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}} With the generic automorphism one gets$ shortformdeltaprimemodadg:={(b(2,2)*xi(2,1))/b(1,1), ss, (b(3,2)*b(2,2)*xi(2,1) + b(2,2)*b(1,1)**2*xi(3,1) - b(2,1)*b(1,1)**2*xi(3,2))/(b (2,2)*b(1,1)), (b(1,1)**2*xi(3,2))/b(2,2), ss, (b(2,2)*xi(4,3))/b(1,1), ss, (b(5,3)*b(2,2)*b(1,1)*xi(3,2) + b(4,3)*b(3,2)*b(1,1)*xi(3,2) - b(4,2)*b(1,1)**3* xi(3,2) - b(3,2)**2*b(2,2)*xi(4,3) - b(3,2)*b(2,2)*b(1,1)**2*xi(5,3) + b(2,2)*b( 1,1)**4*xi(5,2))/(b(2,2)**2*b(1,1)), ( - 2*b(4,3)*b(1,1)*xi(3,2) + 2*b(3,2)*b(2,2)*xi(4,3) + b(2,2)*b(1,1)**2*xi(5,3) )/(b(2,2)*b(1,1)), ss, (b(6,3)*b(2,2)*b(1,1)**3*xi(3,2) + b(5,3)*b(3,2)*b(2,2)**2*xi(4,3) - b(5,3)*b(3, 2)*b(2,2)**2*xi(2,1) + b(5,3)*b(2,2)**2*b(1,1)**2*xi(3,1) - b(5,3)*b(2,2)*b(2,1) *b(1,1)**2*xi(3,2) - b(5,2)*b(2,2)**2*b(1,1)**2*xi(4,3) + 2*b(5,2)*b(2,2)**2*b(1 ,1)**2*xi(2,1) + b(4,3)**2*b(3,2)*b(1,1)*xi(3,2) - b(4,3)*b(4,2)*b(1,1)**3*xi(3, 2) - b(4,3)*b(3,2)**2*b(2,2)*xi(4,3) + b(4,3)*b(3,2)**2*b(2,2)*xi(2,1) - b(4,3)* b(3,2)*b(2,2)*b(1,1)**2*xi(5,3) + b(4,3)*b(3,2)*b(2,2)*b(1,1)**2*xi(3,1) - 2*b(4 ,3)*b(3,2)*b(2,1)*b(1,1)**2*xi(3,2) + b(4,3)*b(3,1)*b(2,2)*b(1,1)**2*xi(3,2) + b (4,3)*b(2,2)*b(1,1)**4*xi(5,2) - b(4,2)*b(3,2)*b(2,2)*b(1,1)**2*xi(2,1) - b(4,2) *b(2,2)*b(1,1)**4*xi(3,1) + 2*b(4,2)*b(2,1)*b(1,1)**4*xi(3,2) - b(4,1)*b(2,2)*b( 1,1)**4*xi(3,2) + 2*b(3,2)**2*b(2,2)*b(2,1)*b(1,1)*xi(4,3) - 2*b(3,2)*b(3,1)*b(2 ,2)**2*b(1,1)*xi(4,3) - b(3,2)*b(2,2)**2*b(1,1)**3*xi(6,3) + 2*b(3,2)*b(2,2)*b(2 ,1)*b(1,1)**3*xi(5,3) - b(3,1)*b(2,2)**2*b(1,1)**3*xi(5,3) + b(2,2)**2*b(1,1)**5 *xi(6,2) - 2*b(2,2)*b(2,1)*b(1,1)**5*xi(5,2))/(b(2,2)**2*b(1,1)**3), ( - b(5,3)*b(2,2)**2*xi(4,3) + b(5,3)*b(2,2)**2*xi(2,1) - b(4,3)**2*b(1,1)*xi(3, 2) + b(4,3)*b(3,2)*b(2,2)*xi(4,3) - b(4,3)*b(3,2)*b(2,2)*xi(2,1) + b(4,3)*b(2,2) *b(1,1)**2*xi(5,3) - 2*b(4,3)*b(2,2)*b(1,1)**2*xi(3,1) + 2*b(4,3)*b(2,1)*b(1,1) **2*xi(3,2) + b(4,2)*b(2,2)*b(1,1)**2*xi(4,3) - b(4,2)*b(2,2)*b(1,1)**2*xi(2,1) - 2*b(3,2)*b(2,2)*b(2,1)*b(1,1)*xi(4,3) + 2*b(3,1)*b(2,2)**2*b(1,1)*xi(4,3) + b( 2,2)**2*b(1,1)**3*xi(6,3) - b(2,2)*b(2,1)*b(1,1)**3*xi(5,3))/(b(2,2)*b(1,1)**3)} $ deltaprimemodg(2,1):=(b(2,2)*xi(2,1))/b(1,1)$ deltaprimemodg(3,1):=(b(3,2)*b(2,2)*xi(2,1) + b(2,2)*b(1,1)**2*xi(3,1) - b(2,1)* b(1,1)**2*xi(3,2))/(b(2,2)*b(1,1))$ deltaprimemodg(3,2):=(b(1,1)**2*xi(3,2))/b(2,2)$ deltaprimemodg(4,3):=(b(2,2)*xi(4,3))/b(1,1)$ deltaprimemodg(5,2):=(b(5,3)*b(2,2)*b(1,1)*xi(3,2) + b(4,3)*b(3,2)*b(1,1)*xi(3,2 ) - b(4,2)*b(1,1)**3*xi(3,2) - b(3,2)**2*b(2,2)*xi(4,3) - b(3,2)*b(2,2)*b(1,1)** 2*xi(5,3) + b(2,2)*b(1,1)**4*xi(5,2))/(b(2,2)**2*b(1,1))$ deltaprimemodg(5,3):=( - 2*b(4,3)*b(1,1)*xi(3,2) + 2*b(3,2)*b(2,2)*xi(4,3) + b(2 ,2)*b(1,1)**2*xi(5,3))/(b(2,2)*b(1,1))$ deltaprimemodg(6,2):=(b(6,3)*b(2,2)*b(1,1)**3*xi(3,2) + b(5,3)*b(3,2)*b(2,2)**2* xi(4,3) - b(5,3)*b(3,2)*b(2,2)**2*xi(2,1) + b(5,3)*b(2,2)**2*b(1,1)**2*xi(3,1) - b(5,3)*b(2,2)*b(2,1)*b(1,1)**2*xi(3,2) - b(5,2)*b(2,2)**2*b(1,1)**2*xi(4,3) + 2 *b(5,2)*b(2,2)**2*b(1,1)**2*xi(2,1) + b(4,3)**2*b(3,2)*b(1,1)*xi(3,2) - b(4,3)*b (4,2)*b(1,1)**3*xi(3,2) - b(4,3)*b(3,2)**2*b(2,2)*xi(4,3) + b(4,3)*b(3,2)**2*b(2 ,2)*xi(2,1) - b(4,3)*b(3,2)*b(2,2)*b(1,1)**2*xi(5,3) + b(4,3)*b(3,2)*b(2,2)*b(1, 1)**2*xi(3,1) - 2*b(4,3)*b(3,2)*b(2,1)*b(1,1)**2*xi(3,2) + b(4,3)*b(3,1)*b(2,2)* b(1,1)**2*xi(3,2) + b(4,3)*b(2,2)*b(1,1)**4*xi(5,2) - b(4,2)*b(3,2)*b(2,2)*b(1,1 )**2*xi(2,1) - b(4,2)*b(2,2)*b(1,1)**4*xi(3,1) + 2*b(4,2)*b(2,1)*b(1,1)**4*xi(3, 2) - b(4,1)*b(2,2)*b(1,1)**4*xi(3,2) + 2*b(3,2)**2*b(2,2)*b(2,1)*b(1,1)*xi(4,3) - 2*b(3,2)*b(3,1)*b(2,2)**2*b(1,1)*xi(4,3) - b(3,2)*b(2,2)**2*b(1,1)**3*xi(6,3) + 2*b(3,2)*b(2,2)*b(2,1)*b(1,1)**3*xi(5,3) - b(3,1)*b(2,2)**2*b(1,1)**3*xi(5,3) + b(2,2)**2*b(1,1)**5*xi(6,2) - 2*b(2,2)*b(2,1)*b(1,1)**5*xi(5,2))/(b(2,2)**2*b( 1,1)**3)$ deltaprimemodg(6,3):=( - b(5,3)*b(2,2)**2*xi(4,3) + b(5,3)*b(2,2)**2*xi(2,1) - b (4,3)**2*b(1,1)*xi(3,2) + b(4,3)*b(3,2)*b(2,2)*xi(4,3) - b(4,3)*b(3,2)*b(2,2)*xi (2,1) + b(4,3)*b(2,2)*b(1,1)**2*xi(5,3) - 2*b(4,3)*b(2,2)*b(1,1)**2*xi(3,1) + 2* b(4,3)*b(2,1)*b(1,1)**2*xi(3,2) + b(4,2)*b(2,2)*b(1,1)**2*xi(4,3) - b(4,2)*b(2,2 )*b(1,1)**2*xi(2,1) - 2*b(3,2)*b(2,2)*b(2,1)*b(1,1)*xi(4,3) + 2*b(3,1)*b(2,2)**2 *b(1,1)*xi(4,3) + b(2,2)**2*b(1,1)**3*xi(6,3) - b(2,2)*b(2,1)*b(1,1)**3*xi(5,3)) /(b(2,2)*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)*xi(2,1) (----------------,0,0,0,0,0), b(1,1) 2 (b(2,2)*xi(3,1) - b(2,1)*xi(3,2))*b(1,1) + b(3,2)*b(2,2)*xi(2,1) (-------------------------------------------------------------------, b(2,2)*b(1,1) 