Overloading Functions for the Polynom Class :: Classes and Objects (Programming)

Programming

Overloading Functions for the Polynom Class

MATLAB already has several functions for working with polynomials represented by coefficient vectors. They should be overloaded to also work with the new polynom object. In many cases, the overloading methods can simply apply the original function to the coefficient field.

Overloading roots for the Polynom Class

The method @polynom/roots.m finds the roots of polynom objects.

function r = roots(p)
% POLYNOM/ROOTS.  ROOTS(p) is a vector containing the roots of p.
r = roots(p.c);

The statement

```
roots(p)
```

results in

ans =
    2.0946
    -1.0473 + 1.1359i
    -1.0473 - 1.1359i

Overloading polyval for the Polynom Class

The function polyval evaluates a polynomial at a given set of points. @polynom/polyval.m uses nested multiplication, or Horner's method to reduce the number of multiplication operations used to compute the various powers of x.

function y = polyval(p,x)
% POLYNOM/POLYVAL  POLYVAL(p,x) evaluates p at the points x.
y = 0;
for a = p.c
   y = y.*x + a;
end

Overloading plot for the Polynom Class

The overloaded plot function uses both root and polyval. The function selects the domain of the independent variable to be slightly larger than an interval containing all real roots. Then polyval is used to evaluate the polynomial at a few hundred points in the domain.

function plot(p)
% POLYNOM/PLOT  PLOT(p) plots the polynom p.
r = max(abs(roots(p)));
x = (-1.1:0.01:1.1)*r;
y = polyval(p,x);
plot(x,y);
title(char(p))
grid on

Overloading diff for the Polynom Class

The method @polynom/diff.m differentiates a polynomial by reducing the degree by 1 and multiplying each coefficient by its original degree.

function q = diff(p)
% POLYNOM/DIFF  DIFF(p) is the derivative of the polynom p.
c = p.c;
d = length(c) - 1;  % degree
q = polynom(p.c(1:d).*(d:-1:1));

Overloading Arithmetic Operators for polynom Listing Class Methods