


from math import factorial
class 						lowerCamelCase_							:



					'''simple docstring'''







					def __init__(					self			,							snake_case_			,							snake_case_    ) ->      List[Any]:







								'''simple docstring'''

								__lowercase			       = real
								if isinstance(__snake_case			,							__snake_case    ):
											__lowercase			       = [1] * rank
								else:
											__lowercase			       = rank






					def __repr__(					self    ) ->      List[str]:







								'''simple docstring'''

								return (
								    F'{self.real}+'
								    F'{"+".join(str(__snake_case    )+"E"+str(n+1    )for n,dual in enumerate(self.duals    )    )}'
								)






					def A   (					self    ) ->      Optional[Any]:







								'''simple docstring'''

								__lowercase			       = self.duals.copy()
								while cur[-1] == 0:
											cur.pop(-1    )
								return Dual(self.real			,							__snake_case    )






					def __add__(					self			,							snake_case_    ) ->      Any:







								'''simple docstring'''

								if not isinstance(__snake_case			,							__snake_case    ):
											return Dual(self.real + other			,							self.duals    )
								__lowercase			       = self.duals.copy()
								__lowercase			       = other.duals.copy()
								if len(__snake_case    ) > len(__snake_case    ):
											o_dual.extend([1] * (len(__snake_case    ) - len(__snake_case    ))    )
								elif len(__snake_case    ) < len(__snake_case    ):
											s_dual.extend([1] * (len(__snake_case    ) - len(__snake_case    ))    )
								__lowercase			       = []
								for i in range(len(__snake_case    )    ):
											new_duals.append(s_dual[i] + o_dual[i]    )
								return Dual(self.real + other.real			,							__snake_case    )

					__UpperCAmelCase							  =					__add__






					def __sub__(					self			,							snake_case_    ) ->      str:







								'''simple docstring'''

								return self + other * -1






					def __mul__(					self			,							snake_case_    ) ->      Dict:







								'''simple docstring'''

								if not isinstance(__snake_case			,							__snake_case    ):
											__lowercase			       = []
											for i in self.duals:
														new_duals.append(i * other    )
											return Dual(self.real * other			,							__snake_case    )
								__lowercase			       = [0] * (len(self.duals    ) + len(other.duals    ) + 1)
								for i, item in enumerate(self.duals    ):
											for j, jtem in enumerate(other.duals    ):
														new_duals[i + j + 1] += item * jtem
								for k in range(len(self.duals    )    ):
											new_duals[k] += self.duals[k] * other.real
								for index in range(len(other.duals    )    ):
											new_duals[index] += other.duals[index] * self.real
								return Dual(self.real * other.real			,							__snake_case    )

					__UpperCAmelCase							  =					__mul__






					def __truediv__(					self			,							snake_case_    ) ->      Dict:







								'''simple docstring'''

								if not isinstance(__snake_case			,							__snake_case    ):
											__lowercase			       = []
											for i in self.duals:
														new_duals.append(i / other    )
											return Dual(self.real / other			,							__snake_case    )
								raise ValueError






					def __floordiv__(					self			,							snake_case_    ) ->      Optional[Any]:







								'''simple docstring'''

								if not isinstance(__snake_case			,							__snake_case    ):
											__lowercase			       = []
											for i in self.duals:
														new_duals.append(i // other    )
											return Dual(self.real // other			,							__snake_case    )
								raise ValueError






					def __pow__(					self			,							snake_case_    ) ->      List[str]:







								'''simple docstring'''

								if n < 0 or isinstance(__snake_case			,							__snake_case    ):
											raise ValueError('''power must be a positive integer'''    )
								if n == 0:
											return 1
								if n == 1:
											return self
								__lowercase			       = self
								for _ in range(n - 1    ):
											x *= self
								return x




def 		lowercase_	(  _UpperCamelCase							,      _UpperCamelCase							,      _UpperCamelCase	):


			'''simple docstring'''







			if not callable(__UpperCAmelCase	):
						raise ValueError('''differentiate() requires a function as input for func'''	)
			if not isinstance(__UpperCAmelCase							,      (float, int)	):
						raise ValueError('''differentiate() requires a float as input for position'''	)
			if not isinstance(__UpperCAmelCase							,      __UpperCAmelCase	):
						raise ValueError('''differentiate() requires an int as input for order'''	)
			__lowercase			       = Dual(__UpperCAmelCase							,      1	)
			__lowercase			       = func(__UpperCAmelCase	)
			if order == 0:
						return result.real
			return result.duals[order - 1] * factorial(__UpperCAmelCase	)


if __name__ == "__main__":
	import doctest

	doctest.testmod()


	def 		lowercase_	(  _UpperCamelCase	):


				'''simple docstring'''







				return y**2 * y**4





	print(differentiate(f, 9, 2))










