The generic automorphism phi of C x g_{5,4} as computed by calculautom6_54xC.r\ ed : phi:= mat((b(1,1),b(1,2),0,0,0,0), (b(2,1),b(2,2),0,0,0,0), (b(3,1),b(3,2), - b(2,1)*b(1,2) + b(2,2)*b(1,1),0,0,0), (b(4,1),b(4,2), - b(3,1)*b(1,2) + b(3,2)*b(1,1), b(1,1)*( - b(2,1)*b(1,2) + b(2,2)*b(1,1)), b(1,2)*( - b(2,1)*b(1,2) + b(2,2)*b(1,1)),b(4,6)), (b(5,1),b(5,2), - b(3,1)*b(2,2) + b(3,2)*b(2,1), b(2,1)*( - b(2,1)*b(1,2) + b(2,2)*b(1,1)), b(2,2)*( - b(2,1)*b(1,2) + b(2,2)*b(1,1)),b(5,6)), (b(6,1),b(6,2),0,0,0,b(6,6))) 5 det(phi):=( - b(2,1)*b(1,2) + b(2,2)*b(1,1)) *b(6,6) generic derivation : delta:= mat((xi(1,1),xi(1,2),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),xi(1,2),xi(4,6)), (xi(5,1),xi(5,2), - xi(3,1),xi(2,1),xi(1,1) + 2*xi(2,2),xi(5,6)), (xi(6,1),xi(6,2),0,0,0,xi(6,6))) [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 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] adx2 := [ ] [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 0 0 0 0 0] adx3 := [ ] [-1 0 0 0 0 0] [ ] [0 -1 0 0 0 0] [ ] [0 0 0 0 0 0] The generic nilpotent derivation : the eigenvalues are 0 xi(6,6):=0 And the matrix A:=(xi(1,1),xi(1,2)),(xi(2,1),xi(2,2)) is nilpotent We hence get 2 cases acoording to whether A neq 0 or A=0. We consider here the case 2 where A = 0. xi(1,1):=0,xi(1,2):=1,xi(2,1):=0,xi(2,2):=0 by subtracting adjoints one then may suppose: xi(3,1):=0,xi(3,2):=0,xi(4,1):=0 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 xi(4,6)] [ ] [xi(5,1) xi(5,2) 0 0 0 xi(5,6)] [ ] [xi(6,1) xi(6,2) 0 0 0 0 ] We denote this delta by the shortform shortformdelta:={xi(4,2), xi(4,6), ss, xi(5,1), xi(5,2), xi(5,6), ss, xi(6,1), xi(6,2)} paramindexeslist:={{4,2},{4,6},{5,1},{5,2},{5,6},{6,1},{6,2}} With the first kind automorphism one gets$ shortformdeltaprimemodadg:={( - b(6,1)*b(2,1)*b(1,2)**2*b(1,1)*xi(4,6) - b(6,1)* b(2,1)*b(1,2)**3*xi(5,6) + b(6,1)*b(2,2)*b(1,2)*b(1,1)**2*xi(4,6) + b(6,1)*b(2,2 )*b(1,2)**2*b(1,1)*xi(5,6) + b(6,2)*b(2,1)*b(1,2)*b(1,1)**2*xi(4,6) + b(6,2)*b(2 ,1)*b(1,2)**2*b(1,1)*xi(5,6) - b(6,2)*b(2,2)*b(1,1)**3*xi(4,6) - b(6,2)*b(2,2)*b (1,2)*b(1,1)**2*xi(5,6) - b(6,6)*b(2,1)*b(1,2)*b(1,1)**2*xi(4,2) - b(6,6)*b(2,1) *b(1,2)**2*b(1,1)*xi(5,2) + b(6,6)*b(2,1)*b(1,2)**3*xi(5,1) + b(6,6)*b(2,2)*b(1, 1)**3*xi(4,2) + b(6,6)*b(2,2)*b(1,2)*b(1,1)**2*xi(5,2) - b(6,6)*b(2,2)*b(1,2)**2 *b(1,1)*xi(5,1) + b(6,6)*b(4,6)*b(1,1)*xi(6,2) - b(6,6)*b(4,6)*b(1,2)*xi(6,1))/( b(6,6)*( - b(2,1)*b(1,2) + b(2,2)*b(1,1))), ( - b(2,1)*b(1,2)*b(1,1)*xi(4,6) - b(2,1)*b(1,2)**2*xi(5,6) + b(2,2)*b(1,1)**2* xi(4,6) + b(2,2)*b(1,2)*b(1,1)*xi(5,6))/b(6,6), ss, (b(6,1)*b(2,2)*b(2,1)**2*b(1,2)*xi(4,6) - b(6,1)*b(2,2)**2*b(2,1)*b(1,1)*xi(4,6) + b(6,1)*b(2,2)**2*b(2,1)*b(1,2)*xi(5,6) - b(6,1)*b(2,2)**3*b(1,1)*xi(5,6) - b( 6,2)*b(2,1)**3*b(1,2)*xi(4,6) + b(6,2)*b(2,2)*b(2,1)**2*b(1,1)*xi(4,6) - b(6,2)* b(2,2)*b(2,1)**2*b(1,2)*xi(5,6) + b(6,2)*b(2,2)**2*b(2,1)*b(1,1)*xi(5,6) + b(6,6 )*b(2,1)**3*b(1,2)*xi(4,2) - b(6,6)*b(2,2)*b(2,1)**2*b(1,1)*xi(4,2) + b(6,6)*b(2 ,2)*b(2,1)**2*b(1,2)*xi(5,2) - b(6,6)*b(2,2)**2*b(2,1)*b(1,1)*xi(5,2) - b(6,6)*b (2,2)**2*b(2,1)*b(1,2)*xi(5,1) + b(6,6)*b(2,2)**3*b(1,1)*xi(5,1) - b(6,6)*b(5,6) *b(2,1)*xi(6,2) + b(6,6)*b(5,6)*b(2,2)*xi(6,1))/(b(6,6)*( - b(2,1)*b(1,2) + b(2, 