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


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


The generic nilpotent derivation : the eigenvalues are 0

xi(1,1):=0

xi(6,6):=0

by subtracting adjoints one then may suppose:

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

delta:=

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


We denote this delta by the shortform

shortformdelta:={xi(2,1),

                 ss,

                 xi(4,2),

                 ss,

                 xi(5,2),

                 xi(5,6),

                 ss,

                 xi(6,1),

                 xi(6,2)}

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

a neq {}$

a:=a$

delta:=
mat((0,0,0,0,0,0),(1,0,0,0,0,0),(0,0,0,0,0,0),(0,1,0,0,0,0),(0,0,1,1,0,1),(0,a,0
,0,0,0))$
$

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

on resout l'equation {{0,1},0} qui est  maintenant AA:= - d(0,2)$

Unknown: d(0,2)
Unknown: d(0,2)
bonne inconnue W:=d(0,2)$

sa valeur doit etre WW:=0$

on resout l'equation {{0,1},1} qui est  maintenant AA:= - d(1,2)$

Unknown: d(1,2)
Unknown: d(1,2)
bonne inconnue W:=d(1,2)$

sa valeur doit etre WW:=0$

on resout l'equation {{0,1},2} qui est  maintenant AA:= - d(2,2) + d(1,1) + d(0,
0)$

Unknowns: {d(2,2),d(1,1),d(0,0)}
Unknowns: {d(2,2),d(1,1),d(0,0)}
bonne inconnue W:=d(2,2)$

sa valeur doit etre WW:=d(1,1) + d(0,0)$

on resout l'equation {{0,1},3} qui est  maintenant AA:= - (d(3,2) + d(2,0))$

Unknowns: {d(3,2),d(2,0)}
Unknowns: {d(3,2),d(2,0)}
bonne inconnue W:=d(3,2)$

sa valeur doit etre WW:= - d(2,0)$

on resout l'equation {{0,1},4} qui est  maintenant AA:= - d(4,2) - d(3,0) + d(2,
1)$

Unknowns: {d(4,2),d(3,0),d(2,1)}
Unknowns: {d(4,2),d(3,0),d(2,1)}
bonne inconnue W:=d(4,2)$

sa valeur doit etre WW:= - d(3,0) + d(2,1)$

on resout l'equation {{0,1},5} qui est  maintenant AA:=d(6,1) - d(5,2) + d(4,1) 
- d(4,0) + d(3,1)$

Unknowns: {d(6,1),d(5,2),d(4,1),d(4,0),d(3,1)}
Unknowns: {d(6,1),d(5,2),d(4,1),d(4,0),d(3,1)}
bonne inconnue W:=d(6,1)$

sa valeur doit etre WW:=d(5,2) - d(4,1) + d(4,0) - d(3,1)$

on resout l'equation {{0,1},6} qui est  maintenant AA:= - d(6,2) + d(2,1)*a$

Unknowns: {d(6,2),d(2,1),a}
Unknowns: {d(6,2),d(2,1),a}
bonne inconnue W:=d(6,2)$

sa valeur doit etre WW:=d(2,1)*a$

on resout l'equation {{0,2},0} qui est  maintenant AA:= - (d(0,6)*a + d(0,4))$

Unknowns: {d(0,6),d(0,4),a}
Unknowns: {d(0,6),d(0,4),a}
bonne inconnue W:=d(0,4)$

sa valeur doit etre WW:= - d(0,6)*a$

on resout l'equation {{0,2},1} qui est  maintenant AA:= - (d(1,6)*a + d(1,4))$

Unknowns: {d(1,6),d(1,4),a}
Unknowns: {d(1,6),d(1,4),a}
bonne inconnue W:=d(1,4)$

sa valeur doit etre WW:= - d(1,6)*a$

on resout l'equation {{0,2},2} qui est  maintenant AA:= - (d(2,6)*a + d(2,4))$

Unknowns: {d(2,6),d(2,4),a}
Unknowns: {d(2,6),d(2,4),a}
bonne inconnue W:=d(2,4)$

sa valeur doit etre WW:= - d(2,6)*a$

on resout l'equation {{0,2},3} qui est  maintenant AA:= - d(3,6)*a - d(3,4) + d(
1,0)$

Unknowns: {d(3,6),d(3,4),d(1,0),a}
Unknowns: {d(3,6),d(3,4),d(1,0),a}
bonne inconnue W:=d(3,4)$

sa valeur doit etre WW:= - d(3,6)*a + d(1,0)$

on resout l'equation {{0,2},4} qui est  maintenant AA:= - d(4,6)*a - d(4,4) + d(
1,1) + 2*d(0,0)$

Unknowns: {d(4,6),d(4,4),d(1,1),d(0,0),a}
Unknowns: {d(4,6),d(4,4),d(1,1),d(0,0),a}
bonne inconnue W:=d(4,4)$

sa valeur doit etre WW:= - d(4,6)*a + d(1,1) + 2*d(0,0)$

on resout l'equation {{0,2},5} qui est  maintenant AA:= - d(5,6)*a - d(5,4) - 2*
d(3,0) + d(2,1)*a + d(2,1) - d(2,0)$

Unknowns: {d(5,6),d(5,4),d(3,0),d(2,1),d(2,0),a}
Unknowns: {d(5,6),d(5,4),d(3,0),d(2,1),d(2,0),a}
bonne inconnue W:=d(5,4)$

sa valeur doit etre WW:= - d(5,6)*a - 2*d(3,0) + d(2,1)*a + d(2,1) - d(2,0)$

on resout l'equation {{0,2},6} qui est  maintenant AA:= - d(6,6)*a - d(6,4) + d(
1,1)*a + 2*d(0,0)*a$

