rreducparautommodg6_51xCN2.r


The generic automorphism phi of C x g_{5,1} as computed by calculautom6_51xC.r\
ed :

They fall into 4 kinds: 

The first  kind (which contains the identity component) is: 

The parameters are subject to the supplementary conditions :

b(2,2)*( - b(3,1)*b(1,3) + b(3,3)*b(1,1))neq 0

phi:=

mat((b(1,1),b(1,2),b(1,3),b(1,4),0,0),

    ((b(3,1)*b(2,2)*b(1,4) - b(3,1)*b(2,4)*b(1,2) + b(3,2)*b(2,4)*b(1,1)

       - b(3,4)*b(2,2)*b(1,1))/( - b(3,1)*b(1,3) + b(3,3)*b(1,1)),b(2,2),(

        b(3,2)*b(2,4)*b(1,3) + b(3,3)*b(2,2)*b(1,4) - b(3,3)*b(2,4)*b(1,2)

         - b(3,4)*b(2,2)*b(1,3))/( - b(3,1)*b(1,3) + b(3,3)*b(1,1)),b(2,4),0,0),

    (b(3,1),b(3,2),b(3,3),b(3,4),0,0),

            2
    ((b(3,1) *b(1,3)*b(1,2) - b(3,2)*b(3,1)*b(1,3)*b(1,1)

                                                           2
       - b(3,3)*b(3,1)*b(1,2)*b(1,1) + b(3,3)*b(3,2)*b(1,1)

       + b(4,2)*b(3,1)*b(2,2)*b(1,4) - b(4,2)*b(3,1)*b(2,4)*b(1,2)

       + b(4,2)*b(3,2)*b(2,4)*b(1,1) - b(4,2)*b(3,4)*b(2,2)*b(1,1))/(b(2,2)

                                                                            2
        *( - b(3,1)*b(1,3) + b(3,3)*b(1,1))),b(4,2),( - b(3,2)*b(3,1)*b(1,3)

         + b(3,3)*b(3,1)*b(1,3)*b(1,2) + b(3,3)*b(3,2)*b(1,3)*b(1,1)

                 2
         - b(3,3) *b(1,2)*b(1,1) + b(4,2)*b(3,2)*b(2,4)*b(1,3)

         + b(4,2)*b(3,3)*b(2,2)*b(1,4) - b(4,2)*b(3,3)*b(2,4)*b(1,2)

         - b(4,2)*b(3,4)*b(2,2)*b(1,3))/(b(2,2)

        *( - b(3,1)*b(1,3) + b(3,3)*b(1,1))),

       - b(3,1)*b(1,3) + b(3,3)*b(1,1) + b(4,2)*b(2,4)
     --------------------------------------------------,0,0),
                           b(2,2)

    (b(5,1),b(5,2),b(5,3),b(5,4),

      - b(3,1)*b(1,3) - b(3,2)*b(1,4) + b(3,3)*b(1,1) + b(3,4)*b(1,2),b(5,6)),

    (b(6,1),b(6,2),b(6,3),b(6,4),0,b(6,6)))


                                                                            3
det(phi):=( - b(3,1)*b(1,3) - b(3,2)*b(1,4) + b(3,3)*b(1,1) + b(3,4)*b(1,2))

          *b(6,6)

condition11:=( - b(3,1)*b(1,3) + b(3,3)*b(1,1))*b(2,2) neq 0

generic derivation : delta:=

mat((xi(1,1),xi(1,2),xi(1,3),xi(1,4),0,0),

    (xi(2,1),xi(2,2),xi(1,4),xi(2,4),0,0),

    (xi(3,1),xi(3,2),xi(3,3), - xi(2,1),0,0),

    (xi(3,2),xi(4,2), - xi(1,2), - ( - xi(3,3) - xi(1,1) + xi(2,2)),0,0),

    (xi(5,1),xi(5,2),xi(5,3),xi(5,4),xi(1,1) + xi(3,3),xi(5,6)),

    (xi(6,1),xi(6,2),xi(6,3),xi(6,4),0,xi(6,6)))


