






from __future__ import annotations

from collections.abc import MutableSequence






class     a_						:

  def __init__(				self      ,		_SCREAMING_SNAKE_CASE      ,		_SCREAMING_SNAKE_CASE				)  ->				None:



        """simple docstring"""






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

        UpperCamelCase      = list(lowerCAmelCase__				)
        UpperCamelCase      = degree

  def __add__(				self      ,		_SCREAMING_SNAKE_CASE				)  ->				Polynomial:



        """simple docstring"""






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

  def __sub__(				self      ,		_SCREAMING_SNAKE_CASE				)  ->				Polynomial:



        """simple docstring"""






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

  def __neg__(				self				)  ->				Polynomial:



        """simple docstring"""






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

  def __mul__(				self      ,		_SCREAMING_SNAKE_CASE				)  ->				Polynomial:



        """simple docstring"""






        UpperCamelCase      = [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      ,		lowerCAmelCase__				)

  def   A__						(				self      ,		_SCREAMING_SNAKE_CASE				)  ->				int | float:



        """simple docstring"""






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

  def __str__(				self				)  ->				str:



        """simple docstring"""






        UpperCamelCase      = """"""
        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(lowerCAmelCase__				)

        return polynomial

  def __repr__(				self				)  ->				str:



        """simple docstring"""






        return self.__str__()

  def   A__						(				self				)  ->				Polynomial:



        """simple docstring"""






        UpperCamelCase      = [0] * self.degree
        for i in range(self.degree				):
              UpperCamelCase      = self.coefficients[i + 1] * (i + 1)
        return Polynomial(self.degree - 1      ,		lowerCAmelCase__				)

  def   A__						(				self      ,		_SCREAMING_SNAKE_CASE = 0				)  ->				Polynomial:



        """simple docstring"""






        UpperCamelCase      = [0] * (self.degree + 2)
        UpperCamelCase      = constant
        for i in range(self.degree + 1				):
              UpperCamelCase      = self.coefficients[i] / (i + 1)
        return Polynomial(self.degree + 1      ,		lowerCAmelCase__				)

  def __eq__(				self      ,		_SCREAMING_SNAKE_CASE				)  ->				bool:



        """simple docstring"""






        if not isinstance(lowerCAmelCase__      ,		lowerCAmelCase__				):
              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      ,		_SCREAMING_SNAKE_CASE				)  ->				bool:



        """simple docstring"""






        return not self.__eq__(lowerCAmelCase__				)








'''simple docstring'''

import importlib
import os
from dataclasses import dataclass
from enum import Enum
from typing import Any, Dict, Optional, Union

import torch

from ..utils import BaseOutput


SCREAMING_SNAKE_CASE__     =       'scheduler_config.json'






class     a_						(      lowerCamelCase    ):
  lowercase							=				1
  lowercase							=				2
  lowercase							=				3
  lowercase							=				4
  lowercase							=				5
  lowercase							=				6
  lowercase							=				7
  lowercase							=				8
  lowercase							=				9
  lowercase							=				10
  lowercase							=				11
  lowercase							=				12
  lowercase							=				13
  lowercase							=				14






@dataclass
class     a_						(      lowerCamelCase    ):
  lowercase							=				42






class     a_						:
  lowercase							=				SCHEDULER_CONFIG_NAME
  lowercase							=				[]
  lowercase							=				True

  @classmethod
  def   A__						(				cls      ,		_SCREAMING_SNAKE_CASE = None      ,		_SCREAMING_SNAKE_CASE = None      ,		_SCREAMING_SNAKE_CASE=False      ,		**_SCREAMING_SNAKE_CASE      ,		)  ->				Optional[Any]:



        """simple docstring"""






        UpperCamelCase  ,UpperCamelCase  ,UpperCamelCase      = cls.load_config(
            pretrained_model_name_or_path=_SCREAMING_SNAKE_CASE      ,		subfolder=_SCREAMING_SNAKE_CASE      ,		return_unused_kwargs=_SCREAMING_SNAKE_CASE      ,		return_commit_hash=_SCREAMING_SNAKE_CASE      ,		**_SCREAMING_SNAKE_CASE      ,		)
        return cls.from_config(_SCREAMING_SNAKE_CASE      ,		return_unused_kwargs=_SCREAMING_SNAKE_CASE      ,		**_SCREAMING_SNAKE_CASE				)

  def   A__						(				self      ,		_SCREAMING_SNAKE_CASE      ,		_SCREAMING_SNAKE_CASE = False      ,		**_SCREAMING_SNAKE_CASE				)  ->				Dict:



        """simple docstring"""






        self.save_config(save_directory=_SCREAMING_SNAKE_CASE      ,		push_to_hub=_SCREAMING_SNAKE_CASE      ,		**_SCREAMING_SNAKE_CASE				)

  @property
  def   A__						(				self				)  ->				Tuple:



        """simple docstring"""






        return self._get_compatibles()


  @classmethod
  def   A__						(				cls				)  ->				List[Any]:



        """simple docstring"""






        UpperCamelCase      = list(set([cls.__name__] + cls._compatibles				)				)
        UpperCamelCase      = importlib.import_module(__name__.split("""."""				)[0]				)
        UpperCamelCase      = [
            getattr(_SCREAMING_SNAKE_CASE      ,		_SCREAMING_SNAKE_CASE				) for c in compatible_classes_str if hasattr(_SCREAMING_SNAKE_CASE      ,		_SCREAMING_SNAKE_CASE				)
        ]
        return compatible_classes
