delta:=
mat((0,1,0,0,0,0),(0,0,0,0,0,0),(1,0,0,0,0,0),(0,0,0,0,0,0),(0,0,0,-1,0,1),(b,0,
1,0,0,0))$

phase 1 de la resolution des equations$

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

sa valeur doit etre WW:=d(5,6)*b + d(5,3) + d(4,1) + d(4,0)$

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

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

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

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

Unknown: d(0,1)
Unknown: d(0,1)
bonne inconnue W:=d(0,1)$

sa valeur doit etre WW:=0$

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

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

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

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

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

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

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

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

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

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

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

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

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

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

sa valeur doit etre WW:= - d(5,6)*b - 2*d(4,0) + d(3,2) + d(1,2)*b - d(1,0)$

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

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

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

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

Unknown: d(4,6)
Unknown: d(4,6)
bonne inconnue W:=d(4,6)$

sa valeur doit etre WW:=0$

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

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

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

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

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

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

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

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

sa valeur doit etre WW:= - d(1,5)$

on resoud l'equation {{0,4},2} qui est  maintenant AA:=d(2,5)$

Unknown: d(2,5)
Unknown: d(2,5)
bonne inconnue W:=d(2,5)$

sa valeur doit etre WW:=0$

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

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

sa valeur doit etre WW:= - d(1,4)$

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

Unknown: d(4,5)
Unknown: d(4,5)
bonne inconnue W:=d(4,5)$

sa valeur doit etre WW:=0$

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

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

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

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

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

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

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

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

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

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

Unknown: d(1,4)
Unknown: d(1,4)
bonne inconnue W:=d(1,4)$

sa valeur doit etre WW:=0$

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

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

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

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

Unknown: d(0,4)
Unknown: d(0,4)
bonne inconnue W:=d(0,4)$

sa valeur doit etre WW:=0$

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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},0},
{{{0,5},1},0},
{{{0,5},3},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},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},3},0},
{{{1,5},4},0},
{{{1,5},5},0},
{{{1,5},6},0},
{{{1,6},3},0},
{{{1,6},4},0},
{{{1,6},5},0},
{{{1,6},6},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},0},0},
{{{2,4},1},0},
{{{2,4},2},0},
{{{2,4},3},0},
{{{2,4},4},0},
{{{2,4},5},0},
{{{2,4},6},0},
{{{2,5},1},0},
{{{2,5},4},0},
{{{2,5},5},0},
{{{2,5},6},0},
{{{2,6},1},0},
{{{2,6},4},0},
{{{2,6},5},0},
{{{2,6},6},0},
{{{3,4},5},0},
{{{3,4},6},0},
{{{3,5},5},0},
{{{3,5},6},0},
{{{3,6},5},0},
{{{3,6},6},0},
{{{4,5},5},0},
{{{4,5},6},0},
{{{4,6},5},0},
{{{4,6},6},0},
{{{5,6},5},0}}$

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},1},0},
{{{0,5},3},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},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},3},0},
{{{1,5},4},0},
{{{1,5},5},0},
{{{1,5},6},0},
{{{1,6},3},0},
{{{1,6},4},0},
{{{1,6},5},0},
{{{1,6},6},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},0},0},
{{{2,4},1},0},
{{{2,4},2},0},
{{{2,4},3},0},
{{{2,4},4},0},
{{{2,4},5},0},
{{{2,4},6},0},
{{{2,5},1},0},
{{{2,5},4},0},
{{{2,5},5},0},
{{{2,5},6},0},
{{{2,6},1},0},
{{{2,6},4},0},
{{{2,6},5},0},
{{{2,6},6},0},
{{{3,4},5},0},
{{{3,4},6},0},
{{{3,5},5},0},
{{{3,5},6},0},
{{{3,6},5},0},
{{{3,6},6},0},
{{{4,5},5},0},
{{{4,5},6},0},
{{{4,6},5},0},
{{{4,6},6},0},
{{{5,6},5},0}}$

derivation generique de gtildedelta:$

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

pour delta:=
mat((0,1,0,0,0,0),(0,0,0,0,0,0),(1,0,0,0,0,0),(0,0,0,0,0,0),(0,0,0,-1,0,1),(b,0,
1,0,0,0))$

Unknowns: {d(6,0),
d(5,2),
d(5,1),
d(5,0),
d(4,2),
d(4,0),
d(3,2),
d(3,0),
d(1,2),
d(1,0),
b}
Unknowns: {d(6,0),
d(5,2),
d(5,1),
d(5,0),
d(4,2),
d(4,0),
d(3,2),
d(3,0),
d(1,2),
d(1,0),
b}
dim Der(gtildedelta):=10$

seul candidat a etre un element t1 d'un tore $

t1:=D(0,0)$

t1:=

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


    7
 - x

{{x,

  7,


  [arbcomplex(193)]
  [               ]
  [       0       ]
  [               ]
  [       0       ]
  [               ]
  [       0       ]
  [               ]
  [arbcomplex(195)]
  [               ]
  [arbcomplex(194)]
  [               ]
  [arbcomplex(195)]