2)*b(1,1))), ( - b(6,1)*b(2,1)**2*b(1,2)**2*xi(4,6) - 2*b(6,1)*b(2,2)*b(2,1)*b(1,2)**2*xi(5,6 ) + b(6,1)*b(2,2)**2*b(1,1)**2*xi(4,6) + 2*b(6,1)*b(2,2)**2*b(1,2)*b(1,1)*xi(5,6 ) + 2*b(6,2)*b(2,1)**2*b(1,2)*b(1,1)*xi(4,6) + b(6,2)*b(2,1)**2*b(1,2)**2*xi(5,6 ) - 2*b(6,2)*b(2,2)*b(2,1)*b(1,1)**2*xi(4,6) - b(6,2)*b(2,2)**2*b(1,1)**2*xi(5,6 ) - 2*b(6,6)*b(2,1)**2*b(1,2)*b(1,1)*xi(4,2) - b(6,6)*b(2,1)**2*b(1,2)**2*xi(5,2 ) + 2*b(6,6)*b(2,2)*b(2,1)*b(1,1)**2*xi(4,2) + 2*b(6,6)*b(2,2)*b(2,1)*b(1,2)**2* xi(5,1) + b(6,6)*b(2,2)**2*b(1,1)**2*xi(5,2) - 2*b(6,6)*b(2,2)**2*b(1,2)*b(1,1)* xi(5,1) + b(6,6)*b(4,6)*b(2,1)*xi(6,2) - b(6,6)*b(4,6)*b(2,2)*xi(6,1) + b(6,6)*b (5,6)*b(1,1)*xi(6,2) - b(6,6)*b(5,6)*b(1,2)*xi(6,1))/(b(6,6)*( - b(2,1)*b(1,2) + b(2,2)*b(1,1))), ( - b(2,1)**2*b(1,2)*xi(4,6) + b(2,2)*b(2,1)*b(1,1)*xi(4,6) - b(2,2)*b(2,1)*b(1, 2)*xi(5,6) + b(2,2)**2*b(1,1)*xi(5,6))/b(6,6), ss, (b(6,6)*( - b(2,1)*xi(6,2) + b(2,2)*xi(6,1)))/( - b(2,1)*b(1,2) + b(2,2)*b(1,1)) , (b(6,6)*(b(1,1)*xi(6,2) - b(1,2)*xi(6,1)))/( - b(2,1)*b(1,2) + b(2,2)*b(1,1))}$ deltaprimemodg(4,2):=( - b(6,1)*b(2,1)*b(1,2)**2*b(1,1)*xi(4,6) - b(6,1)*b(2,1)* b(1,2)**3*xi(5,6) + b(6,1)*b(2,2)*b(1,2)*b(1,1)**2*xi(4,6) + b(6,1)*b(2,2)*b(1,2 )**2*b(1,1)*xi(5,6) + b(6,2)*b(2,1)*b(1,2)*b(1,1)**2*xi(4,6) + b(6,2)*b(2,1)*b(1 ,2)**2*b(1,1)*xi(5,6) - b(6,2)*b(2,2)*b(1,1)**3*xi(4,6) - b(6,2)*b(2,2)*b(1,2)*b (1,1)**2*xi(5,6) - b(6,6)*b(2,1)*b(1,2)*b(1,1)**2*xi(4,2) - b(6,6)*b(2,1)*b(1,2) **2*b(1,1)*xi(5,2) + b(6,6)*b(2,1)*b(1,2)**3*xi(5,1) + b(6,6)*b(2,2)*b(1,1)**3* xi(4,2) + b(6,6)*b(2,2)*b(1,2)*b(1,1)**2*xi(5,2) - b(6,6)*b(2,2)*b(1,2)**2*b(1,1 )*xi(5,1) + b(6,6)*b(4,6)*b(1,1)*xi(6,2) - b(6,6)*b(4,6)*b(1,2)*xi(6,1))/(b(6,6) *( - b(2,1)*b(1,2) + b(2,2)*b(1,1)))$ deltaprimemodg(4,6):=( - b(2,1)*b(1,2)*b(1,1)*xi(4,6) - b(2,1)*b(1,2)**2*xi(5,6) + b(2,2)*b(1,1)**2*xi(4,6) + b(2,2)*b(1,2)*b(1,1)*xi(5,6))/b(6,6)$ deltaprimemodg(5,1):=(b(6,1)*b(2,2)*b(2,1)**2*b(1,2)*xi(4,6) - b(6,1)*b(2,2)**2* b(2,1)*b(1,1)*xi(4,6) + b(6,1)*b(2,2)**2*b(2,1)*b(1,2)*xi(5,6) - b(6,1)*b(2,2)** 3*b(1,1)*xi(5,6) - b(6,2)*b(2,1)**3*b(1,2)*xi(4,6) + b(6,2)*b(2,2)*b(2,1)**2*b(1 ,1)*xi(4,6) - b(6,2)*b(2,2)*b(2,1)**2*b(1,2)*xi(5,6) + b(6,2)*b(2,2)**2*b(2,1)*b (1,1)*xi(5,6) + b(6,6)*b(2,1)**3*b(1,2)*xi(4,2) - b(6,6)*b(2,2)*b(2,1)**2*b(1,1) *xi(4,2) + b(6,6)*b(2,2)*b(2,1)**2*b(1,2)*xi(5,2) - b(6,6)*b(2,2)**2*b(2,1)*b(1, 1)*xi(5,2) - b(6,6)*b(2,2)**2*b(2,1)*b(1,2)*xi(5,1) + b(6,6)*b(2,2)**3*b(1,1)*xi (5,1) - b(6,6)*b(5,6)*b(2,1)*xi(6,2) + b(6,6)*b(5,6)*b(2,2)*xi(6,1))/(b(6,6)*( - b(2,1)*b(1,2) + b(2,2)*b(1,1)))$ deltaprimemodg(5,2):=( - b(6,1)*b(2,1)**2*b(1,2)**2*xi(4,6) - 2*b(6,1)*b(2,2)*b( 2,1)*b(1,2)**2*xi(5,6) + b(6,1)*b(2,2)**2*b(1,1)**2*xi(4,6) + 2*b(6,1)*b(2,2)**2 *b(1,2)*b(1,1)*xi(5,6) + 2*b(6,2)*b(2,1)**2*b(1,2)*b(1,1)*xi(4,6) + b(6,2)*b(2,1 )**2*b(1,2)**2*xi(5,6) - 2*b(6,2)*b(2,2)*b(2,1)*b(1,1)**2*xi(4,6) - b(6,2)*b(2,2 )**2*b(1,1)**2*xi(5,6) - 2*b(6,6)*b(2,1)**2*b(1,2)*b(1,1)*xi(4,2) - b(6,6)*b(2,1 )**2*b(1,2)**2*xi(5,2) + 2*b(6,6)*b(2,2)*b(2,1)*b(1,1)**2*xi(4,2) + 2*b(6,6)*b(2 ,2)*b(2,1)*b(1,2)**2*xi(5,1) + b(6,6)*b(2,2)**2*b(1,1)**2*xi(5,2) - 2*b(6,6)*b(2 ,2)**2*b(1,2)*b(1,1)*xi(5,1) + b(6,6)*b(4,6)*b(2,1)*xi(6,2) - b(6,6)*b(4,6)*b(2, 