"""simple docstring"""





import json
import os
import unittest

from transformers import OpenAIGPTTokenizer, OpenAIGPTTokenizerFast
from transformers.models.openai.tokenization_openai import VOCAB_FILES_NAMES
from transformers.testing_utils import require_ftfy, require_spacy, require_tokenizers

from ...test_tokenization_common import TokenizerTesterMixin



@require_tokenizers
class       __A		(   SCREAMING_SNAKE_CASE_     ,unittest.TestCase			):
					UpperCAmelCase__								=				OpenAIGPTTokenizer
					UpperCAmelCase__								=				OpenAIGPTTokenizerFast
					UpperCAmelCase__								=				True
					UpperCAmelCase__								=				False

					def   lowerCamelCase__   (			self  :      Dict					)			->							Optional[Any]:
											super().setUp()

											# Adapted from Sennrich et al. 2015 and https://github.com/rsennrich/subword-nmt
											__magic_name__:	str							=       [
											    """l""",
											    """o""",
											    """w""",
											    """e""",
											    """r""",
											    """s""",
											    """t""",
											    """i""",
											    """d""",
											    """n""",
											    """w</w>""",
											    """r</w>""",
											    """t</w>""",
											    """lo""",
											    """low""",
											    """er</w>""",
											    """low</w>""",
											    """lowest</w>""",
											    """newer</w>""",
											    """wider</w>""",
											    """<unk>""",
											]
											__magic_name__:	Any							=       dict(zip(__snake_case     ,		range(len(__snake_case					)					)					)					)
											__magic_name__:	List[str]							=       ["""#version: 0.2""", """l o""", """lo w""", """e r</w>""", """"""]

											__magic_name__:	Optional[Any]							=       os.path.join(self.tmpdirname     ,		VOCAB_FILES_NAMES["""vocab_file"""]					)
											__magic_name__:	Any							=       os.path.join(self.tmpdirname     ,		VOCAB_FILES_NAMES["""merges_file"""]					)
											with open(self.vocab_file     ,		"""w"""					) as fp:
																	fp.write(json.dumps(__snake_case					)					)
											with open(self.merges_file     ,		"""w"""					) as fp:
																	fp.write("""\n""".join(__snake_case					)					)

					def   lowerCamelCase__   (			self  :      List[Any]     ,		__snake_case  :      Optional[Any]					)			->							Optional[int]:
											return "lower newer", "lower newer"

					def   lowerCamelCase__   (			self  :      List[Any]					)			->							Union[str, Any]:
											__magic_name__:	Optional[Any]							=       OpenAIGPTTokenizer(self.vocab_file     ,		self.merges_file					)

											__magic_name__:	Union[str, Any]							=       """lower"""
											__magic_name__:	Optional[int]							=       ["""low""", """er</w>"""]
											__magic_name__:	List[Any]							=       tokenizer.tokenize(__snake_case					)
											self.assertListEqual(__snake_case     ,		__snake_case					)

											__magic_name__:	Optional[int]							=       tokens + ["""<unk>"""]
											__magic_name__:	List[str]							=       [1_4, 1_5, 2_0]
											self.assertListEqual(tokenizer.convert_tokens_to_ids(__snake_case					)     ,		__snake_case					)

					def   lowerCamelCase__   (			self  :      Optional[Any]     ,		__snake_case  :      Any=1_5					)			->							Tuple:
											for tokenizer, pretrained_name, kwargs in self.tokenizers_list:
																	with self.subTest(F'{tokenizer.__class__.__name__} ({pretrained_name})'					):
																							__magic_name__:	str							=       self.rust_tokenizer_class.from_pretrained(__snake_case     ,		**__snake_case					)

																							# Simple input
																							__magic_name__:	Dict							=       """This is a simple input"""
																							__magic_name__:	Any							=       ["""This is a simple input 1""", """This is a simple input 2"""]
																							__magic_name__:	int							=       ("""This is a simple input""", """This is a pair""")
																							__magic_name__:	int							=       [
																							    ("""This is a simple input 1""", """This is a simple input 2"""),
																							    ("""This is a simple pair 1""", """This is a simple pair 2"""),
																							]

																							# Simple input tests
																							self.assertRaises(__snake_case     ,		tokenizer_r.encode     ,		__snake_case     ,		max_length=__snake_case     ,		padding="""max_length"""					)

																							# Simple input
																							self.assertRaises(__snake_case     ,		tokenizer_r.encode_plus     ,		__snake_case     ,		max_length=__snake_case     ,		padding="""max_length"""					)

																							# Simple input
																							self.assertRaises(
																							    __snake_case     ,		tokenizer_r.batch_encode_plus     ,		__snake_case     ,		max_length=__snake_case     ,		padding="""max_length"""     ,		)

																							# Pair input
																							self.assertRaises(__snake_case     ,		tokenizer_r.encode     ,		__snake_case     ,		max_length=__snake_case     ,		padding="""max_length"""					)

																							# Pair input
																							self.assertRaises(__snake_case     ,		tokenizer_r.encode_plus     ,		__snake_case     ,		max_length=__snake_case     ,		padding="""max_length"""					)

																							# Pair input
																							self.assertRaises(
																							    __snake_case     ,		tokenizer_r.batch_encode_plus     ,		__snake_case     ,		max_length=__snake_case     ,		padding="""max_length"""     ,		)






					def   lowerCamelCase__   (			self  :      Dict					)			->							Any:
											pass



@require_ftfy
@require_spacy
@require_tokenizers
class       __A		(   SCREAMING_SNAKE_CASE_			):
					pass