2 b(1,1) *xi(3,2) -----------------,0,0,0,0), b(2,2) b(2,2)*xi(4,3) (0,0,----------------,0,0,0), b(1,1) 2 2 4 (0,( - ((b(3,2) *xi(4,3) + b(3,2)*b(1,1) *xi(5,3) - b(1,1) *xi(5,2))*b(2,2) 3 + b(4,2)*b(1,1) *xi(3,2) - b(4,3)*b(3,2)*b(1,1)*xi(3,2) 2 - b(5,3)*b(2,2)*b(1,1)*xi(3,2)))/(b(2,2) *b(1,1)), 2 (2*b(3,2)*xi(4,3) + b(1,1) *xi(5,3))*b(2,2) - 2*b(4,3)*b(1,1)*xi(3,2) -----------------------------------------------------------------------, b(2,2)*b(1,1) 2 b(1,1) *xi(3,2) -----------------,0,0), b(2,2) 2 (0,(((((b(2,2)*xi(6,2) - 2*b(2,1)*xi(5,2))*b(1,1) - b(3,1)*b(2,2)*xi(5,3)) 2 2 3 *b(1,1) + 2*b(3,2) *b(2,1)*xi(4,3) - b(4,1)*b(1,1) *xi(3,2))*b(2,2) 2 2 + b(4,3) *b(3,2)*xi(3,2) + b(6,3)*b(2,2)*b(1,1) *xi(3,2) 2 - (xi(4,3) - 2*xi(2,1))*b(5,2)*b(2,2) *b(1,1) - 2 ((b(2,2)*xi(3,1) - 2*b(2,1)*xi(3,2))*b(1,1) + b(3,2)*b(2,2)*xi(2,1)) 2 *b(4,2)*b(1,1))*b(1,1) + ((b(2,2)*xi(3,1) - b(2,1)*xi(3,2))*b(1,1) + (xi(4,3) - xi(2,1))*b(3,2)*b(2,2))*b(5,3)*b(2,2) - 2 ((b(2,2)*xi(6,3) - 2*b(2,1)*xi(5,3))*b(1,1) + 2*b(3,1)*b(2,2)*xi(4,3)) *b(3,2)*b(2,2)*b(1,1) + ( 2 ((b(3,1)*xi(3,2) + b(1,1) *xi(5,2))*b(2,2) - b(4,2)*b(1,1)*xi(3,2)) 2 2 *b(1,1) - (xi(4,3) - xi(2,1))*b(3,2) *b(2,2) 2 - ((xi(5,3) - xi(3,1))*b(2,2) + 2*b(2,1)*xi(3,2))*b(3,2)*b(1,1) ) 2 3 2 *b(4,3))/(b(2,2) *b(1,1) ),((((b(2,2)*xi(6,3) - b(2,1)*xi(5,3))*b(1,1) + 2*b(3,1)*b(2,2)*xi(4,3) - 2*b(3,2)*b(2,1)*xi(4,3))*b(2,2) 2 - b(4,3) *xi(3,2))*b(1,1) 2 - (b(5,3)*b(2,2) - b(4,2)*b(1,1) )*(xi(4,3) - xi(2,1))*b(2,2) + ( 2 (xi(4,3) - xi(2,1))*b(3,2)*b(2,2) + 2*b(2,1)*b(1,1) *xi(3,2) 2 3 + (xi(5,3) - 2*xi(3,1))*b(2,2)*b(1,1) )*b(4,3))/(b(2,2)*b(1,1) ), 2 (b(2,2)*xi(3,1) - b(2,1)*xi(3,2))*b(1,1) + b(3,2)*b(2,2)*xi(2,1) -------------------------------------------------------------------, b(2,2)*b(1,1) (xi(4,3) - xi(2,1))*b(2,2) ----------------------------,0)) b(1,1) %%%%%%%%%%% CASE 1 : SUPPOSE xi(2,1) NEQ 0 .%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$ We stay in that case by projective equivalence.$ Then we may suppose xi(2,1):=1.