


def  __SCREAMING_SNAKE_CASE       (				lowercase__  :list[list[int]]				)       ->  str:
						if len(lowercase__				) == 0 or not all(len(lowercase__				) == 2 for pair in coordinates				):
												raise ValueError('The program cannot work out a fitting polynomial.'				)

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

						__magic_name__				:							Optional[int]				=      {x for x, _ in coordinates}
						if len(lowercase__				) == 1:
												return f"x={coordinates[0][0]}"

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

						__magic_name__				:							List[str]				=      len(lowercase__				)

						__magic_name__				:							Optional[int]				=      0
						__magic_name__				:							list[list[float]]				=      []
						# put the x and x to the power values in a matrix
						while count_of_line < x:
												__magic_name__				:							List[str]				=      0
												__magic_name__				:							Tuple				=      coordinates[count_of_line][0]
												__magic_name__				:							list[float]				=      []
												while count_in_line < x:
																		count_line.append(a ** (x - (count_in_line + 1))				)
																		count_in_line += 1
												matrix.append(lowercase__				)
												count_of_line += 1

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

						__magic_name__				:							List[Any]				=      0

						while count < x:
												__magic_name__				:							Tuple				=      0
												while zahlen < x:
																		if count == zahlen:
																								zahlen += 1
																		if zahlen == x:
																								break
																		__magic_name__				:							List[str]				=      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

						__magic_name__				:							Union[str, Any]				=      0
						# make solutions
						__magic_name__				:							list[str]				=      []
						while count < x:
												solution.append(str(vector[count] / matrix[count][count]				)				)
												count += 1

						__magic_name__				:							Tuple				=      0
						__magic_name__				:							Tuple				=      'f(x)='

						while count < x:
												__magic_name__				:							list[str]				=      solution[count].split('E'				)
												if len(lowercase__				) > 1:
																		__magic_name__				:							int				=      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]]))






# Copyright 2023 The HuggingFace Inc. team. All rights reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
import ast
import difflib
from collections.abc import Mapping
from typing import Any, Callable, Dict



class     snake_case__  (      _A  ):
				pass






def  __SCREAMING_SNAKE_CASE       (				lowercase__  :str      ,						lowercase__  :Dict[str, Callable]      ,						lowercase__  :Union[str, Any]=None      ,						lowercase__  :str=False				)       ->  List[str]:
						try:
												__magic_name__				:							str				=      ast.parse(lowercase__				)
						except SyntaxError as e:
												print('The code generated by the agent is not valid.\n'      ,						lowercase__				)
												return
						if state is None:
												__magic_name__				:							Optional[Any]				=      {}
						__magic_name__				:							Dict				=      None
						for idx, node in enumerate(expression.body				):
												try:
																		__magic_name__				:							Any				=      evaluate_ast(lowercase__      ,						lowercase__      ,						lowercase__				)
												except InterpretorError as e:
																		__magic_name__				:							Tuple				=      f"Evaluation of the code stopped at line {idx} before the end because of the following error"
																		if chat_mode:
																								msg += (
																								    f". Copy paste the following error message and send it back to the agent:\nI get an error: '{e}'"
																								)
																		else:
																								msg += f":\n{e}"
																		print(lowercase__				)
																		break
												if line_result is not None:
																		__magic_name__				:							List[str]				=      line_result