Unknowns: {d(6,6),d(6,4),d(1,1),d(0,0),a}
Unknowns: {d(6,6),d(6,4),d(1,1),d(0,0),a}
bonne inconnue W:=d(6,4)$

sa valeur doit etre WW:=a*( - d(6,6) + d(1,1) + 2*d(0,0))$

on resout l'equation {{0,3},0} qui est  maintenant AA:= - d(0,5)$

Unknown: d(0,5)
Unknown: d(0,5)
bonne inconnue W:=d(0,5)$

sa valeur doit etre WW:=0$

on resout l'equation {{0,3},1} qui est  maintenant AA:= - d(1,5)$

Unknown: d(1,5)
Unknown: d(1,5)
bonne inconnue W:=d(1,5)$

sa valeur doit etre WW:=0$

on resout l'equation {{0,3},2} qui est  maintenant AA:= - d(2,5) + d(1,3)$

Unknowns: {d(2,5),d(1,3)}
Unknowns: {d(2,5),d(1,3)}
bonne inconnue W:=d(2,5)$

sa valeur doit etre WW:=d(1,3)$

on resout l'equation {{0,3},3} qui est  maintenant AA:= - d(3,5)$

Unknown: d(3,5)
Unknown: d(3,5)
bonne inconnue W:=d(3,5)$

sa valeur doit etre WW:=0$

on resout l'equation {{0,3},4} qui est  maintenant AA:= - d(4,5) + d(2,3) + d(1,
0)$

Unknowns: {d(4,5),d(2,3),d(1,0)}
Unknowns: {d(4,5),d(2,3),d(1,0)}
bonne inconnue W:=d(4,5)$

sa valeur doit etre WW:=d(2,3) + d(1,0)$

on resout l'equation {{0,3},5} qui est  maintenant AA:=d(6,3) - d(5,5) + d(4,3) 
+ d(3,3) + d(2,0) + d(0,0)$

Unknowns: {d(6,3),d(5,5),d(4,3),d(3,3),d(2,0),d(0,0)}
Unknowns: {d(6,3),d(5,5),d(4,3),d(3,3),d(2,0),d(0,0)}
bonne inconnue W:=d(6,3)$

sa valeur doit etre WW:=d(5,5) - d(4,3) - d(3,3) - d(2,0) - d(0,0)$

on resout l'equation {{0,3},6} qui est  maintenant AA:= - d(6,5) + d(2,3)*a$

Unknowns: {d(6,5),d(2,3),a}
Unknowns: {d(6,5),d(2,3),a}
bonne inconnue W:=d(6,5)$

sa valeur doit etre WW:=d(2,3)*a$

on resout l'equation {{0,4},2} qui est  maintenant AA:= - (d(1,6)*a + d(1,3))$

Unknowns: {d(1,6),d(1,3),a}
Unknowns: {d(1,6),d(1,3),a}
bonne inconnue W:=d(1,3)$

sa valeur doit etre WW:= - d(1,6)*a$

on resout l'equation {{0,4},4} qui est  maintenant AA:= - (d(2,6)*a + d(2,3) + d
(1,0))$

Unknowns: {d(2,6),d(2,3),d(1,0),a}
Unknowns: {d(2,6),d(2,3),d(1,0),a}
bonne inconnue W:=d(2,3)$

sa valeur doit etre WW:= - (d(2,6)*a + d(1,0))$

on resout l'equation {{0,4},5} qui est  maintenant AA:= - d(6,6)*a - d(5,5) - d(
4,6)*a - d(3,6)*a + d(1,1)*a + d(1,1) + 2*d(1,0) + 2*d(0,0)*a + 3*d(0,0)$

Unknowns: {d(6,6),d(5,5),d(4,6),d(3,6),d(1,1),d(1,0),d(0,0),a}
Unknowns: {d(6,6),d(5,5),d(4,6),d(3,6),d(1,1),d(1,0),d(0,0),a}
bonne inconnue W:=d(5,5)$

sa valeur doit etre WW:= - d(6,6)*a - d(4,6)*a - d(3,6)*a + d(1,1)*a + d(1,1) + 
2*d(1,0) + 2*d(0,0)*a + 3*d(0,0)$

on resout l'equation {{0,4},6} qui est  maintenant AA:=d(1,0)*a$

Unknowns: {d(1,0),a}
Unknowns: {d(1,0),a}
pas de selection possible de variable a coefficient numerique dans d(1,0)*a
on resout l'equation {{0,5},4} qui est  maintenant AA:= - d(1,6)*a$

Unknowns: {d(1,6),a}
Unknowns: {d(1,6),a}
pas de selection possible de variable a coefficient numerique dans  - d(1,6)*a
on resout l'equation {{0,5},5} qui est  maintenant AA:= - a*(d(2,6)*a + d(2,6) +
 d(1,0))$

Unknowns: {d(2,6),d(1,0),a}
Unknowns: {d(2,6),d(1,0),a}
pas de selection possible de variable a coefficient numerique dans  - a*(d(2,6)*
a + d(2,6) + d(1,0))
on resout l'equation {{0,5},6} qui est  maintenant AA:= - d(1,6)*a**2$

Unknowns: {d(1,6),a}
Unknowns: {d(1,6),a}
pas de selection possible de variable a coefficient numerique dans  - d(1,6)*a**
2
on resout l'equation {{0,6},2} qui est  maintenant AA:=d(1,6)*(a + 1)$

Unknowns: {d(1,6),a}
Unknowns: {d(1,6),a}
pas de selection possible de variable a coefficient numerique dans d(1,6)*(a + 1
)
on resout l'equation {{0,6},4} qui est  maintenant AA:=d(2,6)*(a + 1)$

Unknowns: {d(2,6),a}
Unknowns: {d(2,6),a}
pas de selection possible de variable a coefficient numerique dans d(2,6)*(a + 1
)
on resout l'equation {{0,6},5} qui est  maintenant AA:=d(6,6)*a + d(6,6) + d(4,6
)*a + d(4,6) + d(3,6)*a + d(3,6) - d(1,1)*a - d(1,1) - 2*d(1,0) - 2*d(0,0)*a - 2
*d(0,0)$

