


from __future__ import annotations

from collections.abc import MutableSequence
class 	lowerCamelCase_       :



					'''simple docstring'''







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







								'''simple docstring'''

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

								__lowercase 					=   list(snake_case_						)
								__lowercase 					=   degree






					def __add__(				self ,       snake_case_						)   ->			Polynomial:







								'''simple docstring'''

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






					def __sub__(				self ,       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 ,       snake_case_						)   ->			Polynomial:







								'''simple docstring'''

								__lowercase 					=   [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 ,       snake_case_						)






					def A      (				self ,       snake_case_						)   ->			int | float:







								'''simple docstring'''

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






					def __str__(				self						)   ->			str:







								'''simple docstring'''

								__lowercase 					=   ''''''
								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(snake_case_						)

								return polynomial






					def __repr__(				self						)   ->			str:







								'''simple docstring'''

								return self.__str__()






					def A      (				self						)   ->			Polynomial:







								'''simple docstring'''

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






					def A      (				self ,       snake_case_ = 0						)   ->			Polynomial:







								'''simple docstring'''

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






					def __eq__(				self ,       snake_case_						)   ->			bool:







								'''simple docstring'''

								if not isinstance(snake_case_ ,       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 ,       snake_case_						)   ->			bool:







								'''simple docstring'''

								return not self.__eq__(snake_case_						)






from ..utils import DummyObject, requires_backends
class 	lowerCamelCase_       (				metaclass=lowerCAmelCase__				):



					'''simple docstring'''







					__UpperCAmelCase            =				["onnx"]






					def __init__(				self ,       *snake_case_ ,       **snake_case_						)   ->			List[Any]:







								'''simple docstring'''

								requires_backends(self ,       ['''onnx''']						)






					@classmethod
					def A      (				cls ,       *snake_case_ ,       **snake_case_						)   ->			int:







								'''simple docstring'''

								requires_backends(cls ,       ['''onnx''']						)






					@classmethod
					def A      (				cls ,       *snake_case_ ,       **snake_case_						)   ->			List[str]:







								'''simple docstring'''

								requires_backends(cls ,       ['''onnx''']						)


