"Verify spin operator table"

u = (1,0)
d = (0,1)

uu = kronecker(u,u)
ud = kronecker(u,d)
du = kronecker(d,u)
dd = kronecker(d,d)

sigmaz = ((1,0),(0,-1))
sigmax = ((0,1),(1,0))
sigmay = ((0,-i),(i,0))

tauz = ((1,0),(0,-1))
taux = ((0,1),(1,0))
tauy = ((0,-i),(i,0))

I = ((1,0),(0,1))

sigmaz = kronecker(sigmaz,I)
sigmax = kronecker(sigmax,I)
sigmay = kronecker(sigmay,I)

tauz = kronecker(I,tauz)
taux = kronecker(I,taux)
tauy = kronecker(I,tauy)

check(dot(sigmaz,uu) == uu)
check(dot(sigmaz,ud) == ud)
check(dot(sigmaz,du) == -du)
check(dot(sigmaz,dd) == -dd)

check(dot(sigmax,uu) == du)
check(dot(sigmax,ud) == dd)
check(dot(sigmax,du) == uu)
check(dot(sigmax,dd) == ud)

check(dot(sigmay,uu) == i du)
check(dot(sigmay,ud) == i dd)
check(dot(sigmay,du) == -i uu)
check(dot(sigmay,dd) == -i ud)

check(dot(tauz,uu) == uu)
check(dot(tauz,ud) == -ud)
check(dot(tauz,du) == du)
check(dot(tauz,dd) == -dd)

check(dot(taux,uu) == ud)
check(dot(taux,ud) == uu)
check(dot(taux,du) == dd)
check(dot(taux,dd) == du)

check(dot(tauy,uu) == i ud)
check(dot(tauy,ud) == -i uu)
check(dot(tauy,du) == i dd)
check(dot(tauy,dd) == -i du)

"ok"