function r = eq(a, b)
% ==  Equal.
% (Quaternion overloading of standard Matlab function.)
%
% If one of the operands is not a quaternion and the other has zero vector part,
% the result is obtained by comparing the non-quaternion operand with the scalar
% part of the quaternion operand.

% Copyright © 2005 Stephen J. Sangwine and Nicolas Le Bihan.
% See the file : Copyright.m for further details.

error(nargchk(2, 2, nargin)), error(nargoutchk(0, 1, nargout)) 

if isa(a, 'quaternion') & isa(b, 'quaternion')
    
    if ispure(a) & ispure(b)
        r = x(a) == x(b) & y(a) == y(b) & z(a) == z(b);
    elseif ispure(a)
        % a is pure, but b isn't, so they can only be equal if the
        % scalar part of b is zero and the vector parts are equal.
        
        r = s(b) == 0 & v(a) == v(b);
    elseif ispure(b)
        % b is pure, but a isn't, so they can only be equal if the
        % scalar part of a is zero and the vector parts are equal.
        
        r = s(a) == 0 & v(a) == v(b);
    else
        r = s(a) == s(b) & v(a) == v(b);
    end
    
else
    % One of the arguments is not a quaternion (the other must be,
    % otherwise Matlab would not call this function).
    
    if isa(a, 'quaternion')
        if ispure(a)
            % a has no scalar part, and b has no vector part, since it is not
            % a quaternion. The result can only be true if b is zero, and a
            % has zero vector part.
            
            r = b == 0 & a == quaternion(0, 0, 0);
        else
            % a is a full quaternion, so the result can be true only if a has
            % zero vector part, and b is equal to the scalar part of a.
            
            r = s(a) == b & v(a) == quaternion(0, 0, 0);
        end
    elseif isa(b, 'quaternion')
        r = b == a; % Swap the order and compare them using the code above.
    else
        error('Programming error: neither argument is a quaternion?');    
    end
end