        [0  0  0  0  0  0]
        [                ]
        [0  0  0  0  0  0]
        [                ]
        [0  0  0  0  0  0]
adx1 := [                ]
        [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]
        [                ]
        [0  0  0  0  0  0]
adx2 := [                ]
        [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   0  0  0  0  0]
adx3 := [                 ]
        [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  0]
adx4 := [                 ]
        [0  0   0  0  0  0]
        [                 ]
        [0  -1  0  0  0  0]
        [                 ]
        [0  0   0  0  0  0]


The generic nilpotent derivation : the eigenvalues are 0

xi(3,3):= - xi(1,1)

xi(6,6):=0

And the matrix A:=

[xi(1,1)  xi(1,2)   xi(1,3)     xi(1,4)  ]
[                                        ]
[xi(2,1)  xi(2,2)   xi(1,4)     xi(2,4)  ]
[                                        ]
[xi(3,1)  xi(3,2)   - xi(1,1)   - xi(2,1)]
[                                        ]
[xi(3,2)  xi(4,2)   - xi(1,2)   - xi(2,2)]


is nilpotent.

     [xi(1,1)  xi(1,2)   xi(1,3)     xi(1,4)  ]
     [                                        ]
     [xi(2,1)  xi(2,2)   xi(1,4)     xi(2,4)  ]
m := [                                        ]
     [xi(3,1)  xi(3,2)   - xi(1,1)   - xi(2,1)]
     [                                        ]
     [xi(3,2)  xi(4,2)   - xi(1,2)   - xi(2,2)]


we may suppose that A is an element of sp(4,C)+, that is:

xi(1,1):=0

xi(2,1):=0

xi(2,2):=0

xi(3,1):=0

xi(3,2):=0

xi(4,2):=0

M**1:=

[0  xi(1,2)   xi(1,3)    xi(1,4)]
[                               ]
[0     0      xi(1,4)    xi(2,4)]
[                               ]
[0     0         0          0   ]
[                               ]
[0     0      - xi(1,2)     0   ]


M**2:=

[0  0          0           xi(2,4)*xi(1,2)]
[                                         ]
[0  0   - xi(2,4)*xi(1,2)         0       ]
[                                         ]
[0  0          0                  0       ]
[                                         ]
[0  0          0                  0       ]


M**3:=

[                        2   ]
[0  0   - xi(2,4)*xi(1,2)   0]
[                            ]
[0  0           0           0]
[                            ]
[0  0           0           0]
[                            ]
[0  0           0           0]


M**4:=

[0  0  0  0]
[          ]
[0  0  0  0]
[          ]
[0  0  0  0]
[          ]
[0  0  0  0]


Trace(M**1)/2:=0$

Trace(M**2)/2:=0$

Trace(M**3)/2:=0$

Trace(M**4)/2:=0$

************************************************************************$

*******Suppose xi(1,2) neq 0.$

************************************************************************$

By subtracting adjoints one then may suppose:$

xi(5,1):=0,xi(5,2):=0,xi(5,3):=0,xi(5,4):=0$

delta:=
mat((0,xi(1,2),xi(1,3),xi(1,4),0,0),(0,0,xi(1,4),xi(2,4),0,0),(0,0,0,0,0,0),(0,0
, - xi(1,2),0,0,0),(0,0,0,0,0,xi(5,6)),(xi(6,1),xi(6,2),xi(6,3),xi(6,4),0,0))$

