
from math import factorial





class 				UpperCAmelCase :




	'''simple docstring'''





	def __init__(			self   :					List[str]				,A   :					Optional[int]				,A   :					int					):
					__A       =					real
					if isinstance(A				,A					):
									__A       =					[1] * rank
					else:
									__A       =					rank






	def __repr__(			self   :					Tuple					):
					return (
					    f'''{self.real}+'''
					    f'''{'+'.join(str(A					)+'E'+str(n+1					)for n,dual in enumerate(self.duals					)					)}'''
					)






	def 							UpperCamelCase_    (			self   :					List[Any]					):
					__A       =					self.duals.copy()
					while cur[-1] == 0:
									cur.pop(-1					)
					return Dual(self.real				,A					)






	def __add__(			self   :					Optional[Any]				,A   :					List[Any]					):
					if not isinstance(A				,A					):
									return Dual(self.real + other				,self.duals					)
					__A       =					self.duals.copy()
					__A       =					other.duals.copy()
					if len(A					) > len(A					):
									o_dual.extend([1] * (len(A					) - len(A					))					)
					elif len(A					) < len(A					):
									s_dual.extend([1] * (len(A					) - len(A					))					)
					__A       =					[]
					for i in range(len(A					)					):
									new_duals.append(s_dual[i] + o_dual[i]					)
					return Dual(self.real + other.real				,A					)

	snake_case_          =	__add__






	def __sub__(			self   :					int				,A   :					Dict					):
					return self + other * -1






	def __mul__(			self   :					List[Any]				,A   :					List[str]					):
					if not isinstance(A				,A					):
									__A       =					[]
									for i in self.duals:
													new_duals.append(i * other					)
									return Dual(self.real * other				,A					)
					__A       =					[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				,A					)

	snake_case_          =	__mul__






	def __truediv__(			self   :					Tuple				,A   :					Dict					):
					if not isinstance(A				,A					):
									__A       =					[]
									for i in self.duals:
													new_duals.append(i / other					)
									return Dual(self.real / other				,A					)
					raise ValueError






	def __floordiv__(			self   :					List[str]				,A   :					Tuple					):
					if not isinstance(A				,A					):
									__A       =					[]
									for i in self.duals:
													new_duals.append(i // other					)
									return Dual(self.real // other				,A					)
					raise ValueError







	def __pow__(			self   :					Optional[Any]				,A   :					List[str]					):
					if n < 0 or isinstance(A				,A					):
									raise ValueError("power must be a positive integer"					)
					if n == 0:
									return 1
					if n == 1:
									return self
					__A       =					self
					for _ in range(n - 1					):
									x *= self
					return x





def 		UpperCAmelCase     (      a_						,  a_						,  a_		)						->      List[str]:







				"""simple docstring"""



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


if __name__ == "__main__":
					import doctest

					doctest.testmod()


					def 		UpperCAmelCase     (      a_		)						->      Dict:







									"""simple docstring"""



									return y**2 * y**4
					print(differentiate(f, 9, 2))






from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_tokenizers_available, is_torch_available


SCREAMING_SNAKE_CASE__     :     str		    =       {
    "configuration_altclip": [
        "ALTCLIP_PRETRAINED_CONFIG_ARCHIVE_MAP",
        "AltCLIPConfig",
        "AltCLIPTextConfig",
        "AltCLIPVisionConfig",
    ],
    "processing_altclip": ["AltCLIPProcessor"],
}

try:
				if not is_torch_available():
								raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
				pass
else:
				SCREAMING_SNAKE_CASE__     :     Any		    =       [
				    "ALTCLIP_PRETRAINED_MODEL_ARCHIVE_LIST",
				    "AltCLIPPreTrainedModel",
				    "AltCLIPModel",
				    "AltCLIPTextModel",
				    "AltCLIPVisionModel",
				]


if TYPE_CHECKING:
				from .configuration_altclip import (
				    ALTCLIP_PRETRAINED_CONFIG_ARCHIVE_MAP,
				    AltCLIPConfig,
				    AltCLIPTextConfig,
				    AltCLIPVisionConfig,
				)
				from .processing_altclip import AltCLIPProcessor

				try:
								if not is_torch_available():
												raise OptionalDependencyNotAvailable()
				except OptionalDependencyNotAvailable:
								pass
				else:
								from .modeling_altclip import (
								    ALTCLIP_PRETRAINED_MODEL_ARCHIVE_LIST,
								    AltCLIPModel,
								    AltCLIPPreTrainedModel,
								    AltCLIPTextModel,
								    AltCLIPVisionModel,
								)


else:
				import sys

				SCREAMING_SNAKE_CASE__     :     Tuple		    =       _LazyModule(__name__, globals()["__file__"], _import_structure, module_spec=__spec__)
