






'''simple docstring'''







import mpmath  # for roots of unity
import numpy as np




class 		UpperCamelCase__     :




		'''simple docstring'''





		def __init__(   self ,_lowerCAmelCase=None ,_lowerCAmelCase=None							):
								# Input as list
								lowerCamelCase__								=	list(poly_a or [0]							)[:]
								lowerCamelCase__								=	list(poly_b or [0]							)[:]

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

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

								# Add 0 to make lengths equal a power of 2
								lowerCamelCase__								=	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
								lowerCamelCase__								=	complex(mpmath.root(x=1 ,n=self.c_max_length ,k=1							)							)

								# The product
								lowerCamelCase__								=	self.__multiply()






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

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






		def       UpperCamelCase_       (   self							):
								lowerCamelCase__								=	self.__dft("""A"""							)
								lowerCamelCase__								=	self.__dft("""B"""							)
								lowerCamelCase__								=	[[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
								lowerCamelCase__								=	2
								while next_ncol <= self.c_max_length:
														lowerCamelCase__								=	[[] for i in range(__a							)]
														lowerCamelCase__								=	self.root ** (next_ncol // 2)
														lowerCamelCase__								=	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
														lowerCamelCase__								=	new_inverse_c
														next_ncol *= 2
								# Unpack
								lowerCamelCase__								=	[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							):
								lowerCamelCase__								=	"""A = """ + """ + """.join(
								    F'''{coef}*x^{i}''' for coef, i in enumerate(self.polyA[: self.len_A]							)							)
								lowerCamelCase__								=	"""B = """ + """ + """.join(
								    F'''{coef}*x^{i}''' for coef, i in enumerate(self.polyB[: self.len_B]							)							)
								lowerCamelCase__								=	"""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 __future__ import annotations

from collections import namedtuple


def    __lowerCamelCase   (      A__						: float						,						A__						: float						,						A__						: float					)     ->    tuple:
   lowerCamelCase_						:   Dict		= namedtuple("""result"""						,						"""name value"""					)
   if (voltage, current, power).count(0					) != 1:
      raise ValueError("""Only one argument must be 0"""					)
   elif power < 0:
      raise ValueError(
          """Power cannot be negative in any electrical/electronics system"""					)
   elif voltage == 0:
      return result("""voltage"""						,						power / current					)
   elif current == 0:
      return result("""current"""						,						power / voltage					)
   elif power == 0:
      return result("""power"""						,						float(round(abs(voltage * current					)						,						2					)					)					)
   else:
      raise ValueError("""Exactly one argument must be 0"""					)


if __name__ == "__main__":
      import doctest

      doctest.testmod()