We denote this delta by the shortform$

shortformdelta:={xi(1,2),
xi(1,3),
xi(1,4),
ss,
xi(2,4),
ss,
xi(5,6),
ss,
xi(6,1),
xi(6,2),
xi(6,3),
xi(6,4)}$

paramindexeslist:={{1,2},{1,3},{1,4},{2,4},{5,6},{6,1},{6,2},{6,3},{6,4}}$

Take:$

b(3,1):=0$

b(3,2):=0$

b(4,2):=0$

b(3,4):=0$

With the first kind automorphism one gets$

shortformdeltaprimemodadg:={(b(1,1)*xi(1,2))/b(2,2),
(b(1,1)**2*xi(1,3) + 2*b(1,2)*b(1,1)*xi(1,4) + b(1,2)**2*xi(2,4) - 2*b(1,4)*b(1,
1)*xi(1,2))/(b(3,3)*b(1,1)),
(b(2,2)*b(1,1)*xi(1,4) + b(2,2)*b(1,2)*xi(2,4) - b(2,4)*b(1,1)*xi(1,2))/(b(3,3)*
b(1,1)),
ss,
(b(2,2)**2*xi(2,4))/(b(3,3)*b(1,1)),
ss,
(b(3,3)*b(1,1)*xi(5,6))/b(6,6),
ss,
(b(6,6)*xi(6,1))/b(1,1),
(b(6,1)*b(1,1)*xi(1,2) + b(6,6)*b(1,1)*xi(6,2) - b(6,6)*b(1,2)*xi(6,1))/(b(2,2)*
b(1,1)),
(b(6,1)*b(1,1)*xi(1,3) + b(6,1)*b(1,2)*xi(1,4) - b(6,1)*b(1,4)*xi(1,2) + b(6,2)*
b(1,1)*xi(1,4) + b(6,2)*b(1,2)*xi(2,4) - b(6,4)*b(1,1)*xi(1,2) + b(6,6)*b(1,1)*
xi(6,3) + b(6,6)*b(1,2)*xi(6,4) - b(6,6)*b(1,3)*xi(6,1) - b(6,6)*b(1,4)*xi(6,2))
/(b(3,3)*b(1,1)),
(b(6,1)*b(2,2)*b(1,1)*xi(1,4) - b(6,1)*b(2,4)*b(1,1)*xi(1,2) + b(6,2)*b(2,2)*b(1
,1)*xi(2,4) + b(6,6)*b(2,2)*b(1,1)*xi(6,4) - b(6,6)*b(2,2)*b(1,4)*xi(6,1) - b(6,
6)*b(2,4)*b(1,1)*xi(6,2) + b(6,6)*b(2,4)*b(1,2)*xi(6,1))/(b(3,3)*b(1,1)**2)}$

deltaprimemodg(1,2):=(b(1,1)*xi(1,2))/b(2,2)$

deltaprimemodg(1,3):=(b(1,1)**2*xi(1,3) + 2*b(1,2)*b(1,1)*xi(1,4) + b(1,2)**2*xi
(2,4) - 2*b(1,4)*b(1,1)*xi(1,2))/(b(3,3)*b(1,1))$

deltaprimemodg(1,4):=(b(2,2)*b(1,1)*xi(1,4) + b(2,2)*b(1,2)*xi(2,4) - b(2,4)*b(1
,1)*xi(1,2))/(b(3,3)*b(1,1))$

deltaprimemodg(2,4):=(b(2,2)**2*xi(2,4))/(b(3,3)*b(1,1))$

deltaprimemodg(5,6):=(b(3,3)*b(1,1)*xi(5,6))/b(6,6)$

deltaprimemodg(6,1):=(b(6,6)*xi(6,1))/b(1,1)$

deltaprimemodg(6,2):=(b(6,1)*b(1,1)*xi(1,2) + b(6,6)*b(1,1)*xi(6,2) - b(6,6)*b(1
,2)*xi(6,1))/(b(2,2)*b(1,1))$

