rreducparautommodg6_nxC3case6N1.r The generic automorphism phi of n x C**3 : phi:= [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) b(3,4) b(3,5) b(3,6)] [ ] [b(4,1) b(4,2) 0 b(4,4) b(4,5) b(4,6)] [ ] [b(5,1) b(5,2) 0 b(5,4) b(5,5) b(5,6)] [ ] [b(6,1) b(6,2) 0 b(6,4) b(6,5) b(6,6)] det(phi):=(( - b(5,4)*b(4,5) + b(5,5)*b(4,4))*b(6,6) - ( - b(5,4)*b(4,6) + b(5,6)*b(4,4))*b(6,5) + ( - b(5,5)*b(4,6) + b(5,6)*b(4,5))*b(6,4)) 2 *( - b(2,1)*b(1,2) + b(2,2)*b(1,1)) generic derivation : delta:= [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) xi(3,4) xi(3,5) xi(3,6)] [ ] [xi(4,1) xi(4,2) 0 xi(4,4) xi(4,5) xi(4,6)] [ ] [xi(5,1) xi(5,2) 0 xi(5,4) xi(5,5) xi(5,6)] [ ] [xi(6,1) xi(6,2) 0 xi(6,4) xi(6,5) xi(6,6)] [0 0 0 0 0 0] [ ] [0 0 0 0 0 0] [ ] [0 1 0 0 0 0] adx1 := [ ] [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] [ ] [-1 0 0 0 0 0] adx2 := [ ] [0 0 0 0 0 0] [ ] [0 0 0 0 0 0] [ ] [0 0 0 0 0 0] The generic nilpotent derivation : The matrices MATA:=((xi(1,1),xi(1,2)),(xi(2,1),xi(2,2))) is nilpotent And MATB:=((xi(4,4),xi(4,5),xi(4,6)),(xi(5,4),xi(5,5),xi(5,6)),(xi(6,4),xi(6,\ 5),xi(6,6))) are nilpotent (WE denote MATA,MATB, since B is already for the entries of phi) ****** We consider here the case 6 where MATA has nilpotent order 1 and MATB has nilpotent order 2.*** MATB:= [xi(4,4) xi(4,5) xi(4,6)] [ ] [xi(5,4) xi(5,5) xi(5,6)] [ ] [xi(6,4) xi(6,5) xi(6,6)] MATC:= [xi(3,4)] [ ] [xi(3,5)] [ ] [xi(3,6)] MATD:= [xi(4,1) xi(4,2)] [ ] [xi(5,1) xi(5,2)] [ ] [xi(6,1) xi(6,2)] In block matrices, we get : phi:=mat((MATU,0,0),(MATR,det(MATU),MATS),(MATT,0,MATV)) where MATU is in GL(2), MATV in GL(3). delta:=mat((MATA,0,0),(0,0,MATC),(MATD,0,MATB)) Under the action of phi one gets: phi*delta*phi**(-1):=mat((MATU*MATA*MATU**(-1),0,0),(**,0,MATCprime),(MATDprim\ e,0,MATV*MATB*MATV**(-1))) As MATA has nilpotent order 1, we may suppose : xi(1,1):= 0 xi(1,2):= 1 xi(2,1):= 0 xi(2,2):= 0 As MATB has nilpotent order 2, we may suppose : MATB:= [0 1 0] [ ] [0 0 1] [ ] [0 0 0] by subtracting adjoints one then may suppose: xi(3,1):=0,xi(3,2):=0. delta:= [ 