKE_CASE							(					lowercase__	:Optional[int]   ,    lowercase__	:List[Any] = True					)							->	list[list[int]] | map[list[int]]:
						if _check_not_integer(lowerCAmelCase_					):
												if return_map:
																		return map(lowerCAmelCase_   ,    zip(*lowerCAmelCase_					)					)
												else:
																		return list(map(lowerCAmelCase_   ,    zip(*lowerCAmelCase_					)					)					)
						raise TypeError('Expected a matrix, got int/list instead'					)
def 			__SCREAMING_SNAKE_CASE							(					lowercase__	:Any   ,    lowercase__	:Optional[Any]   ,    lowercase__	:Dict					)							->	list[list[int]]:
						__magic_name__					:				int				=   matrix[:row] + matrix[row + 1 :]
						return [row[:column] + row[column + 1 :] for row in minor]
def 			__SCREAMING_SNAKE_CASE							(					lowercase__	:List[Any]					)							->	Any:
						if len(lowerCAmelCase_					) == 1:
												return matrix[0][0]

						return sum(
						    x * determinant(minor(lowerCAmelCase_   ,    0   ,    lowerCAmelCase_					)					) * (-1) ** i
						    for i, x in enumerate(matrix[0]					)					)
def 			__SCREAMING_SNAKE_CASE							(					lowercase__	:Union[str, Any]					)							->	list[list[float]] | None:
						__magic_name__					:				List[Any]				=   determinant(lowerCAmelCase_					)
						if det == 0:
												return None

						__magic_name__					:				List[str]				=   [
						    [determinant(minor(lowerCAmelCase_   ,    lowerCAmelCase_   ,    lowerCAmelCase_					)					) for j in range(len(lowerCAmelCase_					)					)]
						    for i in range(len(lowerCAmelCase_					)					)
						]

						__magic_name__					:				Tuple				=   [
						    [x * (-1) ** (row + col) for col, x in enumerate(matrix_minor[row]					)]
						    for row in range(len(lowerCAmelCase_					)					)
						]
						__magic_name__					:				str				=   list(transpose(lowerCAmelCase_					)					)
						return scalar_multiply(lowerCAmelCase_   ,    1 / det					)
def 			__SCREAMING_SNAKE_CASE							(					lowercase__	:Tuple					)							->	bool:
						return not isinstance(lowerCAmelCase_   ,    lowerCAmelCase_					) and not isinstance(matrix[0]   ,    lowerCAmelCase_					)
def 			__SCREAMING_SNAKE_CASE							(					lowercase__	:str					)							->	tuple[int, int]:
						return len(lowerCAmelCase_					), len(matrix[0]					)
def 			__SCREAMING_SNAKE_CASE							(					lowercase__	:Optional[Any]   ,    lowercase__	:int					)							->	tuple[tuple[int, int], tuple[int, int]]:
						__magic_name__					:				Union[str, Any]				=   _shape(lowerCAmelCase_					) + _shape(lowerCAmelCase_					)
						if shape[0] != shape[3] or shape[1] != shape[2]:
												__magic_name__					:				Optional[Any]				=   (
												    '''operands could not be broadcast together with shape '''
												    f"({shape[0], shape[1]}), ({shape[2], shape[3]})"
												)
												raise ValueError(lowerCAmelCase_					)
						return (shape[0], shape[2]), (shape[1], shape[3])
def 			__SCREAMING_SNAKE_CASE							(					)							->	None:
						__magic_name__					:				str				=   [[1_2, 1_0], [3, 9]]
						__magic_name__					:				List[str]				=   [[3, 4], [7, 4]]
						__magic_name__					:				str				=   [[1_1, 1_2, 1_3, 1_4], [2_1, 2_2, 2_3, 2_4], [3_1, 3_2, 3_3, 3_4], [4_1, 4_2, 4_3, 4_4]]
						__magic_name__					:				List[str]				=   [[3, 0, 2], [2, 0, -2], [0, 1, 1]]
						print(f"Add Operation, {add(lowerCAmelCase_   ,    lowerCAmelCase_					) = } \n"					)
						print(
						    f"Multiply Operation, {multiply(lowerCAmelCase_   ,    lowerCAmelCase_					) = } \n"   ,    )
						print(f"Identity: {identity(5					)}\n"					)
						print(f"Minor of {matrix_c} = {minor(lowerCAmelCase_   ,    1   ,    2					)} \n"					)
						print(f"Determinant of {matrix_b} = {determinant(lowerCAmelCase_					)} \n"					)
						print(f"Inverse of {matrix_d} = {inverse(lowerCAmelCase_					)}\n"					)


if __name__ == "__main__":
			import doctest

			doctest.testmod()
			main()






import doctest

import projectq
from projectq.ops import H, Measure



def       lowerCAmelCase			(		lowerCAmelCase_			)->			int:
				lowerCAmelCase_			:   List[Any]     					=					quantum_engine.allocate_qubit()
				H | qubit
				Measure | qubit
				return int(lowerCAmelCase_			)


if __name__ == "__main__":
						doctest.testmod()

						# initialises a new quantum backend
						_UpperCAmelCase      :	str  =projectq.MainEngine()

						# Generate a list of 10 random numbers
						_UpperCAmelCase      :	Optional[int]  =[get_random_number(quantum_engine) for _ in range(10)]

						# Flushes the quantum engine from memory
						quantum_engine.flush()

						print("""Random numbers""", random_numbers_list)