
'''simple docstring'''
from __future__ import annotations

from typing import Any

def   UpperCamelCase_       (		*__SCREAMING_SNAKE_CASE    ):
    """simple docstring"""






    if all(_check_not_integer(__SCREAMING_SNAKE_CASE    ) for m in matrix_s    ):
        for i in matrix_s[1:]:
            _verify_matrix_sizes(matrix_s[0],						__SCREAMING_SNAKE_CASE    )
        return [[sum(__SCREAMING_SNAKE_CASE    ) for t in zip(*__SCREAMING_SNAKE_CASE    )] for m in zip(*__SCREAMING_SNAKE_CASE    )]
    raise TypeError("Expected a matrix, got int/list instead"    )

def   UpperCamelCase_       (		__SCREAMING_SNAKE_CASE,						__SCREAMING_SNAKE_CASE    ):
    """simple docstring"""






    if (
        _check_not_integer(__SCREAMING_SNAKE_CASE    )
        and _check_not_integer(__SCREAMING_SNAKE_CASE    )
        and _verify_matrix_sizes(__SCREAMING_SNAKE_CASE,						__SCREAMING_SNAKE_CASE    )
    ):
        return [[i - j for i, j in zip(*__SCREAMING_SNAKE_CASE    )] for m in zip(__SCREAMING_SNAKE_CASE,						__SCREAMING_SNAKE_CASE    )]
    raise TypeError("Expected a matrix, got int/list instead"    )

def   UpperCamelCase_       (		__SCREAMING_SNAKE_CASE,						__SCREAMING_SNAKE_CASE    ):
    """simple docstring"""






    return [[x * n for x in row] for row in matrix]

def   UpperCamelCase_       (		__SCREAMING_SNAKE_CASE,						__SCREAMING_SNAKE_CASE    ):
    """simple docstring"""






    if _check_not_integer(__SCREAMING_SNAKE_CASE    ) and _check_not_integer(__SCREAMING_SNAKE_CASE    ):
        snake_case_     ,	snake_case_	:      List[str]            =  _verify_matrix_sizes(__SCREAMING_SNAKE_CASE,						__SCREAMING_SNAKE_CASE    )

    if cols[0] != rows[1]:
        snake_case_	:      Union[str, Any]            =  (
            "Cannot multiply matrix of dimensions "
            f'({rows[0]},{cols[0]}) and ({rows[1]},{cols[1]})'
        )
        raise ValueError(__SCREAMING_SNAKE_CASE    )
    return [
        [sum(m * n for m, n in zip(__SCREAMING_SNAKE_CASE,						__SCREAMING_SNAKE_CASE    )    ) for j in zip(*__SCREAMING_SNAKE_CASE    )] for i in matrix_a
    ]

def   UpperCamelCase_       (		__SCREAMING_SNAKE_CASE    ):
    """simple docstring"""






    snake_case_	:      str            =  int(__SCREAMING_SNAKE_CASE    )
    return [[int(row == column    ) for column in range(__SCREAMING_SNAKE_CASE    )] for row in range(__SCREAMING_SNAKE_CASE    )]

def   UpperCamelCase_       (		__SCREAMING_SNAKE_CASE,						__SCREAMING_SNAKE_CASE = True    ):
    """simple docstring"""






    if _check_not_integer(__SCREAMING_SNAKE_CASE    ):
        if return_map:
            return map(__SCREAMING_SNAKE_CASE,						zip(*__SCREAMING_SNAKE_CASE    )    )
        else:
            return list(map(__SCREAMING_SNAKE_CASE,						zip(*__SCREAMING_SNAKE_CASE    )    )    )
    raise TypeError("Expected a matrix, got int/list instead"    )

def   UpperCamelCase_       (		__SCREAMING_SNAKE_CASE,						__SCREAMING_SNAKE_CASE,						__SCREAMING_SNAKE_CASE    ):
    """simple docstring"""






    snake_case_	:      Optional[int]            =  matrix[:row] + matrix[row + 1 :]
    return [row[:column] + row[column + 1 :] for row in minor]

def   UpperCamelCase_       (		__SCREAMING_SNAKE_CASE    ):
    """simple docstring"""






    if len(__SCREAMING_SNAKE_CASE    ) == 1:
        return matrix[0][0]

    return sum(
        x * determinant(minor(__SCREAMING_SNAKE_CASE,						0,						__SCREAMING_SNAKE_CASE    )    ) * (-1) ** i
        for i, x in enumerate(matrix[0]    )    )

def   UpperCamelCase_       (		__SCREAMING_SNAKE_CASE    ):
    """simple docstring"""