0 1 0 0 0 0 ] [ ] [ 0 0 0 0 0 0 ] [ ] [ 0 0 0 xi(3,4) xi(3,5) xi(3,6)] [ ] [xi(4,1) xi(4,2) 0 0 1 0 ] [ ] [xi(5,1) xi(5,2) 0 0 0 1 ] [ ] [xi(6,1) xi(6,2) 0 0 0 0 ] We denote this delta by the shortform shortformdelta:={xi(4,1), xi(4,2), ss, xi(5,1), xi(5,2), ss, xi(6,1), xi(6,2), ss, xi(3,4), xi(3,5), xi(3,6)} paramindexeslist:={{4,1},{4,2},{5,1},{5,2},{6,1},{6,2},{3,4},{3,5},{3,6}} MATU*MATA-MATA*MATU:= mat(( - b(2,1)*k, - ( - b(1,1) + b(2,2)*k)),(0,b(2,1)))$ to keep in MATA deltaprimemodadg(1,2):=k, and the others zero, one has to take : $ MATU:= mat((b(2,2)*k,b(1,2)),(0,b(2,2)))$ MATV*MATB-MATB*MATV:= mat(( - b(5,4)*k,b(4,4) - b(5,5)*k,b(4,5) - b(5,6)*k),( - b(6,4)*k,b(5,4) - b(6, 5)*k,b(5,5) - b(6,6)*k),(0,b(6,4),b(6,5)))$ to keep in MATB deltaprimemodadg(4,5):=k,deltaprimemodadg(5,6):=k,$ and the others zero, one has to take :$ b(5,4):=0$ b(4,4):=b(5,5)*k$ b(4,5):=b(5,6)*k$ b(6,4):=0$ b(6,5):=0$ b(5,5):=b(6,6)*k$ With the generic automorphism one gets$ shortformdeltaprimemodadg:={(b(4,6)*xi(6,1) - b(5,1)*k + b(5,6)*xi(5,1)*k + b(6, 6)*xi(4,1)*k**2)/(b(2,2)*k), (b(4,1)*b(2,2)*k - b(4,6)*b(1,2)*xi(6,1) + b(4,6)*b(2,2)*xi(6,2)*k + b(5,1)*b(1, 2)*k - b(5,2)*b(2,2)*k**2 - b(5,6)*b(1,2)*xi(5,1)*k + b(5,6)*b(2,2)*xi(5,2)*k**2 - b(6,6)*b(1,2)*xi(4,1)*k**2 + b(6,6)*b(2,2)*xi(4,2)*k**3)/(b(2,2)**2*k), ss, (b(5,6)*xi(6,1) - b(6,1)*k + b(6,6)*xi(5,1)*k)/(b(2,2)*k), (b(5,1)*b(2,2)*k - b(5,6)*b(1,2)*xi(6,1) + b(5,6)*b(2,2)*xi(6,2)*k + b(6,1)*b(1, 2)*k - b(6,2)*b(2,2)*k**2 - b(6,6)*b(1,2)*xi(5,1)*k + b(6,6)*b(2,2)*xi(5,2)*k**2 )/(b(2,2)**2*k), ss, (b(6,6)*xi(6,1))/(b(2,2)*k), (b(6,1)*b(2,2)*k - b(6,6)*b(1,2)*xi(6,1) + b(6,6)*b(2,2)*xi(6,2)*k)/(b(2,2)**2*k ), ss, (b(2,2)**2*xi(3,4))/(b(6,6)*k), ( - b(5,6)*b(2,2)**2*xi(3,4) + b(6,6)*b(2,2)**2*xi(3,5)*k + b(6,6)*b(3,4))/(b(6, 6)**2*k), (b(5,6)**2*b(2,2)**2*xi(3,4) - b(6,6)*b(4,6)*b(2,2)**2*xi(3,4) - b(6,6)*b(5,6)*b (2,2)**2*xi(3,5)*k - b(6,6)*b(5,6)*b(3,4) + b(6,6)**2*b(2,2)**2*xi(3,6)*k**2 + b (6,6)**2*b(3,5)*k)/(b(6,6)**3*k)}$ deltaprimemodg(4,1):=(b(4,6)*xi(6,1) - b(5,1)*k + b(5,6)*xi(5,1)*k + b(6,6)*xi(4 ,1)*k**2)/(b(2,2)*k)$ deltaprimemodg(4,2):=(b(4,1)*b(2,2)*k - b(4,6)*b(1,2)*xi(6,1) + b(4,6)*b(2,2)*xi (6,2)*k + b(5,1)*b(1,2)*k - b(5,2)*b(2,2)*k**2 - b(5,6)*b(1,2)*xi(5,1)*k + b(5,6 )*b(2,2)*xi(5,2)*k**2 - b(6,6)*b(1,2)*xi(4,1)*k**2 + b(6,6)*b(2,2)*xi(4,2)*k**3) /(b(2,2)**2*k)$ deltaprimemodg(5,1):=(b(5,6)*xi(6,1) - b(6,1)*k + b(6,6)*xi(5,1)*k)/(b(2,2)*k)$ deltaprimemodg(5,2):=(b(5,1)*b(2,2)*k - b(5,6)*b(1,2)*xi(6,1) + b(5,6)*b(2,2)*xi (6,2)*k + b(6,1)*b(1,2)*k - b(6,2)*b(2,2)*k**2 - b(6,6)*b(1,2)*xi(5,1)*k + b(6,6 )*b(2,2)*xi(5,2)*k**2)/(b(2,2)**2*k)$ deltaprimemodg(6,1):=(b(6,6)*xi(6,1))/(b(2,2)*k)$ deltaprimemodg(6,2):=(b(6,1)*b(2,2)*k - b(6,6)*b(1,2)*xi(6,1) + b(6,6)*b(2,2)*xi (6,2)*k)/(b(2,2)**2*k)$ deltaprimemodg(3,4):=(b(2,2)**2*xi(3,4))/(b(6,6)*k)$ deltaprimemodg(3,5):=( - b(5,6)*b(2,2)**2*xi(3,4) + b(6,6)*b(2,2)**2*xi(3,5)*k + b(6,6)*b(3,4))/(b(6,6)**2*k)$ deltaprimemodg(3,6):=(b(5,6)**2*b(2,2)**2*xi(3,4) - b(6,6)*b(4,6)*b(2,2)**2*xi(3 ,4) - b(6,6)*b(5,6)*b(2,2)**2*xi(3,5)*k - b(6,6)*b(5,6)*b(3,4) + b(6,6)**2*b(2,2 )**2*xi(3,6)*k**2 + b(6,6)**2*b(3,5)*k)/(b(6,6)**3*k)$ det(AUTOM):=b(6,6)**3*b(2,2)**4*k**5$ DELTAPRIMEMODADG:= mat((0,k,0,0,0,0), (0,0,0,0,0,0), 2 b(2,2) *xi(3,4) (0,0,0,-----------------, b(6,6)*k 2 2 - b(5,6)*b(2,2) *xi(3,4) + b(6,6)*b(2,2) *xi(3,5)*k + b(6,6)*b(3,4) ----------------------------------------------------------------------,( 2 b(6,6) *k 2 2 2 b(5,6) *b(2,2) *xi(3,4) - b(6,6)*b(4,6)*b(2,2) *xi(3,4) 2 - b(6,6)*b(5,6)*b(2,2) *xi(3,5)*k - b(6,6)*b(5,6)*b(3,4) 2 2 2 2 3 + b(6,6) *b(2,2) *xi(3,6)*k + b(6,6) *b(3,5)*k)/(b(6,6) *k)), 2 b(4,6)*xi(6,1) - b(5,1)*k + b(5,6)*xi(5,1)*k + b(6,6)*xi(4,1)*k (------------------------------------------------------------------,( b(2,2)*k b(4,1)*b(2,2)*k - b(4,6)*b(1,2)*xi(6,1) + b(4,6)*b(2,2)*xi(6,2)*k 2 + b(5,1)*b(1,2)*k - b(5,2)*b(2,2)*k - b(5,6)*b(1,2)*xi(5,1)*k 2 2 + b(5,6)*b(2,2)*xi(5,2)*k - b(6,6)*b(1,2)*xi(4,1)*k 3 2 + b(6,6)*b(2,2)*xi(4,2)*k )/(b(2,2) *k),0,0,k,0), b(5,6)*xi(6,1) - b(6,1)*k + b(6,6)*xi(5,1)*k (----------------------------------------------,(b(5,1)*b(2,2)*k