2)*xi(6,1) + b(6,6)*b(5,6)*b(1,1)*xi(6,2) - b(6,6)*b(5,6)*b(1,2)*xi(6,1))/(b(6,6 )*( - b(2,1)*b(1,2) + b(2,2)*b(1,1)))$ deltaprimemodg(5,6):=( - b(2,1)**2*b(1,2)*xi(4,6) + b(2,2)*b(2,1)*b(1,1)*xi(4,6) - b(2,2)*b(2,1)*b(1,2)*xi(5,6) + b(2,2)**2*b(1,1)*xi(5,6))/b(6,6)$ deltaprimemodg(6,1):=(b(6,6)*( - b(2,1)*xi(6,2) + b(2,2)*xi(6,1)))/( - b(2,1)*b( 1,2) + b(2,2)*b(1,1))$ deltaprimemodg(6,2):=(b(6,6)*(b(1,1)*xi(6,2) - b(1,2)*xi(6,1)))/( - b(2,1)*b(1,2 ) + b(2,2)*b(1,1))$ det(AUTOM):=b(6,6)*( - b(2,1)**5*b(1,2)**5 + 5*b(2,2)*b(2,1)**4*b(1,2)**4*b(1,1) - 10*b(2,2)**2*b(2,1)**3*b(1,2)**3*b(1,1)**2 + 10*b(2,2)**3*b(2,1)**2*b(1,2)**2 *b(1,1)**3 - 5*b(2,2)**4*b(2,1)*b(1,2)*b(1,1)**4 + b(2,2)**5*b(1,1)**5)$ DELTAPRIMEMODADG:= mat((0,0,0,0,0,0), (0,0,0,0,0,0), (0,0,0,0,0,0), 2 3 (0,( - b(6,1)*b(2,1)*b(1,2) *b(1,1)*xi(4,6) - b(6,1)*b(2,1)*b(1,2) *xi(5,6) 2 + b(6,1)*b(2,2)*b(1,2)*b(1,1) *xi(4,6) 2 + b(6,1)*b(2,2)*b(1,2) *b(1,1)*xi(5,6) 2 + b(6,2)*b(2,1)*b(1,2)*b(1,1) *xi(4,6) 2 3 + b(6,2)*b(2,1)*b(1,2) *b(1,1)*xi(5,6) - b(6,2)*b(2,2)*b(1,1) *xi(4,6) 2 - b(6,2)*b(2,2)*b(1,2)*b(1,1) *xi(5,6) 2 - b(6,6)*b(2,1)*b(1,2)*b(1,1) *xi(4,2) 2 3 - b(6,6)*b(2,1)*b(1,2) *b(1,1)*xi(5,2) + b(6,6)*b(2,1)*b(1,2) *xi(5,1) 3 2 + b(6,6)*b(2,2)*b(1,1) *xi(4,2) + b(6,6)*b(2,2)*b(1,2)*b(1,1) *xi(5,2) 2 - b(6,6)*b(2,2)*b(1,2) *b(1,1)*xi(5,1) + b(6,6)*b(4,6)*b(1,1)*xi(6,2) - b(6,6)*b(4,6)*b(1,2)*xi(6,1))/(b(6,6) *( - b(2,1)*b(1,2) + b(2,2)*b(1,1))),0,0,0,( 2 - b(2,1)*b(1,2)*b(1,1)*xi(4,6) - b(2,1)*b(1,2) *xi(5,6) 2 + b(2,2)*b(1,1) *xi(4,6) + b(2,2)*b(1,2)*b(1,1)*xi(5,6))/b(6,6)), 2 ((b(6,1)*b(2,2)*b(2,1) *b(1,2)*xi(4,6) 2 - b(6,1)*b(2,2) *b(2,1)*b(1,1)*xi(4,6) 2 3 + b(6,1)*b(2,2) *b(2,1)*b(1,2)*xi(5,6) - b(6,1)*b(2,2) *b(1,1)*xi(5,6) 3 2 - b(6,2)*b(2,1) *b(1,2)*xi(4,6) + b(6,2)*b(2,2)*b(2,1) *b(1,1)*xi(4,6) 2 - b(6,2)*b(2,2)*b(2,1) *b(1,2)*xi(5,6) 2 3 + b(6,2)*b(2,2) *b(2,1)*b(1,1)*xi(5,6) + b(6,6)*b(2,1) *b(1,2)*xi(4,2) 2 - b(6,6)*b(2,2)*b(2,1) *b(1,1)*xi(4,2) 2 + b(6,6)*b(2,2)*b(2,1) *b(1,2)*xi(5,2) 2 - b(6,6)*b(2,2) *b(2,1)*b(1,1)*xi(5,2) 2 3 - b(6,6)*b(2,2) *b(2,1)*b(1,2)*xi(5,1) + b(6,6)*b(2,2) *b(1,1)*xi(5,1) - b(6,6)*b(5,6)*b(2,1)*xi(6,2) + b(6,6)*b(5,6)*b(2,2)*xi(6,1))/(b(6,6) 2 2 *( - b(2,1)*b(1,2) + b(2,2)*b(1,1))),( - b(6,1)*b(2,1) *b(1,2) *xi(4,6) 2 - 2*b(6,1)*b(2,2)*b(2,1)*b(1,2) *xi(5,6) 2 2 + b(6,1)*b(2,2) *b(1,1) *xi(4,6) 2 + 2*b(6,1)*b(2,2) *b(1,2)*b(1,1)*xi(5,6) 2 + 2*b(6,2)*b(2,1) *b(1,2)*b(1,1)*xi(4,6) 2 2 + b(6,2)*b(2,1) *b(1,2) *xi(5,6) 2 - 2*b(6,2)*b(2,2)*b(2,1)*b(1,1) *xi(4,6) 2 2 - b(6,2)*b(2,2) *b(1,1) *xi(5,6) 2 - 2*b(6,6)*b(2,1) *b(1,2)*b(1,1)*xi(4,2) 2 2 - b(6,6)*b(2,1) *b(1,2) *xi(5,2) 2 + 2*b(6,6)*b(2,2)*b(2,1)*b(1,1) *xi(4,2) 2 + 2*b(6,6)*b(2,2)*b(2,1)*b(1,2) *xi(5,1) 2 2 + b(6,6)*b(2,2) *b(1,1) *xi(5,2) 2 - 2*b(6,6)*b(2,2) *b(1,2)*b(1,1)*xi(5,1) + b(6,6)*b(4,6)*b(2,1)*xi(6,2) - b(6,6)*b(4,6)*b(2,2)*xi(6,1) + b(6,6)*b(5,6)*b(1,1)*xi(6,2) - b(6,6)*b(5,6)*b(1,2)*xi(6,1))/(b(6,6) 2 *( - b(2,1)*b(1,2) + b(2,2)*b(1,1))),0,0,0,( - b(2,1) *b(1,2)*xi(4,6) + b(2,2)*b(2,1)*b(1,1)*xi(4,6) - b(2,2)*b(2,1)*b(1,2)*xi(5,6) 2 + b(2,2) *b(1,1)*xi(5,6))/b(6,6)), b(6,6)*( - b(2,1)*xi(6,2) + b(2,2)*xi(6,1)) (---------------------------------------------, - b(2,1)*b(1,2) + b(2,2)*b(1,1) b(6,6)*(b(1,1)*xi(6,2) - b(1,2)*xi(6,1)) ------------------------------------------,0,0,0,0)) - b(2,1)*b(1,2) + b(2,2)*b(1,1) *************************** SUBCASE 2 : ***************************************$ ************ Suppose xi(6,1) and xi(6,2) simultaneously zero.