Unknowns: {d(6,6),d(4,6),d(3,6),d(1,1),d(1,0),d(0,0),a}
Unknowns: {d(6,6),d(4,6),d(3,6),d(1,1),d(1,0),d(0,0),a}
bonne inconnue W:=d(1,0)$

sa valeur doit etre WW:=(d(6,6)*a + d(6,6) + d(4,6)*a + d(4,6) + d(3,6)*a + d(3,
6) - d(1,1)*a - d(1,1) - 2*d(0,0)*a - 2*d(0,0))/2$

on resout l'equation {{0,6},6} qui est  maintenant AA:=(a*(d(6,6)*a + d(6,6) + d
(4,6)*a + d(4,6) + d(3,6)*a + d(3,6) + 2*d(2,6)*a + 2*d(2,6) - d(1,1)*a - d(1,1)
 - 2*d(0,0)*a - 2*d(0,0)))/2$

Unknowns: {d(6,6),d(4,6),d(3,6),d(2,6),d(1,1),d(0,0),a}
Unknowns: {d(6,6),d(4,6),d(3,6),d(2,6),d(1,1),d(0,0),a}
pas de selection possible de variable a coefficient numerique dans (a*(d(6,6)*a 
+ d(6,6) + d(4,6)*a + d(4,6) + d(3,6)*a + d(3,6) + 2*d(2,6)*a + 2*d(2,6) - d(1,1
)*a - d(1,1) - 2*d(0,0)*a - 2*d(0,0)))/2
on resout l'equation {{1,2},0} qui est  maintenant AA:= - d(0,3)$

Unknown: d(0,3)
Unknown: d(0,3)
bonne inconnue W:=d(0,3)$

sa valeur doit etre WW:=0$

on resout l'equation {{1,2},1} qui est  maintenant AA:=d(1,6)*a$

Unknowns: {d(1,6),a}
Unknowns: {d(1,6),a}
pas de selection possible de variable a coefficient numerique dans d(1,6)*a
on resout l'equation {{1,2},2} qui est  maintenant AA:=(d(6,6)*a + d(6,6) + d(4,
6)*a + d(4,6) + d(3,6)*a + d(3,6) + 2*d(2,6)*a - d(1,1)*a - d(1,1) - 2*d(0,0)*a 
- 2*d(0,0))/2$

Unknowns: {d(6,6),d(4,6),d(3,6),d(2,6),d(1,1),d(0,0),a}
Unknowns: {d(6,6),d(4,6),d(3,6),d(2,6),d(1,1),d(0,0),a}
pas de selection possible de variable a coefficient numerique dans (d(6,6)*a + d
(6,6) + d(4,6)*a + d(4,6) + d(3,6)*a + d(3,6) + 2*d(2,6)*a - d(1,1)*a - d(1,1) -
 2*d(0,0)*a - 2*d(0,0))/2
on resout l'equation {{1,2},3} qui est  maintenant AA:= - d(3,3) + 2*d(1,1) + d(
0,0)$

Unknowns: {d(3,3),d(1,1),d(0,0)}
Unknowns: {d(3,3),d(1,1),d(0,0)}
bonne inconnue W:=d(3,3)$

sa valeur doit etre WW:=2*d(1,1) + d(0,0)$

on resout l'equation {{1,2},4} qui est  maintenant AA:= - d(4,3) - d(2,0) + d(0,
1)$

Unknowns: {d(4,3),d(2,0),d(0,1)}
Unknowns: {d(4,3),d(2,0),d(0,1)}
bonne inconnue W:=d(4,3)$

sa valeur doit etre WW:= - d(2,0) + d(0,1)$

on resout l'equation {{1,2},5} qui est  maintenant AA:= - d(5,3) - d(3,1) - d(3,
0) + d(2,1)$

Unknowns: {d(5,3),d(3,1),d(3,0),d(2,1)}
Unknowns: {d(5,3),d(3,1),d(3,0),d(2,1)}
bonne inconnue W:=d(5,3)$

sa valeur doit etre WW:= - d(3,1) - d(3,0) + d(2,1)$

on resout l'equation {{1,2},6} qui est  maintenant AA:= - d(6,6) - d(4,6) - d(3,
6) + 2*d(1,1) + d(0,1)*a + d(0,1) + d(0,0)$

Unknowns: {d(6,6),d(4,6),d(3,6),d(1,1),d(0,1),d(0,0),a}
Unknowns: {d(6,6),d(4,6),d(3,6),d(1,1),d(0,1),d(0,0),a}
bonne inconnue W:=d(6,6)$

sa valeur doit etre WW:= - d(4,6) - d(3,6) + 2*d(1,1) + d(0,1)*a + d(0,1) + d(0,
0)$

on resout l'equation {{1,3},0} qui est  maintenant AA:=d(0,6)*a$

Unknowns: {d(0,6),a}
Unknowns: {d(0,6),a}
pas de selection possible de variable a coefficient numerique dans d(0,6)*a
on resout l'equation {{1,3},1} qui est  maintenant AA:=d(1,6)*a$

Unknowns: {d(1,6),a}
Unknowns: {d(1,6),a}
pas de selection possible de variable a coefficient numerique dans d(1,6)*a
on resout l'equation {{1,3},2} qui est  maintenant AA:=d(2,6)*a$

Unknowns: {d(2,6),a}
Unknowns: {d(2,6),a}
pas de selection possible de variable a coefficient numerique dans d(2,6)*a
on resout l'equation {{1,3},3} qui est  maintenant AA:=d(3,6)*a - d(2,6)*a - d(1
,1)*a - d(1,1) - d(0,1)*a**2 - 2*d(0,1)*a - d(0,1) + d(0,0)*a + d(0,0)$

Unknowns: {d(3,6),d(2,6),d(1,1),d(0,1),d(0,0),a}
Unknowns: {d(3,6),d(2,6),d(1,1),d(0,1),d(0,0),a}
pas de selection possible de variable a coefficient numerique dans d(3,6)*a - d(
2,6)*a - d(1,1)*a - d(1,1) - d(0,1)*a**2 - 2*d(0,1)*a - d(0,1) + d(0,0)*a + d(0,
0)
on resout l'equation {{1,3},4} qui est  maintenant AA:=d(4,6)*a + 2*d(1,1) - d(0
,0)$

