> restart:
> with(LinearAlgebra):
> Pauli := [
>    Matrix([[0, 1],[1, 0]]),
>    Matrix([[0,-I],[I, 0]]),
>    Matrix([[1, 0],[0,-1]])
> ]:
> F := Vector(8,(i) -> f[i]):
> M1 := Omega[1]*Omega[4]         *KroneckerProduct(Pauli[1],KroneckerProduct(Pauli[1],Pauli[1])):
> M2 := Omega[1]*Omega[3]         *KroneckerProduct(Pauli[1],KroneckerProduct(Pauli[1],IdentityMatrix(2))):
> M3 := Omega[1]*Omega[2]*Omega[4]*KroneckerProduct(Pauli[1],IdentityMatrix(4)):
> M4 := Omega[1]*Omega[2]*Omega[3]*KroneckerProduct(Pauli[1],KroneckerProduct(IdentityMatrix(2),Pauli[1])):
> EQS := 
>    convert(M1 . F - F,set) union
>    convert(M2 . F - F,set) union
>    convert(M3 . F - F,set) union
>    convert(M4 . F - F,set);
{Omega[1] Omega[3] f[7] - f[1], Omega[1] Omega[3] f[1] - f[7], 



  Omega[1] Omega[3] f[8] - f[2], Omega[1] Omega[3] f[2] - f[8], 



  Omega[1] Omega[3] f[5] - f[3], Omega[1] Omega[3] f[3] - f[5], 



  Omega[1] Omega[3] f[6] - f[4], Omega[1] Omega[3] f[4] - f[6], 



  Omega[1] Omega[4] f[8] - f[1], Omega[1] Omega[4] f[1] - f[8], 



  Omega[1] Omega[4] f[7] - f[2], Omega[1] Omega[4] f[2] - f[7], 



  Omega[1] Omega[4] f[6] - f[3], Omega[1] Omega[4] f[3] - f[6], 



  Omega[1] Omega[4] f[5] - f[4], Omega[1] Omega[4] f[4] - f[5], 



  Omega[1] Omega[2] Omega[3] f[6] - f[1], 



  Omega[1] Omega[2] Omega[3] f[1] - f[6], 



  Omega[1] Omega[2] Omega[3] f[5] - f[2], 



  Omega[1] Omega[2] Omega[3] f[2] - f[5], 



  Omega[1] Omega[2] Omega[3] f[8] - f[3], 



  Omega[1] Omega[2] Omega[3] f[3] - f[8], 



  Omega[1] Omega[2] Omega[3] f[7] - f[4], 



  Omega[1] Omega[2] Omega[3] f[4] - f[7], 



  Omega[1] Omega[2] Omega[4] f[5] - f[1], 



  Omega[1] Omega[2] Omega[4] f[1] - f[5], 



  Omega[1] Omega[2] Omega[4] f[6] - f[2], 



  Omega[1] Omega[2] Omega[4] f[2] - f[6], 



  Omega[1] Omega[2] Omega[4] f[7] - f[3], 



  Omega[1] Omega[2] Omega[4] f[3] - f[7], 



  Omega[1] Omega[2] Omega[4] f[8] - f[4], 



  Omega[1] Omega[2] Omega[4] f[4] - f[8]}
>