





"""simple docstring"""
def    A__							(     UpperCamelCase			):
							if len(a_			) == 0 or not all(len(a_			) == 2 for pair in coordinates			):
														raise ValueError("The program cannot work out a fitting polynomial."			)

							if len({tuple(a_			) for pair in coordinates}			) != len(a_			):
														raise ValueError("The program cannot work out a fitting polynomial."			)

							A						=    {x for x, _ in coordinates}
							if len(a_			) == 1:
														return F"x={coordinates[0][0]}"

							if len(a_			) != len(a_			):
														raise ValueError("The program cannot work out a fitting polynomial."			)

							A						=    len(a_			)

							A						=    0
							A						=    []
							# put the x and x to the power values in a matrix
							while count_of_line < x:
														A						=    0
														A						=    coordinates[count_of_line][0]
														A						=    []
														while count_in_line < x:
																					count_line.append(a ** (x - (count_in_line + 1))			)
																					count_in_line += 1
														matrix.append(a_			)
														count_of_line += 1

							A						=    0
							# put the y values into a vector
							A						=    []
							while count_of_line < x:
														vector.append(coordinates[count_of_line][1]			)
														count_of_line += 1

							A						=    0

							while count < x:
														A						=    0
														while zahlen < x:
																					if count == zahlen:
																												zahlen += 1
																					if zahlen == x:
																												break
																					A						=    matrix[zahlen][count] / matrix[count][count]
																					for counting_columns, item in enumerate(matrix[count]			):
																												# manipulating all the values in the matrix
																												matrix[zahlen][counting_columns] -= item * bruch
																					# manipulating the values in the vector
																					vector[zahlen] -= vector[count] * bruch
																					zahlen += 1
														count += 1

							A						=    0
							# make solutions
							A						=    []
							while count < x:
														solution.append(str(vector[count] / matrix[count][count]			)			)
														count += 1

							A						=    0
							A						=    '''f(x)='''

							while count < x:
														A						=    solution[count].split("E"			)
														if len(a_			) > 1:
																					A						=    F"{remove_e[0]}*10^{remove_e[1]}"
														solved += F"x^{x - (count + 1)}*{solution[count]}"
														if count + 1 != x:
																					solved += "+"
														count += 1

							return solved


if __name__ == "__main__":
		print(points_to_polynomial([]))
		print(points_to_polynomial([[]]))
		print(points_to_polynomial([[1, 0], [2, 0], [3, 0]]))
		print(points_to_polynomial([[1, 1], [2, 1], [3, 1]]))
		print(points_to_polynomial([[1, 3], [2, 3], [3, 3]]))
		print(points_to_polynomial([[1, 1], [2, 2], [3, 3]]))
		print(points_to_polynomial([[1, 1], [2, 4], [3, 9]]))
		print(points_to_polynomial([[1, 3], [2, 6], [3, 11]]))
		print(points_to_polynomial([[1, -3], [2, -6], [3, -11]]))
		print(points_to_polynomial([[1, 5], [2, 2], [3, 9]]))










'''simple docstring'''







from ctypes import c_float, sizeof
from enum import Enum
from typing import TYPE_CHECKING, Optional, Union


if TYPE_CHECKING:
  from .. import AutoFeatureExtractor, AutoProcessor, AutoTokenizer  # tests_ignore




class 					__UpperCAmelCase (		UpperCamelCase__	):

      '''simple docstring'''





      SCREAMING_SNAKE_CASE				:    Dict				       =					c_float




      @property
      def 							lowerCamelCase     (					self						):
             return sizeof(self.value						)






def  lowerCAmelCase__		(					a_  :     int			,						a_  :     int			,						a_  :     int = 0			)   -> int:
       # < 0 is possible if using a dynamic axis
       if dimension <= 0:
              UpperCAmelCase__	:   List[Any]												=	fixed_dimension

       dimension -= num_token_to_add
       return dimension






def  lowerCAmelCase__		(					a_  :     int			,						a_  :     ParameterFormat			)   -> int:
       return num_parameters * dtype.size






def  lowerCAmelCase__		(					a_  :     str			)   -> Optional[Union["AutoTokenizer", "AutoFeatureExtractor", "AutoProcessor"]]:
       from .. import AutoFeatureExtractor, AutoProcessor, AutoTokenizer  # tests_ignore

       try:
              return AutoProcessor.from_pretrained(a_			)
       except (ValueError, OSError, KeyError):
              UpperCAmelCase__							,							UpperCAmelCase__	:   Dict												=	None, None
              try:
                     UpperCAmelCase__	:   Union[str, Any]												=	AutoTokenizer.from_pretrained(a_			)
              except (OSError, KeyError):
                     pass
              try:
                     UpperCAmelCase__	:   List[str]												=	AutoFeatureExtractor.from_pretrained(a_			)
              except (OSError, KeyError):
                     pass

              if tokenizer is not None and feature_extractor is not None:
                     raise ValueError(
                         f"""Couldn't auto-detect preprocessor for {model_name}. Found both a tokenizer and a feature extractor."""			)
              elif tokenizer is None and feature_extractor is None:
                     return None
              elif tokenizer is not None:
                     return tokenizer
              else:
                     return feature_extractor