sigmax = ((0,1),(1,0)) sigmay = ((0,-i),(i,0)) sigmaz = ((1,0),(0,-1)) sigma = (sigmax,sigmay,sigmaz) "Verify spin commutation relations" check(dot(sigmax,sigmay) - dot(sigmay,sigmax) == 2 i sigmaz) check(dot(sigmay,sigmaz) - dot(sigmaz,sigmay) == 2 i sigmax) check(dot(sigmaz,sigmax) - dot(sigmax,sigmaz) == 2 i sigmay) "ok" "Verify spin direction vector" s = (cos(theta/2), sin(theta/2) exp(i phi)) u = (sin(theta) cos(phi), sin(theta) sin(phi), cos(theta)) check(dot(conj(s),transpose(sigma),s) == u) "ok" Run