function C = dual(A)%dual(A): Computes the dual, A/I3%%See also gable.% GABLE, Copyright (c) 1999, University of Amsterdam% Copying, use and development for non-commercial purposes permitted.%          All rights for commercial use reserved; for more information%          contact Leo Dorst (leo@wins.uva.nl).%%          This software is unsupported.%The dual is calculated by right multiplication by the inverse of the% pseudoscalar. In this case we get a negative sign from the grade of % the pseudoscalar and the other term from the signature.    S=GAsignature;% Conceptually we want%    T=GAproduct(A,GA([0;0;0;0;0;0;0;-prod(S)]));% but the code is more efficient as    T = GA([A.m(8);S(1)*A.m(6);S(2)*A.m(7);S(3)*A.m(5);-S(1)*S(2)*A.m(4);-S(2)*S(3)*A.m(2);-S(3)*S(1)*A.m(3);-S(1)*S(2)*S(3)*A.m(1)]);    if GAautoscalar&isascalar(T)       C=T.m(1);    else       C=T;    end