Polynomials (polynomial)
========================

.. currentmodule:: numpycore.polynomial

The ``polynomial`` module provides classes and functions for polynomial operations.

Example
-------

.. code-block:: python

   import numpycore as np

   # Create polynomial: 1 + 2x + 3x^2
   p = np.polynomial.Polynomial([1, 2, 3])

   # Evaluate at x = 2
   print(p(2))  # 17.0

   # Polynomial arithmetic
   q = np.polynomial.Polynomial([1, 1])
   print(p + q)  # Add polynomials
   print(p * q)  # Multiply polynomials

   # Polynomial fitting
   x = np.array([0, 1, 2, 3, 4])
   y = np.array([0, 1, 4, 9, 16])
   coeffs = np.polyfit(x, y, 2)

Polynomial Class
----------------

.. list-table::
   :widths: 30 70
   :header-rows: 1

   * - Method
     - Description
   * - Polynomial(coef)
     - Create polynomial from coefficients
   * - __call__(x)
     - Evaluate polynomial at x
   * - deriv(m=1)
     - Derivative of polynomial
   * - integ(m=1)
     - Indefinite integral
   * - roots()
     - Polynomial roots
   * - fit(x, y, deg)
     - Least squares fit

Polynomial Functions
--------------------

.. list-table::
   :widths: 25 75
   :header-rows: 1

   * - Function
     - Description
   * - polyval(x, c)
     - Evaluate polynomial at points x
   * - polyfit(x, y, deg)
     - Least squares polynomial fit
   * - polyadd(c1, c2)
     - Add two polynomials
   * - polysub(c1, c2)
     - Subtract two polynomials
   * - polymul(c1, c2)
     - Multiply two polynomials
   * - polydiv(c1, c2)
     - Divide two polynomials
   * - polyder(c)
     - Polynomial derivative
   * - polyint(c)
     - Polynomial integral
   * - polyroots(c)
     - Roots of polynomial

Special Polynomials
-------------------

.. list-table::
   :widths: 25 75
   :header-rows: 1

   * - Class
     - Description
   * - Chebyshev
     - Chebyshev polynomials
   * - Legendre
     - Legendre polynomials
   * - Hermite
     - Hermite polynomials (physicist's)
   * - HermiteE
     - Hermite polynomials (probabilist's)
   * - Laguerre
     - Laguerre polynomials