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Any Octave function can be overloaded, and allows an object specific
version of this function to be called as needed. A pertinent example
for our polynomial class might be to overload the `polyval`

function
like

function [y, dy] = polyval (p, varargin) if (nargout == 2) [y, dy] = polyval (fliplr (p.poly), varargin{:}); else y = polyval (fliplr (p.poly), varargin{:}); endif endfunction

This function just hands off the work to the normal Octave `polyval`

function. Another interesting example for an overloaded function for our
polynomial class is the `plot`

function.

function h = plot (p, varargin) n = 128; rmax = max (abs (roots (p.poly))); x = [0 : (n - 1)] / (n - 1) * 2.2 * rmax - 1.1 * rmax; if (nargout > 0) h = plot (x, p(x), varargin{:}); else plot (x, p(x), varargin{:}); endif endfunction

which allows polynomials to be plotted in the domain near the region of the roots of the polynomial.

Functions that are of particular interest to be overloaded are the class
conversion functions such as `double`

. Overloading these functions
allows the `cast`

function to work with the user class and can aid
in the use of methods of other classes with the user class. An example
`double`

function for our polynomial class might look like.

function b = double (a) b = a.poly; endfunction