




"""simple docstring"""



from math import factorial




class      UpperCAmelCase_  :




    def __init__(   self						:	Dict     ,			snake_case_						:	int     ,			snake_case_						:	List[Any]				)				->							Union[str, Any]:




     '''simple docstring'''

     A__	=    real
     if isinstance(snake_case_     ,			snake_case_				):
      A__	=    [1] * rank
     else:
      A__	=    rank




    def __repr__(   self						:	List[Any]				)				->							int:




     '''simple docstring'''

     return (
         F"""{self.real}+"""
         F"""{"+".join(str(snake_case_				)+"E"+str(n+1				)for n,dual in enumerate(self.duals				)				)}"""
     )




    def 							__magic_name__							(   self						:	List[str]				)				->							Any:




     '''simple docstring'''

     A__	=    self.duals.copy()
     while cur[-1] == 0:
      cur.pop(-1				)
     return Dual(self.real     ,			snake_case_				)




    def __add__(   self						:	Tuple     ,			snake_case_						:	List[str]				)				->							List[str]:




     '''simple docstring'''

     if not isinstance(snake_case_     ,			snake_case_				):
      return Dual(self.real + other     ,			self.duals				)
     A__	=    self.duals.copy()
     A__	=    other.duals.copy()
     if len(snake_case_				) > len(snake_case_				):
      o_dual.extend([1] * (len(snake_case_				) - len(snake_case_				))				)
     elif len(snake_case_				) < len(snake_case_				):
      s_dual.extend([1] * (len(snake_case_				) - len(snake_case_				))				)
     A__	=    []
     for i in range(len(snake_case_				)				):
      new_duals.append(s_dual[i] + o_dual[i]				)
     return Dual(self.real + other.real     ,			snake_case_				)

    lowercase__						 =				__add__




    def __sub__(   self						:	List[Any]     ,			snake_case_						:	Tuple				)				->							Optional[int]:




     '''simple docstring'''

     return self + other * -1




    def __mul__(   self						:	Optional[int]     ,			snake_case_						:	List[Any]				)				->							str:




     '''simple docstring'''

     if not isinstance(snake_case_     ,			snake_case_				):
      A__	=    []
      for i in self.duals:
       new_duals.append(i * other				)
      return Dual(self.real * other     ,			snake_case_				)
     A__	=    [0] * (len(self.duals				) + len(other.duals				) + 1)
     for i, item in enumerate(self.duals				):
      for j, jtem in enumerate(other.duals				):
       new_duals[i + j + 1] += item * jtem
     for k in range(len(self.duals				)				):
      new_duals[k] += self.duals[k] * other.real
     for index in range(len(other.duals				)				):
      new_duals[index] += other.duals[index] * self.real
     return Dual(self.real * other.real     ,			snake_case_				)

    lowercase__						 =				__mul__




    def __truediv__(   self						:	Union[str, Any]     ,			snake_case_						:	Optional[Any]				)				->							List[Any]:




     '''simple docstring'''

     if not isinstance(snake_case_     ,			snake_case_				):
      A__	=    []
      for i in self.duals:
       new_duals.append(i / other				)
      return Dual(self.real / other     ,			snake_case_				)
     raise ValueError




    def __floordiv__(   self						:	Optional[int]     ,			snake_case_						:	List[Any]				)				->							Optional[int]:




     '''simple docstring'''

     if not isinstance(snake_case_     ,			snake_case_				):
      A__	=    []
      for i in self.duals:
       new_duals.append(i // other				)
      return Dual(self.real // other     ,			snake_case_				)
     raise ValueError




    def __pow__(   self						:	Any     ,			snake_case_						:	List[Any]				)				->							Any:




     '''simple docstring'''

     if n < 0 or isinstance(snake_case_     ,			snake_case_				):
      raise ValueError("power must be a positive integer"				)
     if n == 0:
      return 1
     if n == 1:
      return self
     A__	=    self
     for _ in range(n - 1				):
      x *= self
     return x







def   _SCREAMING_SNAKE_CASE       (							lowercase_      ,			lowercase_      ,			lowercase_						)						->		int:
 if not callable(lowercase_						):
  raise ValueError("differentiate() requires a function as input for func"						)
 if not isinstance(lowercase_      ,			(float, int)						):
  raise ValueError("differentiate() requires a float as input for position"						)
 if not isinstance(lowercase_      ,			lowercase_						):
  raise ValueError("differentiate() requires an int as input for order"						)
 A__	=    Dual(lowercase_      ,			1						)
 A__	=    func(lowercase_						)
 if order == 0:
  return result.real
 return result.duals[order - 1] * factorial(lowercase_						)


if __name__ == "__main__":
      import doctest

      doctest.testmod()







      def   _SCREAMING_SNAKE_CASE       (							lowercase_						)						->		Optional[int]:
       return y**2 * y**4






      print(differentiate(f, 9, 2))











"""simple docstring"""



SCREAMING_SNAKE_CASE    =	"\n# Transformers installation\n! pip install transformers datasets\n# To install from source instead of the last release, comment the command above and uncomment the following one.\n# ! pip install git+https://github.com/huggingface/transformers.git\n"

SCREAMING_SNAKE_CASE    =	[{"type": "code", "content": INSTALL_CONTENT}]
SCREAMING_SNAKE_CASE    =	{
    "{processor_class}": "FakeProcessorClass",
    "{model_class}": "FakeModelClass",
    "{object_class}": "FakeObjectClass",
}





