The generic automorphism phi of g_{6,13} as computed by calculautom6_13.red : phi:= mat((b(1,1),0,0,0,0,0), (b(2,1),b(2,2),0,0,0,0), 2 (0,0,b(1,1) ,0,0,0), (b(4,1),b(4,2), - b(2,1)*b(1,1),b(2,2)*b(1,1),0,0), 2 (b(5,1),b(5,2), - b(4,1)*b(1,1),b(4,2)*b(1,1),b(2,2)*b(1,1) ,0), 2 3 (b(6,1),b(6,2),b(6,3),b(5,2)*b(1,1),b(4,2)*b(1,1) ,b(2,2)*b(1,1) )) 4 9 det(phi):=b(2,2) *b(1,1) generic derivation : delta:= mat((xi(1,1),0,0,0,0,0), (xi(2,1),xi(2,2),0,0,0,0), (0,0,2*xi(1,1),0,0,0), (xi(4,1),xi(4,2), - xi(2,1),xi(1,1) + xi(2,2),0,0), (xi(5,1),xi(5,2), - xi(4,1),xi(4,2),2*xi(1,1) + xi(2,2),0), (xi(6,1),xi(6,2),xi(6,3),xi(5,2),xi(4,2),3*xi(1,1) + 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 1 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 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 0] adx3 := [ ] [0 0 0 0 0 0] [ ] [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] adx4 := [ ] [0 0 0 0 0 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] adx5 := [ ] [0 0 0 0 0 0] [ ] [0 0 0 0 0 0] [ ] [-1 0 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(5,2):=0,xi(6,1):=0 delta:= [ 0 0 0 0 0 0] [ ] [xi(2,1) 0 0 0 0 0] [ ] [ 0 0 0 0 0 0] [ ] [ 0 0 - xi(2,1) 0 0 0] [ ] [ 0 0 0 0 0 0] [ ] [ 0 xi(6,2) xi(6,3) 0 0 0] We denote this delta by the shortform shortformdelta:={xi(2,1), ss, xi(6,2), ss, xi(6,3)} paramindexeslist:={{2,1},{6,2},{6,3}} With the generic automorphism one gets$ shortformdeltaprimemodadg:={(b(2,2)*xi(2,1))/b(1,1), ss, b(1,1)**3*xi(6,2), ss, b(2,2)*b(1,1)*xi(6,3)}$ deltaprimemodg(2,1):=(b(2,2)*xi(2,1))/b(1,1)$ deltaprimemodg(6,2):=b(1,1)**3*xi(6,2)$ deltaprimemodg(6,3):=b(2,2)*b(1,1)*xi(6,3)$ det(AUTOM):=b(2,2)**4*b(1,1)**9$ DELTAPRIMEMODADG:= [ 0 0 0 0 0 0] [ ] [ b(2,2)*xi(2,1) ] [---------------- 0 0 0 0 0] [ b(1,1) ] [ ] [ 0 0 0 0 0 0] [ ] [ - b(2,2)*xi(2,1) ] [ 0 0 ------------------- 0 0 0] [ b(1,1) ] [ ] [ 0 0 0 0 0 0] [ ] [ 3 ] [ 0 b(1,1) *xi(6,2) b(2,2)*b(1,1)*xi(6,3) 0 0 0] ****************** CASE 2 : xi(2,1) = 0 *************************$ xi(2,1):=0$ With the generic automorphism one gets$ shortformdeltaprimemodadg:={0, ss, b(1,1)**3*xi(6,2), ss, b(2,2)*b(1,1)*xi(6,3)}$ deltaprimemodg(2,1):=0$ deltaprimemodg(6,2):=b(1,1)**3*xi(6,2)$ deltaprimemodg(6,3):=b(2,2)*b(1,1)*xi(6,3)$ det(AUTOM):=b(2,2)**4*b(1,1)**9$ 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 0 0 0 0] [ ] [ 3 ] [0 b(1,1) *xi(6,2) b(2,2)*b(1,1)*xi(6,3) 0 0 0] ****************** SUBCASE 2.1 : xi(6,2) NEQ 0 *************************$ Then one may suppose xi(6,2):=1.$ xi(6,2):=1$ Then one keeps deltaprimemodg(6,2)=k by taking :$ b(1,1):=k**(1/3)$ With the generic automorphism one gets$ shortformdeltaprimemodadg:={0, ss, k, ss, (b(2,2)*xi(6,3)*k)/k**(2/3)}$ deltaprimemodg(2,1):=0$ deltaprimemodg(6,2):=k$ deltaprimemodg(6,3):=(b(2,2)*xi(6,3)*k)/k**(2/3)$ det(AUTOM):=b(2,2)**4*k**3$ 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 0 0 0 0] [ ] [ b(2,2)*xi(6,3)*k ] [0 k ------------------ 0 0 0] [ 2/3 ] [ k ] Then if xi(6,3) neq 0, one gets deltaprimemodg(6,3)=k by taking:$ b(2,2):=k**(2/3)/xi(6,3)$ With the generic automorphism one gets$ shortformdeltaprimemodadg:={0,ss,k,ss,k}$ deltaprimemodg(2,1):=0$ deltaprimemodg(6,2):=k$ deltaprimemodg(6,3):=k$ det(AUTOM):=(k**(2/3)*k**5)/xi(6,3)**4$ 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 0 0 0 0] [ ] [0 k k 0 0 0] Hence, we are reduced in the subcase 2.1 under consideration to:$ shortformdeltaprime ={0,SS,1,SS,epsilon}$ where epsilon=xi(6,3) =0,1.$ ****************** SUBCASE 2.2 : xi(6,2) = 0 *************************$ clear b(1,1),b(2,2)$ xi(6,2):=0$ !In! that! case! we! necessarily! have! xi(6,3)! !N!E!Q! 0,! hence! one! may! su ppose! xi(6,3):\ =1.$ Hence, we are reduced in the subcase 2.2 under consideration to:$ shortformdeltaprime ={0,SS,0,SS,1}.$