maths.matrix_exponentiation
===========================

.. py:module:: maths.matrix_exponentiation

.. autoapi-nested-parse::

   Matrix Exponentiation



Classes
-------

.. autoapisummary::

   maths.matrix_exponentiation.Matrix


Functions
---------

.. autoapisummary::

   maths.matrix_exponentiation.fibonacci_with_matrix_exponentiation
   maths.matrix_exponentiation.main
   maths.matrix_exponentiation.matrix_exponentiation_time
   maths.matrix_exponentiation.modular_exponentiation
   maths.matrix_exponentiation.simple_fibonacci
   maths.matrix_exponentiation.simple_fibonacci_time


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

.. py:class:: Matrix(arg)

   .. py:method:: __mul__(b)


.. py:function:: fibonacci_with_matrix_exponentiation(n, f1, f2)

   Returns the nth number of the Fibonacci sequence that
   starts with f1 and f2
   Uses the matrix exponentiation
   >>> fibonacci_with_matrix_exponentiation(1, 5, 6)
   5
   >>> fibonacci_with_matrix_exponentiation(2, 10, 11)
   11
   >>> fibonacci_with_matrix_exponentiation(13, 0, 1)
   144
   >>> fibonacci_with_matrix_exponentiation(10, 5, 9)
   411
   >>> fibonacci_with_matrix_exponentiation(9, 2, 3)
   89


.. py:function:: main()

.. py:function:: matrix_exponentiation_time()

.. py:function:: modular_exponentiation(a, b)

.. py:function:: simple_fibonacci(n, f1, f2)

   Returns the nth number of the Fibonacci sequence that
   starts with f1 and f2
   Uses the definition
   >>> simple_fibonacci(1, 5, 6)
   5
   >>> simple_fibonacci(2, 10, 11)
   11
   >>> simple_fibonacci(13, 0, 1)
   144
   >>> simple_fibonacci(10, 5, 9)
   411
   >>> simple_fibonacci(9, 2, 3)
   89


.. py:function:: simple_fibonacci_time()