phi:= mat((b(1,1),0,0,0,0,0), (b(2,1),b(2,2),0,0,0,0), 2 (b(3,1),b(3,2),b(1,1) ,0,0,0), (b(4,1),b(4,2),b(4,3),b(2,2)*b(1,1),0,0), 3 (b(5,1),b(5,2),b(5,3),b(3,2)*b(1,1),b(1,1) ,0), (b(6,1),b(6,2),b(6,3),b(4,2)*b(1,1) - b(3,2)*b(2,1) + b(3,1)*b(2,2), 2 b(1,1)*(b(4,3) - b(2,1)*b(1,1)),b(2,2)*b(1,1) )) 3 9 det(phi):=b(2,2) *b(1,1) generic derivation : delta:= [ 0 0 0 0 0 0] [ ] [xi(2,1) 0 0 0 0 0] [ ] [xi(3,1) xi(3,2) 0 0 0 0] [ ] [xi(4,1) xi(4,2) xi(4,3) 0 0 0] [ ] [xi(5,1) xi(5,2) xi(5,3) xi(3,2) 0 0] [ ] [xi(6,1) xi(6,2) xi(6,3) xi(4,2) + xi(3,1) xi(4,3) - xi(2,1) 0] [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 1 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 -1 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 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] [ ] [0 0 0 0 0 0] [ ] [-1 0 0 0 0 0] delta:= [ 0 0 0 0 0 0] [ ] [xi(2,1) 0 0 0 0 0] [ ] [xi(3,1) xi(3,2) 0 0 0 0] [ ] [ 0 0 xi(4,3) 0 0 0] [ ] [ 0 xi(5,2) xi(5,3) xi(3,2) 0 0] [ ] [ 0 xi(6,2) xi(6,3) xi(3,1) xi(4,3) - xi(2,1) 0] We denote this delta by the shortform shortformdelta:={xi(2,1), ss, xi(3,1), xi(3,2), ss, xi(4,3), ss, xi(5,2), xi(5,3), ss, xi(6,2), xi(6,3)} paramindexeslist:={{2,1},{3,1},{3,2},{4,3},{5,2},{5,3},{6,2},{6,3}} shortformdelta:={1, ss, 0, 0, ss, xi(4,3), ss, 0, 0, ss, xi(6,2), 0}$ With the generic automorphism one gets$ shortformdeltaprimemodadg:={b(2,2)/b(1,1), ss, b(3,2)/b(1,1), 0, ss, (b(2,2)*xi(4,3))/b(1,1), ss, ( - b(3,2)**2*xi(4,3))/(b(2,2)*b(1,1)), (2*b(3,2)*xi(4,3))/b(1,1), ss, (b(5,3)*b(3,2)*b(2,2)*xi(4,3) - b(5,3)*b(3,2)*b(2,2) - b(5,2)*b(2,2)*b(1,1)**2* xi(4,3) + 2*b(5,2)*b(2,2)*b(1,1)**2 - b(4,3)*b(3,2)**2*xi(4,3) + b(4,3)*b(3,2)** 2 - b(4,2)*b(3,2)*b(1,1)**2 + 2*b(3,2)**2*b(2,1)*b(1,1)*xi(4,3) - 2*b(3,2)*b(3,1 )*b(2,2)*b(1,1)*xi(4,3) + b(2,2)*b(1,1)**5*xi(6,2))/(b(2,2)*b(1,1)**3), ( - b(5,3)*b(2,2)*xi(4,3) + b(5,3)*b(2,2) + b(4,3)*b(3,2)*xi(4,3) - b(4,3)*b(3,2 ) + b(4,2)*b(1,1)**2*xi(4,3) - b(4,2)*b(1,1)**2 - 2*b(3,2)*b(2,1)*b(1,1)*xi(4,3) + 2*b(3,1)*b(2,2)*b(1,1)*xi(4,3))/b(1,1)**3}$ deltaprimemodg(2,1):=b(2,2)/b(1,1)$ deltaprimemodg(3,1):=b(3,2)/b(1,1)$ deltaprimemodg(3,2):=0$ deltaprimemodg(4,3):=(b(2,2)*xi(4,3))/b(1,1)$ deltaprimemodg(5,2):=( - b(3,2)**2*xi(4,3))/(b(2,2)*b(1,1))$ deltaprimemodg(5,3):=(2*b(3,2)*xi(4,3))/b(1,1)$ deltaprimemodg(6,2):=(b(5,3)*b(3,2)*b(2,2)*xi(4,3) - b(5,3)*b(3,2)*b(2,2) - b(5, 2)*b(2,2)*b(1,1)**2*xi(4,3) + 2*b(5,2)*b(2,2)*b(1,1)**2 - b(4,3)*b(3,2)**2*xi(4, 3) + b(4,3)*b(3,2)**2 - b(4,2)*b(3,2)*b(1,1)**2 + 2*b(3,2)**2*b(2,1)*b(1,1)*xi(4 ,3) - 