Unknowns: {d(4,6),d(1,1),d(0,0),a}
Unknowns: {d(4,6),d(1,1),d(0,0),a}
bonne inconnue W:=d(1,1)$

sa valeur doit etre WW:=( - d(4,6)*a + d(0,0))/2$

on resout l'equation {{1,3},5} qui est  maintenant AA:=d(5,6)*a + 2*d(3,0) - d(2
,1)*a + 2*d(0,1)$

Unknowns: {d(5,6),d(3,0),d(2,1),d(0,1),a}
Unknowns: {d(5,6),d(3,0),d(2,1),d(0,1),a}
bonne inconnue W:=d(3,0)$

sa valeur doit etre WW:=( - d(5,6)*a + d(2,1)*a - 2*d(0,1))/2$

on resout l'equation {{1,3},6} qui est  maintenant AA:=(a*( - d(4,6)*a - 2*d(4,6
) - 2*d(3,6) + 2*d(0,1)*a + 2*d(0,1) - d(0,0)))/2$

Unknowns: {d(4,6),d(3,6),d(0,1),d(0,0),a}
Unknowns: {d(4,6),d(3,6),d(0,1),d(0,0),a}
pas de selection possible de variable a coefficient numerique dans (a*( - d(4,6)
*a - 2*d(4,6) - 2*d(3,6) + 2*d(0,1)*a + 2*d(0,1) - d(0,0)))/2
on resout l'equation {{1,4},2} qui est  maintenant AA:=a*(d(1,6) + d(0,6))$

Unknowns: {d(1,6),d(0,6),a}
Unknowns: {d(1,6),d(0,6),a}
pas de selection possible de variable a coefficient numerique dans a*(d(1,6) + d
(0,6))
on resout l'equation {{1,4},3} qui est  maintenant AA:= - d(2,6)*a$

Unknowns: {d(2,6),a}
Unknowns: {d(2,6),a}
pas de selection possible de variable a coefficient numerique dans  - d(2,6)*a
on resout l'equation {{1,4},4} qui est  maintenant AA:=( - d(4,6)*a**2 - d(4,6)*
a - 4*d(3,6)*a + 4*d(2,6)*a + 2*d(0,1)*a**2 + 4*d(0,1)*a + 2*d(0,1) - d(0,0)*a -
 d(0,0))/4$

Unknowns: {d(4,6),d(3,6),d(2,6),d(0,1),d(0,0),a}
Unknowns: {d(4,6),d(3,6),d(2,6),d(0,1),d(0,0),a}
pas de selection possible de variable a coefficient numerique dans ( - d(4,6)*a
**2 - d(4,6)*a - 4*d(3,6)*a + 4*d(2,6)*a + 2*d(0,1)*a**2 + 4*d(0,1)*a + 2*d(0,1)
 - d(0,0)*a - d(0,0))/4
on resout l'equation {{1,4},5} qui est  maintenant AA:= - a*(d(4,6) + d(0,1))$

Unknowns: {d(4,6),d(0,1),a}
Unknowns: {d(4,6),d(0,1),a}
pas de selection possible de variable a coefficient numerique dans  - a*(d(4,6) 
+ d(0,1))
on resout l'equation {{1,4},6} qui est  maintenant AA:=(a*( - d(4,6)*a**2 - d(4,
6)*a + 4*d(2,6)*a + 2*d(0,1)*a**2 + 4*d(0,1)*a + 2*d(0,1) - d(0,0)*a - d(0,0)))/
4$

Unknowns: {d(4,6),d(2,6),d(0,1),d(0,0),a}
Unknowns: {d(4,6),d(2,6),d(0,1),d(0,0),a}
pas de selection possible de variable a coefficient numerique dans (a*( - d(4,6)
*a**2 - d(4,6)*a + 4*d(2,6)*a + 2*d(0,1)*a**2 + 4*d(0,1)*a + 2*d(0,1) - d(0,0)*a
 - d(0,0)))/4
on resout l'equation {{1,5},3} qui est  maintenant AA:= - d(1,6)*a$

Unknowns: {d(1,6),a}
Unknowns: {d(1,6),a}
pas de selection possible de variable a coefficient numerique dans  - d(1,6)*a
on resout l'equation {{1,5},5} qui est  maintenant AA:= - d(2,6)*a$

Unknowns: {d(2,6),a}
Unknowns: {d(2,6),a}
pas de selection possible de variable a coefficient numerique dans  - d(2,6)*a
on resout l'equation {{1,6},2} qui est  maintenant AA:= - d(0,6)$

Unknown: d(0,6)
Unknown: d(0,6)
bonne inconnue W:=d(0,6)$

sa valeur doit etre WW:=0$

on resout l'equation {{1,6},3} qui est  maintenant AA:=d(2,6)$

Unknown: d(2,6)
Unknown: d(2,6)
bonne inconnue W:=d(2,6)$

sa valeur doit etre WW:=0$

on resout l'equation {{1,6},4} qui est  maintenant AA:=d(3,6)$

Unknown: d(3,6)
Unknown: d(3,6)
bonne inconnue W:=d(3,6)$

sa valeur doit etre WW:=0$

on resout l'equation {{1,6},5} qui est  maintenant AA:=d(4,6) + d(0,1)$

Unknowns: {d(4,6),d(0,1)}
Unknowns: {d(4,6),d(0,1)}
bonne inconnue W:=d(4,6)$

sa valeur doit etre WW:= - d(0,1)$

on resout l'equation {{2,3},2} qui est  maintenant AA:=d(1,6)*a$

Unknowns: {d(1,6),a}
Unknowns: {d(1,6),a}
pas de selection possible de variable a coefficient numerique dans d(1,6)*a
on resout l'equation {{2,3},3} qui est  maintenant AA:=d(1,6)*a$

Unknowns: {d(1,6),a}
Unknowns: {d(1,6),a}
pas de selection possible de variable a coefficient numerique dans d(1,6)*a
on resout l'equation {{2,3},5} qui est  maintenant AA:=( - d(0,1)*a - 2*d(0,1) +
 d(0,0))/2$

