rreducparautommodg6_52xCcase2N2.r The generic automorphism phi of C x g_{5,2} as computed by calculautom6_52xC.r\ ed : phi:= [b(1,1) 0 0 0 0 0 ] [ ] [b(2,1) b(2,2) b(2,3) 0 0 0 ] [ ] [b(3,1) b(3,2) b(3,3) 0 0 0 ] [ ] [b(4,1) b(4,2) b(4,3) b(2,2)*b(1,1) b(2,3)*b(1,1) b(4,6)] [ ] [b(5,1) b(5,2) b(5,3) b(3,2)*b(1,1) b(3,3)*b(1,1) b(5,6)] [ ] [b(6,1) b(6,2) b(6,3) 0 0 b(6,6)] 2 3 det(phi):=( - b(3,2)*b(2,3) + b(3,3)*b(2,2)) *b(6,6)*b(1,1) generic derivation : delta:= [xi(1,1) 0 0 0 0 0 ] [ ] [xi(2,1) xi(2,2) xi(2,3) 0 0 0 ] [ ] [xi(3,1) xi(3,2) xi(3,3) 0 0 0 ] [ ] [xi(4,1) xi(4,2) xi(4,3) xi(1,1) + xi(2,2) xi(2,3) xi(4,6)] [ ] [xi(5,1) xi(5,2) xi(5,3) xi(3,2) xi(1,1) + xi(3,3) xi(5,6)] [ ] [xi(6,1) xi(6,2) xi(6,3) 0 0 xi(6,6)] [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 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] adx2 := [ ] [-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] [ ] [0 0 0 0 0 0] adx3 := [ ] [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(6,6):=0 And the matrix A:=(xi(2,2),xi(2,3)),(xi(3,2),xi(3,3)) is nilpotent We hence get 2 cases according to whether A neq 0 or A=0. We consider here the case 2 where A = 0. xi(2,2):=0 xi(2,3):=0 xi(3,2):=0 xi(3,3):=0 by subtracting adjoints one then may suppose: xi(4,1):=0,xi(4,2):=0,xi(5,1):=0 delta:= [ 0 0 0 0 0 0 ] [ ] [xi(2,1) 0 0 0 0 0 ] [ ] [xi(3,1) 0 0 0 0 0 ] [ ] [ 0 0 xi(4,3) 0 0 xi(4,6)] [ ] [ 0 xi(5,2) xi(5,3) 0 0 xi(5,6)] [ ] [xi(6,1) xi(6,2) xi(6,3) 0 0 0 ] We denote this delta by the shortform shortformdelta:={xi(2,1), xi(3,1), xi(6,1), ss, xi(5,2), xi(6,2), ss, xi(4,3), xi(5,3), xi(6,3), ss, xi(4,6), xi(5,6)} paramindexeslist:={{2,1}, {3,1}, {6,1}, {5,2}, {6,2}, {4,3}, {5,3}, {6,3}, {4,6}, {5,6}} With the generic automorphism one gets$ shortformdeltaprimemodadg:={(b(2,2)*xi(2,1) + b(2,3)*xi(3,1))/b(1,1), (b(3,2)*xi(2,1) + b(3,3)*xi(3,1))/b(1,1), ( - b(6,2)*b(3,2)*b(2,3)*xi(2,1) + b(6,2)*b(3,3)*b(2,2)*xi(2,1) - b(6,3)*b(3,2)* b(2,3)*xi(3,1) + b(6,3)*b(3,3)*b(2,2)*xi(3,1) - b(6,6)*b(3,1)*b(2,2)*xi(6,3) + b (6,6)*b(3,1)*b(2,3)*xi(6,2) + b(6,6)*b(3,2)*b(2,1)*xi(6,3) - b(6,6)*b(3,2)*b(2,3 )*xi(6,1) - b(6,6)*b(3,3)*b(2,1)*xi(6,2) + b(6,6)*b(3,3)*b(2,2)*xi(6,1))/(b(1,1) *( - b(3,2)*b(2,3) + b(3,3)*b(2,2))), ss, ( - b(6,2)*b(3,3)*b(3,2)*b(1,1)*xi(4,6) - b(6,2)*b(3,3)**2*b(1,1)*xi(5,6) + b(6, 3)*b(3,2)**2*b(1,1)*xi(4,6) + b(6,3)*b(3,3)*b(3,2)*b(1,1)*xi(5,6) - b(6,6)*b(3,2 )**2*b(1,1)*xi(4,3) - b(6,6)*b(3,3)*b(3,2)*b(1,1)*xi(5,3) + b(6,6)*b(3,3)**2*b(1 ,1)*xi(5,2) - b(6,6)*b(5,6)*b(3,2)*xi(6,3) + b(6,6)*b(5,6)*b(3,3)*xi(6,2))/(b(6, 6)*( - b(3,2)*b(2,3) + b(3,3)*b(2,2))), (b(6,6)*( - b(3,2)*xi(6,3) + b(3,3)*xi(6,2)))/( - b(3,2)*b(2,3) + b(3,3)*b(2,2)) , ss, (b(6,2)*b(2,3)*b(2,2)*b(1,1)*xi(4,6) + b(6,2)*b(2,3)**2*b(1,1)*xi(5,6) - b(6,3)* b(2,2)**2*b(1,1)*xi(4,6) - b(6,3)*b(2,3)*b(2,2)*b(1,1)*xi(5,6) + b(6,6)*b(2,2)** 2*b(1,1)*xi(4,3) + b(6,6)*b(2,3)*b(2,2)*b(1,1)*xi(5,3) - b(6,6)*b(2,3)**2*b(1,1) *xi(5,2) + b(6,6)*b(4,6)*b(2,2)*xi(6,3) - b(6,6)*b(4,6)*b(2,3)*xi(6,2))/(b(6,6)* ( - b(3,2)*b(2,3) + b(3,3)*b(2,2))), (b(6,2)*b(3,2)*b(2,3)*b(1,1)*xi(4,6) + b(6,2)*b(3,3)*b(2,2)*b(1,1)*xi(4,6) + 2*b (6,2)*b(3,3)*b(2,3)*b(1,1)*xi(5,6) - 2*b(6,3)*b(3,2)*b(2,2)*b(1,1)*xi(4,6) - b(6 ,3)*b(3,2)*b(2,3)*b(1,1)*xi(5,6) - b(6,3)*b(3,3)*b(2,2)*b(1,1)*xi(5,6) + 2*b(6,6 )*b(3,2)*b(2,2)*b(1,1)*xi(4,3) + b(6,6)*b(3,2)*b(2,3)*b(1,1)*xi(5,3) + b(6,6)*b( 3,3)*b(2,2)*b(1,1)*xi(5,3) - 2*b(6,6)*b(3,3)*b(2,3)*b(1,1)*xi(5,2) + b(6,6)*b(4, 6)*b(3,2)*xi(6,3) - b(6,6)*b(4,6)*b(3,3)*xi(6,2) + b(6,6)*b(5,6)*b(2,2)*xi(6,3) - b(6,6)*b(5,6)*b(2,3)*xi(6,2))/(b(6,6)*( - b(3,2)*b(2,3) + b(3,3)*b(2,2))), (b(6,6)*(b(2,2)*xi(6,3) - b(2,3)*xi(6,2)))/( - b(3,2)*b(2,3) + b(3,3)*b(2,2)), ss, (b(1,1)*(b(2,2)*xi(4,6) + b(2,3)*xi(5,6)))/b(6,6), (b(1,1)*(b(3,2)*xi(4,6) + b(3,3)*xi(5,6)))/b(6,6)}$ deltaprimemodg(2,1):=(b(2,2)*xi(2,1) + b(2,3)*xi(3,1))/b(1,1)$ deltaprimemodg(3,1):=(b(3,2)*xi(2,1) + b(3,3)*xi(3,1))/b(1,1)$ deltaprimemodg(6,1):=( - b(6,2)*b(3,2)*b(2,3)*xi(2,1) + b(6,2)*b(3,3)*b(2,2)*xi( 2,1) - b(6,3)*b(3,2)*b(2,3)*xi(3,1) + b(6,3)*b(3,3)*b(2,2)*xi(3,1) - b(6,6)*b(3, 1)*b(2,2)*xi(6,3) + b(6,6)*b(3,1)*b(2,3)*xi(6,2) + b(6,6)*b(3,2)*b(2,1)*xi(6,3) - b(6,6)*b(3,2)*b(2,3)*xi(6,1) - b(6,6)*b(3,3)*b(2,1)*xi(6,2) + b(6,6)*b(3,3)*b( 2,2)*xi(6,1))/(b(1,1)*( - b(3,2)*b(2,3) + b(3,3)*b(2,2)))$ deltaprimemodg(5,2):=( - b(6,2)*b(3,3)*b(3,2)*b(1,1)*xi(4,6) - b(6,2)*b(3,3)**2* b(1,1)*xi(5,6) + b(6,3)*b(3,2)**2*b(1,1)*xi(4,6) + b(6,3)*b(3,3)*b(3,2)*b(1,1)* xi(5,6) - b(6,6)*b(3,2)**2*b(1,1)*xi(4,3) - b(6,6)*b(3,3)*b(3,2)*b(1,1)*xi(5,3) + b(6,6)*b(3,3)**2*b(1,1)*xi(5,2) - b(6,6)*b(5,6)*b(3,2)*xi(6,3) + b(6,6)*b(5,6) *b(3,3)*xi(6,2))/(b(6,6)*( - b(3,2)*b(2,3) + b(3,3)*b(2,2)))$ deltaprimemodg(6,2):=(b(6,6)*( - b(3,2)*xi(6,3) + b(3,3)*xi(6,2)))/( - b(3,2)*b( 2,3) + b(3,3)*b(2,2))$ deltaprimemodg(4,3):=(b(6,2)*b(2,3)*b(2,2)*b(1,1)*xi(4,6) + b(6,2)*b(2,3)**2*b(1 ,1)*xi(5,6) - b(6,3)*b(2,2)**2*b(1,1)*xi(4,6) - b(6,3)*b(2,3)*b(2,2)*b(1,1)*xi(5 ,6) + b(6,6)*b(2,2)**2*b(1,1)*xi(4,3) + b(6,6)*b(2,3)*b(2,2)*b(1,1)*xi(5,3) - b( 6,6)*b(2,3)**2*b(1,1)*xi(5,2) + b(6,6)*b(4,6)*b(2,2)*xi(6,3) - b(6,6)*b(4,6)*b(2 ,3)*xi(6,2))/(b(6,6)*( - b(3,2)*b(2,3) + b(3,3)*b(2,2)))$ deltaprimemodg(5,3):=(b(6,2)*b(3,2)*b(2,3)*b(1,1)*xi(4,6) + b(6,2)*b(3,3)*b(2,2) *b(1,1)*xi(4,6) + 2*b(6,2)*b(3,3)*b(2,3)*b(1,1)*xi(5,6) - 2*b(6,3)*b(3,2)*b(2,2) *b(1,1)*xi(4,6) - b(6,3)*b(3,2)*b(2,3)*b(1,1)*xi(5,6) - b(6,3)*b(3,3)*b(2,2)*b(1 ,1)*xi(5,6) + 2*b(6,6)*b(3,2)*b(2,2)*b(1,1)*xi(4,3) + b(6,6)*b(3,2)*b(2,3)*b(1,1 )*xi(5,3) + b(6,6)*b(3,3)*b(2,2)*b(1,1)*xi(5,3) - 2*b(6,6)*b(3,3)*b(2,3)*b(1,1)* xi(5,2) + b(6,6)*b(4,6)*b(3,2)*xi(6,3) - b(6,6)*b(4,6)*b(3,3)*xi(6,2) + b(6,6)*b (5,6)*b(2,2)*xi(6,3) - b(6,6)*b(5,6)*b(2,3)*xi(6,2))/(b(6,6)*( - b(3,2)*b(2,3) + b(3,3)*b(2,2)))$ deltaprimemodg(6,3):=(b(6,6)*(b(2,2)*xi(6,3) - b(2,3)*xi(6,2)))/( - b(3,2)*b(2,3 ) + b(3,3)*b(2,2))$ deltaprimemodg(4,6):=(b(1,1)*(b(2,2)*xi(4,6) + b(2,3)*xi(5,6)))/b(6,6)$ deltaprimemodg(5,6):=(b(1,1)*(b(3,2)*xi(4,6) + b(3,3)*xi(5,6)))/b(6,6)$ det(AUTOM):=( - b(3,2)*b(2,3) + b(3,3)*b(2,2))**2*b(6,6)*b(1,1)**3$ DELTAPRIMEMODADG:= mat((0,0,0,0,0,0), b(2,2)*xi(2,1) + b(2,3)*xi(3,1) (---------------------------------,0,0,0,0,0), b(1,1) b(3,2)*xi(2,1) + b(3,3)*xi(3,1) (---------------------------------,0,0,0,0,0), b(1,1) (0,0,( - (( - b(6,2)*b(2,3) + b(6,3)*b(2,2)) *(b(2,2)*xi(4,6) + b(2,3)*xi(5,6))*b(1,1) + ( ( - b(2,2)*xi(6,3) + b(2,3)*xi(6,2))*b(4,6) + 2 2 ( - b(2,2) *xi(4,3) - b(2,3)*b(2,2)*xi(5,3) + b(2,3) *xi(5,2)) *b(1,1))*b(6,6)))/(( - b(3,2)*b(2,3) + b(3,3)*b(2,2))*b(6,6)),0 (b(2,2)*xi(4,6) + b(2,3)*xi(5,6))*b(1,1) ,0,------------------------------------------), b(6,6) (0,(( - b(6,2)*b(3,3) + b(6,3)*b(3,2))*(b(3,2)*xi(4,6) + b(3,3)*xi(5,6)) *b(1,1) + (( - b(3,2)*xi(6,3) + b(3,3)*xi(6,2))*b(5,6) + 2 2 ( - b(3,2) *xi(4,3) - b(3,3)*b(3,2)*xi(5,3) + b(3,3) *xi(5,2))*b(1,1) )*b(6,6))/(( - b(3,2)*b(2,3) + b(3,3)*b(2,2))*b(6,6)),(( - (b(3,3)*b(2,2)*xi(5,6) + (2*b(2,2)*xi(4,6) + b(2,3)*xi(5,6))*b(3,2)) *b(6,3) + (b(3,2)*b(2,3)*xi(4,6) + (b(2,2)*xi(4,6) + 2*b(2,3)*xi(5,6))*b(3,3)) *b(6,2))*b(1,1) + ( - ( - b(3,2)*xi(6,3) + b(3,3)*xi(6,2))*b(4,6) - ( - b(2,2)*xi(6,3) + b(2,3)*xi(6,2))*b(5,6) + ( - ( - b(2,2)*xi(5,3) + 