$ xi(2,1):=1$ and we keep deltaprime(2,1)=k (k nonzero) if we take$ b(2,2):=b(1,1)*k$ we get deltaprime(3,1)=0 if we take$ b(3,2):=((b(2,1)*xi(3,2) - b(1,1)*xi(3,1)*k)*b(1,1))/k$ With the generic automorphism one gets$ shortformdeltaprimemodadg:={k, ss, 0, (b(1,1)*xi(3,2))/k, ss, xi(4,3)*k, ss, (b(5,3)*xi(3,2)*k**2 + b(4,3)*b(2,1)*xi(3,2)**2 - b(4,3)*b(1,1)*xi(3,2)*xi(3,1)* k - b(4,2)*b(1,1)*xi(3,2)*k - b(2,1)**2*b(1,1)*xi(4,3)*xi(3,2)**2 - b(2,1)*b(1,1 )**2*xi(5,3)*xi(3,2)*k + 2*b(2,1)*b(1,1)**2*xi(4,3)*xi(3,2)*xi(3,1)*k + b(1,1)** 3*xi(5,3)*xi(3,1)*k**2 + b(1,1)**3*xi(5,2)*k**2 - b(1,1)**3*xi(4,3)*xi(3,1)**2*k **2)/(b(1,1)*k**3), ( - 2*b(4,3)*xi(3,2) + 2*b(2,1)*b(1,1)*xi(4,3)*xi(3,2) + b(1,1)**2*xi(5,3)*k - 2 *b(1,1)**2*xi(4,3)*xi(3,1)*k)/(b(1,1)*k), ss, (b(6,3)*b(1,1)**2*xi(3,2)*k**2 + b(5,3)*b(2,1)*b(1,1)*xi(4,3)*xi(3,2)*k**2 - 2*b (5,3)*b(2,1)*b(1,1)*xi(3,2)*k**2 - b(5,3)*b(1,1)**2*xi(4,3)*xi(3,1)*k**3 + 2*b(5 ,3)*b(1,1)**2*xi(3,1)*k**3 - b(5,2)*b(1,1)**2*xi(4,3)*k**3 + 2*b(5,2)*b(1,1)**2* k**3 + b(4,3)**2*b(2,1)*xi(3,2)**2 - b(4,3)**2*b(1,1)*xi(3,2)*xi(3,1)*k - b(4,3) *b(4,2)*b(1,1)*xi(3,2)*k + b(4,3)*b(3,1)*b(1,1)*xi(3,2)*k**2 - b(4,3)*b(2,1)**2* b(1,1)*xi(4,3)*xi(3,2)**2 - b(4,3)*b(2,1)**2*b(1,1)*xi(3,2)**2 - b(4,3)*b(2,1)*b (1,1)**2*xi(5,3)*xi(3,2)*k + 2*b(4,3)*b(2,1)*b(1,1)**2*xi(4,3)*xi(3,2)*xi(3,1)*k + b(4,3)*b(2,1)*b(1,1)**2*xi(3,2)*xi(3,1)*k + b(4,3)*b(1,1)**3*xi(5,3)*xi(3,1)* k**2 + b(4,3)*b(1,1)**3*xi(5,2)*k**2 - b(4,3)*b(1,1)**3*xi(4,3)*xi(3,1)**2*k**2 + b(4,2)*b(2,1)*b(1,1)**2*xi(3,2)*k - b(4,1)*b(1,1)**3*xi(3,2)*k**2 - 2*b(3,1)*b (2,1)*b(1,1)**2*xi(4,3)*xi(3,2)*k**2 - b(3,1)*b(1,1)**3*xi(5,3)*k**3 + 2*b(3,1)* b(1,1)**3*xi(4,3)*xi(3,1)*k**3 + 2*b(2,1)**3*b(1,1)**2*xi(4,3)*xi(3,2)**2 + 2*b( 2,1)**2*b(1,1)**3*xi(5,3)*xi(3,2)*k - 4*b(2,1)**2*b(1,1)**3*xi(4,3)*xi(3,2)*xi(3 ,1)*k - b(2,1)*b(1,1)**4*xi(6,3)*xi(3,2)*k**2 - 2*b(2,1)*b(1,1)**4*xi(5,3)*xi(3, 1)*k**2 - 2*b(2,1)*b(1,1)**4*xi(5,2)*k**2 + 2*b(2,1)*b(1,1)**4*xi(4,3)*xi(3,1)** 2*k**2 + b(1,1)**5*xi(6,3)*xi(3,1)*k**3 + b(1,1)**5*xi(6,2)*k**3)/(b(1,1)**3*k** 3), ( - b(5,3)*b(1,1)*xi(4,3)*k**2 + b(5,3)*b(1,1)*k**2 - b(4,3)**2*xi(3,2) + b(4,3) *b(2,1)*b(1,1)*xi(4,3)*xi(3,2) + b(4,3)*b(2,1)*b(1,1)*xi(3,2) + b(4,3)*b(1,1)**2 *xi(5,3)*k - b(4,3)*b(1,1)**2*xi(4,3)*xi(3,1)*k - b(4,3)*b(1,1)**2*xi(3,1)*k + b (4,2)*b(1,1)**2*xi(4,3)*k - b(4,2)*b(1,1)**2*k + 2*b(3,1)*b(1,1)**2*xi(4,3)*k**2 - 2*b(2,1)**2*b(1,1)**2*xi(4,3)*xi(3,2) - b(2,1)*b(1,1)**3*xi(5,3)*k + 2*b(2,1) *b(1,1)**3*xi(4,3)*xi(3,1)*k + b(1,1)**4*xi(6,3)*k**2)/(b(1,1)**3*k)}$ deltaprimemodg(2,1):=k$ deltaprimemodg(3,1):=0$ deltaprimemodg(3,2):=(b(1,1)*xi(3,2))/k$ deltaprimemodg(4,3):=xi(4,3)*k$ deltaprimemodg(5,2):=(b(5,3)*xi(3,2)*k**2 + b(4,3)*b(2,1)*xi(3,2)**2 - b(4,3)*b( 1,1)*xi(3,2)*xi(3,1)*k - b(4,2)*b(1,1)*xi(3,2)*k - b(2,1)**2*b(1,1)*xi(4,3)*xi(3 ,2)**2 - b(2,1)*b(1,1)**2*xi(5,3)*xi(3,2)*k + 2*b(2,1)*b(1,1)**2*xi(4,3)*xi(3,2) *xi(3,1)*k + b(1,1)**3*xi(5,3)*xi(3,1)*k**2 + b(1,1)**3*xi(5,2)*k**2 - b(1,1)**3 *xi(4,3)*xi(3,1)**2*k**2)/(b(1,1)*k**3)$ deltaprimemodg(5,3):=( - 2*b(4,3)*xi(3,2) + 2*b(2,1)*b(1,1)*xi(4,3)*xi(3,2) + b( 1,1)**2*xi(5,3)*k - 2*b(1,1)**2*xi(4,3)*xi(3,1)*k)/(b(1,1)*k)$ deltaprimemodg(6,2):=(b(6,3)*b(1,1)**2*xi(3,2)*k**2 + b(5,3)*b(2,1)*b(1,1)*xi(4, 3)*xi(3,2)*k**2 - 2*b(5,3)*b(2,1)*b(1,1)*xi(3,2)*k**2 - b(5,3)*b(1,1)**2*xi(4,3) *xi(3,1)*k**3 + 2*b(5,3)*b(1,1)**2*xi(3,1)*k**3 - b(5,2)*b(1,1)**2*xi(4,3)*k**3 + 2*b(5,2)*b(1,1)**2*k**3 + b(4,3)**2*b(2,1)*xi(3,2)**2 - b(4,3)**2*b(1,1)*xi(3, 2)*xi(3,1)*k - b(4,3)*b(4,2)*b(1,1)*xi(3,2)*k + b(4,3)*b(3,1)*b(1,1)*xi(3,2)*k** 2 - b(4,3)*b(2,1)**2*b(1,1)*xi(4,3)*xi(3,2)**2 - b(4,3)*b(2,1)**2*b(1,1)*xi(3,2) **2 - b(4,3)*b(2,1)*b(1,1)**2*xi(5,3)*xi(3,2)*k + 2*b(4,3)*b(2,1)*b(1,1)**2*xi(4 ,3)*xi(3,2)*xi(3,1)*k + b(4,3)*b(2,1)*b(1,1)**2*xi(3,2)*xi(3,1)*k + b(4,3)*b(1,1 )**3*xi(5,3)*xi(3,1)*k**2 + b(4,3)*b(1,1)**3*xi(5,2)*k**2 - b(4,3)*b(1,1)**3*xi( 4,3)*xi(3,1)**2*k**2 + b(4,2)*b(2,1)*b(1,1)**2*xi(3,2)*k - b(4,1)*b(1,1)**3*xi(3 ,2)*k**2 - 2*b(3,1)*b(2,1)*b(1,1)**2*xi(4,3)*xi(3,2)*k**2 - b(3,1)*b(1,1)**3*xi( 5,3)*k**3 + 2*b(3,1)*b(1,1)**3*xi(4,3)*xi(3,1)*k**3 + 2*b(2,1)**3*b(1,1)**2*xi(4 ,3)*xi(3,2)**2 + 2*b(2,1)**2*b(1,1)**3*xi(5,3)*xi(3,2)*k - 4*b(2,1)**2*b(1,1)**3 *xi(4,3)*xi(3,2)*xi(3,1)*k - b(2,1)*b(1,1)**4*xi(6,3)*xi(3,2)*k**2 - 2*b(2,1)*b( 1,1)**4*xi(5,3)*xi(3,1)*k**2 - 2*b(2,1)*b(1,1)**4*xi(5,2)*k**2 + 2*b(2,1)*b(1,1) **4*xi(4,3)*xi(3,1)**2*k**2 + b(1,1)**5*xi(6,3)*xi(3,1)*k**3 + b(1,1)**5*xi(6,2) *k**3)/(b(1,1)**3*k**3)$ deltaprimemodg(6,3):=( - b(5,3)*b(1,1)*xi(4,3)*k**2 + b(5,3)*b(1,1)*k**2 - b(4,3 )**2*xi(3,2) + b(4,3)*b(2,1)*b(1,1)*xi(4,3)*xi(3,2) + b(4,3)*b(2,1)*b(1,1)*xi(3, 2) + b(4,3)*b(1,1)**2*xi(5,3)*k - b(4,3)*b(1,1)**2*xi(4,3)*xi(3,1)*k - b(4,3)*b( 