deltaprimemodg(6,3):=(b(6,1)*b(1,1)*xi(1,3) + b(6,1)*b(1,2)*xi(1,4) - b(6,1)*b(1
,4)*xi(1,2) + b(6,2)*b(1,1)*xi(1,4) + b(6,2)*b(1,2)*xi(2,4) - b(6,4)*b(1,1)*xi(1
,2) + b(6,6)*b(1,1)*xi(6,3) + b(6,6)*b(1,2)*xi(6,4) - b(6,6)*b(1,3)*xi(6,1) - b(
6,6)*b(1,4)*xi(6,2))/(b(3,3)*b(1,1))$

deltaprimemodg(6,4):=(b(6,1)*b(2,2)*b(1,1)*xi(1,4) - b(6,1)*b(2,4)*b(1,1)*xi(1,2
) + b(6,2)*b(2,2)*b(1,1)*xi(2,4) + b(6,6)*b(2,2)*b(1,1)*xi(6,4) - b(6,6)*b(2,2)*
b(1,4)*xi(6,1) - b(6,6)*b(2,4)*b(1,1)*xi(6,2) + b(6,6)*b(2,4)*b(1,2)*xi(6,1))/(b
(3,3)*b(1,1)**2)$

det(AUTOM):=b(6,6)*b(3,3)**3*b(1,1)**3$

DELTAPRIMEMODADG:=
mat((0,(b(1,1)*xi(1,2))/b(2,2),( - 2*b(1,4)*b(1,1)*xi(1,2) + b(1,1)**2*xi(1,3) +
 2*b(1,2)*b(1,1)*xi(1,4) + b(1,2)**2*xi(2,4))/(b(3,3)*b(1,1)),( - b(2,4)*b(1,1)*
xi(1,2) + (b(1,1)*xi(1,4) + b(1,2)*xi(2,4))*b(2,2))/(b(3,3)*b(1,1)),0,0),(0,0,( 
- b(2,4)*b(1,1)*xi(1,2) + (b(1,1)*xi(1,4) + b(1,2)*xi(2,4))*b(2,2))/(b(3,3)*b(1,
1)),(b(2,2)**2*xi(2,4))/(b(3,3)*b(1,1)),0,0),(0,0,0,0,0,0),(0,0,( - b(1,1)*xi(1,
2))/b(2,2),0,0,0),(0,0,0,0,0,(b(3,3)*b(1,1)*xi(5,6))/b(6,6)),((b(6,6)*xi(6,1))/b
(1,1),( - ( - b(6,1)*b(1,1)*xi(1,2) + ( - b(1,1)*xi(6,2) + b(1,2)*xi(6,1))*b(6,6
)))/(b(2,2)*b(1,1)),(( - b(1,4)*xi(1,2) + b(1,1)*xi(1,3) + b(1,2)*xi(1,4))*b(6,1
) - b(6,4)*b(1,1)*xi(1,2) + (b(1,1)*xi(1,4) + b(1,2)*xi(2,4))*b(6,2) + ( - b(1,4
)*xi(6,2) - b(1,3)*xi(6,1) + b(1,1)*xi(6,3) + b(1,2)*xi(6,4))*b(6,6))/(b(3,3)*b(
1,1)),( - (( - ( - b(1,1)*xi(6,2) + b(1,2)*xi(6,1))*b(2,4) + ( - b(1,1)*xi(6,4) 
+ b(1,4)*xi(6,1))*b(2,2))*b(6,6) + ( - b(6,2)*b(2,2)*xi(2,4) + ( - b(2,2)*xi(1,4
) + b(2,4)*xi(1,2))*b(6,1))*b(1,1)))/(b(3,3)*b(1,1)**2),0,0))$

