'''simple docstring'''

from __future__ import annotations

from collections.abc import MutableSequence


class 	a__     :


	def __init__(self : Optional[Any],					__UpperCAmelCase : int,					__UpperCAmelCase : MutableSequence[float]      )     ->			None:

					"""simple docstring"""

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

					SCREAMING_SNAKE_CASE  :						list[float]      					= list(__UpperCAmelCase      )
					SCREAMING_SNAKE_CASE  :						Optional[Any]      					= degree


	def __add__(self : Dict,					__UpperCAmelCase : Polynomial      )     ->			Polynomial:

					"""simple docstring"""

					if self.degree > polynomial_a.degree:
									SCREAMING_SNAKE_CASE  :						str      					= self.coefficients[:]
									for i in range(polynomial_a.degree + 1      ):
													coefficients[i] += polynomial_a.coefficients[i]
									return Polynomial(self.degree,					__UpperCAmelCase      )
					else:
									SCREAMING_SNAKE_CASE  :						str      					= polynomial_a.coefficients[:]
									for i in range(self.degree + 1      ):
													coefficients[i] += self.coefficients[i]
									return Polynomial(polynomial_a.degree,					__UpperCAmelCase      )


	def __sub__(self : str,					__UpperCAmelCase : Polynomial      )     ->			Polynomial:

					"""simple docstring"""

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


	def __neg__(self : Optional[int]      )     ->			Polynomial:

					"""simple docstring"""

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


	def __mul__(self : List[Any],					__UpperCAmelCase : Polynomial      )     ->			Polynomial:

					"""simple docstring"""

					SCREAMING_SNAKE_CASE  :						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,					__UpperCAmelCase      )


	def 				lowercase__  (self : Optional[Any],					__UpperCAmelCase : int | float      )     ->			int | float:

					"""simple docstring"""

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


	def __str__(self : List[str]      )     ->			str:

					"""simple docstring"""

					SCREAMING_SNAKE_CASE  :						Any      					= ''''''
					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(__UpperCAmelCase      )

					return polynomial


	def __repr__(self : Optional[Any]      )     ->			str:

					"""simple docstring"""

					return self.__str__()


	def 				lowercase__  (self : Dict      )     ->			Polynomial:

					"""simple docstring"""

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


	def 				lowercase__  (self : int,					__UpperCAmelCase : int | float = 0      )     ->			Polynomial:

					"""simple docstring"""

					SCREAMING_SNAKE_CASE  :						list[float]      					= [0] * (self.degree + 2)
					SCREAMING_SNAKE_CASE  :						int      					= constant
					for i in range(self.degree + 1      ):
									SCREAMING_SNAKE_CASE  :						Dict      					= self.coefficients[i] / (i + 1)
					return Polynomial(self.degree + 1,					__UpperCAmelCase      )


	def __eq__(self : List[Any],					__UpperCAmelCase : object      )     ->			bool:

					"""simple docstring"""

					if not isinstance(__UpperCAmelCase,					__UpperCAmelCase      ):
									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 : str,					__UpperCAmelCase : object      )     ->			bool:

					"""simple docstring"""

					return not self.__eq__(__UpperCAmelCase      )









'''simple docstring'''

from ...utils import is_torch_available, is_transformers_available


if is_transformers_available() and is_torch_available():
	from .pipeline_vq_diffusion import LearnedClassifierFreeSamplingEmbeddings, VQDiffusionPipeline




