



import mpmath  # for roots of unity
import numpy as np





class  __magic_name__   :






		def __init__(						self      :     Dict				,		UpperCamelCase__      :     Any=None				,		UpperCamelCase__      :     Union[str, Any]=None      )				->					Optional[int]:
								'''simple docstring'''







								UpperCAmelCase         =     list(poly_a or [0]      )[:]
								UpperCAmelCase         =     list(poly_b or [0]      )[:]

								# Remove leading zero coefficients
								while self.polyA[-1] == 0:
														self.polyA.pop()
								UpperCAmelCase         =     len(self.polyA      )

								while self.polyB[-1] == 0:
														self.polyB.pop()
								UpperCAmelCase         =     len(self.polyB      )

								# Add 0 to make lengths equal a power of 2
								UpperCAmelCase         =     int(
								    2 ** np.ceil(np.loga(len(self.polyA      ) + len(self.polyB      ) - 1      )      )      )

								while len(self.polyA      ) < self.c_max_length:
														self.polyA.append(0      )
								while len(self.polyB      ) < self.c_max_length:
														self.polyB.append(0      )
								# A complex root used for the fourier transform
								UpperCAmelCase         =     complex(mpmath.root(x=1				,		n=self.c_max_length				,		k=1      )      )

								# The product
								UpperCAmelCase         =     self.__multiply()






		def SCREAMING_SNAKE_CASE_			(						self      :     int				,		UpperCamelCase__      :     str      )				->					List[str]:
								'''simple docstring'''







								UpperCAmelCase         =     [[x] for x in self.polyA] if which == "A" else [[x] for x in self.polyB]
								# Corner case
								if len(UpperCamelCase__      ) <= 1:
														return dft[0]
								#
								UpperCAmelCase         =     self.c_max_length // 2
								while next_ncol > 0:
														UpperCAmelCase         =     [[] for i in range(UpperCamelCase__      )]
														UpperCAmelCase         =     self.root**next_ncol

														# First half of next step
														UpperCAmelCase         =     1
														for j in range(self.c_max_length // (next_ncol * 2)      ):
																				for i in range(UpperCamelCase__      ):
																										new_dft[i].append(dft[i][j] + current_root * dft[i + next_ncol][j]      )
																				current_root *= root
														# Second half of next step
														UpperCAmelCase         =     1
														for j in range(self.c_max_length // (next_ncol * 2)      ):
																				for i in range(UpperCamelCase__      ):
																										new_dft[i].append(dft[i][j] - current_root * dft[i + next_ncol][j]      )
																				current_root *= root
														# Update
														UpperCAmelCase         =     new_dft
														UpperCAmelCase         =     next_ncol // 2
								return dft[0]






		def SCREAMING_SNAKE_CASE_			(						self      :     Any      )				->					Union[str, Any]:
								'''simple docstring'''







								UpperCAmelCase         =     self.__dft("A"      )
								UpperCAmelCase         =     self.__dft("B"      )
								UpperCAmelCase         =     [[dft_a[i] * dft_b[i] for i in range(self.c_max_length      )]]
								del dft_a
								del dft_b

								# Corner Case
								if len(inverce_c[0]      ) <= 1:
														return inverce_c[0]
								# Inverse DFT
								UpperCAmelCase         =     2
								while next_ncol <= self.c_max_length:
														UpperCAmelCase         =     [[] for i in range(UpperCamelCase__      )]
														UpperCAmelCase         =     self.root ** (next_ncol // 2)
														UpperCAmelCase         =     1
														# First half of next step
														for j in range(self.c_max_length // next_ncol      ):
																				for i in range(next_ncol // 2      ):
																										# Even positions
																										new_inverse_c[i].append(
																										    (
																										        inverce_c[i][j]
																										        + inverce_c[i][j + self.c_max_length // next_ncol]
																										    )
																										    / 2      )
																										# Odd positions
																										new_inverse_c[i + next_ncol // 2].append(
																										    (
																										        inverce_c[i][j]
																										        - inverce_c[i][j + self.c_max_length // next_ncol]
																										    )
																										    / (2 * current_root)      )
																				current_root *= root
														# Update
														UpperCAmelCase         =     new_inverse_c
														next_ncol *= 2
								# Unpack
								UpperCAmelCase         =     [round(x[0].real				,		8      ) + round(x[0].imag				,		8      ) * 1j for x in inverce_c]

								# Remove leading 0's
								while inverce_c[-1] == 0:
														inverce_c.pop()
								return inverce_c







		def __str__(						self      :     Optional[int]      )				->					Any:
								'''simple docstring'''







								UpperCAmelCase         =     "A = " + " + ".join(
								    F'{coef}*x^{i}' for coef, i in enumerate(self.polyA[: self.len_A]      )      )
								UpperCAmelCase         =     "B = " + " + ".join(
								    F'{coef}*x^{i}' for coef, i in enumerate(self.polyB[: self.len_B]      )      )
								UpperCAmelCase         =     "A*B = " + " + ".join(
								    F'{coef}*x^{i}' for coef, i in enumerate(self.product      )      )

								return F'{a}\n{b}\n{c}'


# Unit tests
if __name__ == "__main__":
		import doctest

		doctest.testmod()








from argparse import ArgumentParser

from .env import EnvironmentCommand

def    lowerCamelCase_() ->       Any:
						UpperCAmelCase         =     ArgumentParser("Diffusers CLI tool"    ,   usage="diffusers-cli <command> [<args>]"    )
						UpperCAmelCase         =     parser.add_subparsers(help="diffusers-cli command helpers"    )

						# Register commands
						EnvironmentCommand.register_subcommand(lowerCamelCase_    )

						# Let's go
						UpperCAmelCase         =     parser.parse_args()

						if not hasattr(lowerCamelCase_    ,   "func"    ):
												parser.print_help()
												exit(1    )

						# Run
						UpperCAmelCase         =     args.func(lowerCamelCase_    )
						service.run()


if __name__ == "__main__":
		main()



