



from __future__ import annotations

from collections.abc import MutableSequence
class    __UpperCamelCase			:

 """simple docstring"""



 def __init__(	self		,				SCREAMING_SNAKE_CASE		,				SCREAMING_SNAKE_CASE      ) ->			None:
  if len(SCREAMING_SNAKE_CASE      ) != degree + 1:
   raise ValueError(
       '''The number of coefficients should be equal to the degree + 1.'''      )

  a__												= list(SCREAMING_SNAKE_CASE      )
  a__												= degree

 def __add__(	self		,				SCREAMING_SNAKE_CASE      ) ->			Polynomial:

  if self.degree > polynomial_a.degree:
   a__												= 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__												= 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		,				SCREAMING_SNAKE_CASE      ) ->			Polynomial:
  return self + polynomial_a * Polynomial(0		,				[-1]      )

 def __neg__(	self      ) ->			Polynomial:
  return Polynomial(self.degree		,				[-c for c in self.coefficients]      )

 def __mul__(	self		,				SCREAMING_SNAKE_CASE      ) ->			Polynomial:
  a__												= [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 						_UpperCAmelCase       (	self		,				SCREAMING_SNAKE_CASE      ) ->			int | float:
  a__												= 0
  for i in range(self.degree + 1      ):
   result += self.coefficients[i] * (substitution**i)
  return result

 def __str__(	self      ) ->			str:
  a__												= ''''''
  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      ) ->			str:
  return self.__str__()

 def 						_UpperCAmelCase       (	self      ) ->			Polynomial:
  a__												= [0] * self.degree
  for i in range(self.degree      ):
   a__												= self.coefficients[i + 1] * (i + 1)
  return Polynomial(self.degree - 1		,				SCREAMING_SNAKE_CASE      )

 def 						_UpperCAmelCase       (	self		,				SCREAMING_SNAKE_CASE = 0      ) ->			Polynomial:
  a__												= [0] * (self.degree + 2)
  a__												= constant
  for i in range(self.degree + 1      ):
   a__												= self.coefficients[i] / (i + 1)
  return Polynomial(self.degree + 1		,				SCREAMING_SNAKE_CASE      )

 def __eq__(	self		,				SCREAMING_SNAKE_CASE      ) ->			bool:
  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		,				SCREAMING_SNAKE_CASE      ) ->			bool:
  return not self.__eq__(SCREAMING_SNAKE_CASE      )










import logging
import os

from .state import PartialState
class    __UpperCamelCase			(       logging.LoggerAdapter				):

 """simple docstring"""



 @staticmethod
 def 						_UpperCAmelCase       (	SCREAMING_SNAKE_CASE      ) ->			Optional[Any]:
  a__												= PartialState()
  return not main_process_only or (main_process_only and state.is_main_process)



 def 						_UpperCAmelCase       (	self		,				SCREAMING_SNAKE_CASE		,				SCREAMING_SNAKE_CASE		,				*SCREAMING_SNAKE_CASE		,				**SCREAMING_SNAKE_CASE      ) ->			Optional[int]:
  if PartialState._shared_state == {}:
   raise RuntimeError(
       '''You must initialize the accelerate state by calling either `PartialState()` or `Accelerator()` before using the logging utility.'''      )
  a__												= kwargs.pop('''main_process_only'''		,				SCREAMING_SNAKE_CASE      )
  a__												= kwargs.pop('''in_order'''		,				SCREAMING_SNAKE_CASE      )

  if self.isEnabledFor(SCREAMING_SNAKE_CASE      ):
   if self._should_log(SCREAMING_SNAKE_CASE      ):
    a__							,			a__												= self.process(SCREAMING_SNAKE_CASE		,				SCREAMING_SNAKE_CASE      )
    self.logger.log(SCREAMING_SNAKE_CASE		,				SCREAMING_SNAKE_CASE		,				*SCREAMING_SNAKE_CASE		,				**SCREAMING_SNAKE_CASE      )

   elif in_order:
    a__												= PartialState()
    for i in range(state.num_processes      ):
     if i == state.process_index:
      a__							,			a__												= self.process(SCREAMING_SNAKE_CASE		,				SCREAMING_SNAKE_CASE      )
      self.logger.log(SCREAMING_SNAKE_CASE		,				SCREAMING_SNAKE_CASE		,				*SCREAMING_SNAKE_CASE		,				**SCREAMING_SNAKE_CASE      )
     state.wait_for_everyone()






def     __a					(		__UpperCAmelCase							,  __UpperCAmelCase = None       ):
 if log_level is None:
  a__												= os.environ.get('''ACCELERATE_LOG_LEVEL'''							,  __UpperCAmelCase       )
 a__												= logging.getLogger(__UpperCAmelCase       )
 if log_level is not None:
  logger.setLevel(log_level.upper()       )
  logger.root.setLevel(log_level.upper()       )
 return MultiProcessAdapter(__UpperCAmelCase							,  {}       )





