





'''simple docstring'''

import math
import unittest

def     __magic_name__							(				__UpperCAmelCase   )    ->       bool:

   '''simple docstring'''







   assert isinstance(__lowercase				,						__lowercase   ) and (
       number >= 0
   ), "'number' must been an int and positive"

   if 1 < number < 4:
      # 2 and 3 are primes
      return True
   elif number < 2 or number % 2 == 0 or number % 3 == 0:
      # Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
      return False

   # All primes number are in format of 6k +/- 1
   for i in range(5				,						int(math.sqrt(__lowercase   ) + 1   )				,						6   ):
      if number % i == 0 or number % (i + 2) == 0:
         return False
   return True







class __a			( unittest.TestCase      ):





   def   UpperCAmelCase__  (       self					:      Optional[Any]     ):

      '''simple docstring'''

      self.assertTrue(is_prime(2     )     )
      self.assertTrue(is_prime(3     )     )
      self.assertTrue(is_prime(5     )     )
      self.assertTrue(is_prime(7     )     )
      self.assertTrue(is_prime(11     )     )
      self.assertTrue(is_prime(13     )     )
      self.assertTrue(is_prime(17     )     )
      self.assertTrue(is_prime(19     )     )
      self.assertTrue(is_prime(23     )     )
      self.assertTrue(is_prime(29     )     )





   def   UpperCAmelCase__  (       self					:      Union[str, Any]     ):

      '''simple docstring'''

      with self.assertRaises(UpperCamelCase_     ):
         is_prime(-19     )
      self.assertFalse(
          is_prime(0     )					,"""Zero doesn't have any positive factors, primes must have exactly two."""					,)
      self.assertFalse(
          is_prime(1     )					,"""One only has 1 positive factor, primes must have exactly two."""					,)
      self.assertFalse(is_prime(2 * 2     )     )
      self.assertFalse(is_prime(2 * 3     )     )
      self.assertFalse(is_prime(3 * 3     )     )
      self.assertFalse(is_prime(3 * 5     )     )
      self.assertFalse(is_prime(3 * 5 * 7     )     )


if __name__ == "__main__":
    unittest.main()













from __future__ import annotations

from typing import Any


class    __lowercase   :







     '''simple docstring'''




     def __init__(					self							:      Dict			,						UpperCamelCase_							:      int			,						UpperCamelCase_							:      int			,						UpperCamelCase_							:      float = 0					):


         """simple docstring"""



         __A     ,						__A       =						row, column
         __A       =						[[default_value for c in range(UpperCamelCase_					)] for r in range(UpperCamelCase_					)]




     def __str__(					self							:      Any					):


         """simple docstring"""



         __A       =						F"Matrix consist of {self.row} rows and {self.column} columns\n"

         # Make string identifier
         __A       =						0
         for row_vector in self.array:
             for obj in row_vector:
                 __A       =						max(UpperCamelCase_			,						len(str(UpperCamelCase_					)					)					)
         __A       =						F"%{max_element_length}s"

         # Make string and return
         def single_line(UpperCamelCase_							:      list[float]					) -> str:
             nonlocal string_format_identifier
             __A       =						"""["""
             line += ", ".join(string_format_identifier % (obj,) for obj in row_vector					)
             line += "]"
             return line

         s += "\n".join(single_line(UpperCamelCase_					) for row_vector in self.array					)
         return s




     def __repr__(					self							:      Optional[Any]					):


         """simple docstring"""



         return str(self					)




     def 		lowerCAmelCase_  (					self							:      Optional[int]			,						UpperCamelCase_							:      tuple[int, int]					):


         """simple docstring"""



         if not (isinstance(UpperCamelCase_			,						(list, tuple)					) and len(UpperCamelCase_					) == 2):
             return False
         elif not (0 <= loc[0] < self.row and 0 <= loc[1] < self.column):
             return False
         else:
             return True




     def __getitem__(					self							:      Optional[int]			,						UpperCamelCase_							:      tuple[int, int]					):


