
from __future__ import annotations

from collections.abc import MutableSequence





class 							lowerCAmelCase_						:




			'''simple docstring'''


			def __init__(	self    ,							__UpperCAmelCase    ,							__UpperCAmelCase  ):
										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_	:							Union[str, Any]											=degree







			def __add__(	self    ,							__UpperCAmelCase  ):

										if self.degree > polynomial_a.degree:
																	SCREAMING_SNAKE_CASE_	:							Optional[int]											=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_	:							Dict											=polynomial_a.coefficients[:]
																	for i in range(self.degree + 1  ):
																								coefficients[i] += self.coefficients[i]
																	return Polynomial(polynomial_a.degree    ,							UpperCAmelCase__  )







			def __sub__(	self    ,							__UpperCAmelCase  ):
										return self + polynomial_a * Polynomial(0    ,							[-1]  )







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







			def __mul__(	self    ,							__UpperCAmelCase  ):
										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      __lowerCamelCase    (	self    ,							__UpperCAmelCase  ):
										SCREAMING_SNAKE_CASE_	:							int | float											=0
										for i in range(self.degree + 1  ):
																	result += self.coefficients[i] * (substitution**i)
										return result







			def __str__(	self  ):
										SCREAMING_SNAKE_CASE_	:							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(UpperCAmelCase__  )

										return polynomial







			def __repr__(	self  ):
										return self.__str__()







			def      __lowerCamelCase    (	self  ):
										SCREAMING_SNAKE_CASE_	:							list[float]											=[0] * self.degree
										for i in range(self.degree  ):
																	SCREAMING_SNAKE_CASE_	:							Tuple											=self.coefficients[i + 1] * (i + 1)
										return Polynomial(self.degree - 1    ,							UpperCAmelCase__  )







			def      __lowerCamelCase    (	self    ,							__UpperCAmelCase = 0  ):
										SCREAMING_SNAKE_CASE_	:							list[float]											=[0] * (self.degree + 2)
										SCREAMING_SNAKE_CASE_	:							str											=constant
										for i in range(self.degree + 1  ):
																	SCREAMING_SNAKE_CASE_	:							Union[str, Any]											=self.coefficients[i] / (i + 1)
										return Polynomial(self.degree + 1    ,							UpperCAmelCase__  )







			def __eq__(	self    ,							__UpperCAmelCase  ):
										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    ,							__UpperCAmelCase  ):
										return not self.__eq__(UpperCAmelCase__  )








'''simple docstring'''





from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_flax_available,
    is_sentencepiece_available,
    is_tf_available,
    is_tokenizers_available,
    is_torch_available,
)


UpperCamelCase_    						=       {"""configuration_mbart""": ["""MBART_PRETRAINED_CONFIG_ARCHIVE_MAP""", """MBartConfig""", """MBartOnnxConfig"""]}

try:
							if not is_sentencepiece_available():
														raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
							pass
else:
							UpperCamelCase_    						=       ["""MBartTokenizer"""]

try:
							if not is_tokenizers_available():
														raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
							pass
else:
							UpperCamelCase_    						=       ["""MBartTokenizerFast"""]

try:
							if not is_torch_available():
														raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
							pass
else:
							UpperCamelCase_    						=       [
							    """MBART_PRETRAINED_MODEL_ARCHIVE_LIST""",
							    """MBartForCausalLM""",
							    """MBartForConditionalGeneration""",
							    """MBartForQuestionAnswering""",
							    """MBartForSequenceClassification""",
							    """MBartModel""",
							    """MBartPreTrainedModel""",
							]

try:
							if not is_tf_available():
														raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
							pass
else:
							UpperCamelCase_    						=       [
							    """TFMBartForConditionalGeneration""",
							    """TFMBartModel""",
							    """TFMBartPreTrainedModel""",
							]

try:
							if not is_flax_available():
														raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
							pass
else:
							UpperCamelCase_    						=       [
							    """FlaxMBartForConditionalGeneration""",
							    """FlaxMBartForQuestionAnswering""",
							    """FlaxMBartForSequenceClassification""",
							    """FlaxMBartModel""",
							    """FlaxMBartPreTrainedModel""",
							]


if TYPE_CHECKING:
							from .configuration_mbart import MBART_PRETRAINED_CONFIG_ARCHIVE_MAP, MBartConfig, MBartOnnxConfig

							try:
														if not is_sentencepiece_available():
																					raise OptionalDependencyNotAvailable()
							except OptionalDependencyNotAvailable:
														pass
							else:
														from .tokenization_mbart import MBartTokenizer

							try:
														if not is_tokenizers_available():
																					raise OptionalDependencyNotAvailable()
							except OptionalDependencyNotAvailable:
														pass
							else:
														from .tokenization_mbart_fast import MBartTokenizerFast

							try:
														if not is_torch_available():
																					raise OptionalDependencyNotAvailable()
							except OptionalDependencyNotAvailable:
														pass
							else:
														from .modeling_mbart import (
														    MBART_PRETRAINED_MODEL_ARCHIVE_LIST,
														    MBartForCausalLM,
														    MBartForConditionalGeneration,
														    MBartForQuestionAnswering,
														    MBartForSequenceClassification,
														    MBartModel,
														    MBartPreTrainedModel,
														)

							try:
														if not is_tf_available():
																					raise OptionalDependencyNotAvailable()
							except OptionalDependencyNotAvailable:
														pass
							else:
														from .modeling_tf_mbart import TFMBartForConditionalGeneration, TFMBartModel, TFMBartPreTrainedModel

							try:
														if not is_flax_available():
																					raise OptionalDependencyNotAvailable()
							except OptionalDependencyNotAvailable:
														pass
							else:
														from .modeling_flax_mbart import (
														    FlaxMBartForConditionalGeneration,
														    FlaxMBartForQuestionAnswering,
														    FlaxMBartForSequenceClassification,
														    FlaxMBartModel,
														    FlaxMBartPreTrainedModel,
														)

else:
							import sys

							UpperCamelCase_    						=       _LazyModule(__name__, globals()["""__file__"""], _import_structure, module_spec=__spec__)





