

'''simple docstring'''





from __future__ import annotations

from collections.abc import MutableSequence





class 		__SCREAMING_SNAKE_CASE							:







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

										lowercase :							list[float]    		=list(UpperCAmelCase__   )
										lowercase :							Union[str, Any]    		=degree







				def __add__(       self     :		Any		,					UpperCAmelCase__     :		Polynomial   ):
										'''simple docstring'''

										if self.degree > polynomial_a.degree:
																lowercase :							Optional[int]    		=self.coefficients[:]
																for i in range(polynomial_a.degree + 1   ):
																						coefficients[i] += polynomial_a.coefficients[i]
																return Polynomial(self.degree		,					UpperCAmelCase__   )
										else:
																lowercase :							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     :		List[str]		,					UpperCAmelCase__     :		Polynomial   ):
										'''simple docstring'''
										return self + polynomial_a * Polynomial(0		,					[-1]   )







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







				def __mul__(       self     :		Optional[int]		,					UpperCAmelCase__     :		Polynomial   ):
										'''simple docstring'''
										lowercase :							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     :		int		,					UpperCAmelCase__     :		int | float   ):
										'''simple docstring'''
										lowercase :							int | float    		=0
										for i in range(self.degree + 1   ):
																result += self.coefficients[i] * (substitution**i)
										return result







				def __str__(       self     :		str   ):
										'''simple docstring'''
										lowercase :							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     :		Dict   ):
										'''simple docstring'''
										return self.__str__()







				def  lowerCamelCase_	(       self     :		int   ):
										'''simple docstring'''
										lowercase :							list[float]    		=[0] * self.degree
										for i in range(self.degree   ):
																lowercase :							Tuple    		=self.coefficients[i + 1] * (i + 1)
										return Polynomial(self.degree - 1		,					UpperCAmelCase__   )







				def  lowerCamelCase_	(       self     :		int		,					UpperCAmelCase__     :		int | float = 0   ):
										'''simple docstring'''
										lowercase :							list[float]    		=[0] * (self.degree + 2)
										lowercase :							str    		=constant
										for i in range(self.degree + 1   ):
																lowercase :							Union[str, Any]    		=self.coefficients[i] / (i + 1)
										return Polynomial(self.degree + 1		,					UpperCAmelCase__   )







				def __eq__(       self     :		str		,					UpperCAmelCase__     :		object   ):
										'''simple docstring'''
										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     :		Tuple		,					UpperCAmelCase__     :		object   ):
										'''simple docstring'''
										return not self.__eq__(UpperCAmelCase__   )











from dataclasses import dataclass, field
from typing import TYPE_CHECKING, Any, ClassVar, Dict, List, Optional, Union

import pyarrow as pa


if TYPE_CHECKING:
							from .features import FeatureType




@dataclass
class 		__A   :
						UpperCamelCase      =       42
						UpperCamelCase      =       None
						# Automatically constructed
						UpperCamelCase      =       "dict"
						UpperCamelCase      =       None
						UpperCamelCase      =       field(default="""Translation"""       ,    init=UpperCamelCase__       ,    repr=UpperCamelCase__      )

						def __call__(		self :Union[str, Any]			):
										'''simple docstring'''

										return pa.struct({lang: pa.string() for lang in sorted(self.languages			)}			)


						def      A__    (		self :List[Any]			):
										'''simple docstring'''

										from .features import Value

										return {k: Value("""string"""			) for k in sorted(self.languages			)}




@dataclass
class 		__A   :
						UpperCamelCase      =       None
						UpperCamelCase      =       None
						UpperCamelCase      =       None
						# Automatically constructed
						UpperCamelCase      =       "dict"
						UpperCamelCase      =       None
						UpperCamelCase      =       field(default="""TranslationVariableLanguages"""       ,    init=UpperCamelCase__       ,    repr=UpperCamelCase__      )

						def      A__    (		self :Optional[Any]			):
										'''simple docstring'''

										__magic_name__						:						List[Any]										=sorted(set(self.languages			)			) if self.languages else None
										__magic_name__						:						Optional[int]										=len(self.languages			) if self.languages else None

						def __call__(		self :List[str]			):
										'''simple docstring'''

										return pa.struct({"""language""": pa.list_(pa.string()			), """translation""": pa.list_(pa.string()			)}			)

						def      A__    (		self :str     ,			__snake_case :str			):
										'''simple docstring'''

										__magic_name__						:						Optional[int]										=set(self.languages			)
										if self.languages and set(__snake_case			) - lang_set:
														raise ValueError(
														    f"Some languages in example ({', '.join(sorted(set(__snake_case			) - lang_set			)			)}) are not in valid set ({', '.join(__snake_case			)})."			)

										# Convert dictionary into tuples, splitting out cases where there are
										# multiple translations for a single language.
										__magic_name__						:						Any										=[]
										for lang, text in translation_dict.items():
														if isinstance(__snake_case     ,			__snake_case			):
																		translation_tuples.append((lang, text)			)
														else:
																		translation_tuples.extend([(lang, el) for el in text]			)

        # Ensure translations are in ascending order by language code.
										__magic_name__					,			__magic_name__						:						List[str]										=zip(*sorted(__snake_case			)			)

										return {"language": languages, "translation": translations}


						def      A__    (		self :List[Any]			):
										'''simple docstring'''

										from .features import Sequence, Value

										return {
										    "language": Sequence(Value("""string"""			)			),
										    "translation": Sequence(Value("""string"""			)			),
										}