1,1)**2*xi(3,1)*k + b(4,2)*b(1,1)**2*xi(4,3)*k - b(4,2)*b(1,1)**2*k + 2*b(3,1)*b (1,1)**2*xi(4,3)*k**2 - 2*b(2,1)**2*b(1,1)**2*xi(4,3)*xi(3,2) - b(2,1)*b(1,1)**3 *xi(5,3)*k + 2*b(2,1)*b(1,1)**3*xi(4,3)*xi(3,1)*k + b(1,1)**4*xi(6,3)*k**2)/(b(1 ,1)**3*k)$ det(AUTOM):=b(1,1)**12*k**3$ DELTAPRIMEMODADG:= mat((0,0,0,0,0,0), (k,0,0,0,0,0), b(1,1)*xi(3,2) (0,----------------,0,0,0,0), k (0,0,xi(4,3)*k,0,0,0), 2 2 (0,( - (((b(4,2)*k + b(2,1) *xi(4,3)*xi(3,2))*b(1,1) - b(5,3)*k 2 + (xi(5,3) - 2*xi(4,3)*xi(3,1))*b(2,1)*b(1,1) *k - (b(2,1)*xi(3,2) - b(1,1)*xi(3,1)*k)*b(4,3))*xi(3,2) 2 3 2 - (xi(5,2) - xi(4,3)*xi(3,1) + xi(5,3)*xi(3,1))*b(1,1) *k ))/( 3 b(1,1)*k ),( - (2*(b(4,3) - b(2,1)*b(1,1)*xi(4,3))*xi(3,2) 2 - (xi(5,3) - 2*xi(4,3)*xi(3,1))*b(1,1) *k))/(b(1,1)*k), b(1,1)*xi(3,2) ----------------,0,0), k 2 3 (0,( - (((b(4,1)*b(1,1)*k - 2*b(2,1) *xi(4,3)*xi(3,2) - b(4,2)*b(2,1)*k 2 3 - b(6,3)*k )*xi(3,2) + (xi(4,3) - 2)*b(5,2)*k 2 - 2*(xi(5,3) - 2*xi(4,3)*xi(3,1))*b(2,1) *b(1,1)*xi(3,2)*k 3 3 2 - (xi(6,3)*xi(3,1) + xi(6,2))*b(1,1) *k )*b(1,1) - 2 2 ((xi(4,3) - 2)*b(5,3)*b(1,1)*k + b(4,3) *xi(3,2)) *(b(2,1)*xi(3,2) - b(1,1)*xi(3,1)*k) + ((xi(5,3) - 2*xi(4,3)*xi(3,1))*b(1,1)*k + 2*b(2,1)*xi(4,3)*xi(3,2)) 2 2 *b(3,1)*b(1,1) *k + 2 (2*(xi(5,2) - xi(4,3)*xi(3,1) + xi(5,3)*xi(3,1)) + xi(6,3)*xi(3,2)) 4 2 *b(2,1)*b(1,1) *k + (((b(4,2) - b(3,1)*k)*k 2 + (xi(4,3) + 1)*b(2,1) *xi(3,2) - ((2*xi(4,3) + 1)*xi(3,1) - xi(5,3))*b(2,1)*b(1,1)*k) *xi(3,2) 2 2 2 - (xi(5,2) - xi(4,3)*xi(3,1) + xi(5,3)*xi(3,1))*b(1,1) *k ) 3 3 2 *b(4,3)*b(1,1)))/(b(1,1) *k ),( - ((2*b(2,1) *xi(4,3)*xi(3,2) 2 2 2 2 - b(1,1) *xi(6,3)*k - 2*b(3,1)*xi(4,3)*k )*b(1,1) 2 + b(4,3) *xi(3,2) + (b(5,3)*k - b(4,2)*b(1,1))*(xi(4,3) - 1)*b(1,1)*k 3 + (xi(5,3) - 2*xi(4,3)*xi(3,1))*b(2,1)*b(1,1) *k + ( ((xi(4,3) + 1)*xi(3,1) - xi(5,3))*b(1,1)*k 3 - (xi(4,3) + 1)*b(2,1)*xi(3,2))*b(4,3)*b(1,1)))/(b(1,1) *k),0, (xi(4,3) - 1)*k,0)) Hence we may suppose xi(3,1):=0.$ xi(3,1):=0$ %%%%%%%%%%% SUBCASE 1.2 : SUPPOSE xi(3,2) := 0 .%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$ We stay in that case by projective equivalence.