						return result
def  __SCREAMING_SNAKE_CASE       (				lowercase__  :ast.AST      ,						lowercase__  :Dict[str, Any]      ,						lowercase__  :Dict[str, Callable]				)       ->  Dict:
						if isinstance(lowercase__      ,						ast.Assign				):
												# Assignement -> we evaluate the assignement which should update the state
												# We return the variable assigned as it may be used to determine the final result.
												return evaluate_assign(lowercase__      ,						lowercase__      ,						lowercase__				)
						elif isinstance(lowercase__      ,						ast.Call				):
												# Function call -> we return the value of the function call
												return evaluate_call(lowercase__      ,						lowercase__      ,						lowercase__				)
						elif isinstance(lowercase__      ,						ast.Constant				):
												# Constant -> just return the value
												return expression.value
						elif isinstance(lowercase__      ,						ast.Dict				):
												# Dict -> evaluate all keys and values
												__magic_name__				:							Any				=      [evaluate_ast(lowercase__      ,						lowercase__      ,						lowercase__				) for k in expression.keys]
												__magic_name__				:							Dict				=      [evaluate_ast(lowercase__      ,						lowercase__      ,						lowercase__				) for v in expression.values]
												return dict(zip(lowercase__      ,						lowercase__				)				)
						elif isinstance(lowercase__      ,						ast.Expr				):
												# Expression -> evaluate the content
												return evaluate_ast(expression.value      ,						lowercase__      ,						lowercase__				)
						elif isinstance(lowercase__      ,						ast.For				):
												# For loop -> execute the loop
												return evaluate_for(lowercase__      ,						lowercase__      ,						lowercase__				)
						elif isinstance(lowercase__      ,						ast.FormattedValue				):
												# Formatted value (part of f-string) -> evaluate the content and return
												return evaluate_ast(expression.value      ,						lowercase__      ,						lowercase__				)
						elif isinstance(lowercase__      ,						ast.If				):
												# If -> execute the right branch
												return evaluate_if(lowercase__      ,						lowercase__      ,						lowercase__				)
						elif hasattr(lowercase__      ,						'Index'				) and isinstance(lowercase__      ,						ast.Index				):
												return evaluate_ast(expression.value      ,						lowercase__      ,						lowercase__				)
						elif isinstance(lowercase__      ,						ast.JoinedStr				):
												return "".join([str(evaluate_ast(lowercase__      ,						lowercase__      ,						lowercase__				)				) for v in expression.values]				)
						elif isinstance(lowercase__      ,						ast.List				):
												# List -> evaluate all elements
												return [evaluate_ast(lowercase__      ,						lowercase__      ,						lowercase__				) for elt in expression.elts]
						elif isinstance(lowercase__      ,						ast.Name				):
												# Name -> pick up the value in the state
												return evaluate_name(lowercase__      ,						lowercase__      ,						lowercase__				)
						elif isinstance(lowercase__      ,						ast.Subscript				):
												# Subscript -> return the value of the indexing
												return evaluate_subscript(lowercase__      ,						lowercase__      ,						lowercase__				)
						else:
												# For now we refuse anything else. Let's add things as we need them.
												raise InterpretorError(f"{expression.__class__.__name__} is not supported."				)
def  __SCREAMING_SNAKE_CASE       (				lowercase__  :List[Any]      ,						lowercase__  :Optional[Any]      ,						lowercase__  :Union[str, Any]				)       ->  List[Any]:
						__magic_name__				:							Union[str, Any]				=      assign.targets
						__magic_name__				:							int				=      evaluate_ast(assign.value      ,						lowercase__      ,						lowercase__				)

						if len(lowercase__				) == 1:
												__magic_name__				:							Any				=      result
						else:
												if len(lowercase__				) != len(lowercase__				):
																		raise InterpretorError(f"Expected {len(lowercase__				)} values but got {len(lowercase__				)}."				)
												for var_name, r in zip(lowercase__      ,						lowercase__				):
																		__magic_name__				:							str				=      r
						return result
def  __SCREAMING_SNAKE_CASE       (				lowercase__  :List[str]      ,						lowercase__  :List[str]      ,						lowercase__  :Tuple				)       ->  Optional[Any]:
						if not isinstance(call.func      ,						ast.Name				):
												raise InterpretorError(
												    f"It is not permitted to evaluate other functions than the provided tools (tried to execute {call.func} of "
												    f"type {type(call.func				)}."				)
						__magic_name__				:							Dict				=      call.func.id
						if func_name not in tools:
												raise InterpretorError(
												    f"It is not permitted to evaluate other functions than the provided tools (tried to execute {call.func.id})."				)

						__magic_name__				:							Tuple				=      tools[func_name]
						# Todo deal with args
						__magic_name__				:							List[str]				=      [evaluate_ast(lowercase__      ,						lowercase__      ,						lowercase__				) for arg in call.args]
						__magic_name__				:							int				=      {keyword.arg: evaluate_ast(keyword.value      ,						lowercase__      ,						lowercase__				) for keyword in call.keywords}
						return func(*lowercase__      ,						**lowercase__				)
def  __SCREAMING_SNAKE_CASE       (				lowercase__  :Union[str, Any]      ,						lowercase__  :int      ,						lowercase__  :int				)       ->  List[Any]:
						__magic_name__				:							Optional[int]				=      evaluate_ast(subscript.slice      ,						lowercase__      ,						lowercase__				)
						__magic_name__				:							Union[str, Any]				=      evaluate_ast(subscript.value      ,						lowercase__      ,						lowercase__				)
						if isinstance(lowercase__      ,						(list, tuple)				):
												return value[int(lowercase__				)]
						if index in value:
												return value[index]
						if isinstance(lowercase__      ,						lowercase__				) and isinstance(lowercase__      ,						lowercase__				):
												__magic_name__				:							Any				=      difflib.get_close_matches(lowercase__      ,						list(value.keys()				)				)
												if len(lowercase__				) > 0:
																		return value[close_matches[0]]

