Overview of the package
=======================

.. figure:: local_static/cube-eval-plot.png
   :align: right
   :alt: plot of a polynomial

The mvpoly package is a cross-language collection of basic
operations on various numeric representation of multivariate
polynomials.

This is not a symbolic algebra package, by a numeric
representation we mean some data-structure of floating
point numbers representing the coefficients of the
polynomial.  For dense polynomials (those with mostly
non-zero coefficients) an array is the obvious choice
of a data-structure, for a sparse polynomial a dictionary
stucture may give better performance.

By our choice, the number of basic operations on
multivariate polynomials is quite small: addition,
mutliplication, evaluation at point or set of points,
composition, differentiation, integration (definite and
indefinite), and we implement these operations as
object methods in subclasses of a basic class :class:`MVPoly`.
We have implemented an :class:`MVPolyCube <class-cube>` subclass
which uses :class:`numpy.ndarray` for the coefficients, and
a :class:`MVPolyDict <class-dict>` subclass which uses a
dictionary.

Arrays, numerics, object methods: clearly we are talking
about high-level scientific environment such as Python,
Matlab/Octave, Julia and the like.  The basic ideas should
be fairly straightforward to move between them, so far
the package is ported to Python and
:ref:`Octave/Matlab <section-octmat>`.  Python's OO is rather
slick and allows some nice syntactic sugar, for example::

   import numpy as np
   from mvpoly.cube import MVPolyCube

   x, y = MVPolyCube.variables(2)
   p = x*(1-x)*y*(1-y)

   L = np.linspace(0, 1, 50)
   Gx, Gy = np.meshgrid(L, L)
   Gp = p(Gx, Gy)

used to generate the grid of value of the bivariate polynomial
plotted above (see the file :file:`examples/cube-eval-plot.py`
included with the distribution).