Unknowns: {d(0,1),d(0,0),a}
Unknowns: {d(0,1),d(0,0),a}
bonne inconnue W:=d(0,0)$

sa valeur doit etre WW:=d(0,1)*(a + 2)$

on resout l'equation {{2,3},6} qui est  maintenant AA:=(d(0,1)*a**2*(a + 1))/2$

Unknowns: {d(0,1),a}
Unknowns: {d(0,1),a}
pas de selection possible de variable a coefficient numerique dans (d(0,1)*a**2*
(a + 1))/2
on resout l'equation {{2,4},3} qui est  maintenant AA:=d(1,6)*a$

Unknowns: {d(1,6),a}
Unknowns: {d(1,6),a}
pas de selection possible de variable a coefficient numerique dans d(1,6)*a
on resout l'equation {{2,4},5} qui est  maintenant AA:=(d(0,1)*a*(a + 1))/2$

Unknowns: {d(0,1),a}
Unknowns: {d(0,1),a}
pas de selection possible de variable a coefficient numerique dans (d(0,1)*a*(a 
+ 1))/2
on resout l'equation {{2,6},3} qui est  maintenant AA:= - d(1,6)$

Unknown: d(1,6)
Unknown: d(1,6)
bonne inconnue W:=d(1,6)$

sa valeur doit etre WW:=0$

Derivation equations to cancel (Reduce output) : \\{{{{0,1},0},0},
{{{0,1},1},0},
{{{0,1},2},0},
{{{0,1},3},0},
{{{0,1},4},0},
{{{0,1},5},0},
{{{0,1},6},0},
{{{0,2},0},0},
{{{0,2},1},0},
{{{0,2},2},0},
{{{0,2},3},0},
{{{0,2},4},0},
{{{0,2},5},0},
{{{0,2},6},0},
{{{0,3},0},0},
{{{0,3},1},0},
{{{0,3},2},0},
{{{0,3},3},0},
{{{0,3},4},0},
{{{0,3},5},0},
{{{0,3},6},0},
{{{0,4},0},0},
{{{0,4},1},0},
{{{0,4},2},0},
{{{0,4},3},0},
{{{0,4},4},0},
{{{0,4},5},0},
{{{0,4},6},(d(0,1)*a**2*(a + 1))/2},
{{{0,5},2},0},
{{{0,5},4},0},
{{{0,5},5},( - d(0,1)*a**2*(a + 1))/2},
{{{0,5},6},0},
{{{0,6},0},0},
{{{0,6},1},0},
{{{0,6},2},0},
{{{0,6},3},0},
{{{0,6},4},0},
{{{0,6},5},0},
{{{0,6},6},(d(0,1)*a**2*(a + 1))/2},
{{{1,2},0},0},
{{{1,2},1},0},
{{{1,2},2},(d(0,1)*a*(a + 1))/2},
{{{1,2},3},0},
{{{1,2},4},0},
{{{1,2},5},0},
{{{1,2},6},0},
{{{1,3},0},0},
{{{1,3},1},0},
{{{1,3},2},0},
{{{1,3},3}, - d(0,1)*a*(a + 1)},
{{{1,3},4},0},
{{{1,3},5},0},
{{{1,3},6},d(0,1)*a*(a + 1)},
{{{1,4},0},0},
{{{1,4},1},0},
{{{1,4},2},0},
{{{1,4},3},0},
{{{1,4},4},(d(0,1)*a*(a + 1))/2},
{{{1,4},5},0},
{{{1,4},6},(d(0,1)*a**2*(a + 1))/2},
{{{1,5},2},0},
{{{1,5},3},0},
{{{1,5},4},0},
{{{1,5},5},0},
{{{1,6},2},0},
{{{1,6},3},0},
{{{1,6},4},0},
{{{1,6},5},0},
{{{2,3},0},0},
{{{2,3},1},0},
{{{2,3},2},0},
{{{2,3},3},0},
{{{2,3},4},0},
{{{2,3},5},0},
{{{2,3},6},(d(0,1)*a**2*(a + 1))/2},
{{{2,4},3},0},
{{{2,4},4},0},
{{{2,4},5},(d(0,1)*a*(a + 1))/2},
{{{2,4},6},0},
{{{2,5},3},0},
{{{2,5},4},0},
{{{2,5},5},0},
{{{2,5},6},0},
{{{2,6},3},0},
{{{2,6},4},0},
{{{2,6},5},0},
{{{2,6},6},0},
{{{3,4},4},0},
{{{3,4},5},0},
{{{3,5},4},0},
{{{3,5},5},0},
{{{3,6},4},0},
{{{3,6},5},0},
{{{4,5},5},0},
{{{4,6},5},0},
{{{5,6},5},0}}$

Il y a une phase 2$

collect_eq:={{{{0,1},0},0},
{{{0,1},1},0},
{{{0,1},2},0},
{{{0,1},3},0},
{{{0,1},4},0},
{{{0,1},5},0},
{{{0,1},6},0},
{{{0,2},0},0},
{{{0,2},1},0},
{{{0,2},2},0},
{{{0,2},3},0},
{{{0,2},4},0},
{{{0,2},5},0},
{{{0,2},6},0},
{{{0,3},0},0},
{{{0,3},1},0},
{{{0,3},2},0},
{{{0,3},3},0},
{{{0,3},4},0},
{{{0,3},5},0},
{{{0,3},6},0},
{{{0,4},0},0},
{{{0,4},1},0},
{{{0,4},2},0},
{{{0,4},3},0},
{{{0,4},4},0},
{{{0,4},5},0},
{{{0,4},6},0},
{{{0,5},2},0},
{{{0,5},4},0},
{{{0,5},5},0},
{{{0,5},6},0},
{{{0,6},0},0},
{{{0,6},1},0},
{{{0,6},2},0},
{{{0,6},3},0},
{{{0,6},4},0},
{{{0,6},5},0},
{{{0,6},6},0},
{{{1,2},0},0},
{{{1,2},1},0},
{{{1,2},2},0},
{{{1,2},3},0},
{{{1,2},4},0},
{{{1,2},5},0},
{{{1,2},6},0},
{{{1,3},0},0},
{{{1,3},1},0},
{{{1,3},2},0},
{{{1,3},3},0},
{{{1,3},4},0},
{{{1,3},5},0},
{{{1,3},6},0},
{{{1,4},0},0},
{{{1,4},1},0},
{{{1,4},2},0},
{{{1,4},3},0},
{{{1,4},4},0},
{{{1,4},5},0},
{{{1,4},6},0},
{{{1,5},2},0},
{{{1,5},3},0},
{{{1,5},4},0},
{{{1,5},5},0},
{{{1,6},2},0},
{{{1,6},3},0},
{{{1,6},4},0},
{{{1,6},5},0},
{{{2,3},0},0},
{{{2,3},1},0},
{{{2,3},2},0},
{{{2,3},3},0},
{{{2,3},4},0},
{{{2,3},5},0},
{{{2,3},6},0},
{{{2,4},3},0},
{{{2,4},4},0},
{{{2,4},5},0},
{{{2,4},6},0},
{{{2,5},3},0},
{{{2,5},4},0},
{{{2,5},5},0},
{{{2,5},6},0},
{{{2,6},3},0},
{{{2,6},4},0},
{{{2,6},5},0},
{{{2,6},6},0},
{{{3,4},4},0},
{{{3,4},5},0},
{{{3,5},4},0},
{{{3,5},5},0},
{{{3,6},4},0},
{{{3,6},5},0},
{{{4,5},5},0},
{{{4,6},5},0},
{{{5,6},5},0}}$

