The generic automorphism phi of g_{6,17} as computed by calculautom6_17.red : phi:= mat((b(1,1),0,0,0,0,0), 3 (b(2,1),b(1,1) ,0,0,0,0), 4 (b(3,1),b(3,2),b(1,1) ,0,0,0), 5 (b(4,1),b(4,2),b(3,2)*b(1,1),b(1,1) ,0,0), 2 6 (b(5,1),b(5,2),b(4,2)*b(1,1),b(3,2)*b(1,1) ,b(1,1) ,0), 3 (b(6,1),b(6,2),b(5,2)*b(1,1) + b(3,2)*b(2,1) - b(3,1)*b(1,1) , 2 2 3 7 b(1,1) *(b(4,2) + b(2,1)*b(1,1) ),b(3,2)*b(1,1) ,b(1,1) )) 26 det(phi):=b(1,1) generic derivation : delta:= [xi(1,1) 0 0 0 0 0 ] [ ] [xi(2,1) 3*xi(1,1) 0 0 0 0 ] [ ] [xi(3,1) xi(3,2) 4*xi(1,1) 0 0 0 ] [ ] [xi(4,1) xi(4,2) xi(3,2) 5*xi(1,1) 0 0 ] [ ] [xi(5,1) xi(5,2) xi(4,2) xi(3,2) 6*xi(1,1) 0 ] [ ] [xi(6,1) xi(6,2) xi(5,2) - xi(3,1) xi(4,2) + xi(2,1) xi(3,2) 7*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 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] [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 as in (Cohomology tables page 50) : the eigen\ values are 0 by subtracting adjoints one then may suppose xi(3,1)=xi(3,2)=xi(4,1)=xi(5,1)=x\ i(6,1)=0 phi:= mat((b(1,1),0,0,0,0,0), 3 (b(2,1),b(1,1) ,0,0,0,0), 4 (b(3,1),b(3,2),b(1,1) ,0,0,0), 5 (b(4,1),b(4,2),b(3,2)*b(1,1),b(1,1) ,0,0), 2 6 (b(5,1),b(5,2),b(4,2)*b(1,1),b(3,2)*b(1,1) ,b(1,1) ,0), 3 (b(6,1),b(6,2),b(3,2)*b(2,1) - b(3,1)*b(1,1) + b(5,2)*b(1,1), 2 2 3 7 (b(4,2) + b(2,1)*b(1,1) )*b(1,1) ,b(3,2)*b(1,1) ,b(1,1) )) 26 det(phi):=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] [ ] [ 0 xi(6,2) xi(5,2) xi(4,2) + 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(6,2)} paramindexeslist:={{2,1},{4,2},{5,2},{6,2}} shortformdeltaprimemodadg:={b(1,1)**2*xi(2,1), ss, b(1,1)**2*xi(4,2), ss, b(1,1)**3*xi(5,2), ss, ( - (2*b(4,2)*b(1,1)**3*xi(2,1) - b(3,2)**2*xi(2,1) - 2*b(2,1)*b(1,1)**5*xi(4,2) - b(1,1)**8*xi(6,2)))/b(1,1)**4}$ deltaprimemodg(2,1):=b(1,1)**2*xi(2,1)$ deltaprimemodg(4,2):=b(1,1)**2*xi(4,2)$ deltaprimemodg(5,2):=b(1,1)**3*xi(5,2)$ deltaprimemodg(6,2):=( - (2*b(4,2)*b(1,1)**3*xi(2,1) - b(3,2)**2*xi(2,1) - 2*b(2 ,1)*b(1,1)**5*xi(4,2) - b(1,1)**8*xi(6,2)))/b(1,1)**4$ det(phi):=b(1,1)**26$ DELTAPRIMEMODADG:= mat((0,0,0,0,0,0), 2 (b(1,1) *xi(2,1),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), 3 2 (0,( - (2*b(4,2)*b(1,1) *xi(2,1) - b(3,2) *xi(2,1) 5 8 4 - 2*b(2,1)*b(1,1) *xi(4,2) - b(1,1) *xi(6,2)))/b(1,1) , 3 2 b(1,1) *xi(5,2),(xi(4,2) + xi(2,1))*b(1,1) ,0,0)) ********* Suppose that xi(2,1) = 0.$ xi(2,1):=0$ SUBSUBCASE I : **************** Suppose xi(4,2) NEQ 0$ Then on may suppose xi(4,2):=1$ xi(4,2):=1$ Then one keeps deltaprimemodg(4,2)=k by taking:$ b(1,1):=sqrt(k)$ shortformdeltaprimemodadg:={0, ss, k, ss, (xi(5,2)*k**2)/sqrt(k), ss, ((b(2,1) + sqrt(k)*xi(6,2)*k + b(2,1))*k)/sqrt(k)}$ deltaprimemodg(2,1):=0$ deltaprimemodg(4,2):=k$ deltaprimemodg(5,2):=(xi(5,2)*k**2)/sqrt(k)$ deltaprimemodg(6,2):=((b(2,1) + sqrt(k)*xi(6,2)*k + b(2,1))*k)/sqrt(k)$ det(phi):=k**13$ DELTAPRIMEMODADG:= [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(5,2)*k ] [0 ------------ k 0 0 0] [ sqrt(k) ] [ ] [ (b(2,1) + sqrt(k)*xi(6,2)*k + b(2,1))*k ] [0 ----------------------------------------- sqrt(k)*xi(5,2)*k k 0 0] [ sqrt(k) ] One gets deltaprimemodg(6,2)=0 by taking:$ b(2,1):=( - sqrt(k)*xi(6,2)*k)/2$ shortformdeltaprimemodadg:={0, ss, k, ss, (xi(5,2)*k**2)/sqrt(k), ss, 0}$ deltaprimemodg(2,1):=0$ deltaprimemodg(4,2):=k$ deltaprimemodg(5,2):=(xi(5,2)*k**2)/sqrt(k)$ deltaprimemodg(6,2):=0$ det(phi):=k**13$ DELTAPRIMEMODADG:= [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(5,2)*k ] [0 ------------ k 0 0 0] [ sqrt(k) ] [ ] [0 0 sqrt(k)*xi(5,2)*k k 0 0] If xi(5,2) neq 0$ Then we get deltaprimemodg(5,2)=k by taking for k$ k:=1/xi(5,2)**2$ shortformdeltaprimemodadg:={0, ss, 1/xi(5,2)**2, ss, 1/xi(5,2)**2, ss, 0}$ deltaprimemodg(2,1):=0$ deltaprimemodg(4,2):=1/xi(5,2)**2$ deltaprimemodg(5,2):=1/xi(5,2)**2$ deltaprimemodg(6,2):=0$ det(phi):=1/xi(5,2)**26$ DELTAPRIMEMODADG:= [0 0 0 0 0 0] [ ] [0 0 0 0 0 0] [ ] [0 0 0 0 0 0] [ ] [ 1 ] [0 ---------- 0 0 0 0] [ 2 ] [ xi(5,2) ] [ ] [ 1 1 ] [0 ---------- ---------- 0 0 0] [ 2 2 ] [ xi(5,2) xi(5,2) ] [ ] [ 1 1 ] [0 0 ---------- ---------- 0 0] [ 2 2 ] [ xi(5,2) xi(5,2) ] Hence, we are reduced to:$ shortformdeltaprime ={0,SS,1,SS,epsilon,SS,0}$ where epsilon=xi(5,2):= 0,1$ SUBSUBCASE II : **************** Suppose xi(4,2) = 0$ xi(4,2):=0$ clear b(1,1),b(2,1),k$ shortformdeltaprimemodadg:={0, ss, 0, ss, b(1,1)**3*xi(5,2), ss, b(1,1)**4*xi(6,2)}$ deltaprimemodg(2,1):=0$ 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(phi):=b(1,1)**26$ 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] If xi(5,2) neq 0$ Then on may suppose xi(5,2):=1$ xi(5,2):=1$ Then one keeps deltaprimemodg(5,2)=k by taking:$ b(1,1):=k**(1/3)$ shortformdeltaprimemodadg:={0, ss, 0, ss, k, ss, k**(1/3)*xi(6,2)*k}$ deltaprimemodg(2,1):=0$ deltaprimemodg(4,2):=0$ deltaprimemodg(5,2):=k$ deltaprimemodg(6,2):=k**(1/3)*xi(6,2)*k$ det(phi):=k**(2/3)*k**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] [ ] [0 k 0 0 0 0] [ ] [ 1/3 ] [0 k *xi(6,2)*k k 0 0 0] Then If xi(6,2) neq 0 we get deltaprimemodg(6,2)=k by taking for k$ k:=1/xi(6,2)**3$ shortformdeltaprimemodadg:={0, ss, 0, ss, 1/xi(6,2)**3, ss, 1/xi(6,2)**3}$ deltaprimemodg(2,1):=0$ deltaprimemodg(4,2):=0$ deltaprimemodg(5,2):=1/xi(6,2)**3$ deltaprimemodg(6,2):=1/xi(6,2)**3$ det(phi):=1/xi(6,2)**26$ 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 if xi(4,2)=0 and xi(5,2) neq 0$ we are reduced to:$ shortformdeltaprime ={0,SS,0,SS,1,SS,epsilon}$ where epsilon=xi(6,2):= 0,1$ Finally if xi(4,2)=xi(5,2) neq 0$ xi(5,2):=0$ clear b(1,1),k$ shortformdeltaprimemodadg:={0, ss, 0, ss, 0, ss, b(1,1)**4*xi(6,2)}$ deltaprimemodg(2,1):=0$ deltaprimemodg(4,2):=0$ deltaprimemodg(5,2):=0$ deltaprimemodg(6,2):=b(1,1)**4*xi(6,2)$ det(phi):=b(1,1)**26$ 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] [ ] [ 4 ] [0 b(1,1) *xi(6,2) 0 0 0 0] we are reduced to:$ shortformdeltaprime ={0,SS,0,SS,0,SS,1}$