2*b(2,3)*xi(5,2))*b(3,3) + (2*b(2,2)*xi(4,3) + b(2,3)*xi(5,3))*b(3,2))*b(1,1))*b(6,6))/( ( - b(3,2)*b(2,3) + b(3,3)*b(2,2))*b(6,6)),0,0, (b(3,2)*xi(4,6) + b(3,3)*xi(5,6))*b(1,1) ------------------------------------------), b(6,6) (( - ( - (b(6,2)*xi(2,1) + b(6,3)*xi(3,1)) *( - b(3,2)*b(2,3) + b(3,3)*b(2,2)) + ( - ( - b(2,2)*xi(6,3) + b(2,3)*xi(6,2))*b(3,1) - ( - b(2,1)*xi(6,2) + b(2,2)*xi(6,1))*b(3,3) + ( - b(2,1)*xi(6,3) + b(2,3)*xi(6,1))*b(3,2))*b(6,6)))/( ( - b(3,2)*b(2,3) + b(3,3)*b(2,2))*b(1,1)), ( - b(3,2)*xi(6,3) + b(3,3)*xi(6,2))*b(6,6) ---------------------------------------------, - b(3,2)*b(2,3) + b(3,3)*b(2,2) - ( - b(2,2)*xi(6,3) + b(2,3)*xi(6,2))*b(6,6) ------------------------------------------------,0,0,0)) - b(3,2)*b(2,3) + b(3,3)*b(2,2) ************ SUBCASE 1 : xi(2,1),xi(3,1) NOT SIMULTANEOUSLY ZERO *************$ Then one may suppose :$ xi(3,1):=0$ xi(2,1):=1$ With the generic automorphism one gets$ shortformdeltaprimemodadg:={b(2,2)/b(1,1), b(3,2)/b(1,1), ( - b(6,2)*b(3,2)*b(2,3) + b(6,2)*b(3,3)*b(2,2) - b(6,6)*b(3,1)*b(2,2)*xi(6,3) + b(6,6)*b(3,1)*b(2,3)*xi(6,2) + b(6,6)*b(3,2)*b(2,1)*xi(6,3) - b(6,6)*b(3,2)*b(2 ,3)*xi(6,1) - b(6,6)*b(3,3)*b(2,1)*xi(6,2) + b(6,6)*b(3,3)*b(2,2)*xi(6,1))/(b(1, 1)*( - b(3,2)*b(2,3) + b(3,3)*b(2,2))), ss, ( - b(6,2)*b(3,3)*b(3,2)*b(1,1)*xi(4,6) - b(6,2)*b(3,3)**2*b(1,1)*xi(5,6) + b(6, 3)*b(3,2)**2*b(1,1)*xi(4,6) + b(6,3)*b(3,3)*b(3,2)*b(1,1)*xi(5,6) - b(6,6)*b(3,2 )**2*b(1,1)*xi(4,3) - b(6,6)*b(3,3)*b(3,2)*b(1,1)*xi(5,3) + b(6,6)*b(3,3)**2*b(1 ,1)*xi(5,2) - b(6,6)*b(5,6)*b(3,2)*xi(6,3) + b(6,6)*b(5,6)*b(3,3)*xi(6,2))/(b(6, 6)*( - b(3,2)*b(2,3) + b(3,3)*b(2,2))), (b(6,6)*( - b(3,2)*xi(6,3) + b(3,3)*xi(6,2)))/( - b(3,2)*b(2,3) + b(3,3)*b(2,2)) , ss, (b(6,2)*b(2,3)*b(2,2)*b(1,1)*xi(4,6) + b(6,2)*b(2,3)**2*b(1,1)*xi(5,6) - b(6,3)* b(2,2)**2*b(1,1)*xi(4,6) - b(6,3)*b(2,3)*b(2,2)*b(1,1)*xi(5,6) + b(6,6)*b(2,2)** 2*b(1,1)*xi(4,3) + b(6,6)*b(2,3)*b(2,2)*b(1,1)*xi(5,3) - b(6,6)*b(2,3)**2*b(1,1) *xi(5,2) + b(6,6)*b(4,6)*b(2,2)*xi(6,3) - b(6,6)*b(4,6)*b(2,3)*xi(6,2))/(b(6,6)* ( - b(3,2)*b(2,3) + b(3,3)*b(2,2))), (b(6,2)*b(3,2)*b(2,3)*b(1,1)*xi(4,6) + b(6,2)*b(3,3)*b(2,2)*b(1,1)*xi(4,6) + 2*b (6,2)*b(3,3)*b(2,3)*b(1,1)*xi(5,6) - 2*b(6,3)*b(3,2)*b(2,2)*b(1,1)*xi(4,6) - b(6 ,3)*b(3,2)*b(2,3)*b(1,1)*xi(5,6) - b(6,3)*b(3,3)*b(2,2)*b(1,1)*xi(5,6) + 2*b(6,6 )*b(3,2)*b(2,2)*b(1,1)*xi(4,3) + b(6,6)*b(3,2)*b(2,3)*b(1,1)*xi(5,3) + b(6,6)*b( 3,3)*b(2,2)*b(1,1)*xi(5,3) - 2*b(6,6)*b(3,3)*b(2,3)*b(1,1)*xi(5,2) + b(6,6)*b(4, 6)*b(3,2)*xi(6,3) - b(6,6)*b(4,6)*b(3,3)*xi(6,2) + b(6,6)*b(5,6)*b(2,2)*xi(6,3) - b(6,6)*b(5,6)*b(2,3)*xi(6,2))/(b(6,6)*( - b(3,2)*b(2,3) + b(3,3)*b(2,2))), (b(6,6)*(b(2,2)*xi(6,3) - b(2,3)*xi(6,2)))/( - b(3,2)*b(2,3) + b(3,3)*b(2,2)), ss, (b(1,1)*(b(2,2)*xi(4,6) + b(2,3)*xi(5,6)))/b(6,6), (b(1,1)*(b(3,2)*xi(4,6) + b(3,3)*xi(5,6)))/b(6,6)}$ deltaprimemodg(2,1):=b(2,2)/b(1,1)$ deltaprimemodg(3,1):=b(3,2)/b(1,1)$ deltaprimemodg(6,1):=( - b(6,2)*b(3,2)*b(2,3) + b(6,2)*b(3,3)*b(2,2) - b(6,6)*b( 3,1)*b(2,2)*xi(6,3) + b(6,6)*b(3,1)*b(2,3)*xi(6,2) + b(6,6)*b(3,2)*b(2,1)*xi(6,3 ) - b(6,6)*b(3,2)*b(2,3)*xi(6,1) - b(6,6)*b(3,3)*b(2,1)*xi(6,2) + b(6,6)*b(3,3)* b(2,2)*xi(6,1))/(b(1,1)*( - b(3,2)*b(2,3) + b(3,3)*b(2,2)))$ deltaprimemodg(5,2):=( - b(6,2)*b(3,3)*b(3,2)*b(1,1)*xi(4,6) - b(6,2)*b(3,3)**2* b(1,1)*xi(5,6) + b(6,3)*b(3,2)**2*b(1,1)*xi(4,6) + b(6,3)*b(3,3)*b(3,2)*b(1,1)* xi(5,6) - b(6,6)*b(3,2)**2*b(1,1)*xi(4,3) - b(6,6)*b(3,3)*b(3,2)*b(1,1)*xi(5,3) + b(6,6)*b(3,3)**2*b(1,1)*xi(5,2) - b(6,6)*b(5,6)*b(3,2)*xi(6,3) + b(6,6)*b(5,6) *b(3,3)*xi(6,2))/(b(6,6)*( - b(3,2)*b(2,3) + b(3,3)*b(2,2)))$ deltaprimemodg(6,2):=(b(6,6)*( - b(3,2)*xi(6,3) + b(3,3)*xi(6,2)))/( - b(3,2)*b( 2,3) + b(3,3)*b(2,2))$ deltaprimemodg(4,3):=(b(6,2)*b(2,3)*b(2,2)*b(1,1)*xi(4,6) + b(6,2)*b(2,3)**2*b(1 ,1)*xi(5,6) - b(6,3)*b(2,2)**2*b(1,1)*xi(4,6) - b(6,3)*b(2,3)*b(2,2)*b(1,1)*xi(5 ,6) + b(6,6)*b(2,2)**2*b(1,1)*xi(4,3) + b(6,6)*b(2,3)*b(2,2)*b(1,1)*xi(5,3) - b( 6,6)*b(2,3)**2*b(1,1)*xi(5,2) + b(6,6)*b(4,6)*b(2,2)*xi(6,3) - b(6,6)*b(4,6)*b(2 ,3)*xi(6,2))/(b(6,6)*( - b(3,2)*b(2,3) + b(3,3)*b(2,2)))$ deltaprimemodg(5,3):=(b(6,2)*b(3,2)*b(2,3)*b(1,1)*xi(4,6) + b(6,2)*b(3,3)*b(2,2) *b(1,1)*xi(4,6) + 2*b(6,2)*b(3,3)*b(2,3)*b(1,1)*xi(5,6) - 2*b(6,3)*b(3,2)*b(2,2) *b(1,1)*xi(4,6) - b(6,3)*b(3,2)*b(2,3)*b(1,1)*xi(5,6) - b(6,3)*b(3,3)*b(2,2)*b(1 ,1)*xi(5,6) + 2*b(6,6)*b(3,2)*b(2,2)*b(1,1)*xi(4,3) + b(6,6)*b(3,2)*b(2,3)*b(1,1 )*xi(5,3) + b(6,6)*b(3,3)*b(2,2)*b(1,1)*xi(5,3) - 2*b(6,6)*b(3,3)*b(2,3)*b(1,1)* xi(5,2) + b(6,6)*b(4,6)*b(3,2)*xi(6,3) - b(6,6)*b(4,6)*b(3,3)*xi(6,2) + b(6,6)*b (5,6)*b(2,2)*xi(6,3) - b(6,6)*b(5,6)*b(2,3)*xi(6,2))/(b(6,6)*( - b(3,2)*b(2,3) + b(3,3)*b(2,2)))$ deltaprimemodg(6,3):=(b(6,6)*(b(2,2)*xi(6,3) - b(2,3)*xi(6,2)))/( - b(3,2)*b(2,3 ) + b(3,3)*b(2,2))$ deltaprimemodg(4,6):=(b(1,1)*(b(2,2)*xi(4,6) + b(2,3)*xi(5,6)))/b(6,6)$ deltaprimemodg(5,6):=(b(1,1)*(b(3,2)*xi(4,6) + b(3,3)*xi(5,6)))/b(6,6)$ det(AUTOM):=( - b(3,2)*b(2,3) + b(3,3)*b(2,2))**2*b(6,6)*b(1,1)**3$ DELTAPRIMEMODADG:= mat((0,0,0,0,0,0), b(2,2) (--------,0,0,0,0,0), b(1,1) b(3,2) (--------,0,0,0,0,0), b(1,1) (0,0,( - (( - b(6,2)*b(2,3) + b(6,3)*b(2,2)) *(b(2,2)*xi(4,6) + b(2,3)*xi(5,6))*b(1,1) + ( ( - b(2,2)*xi(6,3) + b(2,3)*xi(6,2))*b(4,6) + 2 2 ( - b(2,2) *xi(4,3) - b(2,3)*b(2,2)*xi(5,3) + b(2,3) *xi(5,2)) *b(1,1))*b(6,6)))/(( - b(3,2)*b(2,3) + b(3,3)*b(2,2))*b(6,6)),0 (b(2,2)*xi(4,6) + b(2,3)*xi(5,6))*b(1,1) ,0,------------------------------------------), b(6,6) (0,(( - b(6,2)*b(3,3) + b(6,3)*b(3,2))*(b(3,2)*xi(4,6) + b(3,3)*xi(5,6)) *b(1,1) + (( - b(3,2)*xi(6,3) + b(3,3)*xi(6,2))*b(5,6) + 2 2 ( - b(3,2) *xi(4,3) - b(3,3)*b(3,2)*xi(5,3) + b(3,3) *xi(5,2))*b(1,1) )*b(6,6))/(( - b(3,2)*b(2,3) + b(3,3)*b(2,2))*b(6,6)),(( - (b(3,3)*b(2,2)*xi(5,6) + (2*b(2,2)*xi(4,6) + b(2,3)*xi(5,6))*b(3,2)) *b(6,3) + (b(3,2)*b(2,3)*xi(4,6) + (b(2,2)*xi(4,6) + 2*b(2,3)*xi(5,6))*b(3,3)) *b(6,2))*b(1,1) + ( - ( - b(3,2)*xi(6,3) + b(3,3)*xi(6,2))*b(4,6) - ( - b(2,2)*xi(6,3) + b(2,3)*xi(6,2))*b(5,6) + ( - ( - b(2,2)*xi(5,3) + 2*b(2,3)*xi(5,2))*b(3,3) + (2*b(2,2)*xi(4,3) + b(2,3)*xi(5,3))*b(3,2))*b(1,1))*b(6,6))/( ( - b(3,2)*b(2,3) + b(3,3)*b(2,2))*b(6,6)),0,0, (b(3,2)*xi(4,6) + b(3,3)*xi(5,6))*b(1,1) ------------------------------------------), b(6,6) (( - ( - ( - b(3,2)*b(2,3) + b(3,3)*b(2,2))*b(6,2) + ( - ( - b(2,2)*xi(6,3) + b(2,3)*xi(6,2))*b(3,1) - ( - b(2,1)*xi(6,2) + b(2,2)*xi(6,1))*b(3,3) + ( - b(2,1)*xi(6,3) + b(2,3)*xi(6,1))*b(3,2))*b(6,6)))/( ( - b(3,2)*b(2,3) + b(3,3)*b(2,2))*b(1,1)), ( - b(3,2)*xi(6,3) + b(3,3)*xi(6,2))*b(6,6) ---------------------------------------------, - b(3,2)*b(2,3) + b(3,3)*b(2,2) - ( - b(2,2)*xi(6,3) + b(2,3)*xi(6,2))*b(6,6) ------------------------------------------------,0,0,0)) - b(3,2)*b(2,3) + b(3,3)*b(2,2) Then one keeps deltaprime(2,1)=k and deltaprime(3,1)=0 by taking :$ b(2,2):=b(1,1)*k$ b(3,2):=0$ With the generic automorphism one gets$ shortformdeltaprimemodadg:={k, 0, (b(6,2)*b(3,3)*b(1,1)*k - b(6,6)*b(3,1)*b(1,1)*xi(6,3)*k + b(6,6)*b(3,1)*b(2,3)* xi(6,2) + b(6,6)*b(3,3)*b(1,1)*xi(6,1)*k - b(6,6)*b(3,3)*b(2,1)*xi(6,2))/(b(3,3) *b(1,1)**2*k), ss, ( - b(6,2)*b(3,3)*b(1,1)*xi(5,6) + b(6,6)*b(3,3)*b(1,1)*xi(5,2) + b(6,6)*b(5,6)* xi(6,2))/(b(6,6)*b(1,1)*k), (b(6,6)*xi(6,2))/(b(1,1)*k), ss, (b(6,2)*b(2,3)*b(1,1)**2*xi(4,6)*k + b(6,2)*b(2,3)**2*b(1,1)*xi(5,6) - b(6,3)*b( 1,1)**3*xi(4,6)*k**2 - b(6,3)*b(2,3)*b(1,1)**2*xi(5,6)*k + b(6,6)*b(1,1)**3*xi(4 ,3)*k**2 + b(6,6)*b(2,3)*b(1,1)**2*xi(5,3)*k - b(6,6)*b(2,3)**2*b(1,1)*xi(5,2) + b(6,6)*b(4,6)*b(1,1)*xi(6,3)*k - b(6,6)*b(4,6)*b(2,3)*xi(6,2))/(b(6,6)*b(3,3)*b (1,1)*k), (b(6,2)*b(3,3)*b(1,1)**2*xi(4,6)*k + 2*b(6,2)*b(3,3)*b(2,3)*b(1,1)*xi(5,6) - b(6 ,3)*b(3,3)*b(1,1)**2*xi(5,6)*k + b(6,6)*b(3,3)*b(1,1)**2*xi(5,3)*k - 2*b(6,6)*b( 3,3)*b(2,3)*b(1,1)*xi(5,2) - b(6,6)*b(4,6)*b(3,3)*xi(6,2) + b(6,6)*b(5,6)*b(1,1) *xi(6,3)*k - b(6,6)*b(5,6)*b(2,3)*xi(6,2))/(b(6,6)*b(3,3)*b(1,1)*k), (b(6,6)*(b(1,1)*xi(6,3)*k - b(2,3)*xi(6,2)))/(b(3,3)*b(1,1)*k), ss, (b(1,1)*(b(1,1)*xi(4,6)*k + b(2,3)*xi(5,6)))/b(6,6), (b(3,3)*b(1,1)*xi(5,6))/b(6,6)}$ deltaprimemodg(2,1):=k$ deltaprimemodg(3,1):=0$ deltaprimemodg(6,1):=(b(6,2)*b(3,3)*b(1,1)*k - b(6,6)*b(3,1)*b(1,1)*xi(6,3)*k + b(6,6)*b(3,1)*b(2,3)*xi(6,2) + b(6,6)*b(3,3)*b(1,1)*xi(6,1)*k - b(6,6)*b(3,3)*b( 2,1)*xi(6,2))/(b(3,3)*b(1,1)**2*k)$ deltaprimemodg(5,2):=( - b(6,2)*b(3,3)*b(1,1)*xi(5,6) + b(6,6)*b(3,3)*b(1,1)*xi( 5,2) + b(6,6)*b(5,6)*xi(6,2))/(b(6,6)*b(1,1)*k)$ deltaprimemodg(6,2):=(b(6,6)*xi(6,2))/(b(1,1)*k)$ deltaprimemodg(4,3):=(b(6,2)*b(2,3)*b(1,1)**2*xi(4,6)*k + b(6,2)*b(2,3)**2*b(1,1 )*xi(5,6) - b(6,3)*b(1,1)**3*xi(4,6)*k**2 - b(6,3)*b(2,3)*b(1,1)**2*xi(5,6)*k + b(6,6)*b(1,1)**3*xi(4,3)*k**2 + b(6,6)*b(2,3)*b(1,1)**2*xi(5,3)*k - b(6,6)*b(2,3 )**2*b(1,1)*xi(5,2) + b(6,6)*b(4,6)*b(1,1)*xi(6,3)*k - b(6,6)*b(4,6)*b(2,3)*xi(6 ,2))/(b(6,6)*b(3,3)*b(1,1)*k)$ deltaprimemodg(5,3):=(b(6,2)*b(3,3)*b(1,1)**2*xi(4,6)*k + 2*b(6,2)*b(3,3)*b(2,3) *b(1,1)*xi(5,6) - b(6,3)*b(3,3)*b(1,1)**2*xi(5,6)*k + b(6,6)*b(3,3)*b(1,1)**2*xi (5,3)*k - 2*b(6,6)*b(3,3)*b(2,3)*b(1,1)*xi(5,2) - b(6,6)*b(4,6)*b(3,3)*xi(6,2) + b(6,6)*b(5,6)*b(1,1)*xi(6,3)*k - b(6,6)*b(5,6)*b(2,3)*xi(6,2))/(b(6,6)*b(3,3)*b (1,1)*k)$ deltaprimemodg(6,3):=(b(6,6)*(b(1,1)*xi(6,3)*k - b(2,3)*xi(6,2)))/(b(3,3)*b(1,1) *k)$ deltaprimemodg(4,6):=(b(1,1)*(b(1,1)*xi(4,6)*k + b(2,3)*xi(5,6)))/b(6,6)$ deltaprimemodg(5,6):=(b(3,3)*b(1,1)*xi(5,6))/b(6,6)$ det(AUTOM):=b(6,6)*b(3,3)**2*b(1,1)**5*k**2$ DELTAPRIMEMODADG:= mat((0,0,0,0,0,0), (k,0,0,0,0,0), (0,0,0,0,0,0), (0,0,( - (( - b(6,2)*b(2,3) + b(6,3)*b(1,1)*k) *(b(1,1)*xi(4,6)*k + b(2,3)*xi(5,6))*b(1,1) + ( ( - b(1,1)*xi(6,3)*k + b(2,3)*xi(6,2))*b(4,6) + ( 2 2 - b(1,1) *xi(4,3)*k - b(2,3)*b(1,1)*xi(5,3)*k 2 + b(2,3) *xi(5,2))*b(1,1))*b(6,6)))/(b(6,6)*b(3,3)*b(1,1)*k (b(1,1)*xi(4,6)*k + b(2,3)*xi(5,6))*b(1,1) ),0,0,--------------------------------------------), b(6,6) (0,( - b(6,2)*b(3,3)*b(1,1)*xi(5,6) + (b(3,3)*b(1,1)*xi(5,2) + b(5,6)*xi(6,2))*b(6,6))/(b(6,6)*b(1,1)*k),( - ( - ( - b(6,3)*b(1,1)*xi(5,6)*k + (b(1,1)*xi(4,6)*k + 2*b(2,3)*xi(5,6))*b(6,2))*b(3,3)*b(1,1) + (( - b(1,1)*xi(6,3)*k + b(2,3)*xi(6,2))*b(5,6) + (b(4,6)*xi(6,2) + ( - b(1,1)*xi(5,3)*k + 2*b(2,3)*xi(5,2))*b(1,1)) *b(3,3))*b(6,6)))/(b(6,6)*b(3,3)*b(1,1)*k),0,0, b(3,3)*b(1,1)*xi(5,6) -----------------------), b(6,6) ((b(6,2)*b(3,3)*b(1,1)*k + ( - ( - b(1,1)*xi(6,1)*k + b(2,1)*xi(6,2))*b(3,3) + ( - b(1,1)*xi(6,3)*k + b(2,3)*xi(6,2))*b(3,1))*b(6,6))/(b(3,3) 2 b(6,6)*xi(6,2) *b(1,1) *k),----------------, b(1,1)*k - ( - b(1,1)*xi(6,3)*k + b(2,3)*xi(6,2))*b(6,6) --------------------------------------------------,0,0,0)) b(3,3)*b(1,1)*k Then one gets deltaprime(6,1)=0 by taking :$ b(6,2):=( - ( - ( - b(1,1)*xi(6,1)*k + b(2,1)*xi(6,2))*b(3,3) + ( - b(1,1)*xi(6, 3)*k + b(2,3)*xi(6,2))*b(3,1))*b(6,6))/(b(3,3)*b(1,1)*k)$ With the generic automorphism one gets$ shortformdeltaprimemodadg:={k, 0, 0, ss, ( - b(3,1)*b(1,1)*xi(6,3)*xi(5,6)*k + b(3,1)*b(2,3)*xi(6,2)*xi(5,6) + b(3,3)*b(1 ,1)*xi(5,2)*k + b(3,3)*b(1,1)*xi(6,1)*xi(5,6)*k - b(3,3)*b(2,1)*xi(6,2)*xi(5,6) + b(5,6)*xi(6,2)*k)/(b(1,1)*k**2), (b(6,6)*xi(6,2))/(b(1,1)*k), ss, ( - b(6,3)*b(3,3)*b(1,1)**3*xi(4,6)*k**3 - b(6,3)*b(3,3)*b(2,3)*b(1,1)**2*xi(5,6 )*k**2 + b(6,6)*b(3,1)*b(2,3)*b(1,1)**2*xi(6,3)*xi(4,6)*k**2 - b(6,6)*b(3,1)*b(2 ,3)**2*b(1,1)*xi(6,2)*xi(4,6)*k + b(6,6)*b(3,1)*b(2,3)**2*b(1,1)*xi(6,3)*xi(5,6) *k - b(6,6)*b(3,1)*b(2,3)**3*xi(6,2)*xi(5,6) + b(6,6)*b(3,3)*b(1,1)**3*xi(4,3)*k **3 + b(6,6)*b(3,3)*b(2,3)*b(1,1)**2*xi(5,3)*k**2 - b(6,6)*b(3,3)*b(2,3)*b(1,1) **2*xi(6,1)*xi(4,6)*k**2 + b(6,6)*b(3,3)*b(2,3)*b(2,1)*b(1,1)*xi(6,2)*xi(4,6)*k - b(6,6)*b(3,3)*b(2,3)**2*b(1,1)*xi(5,2)*k - b(6,6)*b(3,3)*b(2,3)**2*b(1,1)*xi(6 ,1)*xi(5,6)*k + b(6,6)*b(3,3)*b(2,3)**2*b(2,1)*xi(6,2)*xi(5,6) + b(6,6)*b(4,6)*b (3,3)*b(1,1)*xi(6,3)*k**2 - b(6,6)*b(4,6)*b(3,3)*b(2,3)*xi(6,2)*k)/(b(6,6)*b(3,3 )**2*b(1,1)*k**2), ( - b(6,3)*b(3,3)*b(1,1)**2*xi(5,6)*k**2 + b(6,6)*b(3,1)*b(1,1)**2*xi(6,3)*xi(4, 6)*k**2 - b(6,6)*b(3,1)*b(2,3)*b(1,1)*xi(6,2)*xi(4,6)*k + 2*b(6,6)*b(3,1)*b(2,3) *b(1,1)*xi(6,3)*xi(5,6)*k - 2*b(6,6)*b(3,1)*b(2,3)**2*xi(6,2)*xi(5,6) + b(6,6)*b (3,3)*b(1,1)**2*xi(5,3)*k**2 - b(6,6)*b(3,3)*b(1,1)**2*xi(6,1)*xi(4,6)*k**2 + b( 6,6)*b(3,3)*b(2,1)*b(1,1)*xi(6,2)*xi(4,6)*k - 2*b(6,6)*b(3,3)*b(2,3)*b(1,1)*xi(5 ,2)*k - 2*b(6,6)*b(3,3)*b(2,3)*b(1,1)*xi(6,1)*xi(5,6)*k + 2*b(6,6)*b(3,3)*b(2,3) *b(2,1)*xi(6,2)*xi(5,6) - b(6,6)*b(4,6)*b(3,3)*xi(6,2)*k + b(6,6)*b(5,6)*b(1,1)* xi(6,3)*k**2 - b(6,6)*b(5,6)*b(2,3)*xi(6,2)*k)/(b(6,6)*b(3,3)*b(1,1)*k**2), (b(6,6)*(b(1,1)*xi(6,3)*k - b(2,3)*xi(6,2)))/(b(3,3)*b(1,1)*k), ss, (b(1,1)*(b(1,1)*xi(4,6)*k + b(2,3)*xi(5,6)))/b(6,6), (b(3,3)*b(1,1)*xi(5,6))/b(6,6)}$ deltaprimemodg(2,1):=k$ deltaprimemodg(3,1):=0$ deltaprimemodg(6,1):=0$ deltaprimemodg(5,2):=( - b(3,1)*b(1,1)*xi(6,3)*xi(5,6)*k + b(3,1)*b(2,3)*xi(6,2) *xi(5,6) + b(3,3)*b(1,1)*xi(5,2)*k + b(3,3)*b(1,1)*xi(6,1)*xi(5,6)*k - b(3,3)*b( 2,1)*xi(6,2)*xi(5,6) + b(5,6)*xi(6,2)*k)/(b(1,1)*k**2)$ deltaprimemodg(6,2):=(b(6,6)*xi(6,2))/(b(1,1)*k)$ deltaprimemodg(4,3):=( - b(6,3)*b(3,3)*b(1,1)**3*xi(4,6)*k**3 - b(6,3)*b(3,3)*b( 2,3)*b(1,1)**2*xi(5,6)*k**2 + b(6,6)*b(3,1)*b(2,3)*b(1,1)**2*xi(6,3)*xi(4,6)*k** 2 - b(6,6)*b(3,1)*b(2,3)**2*b(1,1)*xi(6,2)*xi(4,6)*k + b(6,6)*b(3,1)*b(2,3)**2*b (1,1)*xi(6,3)*xi(5,6)*k - b(6,6)*b(3,1)*b(2,3)**3*xi(6,2)*xi(5,6) + b(6,6)*b(3,3 )*b(1,1)**3*xi(4,3)*k**3 + b(6,6)*b(3,3)*b(2,3)*b(1,1)**2*xi(5,3)*k**2 - b(6,6)* b(3,3)*b(2,3)*b(1,1)**2*xi(6,1)*xi(4,6)*k**2 + b(6,6)*b(3,3)*b(2,3)*b(2,1)*b(1,1 )*xi(6,2)*xi(4,6)*k - b(6,6)*b(3,3)*b(2,3)**2*b(1,1)*xi(5,2)*k - b(6,6)*b(3,3)*b (2,3)**2*b(1,1)*xi(6,1)*xi(5,6)*k + b(6,6)*b(3,3)*b(2,3)**2*b(2,1)*xi(6,2)*xi(5, 6) + b(6,6)*b(4,6)*b(3,3)*b(1,1)*xi(6,3)*k**2 - b(6,6)*b(4,6)*b(3,3)*b(2,3)*xi(6 ,2)*k)/(b(6,6)*b(3,3)**2*b(1,1)*k**2)$ deltaprimemodg(5,3):=( - b(6,3)*b(3,3)*b(1,1)**2*xi(5,6)*k**2 + b(6,6)*b(3,1)*b( 1,1)**2*xi(6,3)*xi(4,6)*k**2 - b(6,6)*b(3,1)*b(2,3)*b(1,1)*xi(6,2)*xi(4,6)*k + 2 *b(6,6)*b(3,1)*b(2,3)*b(1,1)*xi(6,3)*xi(5,6)*k - 2*b(6,6)*b(3,1)*b(2,3)**2*xi(6, 2)*xi(5,6) + b(6,6)*b(3,3)*b(1,1)**2*xi(5,3)*k**2 - b(6,6)*b(3,3)*b(1,1)**2*xi(6 ,1)*xi(4,6)*k**2 + b(6,6)*b(3,3)*b(2,1)*b(1,1)*xi(6,2)*xi(4,6)*k - 2*b(6,6)*b(3, 3)*b(2,3)*b(1,1)*xi(5,2)*k - 2*b(6,6)*b(3,3)*b(2,3)*b(1,1)*xi(6,1)*xi(5,6)*k + 2 *b(6,6)*b(3,3)*b(2,3)*b(2,1)*xi(6,2)*xi(5,6) - b(6,6)*b(4,6)*b(3,3)*xi(6,2)*k + b(6,6)*b(5,6)*b(1,1)*xi(6,3)*k**2 - b(6,6)*b(5,6)*b(2,3)*xi(6,2)*k)/(b(6,6)*b(3, 3)*b(1,1)*k**2)$ deltaprimemodg(6,3):=(b(6,6)*(b(1,1)*xi(6,3)*k - b(2,3)*xi(6,2)))/(b(3,3)*b(1,1) *k)$ deltaprimemodg(4,6):=(b(1,1)*(b(1,1)*xi(4,6)*k + b(2,3)*xi(5,6)))/b(6,6)$ deltaprimemodg(5,6):=(b(3,3)*b(1,1)*xi(5,6))/b(6,6)$ det(AUTOM):=b(6,6)*b(3,3)**2*b(1,1)**5*k**2$ DELTAPRIMEMODADG:= mat((0,0,0,0,0,0), (k,0,0,0,0,0), (0,0,0,0,0,0), 2 2 (0,0,( - ((b(1,1)*xi(4,6)*k + b(2,3)*xi(5,6))*b(6,3)*b(3,3)*b(1,1) *k + (( b(4,6)*b(3,3)*k + (b(1,1)*xi(4,6)*k + b(2,3)*xi(5,6))*b(3,1)*b(2,3)) *( - b(1,1)*xi(6,3)*k + b(2,3)*xi(6,2)) + (( - b(2,1)*xi(6,2)*xi(5,6) 2 + (xi(5,2) + xi(6,1)*xi(5,6))*b(1,1)*k)*b(2,3) + ( 2 2 - b(1,1) *xi(4,3)*k + ( - b(2,1)*xi(6,2)*xi(4,6) + ( - xi(5,3) + xi(6,1)*xi(4,6))*b(1,1)*k)*b(2,3)) 2 2 *b(1,1)*k)*b(3,3))*b(6,6)))/(b(6,6)*b(3,3) *b(1,1)*k ),0,0, (b(1,1)*xi(4,6)*k + b(2,3)*xi(5,6))*b(1,1) --------------------------------------------), b(6,6) (0,(( - b(2,1)*xi(6,2)*xi(5,6) + (xi(5,2) + xi(6,1)*xi(5,6))*b(1,1)*k) *b(3,3) + b(5,6)*xi(6,2)*k 