**************$ xi(6,1):=0$ xi(6,2):=0$ With the first kind automorphism one gets$ shortformdeltaprimemodadg:={( - (( - b(6,6)*b(1,1)*xi(4,2) + ( - b(6,1)*b(1,2) + b(6,2)*b(1,1))*xi(4,6))*b(1,1) + (( - b(1,1)*xi(5,2) + b(1,2)*xi(5,1))*b(6,6) + ( - b(6,1)*b(1,2) + b(6,2)*b(1,1))*xi(5,6))*b(1,2)))/b(6,6), (( - b(2,1)*b(1,2) + b(2,2)*b(1,1))*(b(1,1)*xi(4,6) + b(1,2)*xi(5,6)))/b(6,6), ss, (( - b(6,6)*b(2,1)*xi(4,2) + ( - b(6,1)*b(2,2) + b(6,2)*b(2,1))*xi(4,6))*b(2,1) + (( - b(2,1)*xi(5,2) + b(2,2)*xi(5,1))*b(6,6) + ( - b(6,1)*b(2,2) + b(6,2)*b(2, 1))*xi(5,6))*b(2,2))/b(6,6), ( - ( - b(6,1)*b(2,1)*b(1,2)*xi(4,6) - b(6,1)*b(2,2)*b(1,1)*xi(4,6) - 2*b(6,1)*b (2,2)*b(1,2)*xi(5,6) + 2*b(6,2)*b(2,1)*b(1,1)*xi(4,6) + b(6,2)*b(2,1)*b(1,2)*xi( 5,6) + b(6,2)*b(2,2)*b(1,1)*xi(5,6) - 2*b(6,6)*b(2,1)*b(1,1)*xi(4,2) - b(6,6)*b( 2,1)*b(1,2)*xi(5,2) - b(6,6)*b(2,2)*b(1,1)*xi(5,2) + 2*b(6,6)*b(2,2)*b(1,2)*xi(5 ,1)))/b(6,6), (( - b(2,1)*b(1,2) + b(2,2)*b(1,1))*(b(2,1)*xi(4,6) + b(2,2)*xi(5,6)))/b(6,6), ss, 0, 0}$ deltaprimemodg(4,2):=( - (( - b(6,6)*b(1,1)*xi(4,2) + ( - b(6,1)*b(1,2) + b(6,2) *b(1,1))*xi(4,6))*b(1,1) + (( - b(1,1)*xi(5,2) + b(1,2)*xi(5,1))*b(6,6) + ( - b( 6,1)*b(1,2) + b(6,2)*b(1,1))*xi(5,6))*b(1,2)))/b(6,6)$ deltaprimemodg(4,6):=(( - b(2,1)*b(1,2) + b(2,2)*b(1,1))*(b(1,1)*xi(4,6) + b(1,2 )*xi(5,6)))/b(6,6)$ deltaprimemodg(5,1):=(( - b(6,6)*b(2,1)*xi(4,2) + ( - b(6,1)*b(2,2) + b(6,2)*b(2 ,1))*xi(4,6))*b(2,1) + (( - b(2,1)*xi(5,2) + b(2,2)*xi(5,1))*b(6,6) + ( - b(6,1) *b(2,2) + b(6,2)*b(2,1))*xi(5,6))*b(2,2))/b(6,6)$ deltaprimemodg(5,2):=( - ( - b(6,1)*b(2,1)*b(1,2)*xi(4,6) - b(6,1)*b(2,2)*b(1,1) *xi(4,6) - 2*b(6,1)*b(2,2)*b(1,2)*xi(5,6) + 2*b(6,2)*b(2,1)*b(1,1)*xi(4,6) + b(6 ,2)*b(2,1)*b(1,2)*xi(5,6) + b(6,2)*b(2,2)*b(1,1)*xi(5,6) - 2*b(6,6)*b(2,1)*b(1,1 )*xi(4,2) - b(6,6)*b(2,1)*b(1,2)*xi(5,2) - b(6,6)*b(2,2)*b(1,1)*xi(5,2) + 2*b(6, 6)*b(2,2)*b(1,2)*xi(5,1)))/b(6,6)$ deltaprimemodg(5,6):=(( - b(2,1)*b(1,2) + b(2,2)*b(1,1))*(b(2,1)*xi(4,6) + b(2,2 )*xi(5,6)))/b(6,6)$ deltaprimemodg(6,1):=0$ deltaprimemodg(6,2):=0$ det(AUTOM):=( - b(2,1)*b(1,2) + b(2,2)*b(1,1))**5*b(6,6)$ DELTAPRIMEMODADG:= mat((0,0,0,0,0,0), (0,0,0,0,0,0), (0,0,0,0,0,0), (0,( - (( - b(6,6)*b(1,1)*xi(4,2) + ( - b(6,1)*b(1,2) + b(6,2)*b(1,1))*xi(4,6))*b(1,1) + ( ( - b(1,1)*xi(5,2) + b(1,2)*xi(5,1))*b(6,6) + ( - b(6,1)*b(1,2) + b(6,2)*b(1,1))*xi(5,6))*b(1,2)))/b(6,6),0, ( - b(2,1)*b(1,2) + b(2,2)*b(1,1))*(b(1,1)*xi(4,6) + b(1,2)*xi(5,6)) 0,0,----------------------------------------------------------------------) b(6,6) , ((( - b(6,6)*b(2,1)*xi(4,2) + ( - b(6,1)*b(2,2) + b(6,2)*b(2,1))*xi(4,6)) *b(2,1) + (( - b(2,1)*xi(5,2) + b(2,2)*xi(5,1))*b(6,6) + ( - b(6,1)*b(2,2) + b(6,2)*b(2,1))*xi(5,6))*b(2,2))/b(6,6),( - ( - b(6,1)*b(2,1)*b(1,2)*xi(4,6) - b(6,1)*b(2,2)*b(1,1)*xi(4,6) - 2*b(6,1)*b(2,2)*b(1,2)*xi(5,6) + 2*b(6,2)*b(2,1)*b(1,1)*xi(4,6) + b(6,2)*b(2,1)*b(1,2)*xi(5,6) + b(6,2)*b(2,2)*b(1,1)*xi(5,6) - 2*b(6,6)*b(2,1)*b(1,1)*xi(4,2) - b(6,6)*b(2,1)*b(1,2)*xi(5,2) - b(6,6)*b(2,2)*b(1,1)*xi(5,2) + 2*b(6,6)*b(2,2)*b(1,2)*xi(5,1)))/b (6,6),0,0,0, ( - b(2,1)*b(1,2) + b(2,2)*b(1,1))*(b(2,1)*xi(4,6) + b(2,2)*xi(5,6)) ----------------------------------------------------------------------), b(6,6) (0,0,0,0,0,0)) ************************ SUBSUBCASE 2.1 : ************************************$ ************ Suppose xi(4,6) and xi(5,6) not simultaneously zero.