a neq {0,-1}$

derivation generique de gtildedelta:$

MATD:=
mat((0,0,0,0,0,0,0),(0,0,0,0,0,0,0),(d(2,0),d(2,1),0,0,0,0,0),(( - (d(5,6) - d(2
,1))*a)/2,d(3,1), - d(2,0),0,0,0,0),(d(4,0),d(4,1),( - ((a - 2)*d(2,1) - d(5,6)*
a))/2, - d(2,0),0,0,0),(d(5,0),d(5,1),d(5,2),( - ((a - 2)*d(2,1) + 2*d(3,1) - d(
5,6)*a))/2,d(2,1) - d(2,0),0,d(5,6)),(d(6,0),d(4,0) - d(3,1) - d(4,1) + d(5,2),d
(2,1)*a,0,0,0,0))$
$

pour delta:=

[0  0  0  0  0  0]
[                ]
[1  0  0  0  0  0]
[                ]
[0  0  0  0  0  0]
[                ]
[0  1  0  0  0  0]
[                ]
[0  0  1  1  0  1]
[                ]
[0  a  0  0  0  0]


pour shortformdelta:={1,ss,1,ss,0,1,ss,0,a}

Unknowns: {d(6,0),
d(5,6),
d(5,2),
d(5,1),
d(5,0),
d(4,1),
d(4,0),
d(3,1),
d(2,1),
d(2,0),
a}
Unknowns: {d(6,0),
d(5,6),
d(5,2),
d(5,1),
d(5,0),
d(4,1),
d(4,0),
d(3,1),
d(2,1),
d(2,0),
a}
listeparametresMATD{d(6,0),
d(5,6),
d(5,2),
d(5,1),
d(5,0),
d(4,1),
d(4,0),
d(3,1),
d(2,1),
d(2,0)}$

dim Der(gtildedelta):=10$

MATD**1:=
mat((0,0,0,0,0,0,0),(0,0,0,0,0,0,0),(d(2,0),d(2,1),0,0,0,0,0),(( - (d(5,6) - d(2
,1))*a)/2,d(3,1), - d(2,0),0,0,0,0),(d(4,0),d(4,1),( - ((a - 2)*d(2,1) - d(5,6)*
a))/2, - d(2,0),0,0,0),(d(5,0),d(5,1),d(5,2),( - ((a - 2)*d(2,1) + 2*d(3,1) - d(
5,6)*a))/2,d(2,1) - d(2,0),0,d(5,6)),(d(6,0),d(4,0) - d(3,1) - d(4,1) + d(5,2),d
(2,1)*a,0,0,0,0))$
$

MATD**2:=
mat((0,0,0,0,0,0,0),(0,0,0,0,0,0,0),(0,0,0,0,0,0,0),( - d(2,0)**2, - d(2,1)*d(2,
0),0,0,0,0,0),((d(5,6)*a - d(2,1)*a + d(2,1))*d(2,0),( - (((a - 2)*d(2,1) - d(5,
6)*a)*d(2,1) + 2*d(3,1)*d(2,0)))/2,d(2,0)**2,0,0,0,0),((((a - 2)*d(2,1) + 2*d(3,
1) - d(5,6)*a)*(d(5,6) - d(2,1))*a + 4*(d(6,0)*d(5,6) + d(5,2)*d(2,0) + (d(2,1) 
- d(2,0))*d(4,0)))/4,( - (((a - 2)*d(2,1) + 2*d(3,1) - d(5,6)*a)*d(3,1) - 2*((d(
2,1) - d(2,0))*d(4,1) + d(5,2)*d(2,1)) - 2*(d(4,0) - d(3,1) - d(4,1) + d(5,2))*d
(5,6)))/2,( - (((a - 2)*d(2,1) - d(5,6)*a)*(d(2,1) - d(2,0)) - 2*d(5,6)*d(2,1)*a
 - ((a - 2)*d(2,1) + 2*d(3,1) - d(5,6)*a)*d(2,0)))/2, - (d(2,1) - d(2,0))*d(2,0)
,0,0,0),(d(2,1)*d(2,0)*a,d(2,1)**2*a,0,0,0,0,0))$
$

MATD**3:=
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),(d(2,0)**3,d
(2,1)*d(2,0)**2,0,0,0,0,0),(((4*d(5,6)*d(2,1)*a - 3*d(5,6)*d(2,0)*a + 2*d(3,1)*d
(2,0) - 2*d(2,1)**2*a + 2*d(2,1)**2 + 3*d(2,1)*d(2,0)*a - 4*d(2,1)*d(2,0))*d(2,0
))/2,(3*d(5,6)*d(2,1)**2*a - 2*d(5,6)*d(2,1)*d(2,0)*a + 2*d(3,1)*d(2,0)**2 - d(2
,1)**3*a + 2*d(2,1)**3 + 2*d(2,1)**2*d(2,0)*a - 4*d(2,1)**2*d(2,0))/2,(d(2,1) - 
d(2,0))*d(2,0)**2,0,0,0,0),(0,0,0,0,0,0,0))$
$

