The command SegreType uses the algorithm of E. Zakhary and J. Carminati, A New Algorithm for the Segre Classification of the Trace-Free Ricci Tensor, General Relativity and Gravitation,Vol 36. (2004), 1015-1038 to Segre type.  The algorithm first calculates the Plebanski-Petrov type and then the Segre type.

If the Plebanski-Petrov type of the Ricci R tensor is "O", then the Segre type of R is [(1,111)], [1,(111)], [(1,11),1], or [(2,11)].

If the Plebanski-Petrov type of the Ricci R tensor is "N", then the Segre type of R is [(2,1)1] or [(3,1)].

If the Plebanski-Petrov type of the Ricci R tensor is "D", then the Segre type of R is [(1,1)(11)], [1,1(11)], [(1,1)11], [2,(11)], or [ZbarZ,(11)].

If the Plebanski-Petrov type of the Ricci R tensor is "III", then the Segre type of R is [3,1].

If the Plebanski-Petrov type of the Ricci R tensor is "II", then the Segre type of R is [2,11].

If the Plebanski-Petrov type of the Ricci R tensor is "I", then the Segre type of R is [1,111] or [ZbarZ11].

The algorithm depends upon certain invariants calculated from the Newman-Penrose Ricci scalars Phi00, Phi01, Phi02, Phi10, Phi11, Phi120, Phi121, Phi22.  These invariants are:

Chi0 = 2*(Phi00*Phi02 - Phi01^2)

Chi1 = Phi00*Phi12 + Phi02*Phi10 - 2*Phi01*Phi11

Chi2 = 1/3*(Phi00*Phi22 - 2*Phi01*Phi21 + Phi02*Phi20 + 4*Phi10*Phi12 - 4*Phi11^2)

Chi3 = Phi10*Phi22 - 2*Phi11*Phi21 + Phi12*Phi20

Chi4 = 2*(Phi20*Phi22 - Phi21^2)

E00 = 4*(Phi00*Phi11 - Phi01*Phi10)

E01 = 2*(Phi00*Phi12 - Phi02*Phi10)

E02 = 2*(Phi01*Phi12 - Phi02*Phi11)

E10 = 2*(Phi00*Phi21 - Phi20*Phi01)

E11 = Phi00*Phi22 - Phi02*Phi20

E12 = 2*(Phi01*Phi22 - Phi02*Phi21)

E20 = 2*(Phi01*Phi21 - Phi20*Phi11)

E21 = 2*(Phi10*Phi22 - Phi20*Phi02)

E22 = 4*(Phi11*Phi22 - Phi12*Phi21)

Delta_Phi = Phi11^2 - Phi01*Phi21)

r1 = 2*(Chi2 - 2*Phi10*Phi12 + 2*Phi11^2)

tildeChi0 = 2*(E00*E02 - E01^2)

tidleChi2 = E00*E22 - 2*E01*E21 + E02*E20 + 4*E10*E12 - 4*E11^2

Ip = 1/3*(Chi0*Chi4 - 4*Chi1*Chi3 + 3*Chi2^2)

Jp = Chi0*Chi2*Chi4 + 2*Chi1*Chi2*Chi3 - Chi0*Chi3^2 - Chi1^2*Chi4 - Chi2^3

H = r1*Ip - Jp

r2 = 2*(Phi00*Phi11*Phi22 + Phi01*Phi12*Phi20 + Phi02*Phi10*Phi21 - Phi00*Phi12*Phi21 -         Phi01*Phi10*Phi22 - Phi02*Phi11*Phi20)

k|_i = Jp*(E_{ii}- 2*r2*Ip*Phi_i/H

Dp = Jp^2 - Ip^3

Here are the details of the algorithm.

The Plebanski-Petrov type of the Ricci R tensor is "O".  Step 1.  If all the Ricci scalars Phi00, Phi01, ... Phi22 = 0, then S = [(1,111)].  Step 2.  Otherwise, if Delta_Phi = 0, then S = [(2,11)].  Step 3.  Otherwise, if  E00 > 0, then S = [1,(111)].  Step 4.  Otherwise, if E00 <= 0, then S = [(1,11)1].

The Plebanski-Petrov type of the Ricci R tensor is "N".  Step 1.  If r1 = 0, then S = [(3,1)], otherwise S = [(2,1)1].

The Plebanski-Petrov type of the Ricci R tensor is "D".  Step 1.  If r1 = 0, then S = [ZZ(1,1)].  Step 2.  If r1 <> 0 and all the E00, E01, ... E22 =0, then S = [(1,1)(11)].  Step 3.  If r1 <> 0, Chi0 <> 0 and tildeChi0 =  0, then S = [(2,11)].  Step 4.  If r1 <>  0, Chi0 <> 0, tildeChi0 = 0 and tildeChi2 = 0, then S = [2,(11)].  Step 5.  If  H= 0, then S = [2,(11)], while if H < 0, then S = [ZZ,(11)].

The Plebanski-Petrov type of the Ricci R tensor is "III".  Then Segre type of R is [3,1].

The Plebanski-Petrov type of the Ricci R tensor is "II".  Then Segre type of R is [2,11].

The Plebanski-Petrov type of the Ricci R tensor is "I".  Step 1.  If Dp < 0, then S =[1,111] while if Dp > 0, then S = [ZZ11].