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

```function [y, dy] = polyval (p, varargin)

if (nargout > 1)
[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 of an overloaded function for the 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, polyval (p, x), varargin{:});
else
plot (x, polyval (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 for overloading are the class conversion functions such as `double`. Overloading these functions allows the `cast` function to work with a user class. It can also aid in the use of a class object with methods and functions from other classes since the object can be transformed to the requisite input form for the new function. An example `double` function for the polynomial class might look like

```function a = double (p)
a = p.poly;
endfunction
```