





"""simple docstring"""






from __future__ import annotations

from typing import Any

def    __lowerCamelCase     (							*SCREAMING_SNAKE_CASE				)		->							Any:






       """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    __lowerCamelCase     (							SCREAMING_SNAKE_CASE,SCREAMING_SNAKE_CASE				)		->							Any:






       """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    __lowerCamelCase     (							SCREAMING_SNAKE_CASE,SCREAMING_SNAKE_CASE				)		->							Any:






       """simple docstring"""




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

def    __lowerCamelCase     (							SCREAMING_SNAKE_CASE,SCREAMING_SNAKE_CASE				)		->							Optional[Any]:






       """simple docstring"""




       if _check_not_integer(SCREAMING_SNAKE_CASE				) and _check_not_integer(SCREAMING_SNAKE_CASE				):
              _UpperCAmelCase			     =  _verify_matrix_sizes(SCREAMING_SNAKE_CASE,SCREAMING_SNAKE_CASE				)

       if cols[0] != rows[1]:
              _UpperCAmelCase			     =  (
                  """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    __lowerCamelCase     (							SCREAMING_SNAKE_CASE				)		->							int:






       """simple docstring"""




       _UpperCAmelCase			     =  int(SCREAMING_SNAKE_CASE				)
       return [[int(row == column				) for column in range(SCREAMING_SNAKE_CASE				)] for row in range(SCREAMING_SNAKE_CASE				)]

def    __lowerCamelCase     (							SCREAMING_SNAKE_CASE,SCREAMING_SNAKE_CASE = True				)		->							Optional[int]:






       """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    __lowerCamelCase     (							SCREAMING_SNAKE_CASE,SCREAMING_SNAKE_CASE,SCREAMING_SNAKE_CASE				)		->							List[Any]:






       """simple docstring"""




       _UpperCAmelCase			     =  matrix[:row] + matrix[row + 1 :]
       return [row[:column] + row[column + 1 :] for row in minor]

def    __lowerCamelCase     (							SCREAMING_SNAKE_CASE				)		->							Optional[int]:






       """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    __lowerCamelCase     (							SCREAMING_SNAKE_CASE				)		->							List[str]:






       """simple docstring"""




       _UpperCAmelCase			     =  determinant(SCREAMING_SNAKE_CASE				)
       if det == 0:
              return None

       _UpperCAmelCase			     =  [
           [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				)				)
       ]

       _UpperCAmelCase			     =  [
           [x * (-1) ** (row + col) for col, x in enumerate(matrix_minor[row]				)]
           for row in range(len(SCREAMING_SNAKE_CASE				)				)
       ]
       _UpperCAmelCase			     =  list(transpose(SCREAMING_SNAKE_CASE				)				)
       return scalar_multiply(SCREAMING_SNAKE_CASE,1 / det				)

def    __lowerCamelCase     (							SCREAMING_SNAKE_CASE				)		->							List[str]:






       """simple docstring"""




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

def    __lowerCamelCase     (							SCREAMING_SNAKE_CASE				)		->							List[Any]:






       """simple docstring"""




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

def    __lowerCamelCase     (							SCREAMING_SNAKE_CASE,SCREAMING_SNAKE_CASE				)		->							str:






       """simple docstring"""




       _UpperCAmelCase			     =  _shape(SCREAMING_SNAKE_CASE				) + _shape(SCREAMING_SNAKE_CASE				)
       if shape[0] != shape[3] or shape[1] != shape[2]:
              _UpperCAmelCase			     =  (
                  """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    __lowerCamelCase     (							)		->							int:






       """simple docstring"""




       _UpperCAmelCase			     =  [[12, 10], [3, 9]]
       _UpperCAmelCase			     =  [[3, 4], [7, 4]]
       _UpperCAmelCase			     =  [[11, 12, 13, 14], [21, 22, 23, 24], [31, 32, 33, 34], [41, 42, 43, 44]]
       _UpperCAmelCase			     =  [[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 				lowerCAmelCase__	(       UpperCAmelCase     ):






       """simple docstring"""





       snake_case__					:	Tuple          =					math.log(2    ,       10     ) * number
       snake_case__					:	int          =					round((log_number - int(UpperCAmelCase     ))    ,       15     )

       return difference



def 				lowerCAmelCase__	(       UpperCAmelCase = 67_8910     ):






       """simple docstring"""





       snake_case__					:	str          =					90
       snake_case__					:	Dict          =					0

       snake_case__					:	List[str]          =					math.log(1.2_3    ,       10     )
       snake_case__					:	Optional[Any]          =					math.log(1.2_4    ,       10     )
       snake_case__					:	Any          =					0

       while position < number:
              snake_case__					:	Tuple          =					log_difference(UpperCAmelCase     )

              if difference >= upper_limit:
                     power_iterator += 93

              elif difference < lower_limit:
                     power_iterator += 196

              else:
                     snake_case__					:	Union[str, Any]          =					power_iterator
                     power_iterator += 196
                     position += 1

       return previous_power


if __name__ == "__main__":
     import doctest

     doctest.testmod()

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




