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

phase 1 de la resolution des equations$

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Unknowns: {d(3,6),a}
Unknowns: {d(3,6),a}
pas de selection possible de variable a coefficient independant des xi dans  - d
(3,6)*a
on resoud l'equation {{0,3},4} qui est  maintenant AA:= - d(4,6)*a$

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

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

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

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

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

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

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

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

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

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(5,5) + d(4,4) + d(0,
0)$

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

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

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

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

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

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

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

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

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

Unknown: d(5,6)
Unknown: d(5,6)
bonne inconnue W:=d(5,6)$

sa valeur doit etre WW:=0$

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

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

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

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

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

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

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(2,1)$

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

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

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

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

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

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

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

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

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

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

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

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

gtildedelta est caracteristiquement nilpotente$

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

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

seul tore maximal: {0}.$



matrice! de! passage! de! la! base! !X(0)=delta,! !X(1),...,! !X(6)! a! une! bas
e! ! 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(3,0),d(3,1),d(2,1),0,0,0,0),

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

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

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

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


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

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

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

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

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

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

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

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

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

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

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

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

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

   {{0,2},x(3)},

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

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

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

   {{0,6},0},

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

   {{1,3},x(5)},

   {{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 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)

*** yy declared operator 

*** diadiay declared operator 

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

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

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

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

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

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

 {{1,7},0},

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

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

 {{2,5},diadiay(7)},

 {{2,6},0},

 {{2,7},0},

 {{3,4}, - diadiay(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 pose :

*** zz declared operator 

ZZ(1):=sqrt(a)*diay(1)

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

ZZ(3):= - sqrt(a)*diay(3)*a

                   2
ZZ(4):= - diay(4)*a

                        2
ZZ(5):=sqrt(a)*diay(5)*a

                3
ZZ(6):=diay(6)*a

                           3
ZZ(7):= - sqrt(a)*diay(7)*a

*** zzz declared operator 

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

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

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

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

 {{1,5},zzz(6)},

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

 {{1,7},0},

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

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

 {{2,5},zzz(7)},

 {{2,6},0},

 {{2,7},0},

 {{3,4},zzz(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}}

C'est  les relations de commutation de g_{7,0.6)} page 167.

cela pour a neq 0