2*b(3,2)*b(3,1)*b(2,2)*b(1,1)*xi(4,3) + b(2,2)*b(1,1)**5*xi(6,2))/(b(2,2)* b(1,1)**3)$ deltaprimemodg(6,3):=( - b(5,3)*b(2,2)*xi(4,3) + b(5,3)*b(2,2) + b(4,3)*b(3,2)* xi(4,3) - b(4,3)*b(3,2) + b(4,2)*b(1,1)**2*xi(4,3) - b(4,2)*b(1,1)**2 - 2*b(3,2) *b(2,1)*b(1,1)*xi(4,3) + 2*b(3,1)*b(2,2)*b(1,1)*xi(4,3))/b(1,1)**3$ det(AUTOM):=b(2,2)**3*b(1,1)**9$ 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) b(2,2)*xi(4,3) (0,0,----------------,0,0,0), b(1,1) 2 - b(3,2) *xi(4,3) 2*b(3,2)*xi(4,3) (0,--------------------,------------------,0,0,0), b(2,2)*b(1,1) b(1,1) 2 (0,((2*b(3,2) *b(2,1)*xi(4,3) - 2*b(3,2)*b(3,1)*b(2,2)*xi(4,3) 4 + b(2,2)*b(1,1) *xi(6,2) - b(4,2)*b(3,2)*b(1,1) - (xi(4,3) - 2)*b(5,2)*b(2,2)*b(1,1))*b(1,1) 3 + (b(5,3)*b(2,2) - b(4,3)*b(3,2))*(xi(4,3) - 1)*b(3,2))/(b(2,2)*b(1,1) 2 ),((b(4,3)*b(3,2) + b(4,2)*b(1,1) - b(5,3)*b(2,2))*(xi(4,3) - 1) 3 - 2*(b(3,2)*b(2,1) - b(3,1)*b(2,2))*b(1,1)*xi(4,3))/b(1,1) , b(3,2) (xi(4,3) - 1)*b(2,2) --------,----------------------,0)) b(1,1) b(1,1) With the generic automorphism one gets$ shortformdeltaprimemodadg:={1, ss, 0, 0, ss, xi(4,3), ss, 0, 0, ss, ( - b(5,2)*xi(4,3) + 2*b(5,2) + b(1,1)**3*xi(6,2))/b(1,1), ( - b(5,3)*xi(4,3) + b(5,3) + b(4,2)*b(1,1)*xi(4,3) - b(4,2)*b(1,1) + 2*b(3,1)*b (1,1)*xi(4,3))/b(1,1)**2}$ deltaprimemodg(2,1):=1$ deltaprimemodg(3,1):=0$ deltaprimemodg(3,2):=0$ deltaprimemodg(4,3):=xi(4,3)$ deltaprimemodg(5,2):=0$ deltaprimemodg(5,3):=0$ deltaprimemodg(6,2):=( - b(5,2)*xi(4,3) + 2*b(5,2) + b(1,1)**3*xi(6,2))/b(1,1)$ deltaprimemodg(6,3):=( - b(5,3)*xi(4,3) + b(5,3) + b(4,2)*b(1,1)*xi(4,3) - b(4,2 )*b(1,1) + 2*b(3,1)*b(1,1)*xi(4,3))/b(1,1)**2$ det(AUTOM):=b(1,1)**12$ DELTAPRIMEMODADG:= mat((0,0,0,0,0,0), (1,0,0,0,0,0), (0,0,0,0,0,0), (0,0,xi(4,3),0,0,0), (0,0,0,0,0,0), 3 - ((xi(4,3) - 2)*b(5,2) - b(1,1) *xi(6,2)) (0,---------------------------------------------, b(1,1) - ((b(5,3) - b(4,2)*b(1,1))*(xi(4,3) - 1) - 2*b(3,1)*b(1,1)*xi(4,3)) -----------------------------------------------------------------------,0, 2 b(1,1) xi(4,3) - 1,0)) With the generic automorphism one gets$ shortformdeltaprimemodadg:={1, ss, 0, 0, ss, xi(4,3), ss, 0, 0, ss, 0, 0}$ deltaprimemodg(2,1):=1$ deltaprimemodg(3,1):=0$ deltaprimemodg(3,2):=0$ deltaprimemodg(4,3):=xi(4,3)$ deltaprimemodg(5,2):=0$ deltaprimemodg(5,3):=0$ deltaprimemodg(6,2):=0$ deltaprimemodg(6,3):=0$ det(AUTOM):=b(1,1)**12$ DELTAPRIMEMODADG:= [0 0 0 0 0 0] [ ] [1 0 0 0 0 0] [ ] [0 0 0 0 0 0] [ ] [0 0 xi(4,3) 0 0 0] [ ] [0 0 0 0 0 0] [ ] [0 0 0 0 xi(4,3) - 1 0] Hence for xi(4,3) neq 2, (1;0,0;xi(4,3);0,0;xi(6,2),0)$ is proj. equiv. to (1;0,0;xi(4,3);0,0;0,0)$