rreducparautommodg6_8N5.r phi:= mat((b(1,1),b(1,2),0,0,0,0), (0,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),0,b(2,2)*b(1,1),0,0), (b(5,1),b(5,2),b(5,3),b(4,2)*b(1,1) - b(4,1)*b(1,2) - b(3,1)*b(2,2), 2 b(2,2)*b(1,1) ,b(2,2)*b(1,2)*b(1,1)), 2 (b(6,1),b(6,2),b(6,3), - b(4,1)*b(2,2),0,b(2,2) *b(1,1))) 5 7 det(phi):=b(2,2) *b(1,1) generic derivation : delta:= [ 0 xi(1,2) 0 0 0 0 ] [ ] [ 0 0 0 0 0 0 ] [ ] [xi(3,1) xi(3,2) 0 0 0 0 ] [ ] [xi(4,1) xi(4,2) 0 0 0 0 ] [ ] [xi(5,1) xi(5,2) xi(5,3) xi(4,2) - xi(3,1) 0 xi(1,2)] [ ] [xi(6,1) xi(6,2) xi(6,3) - xi(4,1) 0 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 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] adx2 := [ ] [-1 0 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] adx3 := [ ] [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 0] adx4 := [ ] [0 0 0 0 0 0] [ ] [-1 0 0 0 0 0] [ ] [0 -1 0 0 0 0] delta:= [ 0 xi(1,2) 0 0 0 0 ] [ ] [ 0 0 0 0 0 0 ] [ ] [xi(3,1) xi(3,2) 0 0 0 0 ] [ ] [ 0 0 0 0 0 0 ] [ ] [ 0 xi(5,2) xi(5,3) - xi(3,1) 0 xi(1,2)] [ ] [xi(6,1) xi(6,2) xi(6,3) 0 0 0 ] We denote this delta by the shortform shortformdelta:={xi(1,2), ss, xi(3,1), xi(3,2), ss, xi(5,3), ss, xi(6,1), xi(6,2), xi(6,3)} paramindexeslist:={{1,2},{3,1},{3,2},{5,3},{6,1},{6,2},{6,3}} With the generic automorphism one gets$ shortformdeltaprimemodadg:={0, ss, b(1,1)*xi(3,1), (b(3,1)*xi(1,2) - b(1,2)*b(1,1)*xi(3,1) + b(1,1)**2*xi(3,2))/b(2,2), ss, ( - b(6,3)*xi(1,2) + b(2,2)**2*b(1,2)*xi(6,3) + b(2,2)**2*b(1,1)*xi(5,3))/(b(2,2 )*b(1,1)), ss, (b(6,3)*b(1,1)*xi(3,1) - b(3,1)*b(2,2)**2*xi(6,3) + b(2,2)**2*b(1,1)**2*xi(6,1)) /b(1,1)**2, ( - b(6,3)*b(3,1)*xi(1,2) - b(6,3)*b(1,2)*b(1,1)*xi(3,1) + b(6,3)*b(1,1)**2*xi(3 ,2) + 2*b(6,1)*b(1,1)**2*xi(1,2) - b(5,3)*b(2,2)*b(1,1)*xi(3,1) + b(4,1)**2*b(1, 1)*xi(1,2) - b(4,1)*b(2,2)*b(1,1)**2*xi(3,1) - b(3,2)*b(2,2)**2*b(1,1)*xi(6,3) + 2*b(3,1)*b(2,2)**2*b(1,2)*xi(6,3) + b(3,1)*b(2,2)**2*b(1,1)*xi(5,3) - 2*b(2,2) **2*b(1,2)*b(1,1)**2*xi(6,1) + b(2,2)**2*b(1,1)**3*xi(6,2))/(b(2,2)*b(1,1)**2), (b(2,2)**2*xi(6,3))/b(1,1)}$ deltaprimemodg(1,2):=(b(1,1)*xi(1,2))/b(2,2)$ deltaprimemodg(3,1):=b(1,1)*xi(3,1)$ deltaprimemodg(3,2):=(b(3,1)*xi(1,2) - b(1,2)*b(1,1)*xi(3,1) + b(1,1)**2*xi(3,2) )/b(2,2)$ deltaprimemodg(5,3):=( - b(6,3)*xi(1,2) + b(2,2)**2*b(1,2)*xi(6,3) + b(2,2)**2*b (1,1)*xi(5,3))/(b(2,2)*b(1,1))$ deltaprimemodg(6,1):=(b(6,3)*b(1,1)*xi(3,1) - b(3,1)*b(2,2)**2*xi(6,3) + b(2,2) **2*b(1,1)**2*xi(6,1))/b(1,1)**2$ deltaprimemodg(6,2):=( - b(6,3)*b(3,1)*xi(1,2) - b(6,3)*b(1,2)*b(1,1)*xi(3,1) + b(6,3)*b(1,1)**2*xi(3,2) + 2*b(6,1)*b(1,1)**2*xi(1,2) - b(5,3)*b(2,2)*b(1,1)*xi( 3,1) + b(4,1)**2*b(1,1)*xi(1,2) - b(4,1)*b(2,2)*b(1,1)**2*xi(3,1) - b(3,2)*b(2,2 )**2*b(1,1)*xi(6,3) + 2*b(3,1)*b(2,2)**2*b(1,2)*xi(6,3) + b(3,1)*b(2,2)**2*b(1,1 )*xi(5,3) - 2*b(2,2)**2*b(1,2)*b(1,1)**2*xi(6,1) + b(2,2)**2*b(1,1)**3*xi(6,2))/ (b(2,2)*b(1,1)**2)$ deltaprimemodg(6,3):=(b(2,2)**2*xi(6,3))/b(1,1)$ det(AUTOM):=b(2,2)**5*b(1,1)**7$ DELTAPRIMEMODADG:= b(1,1)*xi(1,2) mat((0,----------------,0,0,0,0), b(2,2) (0,0,0,0,0,0), (b(1,1)*xi(3,1), - ((b(1,2)*xi(3,1) - b(1,1)*xi(3,2))*b(1,1) - b(3,1)*xi(1,2)) ----------------------------------------------------------------,0,0,0,0), b(2,2) (0,0,0,0,0,0), 2 (b(1,2)*xi(6,3) + b(1,1)*xi(5,3))*b(2,2) - b(6,3)*xi(1,2) (0,0,------------------------------------------------------------, b(2,2)*b(1,1) b(1,1)*xi(1,2) - b(1,1)*xi(3,1),0,----------------), b(2,2) 2 2 - ((b(3,1)*xi(6,3) - b(1,1) *xi(6,1))*b(2,2) - b(6,3)*b(1,1)*xi(3,1)) (-------------------------------------------------------------------------,( 2 b(1,1) 2 2 (b(4,1) *xi(1,2) - b(4,1)*b(2,2)*b(1,1)*xi(3,1) - b(3,2)*b(2,2) *xi(6,3) - b(5,3)*b(2,2)*xi(3,1) + 2*b(6,1)*b(1,1)*xi(1,2) 2 - (2*b(1,2)*xi(6,1) - b(1,1)*xi(6,2))*b(2,2) *b(1,1))*b(1,1) 2 + (2*b(1,2)*xi(6,3) + b(1,1)*xi(5,3))*b(3,1)*b(2,2) - ((b(1,2)*xi(3,1) - b(1,1)*xi(3,2))*b(1,1) + b(3,1)*xi(1,2))*b(6,3))/( 2 2 b(2,2) *xi(6,3) b(2,2)*b(1,1) ),-----------------,0,0,0)) b(1,1) %%%%%%%%%%% CASE 1 : SUPPOSE xi(1,2) NEQ 0 .%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$ We stay in that case by projective equivalence.$ Then we may suppose xi(1,2):=1.$ xi(1,2):=1$ and we keep deltaprime(1,2)=k (k nonzero) if we take$ b(2,2):=b(1,1)/k$ With the generic automorphism one gets$ shortformdeltaprimemodadg:={0, ss, b(1,1)*xi(3,1), (k*(b(3,1) - b(1,2)*b(1,1)*xi(3,1) + b(1,1)**2*xi(3,2)))/b(1,1), ss, ( - b(6,3)*k**2 + b(1,2)*b(1,1)**2*xi(6,3) + b(1,1)**3*xi(5,3))/(b(1,1)**2*k), ss, (b(6,3)*xi(3,1)*k**2 - b(3,1)*b(1,1)*xi(6,3) + b(1,1)**3*xi(6,1))/(b(1,1)*k**2), ( - b(6,3)*b(3,1)*k**2 - b(6,3)*b(1,2)*b(1,1)*xi(3,1)*k**2 + b(6,3)*b(1,1)**2*xi (3,2)*k**2 + 2*b(6,1)*b(1,1)**2*k**2 - b(5,3)*b(1,1)**2*xi(3,1)*k + b(4,1)**2*b( 1,1)*k**2 - b(4,1)*b(1,1)**3*xi(3,1)*k - b(3,2)*b(1,1)**3*xi(6,3) + 2*b(3,1)*b(1 ,2)*b(1,1)**2*xi(6,3) + b(3,1)*b(1,1)**3*xi(5,3) - 2*b(1,2)*b(1,1)**4*xi(6,1) + b(1,1)**5*xi(6,2))/(b(1,1)**3*k), (b(1,1)*xi(6,3))/k**2}$ deltaprimemodg(1,2):=k$ deltaprimemodg(3,1):=b(1,1)*xi(3,1)$ deltaprimemodg(3,2):=(k*(b(3,1) - b(1,2)*b(1,1)*xi(3,1) + b(1,1)**2*xi(3,2)))/b( 1,1)$ deltaprimemodg(5,3):=( - b(6,3)*k**2 + b(1,2)*b(1,1)**2*xi(6,3) + b(1,1)**3*xi(5 ,3))/(b(1,1)**2*k)$ deltaprimemodg(6,1):=(b(6,3)*xi(3,1)*k**2 - b(3,1)*b(1,1)*xi(6,3) + b(1,1)**3*xi (6,1))/(b(1,1)*k**2)$ deltaprimemodg(6,2):=( - b(6,3)*b(3,1)*k**2 - b(6,3)*b(1,2)*b(1,1)*xi(3,1)*k**2 + b(6,3)*b(1,1)**2*xi(3,2)*k**2 + 2*b(6,1)*b(1,1)**2*k**2 - b(5,3)*b(1,1)**2*xi( 3,1)*k + b(4,1)**2*b(1,1)*k**2 - b(4,1)*b(1,1)**3*xi(3,1)*k - b(3,2)*b(1,1)**3* xi(6,3) + 2*b(3,1)*b(1,2)*b(1,1)**2*xi(6,3) + b(3,1)*b(1,1)**3*xi(5,3) - 2*b(1,2 )*b(1,1)**4*xi(6,1) + b(1,1)**5*xi(6,2))/(b(1,1)**3*k)$ deltaprimemodg(6,3):=(b(1,1)*xi(6,3))/k**2$ det(AUTOM):=b(1,1)**12/k**5$ DELTAPRIMEMODADG:= mat((0,k,0,0,0,0), (0,0,0,0,0,0), - ((b(1,2)*xi(3,1) - b(1,1)*xi(3,2))*b(1,1) - b(3,1))*k (b(1,1)*xi(3,1),----------------------------------------------------------,0 b(1,1) ,0,0,0), (0,0,0,0,0,0), 2 2 (b(1,2)*xi(6,3) + b(1,1)*xi(5,3))*b(1,1) - b(6,3)*k (0,0,-------------------------------------------------------, 2 b(1,1) *k - b(1,1)*xi(3,1),0,k), 2 2 - ((b(3,1)*xi(6,3) - b(1,1) *xi(6,1))*b(1,1) - b(6,3)*xi(3,1)*k ) (--------------------------------------------------------------------,( - (( 2 b(1,1)*k ((2*b(1,2)*xi(6,1) - b(1,1)*xi(6,2))*b(1,1) + b(3,2)*xi(6,3)) 2 2 *b(1,1) - (b(4,1)*k - b(1,1) *xi(3,1))*b(4,1)*k 2 + b(5,3)*b(1,1)*xi(3,1)*k - 2*b(6,1)*b(1,1)*k - (2*b(1,2)*xi(6,3) + b(1,1)*xi(5,3))*b(3,1)*b(1,1))*b(1,1) 2 + ((b(1,2)*xi(3,1) - b(1,1)*xi(3,2))*b(1,1) + b(3,1))*b(6,3)*k ))/( 3 b(1,1)*xi(6,3) b(1,1) *k),----------------,0,0,0)) 2 k Then we get deltaprimemodadg(3,2)=0 if we take$ b(3,1):=(b(1,2)*xi(3,1) - b(1,1)*xi(3,2))*b(1,1)$ and deltaprimemodadg(5,3)=0 if we take$ b(6,3):=((b(1,2)*xi(6,3) + b(1,1)*xi(5,3))*b(1,1)**2)/k**2$ With the generic automorphism one gets$ shortformdeltaprimemodadg:={0, ss, b(1,1)*xi(3,1), 0, ss, 0, ss, (b(1,1)**2*(xi(6,3)*xi(3,2) + xi(6,1) + xi(5,3)*xi(3,1)))/k**2, (2*b(6,1)*b(1,1)*k**2 - b(5,3)*b(1,1)*xi(3,1)*k + b(4,1)**2*k**2 - b(4,1)*b(1,1) **2*xi(3,1)*k - b(3,2)*b(1,1)**2*xi(6,3) - 2*b(1,2)*b(1,1)**3*xi(6,1) - b(1,2)*b (1,1)**3*xi(5,3)*xi(3,1) + b(1,1)**4*xi(6,2) + b(1,1)**4*xi(5,3)*xi(3,2))/(b(1,1 )**2*k), (b(1,1)*xi(6,3))/k**2}$ deltaprimemodg(1,2):=k$ deltaprimemodg(3,1):=b(1,1)*xi(3,1)$ deltaprimemodg(3,2):=0$ deltaprimemodg(5,3):=0$ deltaprimemodg(6,1):=(b(1,1)**2*(xi(6,3)*xi(3,2) + xi(6,1) + xi(5,3)*xi(3,1)))/k **2$ deltaprimemodg(6,2):=(2*b(6,1)*b(1,1)*k**2 - b(5,3)*b(1,1)*xi(3,1)*k + b(4,1)**2 *k**2 - b(4,1)*b(1,1)**2*xi(3,1)*k - b(3,2)*b(1,1)**2*xi(6,3) - 2*b(1,2)*b(1,1) **3*xi(6,1) - b(1,2)*b(1,1)**3*xi(5,3)*xi(3,1) + b(1,1)**4*xi(6,2) + b(1,1)**4* xi(5,3)*xi(3,2))/(b(1,1)**2*k)$ deltaprimemodg(6,3):=(b(1,1)*xi(6,3))/k**2$ det(AUTOM):=b(1,1)**12/k**5$ DELTAPRIMEMODADG:= mat((0,k,0,0,0,0), (0,0,0,0,0,0), (b(1,1)*xi(3,1),0,0,0,0,0), (0,0,0,0,0,0), (0,0,0, - b(1,1)*xi(3,1),0,k), 2 (xi(6,1) + xi(5,3)*xi(3,1) + xi(6,3)*xi(3,2))*b(1,1) 2 2 (-------------------------------------------------------,(b(4,1) *k 2 k 2 2 - b(4,1)*b(1,1) *xi(3,1)*k - b(3,2)*b(1,1) *xi(6,3) 2 - b(5,3)*b(1,1)*xi(3,1)*k + 2*b(6,1)*b(1,1)*k 3 - (2*xi(6,1) + xi(5,3)*xi(3,1))*b(1,2)*b(1,1) 4 2 b(1,1)*xi(6,3) + (xi(6,2) + xi(5,3)*xi(3,2))*b(1,1) )/(b(1,1) *k),----------------,0,0 2 k ,0)) Then we get deltaprimemodadg(6,2)=0 if we take$ b(6,1):=( - ((((xi(6,2) + xi(5,3)*xi(3,2))*b(1,1) - (2*xi(6,1) + xi(5,3)*xi(3,1) )*b(1,2))*b(1,1) - b(3,2)*xi(6,3))*b(1,1)**2 + ((b(4,1)*k - b(1,1)**2*xi(3,1))*b (4,1) - b(5,3)*b(1,1)*xi(3,1))*k))/(2*b(1,1)*k**2)$ With the generic automorphism one gets$ shortformdeltaprimemodadg:={0, ss, b(1,1)*xi(3,1), 0, ss, 0, ss, (b(1,1)**2*(xi(6,3)*xi(3,2) + xi(6,1) + xi(5,3)*xi(3,1)))/k**2, 0, (b(1,1)*xi(6,3))/k**2}$ deltaprimemodg(1,2):=k$ deltaprimemodg(3,1):=b(1,1)*xi(3,1)$ deltaprimemodg(3,2):=0$ deltaprimemodg(5,3):=0$ deltaprimemodg(6,1):=(b(1,1)**2*(xi(6,3)*xi(3,2) + xi(6,1) + xi(5,3)*xi(3,1)))/k **2$ deltaprimemodg(6,2):=0$ deltaprimemodg(6,3):=(b(1,1)*xi(6,3))/k**2$ det(AUTOM):=b(1,1)**12/k**5$ DELTAPRIMEMODADG:= mat((0,k,0,0,0,0), (0,0,0,0,0,0), (b(1,1)*xi(3,1),0,0,0,0,0), (0,0,0,0,0,0), (0,0,0, - b(1,1)*xi(3,1),0,k), 2 (xi(6,1) + xi(5,3)*xi(3,1) + xi(6,3)*xi(3,2))*b(1,1) b(1,1)*xi(6,3) (-------------------------------------------------------,0,----------------, 2 2 k k 0,0,0))