Then we get deltaprime(1,2)=1 , deltaprime(1,3)=0, deltaprimemodg(1,4)=0 and$

deltaprime(6,2)=0 by taking:$

b(2,2):=b(1,1)*xi(1,2)$

b(1,4):=(b(1,1)**2*xi(1,3) + 2*b(1,2)*b(1,1)*xi(1,4) + b(1,2)**2*xi(2,4))/(2*b(1
,1)*xi(1,2))$

b(2,4):=b(1,1)*xi(1,4) + b(1,2)*xi(2,4)$

b(6,1):=(( - b(1,1)*xi(6,2) + b(1,2)*xi(6,1))*b(6,6))/(b(1,1)*xi(1,2))$

With the first kind automorphism one gets$

shortformdeltaprimemodadg:={1,
0,
0,
ss,
(b(1,1)*xi(2,4)*xi(1,2)**2)/b(3,3),
ss,
(b(3,3)*b(1,1)*xi(5,6))/b(6,6),
ss,
(b(6,6)*xi(6,1))/b(1,1),
0,
(2*b(6,2)*b(1,1)**3*xi(1,4)*xi(1,2) + 2*b(6,2)*b(1,2)*b(1,1)**2*xi(2,4)*xi(1,2) 
- 2*b(6,4)*b(1,1)**3*xi(1,2)**2 - 2*b(6,6)*b(1,1)**3*xi(6,2)*xi(1,3) + 2*b(6,6)*
b(1,1)**3*xi(6,3)*xi(1,2) + b(6,6)*b(1,2)*b(1,1)**2*xi(6,1)*xi(1,3) - 2*b(6,6)*b
(1,2)*b(1,1)**2*xi(6,2)*xi(1,4) + 2*b(6,6)*b(1,2)*b(1,1)**2*xi(6,4)*xi(1,2) - b(
6,6)*b(1,2)**3*xi(6,1)*xi(2,4) - 2*b(6,6)*b(1,3)*b(1,1)**2*xi(6,1)*xi(1,2))/(2*b
(3,3)*b(1,1)**3*xi(1,2)),
(2*b(6,2)*b(1,1)**2*xi(2,4)*xi(1,2) - b(6,6)*b(1,1)**2*xi(6,1)*xi(1,3) - 2*b(6,6
)*b(1,1)**2*xi(6,2)*xi(1,4) + 2*b(6,6)*b(1,1)**2*xi(6,4)*xi(1,2) - b(6,6)*b(1,2)
**2*xi(6,1)*xi(2,4))/(2*b(3,3)*b(1,1)**2)}$

deltaprimemodg(1,2):=1$

deltaprimemodg(1,3):=0$

deltaprimemodg(1,4):=0$

deltaprimemodg(2,4):=(b(1,1)*xi(2,4)*xi(1,2)**2)/b(3,3)$

deltaprimemodg(5,6):=(b(3,3)*b(1,1)*xi(5,6))/b(6,6)$

deltaprimemodg(6,1):=(b(6,6)*xi(6,1))/b(1,1)$

deltaprimemodg(6,2):=0$

deltaprimemodg(6,3):=(2*b(6,2)*b(1,1)**3*xi(1,4)*xi(1,2) + 2*b(6,2)*b(1,2)*b(1,1
)**2*xi(2,4)*xi(1,2) - 2*b(6,4)*b(1,1)**3*xi(1,2)**2 - 2*b(6,6)*b(1,1)**3*xi(6,2
)*xi(1,3) + 2*b(6,6)*b(1,1)**3*xi(6,3)*xi(1,2) + b(6,6)*b(1,2)*b(1,1)**2*xi(6,1)
*xi(1,3) - 2*b(6,6)*b(1,2)*b(1,1)**2*xi(6,2)*xi(1,4) + 2*b(6,6)*b(1,2)*b(1,1)**2
*xi(6,4)*xi(1,2) - b(6,6)*b(1,2)**3*xi(6,1)*xi(2,4) - 2*b(6,6)*b(1,3)*b(1,1)**2*
xi(6,1)*xi(1,2))/(2*b(3,3)*b(1,1)**3*xi(1,2))$

deltaprimemodg(6,4):=(2*b(6,2)*b(1,1)**2*xi(2,4)*xi(1,2) - b(6,6)*b(1,1)**2*xi(6
,1)*xi(1,3) - 2*b(6,6)*b(1,1)**2*xi(6,2)*xi(1,4) + 2*b(6,6)*b(1,1)**2*xi(6,4)*xi
(1,2) - b(6,6)*b(1,2)**2*xi(6,1)*xi(2,4))/(2*b(3,3)*b(1,1)**2)$

