maths.polynomials.single_indeterminate_operations
=================================================

.. py:module:: maths.polynomials.single_indeterminate_operations

.. autoapi-nested-parse::

   This module implements a single indeterminate polynomials class
   with some basic operations

   Reference: https://en.wikipedia.org/wiki/Polynomial



Classes
-------

.. autoapisummary::

   maths.polynomials.single_indeterminate_operations.Polynomial


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

.. py:class:: Polynomial(degree: int, coefficients: collections.abc.MutableSequence[float])

   .. py:method:: __add__(polynomial_2: Polynomial) -> Polynomial

      Polynomial addition
      >>> p = Polynomial(2, [1, 2, 3])
      >>> q = Polynomial(2, [1, 2, 3])
      >>> p + q
      6x^2 + 4x + 2



   .. py:method:: __eq__(polynomial_2: object) -> bool

      Checks if two polynomials are equal.
      >>> p = Polynomial(2, [1, 2, 3])
      >>> q = Polynomial(2, [1, 2, 3])
      >>> p == q
      True



   .. py:method:: __mul__(polynomial_2: Polynomial) -> Polynomial

      Polynomial multiplication
      >>> p = Polynomial(2, [1, 2, 3])
      >>> q = Polynomial(2, [1, 2, 3])
      >>> p * q
      9x^4 + 12x^3 + 10x^2 + 4x + 1



   .. py:method:: __ne__(polynomial_2: object) -> bool

      Checks if two polynomials are not equal.
      >>> p = Polynomial(2, [1, 2, 3])
      >>> q = Polynomial(2, [1, 2, 3])
      >>> p != q
      False



   .. py:method:: __neg__() -> Polynomial

      Polynomial negation
      >>> p = Polynomial(2, [1, 2, 3])
      >>> -p
       - 3x^2 - 2x - 1



   .. py:method:: __repr__() -> str

      >>> p = Polynomial(2, [1, 2, 3])
      >>> p
      3x^2 + 2x + 1



   .. py:method:: __str__() -> str

      >>> p = Polynomial(2, [1, 2, 3])
      >>> print(p)
      3x^2 + 2x + 1



   .. py:method:: __sub__(polynomial_2: Polynomial) -> Polynomial

      Polynomial subtraction
      >>> p = Polynomial(2, [1, 2, 4])
      >>> q = Polynomial(2, [1, 2, 3])
      >>> p - q
      1x^2



   .. py:method:: derivative() -> Polynomial

      Returns the derivative of the polynomial.
      >>> p = Polynomial(2, [1, 2, 3])
      >>> p.derivative()
      6x + 2



   .. py:method:: evaluate(substitution: float) -> float

      Evaluates the polynomial at x.
      >>> p = Polynomial(2, [1, 2, 3])
      >>> p.evaluate(2)
      17



   .. py:method:: integral(constant: float = 0) -> Polynomial

      Returns the integral of the polynomial.
      >>> p = Polynomial(2, [1, 2, 3])
      >>> p.integral()
      1.0x^3 + 1.0x^2 + 1.0x



   .. py:attribute:: coefficients
      :type:  list[float]


   .. py:attribute:: degree