"Verify equation (13.42)" A = (A0(),A1(),A2(),A3()) X = (x0,x1,x2,x3) gmunu = ((1,0,0,0),(0,-1,0,0),(0,0,-1,0),(0,0,0,-1)) FDD = zero(4,4) for(mu,1,4,for(nu,1,4,FDD[mu,nu] = d(A[nu],X[mu]) - d(A[mu],X[nu]))) FUU = dot(gmunu,FDD,gmunu) U = contract(dot(transpose(FUU),FDD)) V = sum(mu,1,4,sum(nu,1,4, gmunu[mu,mu] gmunu[nu,nu] * (d(A[nu],X[mu]) d(A[nu],X[mu]) - d(A[nu],X[mu]) d(A[mu],X[nu])) )) check(-1/4 U == -1/2 V) "ok" Run