The generic automorphism phi of g_{6,5} as computed by calculautom6_5.red : They fall into 2 kinds. First kind : phi:= mat((b(1,1),0,0,0,0,0), (0,b(2,2),0,0,0,0), (b(3,1),b(3,2),b(2,2)*b(1,1),0,0,0), (b(4,1),b(4,2),0,b(2,2)*b(1,1),0,0), 2 (b(5,1),b(5,2),b(5,3),b(4,2)*b(1,1),b(2,2)*b(1,1) ,0), 2 (b(6,1),b(6,2),b(6,3), - b(2,2)*(b(3,1) + b(4,1)),0,b(2,2) *b(1,1))) 6 6 det(phi):=b(2,2) *b(1,1) Second kind : psi:= mat((0,bb(1,2),0,0,0,0), (bb(2,1),0,0,0,0,0), (bb(3,1),bb(3,2),bb(2,1)*bb(1,2),0,0,0), (bb(4,1),bb(4,2), - bb(2,1)*bb(1,2), - bb(2,1)*bb(1,2),0,0), 2 (bb(5,1),bb(5,2),bb(5,3), - bb(4,1)*bb(1,2),0, - bb(2,1)*bb(1,2) ), 2 (bb(6,1),bb(6,2),bb(6,3),(bb(3,2) + bb(4,2))*bb(2,1), - bb(2,1) *bb(1,2),0)) 6 6 det(psi):= - bb(2,1) *bb(1,2) generic derivation : delta:= mat((xi(1,1),0,0,0,0,0), (0,xi(2,2),0,0,0,0), (xi(3,1),xi(3,2),xi(1,1) + xi(2,2),0,0,0), (xi(4,1),xi(4,2),0,xi(1,1) + xi(2,2),0,0), (xi(5,1),xi(5,2),xi(5,3),xi(4,2),2*xi(1,1) + xi(2,2),0), (xi(6,1),xi(6,2),xi(6,3), - (xi(3,1) + xi(4,1)),0,xi(1,1) + 2*xi(2,2))) [0 0 0 0 0 0] [ ] [0 0 0 0 0 0] [ ] [0 0 0 0 0 0] adx1 := [ ] [0 1 0 0 0 0] [ ] [0 0 0 1 0 0] [ ] [0 0 0 0 0 0] [0 0 0 0 0 0] [ ] [0 0 0 0 0 0] [ ] [0 0 0 0 0 0] adx2 := [ ] [-1 0 0 0 0 0] [ ] [0 0 0 0 0 0] [ ] [0 0 1 1 0 0] [0 0 0 0 0 0] [ ] [0 0 0 0 0 0] [ ] [0 0 0 0 0 0] adx3 := [ ] [0 0 0 0 0 0] [ ] [0 0 0 0 0 0] [ ] [0 -1 0 0 0 0] [0 0 0 0 0 0] [ ] [0 0 0 0 0 0] [ ] [0 0 0 0 0 0] adx4 := [ ] [0 0 0 0 0 0] [ ] [-1 0 0 0 0 0] [ ] [0 -1 0 0 0 0] The generic nilpotent derivation : the eigenvalues are 0 xi(1,1):=0 xi(2,2):=0 by subtracting adjoints one then may suppose: xi(4,1):=0,xi(4,2):=0,xi(5,1):=0,xi(6,2):=0 phi:= mat((b(1,1),0,0,0,0,0), (0,b(2,2),0,0,0,0), (b(3,1),b(3,2),b(2,2)*b(1,1),0,0,0), (b(4,1),b(4,2),0,b(2,2)*b(1,1),0,0), 2 (b(5,1),b(5,2),b(5,3),b(4,2)*b(1,1),b(2,2)*b(1,1) ,0), 2 (b(6,1),b(6,2),b(6,3), - (b(3,1) + b(4,1))*b(2,2),0,b(2,2) *b(1,1))) 6 6 det(phi):=b(2,2) *b(1,1) delta:= [ 0 0 0 0 0 0] [ ] [ 0 0 0 0 0 0] [ ] [xi(3,1) xi(3,2) 0 0 0 0] [ ] [ 0 0 0 0 0 0] [ ] [ 0 xi(5,2) xi(5,3) 0 0 0] [ ] [xi(6,1) 0 xi(6,3) - xi(3,1) 0 0] We denote this delta by the shortform shortformdelta:={xi(3,1), xi(3,2), ss, xi(5,2), xi(5,3), ss, xi(6,1), xi(6,3)} paramindexeslist:={{3,1},{3,2},{5,2},{5,3},{6,1},{6,3}} With the first kind automorphism one gets$ shortformdeltaprimemodadg:={b(2,2)*xi(3,1), b(1,1)*xi(3,2), ss, ( - ( - b(5,3)*xi(3,2) + ( - b(2,2)*b(1,1)*xi(5,2) + b(3,2)*xi(5,3))*b(1,1)))/b( 2,2), b(1,1)*xi(5,3), ss, ( - ( - b(6,3)*xi(3,1) + ( - b(4,1)*xi(3,1) - b(2,2)*b(1,1)*xi(6,1) + b(3,1)*xi( 6,3))*b(2,2)))/b(1,1), b(2,2)*xi(6,3)}$ deltaprimemodg(3,1):=b(2,2)*xi(3,1)$ deltaprimemodg(3,2):=b(1,1)*xi(3,2)$ deltaprimemodg(5,2):=( - ( - b(5,3)*xi(3,2) + ( - b(2,2)*b(1,1)*xi(5,2) + b(3,2) *xi(5,3))*b(1,1)))/b(2,2)$ deltaprimemodg(5,3):=b(1,1)*xi(5,3)$ deltaprimemodg(6,1):=( - ( - b(6,3)*xi(3,1) + ( - b(4,1)*xi(3,1) - b(2,2)*b(1,1) *xi(6,1) + b(3,1)*xi(6,3))*b(2,2)))/b(1,1)$ deltaprimemodg(6,3):=b(2,2)*xi(6,3)$ det(AUTOM):=b(2,2)**6*b(1,1)**6$ DELTAPRIMEMODADG:= mat((0,0,0,0,0,0), (0,0,0,0,0,0), (b(2,2)*xi(3,1),b(1,1)*xi(3,2),0,0,0,0), (0,0,0,0,0,0), (0,( - ( - b(5,3)*xi(3,2) + ( - b(2,2)*b(1,1)*xi(5,2) + b(3,2)*xi(5,3))*b(1,1)))/b(2,2), b(1,1)*xi(5,3),0,0,0), (( - ( - b(6,3)*xi(3,1) + ( - b(4,1)*xi(3,1) - b(2,2)*b(1,1)*xi(6,1) + b(3,1)*xi(6,3))*b(2,2) ))/b(1,1),0,b(2,2)*xi(6,3), - b(2,2)*xi(3,1),0,0)) With the second kind automorphism one gets$ shortformdeltaprimemodadg:={bb(2,1)*xi(3,2), bb(1,2)*xi(3,1), ss, (bb(5,3)*xi(3,1) + ( - bb(2,1)*bb(1,2)*xi(6,1) + bb(3,1)*xi(6,3) + (bb(3,1) + bb (4,1))*xi(3,1))*bb(1,2))/bb(2,1), - (xi(3,1) + xi(6,3))*bb(1,2), ss, (bb(6,3)*xi(3,2) + ( - bb(2,1)*bb(1,2)*xi(5,2) + bb(3,2)*xi(5,3))*bb(2,1))/bb(1, 2), - (xi(3,2) + xi(5,3))*bb(2,1)}$ deltaprimemodg(3,1):=bb(2,1)*xi(3,2)$ deltaprimemodg(3,2):=bb(1,2)*xi(3,1)$ deltaprimemodg(5,2):=(bb(5,3)*xi(3,1) + ( - bb(2,1)*bb(1,2)*xi(6,1) + bb(3,1)*xi (6,3) + (bb(3,1) + bb(4,1))*xi(3,1))*bb(1,2))/bb(2,1)$ deltaprimemodg(5,3):= - (xi(3,1) + xi(6,3))*bb(1,2)$ deltaprimemodg(6,1):=(bb(6,3)*xi(3,2) + ( - bb(2,1)*bb(1,2)*xi(5,2) + bb(3,2)*xi (5,3))*bb(2,1))/bb(1,2)$ deltaprimemodg(6,3):= - (xi(3,2) + xi(5,3))*bb(2,1)$ det(AUTOM):= - bb(2,1)**6*bb(1,2)**6$ DELTAPRIMEMODADG:= mat((0,0,0,0,0,0), (0,0,0,0,0,0), (bb(2,1)*xi(3,2),bb(1,2)*xi(3,1),0,0,0,0), (0,0,0,0,0,0), (0,(bb(5,3)*xi(3,1) + ( - bb(2,1)*bb(1,2)*xi(6,1) + bb(3,1)*xi(6,3) + (bb(3,1) + bb(4,1))*xi(3,1))*bb(1,2))/bb(2,1), - (xi(3,1) + xi(6,3))*bb(1,2),0,0,0), bb(6,3)*xi(3,2) + ( - bb(2,1)*bb(1,2)*xi(5,2) + bb(3,2)*xi(5,3))*bb(2,1) (--------------------------------------------------------------------------, bb(1,2) 0, - (xi(3,2) + xi(5,3))*bb(2,1), - bb(2,1)*xi(3,2),0,0)) In case 3 one has$ xi(3,1):=0$ xi(3,2):=0$ With the first kind automorphism one gets$ shortformdeltaprimemodadg:={0, 0, ss, ( - ( - b(2,2)*b(1,1)*xi(5,2) + b(3,2)*xi(5,3))*b(1,1))/b(2,2), b(1,1)*xi(5,3), ss, ( - ( - b(2,2)*b(1,1)*xi(6,1) + b(3,1)*xi(6,3))*b(2,2))/b(1,1), b(2,2)*xi(6,3)}$ deltaprimemodg(3,1):=0$ deltaprimemodg(3,2):=0$ deltaprimemodg(5,2):=( - ( - b(2,2)*b(1,1)*xi(5,2) + b(3,2)*xi(5,3))*b(1,1))/b(2 ,2)$ deltaprimemodg(5,3):=b(1,1)*xi(5,3)$ deltaprimemodg(6,1):=( - ( - b(2,2)*b(1,1)*xi(6,1) + b(3,1)*xi(6,3))*b(2,2))/b(1 ,1)$ deltaprimemodg(6,3):=b(2,2)*xi(6,3)$ det(AUTOM):=b(2,2)**6*b(1,1)**6$ DELTAPRIMEMODADG:= mat((0,0,0,0,0,0), (0,0,0,0,0,0), (0,0,0,0,0,0), (0,0,0,0,0,0), - ( - b(2,2)*b(1,1)*xi(5,2) + b(3,2)*xi(5,3))*b(1,1) (0,-------------------------------------------------------,b(1,1)*xi(5,3),0, b(2,2) 0,0), - ( - b(2,2)*b(1,1)*xi(6,1) + b(3,1)*xi(6,3))*b(2,2) (-------------------------------------------------------,0,b(2,2)*xi(6,3),0, b(1,1) 0,0)) With the second kind automorphism one gets$ shortformdeltaprimemodadg:={0, 0, ss, (( - bb(2,1)*bb(1,2)*xi(6,1) + bb(3,1)*xi(6,3))*bb(1,2))/bb(2,1), - bb(1,2)*xi(6,3), ss, (( - bb(2,1)*bb(1,2)*xi(5,2) + bb(3,2)*xi(5,3))*bb(2,1))/bb(1,2), - bb(2,1)*xi(5,3)}$ deltaprimemodg(3,1):=0$ deltaprimemodg(3,2):=0$ deltaprimemodg(5,2):=(( - bb(2,1)*bb(1,2)*xi(6,1) + bb(3,1)*xi(6,3))*bb(1,2))/bb (2,1)$ deltaprimemodg(5,3):= - bb(1,2)*xi(6,3)$ deltaprimemodg(6,1):=(( - bb(2,1)*bb(1,2)*xi(5,2) + bb(3,2)*xi(5,3))*bb(2,1))/bb (1,2)$ deltaprimemodg(6,3):= - bb(2,1)*xi(5,3)$ det(AUTOM):= - bb(2,1)**6*bb(1,2)**6$ DELTAPRIMEMODADG:= mat((0,0,0,0,0,0), (0,0,0,0,0,0), (0,0,0,0,0,0), (0,0,0,0,0,0), ( - bb(2,1)*bb(1,2)*xi(6,1) + bb(3,1)*xi(6,3))*bb(1,2) (0,--------------------------------------------------------, bb(2,1) - bb(1,2)*xi(6,3),0,0,0), ( - bb(2,1)*bb(1,2)*xi(5,2) + bb(3,2)*xi(5,3))*bb(2,1) (--------------------------------------------------------,0, bb(1,2) - bb(2,1)*xi(5,3),0,0,0)) We see that we get 3 subcases according to whether xi(5,3),xi(6,3) are$ both nonzero, or only one of them is zero or both are zero.$ We may then suppose in subcase 1 : xi(5,3):=1,xi(6,3):=1$ in subcase 2 : xi(5,3):=0,xi(6,3):=1$ in subcase 3 : xi(5,3):=0,xi(6,3):=0$ *********** SUBCASE 1 : xi(5,3):=1,xi(6,3):=1 ****************************$ xi(5,3):=1$ xi(6,3):=1$ To keep xi(5,3):=k,xi(6,3):=k using a first kind autom one has to take:$ b(1,1):=k$ b(2,2):=k$ With the first kind automorphism one gets$ shortformdeltaprimemodadg:={0, 0, ss, - ( - xi(5,2)*k**2 + b(3,2)), k, ss, - ( - xi(6,1)*k**2 + b(3,1)), k}$ deltaprimemodg(3,1):=0$ deltaprimemodg(3,2):=0$ deltaprimemodg(5,2):= - ( - xi(5,2)*k**2 + b(3,2))$ deltaprimemodg(5,3):=k$ deltaprimemodg(6,1):= - ( - xi(6,1)*k**2 + b(3,1))$ deltaprimemodg(6,3):=k$ det(AUTOM):=k**12$ DELTAPRIMEMODADG:= [ 0 0 0 0 0 0] [ ] [ 0 0 0 0 0 0] [ ] [ 0 0 0 0 0 0] [ ] [ 0 0 0 0 0 0] [ ] [ 2 ] [ 0 - ( - xi(5,2)*k + b(3,2)) k 0 0 0] [ ] [ 2 ] [ - ( - xi(6,1)*k + b(3,1)) 0 k 0 0 0] With the second kind automorphism one gets$ shortformdeltaprimemodadg:={0, 0, ss, (( - bb(2,1)*bb(1,2)*xi(6,1) + bb(3,1))*bb(1,2))/bb(2,1), - bb(1,2), ss, (( - bb(2,1)*bb(1,2)*xi(5,2) + bb(3,2))*bb(2,1))/bb(1,2), - bb(2,1)}$ deltaprimemodg(3,1):=0$ deltaprimemodg(3,2):=0$ deltaprimemodg(5,2):=(( - bb(2,1)*bb(1,2)*xi(6,1) + bb(3,1))*bb(1,2))/bb(2,1)$ deltaprimemodg(5,3):= - bb(1,2)$ deltaprimemodg(6,1):=(( - bb(2,1)*bb(1,2)*xi(5,2) + bb(3,2))*bb(2,1))/bb(1,2)$ deltaprimemodg(6,3):= - bb(2,1)$ det(AUTOM):= - bb(2,1)**6*bb(1,2)**6$ DELTAPRIMEMODADG:= mat((0,0,0,0,0,0), (0,0,0,0,0,0), (0,0,0,0,0,0), (0,0,0,0,0,0), ( - bb(2,1)*bb(1,2)*xi(6,1) + bb(3,1))*bb(1,2) (0,------------------------------------------------, - bb(1,2),0,0,0), bb(2,1) ( - bb(2,1)*bb(1,2)*xi(5,2) + bb(3,2))*bb(2,1) (------------------------------------------------,0, - bb(2,1),0,0,0)) bb(1,2) One then gets xi(6,1)=0 and xi(5,2) = 0 by taking:$ b(3,2):=xi(5,2)*k**2$ b(3,1):=xi(6,1)*k**2$ With the first kind automorphism one gets$ shortformdeltaprimemodadg:={0,0,ss,0,k,ss,0,k}$ deltaprimemodg(3,1):=0$ deltaprimemodg(3,2):=0$ deltaprimemodg(5,2):=0$ deltaprimemodg(5,3):=k$ deltaprimemodg(6,1):=0$ deltaprimemodg(6,3):=k$ det(AUTOM):=k**12$ DELTAPRIMEMODADG:= [0 0 0 0 0 0] [ ] [0 0 0 0 0 0] [ ] [0 0 0 0 0 0] [ ] [0 0 0 0 0 0] [ ] [0 0 k 0 0 0] [ ] [0 0 k 0 0 0] With the second kind automorphism one gets$ shortformdeltaprimemodadg:={0, 0, ss, (( - bb(2,1)*bb(1,2)*xi(6,1) + bb(3,1))*bb(1,2))/bb(2,1), - bb(1,2), ss, (( - bb(2,1)*bb(1,2)*xi(5,2) + bb(3,2))*bb(2,1))/bb(1,2), - bb(2,1)}$ deltaprimemodg(3,1):=0$ deltaprimemodg(3,2):=0$ deltaprimemodg(5,2):=(( - bb(2,1)*bb(1,2)*xi(6,1) + bb(3,1))*bb(1,2))/bb(2,1)$ deltaprimemodg(5,3):= - bb(1,2)$ deltaprimemodg(6,1):=(( - bb(2,1)*bb(1,2)*xi(5,2) + bb(3,2))*bb(2,1))/bb(1,2)$ deltaprimemodg(6,3):= - bb(2,1)$ det(AUTOM):= - bb(2,1)**6*bb(1,2)**6$ DELTAPRIMEMODADG:= mat((0,0,0,0,0,0), (0,0,0,0,0,0), (0,0,0,0,0,0), (0,0,0,0,0,0), ( - bb(2,1)*bb(1,2)*xi(6,1) + bb(3,1))*bb(1,2) (0,------------------------------------------------, - bb(1,2),0,0,0), bb(2,1) ( - bb(2,1)*bb(1,2)*xi(5,2) + bb(3,2))*bb(2,1) (------------------------------------------------,0, - bb(2,1),0,0,0)) bb(1,2) We get no further reduction by using second kind automorphisms$ Hence, we are reduced in SUBCASE 1 to:$ shortformdeltaprime ={0,0,SS,0,1,SS,0,1}$ *********** SUBCASE 2 : xi(5,3):=0,xi(6,3):=1 ****************************$ xi(5,3):=0$ xi(6,3):=1$ clear b(1,1),b(2,2),b(3,1),b(3,2)$ With the first kind automorphism one gets$ shortformdeltaprimemodadg:={0, 0, ss, b(1,1)**2*xi(5,2), 