num_theory.prime_factorization
==============================

.. py:module:: num_theory.prime_factorization


Functions
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.. autoapisummary::

   num_theory.prime_factorization.prime_factorization


Module Contents
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.. py:function:: prime_factorization(n)

   Compute the prime factorization of a given integer.

   :param n: The integer to factorize. Must be a positive integer greater than 1.
   :type n: int

   :returns: A list of tuples where each tuple represents a prime factor and its corresponding power.
             Example: For n=28, the output will be [(2, 2), (7, 1)], indicating 28 = 2^2 * 7^1.
   :rtype: list of tuple

   :raises ValueError: If the input `n` is not a positive integer greater than 1.

   .. rubric:: Examples

   >>> prime_factorization(28)
   [(2, 2), (7, 1)]

   >>> prime_factorization(100)
   [(2, 2), (5, 2)]

   .. rubric:: Notes

   - This function uses trial division to determine the prime factors.
   - For large values of `n`, consider optimized algorithms such as Pollard's Rho or
     the Quadratic Sieve for better performance.