classdef Taylor
    % this class models a degree-3 Taylor series with remainder,
    % a1 + a2 * t + a3 * t^2 + O(t^3)
    properties
        coeffs %length-3 vector of coefficients
    end
    methods
        function obj = Taylor(v)
            % so-called "constructor method".
            % This construct an object of this type starting from a given vector
            obj.coeffs = v;
        end
        function c = mtimes(a, b)
            % this is the function that gets called when Matlab encounters
            % a product that involves an object of type Taylor
            c = Taylor([a.coeffs(1)*b.coeffs(1), ...
                        a.coeffs(2)*b.coeffs(1) + a.coeffs(1)*b.coeffs(2), ...
                        a.coeffs(3)*b.coeffs(1) + a.coeffs(2)*b.coeffs(2) + a.coeffs(1)*b.coeffs(3) ...
                        ]);
        end
        function c = plus(a, b)
            % this is the function that gets called when Matlab encounters
            % a sum that involves an object of type Taylor
            % we add special cases for Taylor + number and number + Taylor
            if isa(b, 'double')
                b = Taylor([b 0 0]);
            end
            if isa(a, 'double')
                a = Taylor([a 0 0]);
            end            
            c = Taylor(a.coeffs + b.coeffs);
        end
    end
end