demospinorderivative.m

这是几何代数的matlab工具包

     disp('>> % |');
     % |
     disp('>> % |  THE DERIVATIVE OF A SPINOR');
     % |  THE DERIVATIVE OF A SPINOR
     disp('>> % |');
     % |
     i = unit(e1^(e2/2+e3/3)); %/  % rotation plane 
     n = 16;                   %/  % number of rotation steps
     phi = i*2*pi/n;           %/  % rotation angle bivector
     R = gexp(-phi/2); %/
     disp('>> a = e1-e2+e3;              % vector to be rotated');
     a = e1-e2+e3;              % vector to be rotated
     clf; %/
     draw(i,'y'); %/
     draw(a,'r'); GAtext(1.1*a,'a'); %/
     axis off; %/
     GAview([-30 30]); %/
     axis([-1.1 1.1 -1.7 0.7 -0.5 2]) %/
     disp('>> % |  Vector a and spinor plane ');
     % |  Vector a and spinor plane 
     disp('>> % |');
     % |
     GAprompt; %/
     disp('>> % |  Derivative is vector proportional to x.i');
     % |  Derivative is vector proportional to x.i
     disp('>> % |');
     % |
     title('constant i, then   \partial_t(e^{-i\phi/2} a e^{i\phi/2}) = (a \bullet i) \partial_t\phi'); %/
     draw(inner(a,phi),'b'); %/
     axis([-1.1 1.1 -1.7 0.7 -0.5 2]) %/
     GAprompt; %/
     disp('>> % |');
     % |
     disp('>> % |  Capable of locally rotating the vector a.');
     % |  Capable of locally rotating the vector a.
     for j=1:n %/
        anow = a; %/
        adernow = inner(anow,phi);  % derivative formula %/
        draw(anow,'r'); %/
        draw(adernow,'b'); %/
        DrawPolyline({anow-adernow/2,anow+adernow/2},'b'); %/
        axis([-1.1 1.1 -1.7 0.7 -0.5 2]) %/
     	drawnow; %/
        a = R*anow/R; %/
     end %/
     GAorbiter(-360,10); %/
     disp('>> % |');
     % |