


from __future__ import annotations

import math
import random






def 		_A		(		_lowercase				,     _lowercase				,     _lowercase   )				->   list[int]:


     """simple docstring"""


     __UpperCamelCase   = d * e - 1
     __UpperCamelCase   = 0
     __UpperCamelCase   = 0
     while p == 0:
          __UpperCamelCase   = random.randint(2				,     n - 1   )
          __UpperCamelCase   = k
          while True:
               if t % 2 == 0:
                    __UpperCamelCase   = t // 2
                    __UpperCamelCase   = (g**t) % n
                    __UpperCamelCase   = math.gcd(x - 1				,     _lowercase   )
                    if x > 1 and y > 1:
                         __UpperCamelCase   = y
                         __UpperCamelCase   = n // y
                         break  # find the correct factors
               else:
                    break  # t is not divisible by 2, break and choose another g
     return sorted([p, q]   )


if __name__ == "__main__":
    import doctest

    doctest.testmod()






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

import numpy
from matplotlib import pyplot

__snake_case             =	0.25 + 0.0j
__snake_case             =	-0.4 + 0.6j
__snake_case             =	-0.1 + 0.6_51j
__snake_case             =	-2.0
__snake_case             =	5_6
__snake_case             =	2.0
__snake_case             =	6_6_6






def 		_A		(		_lowercase				,     _lowercase   )				->   numpy.ndarray:


     """simple docstring"""


     return numpy.exp(_lowercase   ) + c_parameter






def 		_A		(		_lowercase				,     _lowercase   )				->   numpy.ndarray:


     """simple docstring"""


     return z_values * z_values + c_parameter






def 		_A		(		_lowercase				,     _lowercase   )				->   numpy.ndarray:


     """simple docstring"""


     __UpperCamelCase   = numpy.linspace(-window_size				,     _lowercase				,     _lowercase   )
     __UpperCamelCase   = x.reshape((nb_pixels, 1)   )
     __UpperCamelCase   = numpy.linspace(-window_size				,     _lowercase				,     _lowercase   )
     __UpperCamelCase   = y.reshape((1, nb_pixels)   )
     return x + 1.0J * y






def 		_A		(		_lowercase				,     _lowercase				,     _lowercase				,     _lowercase				,     _lowercase = None				,     )				->   numpy.ndarray:


     """simple docstring"""


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






def 		_A		(		_lowercase				,     _lowercase				,     _lowercase				,     _lowercase				,     )				->   None:


     """simple docstring"""


     __UpperCamelCase   = (abs(_lowercase   )).transpose()
     __UpperCamelCase   = 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 		_A		(		)				->   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__":
    __snake_case             =	prepare_grid(window_size, nb_pixels)

    ignore_overflow_warnings()  # See file header for explanations

    __snake_case             =	2_4
    __snake_case             =	2 * abs(c_cauliflower) + 1
    __snake_case             =	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)

    __snake_case             =	6_4
    __snake_case             =	2 * abs(c_polynomial_a) + 1
    __snake_case             =	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)

    __snake_case             =	1_6_1
    __snake_case             =	2 * abs(c_polynomial_a) + 1
    __snake_case             =	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)

    __snake_case             =	1_2
    __snake_case             =	10_000.0
    __snake_case             =	iterate_function(
        eval_exponential,
        c_exponential,
        nb_iterations,
        z_a + 2,
        infinity=1.0e10,
    )
    show_results('''e^z+c''', c_exponential, escape_radius, z_final)