         """simple docstring"""



         assert self.validate_indicies(UpperCamelCase_					)
         return self.array[loc[0]][loc[1]]




     def __setitem__(					self							:      str			,						UpperCamelCase_							:      tuple[int, int]			,						UpperCamelCase_							:      float					):


         """simple docstring"""



         assert self.validate_indicies(UpperCamelCase_					)
         __A       =						value




     def __add__(					self							:      Optional[int]			,						UpperCamelCase_							:      Matrix					):


         """simple docstring"""



         assert isinstance(UpperCamelCase_			,						UpperCamelCase_					)
         assert self.row == another.row and self.column == another.column

         # Add
         __A       =						Matrix(self.row			,						self.column					)
         for r in range(self.row					):
             for c in range(self.column					):
                 __A       =						self[r, c] + another[r, c]
         return result




     def __neg__(					self							:      Any					):


         """simple docstring"""



         __A       =						Matrix(self.row			,						self.column					)
         for r in range(self.row					):
             for c in range(self.column					):
                 __A       =						-self[r, c]
         return result




     def __sub__(					self							:      List[Any]			,						UpperCamelCase_							:      Matrix					):


         """simple docstring"""



         return self + (-another)




     def __mul__(					self							:      Union[str, Any]			,						UpperCamelCase_							:      int | float | Matrix					):


         """simple docstring"""



         if isinstance(UpperCamelCase_			,						(int, float)					):  # Scalar multiplication
             __A       =						Matrix(self.row			,						self.column					)
             for r in range(self.row					):
                 for c in range(self.column					):
                     __A       =						self[r, c] * another
             return result
         elif isinstance(UpperCamelCase_			,						UpperCamelCase_					):  # Matrix multiplication
             assert self.column == another.row
             __A       =						Matrix(self.row			,						another.column					)
             for r in range(self.row					):
                 for c in range(another.column					):
                     for i in range(self.column					):
                         result[r, c] += self[r, i] * another[i, c]
             return result
         else:
             __A       =						F"Unsupported type given for another ({type(UpperCamelCase_					)})"
             raise TypeError(UpperCamelCase_					)




     def 		lowerCAmelCase_  (					self							:      str					):


         """simple docstring"""



         __A       =						Matrix(self.column			,						self.row					)
         for r in range(self.row					):
             for c in range(self.column					):
                 __A       =						self[r, c]
         return result





     def 		lowerCAmelCase_  (					self							:      List[str]			,						UpperCamelCase_							:      Matrix			,						UpperCamelCase_							:      Matrix					):


         """simple docstring"""



         assert isinstance(UpperCamelCase_			,						UpperCamelCase_					) and isinstance(UpperCamelCase_			,						UpperCamelCase_					)
         assert self.row == self.column == u.row == v.row  # u, v should be column vector
         assert u.column == v.column == 1  # u, v should be column vector

         # Calculate
         __A       =						v.transpose()
         __A       =						(v_t * self * u)[0, 0] + 1
         if numerator_factor == 0:
             return None  # It's not invertable
         return self - ((self * u) * (v_t * self) * (1.0 / numerator_factor))


# Testing
if __name__ == "__main__":



  def       _SCREAMING_SNAKE_CASE    (			)    ->   None:





      """simple docstring"""

      __A       =						Matrix(3      ,					3      ,					0     )
      for i in range(3     ):
          __A       =						1
      print(f"a^(-1) is {ainv}"     )
      # u, v
      __A       =						Matrix(3      ,					1      ,					0     )
      __A     ,						__A     ,						__A       =						1, 2, -3
      __A       =						Matrix(3      ,					1      ,					0     )
      __A     ,						__A     ,						__A       =						4, -2, 5
      print(f"u is {u}"     )
      print(f"v is {v}"     )
      print(f"uv^T is {u * v.transpose()}"     )
      # Sherman Morrison
      print(f"(a + uv^T)^(-1) is {ainv.sherman_morrison(__lowercase      ,					__lowercase     )}"     )



  def       _SCREAMING_SNAKE_CASE    (			)    ->   None:





      """simple docstring"""

      import doctest

      doctest.testmod()






  testa()




