

import warnings
from collections.abc import Callable
from typing import Any

import numpy
from matplotlib import pyplot

lowerCamelCase_    =					0.25 + 0.0j
lowerCamelCase_    =					-0.4 + 0.6j
lowerCamelCase_    =					-0.1 + 0.651j
lowerCamelCase_    =					-2.0
lowerCamelCase_    =					56
lowerCamelCase_    =					2.0
lowerCamelCase_    =					666



def    UpperCamelCase(					lowercase_			,					lowercase_							)	->				numpy.ndarray:





  '''simple docstring'''





  return numpy.exp(lowercase_							) + c_parameter



def    UpperCamelCase(					lowercase_			,					lowercase_							)	->				numpy.ndarray:





  '''simple docstring'''





  return z_values * z_values + c_parameter



def    UpperCamelCase(					lowercase_			,					lowercase_							)	->				numpy.ndarray:





  '''simple docstring'''





  snake_case_       						=      numpy.linspace(-window_size			,					lowercase_			,					lowercase_							)
  snake_case_       						=      x.reshape((nb_pixels, 1)							)
  snake_case_       						=      numpy.linspace(-window_size			,					lowercase_			,					lowercase_							)
  snake_case_       						=      y.reshape((1, nb_pixels)							)
  return x + 1.0j * y



def    UpperCamelCase(					lowercase_			,					lowercase_			,					lowercase_			,					lowercase_			,					lowercase_ = None			,					)	->				numpy.ndarray:





  '''simple docstring'''





  snake_case_       						=      z_a.astype("""complex64"""							)
  for _ in range(lowercase_							):
    snake_case_       						=      eval_function(lowercase_			,					lowercase_							)
    if infinity is not None:
      numpy.nan_to_num(lowercase_			,					copy=lowercase_			,					nan=lowercase_							)
      snake_case_       						=      infinity
  return z_n



def    UpperCamelCase(					lowercase_			,					lowercase_			,					lowercase_			,					lowercase_			,					)	->				None:





  '''simple docstring'''





  snake_case_       						=      (abs(lowercase_							)).transpose()
  snake_case_       						=      abs_z_final[::-1, :]
  pyplot.matshow(abs_z_final < escape_radius							)
  pyplot.title(f'''Julia set of ${function_label}$, $c={function_params}$'''							)
  pyplot.show()



def    UpperCamelCase(					)	->				None:





  '''simple docstring'''





  warnings.filterwarnings(
      """ignore"""			,					category=lowercase_			,					message="""overflow encountered in multiply"""							)
  warnings.filterwarnings(
      """ignore"""			,					category=lowercase_			,					message="""invalid value encountered in multiply"""			,					)
  warnings.filterwarnings(
      """ignore"""			,					category=lowercase_			,					message="""overflow encountered in absolute"""							)
  warnings.filterwarnings(
      """ignore"""			,					category=lowercase_			,					message="""overflow encountered in exp"""							)


if __name__ == "__main__":
    lowerCamelCase_    =					prepare_grid(window_size, nb_pixels)

    ignore_overflow_warnings()  # See file header for explanations

    lowerCamelCase_    =					24
    lowerCamelCase_    =					2 * abs(c_cauliflower) + 1
    lowerCamelCase_    =					iterate_function(
        eval_quadratic_polynomial,
        c_cauliflower,
        nb_iterations,
        z_a,
        infinity=1.1 * escape_radius,
    )
    show_results('''z^2+c''', c_cauliflower, escape_radius, z_final)

    lowerCamelCase_    =					64
    lowerCamelCase_    =					2 * abs(c_polynomial_a) + 1
    lowerCamelCase_    =					iterate_function(
        eval_quadratic_polynomial,
        c_polynomial_a,
        nb_iterations,
        z_a,
        infinity=1.1 * escape_radius,
    )
    show_results('''z^2+c''', c_polynomial_a, escape_radius, z_final)

    lowerCamelCase_    =					161
    lowerCamelCase_    =					2 * abs(c_polynomial_a) + 1
    lowerCamelCase_    =					iterate_function(
        eval_quadratic_polynomial,
        c_polynomial_a,
        nb_iterations,
        z_a,
        infinity=1.1 * escape_radius,
    )
    show_results('''z^2+c''', c_polynomial_a, escape_radius, z_final)

    lowerCamelCase_    =					12
    lowerCamelCase_    =					10_000.0
    lowerCamelCase_    =					iterate_function(
        eval_exponential,
        c_exponential,
        nb_iterations,
        z_a + 2,
        infinity=1.0E1_0,
    )
    show_results('''e^z+c''', c_exponential, escape_radius, z_final)


def    UpperCamelCase(					lowercase_							)	->				str:





  '''simple docstring'''





  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."""							)

  snake_case_       						=      {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."""							)

  snake_case_       						=      len(lowercase_							)

  snake_case_       						=      0
  snake_case_       						=      []
  # put the x and x to the power values in a matrix
  while count_of_line < x:
    snake_case_       						=      0
    snake_case_       						=      coordinates[count_of_line][0]
    snake_case_       						=      []
    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

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

  snake_case_       						=      0

  while count < x:
    snake_case_       						=      0
    while zahlen < x:
      if count == zahlen:
        zahlen += 1
      if zahlen == x:
        break
      snake_case_       						=      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

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

  snake_case_       						=      0
  snake_case_       						=      """f(x)="""

  while count < x:
    snake_case_       						=      solution[count].split("""E"""							)
    if len(lowercase_							) > 1:
      snake_case_       						=      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]]))