  }}

Mais  t1 n'est pas seminsimple 

gtildedelta est caracteristiquement nilpotente

MATD**1:=

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

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

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

    (d(3,0),d(1,2),d(3,2),0,0,0,0),

    (d(4,0),d(1,0),d(4,2),0,0,0,0),

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

     ),

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

      - d(1,0),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),

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

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

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

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

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

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

                            2
      + d(3,0)*d(1,2),d(1,2) , - d(1,2)*d(1,0),0,0),

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

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

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

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

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

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

                   2         2
     d(1,2)*(d(1,2)  - d(1,0) ),

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

                   2         2                  2         2
    (d(1,0)*(d(1,2)  - d(1,0) ),0,d(1,2)*(d(1,2)  - d(1,0) ),0,0,0,0))


MATD**4:=

[                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]
[                                                                             ]
[                     2         2            2        2         2             ]
[d(1,2)*d(1,0)*(d(1,2)  - d(1,0) )  0  d(1,2) *(d(1,2)  - d(1,0) )  0  0  0  0]
[                                                                             ]
[                0                  0               0               0  0  0  0]


MATD**5:=

[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:=

[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:=

[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]



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]


P**(-1)*t1*P:=

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


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

P**(-1)*MATD*P:=

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

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

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

    (d(3,0),d(1,2),d(3,2),0,0,0,0),

    (d(4,0),d(1,0),d(4,2),0,0,0,0),

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

     ),

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

      - d(1,0),0,0))


PP**(-1)*MATD*PP:=

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

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

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

    (d(3,0),d(1,2),d(3,2),0,0,0,0),

    (d(4,0),d(1,0),d(4,2),0,0,0,0),

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

     ),

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

      - d(1,0),0,0))


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),

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

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

    (d(3,0),d(1,2),d(3,2),0,0,0,0),

    (d(4,0),d(1,0),d(4,2),0,0,0,0),

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

     ),

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

      - d(1,0),0,0))


on voit apparaitre les poids sur la diagonale

ladiag := {{1,0},{2,0},{3,0},{4,0},{5,0},{6,0},{7,0}}

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

listcommutateursdesx := {{{0,1},x(6)*b + x(3)},

   {{0,2},x(1)},

   {{0,3},x(6)},

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

   {{0,5},0},

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

   {{1,2},x(4)},

   {{1,3},0},

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

   {{1,5},0},

   {{1,6},0},

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

   {{2,4},x(6)},

   {{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 declared operator 

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)

listcommutateursdesdiay := {{{1,2},x(6)*b + x(3)},

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

   {{1,4},x(6)},

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

   {{1,6},0},

   {{1,7},x(5)},

   {{2,3},x(4)},

   {{2,4},0},

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

   {{2,6},0},

   {{2,7},0},

   {{3,4},x(5)},

   {{3,5},x(6)},

   {{3,6},0},

   {{3,7},0},

   {{4,5},0},

   {{4,6},0},

   {{4,7},0},

   {{5,6},0},

   {{5,7},0},

   {{6,7},0}}

*** yy declared operator 

*** diadiay declared operator 

liste des commutateurs des diaY(i) := (diadiaY=diaY

{{{1,2},diadiay(7)*b + diadiay(4)},

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

 {{1,4},diadiay(7)},

 {{1,5}, - diadiay(6)},

 {{1,6},0},

 {{1,7},diadiay(6)},

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

 {{2,4},0},

 {{2,5},diadiay(6)},

 {{2,6},0},

 {{2,7},0},

 {{3,4},diadiay(6)},

 {{3,5},diadiay(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}}

on pose :

*** zz declared operator 

ZZ(1):=i*diay(1)

ZZ(2):= - diay(3)

ZZ(3):= - i*diay(2)

ZZ(4):=diay(7)*b + diay(4)

ZZ(5):= - i*diay(5)

ZZ(6):=i*diay(7)

ZZ(7):= - diay(6)

*** zzz declared operator 

liste des commutateurs des ZZ(i) (ZZZ=ZZ:=

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

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

 {{1,4}, - i*zzz(7)*b + zzz(6)},

 {{1,5},zzz(7)},

 {{1,6},zzz(7)},

 {{1,7},0},

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

 {{2,4},zzz(7)},

 {{2,5},zzz(6)},

 {{2,6},0},

 {{2,7},0},

 {{3,4},0},

 {{3,5},zzz(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}}

dimension des Z^k:= (1,10,48,114,147,110,44,7).

C'est les relations de commutations de g_{7,0.4(i_(-ib))} page 152.