MATD**4:=
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),(0,0,0,0,0,0
,0),((d(2,1) - d(2,0))*d(2,0)**3,(d(2,1) - d(2,0))*d(2,1)*d(2,0)**2,0,0,0,0,0),(
0,0,0,0,0,0,0))$
$

MATD**5:=
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),(0,0,0,0,0,0
,0),(0,0,0,0,0,0,0),(0,0,0,0,0,0,0))$
$

MATD**6:=
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),(0,0,0,0,0,0
,0),(0,0,0,0,0,0,0),(0,0,0,0,0,0,0))$
$

MATD**7:=
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),(0,0,0,0,0,0
,0),(0,0,0,0,0,0,0),(0,0,0,0,0,0,0))$
$

MATD**2:=
mat((0,0,0,0,0,0,0),(0,0,0,0,0,0,0),(0,0,0,0,0,0,0),( - d(2,0)**2, - d(2,1)*d(2,
0),0,0,0,0,0),((d(5,6)*a - d(2,1)*a + d(2,1))*d(2,0),( - (((a - 2)*d(2,1) - d(5,
6)*a)*d(2,1) + 2*d(3,1)*d(2,0)))/2,d(2,0)**2,0,0,0,0),((((a - 2)*d(2,1) + 2*d(3,
1) - d(5,6)*a)*(d(5,6) - d(2,1))*a + 4*(d(6,0)*d(5,6) + d(5,2)*d(2,0) + (d(2,1) 
- d(2,0))*d(4,0)))/4,( - (((a - 2)*d(2,1) + 2*d(3,1) - d(5,6)*a)*d(3,1) - 2*((d(
2,1) - d(2,0))*d(4,1) + d(5,2)*d(2,1)) - 2*(d(4,0) - d(3,1) - d(4,1) + d(5,2))*d
(5,6)))/2,( - (((a - 2)*d(2,1) - d(5,6)*a)*(d(2,1) - d(2,0)) - 2*d(5,6)*d(2,1)*a
 - ((a - 2)*d(2,1) + 2*d(3,1) - d(5,6)*a)*d(2,0)))/2, - (d(2,1) - d(2,0))*d(2,0)
,0,0,0),(d(2,1)*d(2,0)*a,d(2,1)**2*a,0,0,0,0,0))$
$

MATD**3:=
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),(d(2,0)**3,d
(2,1)*d(2,0)**2,0,0,0,0,0),(((4*d(5,6)*d(2,1)*a - 3*d(5,6)*d(2,0)*a + 2*d(3,1)*d
(2,0) - 2*d(2,1)**2*a + 2*d(2,1)**2 + 3*d(2,1)*d(2,0)*a - 4*d(2,1)*d(2,0))*d(2,0
))/2,(3*d(5,6)*d(2,1)**2*a - 2*d(5,6)*d(2,1)*d(2,0)*a + 2*d(3,1)*d(2,0)**2 - d(2
,1)**3*a + 2*d(2,1)**3 + 2*d(2,1)**2*d(2,0)*a - 4*d(2,1)**2*d(2,0))/2,(d(2,1) - 
d(2,0))*d(2,0)**2,0,0,0,0),(0,0,0,0,0,0,0))$
$

MATD**4:=
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),(0,0,0,0,0,0
,0),((d(2,1) - d(2,0))*d(2,0)**3,(d(2,1) - d(2,0))*d(2,1)*d(2,0)**2,0,0,0,0,0),(
0,0,0,0,0,0,0))$
$

MATD**5:=
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),(0,0,0,0,0,0
,0),(0,0,0,0,0,0,0),(0,0,0,0,0,0,0))$
$

***********   gtildedelta est caracteristiquement nilpotente d'ordre5$

rank 0 :gtildedelta is characteristically nilpotent

rkgtildedelta


matrice de passage de la base X(0)=delta, X(1),..., X(6) a une base  diagonali\
sant le tore maximal: on peut prendre

P:=

[1  0  0  0  0  0  0]
[                   ]
[0  1  0  0  0  0  0]
[                   ]
[0  0  1  0  0  0  0]
[                   ]
[0  0  0  1  0  0  0]
[                   ]
[0  0  0  0  1  0  0]
[                   ]
[0  0  0  0  0  1  0]
[                   ]
[0  0  0  0  0  0  1]


matrice des derivations dans cette base diagonalisante Y(1),...,Y(7):

P**(-1)*MATD*P:=
mat((0,0,0,0,0,0,0),(0,0,0,0,0,0,0),(d(2,0),d(2,1),0,0,0,0,0),(( - (d(5,6) - d(2
,1))*a)/2,d(3,1), - d(2,0),0,0,0,0),(d(4,0),d(4,1),( - ((a - 2)*d(2,1) - d(5,6)*
a))/2, - d(2,0),0,0,0),(d(5,0),d(5,1),d(5,2),( - ((a - 2)*d(2,1) + 2*d(3,1) - d(
5,6)*a))/2,d(2,1) - d(2,0),0,d(5,6)),(d(6,0),d(4,0) - d(3,1) - d(4,1) + d(5,2),d
(2,1)*a,0,0,0,0))$
$

PP:=

[1  0  0  0  0  0  0]
[                   ]
[0  1  0  0  0  0  0]
[                   ]
[0  0  1  0  0  0  0]
[                   ]
[0  0  0  1  0  0  0]
[                   ]
[0  0  0  0  1  0  0]
[                   ]
[0  0  0  0  0  1  0]
[                   ]
[0  0  0  0  0  0  1]


avec PP:=P*Q:=

[1  0  0  0  0  0  0]
[                   ]
[0  1  0  0  0  0  0]
[                   ]
[0  0  1  0  0  0  0]
[                   ]
[0  0  0  1  0  0  0]
[                   ]
[0  0  0  0  1  0  0]
[                   ]
[0  0  0  0  0  1  0]
[                   ]
[0  0  0  0  0  0  1]


