The generic automorphism phi of g_{6,19} as computed by calculautom6_19.red : phi:= mat((b(1,1),0,0,0,0,0), 2 (0,b(1,1) ,0,0,0,0), 3 (b(3,1),b(3,2),b(1,1) ,0,0,0), 4 (b(4,1),b(4,2),b(3,2)*b(1,1),b(1,1) ,0,0), 2 5 (b(5,1),b(5,2),b(1,1)*( - b(3,1)*b(1,1) + b(4,2)),b(3,2)*b(1,1) ,b(1,1) ,0), (b(6,1),b(6,2),b(1,1)*( - b(4,1)*b(1,1) + b(5,2)), 2 3 6 b(1,1) *( - b(3,1)*b(1,1) + b(4,2)),b(3,2)*b(1,1) ,b(1,1) )) 21 det(phi):=b(1,1) generic derivation : delta:= mat((xi(1,1),0,0,0,0,0), (0,2*xi(1,1),0,0,0,0), (xi(3,1),xi(3,2),3*xi(1,1),0,0,0), (xi(4,1),xi(4,2),xi(3,2),4*xi(1,1),0,0), (xi(5,1),xi(5,2), - xi(3,1) + xi(4,2),xi(3,2),5*xi(1,1),0), (xi(6,1),xi(6,2), - xi(4,1) + xi(5,2), - xi(3,1) + xi(4,2),xi(3,2),6*xi(1,1) )) [0 0 0 0 0 0] [ ] [0 0 0 0 0 0] [ ] [0 1 0 0 0 0] adx1 := [ ] [0 0 1 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] [ ] [-1 0 0 0 0 0] adx2 := [ ] [0 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 0] adx3 := [ ] [-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 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] [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 by subtracting adjoints one then may suppose: xi(3,1):=0,xi(3,2):=0,xi(4,1):=0,xi(5,1):=0,xi(6,1):=0 delta:= [0 0 0 0 0 0] [ ] [0 0 0 0 0 0] [ ] [0 0 0 0 0 0] [ ] [0 xi(4,2) 0 0 0 0] [ ] [0 xi(5,2) xi(4,2) 0 0 0] [ ] [0 xi(6,2) xi(5,2) xi(4,2) 0 0] We denote this delta by the shortform shortformdelta:={xi(4,2), ss, xi(5,2), ss, xi(6,2)} paramindexeslist:={{4,2},{5,2},{6,2}} With the generic automorphism one gets$ shortformdeltaprimemodadg:={b(1,1)**2*xi(4,2), ss, b(1,1)**3*xi(5,2), ss, b(1,1)**4*xi(6,2)}$ deltaprimemodg(4,2):=b(1,1)**2*xi(4,2)$ deltaprimemodg(5,2):=b(1,1)**3*xi(5,2)$ deltaprimemodg(6,2):=b(1,1)**4*xi(6,2)$ det(AUTOM):=b(1,1)**21$ DELTAPRIMEMODADG:= [0 0 0 0 0 0] [ ] [0 0 0 0 0 0] [ ] [0 0 0 0 0 0] [ ] [ 2 ] [0 b(1,1) *xi(4,2) 0 0 0 0] [ ] [ 3 2 ] [0 b(1,1) *xi(5,2) b(1,1) *xi(4,2) 0 0 0] [ ] [ 4 3 2 ] [0 b(1,1) *xi(6,2) b(1,1) *xi(5,2) b(1,1) *xi(4,2) 0 0] ****************** CASE 2 : xi(4,2) = 0 *************************$ xi(4,2):=0$ With the generic automorphism one gets$ shortformdeltaprimemodadg:={0, ss, b(1,1)**3*xi(5,2), ss, b(1,1)**4*xi(6,2)}$ deltaprimemodg(4,2):=0$ deltaprimemodg(5,2):=b(1,1)**3*xi(5,2)$ deltaprimemodg(6,2):=b(1,1)**4*xi(6,2)$ det(AUTOM):=b(1,1)**21$ 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] [ ] [ 3 ] [0 b(1,1) *xi(5,2) 0 0 0 0] [ ] [ 4 3 ] [0 b(1,1) *xi(6,2) b(1,1) *xi(5,2) 0 0 0] ****************** SUBCASE 2.1 : xi(5,2) NEQ 0 *************************$ Then one may suppose xi(5,2):=1 and one keeps deltaprimemodg(2,2)=k by taking :$ xi(5,2):=1$ b(1,1):=k**(1/3)$ With the generic automorphism one gets$ shortformdeltaprimemodadg:={0, ss, k, ss, (xi(6,2)*k**2)/k**(2/3)}$ deltaprimemodg(4,2):=0$ deltaprimemodg(5,2):=k$ deltaprimemodg(6,2):=(xi(6,2)*k**2)/k**(2/3)$ det(AUTOM):=k**7$ 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 k 0 0 0 0] [ ] [ 2 ] [ xi(6,2)*k ] [0 ------------ k 0 0 0] [ 2/3 ] [ k ] In that case, if xi(6,2) neq 0, then one gets deltaprimemodg(6,2)=k by taking :$ k:=1/xi(6,2)**3$ With the generic automorphism one gets$ shortformdeltaprimemodadg:={0, ss, 1/xi(6,2)**3, ss, 1/xi(6,2)**3}$ deltaprimemodg(4,2):=0$ deltaprimemodg(5,2):=1/xi(6,2)**3$ deltaprimemodg(6,2):=1/xi(6,2)**3$ det(AUTOM):=1/xi(6,2)**21$ 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] [ ] [ 1 ] [0 ---------- 0 0 0 0] [ 3 ] [ xi(6,2) ] [ ] [ 1 1 ] [0 ---------- ---------- 0 0 0] [ 3 3 ] [ xi(6,2) xi(6,2) ] Hence, we are reduced in the subcase 2.1 under consideration to:$ shortformdeltaprime ={0,SS,1,SS,epsilon}$ where epsilon=xi(6,2) =0,1.$ ****************** SUBCASE 2.2 : xi(5,2) = 0 *************************$ clear b(1,1),k$ xi(5,2):=0$ !Then! as! delta! is! supposed! nonzero,! one! has! xi(6,2)! !N!E!Q! 0! and! we! may! suppose! xi\ (6,2):=1.! :$ Hence, we are reduced in the subcase 2.2 under consideration to:$ shortformdeltaprime ={0,SS,0,SS,1}$