disp('>> %	QUATERNIONS IN GEOMETRIC ALGEBRA');     %	QUATERNIONS IN GEOMETRIC ALGEBRA     GAfigure; clc; %/     disp('>> %	QUATERNIONS IN GEOMETRIC ALGEBRA');     %	QUATERNIONS IN GEOMETRIC ALGEBRA     global i j k u q bivector Rangle Raxis; %/     clf; %/     disp('>> % The basic ''vectors'' in quaternions are unit bivectors.');     % The basic 'vectors' in quaternions are unit bivectors.     fprintf(1,'>> i = e1*I3     ');     input('');     i = e1*I3    %w     fprintf(1,'>> j = -e2*I3     ');     input('');     j = -e2*I3    %w     fprintf(1,'>> k = e3*I3     ');     input('');     k = e3*I3    %w     disp('>> % The quaternion product is the geometric prodcut:');     % The quaternion product is the geometric prodcut:     fprintf(1,'>> i*i 		 ');     input('');     i*i 		%w     fprintf(1,'>> j*j 		 ');     input('');     j*j 		%w     fprintf(1,'>> k*k 		 ');     input('');     k*k 		%w     fprintf(1,'>> i*j 		 ');     input('');     i*j 		%w     fprintf(1,'>> i*j*k 		 ');     input('');     i*j*k 		%w     disp('>> % A (unit) quaternion is a rotor:');     % A (unit) quaternion is a rotor:     fprintf(1,'>> q = 1 + i +j +k  ');     input('');     q = 1 + i +j +k %w     GAprompt; %/     fprintf(1,'>> u = q/norm(q) 	 ');     input('');     u = q/norm(q) 	%w     bivector = sLog(u); %/     Rangle = norm(bivector); %/     Raxis = bivector/I3; %/     disp('>> % A quaternion can be applied to a vector, bivector etc.,');     % A quaternion can be applied to a vector, bivector etc.,     disp('>> % without converting it to a matrix first');     % without converting it to a matrix first     disp('>> % (and without normalization).');     % (and without normalization).     clf; %/     x = e1; %/     draw(x,'b'); %/     axis off; %/     GAtext(1.1*x,'x','b'); %/     draw(bivector,'r'); %/     draw(Raxis,'k'); %/     label = -0.5*unit(grade(inner(x + q*x/q,bivector)/bivector,1))+ 0.1*unit(Raxis); %/     GAtext(label, 'log(q)'); %/     axis([-1 1 -1 1 -1 1]); %/     GAview([45 30]); %/     GAprompt; %/     fprintf(1,'>> Rx = q*x/q   ');     input('');     Rx = q*x/q  %w     draw(Rx,'g'); %/     GAtext(1.1*Rx,'q x q^{-1}','k'); %/     axis([-1 1 -1 1 -1 1]); %/     GAprompt; %/     GAorbiter(360,10); %/     GAprompt; %/     disp('>> % And it can be applied directly to bivectors:');     % And it can be applied directly to bivectors:     disp('>> B = x^(e2+e3); ');     B = x^(e2+e3);      draw(B,'b'); %/     axis([-1 1 -1 1 -1 1]); %/     label = grade(meet(B,bivector),1); %/     GAtext(0.75*label,'B','b'); %/     fprintf(1,'>> RB = q*B/q   ');     input('');     RB = q*B/q  %w     draw(RB,'g'); %/     GAtext(0.75*q*label/q,'q B q^{-1}','k'); %/     axis([-1 1 -1 1 -1 1]); %/     GAprompt; %/     GAorbiter(360,10); %/     disp('>> ');