************** $ Then one may suppose xi(4,6)=1 and xi(5,6)=0.$ In fact there exists then a bijective linear map of C^2 to C^2 sending$ the nonzero vector (xi(4,6),xi(5,6)) on the vector (1,0).$ If we take moreover b(6,6) equal to the determinant of that linear map, we get$ deltaprime(4,6):=1, deltaprime(5,6):=0.$ xi(4,6):=1$ xi(5,6):=0$ With the first kind automorphism one gets$ shortformdeltaprimemodadg:={( - (( - b(1,1)*xi(5,2) + b(1,2)*xi(5,1))*b(6,6)*b(1 ,2) + ( - b(6,6)*b(1,1)*xi(4,2) - b(6,1)*b(1,2) + b(6,2)*b(1,1))*b(1,1)))/b(6,6) , (( - b(2,1)*b(1,2) + b(2,2)*b(1,1))*b(1,1))/b(6,6), ss, (( - b(2,1)*xi(5,2) + b(2,2)*xi(5,1))*b(6,6)*b(2,2) + ( - b(6,6)*b(2,1)*xi(4,2) - b(6,1)*b(2,2) + b(6,2)*b(2,1))*b(2,1))/b(6,6), ( - ( - b(6,1)*b(2,1)*b(1,2) - b(6,1)*b(2,2)*b(1,1) + 2*b(6,2)*b(2,1)*b(1,1) - 2 *b(6,6)*b(2,1)*b(1,1)*xi(4,2) - b(6,6)*b(2,1)*b(1,2)*xi(5,2) - b(6,6)*b(2,2)*b(1 ,1)*xi(5,2) + 2*b(6,6)*b(2,2)*b(1,2)*xi(5,1)))/b(6,6), (( - b(2,1)*b(1,2) + b(2,2)*b(1,1))*b(2,1))/b(6,6), ss, 0, 0}$ deltaprimemodg(4,2):=( - (( - b(1,1)*xi(5,2) + b(1,2)*xi(5,1))*b(6,6)*b(1,2) + ( - b(6,6)*b(1,1)*xi(4,2) - b(6,1)*b(1,2) + b(6,2)*b(1,1))*b(1,1)))/b(6,6)$ deltaprimemodg(4,6):=(( - b(2,1)*b(1,2) + b(2,2)*b(1,1))*b(1,1))/b(6,6)$ deltaprimemodg(5,1):=(( - b(2,1)*xi(5,2) + b(2,2)*xi(5,1))*b(6,6)*b(2,2) + ( - b (6,6)*b(2,1)*xi(4,2) - b(6,1)*b(2,2) + b(6,2)*b(2,1))*b(2,1))/b(6,6)$ deltaprimemodg(5,2):=( - ( - b(6,1)*b(2,1)*b(1,2) - b(6,1)*b(2,2)*b(1,1) + 2*b(6 ,2)*b(2,1)*b(1,1) - 2*b(6,6)*b(2,1)*b(1,1)*xi(4,2) - b(6,6)*b(2,1)*b(1,2)*xi(5,2 ) - b(6,6)*b(2,2)*b(1,1)*xi(5,2) + 2*b(6,6)*b(2,2)*b(1,2)*xi(5,1)))/b(6,6)$ deltaprimemodg(5,6):=(( - b(2,1)*b(1,2) + b(2,2)*b(1,1))*b(2,1))/b(6,6)$ deltaprimemodg(6,1):=0$ deltaprimemodg(6,2):=0$ det(AUTOM):=( - b(2,1)*b(1,2) + b(2,2)*b(1,1))**5*b(6,6)$ DELTAPRIMEMODADG:= mat((0,0,0,0,0,0), (0,0,0,0,0,0), (0,0,0,0,0,0), (0,( - (( - b(1,1)*xi(5,2) + b(1,2)*xi(5,1))*b(6,6)*b(1,2) + ( - b(6,6)*b(1,1)*xi(4,2) - b(6,1)*b(1,2) + b(6,2)*b(1,1))*b(1,1) ( - b(2,1)*b(1,2) + b(2,2)*b(1,1))*b(1,1) ))/b(6,6),0,0,0,-------------------------------------------), b(6,6) ((( - b(2,1)*xi(5,2) + b(2,2)*xi(5,1))*b(6,6)*b(2,2) + ( - b(6,6)*b(2,1)*xi(4,2) - b(6,1)*b(2,2) + b(6,2)*b(2,1))*b(2,1))/b(6, 6),( - ( - b(6,1)*b(2,1)*b(1,2) - b(6,1)*b(2,2)*b(1,1) + 2*b(6,2)*b(2,1)*b(1,1) - 2*b(6,6)*b(2,1)*b(1,1)*xi(4,2) - b(6,6)*b(2,1)*b(1,2)*xi(5,2) - b(6,6)*b(2,2)*b(1,1)*xi(5,2) + 2*b(6,6)*b(2,2)*b(1,2)*xi(5,1)))/b(6,6),0,0,0, ( - b(2,1)*b(1,2) + b(2,2)*b(1,1))*b(2,1) -------------------------------------------), b(6,6) (0,0,0,0,0,0)) Then to keep deltaprime(4,6)=k and deltaprime(5,6)=0 one has to take:$ b(2,1):=0$ b(2,2):=(b(6,6)*k)/b(1,1)**2$ With the first kind automorphism one gets$ shortformdeltaprimemodadg:={(b(6,1)*b(1,2)*b(1,1) - b(6,2)*b(1,1)**2 + b(6,6)*b( 1,1)**2*xi(4,2) + b(6,6)*b(1,2)*b(1,1)*xi(5,2) - b(6,6)*b(1,2)**2*xi(5,1))/b(6,6 ), k, ss, (b(6,6)**2*xi(5,1)*k**2)/b(1,1)**4, (k*(b(6,1)*b(1,1) + b(6,6)*b(1,1)*xi(5,2) - 2*b(6,6)*b(1,2)*xi(5,1)))/b(1,1)**2, 0, ss, 0, 0}$ deltaprimemodg(4,2):=(b(6,1)*b(1,2)*b(1,1) - b(6,2)*b(1,1)**2 + b(6,6)*b(1,1)**2 *xi(4,2) + b(6,6)*b(1,2)*b(1,1)*xi(5,2) - b(6,6)*b(1,2)**2*xi(5,1))/b(6,6)$ deltaprimemodg(4,6):=k$ deltaprimemodg(5,1):=(b(6,6)**2*xi(5,1)*k**2)/b(1,1)**4$ deltaprimemodg(5,2):=(k*(b(6,1)*b(1,1) + b(6,6)*b(1,1)*xi(5,2) - 2*b(6,6)*b(1,2) *xi(5,1)))/b(1,1)**2$ deltaprimemodg(5,6):=0$ deltaprimemodg(6,1):=0$ deltaprimemodg(6,2):=0$ det(AUTOM):=(b(6,6)**6*k**5)/b(1,1)**5$ DELTAPRIMEMODADG:= mat((0,0,0,0,0,0), (0,0,0,0,0,0), (0,0,0,0,0,0), 2 2 (0,(b(6,1)*b(1,2)*b(1,1) - b(6,2)*b(1,1) + b(6,6)*b(1,1) *xi(4,2) 2 + b(6,6)*b(1,2)*b(1,1)*xi(5,2) - b(6,6)*b(1,2) *xi(5,1))/b(6,6),0,0,0,k ), 2 2 b(6,6) *xi(5,1)*k (--------------------, 4 b(1,1) k*(b(6,1)*b(1,1) + b(6,6)*b(1,1)*xi(5,2) - 2*b(6,6)*b(1,2)*xi(5,1)) ---------------------------------------------------------------------,0,0,0 2 b(1,1) ,0), (0,0,0,0,0,0)) Then one gets deltaprime(4,2)=0 by taking :$ b(6,2):=(b(6,1)*b(1,2)*b(1,1) + b(6,6)*b(1,1)**2*xi(4,2) + b(6,6)*b(1,2)*b(1,1)* xi(5,2) - b(6,6)*b(1,2)**2*xi(5,1))/b(1,1)**2$ and one gets deltaprime(5,2)=0 by taking :$ b(6,1):=(b(6,6)*( - b(1,1)*xi(5,2) + 2*b(1,2)*xi(5,1)))/b(1,1)$ With the first kind automorphism one gets$ shortformdeltaprimemodadg:={0, k, ss, (b(6,6)**2*xi(5,1)*k**2)/b(1,1)**4, 0, 0, ss, 0, 0}$ deltaprimemodg(4,2):=0$ deltaprimemodg(4,6):=k$ deltaprimemodg(5,1):=(b(6,6)**2*xi(5,1)*k**2)/b(1,1)**4$ deltaprimemodg(5,2):=0$ deltaprimemodg(5,6):=0$ deltaprimemodg(6,1):=0$ deltaprimemodg(6,2):=0$ det(AUTOM):=(b(6,6)**6*k**5)/b(1,1)**5$ DELTAPRIMEMODADG:= [ 0 0 0 0 0 0] [ ] [ 0 0 0 0 0 0] [ ] [ 0 0 0 0 0 0] [ ] [ 0 0 0 0 0 k] [ ] [ 2 2 ] [ b(6,6) *xi(5,1)*k ] [-------------------- 0 0 0 0 0] [ 4 ] [ b(1,1) ] [ ] [ 0 0 0 0 0 0] Hence, we are reduced in the subsubcase 2.1. under consideration to:$ shortformdeltaprime ={0,1,SS,epsilon,0,0,SS,0,0}$ where epsilon=xi(5,1) =0,1.$ ************************ SUBSUBCASE 2.2 : ************************************$ ************ Suppose xi(4,6) and xi(5,6) simultaneously zero.**************$ xi(4,6):=0$ xi(5,6):=0$ clear b(6,1),b(6,2),b(2,1),b(2,2)$ With the first kind automorphism one gets$ shortformdeltaprimemodadg:={b(1,1)**2*xi(4,2) + b(1,2)*b(1,1)*xi(5,2) - b(1,2)** 2*xi(5,1), 0, ss, - b(2,1)**2*xi(4,2) - b(2,2)*b(2,1)*xi(5,2) + b(2,2)**2*xi(5,1), 2*b(2,1)*b(1,1)*xi(4,2) + b(2,1)*b(1,2)*xi(5,2) + b(2,2)*b(1,1)*xi(5,2) - 2*b(2, 2)*b(1,2)*xi(5,1), 0, ss, 0, 0}$ deltaprimemodg(4,2):=b(1,1)**2*xi(4,2) + b(1,2)*b(1,1)*xi(5,2) - b(1,2)**2*xi(5, 1)$ deltaprimemodg(4,6):=0$ deltaprimemodg(5,1):= - b(2,1)**2*xi(4,2) - b(2,2)*b(2,1)*xi(5,2) + b(2,2)**2*xi (5,1)$ deltaprimemodg(5,2):=2*b(2,1)*b(1,1)*xi(4,2) + b(2,1)*b(1,2)*xi(5,2) + b(2,2)*b( 1,1)*xi(5,2) - 2*b(2,2)*b(1,2)*xi(5,1)$ deltaprimemodg(5,6):=0$ deltaprimemodg(6,1):=0$ deltaprimemodg(6,2):=0$ det(AUTOM):=b(6,6)*( - b(2,1)**5*b(1,2)**5 + 5*b(2,2)*b(2,1)**4*b(1,2)**4*b(1,1) - 10*b(2,2)**2*b(2,1)**3*b(1,2)**3*b(1,1)**2 + 10*b(2,2)**3*b(2,1)**2*b(1,2)**2 *b(1,1)**3 - 5*b(2,2)**4*b(2,1)*b(1,2)*b(1,1)**4 + b(2,2)**5*b(1,1)**5)$ DELTAPRIMEMODADG:= mat((0,0,0,0,0,0), (0,0,0,0,0,0), (0,0,0,0,0,0), 2 2 (0,b(1,1) *xi(4,2) + b(1,2)*b(1,1)*xi(5,2) - b(1,2) *xi(5,1),0,0,0,0), 2 2 ( - b(2,1) *xi(4,2) - b(2,2)*b(2,1)*xi(5,2) + b(2,2) *xi(5,1), 2*b(2,1)*b(1,1)*xi(4,2) + b(2,1)*b(1,2)*xi(5,2) + b(2,2)*b(1,1)*xi(5,2) - 2*b(2,2)*b(1,2)*xi(5,1),0,0,0,0), (0,0,0,0,0,0)) *** Suppose now xi(4,2) NEQ 0.