det(AUTOM):=b(6,6)*b(3,3)**3*b(1,1)**3$

DELTAPRIMEMODADG:=
mat((0,1,0,0,0,0),(0,0,0,(b(1,1)*xi(2,4)*xi(1,2)**2)/b(3,3),0,0),(0,0,0,0,0,0),(
0,0,-1,0,0,0),(0,0,0,0,0,(b(3,3)*b(1,1)*xi(5,6))/b(6,6)),((b(6,6)*xi(6,1))/b(1,1
),0,( - ( - 2*( - b(6,4)*b(1,1)*xi(1,2) + (b(1,1)*xi(1,4) + b(1,2)*xi(2,4))*b(6,
2))*b(1,1)**2*xi(1,2) + (( - 2*xi(6,4)*xi(1,2) - xi(6,1)*xi(1,3) + 2*xi(6,2)*xi(
1,4))*b(1,2)*b(1,1)**2 - 2*( - xi(6,2)*xi(1,3) + xi(6,3)*xi(1,2))*b(1,1)**3 + (b
(1,2)**3*xi(2,4) + 2*b(1,3)*b(1,1)**2*xi(1,2))*xi(6,1))*b(6,6)))/(2*b(3,3)*b(1,1
)**3*xi(1,2)),( - ( - 2*b(6,2)*b(1,1)**2*xi(2,4)*xi(1,2) + (b(1,2)**2*xi(6,1)*xi
(2,4) + ( - 2*xi(6,4)*xi(1,2) + xi(6,1)*xi(1,3) + 2*xi(6,2)*xi(1,4))*b(1,1)**2)*
b(6,6)))/(2*b(3,3)*b(1,1)**2),0,0))$

Then one gets deltaprimemodg(6,3)=0 by taking:$

b(6,4):=( - ( - 2*(b(1,1)*xi(1,4) + b(1,2)*xi(2,4))*b(6,2)*b(1,1)**2*xi(1,2) + (
( - 2*xi(6,4)*xi(1,2) - xi(6,1)*xi(1,3) + 2*xi(6,2)*xi(1,4))*b(1,2)*b(1,1)**2 - 
2*( - xi(6,2)*xi(1,3) + xi(6,3)*xi(1,2))*b(1,1)**3 + (b(1,2)**3*xi(2,4) + 2*b(1,
3)*b(1,1)**2*xi(1,2))*xi(6,1))*b(6,6)))/(2*b(1,1)**3*xi(1,2)**2)$

With the first kind automorphism one gets$

shortformdeltaprimemodadg:={1,
0,
0,
ss,
(b(1,1)*xi(2,4)*xi(1,2)**2)/b(3,3),
ss,
(b(3,3)*b(1,1)*xi(5,6))/b(6,6),
ss,
(b(6,6)*xi(6,1))/b(1,1),
0,
0,
(2*b(6,2)*b(1,1)**2*xi(2,4)*xi(1,2) - b(6,6)*b(1,1)**2*xi(6,1)*xi(1,3) - 2*b(6,6
)*b(1,1)**2*xi(6,2)*xi(1,4) + 2*b(6,6)*b(1,1)**2*xi(6,4)*xi(1,2) - b(6,6)*b(1,2)
**2*xi(6,1)*xi(2,4))/(2*b(3,3)*b(1,1)**2)}$

