


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

from collections.abc import MutableSequence




class 			lowerCamelCase_   :






      def __init__(					self				:    Dict						,						_A				:    int						,						_A				:    MutableSequence[float] ):


          '''simple docstring'''


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

          UpperCAmelCase__			:		list[float]													=				list(_A )
          UpperCAmelCase__			:		Union[str, Any]													=				degree






      def __add__(					self				:    Dict						,						_A				:    Polynomial ):


          '''simple docstring'''


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






      def __sub__(					self				:    Union[str, Any]						,						_A				:    Polynomial ):


          '''simple docstring'''


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






      def __neg__(					self				:    Optional[int] ):


          '''simple docstring'''


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






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


          '''simple docstring'''


          UpperCAmelCase__			:		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						,						_A )






      def lowercase_							(					self				:    Any						,						_A				:    int | float ):


          '''simple docstring'''


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






      def __str__(					self				:    Any ):


          '''simple docstring'''


          UpperCAmelCase__			:		Dict													=				''''''
          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(_A )

          return polynomial






      def __repr__(					self				:    List[str] ):


          '''simple docstring'''


          return self.__str__()






      def lowercase_							(					self				:    Optional[Any] ):


          '''simple docstring'''


          UpperCAmelCase__			:		list[float]													=				[0] * self.degree
          for i in range(self.degree ):
              UpperCAmelCase__			:		List[str]													=				self.coefficients[i + 1] * (i + 1)
          return Polynomial(self.degree - 1						,						_A )






      def lowercase_							(					self				:    int						,						_A				:    int | float = 0 ):


          '''simple docstring'''


          UpperCAmelCase__			:		list[float]													=				[0] * (self.degree + 2)
          UpperCAmelCase__			:		List[str]													=				constant
          for i in range(self.degree + 1 ):
              UpperCAmelCase__			:		Tuple													=				self.coefficients[i] / (i + 1)
          return Polynomial(self.degree + 1						,						_A )






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


          '''simple docstring'''


          if not isinstance(_A						,						_A ):
              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[int]						,						_A				:    object ):


          '''simple docstring'''


          return not self.__eq__(_A )




'''simple docstring'''
import unittest

from accelerate import debug_launcher
from accelerate.test_utils import require_cpu, test_ops, test_script




@require_cpu
class 			lowerCamelCase_   (	unittest.TestCase      ):






      def lowercase_							(					self				:    Tuple ):


          '''simple docstring'''


          debug_launcher(test_script.main )






      def lowercase_							(					self				:    List[str] ):


          '''simple docstring'''


          debug_launcher(test_ops.main )