b(2,2)*k - b(5,6)*b(1,2)*xi(6,1) + b(5,6)*b(2,2)*xi(6,2)*k + b(6,1)*b(1,2)*k 2 2 - b(6,2)*b(2,2)*k - b(6,6)*b(1,2)*xi(5,1)*k + b(6,6)*b(2,2)*xi(5,2)*k 2 )/(b(2,2) *k),0,0,0,k), b(6,6)*xi(6,1) (----------------, b(2,2)*k b(6,1)*b(2,2)*k - b(6,6)*b(1,2)*xi(6,1) + b(6,6)*b(2,2)*xi(6,2)*k -------------------------------------------------------------------,0,0,0,0 2 b(2,2) *k )) One gets deltaprime(4,1):=0 ,deltaprime(5,1):=0 if we take :$ b(5,1):=(b(4,6)*xi(6,1) + b(5,6)*xi(5,1)*k + b(6,6)*xi(4,1)*k**2)/k$ b(6,1):=(b(5,6)*xi(6,1) + b(6,6)*xi(5,1)*k)/k$ With the generic automorphism one gets$ shortformdeltaprimemodadg:={0, (b(4,1) + b(4,6)*xi(6,2) - b(5,2)*k + b(5,6)*xi(5,2)*k + b(6,6)*xi(4,2)*k**2)/b( 2,2), ss, 0, (b(4,6)*xi(6,1) + b(5,6)*xi(5,1)*k + b(5,6)*xi(6,2)*k - b(6,2)*k**2 + b(6,6)*xi( 4,1)*k**2 + b(6,6)*xi(5,2)*k**2)/(b(2,2)*k), ss, (b(6,6)*xi(6,1))/(b(2,2)*k), (b(5,6)*b(2,2)*xi(6,1) - b(6,6)*b(1,2)*xi(6,1) + b(6,6)*b(2,2)*xi(5,1)*k + b(6,6 )*b(2,2)*xi(6,2)*k)/(b(2,2)**2*k), ss, (b(2,2)**2*xi(3,4))/(b(6,6)*k), ( - b(5,6)*b(2,2)**2*xi(3,4) + b(6,6)*b(2,2)**2*xi(3,5)*k + b(6,6)*b(3,4))/(b(6, 6)**2*k), (b(5,6)**2*b(2,2)**2*xi(3,4) - b(6,6)*b(4,6)*b(2,2)**2*xi(3,4) - b(6,6)*b(5,6)*b (2,2)**2*xi(3,5)*k - b(6,6)*b(5,6)*b(3,4) + b(6,6)**2*b(2,2)**2*xi(3,6)*k**2 + b (6,6)**2*b(3,5)*k)/(b(6,6)**3*k)}$ deltaprimemodg(4,1):=0$ deltaprimemodg(4,2):=(b(4,1) + b(4,6)*xi(6,2) - b(5,2)*k + b(5,6)*xi(5,2)*k + b( 6,6)*xi(4,2)*k**2)/b(2,2)$ deltaprimemodg(5,1):=0$ deltaprimemodg(5,2):=(b(4,6)*xi(6,1) + b(5,6)*xi(5,1)*k + b(5,6)*xi(6,2)*k - b(6 ,2)*k**2 + b(6,6)*xi(4,1)*k**2 + b(6,6)*xi(5,2)*k**2)/(b(2,2)*k)$ deltaprimemodg(6,1):=(b(6,6)*xi(6,1))/(b(2,2)*k)$ deltaprimemodg(6,2):=(b(5,6)*b(2,2)*xi(6,1) - b(6,6)*b(1,2)*xi(6,1) + b(6,6)*b(2 ,2)*xi(5,1)*k + b(6,6)*b(2,2)*xi(6,2)*k)/(b(2,2)**2*k)$ deltaprimemodg(3,4):=(b(2,2)**2*xi(3,4))/(b(6,6)*k)$ deltaprimemodg(3,5):=( - b(5,6)*b(2,2)**2*xi(3,4) + b(6,6)*b(2,2)**2*xi(3,5)*k + b(6,6)*b(3,4))/(b(6,6)**2*k)$ deltaprimemodg(3,6):=(b(5,6)**2*b(2,2)**2*xi(3,4) - b(6,6)*b(4,6)*b(2,2)**2*xi(3 ,4) - b(6,6)*b(5,6)*b(2,2)**2*xi(3,5)*k - b(6,6)*b(5,6)*b(3,4) + b(6,6)**2*b(2,2 )**2*xi(3,6)*k**2 + b(6,6)**2*b(3,5)*k)/(b(6,6)**3*k)$ det(AUTOM):=b(6,6)**3*b(2,2)**4*k**5$ DELTAPRIMEMODADG:= mat((0,k,0,0,0,0), (0,0,0,0,0,0), 2 b(2,2) *xi(3,4) (0,0,0,-----------------, b(6,6)*k 2 2 - b(5,6)*b(2,2) *xi(3,4) + b(6,6)*b(2,2) *xi(3,5)*k + b(6,6)*b(3,4) ----------------------------------------------------------------------,( 2 b(6,6) *k 2 2 2 b(5,6) *b(2,2) *xi(3,4) - b(6,6)*b(4,6)*b(2,2) *xi(3,4) 2 - b(6,6)*b(5,6)*b(2,2) *xi(3,5)*k - b(6,6)*b(5,6)*b(3,4) 2 2 2 2 3 + b(6,6) *b(2,2) *xi(3,6)*k + b(6,6) *b(3,5)*k)/(b(6,6) *k)), (0, 2 b(4,1) + b(4,6)*xi(6,2) - b(5,2)*k + b(5,6)*xi(5,2)*k + b(6,6)*xi(4,2)*k --------------------------------------------------------------------------- b(2,2) ,0,0,k,0), 2 (0,(b(4,6)*xi(6,1) + b(5,6)*xi(5,1)*k + b(5,6)*xi(6,2)*k - b(6,2)*k 2 2 + b(6,6)*xi(4,1)*k + b(6,6)*xi(5,2)*k )/(b(2,2)*k),0,0,0,k), b(6,6)*xi(6,1) (----------------,(b(5,6)*b(2,2)*xi(6,1) - b(6,6)*b(1,2)*xi(6,1) b(2,2)*k 2 + b(6,6)*b(2,2)*xi(5,1)*k + b(6,6)*b(2,2)*xi(6,2)*k)/(b(2,2) *k),0,0,0, 0)) One gets deltaprime(4,2):=0 as well if we take :$ b(4,1):= - b(4,6)*xi(6,2) + b(5,2)*k - b(5,6)*xi(5,2)*k - b(6,6)*xi(4,2)*k**2$ With the generic automorphism one gets$ shortformdeltaprimemodadg:={0, 0, ss, 0, (b(4,6)*xi(6,1) + b(5,6)*xi(5,1)*k + b(5,6)*xi(6,2)*k - b(6,2)*k**2 + b(6,6)*xi( 4,1)*k**2 + b(6,6)*xi(5,2)*k**2)/(b(2,2)*k), ss, (b(6,6)*xi(6,1))/(b(2,2)*k), (b(5,6)*b(2,2)*xi(6,1) - b(6,6)*b(1,2)*xi(6,1) + b(6,6)*b(2,2)*xi(5,1)*k + b(6,6 )*b(2,2)*xi(6,2)*k)/(b(2,2)**2*k), ss, (b(2,2)**2*xi(3,4))/(b(6,6)*k), ( - b(5,6)*b(2,2)**2*xi(3,4) + b(6,6)*b(2,2)**2*xi(3,5)*k + b(6,6)*b(3,4))/(b(6, 6)**2*k), (b(5,6)**2*b(2,2)**2*xi(3,4) - b(6,6)*b(4,6)*b(2,2)**2*xi(3,4) - b(6,6)*b(5,6)*b (2,2)**2*xi(3,5)*k - b(6,6)*b(5,6)*b(3,4) + b(6,6)**2*b(2,2)**2*xi(3,6)*k**2 + b (6,6)**2*b(3,5)*k)/(b(6,6)**3*k)}$ deltaprimemodg(4,1):=0$ deltaprimemodg(4,2):=0$ deltaprimemodg(5,1):=0$ deltaprimemodg(5,2):=(b(4,6)*xi(6,1) + b(5,6)*xi(5,1)*k + b(5,6)*xi(6,2)*k - b(6 ,2)*k**2 + b(6,6)*xi(4,1)*k**2 + b(6,6)*xi(5,2)*k**2)/(b(2,2)*k)$ deltaprimemodg(6,1):=(b(6,6)*xi(6,1))/(b(2,2)*k)$ deltaprimemodg(6,2):=(b(5,6)*b(2,2)*xi(6,1) - b(6,6)*b(1,2)*xi(6,1) + b(6,6)*b(2 ,2)*xi(5,1)*k + b(6,6)*b(2,2)*xi(6,2)*k)/(b(2,2)**2*k)$ deltaprimemodg(3,4):=(b(2,2)**2*xi(3,4))/(b(6,6)*k)$ deltaprimemodg(3,5):=( - b(5,6)*b(2,2)**2*xi(3,4) + b(6,6)*b(2,2)**2*xi(3,5)*k + b(6,6)*b(3,4))/(b(6,6)**2*k)$ deltaprimemodg(3,6):=(b(5,6)**2*b(2,2)**2*xi(3,4) - b(6,6)*b(4,6)*b(2,2)**2*xi(3 ,4) - b(6,6)*b(5,6)*b(2,2)**2*xi(3,5)*k - b(6,6)*b(5,6)*b(3,4) + b(6,6)**2*b(2,2 )**2*xi(3,6)*k**2 + b(6,6)**2*b(3,5)*k)/(b(6,6)**3*k)$ det(AUTOM):=b(6,6)**3*b(2,2)**4*k**5$ DELTAPRIMEMODADG:= mat((0,k,0,0,0,0), (0,0,0,0,0,0), 2 b(2,2) *xi(3,4) (0,0,0,-----------------, b(6,6)*k 2 2 - b(5,6)*b(2,2) *xi(3,4) + b(6,6)*b(2,2) *xi(3,5)*k + b(6,6)*b(3,4) ----------------------------------------------------------------------,( 2 b(6,6) *k 2 2 2 b(5,6) *b(2,2) *xi(3,4) - b(6,6)*b(4,6)*b(2,2) *xi(3,4) 2 - b(6,6)*b(5,6)*b(2,2) *xi(3,5)*k - b(6,6)*b(5,6)*b(3,4) 2 2 2 2 3 + b(6,6) *b(2,2) *xi(3,6)*k + b(6,6) *b(3,5)*k)/(b(6,6) *k)), (0,0,0,0,k,0), 2 (0,(b(4,6)*xi(6,1) + b(5,6)*xi(5,1)*k + b(5,6)*xi(6,2)*k - b(6,2)*k 2 2 + b(6,6)*xi(4,1)*k + b(6,6)*xi(5,2)*k )/(b(2,2)*k),0,0,0,k), b(6,6)*xi(6,1) (----------------,(b(5,6)*b(2,2)*xi(6,1) - b(6,6)*b(1,2)*xi(6,1) b(2,2)*k 2 + b(6,6)*b(2,2)*xi(5,1)*k + b(6,6)*b(2,2)*xi(6,2)*k)/(b(2,2) *k),0,0,0, 0)) One gets moreover deltaprime(5,2):=0 and $ deltaprime(3,6):=0 if we take :$ b(6,2):=(b(4,6)*xi(6,1) + b(5,6)*xi(5,1)*k + b(5,6)*xi(6,2)*k + b(6,6)*xi(4,1)*k **2 + b(6,6)*xi(5,2)*k**2)/k**2$ b(3,5):=( - b(5,6)**2*b(2,2)**2*xi(3,4) + b(6,6)*b(4,6)*b(2,2)**2*xi(3,4) + b(6, 6)*b(5,6)*b(2,2)**2*xi(3,5)*k + b(6,6)*b(5,6)*b(3,4) - b(6,6)**2*b(2,2)**2*xi(3, 6)*k**2)/(b(6,6)**2*k)$ With the generic automorphism one gets$ shortformdeltaprimemodadg:={0, 0, ss, 0, 0, ss, (b(6,6)*xi(6,1))/(b(2,2)*k), (b(5,6)*b(2,2)*xi(6,1) - b(6,6)*b(1,2)*xi(6,1) + b(6,6)*b(2,2)*xi(5,1)*k + b(6,6 )*b(2,2)*xi(6,2)*k)/(b(2,2)**2*k), ss, (b(2,2)**2*xi(3,4))/(b(6,6)*k), ( - b(5,6)*b(2,2)**2*xi(3,4) + b(6,6)*b(2,2)**2*xi(3,5)*k + b(6,6)*b(3,4))/(b(6, 6)**2*k), 0}$ deltaprimemodg(4,1):=0$ deltaprimemodg(4,2):=0$ deltaprimemodg(5,1):=0$ deltaprimemodg(5,2):=0$ deltaprimemodg(6,1):=(b(6,6)*xi(6,1))/(b(2,2)*k)$ deltaprimemodg(6,2):=(b(5,6)*b(2,2)*xi(6,1) - b(6,6)*b(1,2)*xi(6,1) + b(6,6)*b(2 ,2)*xi(5,1)*k + b(6,6)*b(2,2)*xi(6,2)*k)/(b(2,2)**2*k)$ deltaprimemodg(3,4):=(b(2,2)**2*xi(3,4))/(b(6,6)*k)$ deltaprimemodg(3,5):=( - b(5,6)*b(2,2)**2*xi(3,4) + b(6,6)*b(2,2)**2*xi(3,5)*k + b(6,6)*b(3,4))/(b(6,6)**2*k)$ deltaprimemodg(3,6):=0$ det(AUTOM):=b(6,6)**3*b(2,2)**4*k**5$ DELTAPRIMEMODADG:= mat((0,k,0,0,0,0), (0,0,0,0,0,0), 2 b(2,2) *xi(3,4) (0,0,0,-----------------, b(6,6)*k 2 2 - b(5,6)*b(2,2) *xi(3,4) + b(6,6)*b(2,2) *xi(3,5)*k + b(6,6)*b(3,4) ----------------------------------------------------------------------,0), 2 b(6,6) *k (0,0,0,0,k,0), (0,0,0,0,0,k), b(6,6)*xi(6,1) (----------------,(b(5,6)*b(2,2)*xi(6,1) - b(6,6)*b(1,2)*xi(6,1) b(2,2)*k 2 + b(6,6)*b(2,2)*xi(5,1)*k + b(6,6)*b(2,2)*xi(6,2)*k)/(b(2,2) *k),0,0,0, 0)) One gets deltaprime(3,5):=0 as well if we take :$ b(3,4):=(b(2,2)**2*(b(5,6)*xi(3,4) - b(6,6)*xi(3,5)*k))/b(6,6)$ With the generic automorphism one gets$ shortformdeltaprimemodadg:={0, 0, ss, 0, 0, ss, (b(6,6)*xi(6,1))/(b(2,2)*k), (b(5,6)*b(2,2)*xi(6,1) - b(6,6)*b(1,2)*xi(6,1) + b(6,6)*b(2,2)*xi(5,1)*k + b(6,6 )*b(2,2)*xi(6,2)*k)/(b(2,2)**2*k), ss, (b(2,2)**2*xi(3,4))/(b(6,6)*k), 0, 0}$ deltaprimemodg(4,1):=0$ deltaprimemodg(4,2):=0$ deltaprimemodg(5,1):=0$ deltaprimemodg(5,2):=0$ deltaprimemodg(6,1):=(b(6,6)*xi(6,1))/(b(2,2)*k)$ deltaprimemodg(6,2):=(b(5,6)*b(2,2)*xi(6,1) - b(6,6)*b(1,2)*xi(6,1) + b(6,6)*b(2 ,2)*xi(5,1)*k + b(6,6)*b(2,2)*xi(6,2)*k)/(b(2,2)**2*k)$ deltaprimemodg(3,4):=(b(2,2)**2*xi(3,4))/(b(6,6)*k)$ deltaprimemodg(3,5):=0$ deltaprimemodg(3,6):=0$ det(AUTOM):=b(6,6)**3*b(2,2)**4*k**5$ DELTAPRIMEMODADG:= mat((0,k,0,0,0,0), (0,0,0,0,0,0), 2 b(2,2) *xi(3,4) (0,0,0,-----------------,0,0), b(6,6)*k (0,0,0,0,k,0), (0,0,0,0,0,k), b(6,6)*xi(6,1) (----------------,(b(5,6)*b(2,2)*xi(6,1) - b(6,6)*b(1,2)*xi(6,1) b(2,2)*k 