0, ss, ( - ( - b(2,2)*b(1,1)*xi(6,1) + b(3,1))*b(2,2))/b(1,1), b(2,2)}$ deltaprimemodg(3,1):=0$ deltaprimemodg(3,2):=0$ deltaprimemodg(5,2):=b(1,1)**2*xi(5,2)$ deltaprimemodg(5,3):=0$ deltaprimemodg(6,1):=( - ( - b(2,2)*b(1,1)*xi(6,1) + b(3,1))*b(2,2))/b(1,1)$ deltaprimemodg(6,3):=b(2,2)$ det(AUTOM):=b(2,2)**6*b(1,1)**6$ DELTAPRIMEMODADG:= mat((0,0,0,0,0,0), (0,0,0,0,0,0), (0,0,0,0,0,0), (0,0,0,0,0,0), 2 (0,b(1,1) *xi(5,2),0,0,0,0), - ( - b(2,2)*b(1,1)*xi(6,1) + b(3,1))*b(2,2) (-----------------------------------------------,0,b(2,2),0,0,0)) b(1,1) With the second kind automorphism one gets$ shortformdeltaprimemodadg:={0, 0, ss, (( - bb(2,1)*bb(1,2)*xi(6,1) + bb(3,1))*bb(1,2))/bb(2,1), - bb(1,2), ss, - bb(2,1)**2*xi(5,2), 0}$ deltaprimemodg(3,1):=0$ deltaprimemodg(3,2):=0$ deltaprimemodg(5,2):=(( - bb(2,1)*bb(1,2)*xi(6,1) + bb(3,1))*bb(1,2))/bb(2,1)$ deltaprimemodg(5,3):= - bb(1,2)$ deltaprimemodg(6,1):= - bb(2,1)**2*xi(5,2)$ deltaprimemodg(6,3):=0$ det(AUTOM):= - bb(2,1)**6*bb(1,2)**6$ DELTAPRIMEMODADG:= mat((0,0,0,0,0,0), (0,0,0,0,0,0), (0,0,0,0,0,0), (0,0,0,0,0,0), ( - bb(2,1)*bb(1,2)*xi(6,1) + bb(3,1))*bb(1,2) (0,------------------------------------------------, - bb(1,2),0,0,0), bb(2,1) 2 ( - bb(2,1) *xi(5,2),0,0,0,0,0)) To keep xi(6,3):=k , one has to take:$ b(2,2):=k$ Second kind automorphism are of no use since they permute xi(5,3) and xi(6,3)$ With the first kind automorphism one gets$ shortformdeltaprimemodadg:={0, 0, ss, b(1,1)**2*xi(5,2), 0, ss, ( - ( - b(1,1)*xi(6,1)*k + b(3,1))*k)/b(1,1), k}$ deltaprimemodg(3,1):=0$ deltaprimemodg(3,2):=0$ deltaprimemodg(5,2):=b(1,1)**2*xi(5,2)$ deltaprimemodg(5,3):=0$ deltaprimemodg(6,1):=( - ( - b(1,1)*xi(6,1)*k + b(3,1))*k)/b(1,1)$ deltaprimemodg(6,3):=k$ det(AUTOM):=b(1,1)**6*k**6$ DELTAPRIMEMODADG:= [ 0 0 0 0 0 0] [ ] [ 0 0 0 0 0 0] [ ] [ 0 0 0 0 0 0] [ ] [ 0 0 0 0 0 0] [ ] [ 2 ] [ 0 b(1,1) *xi(5,2) 0 0 0 0] [ ] [ - ( - b(1,1)*xi(6,1)*k + b(3,1))*k ] [------------------------------------- 0 k 0 0 0] [ b(1,1) ] One then gets xi(6,1)=0 by taking:$ b(3,1):=b(1,1)*xi(6,1)*k$ With the first