classdef Taylor
    properties
        coeff  % 1x3 vector of coefficients
    end
    methods
        function obj = Taylor(v)
            obj.coeff = v;
        end
        function c = plus(a, b)
            if isreal(a)
                a = Taylor([a 0 0]);
            end
            if isreal(b)
                b = Taylor([b 0 0]);
            end
            c = Taylor(a.coeff + b.coeff);
        end
        function c = mtimes(a, b)
            c = Taylor([a.coeff(1)*b.coeff(1), a.coeff(2)*b.coeff(1)+a.coeff(1)*b.coeff(2) ...
                a.coeff(3)*b.coeff(1)+a.coeff(2)*b.coeff(2)+a.coeff(1)*b.coeff(3)
                ]);
        end
        function result = lt(a, b)
            if isreal(a)
                a = Taylor([a 0 0]);
            end
            if isreal(b)
                b = Taylor([b 0 0]);
            end
            result = a.coeff(1) < b.coeff(1);
        end
    end
end