





from __future__ import annotations

from collections.abc import MutableSequence


class     __magic_name__     :





     """simple docstring"""



     def __init__(							self				:Optional[int]	,					snake_case				:int	,					snake_case				:MutableSequence[float]     ):





        '''simple docstring'''




        if len(SCREAMING_SNAKE_CASE_     ) != degree + 1:
           raise ValueError(
               "The number of coefficients should be equal to the degree + 1."     )

        A_    : list[float]								=	list(SCREAMING_SNAKE_CASE_     )
        A_    : int								=	degree



     def __add__(							self				:Tuple	,					snake_case				:Polynomial     ):





        '''simple docstring'''




        if self.degree > polynomial_a.degree:
           A_    : List[Any]								=	self.coefficients[:]
           for i in range(polynomial_a.degree + 1     ):
              coefficients[i] += polynomial_a.coefficients[i]
           return Polynomial(self.degree	,					SCREAMING_SNAKE_CASE_     )
        else:
           A_    : Any								=	polynomial_a.coefficients[:]
           for i in range(self.degree + 1     ):
              coefficients[i] += self.coefficients[i]
           return Polynomial(polynomial_a.degree	,					SCREAMING_SNAKE_CASE_     )



     def __sub__(							self				:List[Any]	,					snake_case				:Polynomial     ):





        '''simple docstring'''




        return self + polynomial_a * Polynomial(0	,					[-1]     )



     def __neg__(							self				:Any     ):





        '''simple docstring'''




        return Polynomial(self.degree	,					[-c for c in self.coefficients]     )



     def __mul__(							self				:List[str]	,					snake_case				:Polynomial     ):





        '''simple docstring'''




        A_    : list[float]								=	[0] * (self.degree + polynomial_a.degree + 1)
        for i in range(self.degree + 1     ):
           for j in range(polynomial_a.degree + 1     ):
              coefficients[i + j] += (
                  self.coefficients[i] * polynomial_a.coefficients[j]
              )

        return Polynomial(self.degree + polynomial_a.degree	,					SCREAMING_SNAKE_CASE_     )



     def   SCREAMING_SNAKE_CASE						(							self				:Dict	,					snake_case				:int | float     ):





        '''simple docstring'''




        A_    : int | float								=	0
        for i in range(self.degree + 1     ):
           result += self.coefficients[i] * (substitution**i)
        return result



     def __str__(							self				:Optional[int]     ):





        '''simple docstring'''




        A_    : List[str]								=	''
        for i in range(self.degree	,					-1	,					-1     ):
           if self.coefficients[i] == 0:
              continue
           elif self.coefficients[i] > 0:
              if polynomial:
                 polynomial += " + "
           else:
              polynomial += " - "

           if i == 0:
              polynomial += str(abs(self.coefficients[i]     )     )
           elif i == 1:
              polynomial += str(abs(self.coefficients[i]     )     ) + "x"
           else:
              polynomial += str(abs(self.coefficients[i]     )     ) + "x^" + str(SCREAMING_SNAKE_CASE_     )

        return polynomial



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





        '''simple docstring'''




        return self.__str__()



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





        '''simple docstring'''




        A_    : list[float]								=	[0] * self.degree
        for i in range(self.degree     ):
           A_    : Union[str, Any]								=	self.coefficients[i + 1] * (i + 1)
        return Polynomial(self.degree - 1	,					SCREAMING_SNAKE_CASE_     )



     def   SCREAMING_SNAKE_CASE						(							self				:List[Any]	,					snake_case				:int | float = 0     ):





        '''simple docstring'''




        A_    : list[float]								=	[0] * (self.degree + 2)
        A_    : str								=	constant
        for i in range(self.degree + 1     ):
           A_    : Optional[Any]								=	self.coefficients[i] / (i + 1)
        return Polynomial(self.degree + 1	,					SCREAMING_SNAKE_CASE_     )



     def __eq__(							self				:Any	,					snake_case				:object     ):





        '''simple docstring'''




        if not isinstance(SCREAMING_SNAKE_CASE_	,					SCREAMING_SNAKE_CASE_     ):
           return False

        if self.degree != polynomial_a.degree:
           return False

        for i in range(self.degree + 1     ):
           if self.coefficients[i] != polynomial_a.coefficients[i]:
              return False

        return True





     def __ne__(							self				:Optional[Any]	,					snake_case				:object     ):





        '''simple docstring'''




        return not self.__eq__(SCREAMING_SNAKE_CASE_     )





"""simple docstring"""







import re

def 				UpperCamelCase_    (    lowerCAmelCase__      :				str						)						->   list:

  """simple docstring"""




  return [char.split() for char in re.split(R'[^ a-z A-Z 0-9 \s]'    ,   str_						)]

def 				UpperCamelCase_    (    lowerCAmelCase__      :				str						)						->   str:

  """simple docstring"""




  lowerCAmelCase_   :				str								= split_input(str_						)
  return "".join(
      [''.join([char.capitalize() for char in sub_str]						) for sub_str in string_split]						)

def 				UpperCamelCase_    (    lowerCAmelCase__      :				str    ,   lowerCAmelCase__      :				bool    ,   lowerCAmelCase__      :				str						)						->   str:

  """simple docstring"""




  try:
    lowerCAmelCase_   :				int								= split_input(lowerCAmelCase__						)
    if upper:
      lowerCAmelCase_   :				Optional[int]								= ''.join(
          [
              separator.join([char.upper() for char in sub_str]						)
              for sub_str in string_split
          ]						)
    else:
      lowerCAmelCase_   :				Any								= ''.join(
          [
              separator.join([char.lower() for char in sub_str]						)
              for sub_str in string_split
          ]						)
    return res_str
  except IndexError:
    return "not valid string"

def 				UpperCamelCase_    (    lowerCAmelCase__      :				str						)						->   str:

  """simple docstring"""




  return to_simple_case(lowerCAmelCase__						)

def 				UpperCamelCase_    (    lowerCAmelCase__      :				str						)						->   str:

  """simple docstring"""




  try:
    lowerCAmelCase_   :				Dict								= to_simple_case(lowerCAmelCase__						)
    return res_str[0].lower() + res_str[1:]
  except IndexError:
    return "not valid string"

def 				UpperCamelCase_    (    lowerCAmelCase__      :				str    ,   lowerCAmelCase__      :				bool						)						->   str:

  """simple docstring"""




  return to_complex_case(lowerCAmelCase__    ,   lowerCAmelCase__    ,   '_'						)

def 				UpperCamelCase_    (    lowerCAmelCase__      :				str    ,   lowerCAmelCase__      :				bool						)						->   str:

  """simple docstring"""




  return to_complex_case(lowerCAmelCase__    ,   lowerCAmelCase__    ,   '-'						)


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