						raise InterpretorError(f"Could not index {value} with '{index}'."				)
def  __SCREAMING_SNAKE_CASE       (				lowercase__  :List[str]      ,						lowercase__  :Optional[Any]      ,						lowercase__  :Optional[int]				)       ->  int:
						if name.id in state:
												return state[name.id]
						__magic_name__				:							Union[str, Any]				=      difflib.get_close_matches(name.id      ,						list(state.keys()				)				)
						if len(lowercase__				) > 0:
												return state[close_matches[0]]
						raise InterpretorError(f"The variable `{name.id}` is not defined."				)
def  __SCREAMING_SNAKE_CASE       (				lowercase__  :Any      ,						lowercase__  :Union[str, Any]      ,						lowercase__  :Optional[Any]				)       ->  List[str]:
						if len(condition.ops				) > 1:
												raise InterpretorError('Cannot evaluate conditions with multiple operators'				)

						__magic_name__				:							int				=      evaluate_ast(condition.left      ,						lowercase__      ,						lowercase__				)
						__magic_name__				:							Optional[int]				=      condition.ops[0]
						__magic_name__				:							Union[str, Any]				=      evaluate_ast(condition.comparators[0]      ,						lowercase__      ,						lowercase__				)

						if isinstance(lowercase__      ,						ast.Eq				):
												return left == right
						elif isinstance(lowercase__      ,						ast.NotEq				):
												return left != right
						elif isinstance(lowercase__      ,						ast.Lt				):
												return left < right
						elif isinstance(lowercase__      ,						ast.LtE				):
												return left <= right
						elif isinstance(lowercase__      ,						ast.Gt				):
												return left > right
						elif isinstance(lowercase__      ,						ast.GtE				):
												return left >= right
						elif isinstance(lowercase__      ,						ast.Is				):
												return left is right
						elif isinstance(lowercase__      ,						ast.IsNot				):
												return left is not right
						elif isinstance(lowercase__      ,						ast.In				):
												return left in right
						elif isinstance(lowercase__      ,						ast.NotIn				):
												return left not in right
						else:
												raise InterpretorError(f"Operator not supported: {comparator}"				)
def  __SCREAMING_SNAKE_CASE       (				lowercase__  :Optional[int]      ,						lowercase__  :str      ,						lowercase__  :Tuple				)       ->  int:
						__magic_name__				:							Optional[int]				=      None
						if evaluate_condition(if_statement.test      ,						lowercase__      ,						lowercase__				):
												for line in if_statement.body:
																		__magic_name__				:							List[Any]				=      evaluate_ast(lowercase__      ,						lowercase__      ,						lowercase__				)
																		if line_result is not None:
																								__magic_name__				:							Tuple				=      line_result
						else:
												for line in if_statement.orelse:
																		__magic_name__				:							Optional[int]				=      evaluate_ast(lowercase__      ,						lowercase__      ,						lowercase__				)
																		if line_result is not None:
																								__magic_name__				:							List[Any]				=      line_result
						return result

def  __SCREAMING_SNAKE_CASE       (				lowercase__  :Optional[Any]      ,						lowercase__  :Union[str, Any]      ,						lowercase__  :List[str]				)       ->  Dict:
						__magic_name__				:							int				=      None
						__magic_name__				:							List[Any]				=      evaluate_ast(for_loop.iter      ,						lowercase__      ,						lowercase__				)
						for counter in iterator:
												__magic_name__				:							Tuple				=      counter
												for expression in for_loop.body:
																		__magic_name__				:							Dict				=      evaluate_ast(lowercase__      ,						lowercase__      ,						lowercase__				)
																		if line_result is not None:
																								__magic_name__				:							Dict				=      line_result
						return result