$ Then one may suppose xi(4,2) =1 :$ xi(4,2):=1$ Then to keep deltaprime(4,2)=k one takes:$ b(1,1):=sqrt(k)$ b(1,2):=0$ With the first kind automorphism one gets$ shortformdeltaprimemodadg:={k, 0, ss, - b(2,1)**2 - b(2,2)*b(2,1)*xi(5,2) + b(2,2)**2*xi(5,1), (k*(2*b(2,1) + b(2,2)*xi(5,2)))/sqrt(k), 0, ss, 0, 0}$ deltaprimemodg(4,2):=k$ deltaprimemodg(4,6):=0$ deltaprimemodg(5,1):= - b(2,1)**2 - b(2,2)*b(2,1)*xi(5,2) + b(2,2)**2*xi(5,1)$ deltaprimemodg(5,2):=(k*(2*b(2,1) + b(2,2)*xi(5,2)))/sqrt(k)$ deltaprimemodg(5,6):=0$ deltaprimemodg(6,1):=0$ deltaprimemodg(6,2):=0$ det(AUTOM):=sqrt(k)*b(6,6)*b(2,2)**5*k**2$ DELTAPRIMEMODADG:= mat((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 2 ( - b(2,1) - b(2,2)*b(2,1)*xi(5,2) + b(2,2) *xi(5,1), k*(2*b(2,1) + b(2,2)*xi(5,2)) -------------------------------,0,0,0,0), sqrt(k) (0,0,0,0,0,0)) Then one gets deltaprime(5,2)=0 by taking :$ b(2,1):=( - b(2,2)*xi(5,2))/2$ With the first kind automorphism one gets$ shortformdeltaprimemodadg:={k, 0, ss, (b(2,2)**2*(4*xi(5,1) + xi(5,2)**2))/4, 0, 0, ss, 0, 0}$ deltaprimemodg(4,2):=k$ deltaprimemodg(4,6):=0$ deltaprimemodg(5,1):=(b(2,2)**2*(4*xi(5,1) + xi(5,2)**2))/4$ deltaprimemodg(5,2):=0$ deltaprimemodg(5,6):=0$ deltaprimemodg(6,1):=0$ deltaprimemodg(6,2):=0$ det(AUTOM):=sqrt(k)*b(6,6)*b(2,2)**5*k**2$ 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 2 ] [ b(2,2) *(4*xi(5,1) + xi(5,2) ) ] [-------------------------------- 0 0 0 0 0] [ 4 ] [ ] [ 0 0 0 0 0 0] Hence, we are reduced in the subsubcase 2.2. and if xi(4,2) neq 0 to:$ shortformdeltaprime ={1,0,SS,epsilon,0,0,SS,0,0}.$ where epsilon=xi(5,1) =0,1.$ However, recall that we dismiss all direct products by Cx_7.$ Hence we discard the cases in which xi(4,6)=xi(5,6)=xi(6,1)=xi(6,2)=0.$ The foregoing cases for xi(4,2) neq 0 are thus to be dismissed.$ *** We suppose now xi(4,2) = 0.$ xi(4,2):=0$ clear b(1,1),b(1,2),b(2,1)$ With the first kind automorphism one gets$ shortformdeltaprimemodadg:={b(1,2)*(b(1,1)*xi(5,2) - b(1,2)*xi(5,1)), 0, ss, b(2,2)*( - b(2,1)*xi(5,2) + b(2,2)*xi(5,1)), b(2,1)*b(1,2)*xi(5,2) + b(2,2)*b(1,1)*xi(5,2) - 2*b(2,2)*b(1,2)*xi(5,1), 0, ss, 0, 0}$ deltaprimemodg(4,2):=b(1,2)*(b(1,1)*xi(5,2) - b(1,2)*xi(5,1))$ deltaprimemodg(4,6):=0$ deltaprimemodg(5,1):=b(2,2)*( - b(2,1)*xi(5,2) + b(2,2)*xi(5,1))$ deltaprimemodg(5,2):=b(2,1)*b(1,2)*xi(5,2) + b(2,2)*b(1,1)*xi(5,2) - 2*b(2,2)*b( 1,2)*xi(5,1)$ deltaprimemodg(5,6):=0$ deltaprimemodg(6,1):=0$ deltaprimemodg(6,2):=0$ det(AUTOM):=b(6,6)*( - b(2,1)**5*b(1,2)**5 + 5*b(2,2)*b(2,1)**4*b(1,2)**4*b(1,1) - 10*b(2,2)**2*b(2,1)**3*b(1,2)**3*b(1,1)**2 + 10*b(2,2)**3*b(2,1)**2*b(1,2)**2 *b(1,1)**3 - 5*b(2,2)**4*b(2,1)*b(1,2)*b(1,1)**4 + b(2,2)**5*b(1,1)**5)$ DELTAPRIMEMODADG:= mat((0,0,0,0,0,0), (0,0,0,0,0,0), (0,0,0,0,0,0), (0,b(1,2)*(b(1,1)*xi(5,2) - b(1,2)*xi(5,1)),0,0,0,0), (b(2,2)*( - b(2,1)*xi(5,2) + b(2,2)*xi(5,1)), b(2,1)*b(1,2)*xi(5,2) + b(2,2)*b(1,1)*xi(5,2) - 2*b(2,2)*b(1,2)*xi(5,1),0,0 ,0,0), (0,0,0,0,0,0)) Then one keeps deltaprime(4,2)=0 by taking :$ b(1,2):=0$ With the first kind automorphism one gets$ shortformdeltaprimemodadg:={0, 0, ss, b(2,2)*( - b(2,1)*xi(5,2) + b(2,2)*xi(5,1)), b(2,2)*b(1,1)*xi(5,2), 0, ss, 0, 0}$ deltaprimemodg(4,2):=0$ deltaprimemodg(4,6):=0$ deltaprimemodg(5,1):=b(2,2)*( - b(2,1)*xi(5,2) + b(2,2)*xi(5,1))$ deltaprimemodg(5,2):=b(2,2)*b(1,1)*xi(5,2)$ deltaprimemodg(5,6):=0$ deltaprimemodg(6,1):=0$ deltaprimemodg(6,2):=0$ det(AUTOM):=b(6,6)*b(2,2)**5*b(1,1)**5$ 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] [ ] [b(2,2)*( - b(2,1)*xi(5,2) + b(2,2)*xi(5,1)) b(2,2)*b(1,1)*xi(5,2) 0 0 0 0] [ ] [ 0 0 0 0 0 0] Then if xi(5,2) neq 0, one may suppose xi(5,2):=1.$ xi(5,2):=1$ Then one keeps deltaprime(5,2)=k and we gets deltaprime(5,1):=0 by taking :$ b(2,1):= - b(2,2)*xi(5,1)$ b(2,2):=k/b(1,1)$ With the first kind automorphism one gets$ shortformdeltaprimemodadg:={0, 0, ss, (2*xi(5,1)*k**2)/b(1,1)**2, k, 0, ss, 0, 0}$ deltaprimemodg(4,2):=0$ deltaprimemodg(4,6):=0$ deltaprimemodg(5,1):=(2*xi(5,1)*k**2)/b(1,1)**2$ deltaprimemodg(5,2):=k$ deltaprimemodg(5,6):=0$ deltaprimemodg(6,1):=0$ deltaprimemodg(6,2):=0$ det(AUTOM):=b(6,6)*k**5$ 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 ] [ 2*xi(5,1)*k ] [-------------- k 0 0 0 0] [ 2 ] [ b(1,1) ] [ ] [ 0 0 0 0 0 0] !Hence,! we! are! reduced! in! the! subsubcase! 2.2.! and! if! xi(4,2)=! 0! and! xi(5,2)! neq\ ! 0! to:$ shortformdeltaprime ={0,0,SS,epsilon,1,0,SS,0,0}.$ where epsilon=xi(5,1) =0,1.$ However, recall that we dismiss all direct products by Cx_7.$ Hence we discard the cases in which xi(4,6)=xi(5,6)=xi(6,1)=xi(6,2)=0.$ The foregoing cases for xi(5,2) neq 0 are thus to be dismissed.$ Finally, if xi(5,2) = 0, one has :$ xi(5,2):=0$ clear b(2,1),b(2,2)$ With the first kind automorphism one gets$ shortformdeltaprimemodadg:={0, 0, ss, b(2,2)**2*xi(5,1), 0, 0, ss, 0, 0}$ deltaprimemodg(4,2):=0$ deltaprimemodg(4,6):=0$ deltaprimemodg(5,1):=b(2,2)**2*xi(5,1)$ deltaprimemodg(5,2):=0$ deltaprimemodg(5,6):=0$ deltaprimemodg(6,1):=0$ deltaprimemodg(6,2):=0$ det(AUTOM):=b(6,6)*b(2,2)**5*b(1,1)**5$ 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 ] [b(2,2) *xi(5,1) 0 0 0 0 0] [ ] [ 0 0 0 0 0 0] Then as we suppose delta neq 0 , we have xi(5,1) neq 0, hence we may suppose $ xi(5,1):=1$ With the first kind automorphism one gets$ shortformdeltaprimemodadg:={0,0,ss,b(2,2)**2,0,0,ss,0,0}$ deltaprimemodg(4,2):=0$ deltaprimemodg(4,6):=0$ deltaprimemodg(5,1):=b(2,2)**2$ deltaprimemodg(5,2):=0$ deltaprimemodg(5,6):=0$ deltaprimemodg(6,1):=0$ deltaprimemodg(6,2):=0$ det(AUTOM):=b(6,6)*b(2,2)**5*b(1,1)**5$ 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 ] [b(2,2) 0 0 0 0 0] [ ] [ 0 0 0 0 0 0] Hence, we are reduced in the subsubcase 2.2. and if xi(4,2)= xi(5,2) = 0 to:$ shortformdeltaprime ={0,0,SS,1,0,0,SS,0,0}.$ However, recall that we dismiss all direct products by Cx_7.$ Hence we discard the cases in which xi(4,6)=xi(5,6)=xi(6,1)=xi(6,2)=0.$ The foregoing case is thus to be dismissed.$