deltaprimemodg(1,2):=1$

deltaprimemodg(1,3):=0$

deltaprimemodg(1,4):=0$

deltaprimemodg(2,4):=(b(1,1)*xi(2,4)*xi(1,2)**2)/b(3,3)$

deltaprimemodg(5,6):=(b(3,3)*b(1,1)*xi(5,6))/b(6,6)$

deltaprimemodg(6,1):=(b(6,6)*xi(6,1))/b(1,1)$

deltaprimemodg(6,2):=0$

deltaprimemodg(6,3):=0$

deltaprimemodg(6,4):=(2*b(6,2)*b(1,1)**2*xi(2,4)*xi(1,2) - b(6,6)*b(1,1)**2*xi(6
,1)*xi(1,3) - 2*b(6,6)*b(1,1)**2*xi(6,2)*xi(1,4) + 2*b(6,6)*b(1,1)**2*xi(6,4)*xi
(1,2) - b(6,6)*b(1,2)**2*xi(6,1)*xi(2,4))/(2*b(3,3)*b(1,1)**2)$

det(AUTOM):=b(6,6)*b(3,3)**3*b(1,1)**3$

DELTAPRIMEMODADG:=
mat((0,1,0,0,0,0),(0,0,0,(b(1,1)*xi(2,4)*xi(1,2)**2)/b(3,3),0,0),(0,0,0,0,0,0),(
0,0,-1,0,0,0),(0,0,0,0,0,(b(3,3)*b(1,1)*xi(5,6))/b(6,6)),((b(6,6)*xi(6,1))/b(1,1
),0,0,( - ( - 2*b(6,2)*b(1,1)**2*xi(2,4)*xi(1,2) + (b(1,2)**2*xi(6,1)*xi(2,4) + 
( - 2*xi(6,4)*xi(1,2) + xi(6,1)*xi(1,3) + 2*xi(6,2)*xi(1,4))*b(1,1)**2)*b(6,6)))
/(2*b(3,3)*b(1,1)**2),0,0))$

hence we may suppose :$

xi(1,2):=1$

xi(1,3):=0$

xi(1,4):=0$

xi(6,2):=0$

xi(6,3):=0$

**** Suppose xi(2,4) = 0.$

xi(2,4):=0$

With the first kind automorphism one gets$

shortformdeltaprimemodadg:={1,
0,
0,
ss,
0,
ss,
(b(3,3)*b(1,1)*xi(5,6))/b(6,6),
ss,
(b(6,6)*xi(6,1))/b(1,1),
0,
0,
(b(6,6)*xi(6,4))/b(3,3)}$

deltaprimemodg(1,2):=1$

deltaprimemodg(1,3):=0$

deltaprimemodg(1,4):=0$

deltaprimemodg(2,4):=0$

deltaprimemodg(5,6):=(b(3,3)*b(1,1)*xi(5,6))/b(6,6)$

deltaprimemodg(6,1):=(b(6,6)*xi(6,1))/b(1,1)$

deltaprimemodg(6,2):=0$

deltaprimemodg(6,3):=0$

deltaprimemodg(6,4):=(b(6,6)*xi(6,4))/b(3,3)$

det(AUTOM):=b(6,6)*b(3,3)**3*b(1,1)**3$

DELTAPRIMEMODADG:=
mat((0,1,0,0,0,0),(0,0,0,0,0,0),(0,0,0,0,0,0),(0,0,-1,0,0,0),(0,0,0,0,0,(b(3,3)*
b(1,1)*xi(5,6))/b(6,6)),((b(6,6)*xi(6,1))/b(1,1),0,0,(b(6,6)*xi(6,4))/b(3,3),0,0
))$

Hence we are reduced to shortformdelta:={1,0,0,ss,0,ss,1,ss,epsilon,0,0,eta}$

where epsilon=xi(6,1)=0,1 and eta=xi(6,4)=0,1 in the case xi(5,6) neq 0.$

If xi(5,6) = 0, we are reduced to $

shortformdelta:={1,0,0,ss,0,ss,0,ss,1,0,0,epsilon}$

where epsilon=xi(6,4)=0,1 in the case xi(6,1) neq 0.$

or to shortformdelta:={1,0,0,ss,0,ss,0,ss,0,0,0,1}$

in the case xi(6,1) = 0.$