



"""simple docstring"""


from __future__ import annotations

from collections.abc import MutableSequence







class 				A_      :



						"""simple docstring"""






						def __init__( self			:Any       ,  lowercase_			:int       ,  lowercase_			:MutableSequence[float] )    ->      None:
												if len(lowercase_ ) != degree + 1:
																		raise ValueError(
																		    'The number of coefficients should be equal to the degree + 1.' )

												UpperCAmelCase					=			list(lowercase_ )
												UpperCAmelCase					=			degree






						def __add__( self			:Optional[int]       ,  lowercase_			:Polynomial )    ->      Polynomial:

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






						def __sub__( self			:List[str]       ,  lowercase_			:Polynomial )    ->      Polynomial:
												return self + polynomial_a * Polynomial(0       ,  [-1] )






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






						def __mul__( self			:str       ,  lowercase_			:Polynomial )    ->      Polynomial:
												UpperCAmelCase					=			[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       ,  lowercase_ )






						def      UpperCAmelCase__					( self			:List[Any]       ,  lowercase_			:int | float )    ->      int | float:
												UpperCAmelCase					=			0
												for i in range(self.degree + 1 ):
																		result += self.coefficients[i] * (substitution**i)
												return result






						def __str__( self			:Optional[int] )    ->      str:
												UpperCAmelCase					=			''
												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(lowercase_ )

												return polynomial






						def __repr__( self			:Dict )    ->      str:
												return self.__str__()






						def      UpperCAmelCase__					( self			:Any )    ->      Polynomial:
												UpperCAmelCase					=			[0] * self.degree
												for i in range(self.degree ):
																		UpperCAmelCase					=			self.coefficients[i + 1] * (i + 1)
												return Polynomial(self.degree - 1       ,  lowercase_ )






						def      UpperCAmelCase__					( self			:str       ,  lowercase_			:int | float = 0 )    ->      Polynomial:
												UpperCAmelCase					=			[0] * (self.degree + 2)
												UpperCAmelCase					=			constant
												for i in range(self.degree + 1 ):
																		UpperCAmelCase					=			self.coefficients[i] / (i + 1)
												return Polynomial(self.degree + 1       ,  lowercase_ )






						def __eq__( self			:List[str]       ,  lowercase_			:object )    ->      bool:
												if not isinstance(lowercase_       ,  lowercase_ ):
																		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			:Dict       ,  lowercase_			:object )    ->      bool:
												return not self.__eq__(lowercase_ )










"""simple docstring"""


import importlib
import sys
from argparse import REMAINDER, ArgumentParser
from pathlib import Path

import torch_xla.distributed.xla_multiprocessing as xmp

def 			_lowerCAmelCase				(       ):
						UpperCAmelCase					=			ArgumentParser(
						    description=(
						        'PyTorch TPU distributed training launch helper utility that will spawn up multiple distributed processes'
						    )						)

						# Optional arguments for the launch helper
						parser.add_argument('--num_cores'		,     type=lowercase_		,     default=1		,     help='Number of TPU cores to use (1 or 8).'						)

						# positional
						parser.add_argument(
						    'training_script'		,     type=lowercase_		,     help=(
						        'The full path to the single TPU training '
						        'program/script to be launched in parallel, '
						        'followed by all the arguments for the '
						        'training script'
						    )		,     )

						# rest from the training program
						parser.add_argument('training_script_args'		,     nargs=lowercase_						)

						return parser.parse_args()

def 			_lowerCAmelCase				(       ):
						UpperCAmelCase					=			parse_args()

						# Import training_script as a module.
						UpperCAmelCase					=			Path(args.training_script						)
						sys.path.append(str(script_fpath.parent.resolve()						)						)
						UpperCAmelCase					=			script_fpath.stem
						UpperCAmelCase					=			importlib.import_module(lowercase_						)

						# Patch sys.argv
						UpperCAmelCase					=			[args.training_script] + args.training_script_args + ['--tpu_num_cores', str(args.num_cores						)]

						xmp.spawn(mod._mp_fn		,     args=()		,     nprocs=args.num_cores						)


if __name__ == "__main__":
				main()





