

"""simple docstring"""




from __future__ import annotations

from collections.abc import MutableSequence






class 	A_		:
							def __init__(		self		:      List[Any]       ,SCREAMING_SNAKE_CASE__		:      int       ,SCREAMING_SNAKE_CASE__		:      MutableSequence[float]):
								if len(SCREAMING_SNAKE_CASE__) != degree + 1:
									raise ValueError(
									    'The number of coefficients should be equal to the degree + 1.')

								__lowerCamelCase    :    list[float] 	=			list(SCREAMING_SNAKE_CASE__)
								__lowerCamelCase    :    Dict 	=			degree
							def __add__(		self		:      str       ,SCREAMING_SNAKE_CASE__		:      Polynomial):

								if self.degree > polynomial_a.degree:
									__lowerCamelCase    :    Optional[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:
									__lowerCamelCase    :    List[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		:      Tuple       ,SCREAMING_SNAKE_CASE__		:      Polynomial):
								return self + polynomial_a * Polynomial(0       ,[-1])
							def __neg__(		self		:      str):
								return Polynomial(self.degree       ,[-c for c in self.coefficients])
							def __mul__(		self		:      Optional[int]       ,SCREAMING_SNAKE_CASE__		:      Polynomial):
								__lowerCamelCase    :    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    lowerCAmelCase					(		self		:      List[str]       ,SCREAMING_SNAKE_CASE__		:      int | float):
								__lowerCamelCase    :    int | float 	=			0
								for i in range(self.degree + 1):
									result += self.coefficients[i] * (substitution**i)
								return result
							def __str__(		self		:      Any):
								__lowerCamelCase    :    Union[str, 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(SCREAMING_SNAKE_CASE__)

								return polynomial
							def __repr__(		self		:      List[Any]):
								return self.__str__()
							def    lowerCAmelCase					(		self		:      List[Any]):
								__lowerCamelCase    :    list[float] 	=			[0] * self.degree
								for i in range(self.degree):
									__lowerCamelCase    :    Union[str, Any] 	=			self.coefficients[i + 1] * (i + 1)
								return Polynomial(self.degree - 1       ,SCREAMING_SNAKE_CASE__)
							def    lowerCAmelCase					(		self		:      Dict       ,SCREAMING_SNAKE_CASE__		:      int | float = 0):
								__lowerCamelCase    :    list[float] 	=			[0] * (self.degree + 2)
								__lowerCamelCase    :    Tuple 	=			constant
								for i in range(self.degree + 1):
									__lowerCamelCase    :    int 	=			self.coefficients[i] / (i + 1)
								return Polynomial(self.degree + 1       ,SCREAMING_SNAKE_CASE__)
							def __eq__(		self		:      Union[str, Any]       ,SCREAMING_SNAKE_CASE__		:      object):
								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		:      Union[str, Any]       ,SCREAMING_SNAKE_CASE__		:      object):
								return not self.__eq__(SCREAMING_SNAKE_CASE__)







# This is the module that test_patching.py uses to test patch_submodule()

import os  # noqa: this is just for tests
import os as renamed_os  # noqa: this is just for tests
from os import path  # noqa: this is just for tests
from os import path as renamed_path  # noqa: this is just for tests
from os.path import join  # noqa: this is just for tests
from os.path import join as renamed_join  # noqa: this is just for tests


a		=open  # noqa: we just need to have a builtin inside this module to test it properly