2 + ( - b(1,1)*xi(6,3)*k + b(2,3)*xi(6,2))*b(3,1)*xi(5,6))/(b(1,1)*k ),( 2 2 - (b(6,3)*b(3,3)*b(1,1) *xi(5,6)*k + ((( - b(2,1)*xi(6,2)*xi(4,6) + ( - xi(5,3) + xi(6,1)*xi(4,6))*b(1,1)*k)*b(1,1)*k + 2*( - b(2,1)*xi(6,2)*xi(5,6) + (xi(5,2) + xi(6,1)*xi(5,6))*b(1,1)*k)*b(2,3))*b(3,3) + b(4,6)*b(3,3)*xi(6,2)*k + (b(5,6)*k + (b(1,1)*xi(4,6)*k + 2*b(2,3)*xi(5,6))*b(3,1)) *( - b(1,1)*xi(6,3)*k + b(2,3)*xi(6,2)))*b(6,6)))/(b(6,6)*b(3,3) 2 b(3,3)*b(1,1)*xi(5,6) *b(1,1)*k ),0,0,-----------------------), b(6,6) b(6,6)*xi(6,2) - ( - b(1,1)*xi(6,3)*k + b(2,3)*xi(6,2))*b(6,6) (0,----------------,--------------------------------------------------,0,0,0 b(1,1)*k b(3,3)*b(1,1)*k )) *************** SUBSUBCASE 1.2 : xi(6,2) := 0 *************************$ xi(6,2):=0$ With the generic automorphism one gets$ shortformdeltaprimemodadg:={k, 0, 0, ss, ( - b(3,1)*xi(6,3)*xi(5,6) + b(3,3)*xi(5,2) + b(3,3)*xi(6,1)*xi(5,6))/k, 0, ss, ( - b(6,3)*b(3,3)*b(1,1)**2*xi(4,6)*k**2 - b(6,3)*b(3,3)*b(2,3)*b(1,1)*xi(5,6)*k + b(6,6)*b(3,1)*b(2,3)*b(1,1)*xi(6,3)*xi(4,6)*k + b(6,6)*b(3,1)*b(2,3)**2*xi(6, 3)*xi(5,6) + b(6,6)*b(3,3)*b(1,1)**2*xi(4,3)*k**2 + b(6,6)*b(3,3)*b(2,3)*b(1,1)* xi(5,3)*k - b(6,6)*b(3,3)*b(2,3)*b(1,1)*xi(6,1)*xi(4,6)*k - b(6,6)*b(3,3)*b(2,3) **2*xi(5,2) - b(6,6)*b(3,3)*b(2,3)**2*xi(6,1)*xi(5,6) + b(6,6)*b(4,6)*b(3,3)*xi( 6,3)*k)/(b(6,6)*b(3,3)**2*k), ( - b(6,3)*b(3,3)*b(1,1)*xi(5,6)*k + b(6,6)*b(3,1)*b(1,1)*xi(6,3)*xi(4,6)*k + 2* b(6,6)*b(3,1)*b(2,3)*xi(6,3)*xi(5,6) + b(6,6)*b(3,3)*b(1,1)*xi(5,3)*k - b(6,6)*b (3,3)*b(1,1)*xi(6,1)*xi(4,6)*k - 2*b(6,6)*b(3,3)*b(2,3)*xi(5,2) - 2*b(6,6)*b(3,3 )*b(2,3)*xi(6,1)*xi(5,6) + b(6,6)*b(5,6)*xi(6,3)*k)/(b(6,6)*b(3,3)*k), (b(6,6)*xi(6,3))/b(3,3), ss, (b(1,1)*(b(1,1)*xi(4,6)*k + b(2,3)*xi(5,6)))/b(6,6), (b(3,3)*b(1,1)*xi(5,6))/b(6,6)}$ deltaprimemodg(2,1):=k$ deltaprimemodg(3,1):=0$ deltaprimemodg(6,1):=0$ deltaprimemodg(5,2):=( - b(3,1)*xi(6,3)*xi(5,6) + b(3,3)*xi(5,2) + b(3,3)*xi(6,1 )*xi(5,6))/k$ deltaprimemodg(6,2):=0$ deltaprimemodg(4,3):=( - b(6,3)*b(3,3)*b(1,1)**2*xi(4,6)*k**2 - b(6,3)*b(3,3)*b( 2,3)*b(1,1)*xi(5,6)*k + b(6,6)*b(3,1)*b(2,3)*b(1,1)*xi(6,3)*xi(4,6)*k + b(6,6)*b (3,1)*b(2,3)**2*xi(6,3)*xi(5,6) + b(6,6)*b(3,3)*b(1,1)**2*xi(4,3)*k**2 + b(6,6)* b(3,3)*b(2,3)*b(1,1)*xi(5,3)*k - b(6,6)*b(3,3)*b(2,3)*b(1,1)*xi(6,1)*xi(4,6)*k - b(6,6)*b(3,3)*b(2,3)**2*xi(5,2) - b(6,6)*b(3,3)*b(2,3)**2*xi(6,1)*xi(5,6) + b(6 ,6)*b(4,6)*b(3,3)*xi(6,3)*k)/(b(6,6)*b(3,3)**2*k)$ deltaprimemodg(5,3):=( - b(6,3)*b(3,3)*b(1,1)*xi(5,6)*k + b(6,6)*b(3,1)*b(1,1)* xi(6,3)*xi(4,6)*k + 2*b(6,6)*b(3,1)*b(2,3)*xi(6,3)*xi(5,6) + b(6,6)*b(3,3)*b(1,1 )*xi(5,3)*k - b(6,6)*b(3,3)*b(1,1)*xi(6,1)*xi(4,6)*k - 2*b(6,6)*b(3,3)*b(2,3)*xi (5,2) - 2*b(6,6)*b(3,3)*b(2,3)*xi(6,1)*xi(5,6) + b(6,6)*b(5,6)*xi(6,3)*k)/(b(6,6 )*b(3,3)*k)$ deltaprimemodg(6,3):=(b(6,6)*xi(6,3))/b(3,3)$ deltaprimemodg(4,6):=(b(1,1)*(b(1,1)*xi(4,6)*k + b(2,3)*xi(5,6)))/b(6,6)$ deltaprimemodg(5,6):=(b(3,3)*b(1,1)*xi(5,6))/b(6,6)$ det(AUTOM):=b(6,6)*b(3,3)**2*b(1,1)**5*k**2$ DELTAPRIMEMODADG:= mat((0,0,0,0,0,0), (k,0,0,0,0,0), (0,0,0,0,0,0), (0,0,( - ((b(1,1)*xi(4,6)*k + b(2,3)*xi(5,6))*b(6,3)*b(3,3)*b(1,1)*k + ( - ( b(4,6)*b(3,3)*k + (b(1,1)*xi(4,6)*k + b(2,3)*xi(5,6))*b(3,1)*b(2,3)) 2 *xi(6,3) + ((xi(5,2) + xi(6,1)*xi(5,6))*b(2,3) + ( - b(1,1)*xi(4,3)*k + ( - xi(5,3) + xi(6,1)*xi(4,6))*b(2,3))*b(1,1)*k) 2 *b(3,3))*b(6,6)))/(b(6,6)*b(3,3) *k),0,0, (b(1,1)*xi(4,6)*k + b(2,3)*xi(5,6))*b(1,1) --------------------------------------------), b(6,6) - b(3,1)*xi(6,3)*xi(5,6) + (xi(5,2) + xi(6,1)*xi(5,6))*b(3,3) (0,----------------------------------------------------------------,( k - b(6,3)*b(3,3)*b(1,1)*xi(5,6)*k + ( - ( ( - xi(5,3) + xi(6,1)*xi(4,6))*b(1,1)*k + 2*(xi(5,2) + xi(6,1)*xi(5,6))*b(2,3))*b(3,3) + (b(5,6)*k + (b(1,1)*xi(4,6)*k + 2*b(2,3)*xi(5,6))*b(3,1))*xi(6,3)) b(3,3)*b(1,1)*xi(5,6) *b(6,6))/(b(6,6)*b(3,3)*k),0,0,-----------------------), b(6,6) b(6,6)*xi(6,3) (0,0,----------------,0,0,0)) b(3,3) *************** SUBSUBSUBCASE 1.2.1. : xi(5,6) NEQ 0 ***********************$ Then one gets deltaprime(5,6)=k by taking :$ b(6,6):=(b(3,3)*b(1,1)*xi(5,6))/k$ Hence we may suppose xi(5,6):=1 and we keep deltaprime(5,6):=k by our choice.