input_case nil$ % Vectors % ------- vector u,v,w,m,n; vecdim 3; % space dimension w:=u+v; w.w; clear w; % contraction over repeated indices let u.u=1,v.v=1,u.v=cos(theta); x:=u.m*v.n+m.n; y:=m.n; x*y; index m,n; x*y; x; remind m,n; x; clear x,y; clear u.u,v.v,u.v; % differentiating over u.m and u.n s:=1/u.u; s:=sub(x=0,df(sub(u=u+x*m,s),x)); s:=sub(x=0,df(sub(u=u+x*n,s),x)); % averaging over u directions let u.u=u2; s:=s; clear u.u; for all m,n let u.m*u.n=u2/3*m.n; s:=s; for all m,n clear u.m*u.n; clear s; clear u,v,m,n; end;