MATDDIAGONALISE:=

mat((0,0,0,0,0,0,0),

    (0,0,0,0,0,0,0),

    (d(2,0),d(2,1),0,0,0,0,0),

       - (d(5,6) - d(2,1))*a
    (------------------------,d(3,1), - d(2,0),0,0,0,0),
                2

                     - ((a - 2)*d(2,1) - d(5,6)*a)
    (d(4,0),d(4,1),--------------------------------, - d(2,0),0,0,0),
                                  2

                            - ((a - 2)*d(2,1) + 2*d(3,1) - d(5,6)*a)
    (d(5,0),d(5,1),d(5,2),-------------------------------------------,
                                               2

     d(2,1) - d(2,0),0,d(5,6)),

    (d(6,0),d(4,0) - d(3,1) - d(4,1) + d(5,2),d(2,1)*a,0,0,0,0))


on voit apparaitre les poids sur la diagonale

*** r declared operator 

r(1) := 0

r(2) := 0

r(3) := 0

r(4) := 0

r(5) := 0

r(6) := 0

r(7) := 0

r(1) := 0

r(2) := 0

r(3) := 0

r(4) := 0

r(5) := 0

r(6) := 0

r(7) := 0

Le systeme de poids est le systeme 0.7

calcul de relations de commutation de la base diaY(j) diagonalisant le tore

listcommutateursdesx := {{{0,1},x(2)},

   {{0,2},x(6)*a + x(4)},

   {{0,3},x(5)},

   {{0,4},x(5)},

   {{0,5},0},

   {{0,6},x(5)},

   {{1,2},x(3)},

   {{1,3},x(4)},

   {{1,4},x(5)},

   {{1,5},0},

   {{1,6},0},

   {{2,3},x(5)},

   {{2,4},0},

   {{2,5},0},

   {{2,6},0},

   {{3,4},0},

   {{3,5},0},

   {{3,6},0},

   {{4,5},0},

   {{4,6},0},

   {{5,6},0}}

diaY(1):=x(0)

diaY(2):=x(1)

diaY(3):=x(2)

diaY(4):=x(3)

diaY(5):=x(4)

diaY(6):=x(5)

diaY(7):=x(6)

liste des commutateurs des diaY(i) :$

listcommutateurdesdiaY:={{{1,2},diay(3)},
{{1,3},diay(7)*a + diay(5)},
{{1,4},diay(6)},
{{1,5},diay(6)},
{{1,6},0},
{{1,7},diay(6)},
{{2,3},diay(4)},
{{2,4},diay(5)},
{{2,5},diay(6)},
{{2,6},0},
{{2,7},0},
{{3,4},diay(6)},
{{3,5},0},
{{3,6},0},
{{3,7},0},
{{4,5},0},
{{4,6},0},
{{4,7},0},
{{5,6},0},
{{5,7},0},
{{6,7},0}}$

Now we make explicit the isomorphism with an algebra of the book:$

Namely g_{7,0.7}$

i.e. we go from the basis diaY(i) to the new basis ZZ(i) defined by the matrix:$

on pose :$

avec comme matrice de changement de base :$


mat((a**2/(a + 1),a,0,0,0,0,0),(0, - a,0,0,0,0,0),(0,0,( - a**3)/(a + 1),0,0,0,0
),(0,0,0,0,a**4/(a + 1),0,0),(0,0,0,( - a**5)/(a**2 + 2*a + 1),( - a**4)/(a + 1)
,( - a**5)/(a + 1),0),(0,0,0,0,0,(a**5*( - a + 1))/(a + 1),( - a**7)/(a**2 + 2*a
 + 1)),(0,0,0,( - a**6)/(a**2 + 2*a + 1),( - a**5)/(a + 1),0,0))$
$

det(isom):= a**28/(a + 1)**8$

ZZ(1):=(diay(1)*a**2)/(a + 1)$

ZZ(2):= - (diay(2) - diay(1))*a$

ZZ(3):=( - diay(3)*a**3)/(a + 1)$

ZZ(4):=( - (diay(7)*a + diay(5))*a**5)/(a + 1)**2$

ZZ(5):=( - (diay(5) - diay(4) + diay(7)*a)*a**4)/(a + 1)$

ZZ(6):=( - ((a - 1)*diay(6) + diay(5))*a**5)/(a + 1)$

ZZ(7):=( - diay(6)*a**7)/(a + 1)**2$

listcommutateursdesZZ:=$

{{1,2},zz(3)}$

{{1,3},zz(4)}$

{{1,4},zz(7)}$

{{1,5},zz(7)}$

{{1,6},zz(7)}$

{{1,7},0}$

{{2,3},zz(5)}$

{{2,4},zz(7)}$

{{2,5},zz(6)}$

{{2,6},0}$

{{2,7},0}$

{{3,4},0}$

{{3,5},zz(7)}$

{{3,6},0}$

{{3,7},0}$

{{4,5},0}$

{{4,6},0}$

{{4,7},0}$

{{5,6},0}$

{{5,7},0}$

{{6,7},0}$

We get the commutation relations of$

g_{7,0.7}$

Et cela pour a:=a$

and that for a neq {0,-1}$

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

delta:=
mat((0,0,0,0,0,0),(1,0,0,0,0,0),(0,0,0,0,0,0),(0,1,0,0,0,0),(0,0,1,1,0,1),(0,a,0
,0,0,0))$
$

The isomorphism from g_{7,0.7} to gtildedelta$

was constructed in 2 steps and is given by$

the product matrix P*isom:=
mat((a**2/(a + 1),a,0,0,0,0,0),(0, - a,0,0,0,0,0),(0,0,( - a**3)/(a + 1),0,0,0,0
),(0,0,0,0,a**4/(a + 1),0,0),(0,0,0,( - a**5)/(a + 1)**2,( - a**4)/(a + 1),( - a
**5)/(a + 1),0),(0,0,0,0,0,( - (a - 1)*a**5)/(a + 1),( - a**7)/(a + 1)**2),(0,0,
0,( - a**6)/(a + 1)**2,( - a**5)/(a + 1),0,0))$
$

which we record here under the name PSI$