rreducparautommodg6_51xCN6.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$

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}}$

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

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

*******Suppose xi(1,3) = 0.$

*******Suppose xi(1,4) = 0.$

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

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

xi(1,2):=0$

xi(1,3):=0$

xi(1,4):=0$

xi(2,4):=0$

delta:=

[   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  xi(5,6)]
[                                              ]
[xi(6,1)  xi(6,2)  xi(6,3)  xi(6,4)  0     0   ]


With the first kind automorphism one gets$

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

deltaprimemodg(1,2):=0$

deltaprimemodg(1,3):=0$

deltaprimemodg(1,4):=0$

deltaprimemodg(2,4):=0$

deltaprimemodg(5,6):=(xi(5,6)*( - 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)$

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

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

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

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

det(AUTOM):=( - b(3,1)*b(1,3) - b(3,2)*b(1,4) + b(3,3)*b(1,1) + b(3,4)*b(1,2))**
3*b(6,6)$

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

Take the following values:$

b(1,3):=0$

b(1,2):=0$

b(3,2):=0$

b(4,2):=0$

With the first kind automorphism one gets$

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

deltaprimemodg(1,2):=0$

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

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

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

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

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

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

****** Suppose xi(6,2) neq 0.$

Then we get deltaprime(6,2)=1 by taking:$

b(2,2):=b(6,6)*xi(6,2)$

and we get deltaprime(6,1)=0 by taking:$

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

and we get deltaprime(6,3)=0 by taking:$

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

and we get deltaprime(6,4)=0 by taking:$

b(2,4):=b(6,6)*xi(6,4)$

With the first kind automorphism one gets$

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

deltaprimemodg(1,2):=0$

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):=0$

deltaprimemodg(6,2):=1$

deltaprimemodg(6,3):=0$

deltaprimemodg(6,4):=0$

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

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

Hence if xi(6,2) neq 0, we are reduced to :$

(0,0,0,ss,0,ss,epsilon,ss,0,1,0,0}$

where epsilon=xi(5,6)=0,1.$

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

****** Suppose xi(6,2) = 0.$

xi(6,2):=0$

clear b(2,2),b(3,4),b(1,4),b(2,4)$

With the first kind automorphism one gets$

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

deltaprimemodg(1,2):=0$

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)*( - b(3,1)*xi(6,3) + b(3,3)*xi(6,1)))/(b(3,3)*b(1,1
))$

deltaprimemodg(6,2):=0$

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

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

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

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

****** Suppose xi(6,3) neq 0.$

Then we get deltaprime(6,3)=1 by taking:$

b(3,3):=b(6,6)*xi(6,3)$

and we get deltaprime(6,1)=0 by taking:$

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

and we get deltaprime(6,4)=0 by taking:$

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

With the first kind automorphism one gets$

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

deltaprimemodg(1,2):=0$

deltaprimemodg(1,3):=0$

deltaprimemodg(1,4):=0$

deltaprimemodg(2,4):=0$

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

deltaprimemodg(6,1):=0$

deltaprimemodg(6,2):=0$

deltaprimemodg(6,3):=1$

deltaprimemodg(6,4):=0$

det(AUTOM):=b(6,6)**4*b(1,1)**3*xi(6,3)**3$

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

Hence if xi(6,2)=0 and xi(6,3) neq 0, we are reduced to :$

(0,0,0,ss,0,ss,epsilon,ss,0,0,1,0}$

where epsilon=xi(5,6)=0,1.$

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

****** Suppose xi(6,2) = xi(6,3)= 0.$

xi(6,3):=0$

clear b(3,4),b(3,1),b(3,3)$

With the first kind automorphism one gets$

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

deltaprimemodg(1,2):=0$

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

****** Suppose xi(6,1) neq 0.$

Then we get deltaprime(6,1)=1 by taking:$

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

and we get deltaprime(6,4)=0 by taking:$

b(1,4):=b(6,6)*xi(6,4)$

With the first kind automorphism one gets$

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

deltaprimemodg(1,2):=0$

deltaprimemodg(1,3):=0$

deltaprimemodg(1,4):=0$

deltaprimemodg(2,4):=0$

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

deltaprimemodg(6,1):=1$

deltaprimemodg(6,2):=0$

deltaprimemodg(6,3):=0$

deltaprimemodg(6,4):=0$

det(AUTOM):=b(6,6)**4*b(3,3)**3*xi(6,1)**3$

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

Hence if xi(6,2)=xi(6,3)= 0 and xi(6,1) neq 0, we are reduced to :$

(0,0,0,ss,0,ss,epsilon,ss,1,0,0,0}$

where epsilon=xi(5,6)=0,1.$

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

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

****** Suppose xi(6,2) = xi(6,3)=xi(6,1)= 0.$

xi(6,1):=0$

clear b(1,1),b(1,4)$

With the first kind automorphism one gets$

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

deltaprimemodg(1,2):=0$

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):=0$

deltaprimemodg(6,2):=0$

deltaprimemodg(6,3):=0$

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

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

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

Hence if xi(6,2)=xi(6,3)= xi(6,1) = 0, we are reduced to :$

if xi(5,6) neq 0 :$

(0,0,0,ss,0,ss,1,ss,0,0,0,epsilon}$

where epsilon=xi(6,4)=0,1.$

if xi(5,6) = 0 :$

(0,0,0,ss,0,ss,0,ss,0,0,0,1}$

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