    snake_case_	:      Any            =  determinant(__SCREAMING_SNAKE_CASE    )
    if det == 0:
        return None

    snake_case_	:      Dict            =  [
        [determinant(minor(__SCREAMING_SNAKE_CASE,						__SCREAMING_SNAKE_CASE,						__SCREAMING_SNAKE_CASE    )    ) for j in range(len(__SCREAMING_SNAKE_CASE    )    )]
        for i in range(len(__SCREAMING_SNAKE_CASE    )    )
    ]

    snake_case_	:      List[str]            =  [
        [x * (-1) ** (row + col) for col, x in enumerate(matrix_minor[row]    )]
        for row in range(len(__SCREAMING_SNAKE_CASE    )    )
    ]
    snake_case_	:      Any            =  list(transpose(__SCREAMING_SNAKE_CASE    )    )
    return scalar_multiply(__SCREAMING_SNAKE_CASE,						1 / det    )

def   UpperCamelCase_       (		__SCREAMING_SNAKE_CASE    ):
    """simple docstring"""






    return not isinstance(__SCREAMING_SNAKE_CASE,						__SCREAMING_SNAKE_CASE    ) and not isinstance(matrix[0],						__SCREAMING_SNAKE_CASE    )

def   UpperCamelCase_       (		__SCREAMING_SNAKE_CASE    ):
    """simple docstring"""






    return len(__SCREAMING_SNAKE_CASE    ), len(matrix[0]    )

def   UpperCamelCase_       (		__SCREAMING_SNAKE_CASE,						__SCREAMING_SNAKE_CASE    ):
    """simple docstring"""






    snake_case_	:      List[Any]            =  _shape(__SCREAMING_SNAKE_CASE    ) + _shape(__SCREAMING_SNAKE_CASE    )
    if shape[0] != shape[3] or shape[1] != shape[2]:
        snake_case_	:      str            =  (
            "operands could not be broadcast together with shape "
            f'({shape[0], shape[1]}), ({shape[2], shape[3]})'
        )
        raise ValueError(__SCREAMING_SNAKE_CASE    )
    return (shape[0], shape[2]), (shape[1], shape[3])

def   UpperCamelCase_       (		):
    """simple docstring"""






    snake_case_	:      Any            =  [[1_2, 1_0], [3, 9]]
    snake_case_	:      Optional[Any]            =  [[3, 4], [7, 4]]
    snake_case_	:      Union[str, Any]            =  [[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]]
    snake_case_	:      Union[str, Any]            =  [[3, 0, 2], [2, 0, -2], [0, 1, 1]]
    print(f'Add Operation, {add(__SCREAMING_SNAKE_CASE,						__SCREAMING_SNAKE_CASE    ) = } \n'    )
    print(
        f'Multiply Operation, {multiply(__SCREAMING_SNAKE_CASE,						__SCREAMING_SNAKE_CASE    ) = } \n',						)
    print(f'Identity: {identity(5    )}\n'    )
    print(f'Minor of {matrix_c} = {minor(__SCREAMING_SNAKE_CASE,						1,						2    )} \n'    )
    print(f'Determinant of {matrix_b} = {determinant(__SCREAMING_SNAKE_CASE    )} \n'    )
    print(f'Inverse of {matrix_d} = {inverse(__SCREAMING_SNAKE_CASE    )}\n'    )


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  main()






'''simple docstring'''
import math

def   UpperCamelCase_       (		__SCREAMING_SNAKE_CASE    ):
    """simple docstring"""






    snake_case_	:      Tuple            =  math.log(2,						1_0    ) * number
    snake_case_	:      Dict            =  round((log_number - int(__SCREAMING_SNAKE_CASE    )),						1_5    )

    return difference

def   UpperCamelCase_       (		__SCREAMING_SNAKE_CASE = 6_7_8_9_1_0    ):
    """simple docstring"""






    snake_case_	:      Any            =  9_0
    snake_case_	:      Optional[int]            =  0

    snake_case_	:      Union[str, Any]            =  math.log(1.23,						1_0    )
    snake_case_	:      Dict            =  math.log(1.24,						1_0    )
    snake_case_	:      List[Any]            =  0

    while position < number:
        snake_case_	:      Union[str, Any]            =  log_difference(__SCREAMING_SNAKE_CASE    )

        if difference >= upper_limit:
            power_iterator += 9_3

        elif difference < lower_limit:
            power_iterator += 1_9_6

        else:
            snake_case_	:      Optional[Any]            =  power_iterator
            power_iterator += 1_9_6
            position += 1

    return previous_power


if __name__ == "__main__":
  import doctest

  doctest.testmod()

  print(f"""{solution() = }""")