2 + b(6,6)*b(2,2)*xi(5,1)*k + b(6,6)*b(2,2)*xi(6,2)*k)/(b(2,2) *k),0,0,0, 0)) ************** SUBCASE 1 :xi(6,1) neq 0. ***********************************$ Then we get deltaprimemodadg(6,1)=k by taking :$ b(6,6):=(b(2,2)*k**2)/xi(6,1)$ and deltaprimemodadg(6,2)=0 by taking :$ b(1,2):=(b(2,2)*xi(5,1)*k**3 + b(2,2)*xi(6,2)*k**3 + b(5,6)*xi(6,1)**2)/(xi(6,1) *k**2)$ With the generic automorphism one gets$ shortformdeltaprimemodadg:={0, 0, ss, 0, 0, ss, k, 0, ss, (b(2,2)*xi(6,1)*xi(3,4))/k**3, 0, 0}$ deltaprimemodg(4,1):=0$ deltaprimemodg(4,2):=0$ deltaprimemodg(5,1):=0$ deltaprimemodg(5,2):=0$ deltaprimemodg(6,1):=k$ deltaprimemodg(6,2):=0$ deltaprimemodg(3,4):=(b(2,2)*xi(6,1)*xi(3,4))/k**3$ deltaprimemodg(3,5):=0$ deltaprimemodg(3,6):=0$ det(AUTOM):=(b(2,2)**7*k**11)/xi(6,1)**3$ DELTAPRIMEMODADG:= [0 k 0 0 0 0] [ ] [0 0 0 0 0 0] [ ] [ b(2,2)*xi(6,1)*xi(3,4) ] [0 0 0 ------------------------ 0 0] [ 3 ] [ k ] [ ] [0 0 0 0 k 0] [ ] [0 0 0 0 0 k] [ ] [k 0 0 0 0 0] Hence we are reduced in that subcase 1 to :$ deltaprimemodg:=(0,0;0,0;1,0;epsilon,0,0)_6.$ where epsilon=xi(3,4)=0,1.$ ************** SUBCASE 2 :xi(6,1) = 0. ***********************************$ clear b(1,2), b(6,6)$ xi(6,1):=0$ With the generic automorphism one gets$ shortformdeltaprimemodadg:={0, 0, ss, 0, 0, ss, 0, ((xi(5,1) + xi(6,2))*b(6,6))/b(2,2), ss, (b(2,2)**2*xi(3,4))/(b(6,6)*k), 0, 0}$ deltaprimemodg(4,1):=0$ deltaprimemodg(4,2):=0$ deltaprimemodg(5,1):=0$ deltaprimemodg(5,2):=0$ deltaprimemodg(6,1):=0$ deltaprimemodg(6,2):=((xi(5,1) + xi(6,2))*b(6,6))/b(2,2)$ deltaprimemodg(3,4):=(b(2,2)**2*xi(3,4))/(b(6,6)*k)$ deltaprimemodg(3,5):=0$ deltaprimemodg(3,6):=0$ det(AUTOM):=b(6,6)**3*b(2,2)**4*k**5$ DELTAPRIMEMODADG:= [0 k 0 0 0 0] [ ] [0 0 0 0 0 0] [ ] [ 2 ] [ b(2,2) *xi(3,4) ] [0 0 0 ----------------- 0 0] [ b(6,6)*k ] [ ] [0 0 0 0 k 0] [ ] [0 0 0 0 0 k] [ ] [ (xi(5,1) + xi(6,2))*b(6,6) ] [0 ---------------------------- 0 0 0 0] [ b(2,2) ] Hence we are reduced in that subcase 2 to :$ deltaprimemodg:=(0,0;0,0;0,epsilon;eta,0,0)_6.$ where epsilon=xi(6,2)=0,1 and eta=xi(3,4)=0,1.$