The generic automorphism phi of g_{6,14} as computed by calculautom6_14.red : phi:= mat((b(1,1),0,0,0,0,0), (b(2,1),b(2,2),0,0,0,0), (b(3,1),b(3,2),b(2,2)*b(1,1),0,0,0), 2 (b(4,1),b(4,2),b(3,2)*b(1,1),b(2,2)*b(1,1) ,0,0), 2 3 (b(5,1),b(5,2),b(4,2)*b(1,1),b(3,2)*b(1,1) ,b(2,2)*b(1,1) ,0), (b(6,1),b(6,2), - b(3,1)*b(2,2) + b(3,2)*b(2,1),b(2,2)*b(2,1)*b(1,1),0, 2 b(2,2) *b(1,1))) 6 8 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), (xi(3,1),xi(3,2),xi(1,1) + xi(2,2),0,0,0), (xi(4,1),xi(4,2),xi(3,2),2*xi(1,1) + xi(2,2),0,0), (xi(5,1),xi(5,2),xi(4,2),xi(3,2),3*xi(1,1) + xi(2,2),0), (xi(6,1),xi(6,2), - xi(3,1),xi(2,1),0,xi(1,1) + 2*xi(2,2))) [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 0 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 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] adx3 := [ ] [-1 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 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(3,1):=0,xi(3,2):=0,xi(4,1):=0,xi(5,1):=0 phi:= mat((b(1,1),0,0,0,0,0), (b(2,1),b(2,2),0,0,0,0), (b(3,1),b(3,2),b(2,2)*b(1,1),0,0,0), 2 (b(4,1),b(4,2),b(3,2)*b(1,1),b(2,2)*b(1,1) ,0,0), 2 3 (b(5,1),b(5,2),b(4,2)*b(1,1),b(3,2)*b(1,1) ,b(2,2)*b(1,1) ,0), (b(6,1),b(6,2), - b(3,1)*b(2,2) + b(3,2)*b(2,1),b(2,2)*b(2,1)*b(1,1),0, 2 b(2,2) *b(1,1))) 6 8 det(phi):=b(2,2) *b(1,1) delta:= [ 0 0 0 0 0 0] [ ] [xi(2,1) 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] [ ] [xi(6,1) xi(6,2) 0 xi(2,1) 0 0] We denote this delta by the shortform shortformdelta:={xi(2,1), ss, xi(4,2), ss, xi(5,2), ss, xi(6,1), xi(6,2)} paramindexeslist:={{2,1},{4,2},{5,2},{6,1},{6,2}} shortformdeltaprimemodadg:={(b(2,2)*xi(2,1))/b(1,1), ss, b(1,1)**2*xi(4,2), ss, b(1,1)**3*xi(5,2), ss, ( - b(2,2)*b(2,1)**2*b(1,1)**2*xi(4,2) - b(2,2)**2*b(2,1)*b(1,1)**2*xi(6,2) + b( 2,2)**3*b(1,1)**2*xi(6,1) + b(3,2)*b(3,1)*b(2,2)*xi(2,1) - b(3,2)**2*b(2,1)*xi(2 ,1) - b(4,1)*b(2,2)**2*xi(2,1) + b(4,2)*b(2,2)*b(2,1)*xi(2,1) + b(6,2)*b(2,2)*b( 1,1)*xi(2,1))/(b(2,2)*b(1,1)**2), (2*b(2,2)*b(2,1)*b(1,1)**2*xi(4,2) + b(2,2)**2*b(1,1)**2*xi(6,2) + b(3,2)**2*xi( 2,1) - 2*b(4,2)*b(2,2)*xi(2,1))/(b(2,2)*b(1,1))}$ deltaprimemodg(2,1):=(b(2,2)*xi(2,1))/b(1,1)$ deltaprimemodg(4,2):=b(1,1)**2*xi(4,2)$ deltaprimemodg(5,2):=b(1,1)**3*xi(5,2)$ deltaprimemodg(6,1):=( - b(2,2)*b(2,1)**2*b(1,1)**2*xi(4,2) - b(2,2)**2*b(2,1)*b (1,1)**2*xi(6,2) + b(2,2)**3*b(1,1)**2*xi(6,1) + b(3,2)*b(3,1)*b(2,2)*xi(2,1) - b(3,2)**2*b(2,1)*xi(2,1) - b(4,1)*b(2,2)**2*xi(2,1) + b(4,2)*b(2,2)*b(2,1)*xi(2, 1) + b(6,2)*b(2,2)*b(1,1)*xi(2,1))/(b(2,2)*b(1,1)**2)$ deltaprimemodg(6,2):=(2*b(2,2)*b(2,1)*b(1,1)**2*xi(4,2) + b(2,2)**2*b(1,1)**2*xi (6,2) + b(3,2)**2*xi(2,1) - 2*b(4,2)*b(2,2)*xi(2,1))/(b(2,2)*b(1,1))$ det(AUTOM):=b(2,2)**6*b(1,1)**8$ DELTAPRIMEMODADG:= mat((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), 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), 2 2 2 2 (( - b(2,2)*b(2,1) *b(1,1) *xi(4,2) - b(2,2) *b(2,1)*b(1,1) *xi(6,2) 3 2 + b(2,2) *b(1,1) *xi(6,1) + b(3,2)*b(3,1)*b(2,2)*xi(2,1) 2 2 - b(3,2) *b(2,1)*xi(2,1) - b(4,1)*b(2,2) *xi(2,1) + b(4,2)*b(2,2)*b(2,1)*xi(2,1) + b(6,2)*b(2,2)*b(1,1)*xi(2,1))/(b(2,2) 2 2 2 2 *b(1,1) ),(2*b(2,2)*b(2,1)*b(1,1) *xi(4,2) + b(2,2) *b(1,1) *xi(6,2) 2 + b(3,2) *xi(2,1) - 2*b(4,2)*b(2,2)*xi(2,1))/(b(2,2) b(2,2)*xi(2,1) *b(1,1)),0,----------------,0,0)) b(1,1) ************ SUBCASE 2 : we suppose xi(2,1) = 0 *********************$ xi(2,1):=0$ shortformdeltaprimemodadg:={0, ss, b(1,1)**2*xi(4,2), ss, b(1,1)**3*xi(5,2), ss, - b(2,1)**2*xi(4,2) + ( - b(2,1)*xi(6,2) + b(2,2)*xi(6,1))*b(2,2), (2*b(2,1)*xi(4,2) + b(2,2)*xi(6,2))*b(1,1)}$ deltaprimemodg(2,1):=0$ deltaprimemodg(4,2):=b(1,1)**2*xi(4,2)$ deltaprimemodg(5,2):=b(1,1)**3*xi(5,2)$ deltaprimemodg(6,1):= - b(2,1)**2*xi(4,2) + ( - b(2,1)*xi(6,2) + b(2,2)*xi(6,1)) *b(2,2)$ deltaprimemodg(6,2):=(2*b(2,1)*xi(4,2) + b(2,2)*xi(6,2))*b(1,1)$ det(AUTOM):=b(2,2)**6*b(1,1)**8$ DELTAPRIMEMODADG:= mat((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), 2 ( - b(2,1) *xi(4,2) + ( - b(2,1)*xi(6,2) + b(2,2)*xi(6,1))*b(2,2), (2*b(2,1)*xi(4,2) + b(2,2)*xi(6,2))*b(1,1),0,0,0,0)) ******** SUBSUBCASE 2.2 : we suppose xi(4,2) = 0 *********************$ xi(4,2):=0$ shortformdeltaprimemodadg:={0, ss, 0, ss, b(1,1)**3*xi(5,2), ss, ( - b(2,1)*xi(6,2) + b(2,2)*xi(6,1))*b(2,2), b(2,2)*b(1,1)*xi(6,2)}$ deltaprimemodg(2,1):=0$ deltaprimemodg(4,2):=0$ deltaprimemodg(5,2):=b(1,1)**3*xi(5,2)$ deltaprimemodg(6,1):=( - b(2,1)*xi(6,2) + b(2,2)*xi(6,1))*b(2,2)$ deltaprimemodg(6,2):=b(2,2)*b(1,1)*xi(6,2)$ det(AUTOM):=b(2,2)**6*b(1,1)**8$ 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] [ ] [( - b(2,1)*xi(6,2) + b(2,2)*xi(6,1))*b(2,2) b(2,2)*b(1,1)*xi(6,2) 0 0 0 0] Then , if xi(6,2) NEQ 0 one gets deltaprimemodg(6,2):=k by taking for :$ b(2,2):=k/(b(1,1)*xi(6,2))$ and one gets deltaprime(6,1):=0 by taking :$ b(2,1):=(xi(6,1)*k)/(b(1,1)*xi(6,2)**2)$ shortformdeltaprimemodadg:={0, ss, 0, ss, b(1,1)**3*xi(5,2), ss, 0, k}$ deltaprimemodg(2,1):=0$ deltaprimemodg(4,2):=0$ deltaprimemodg(5,2):=b(1,1)**3*xi(5,2)$ deltaprimemodg(6,1):=0$ deltaprimemodg(6,2):=k$ det(AUTOM):=(b(1,1)**2*k**6)/xi(6,2)**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] [ ] [ 3 ] [0 b(1,1) *xi(5,2) 0 0 0 0] [ ] [0 k 0 0 0 0] Hence, if xi(6,2) NEQ 0, we are reduced to:$ shortformdeltaprime ={0,SS,0,SS,epsilon,SS,0,1}.$ with epsilon=0,1=xi(5,2)$ Suppose now xi(6,2) = 0.$ xi(6,2):=0$ clear b(2,2),b(2,1)$ shortformdeltaprimemodadg:={0, ss, 0, ss, b(1,1)**3*xi(5,2), ss, b(2,2)**2*xi(6,1), 0}$ deltaprimemodg(2,1):=0$ deltaprimemodg(4,2):=0$ deltaprimemodg(5,2):=b(1,1)**3*xi(5,2)$ deltaprimemodg(6,1):=b(2,2)**2*xi(6,1)$ deltaprimemodg(6,2):=0$ det(AUTOM):=b(2,2)**6*b(1,1)**8$ 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] [ ] [ 2 ] [b(2,2) *xi(6,1) 0 0 0 0 0] Hence, if xi(6,2) = 0 and xi(5,2) NEQ 0, we are reduced to:$ shortformdeltaprime ={0,SS,0,SS,1,SS,epsilon,0}.$ with epsilon=0,1=xi(6,1)$ whereas! if! xi(6,2)! =! 0! and! xi(5,2)! =! 0,! ! we! necessarily! have! xi(6,1 )! !N!E!Q! 0! and\ ! are! reduced! to:$ shortformdeltaprime ={0,SS,0,SS,0,SS,1,0}.$ with epsilon=0,1=xi(6,1)$