



def     a(      A       :    Optional[int]       )		->       List[Any]:
					"""simple docstring"""





					if p < 2:
										raise ValueError("p should not be less than 2!"       )
					elif p == 2:
										return True

					a					     =   4
					a					     =   (1 << p) - 1
					for _ in range(p - 2       ):
										a					     =   ((s * s) - 2) % m
					return s == 0


if __name__ == "__main__":
				print(lucas_lehmer_test(7))
				print(lucas_lehmer_test(11))








from typing import Dict

import numpy as np
import torch

from . import residue_constants as rc
from .tensor_utils import tensor_tree_map, tree_map






def   a			(						lowerCamelCase_				):






				'''simple docstring'''
				lowercase__    =			[]
				lowercase__    =			[]
				lowercase__    =			[]

				for rt in rc.restypes:
								lowercase__    =			rc.restype_name_to_atomaa_names[rc.restype_atoa[rt]]
								restype_atomaa_to_atomaa_list.append([(rc.atom_order[name] if name else 0) for name in atom_names]				)
								lowercase__    =			{name: i for i, name in enumerate(lowerCamelCase_				)}
								restype_atomaa_to_atomaa_list.append(
								    [(atom_name_to_idxaa[name] if name in atom_name_to_idxaa else 0) for name in rc.atom_types]				)

								restype_atomaa_mask_list.append([(1.0 if name else 0.0) for name in atom_names]				)

				# Add dummy mapping for restype 'UNK'
				restype_atomaa_to_atomaa_list.append([0] * 14				)
				restype_atomaa_to_atomaa_list.append([0] * 37				)
				restype_atomaa_mask_list.append([0.0] * 14				)

				lowercase__    =			torch.tensor(
				    lowerCamelCase_		,   dtype=torch.intaa		,   device=protein['''aatype'''].device		,   )
				lowercase__    =			torch.tensor(
				    lowerCamelCase_		,   dtype=torch.intaa		,   device=protein['''aatype'''].device		,   )
				lowercase__    =			torch.tensor(
				    lowerCamelCase_		,   dtype=torch.floataa		,   device=protein['''aatype'''].device		,   )
				lowercase__    =			protein['''aatype'''].to(torch.long				)

				# create the mapping for (residx, atom14) --> atom37, i.e. an array
				# with shape (num_res, 14) containing the atom37 indices for this protein
				lowercase__    =			restype_atomaa_to_atomaa[protein_aatype]
				lowercase__    =			restype_atomaa_mask[protein_aatype]

				lowercase__    =			residx_atomaa_mask
				lowercase__    =			residx_atomaa_to_atomaa.long()

				# create the gather indices for mapping back
				lowercase__    =			restype_atomaa_to_atomaa[protein_aatype]
				lowercase__    =			residx_atomaa_to_atomaa.long()

				# create the corresponding mask
				lowercase__    =			torch.zeros([21, 37]		,   dtype=torch.floataa		,   device=protein['''aatype'''].device				)
				for restype, restype_letter in enumerate(rc.restypes				):
								lowercase__    =			rc.restype_atoa[restype_letter]
								lowercase__    =			rc.residue_atoms[restype_name]
								for atom_name in atom_names:
												lowercase__    =			rc.atom_order[atom_name]
												lowercase__    =			1

				lowercase__    =			restype_atomaa_mask[protein_aatype]
				lowercase__    =			residx_atomaa_mask

				return protein






def   a			(						lowerCamelCase_				):






				'''simple docstring'''
				lowercase__    =			tree_map(lambda lowerCamelCase_				: torch.tensor(lowerCamelCase_		,   device=batch['''aatype'''].device				)		,   lowerCamelCase_		,   np.ndarray				)
				lowercase__    =			tensor_tree_map(lambda lowerCamelCase_				: np.array(lowerCamelCase_				)		,   make_atomaa_masks(lowerCamelCase_				)				)
				return out




