maths.pollard_rho
=================

.. py:module:: maths.pollard_rho


Attributes
----------

.. autoapisummary::

   maths.pollard_rho.parser


Functions
---------

.. autoapisummary::

   maths.pollard_rho.pollard_rho


Module Contents
---------------

.. py:function:: pollard_rho(num: int, seed: int = 2, step: int = 1, attempts: int = 3) -> int | None

   Use Pollard's Rho algorithm to return a nontrivial factor of ``num``.
   The returned factor may be composite and require further factorization.
   If the algorithm will return None if it fails to find a factor within
   the specified number of attempts or within the specified number of steps.
   If ``num`` is prime, this algorithm is guaranteed to return None.
   https://en.wikipedia.org/wiki/Pollard%27s_rho_algorithm

   >>> pollard_rho(18446744073709551617)
   274177
   >>> pollard_rho(97546105601219326301)
   9876543191
   >>> pollard_rho(100)
   2
   >>> pollard_rho(17)
   >>> pollard_rho(17**3)
   17
   >>> pollard_rho(17**3, attempts=1)
   >>> pollard_rho(3*5*7)
   21
   >>> pollard_rho(1)
   Traceback (most recent call last):
       ...
   ValueError: The input value cannot be less than 2


.. py:data:: parser