kind automorphism one gets$ shortformdeltaprimemodadg:={0, 0, ss, b(1,1)**2*xi(5,2), 0, ss, 0, k}$ deltaprimemodg(3,1):=0$ deltaprimemodg(3,2):=0$ deltaprimemodg(5,2):=b(1,1)**2*xi(5,2)$ deltaprimemodg(5,3):=0$ deltaprimemodg(6,1):=0$ deltaprimemodg(6,3):=k$ det(AUTOM):=b(1,1)**6*k**6$ DELTAPRIMEMODADG:= [0 0 0 0 0 0] [ ] [0 0 0 0 0 0] [ ] [0 0 0 0 0 0] [ ] [0 0 0 0 0 0] [ ] [ 2 ] [0 b(1,1) *xi(5,2) 0 0 0 0] [ ] [0 0 k 0 0 0] Hence, we are reduced in SUBCASE 2 to:$ shortformdeltaprime ={0,0,SS,epsilon,0,SS,0,1}$ with epsilon =xi(5,2)=0,1.$ *********** SUBCASE 3 : xi(5,3):=0,xi(6,3):=0 ****************************$ xi(5,3):=0$ xi(6,3):=0$ clear b(2,2),b(3,1)$ With the first kind automorphism one gets$ shortformdeltaprimemodadg:={0, 0, ss, b(1,1)**2*xi(5,2), 0, ss, b(2,2)**2*xi(6,1), 0}$ deltaprimemodg(3,1):=0$ deltaprimemodg(3,2):=0$ deltaprimemodg(5,2):=b(1,1)**2*xi(5,2)$ deltaprimemodg(5,3):=0$ deltaprimemodg(6,1):=b(2,2)**2*xi(6,1)$ deltaprimemodg(6,3):=0$ det(AUTOM):=b(2,2)**6*b(1,1)**6$ DELTAPRIMEMODADG:= [ 0 0 0 0 0 0] [ ] [ 0 0 0 0 0 0] [ ] [ 0 0 0 0 0 0] [ ] [ 0 0 0 0 0 0] [ ] [ 2 ] [ 0 b(1,1) *xi(5,2) 0 0 0 0] [ ] [ 2 ] [b(2,2) *xi(6,1) 0 0 0 0 0] With the second kind automorphism one gets$ shortformdeltaprimemodadg:={0, 0, ss, - bb(1,2)**2*xi(6,1), 0, ss, - bb(2,1)**2*xi(5,2), 0}$ deltaprimemodg(3,1):=0$ deltaprimemodg(3,2):=0$ deltaprimemodg(5,2):= - bb(1,2)**2*xi(6,1)$ deltaprimemodg(5,3):=0$ deltaprimemodg(6,1):= - bb(2,1)**2*xi(5,2)$ deltaprimemodg(6,3):=0$ det(AUTOM):= - bb(2,1)**6*bb(1,2)**6$ DELTAPRIMEMODADG:= [ 0 0 0 0 0 0] [ ] [ 0 0 0 0 0 0] [ ] [ 0 0 0 0 0 0] [ ] [ 0 0 0 0 0 0] [ ] [ 2 ] [ 0 - bb(1,2) *xi(6,1) 0 0 0 0] [ ] [ 2 ] [ - bb(2,1) *xi(5,2) 0 0 0 0 0] Hence, we are reduced in SUBCASE 3 to:$ shortformdeltaprime ={0,0,SS,epsilon,0,SS,eta,0}$ with epsilon =xi(5,2)=0,1 and eta =xi(6,1) =0,1 not both zero$ and {0,0,SS,1,0,SS,0,0} and {0,0,SS,0,0,SS,1,0} are projectively equivalent$ under some second kind automorphism$ Finally, we are reduced in SUBCASE 3 to:$ {0,0,SS,1,0,SS,1,0} or {0,0,SS,0,0,SS,1,0}.$