In the present case 2 we suppose A=((0,0),(0,0)).$

a neq {-1}$

a:=a$

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

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

phase 1 de la resolution des equations$

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

Unknown: d(1,3)
Unknown: d(1,3)
bonne inconnue W:=d(1,3)$

sa valeur doit etre WW:=0$

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

Unknown: d(2,3)
Unknown: d(2,3)
bonne inconnue W:=d(2,3)$

sa valeur doit etre WW:=0$

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

sa valeur doit etre WW:=d(3,4)*a$

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

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

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

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

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

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

sa valeur doit etre WW:= - d(6,4)*a + d(5,2)*a - d(5,2)$

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)$

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

sa valeur doit etre WW:=0$

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)$

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

sa valeur doit etre WW:=0$

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

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

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

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

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

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

Unknown: d(3,4)
Unknown: d(3,4)
bonne inconnue W:=d(3,4)$

sa valeur doit etre WW:=0$

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

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

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

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

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

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

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

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

Unknowns: {d(6,6),d(1,1),d(0,0),a}
Unknowns: {d(6,6),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(1,1)*a - d(1,1) + 3*d(0,0)*a - 3*d(0,0)
on resout l'equation {{0,6},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$

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Unknown: d(2,4)
Unknown: d(2,4)
bonne inconnue W:=d(2,4)$

sa valeur doit etre WW:=0$

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

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

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

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},3},0},
{{{0,4},4},0},
{{{0,4},5},0},
{{{0,4},6},0},
{{{0,5},0},0},
{{{0,5},1},0},
{{{0,5},2},0},
{{{0,5},3},0},
{{{0,5},4},0},
{{{0,5},5},0},
{{{0,5},6},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},5},0},
{{{1,3},6},(a + 1)*d(2,1)},
{{{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},5},0},
{{{1,5},6},0},
{{{1,6},3},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},4},0},
{{{2,4},5},0},
{{{2,4},6},0},
{{{2,5},4},0},
{{{2,5},5},0},
{{{2,5},6},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},6},0},
{{{4,6},6},0},
{{{5,6},6},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},3},0},
{{{0,4},4},0},
{{{0,4},5},0},
{{{0,4},6},0},
{{{0,5},0},0},
{{{0,5},1},0},
{{{0,5},2},0},
{{{0,5},3},0},
{{{0,5},4},0},
{{{0,5},5},0},
{{{0,5},6},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},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},5},0},
{{{1,5},6},0},
{{{1,6},3},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},4},0},
{{{2,4},5},0},
{{{2,4},6},0},
{{{2,5},4},0},
{{{2,5},5},0},
{{{2,5},6},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},6},0},
{{{4,6},6},0},
{{{5,6},6},0}}$

derivation generique de gtildedelta:$

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

pour delta:=

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


pour shortformdelta:={1,

   0,

   ss,

   0,

   a,

   ss,

   1,

   0,

   ss,

   0,

   0}

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

dim Der(gtildedelta):=14$

un element t1 d'un tore $

t1:=D(0,0):=

[1  0  0  0  0  0  0]
[                   ]
[0  0  0  0  0  0  0]
[                   ]
[0  0  2  0  0  0  0]
[                   ]
[0  0  0  1  0  0  0]
[                   ]
[0  0  0  0  3  0  0]
[                   ]
[0  0  0  0  0  2  0]
[                   ]
[0  0  0  0  0  0  3]


MATD:=

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

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

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

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

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

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

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

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


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

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

commutant de t1 dans der(gtildedelta):

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

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

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

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

    (0,0,0,0,3*d(0,0),0,0),

    (0,0,d(5,2),0,0,d(1,1) + 2*d(0,0),0),

    (0,0,0,0,d(6,4),0,d(1,1) + 3*d(0,0)))


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

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

t2:=D(1,1):=

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


Unknowns: {d(1,1),d(0,0)}

Unknowns: {d(1,1),d(0,0)}

commutant simultane de t1,t2 dans der(gtildedelta):

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

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

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

    (0,0,0,d(1,1) + d(0,0),0,0,0),

    (0,0,0,0,3*d(0,0),0,0),

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

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


rank 2 with maximal torus t1,t2

2


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:=

[1  0  0  0  0  0  0]
[                   ]
[0  0  0  0  0  0  0]
[                   ]
[0  0  2  0  0  0  0]
[                   ]
[0  0  0  1  0  0  0]
[                   ]
[0  0  0  0  3  0  0]
[                   ]
[0  0  0  0  0  2  0]
[                   ]
[0  0  0  0  0  0  3]

P**(-1)*t2*P:=

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

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

on voit apparaitre les poids sur la diagonale$

r(1) := d(0,0)$

r(2) := d(1,1)$

r(3) := 2*d(0,0)$

r(4) := d(1,1) + d(0,0)$

r(5) := 3*d(0,0)$

r(6) := d(1,1) + 2*d(0,0)$

r(7) := d(1,1) + 3*d(0,0)$

r(1) := gamma1$

r(2) := gamma2$

r(3) := 2*gamma1$

r(4) := gamma1 + gamma2$

r(5) := 3*gamma1$

r(6) := 2*gamma1 + gamma2$

r(7) := 3*gamma1 + gamma2$

Le systeme de poids est le systeme 2.1$

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

listcommutateursdesx := {{{0,1},x(3)},
{{0,2},a*x(4)},
{{0,3},x(5)},
{{0,4},0},
{{0,5},(a - 1)*x(6)},
{{0,6},0},
{{1,2},x(5)},
{{1,3},0},
{{1,4},x(6)},
{{1,5},0},
{{1,6},0},
{{2,3},x(6)},
{{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(4)},
{{1,3},diay(5)*a},
{{1,4},diay(6)},
{{1,5},0},
{{1,6},(a - 1)*diay(7)},
{{1,7},0},
{{2,3},diay(6)},
{{2,4},0},
{{2,5},diay(7)},
{{2,6},0},
{{2,7},0},
{{3,4},diay(7)},
{{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}}$

We suppose a:=1$

 a:=1.$

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

On obtient donc les relations de commutations de $

g_{7,2.1}$

(v)$

Et cela pour a:=1.$

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

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