restart;with(LinearAlgebra):
s1:=Vector([1,alpha1,1]):s2:=Vector([alpha2,1,1]):s3:=Vector([-1,alpha3,1]):s4:=Vector([alpha4,-1,1]):t1:=Vector([1,beta1,1]):t2:=Vector([beta2,1,1]):t3:=Vector([-1,beta3,1]):t4:=Vector([beta4,-1,1]):
S1 := (2+alpha2+alpha4+alpha3*(alpha2-alpha4)) * s1:
S2 := (2+alpha1+alpha3+alpha4*(alpha1-alpha3)) * s2:
S3 := (2-alpha4-alpha2+alpha1*(alpha4-alpha2)) * s3:
S4 := (2-alpha3-alpha1+alpha2*(alpha3-alpha1)) * s4:
T1 := (2+beta2+beta4+beta3*(beta2-beta4)) * t1:
T2 := (2+beta1+beta3+beta4*(beta1-beta3)) * t2:
T3 := (2-beta4-beta2+beta1*(beta4-beta2)) * t3:
T4 := (2-beta3-beta1+beta2*(beta3-beta1)) * t4:
simplify(S1+S3-S2-S4);simplify(T1+T3-T2-T4);
omega:=KroneckerProduct(S1-S2,Transpose(T2))+KroneckerProduct(S3,Transpose(T3))+KroneckerProduct(S2,Transpose(T1)):
factor(-2*omega(3,3)+omega(1,1)+omega(1,2)+omega(2,1)-omega(2,2));