$ xi(5,6):=1$ One gets deltaprime(5,3)=0 and deltaprime(4,6)=0 by taking :$ b(6,3):=( - ( - b(5,6)*xi(6,3)*k + 2*(xi(5,2) + xi(6,1))*b(3,3)*b(2,3)) - ( - xi (5,3) + xi(6,1)*xi(4,6))*b(3,3)*b(1,1)*k + (b(1,1)*xi(4,6)*k + 2*b(2,3))*b(3,1)* xi(6,3))/k**2$ b(2,3):= - b(1,1)*xi(4,6)*k$ Hence we may suppose xi(5,3):=0 and we keep deltaprime(5,3):=0 by our choice.$ and similarly xi(4,6):=0 and we keep deltaprime(4,6):=0 by our choice.$ xi(5,3):=0$ xi(4,6):=0$ With the generic automorphism one gets$ shortformdeltaprimemodadg:={k, 0, 0, ss, ( - b(3,1)*xi(6,3) + b(3,3)*xi(5,2) + b(3,3)*xi(6,1))/k, 0, ss, (b(1,1)**2*xi(4,3)*k + b(4,6)*xi(6,3))/b(3,3), 0, (b(1,1)*xi(6,3))/k, ss, 0, k}$ deltaprimemodg(2,1):=k$ deltaprimemodg(3,1):=0$ deltaprimemodg(6,1):=0$ deltaprimemodg(5,2):=( - b(3,1)*xi(6,3) + b(3,3)*xi(5,2) + b(3,3)*xi(6,1))/k$ deltaprimemodg(6,2):=0$ deltaprimemodg(4,3):=(b(1,1)**2*xi(4,3)*k + b(4,6)*xi(6,3))/b(3,3)$ deltaprimemodg(5,3):=0$ deltaprimemodg(6,3):=(b(1,1)*xi(6,3))/k$ deltaprimemodg(4,6):=0$ deltaprimemodg(5,6):=k$ det(AUTOM):=b(3,3)**3*b(1,1)**6*k$ DELTAPRIMEMODADG:= mat((0,0,0,0,0,0), (k,0,0,0,0,0), (0,0,0,0,0,0), 2 b(1,1) *xi(4,3)*k + b(4,6)*xi(6,3) (0,0,------------------------------------,0,0,0), b(3,3) - b(3,1)*xi(6,3) + (xi(5,2) + xi(6,1))*b(3,3) (0,------------------------------------------------,0,0,0,k), k b(1,1)*xi(6,3) (0,0,----------------,0,0,0)) k ************** Suppose first that xi(6,3) neq 0.$ Then one gets deltaprime(6,3)=k ,$ and one gets deltaprime(5,2)=0 and deltaprime(4,3)=0 by taking :$ b(3,1):=((xi(5,2) + xi(6,1))*b(3,3))/xi(6,3)$ b(4,6):=( - b(1,1)**2*xi(4,3)*k)/xi(6,3)$ b(1,1):=k**2/xi(6,3)$ With the generic automorphism one gets$ shortformdeltaprimemodadg:={k, 0, 0, ss, 0, 0, ss, 0, 0, k, ss, 0, k}$ deltaprimemodg(2,1):=k$ deltaprimemodg(3,1):=0$ deltaprimemodg(6,1):=0$ deltaprimemodg(5,2):=0$ deltaprimemodg(6,2):=0$ deltaprimemodg(4,3):=0$ deltaprimemodg(5,3):=0$ deltaprimemodg(6,3):=k$ deltaprimemodg(4,6):=0$ deltaprimemodg(5,6):=k$ det(AUTOM):=(b(3,3)**3*k**13)/xi(6,3)**6$ DELTAPRIMEMODADG:= [0 0 0 0 0 0] [ ] [k 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 k 0 0 0] Hence, we are reduced in the subsubsubcase 1.2.1 if xi(6,3) neq 0 to:$ shortformdeltaprime:={1,0,0,ss,0,0,ss,0,0,1,ss,0,1}$ ************** Suppose now that xi(6,3) = 0.$ clear b(3,1),b(4,6),b(1,1)$ xi(6,3):=0$ With the generic automorphism one gets$ shortformdeltaprimemodadg:={k, 0, 0, ss, (b(3,3)*(xi(5,2) + xi(6,1)))/k, 0, ss, (b(1,1)**2*xi(4,3)*k)/b(3,3), 0, 0, ss, 0, k}$ deltaprimemodg(2,1):=k$ deltaprimemodg(3,1):=0$ deltaprimemodg(6,1):=0$ deltaprimemodg(5,2):=(b(3,3)*(xi(5,2) + xi(6,1)))/k$ deltaprimemodg(6,2):=0$ deltaprimemodg(4,3):=(b(1,1)**2*xi(4,3)*k)/b(3,3)$ deltaprimemodg(5,3):=0$ deltaprimemodg(6,3):=0$ deltaprimemodg(4,6):=0$ deltaprimemodg(5,6):=k$ det(AUTOM):=b(3,3)**3*b(1,1)**6*k$ DELTAPRIMEMODADG:= [0 0 0 0 0 0] [ ] [k 0 0 0 0 0] [ ] [0 0 0 0 0 0] [ ] [ 2 ] [ b(1,1) *xi(4,3)*k ] [0 0 ------------------- 0 0 0] [ b(3,3) ] [ ] [ (xi(5,2) + xi(6,1))*b(3,3) ] [0 ---------------------------- 0 0 0 k] [ k ] [ ] [0 0 0 0 0 0] Hence, we are reduced in the subsubsubcase 1.2.1 if xi(6,3) := 0 to:$ shortformdeltaprime:={1,0,0,ss,epsilon,0,ss,eta,0,0,ss,0,1}$ where epsilon=xi(5,2)=0,1. and eta=xi(4,3)=0,1.$