The command PetrovType uses the algorithm of M. A. Acvevedo, M. M. Enciso-Aguilar, J. Lopez-Bonilla, M. A. Acvevedo, Petrov classification of the conformal tensor, Electronic Journal of Theoretical Physics, Vol .9. (2006), 79-82 to determine the Petrov type.  The algorithm depends upon certain invariants calculated from the Newman Penrose Weyl scalars Psi0, Psi1, Psi2, Psi3, Psi4.  These invariants are:

G[0] = 2*(Psi0*Psi2 - Psi1^2)

G[1] = 2*(Psi0*Psi3 - Psi1*Psi2)

G[2] =  Psi0^2 + Psi0Psi4 - 2*Psi1*Psi3)

G[3] = Psi1*Psi4 - Psi2*Psi3)

G[4] = 2*(Psi2*Psi4 - Psi3^2)

G[5] = 2*(Psi1*Psi3 - Psi2^2)

I = G[2] - G[5]

J = -Psi3*G[1] + 1/2*(Psi2*G[5] + Psi4*G[0])

if I^3  <> 27J^2 then lambda is determined by lambda^2 = I/3 and lambda^3 = -J.

M[r] = G[r] + lambda*Psi[r], r = 0, 1, 2, 3, 4

L = G[2] + 2*G[5] + 3*lambda*Psi[2] 

The algorithm is as follows.  Step 1.  If all the Psi0, Psi1, Psi2, Psi3, Psi4 = 0, then the Petrov type is "O".  Step 2.  Otherwise, if all the invariants G[0], G[2], G[3], G[4], G[5] = 0, then the Petrov type is "N".  Step 3.  Otherwise, if I = J = 0, then the Petrov type is "III".  Step 4.  Otherwise, if I^3  <> 27J^2, then the Petrov type is "I".  Step 5.  If I^3 = 27J^2 and M[r] = 0 for r = 0, 1, 2, 3, 4, and G[2] + 2*G[5] + 3*lambda*Psi[2] = 0, then the Petrov type is "D". Step 6.  Oherwise, the Petrov type is "II".