$ xi(3,2):=0$ With the generic automorphism one gets$ shortformdeltaprimemodadg:={k, ss, 0, 0, ss, xi(4,3)*k, ss, (b(1,1)**2*xi(5,2))/k, b(1,1)*xi(5,3), ss, ( - b(5,2)*xi(4,3)*k + 2*b(5,2)*k + b(4,3)*b(1,1)*xi(5,2) - b(3,1)*b(1,1)*xi(5,3 )*k - 2*b(2,1)*b(1,1)**2*xi(5,2) + b(1,1)**3*xi(6,2)*k)/(b(1,1)*k), ( - b(5,3)*xi(4,3)*k + b(5,3)*k + b(4,3)*b(1,1)*xi(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)*k - b(2,1)*b(1,1)**2*xi(5,3) + b(1,1) **3*xi(6,3)*k)/b(1,1)**2}$ deltaprimemodg(2,1):=k$ deltaprimemodg(3,1):=0$ deltaprimemodg(3,2):=0$ deltaprimemodg(4,3):=xi(4,3)*k$ deltaprimemodg(5,2):=(b(1,1)**2*xi(5,2))/k$ deltaprimemodg(5,3):=b(1,1)*xi(5,3)$ deltaprimemodg(6,2):=( - b(5,2)*xi(4,3)*k + 2*b(5,2)*k + b(4,3)*b(1,1)*xi(5,2) - b(3,1)*b(1,1)*xi(5,3)*k - 2*b(2,1)*b(1,1)**2*xi(5,2) + b(1,1)**3*xi(6,2)*k)/(b( 1,1)*k)$ deltaprimemodg(6,3):=( - b(5,3)*xi(4,3)*k + b(5,3)*k + b(4,3)*b(1,1)*xi(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)*k - b(2,1)*b(1,1) **2*xi(5,3) + b(1,1)**3*xi(6,3)*k)/b(1,1)**2$ det(AUTOM):=b(1,1)**12*k**3$ DELTAPRIMEMODADG:= mat((0,0,0,0,0,0), (k,0,0,0,0,0), (0,0,0,0,0,0), (0,0,xi(4,3)*k,0,0,0), 2 b(1,1) *xi(5,2) (0,-----------------,b(1,1)*xi(5,3),0,0,0), k (0,( - (((2*b(2,1)*xi(5,2) - b(1,1)*xi(6,2)*k)*b(1,1) + b(3,1)*xi(5,3)*k - b(4,3)*xi(5,2))*b(1,1) + (xi(4,3) - 2)*b(5,2)*k))/(b(1,1)*k),( - (((b(2,1)*xi(5,3) - b(1,1)*xi(6,3)*k)*b(1,1) - 2*b(3,1)*xi(4,3)*k - b(4,3)*xi(5,3))*b(1,1) + (b(5,3)*k - b(4,2)*b(1,1))*(xi(4,3) - 1)) 2 )/b(1,1) ,0,(xi(4,3) - 1)*k,0)) ************* Suppose xi(4,3) and xi(5,3) BOTH nonzero.$ With the generic automorphism one gets$ shortformdeltaprimemodadg:={k, ss, 0, 0, ss, xi(4,3)*k, ss, (b(1,1)**2*xi(5,2))/k, b(1,1)*xi(5,3), ss, ( - b(5,2)*xi(4,3)*k + 2*b(5,2)*k + b(4,3)*b(1,1)*xi(5,2) - b(3,1)*b(1,1)*xi(5,3 )*k - 2*b(2,1)*b(1,1)**2*xi(5,2) + b(1,1)**3*xi(6,2)*k)/(b(1,1)*k), ( - b(5,3)*xi(4,3)*k + b(5,3)*k + b(4,3)*b(1,1)*xi(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)*k - b(2,1)*b(1,1)**2*xi(5,3) + b(1,1) **3*xi(6,3)*k)/b(1,1)**2}$ deltaprimemodg(2,1):=k$ deltaprimemodg(3,1):=0$ deltaprimemodg(3,2):=0$ deltaprimemodg(4,3):=xi(4,3)*k$ deltaprimemodg(5,2):=(b(1,1)**2*xi(5,2))/k$ deltaprimemodg(5,3):=b(1,1)*xi(5,3)$ deltaprimemodg(6,2):=( - b(5,2)*xi(4,3)*k + 2*b(5,2)*k + b(4,3)*b(1,1)*xi(5,2) - b(3,1)*b(1,1)*xi(5,3)*k - 2*b(2,1)*b(1,1)**2*xi(5,2) + b(1,1)**3*xi(6,2)*k)/(b( 1,1)*k)$ deltaprimemodg(6,3):=( - b(5,3)*xi(4,3)*k + b(5,3)*k + b(4,3)*b(1,1)*xi(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)*k - b(2,1)*b(1,1) **2*xi(5,3) + b(1,1)**3*xi(6,3)*k)/b(1,1)**2$ det(AUTOM):=b(1,1)**12*k**3$ DELTAPRIMEMODADG:= mat((0,0,0,0,0,0), (k,0,0,0,0,0), (0,0,0,0,0,0), (0,0,xi(4,3)*k,0,0,0), 2 b(1,1) *xi(5,2) (0,-----------------,b(1,1)*xi(5,3),0,0,0), k (0,( - (((2*b(2,1)*xi(5,2) - b(1,1)*xi(6,2)*k)*b(1,1) + b(3,1)*xi(5,3)*k - b(4,3)*xi(5,2))*b(1,1) + (xi(4,3) - 2)*b(5,2)*k))/(b(1,1)*k),( - (((b(2,1)*xi(5,3) - b(1,1)*xi(6,3)*k)*b(1,1) - 2*b(3,1)*xi(4,3)*k - b(4,3)*xi(5,3))*b(1,1) + (b(5,3)*k - b(4,2)*b(1,1))*(xi(4,3) - 1)) 2 )/b(1,1) ,0,(xi(4,3) - 1)*k,0)) We get deltaprime(5,3)=k if we take$ b(1,1):=k/xi(5,3)$ and we get deltaprime(6,2)=0 if we take$ b(3,1):=(((b(4,3)*xi(5,3) - 2*b(2,1)*k)*xi(5,2) - (xi(4,3) - 2)*b(5,2)*xi(5,3)** 2)*xi(5,3) + xi(6,2)*k**3)/(xi(5,3)**3*k)$ Hence we may suppose:$ xi(5,3):=xi(5,2)$ xi(6,2):=0$ With the generic automorphism one gets$ shortformdeltaprimemodadg:={k, ss, 0, 0, ss, xi(4,3)*k, ss, xi(5,2)*k, k, ss, 0, ( - b(5,3)*xi(4,3) + b(5,3) - 2*b(5,2)*xi(4,3)**2 + 4*b(5,2)*xi(4,3) + 2*b(4,3)* xi(5,2)*xi(4,3) + b(4,3) + b(4,2)*xi(4,3) - b(4,2) - 4*b(2,1)*xi(5,2)*xi(4,3)*k - b(2,1)*k + xi(6,3)*k**3)/k}$ deltaprimemodg(2,1):=k$ deltaprimemodg(3,1):=0$ deltaprimemodg(3,2):=0$ deltaprimemodg(4,3):=xi(4,3)*k$ deltaprimemodg(5,2):=xi(5,2)*k$ deltaprimemodg(5,3):=k$ deltaprimemodg(6,2):=0$ deltaprimemodg(6,3):=( - b(5,3)*xi(4,3) + b(5,3) - 2*b(5,2)*xi(4,3)**2 + 4*b(5,2 )*xi(4,3) + 2*b(4,3)*xi(5,2)*xi(4,3) + b(4,3) + b(4,2)*xi(4,3) - b(4,2) - 4*b(2, 1)*xi(5,2)*xi(4,3)*k - b(2,1)*k + xi(6,3)*k**3)/k$ det(AUTOM):=k**15$ DELTAPRIMEMODADG:= mat((0,0,0,0,0,0), (k,0,0,0,0,0), (0,0,0,0,0,0), (0,0,xi(4,3)*k,0,0,0), (0,xi(5,2)*k,k,0,0,0), 3 (0,0,( - (2*(xi(4,3) - 2)*b(5,2)*xi(4,3) - xi(6,3)*k + (b(5,3) - b(4,2))*(xi(4,3) - 1) - (2*xi(5,2)*xi(4,3) + 1)*b(4,3) + (4*xi(5,2)*xi(4,3) + 1)*b(2,1)*k))/k,0,(xi(4,3) - 1)*k,0)) If xi(4,3) neq 1, one gets deltaprime(6,3)=0 by suitable value for b(5,3).$ If xi(4,3) = 1, one gets deltaprime(6,3)=0 by suitable value for b(5,2).$ Hence in the case 1.2 and if xi(4,3)xi(5,3) NEQ 0, we are reduced to the case $ shortformprimedelta:={1;0,0;a;b,1;0,0} , where a=xi(4,3) neq 0,$ and b=xi(5,2).$