a:=0$

b:=0$

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

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

phase 1 de la resolution des equations$

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

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

sa valeur doit etre WW:=0$

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

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

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

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

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

sa valeur doit etre WW:=0$

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

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

sa valeur doit etre WW:=0$

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

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

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

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

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

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

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

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

sa valeur doit etre WW:=0$

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

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

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

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

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

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

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

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

sa valeur doit etre WW:=d(5,4)$

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

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

sa valeur doit etre WW:=0$

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

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

sa valeur doit etre WW:=0$

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

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

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

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

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

sa valeur doit etre WW:=d(3,6)$

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Derivation equations to cancel (Reduce output) : \\{{{{0,1},1},0},
{{{0,1},4},0},
{{{0,1},5},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},1},0},
{{{0,4},4},0},
{{{0,4},5},0},
{{{0,5},1},0},
{{{0,5},4},0},
{{{0,5},5},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},4},0},
{{{1,3},6},0},
{{{1,4},4},0},
{{{1,4},5},0},
{{{1,5},4},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},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},4},0},
{{{3,4},5},0},
{{{3,4},6},0},
{{{3,5},4},0},
{{{3,5},6},0},
{{{3,6},4},0},
{{{3,6},5},0},
{{{3,6},6},0},
{{{4,5},5},0},
{{{4,6},5},0},
{{{5,6},5},0}}$

il n'y a pas de phase 2$

derivation generique de gtildedelta:$

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

pour delta:=

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


pour shortformdelta:={1,

   ss,

   0,

   0,

   ss,

   1,

   ss,

   0,

   0,

   ss,

   0,

   0}

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

dim Der(gtildedelta):=14$

un element t1 d'un tore $

t1:=D(0,0)$

t1:=

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


MATD:=

mat((d(0,0),0,d(0,2),0,0,0,0),

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

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

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

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

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

     ),

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


Unknowns: {d(5,3),d(4,2),d(1,1),d(0,0)}

Unknowns: {d(5,3),d(4,2),d(1,1),d(0,0)}

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

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

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

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

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


Unknowns: {d(5,3),d(4,2),d(1,1),d(0,0)}

Unknowns: {d(5,3),d(4,2),d(1,1),d(0,0)}

t2:=D(1,1):=

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


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

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

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

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

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



le calcul du commutant de t1 et t2 et t3 dans der(gtildedelta) montre  que t1,\
t2,t3 est un tore maximal.

 t1,t2 est un tore maximal.


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


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

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

PP**(-1)*t1*PP:=
mat((1,0,0,0,0,0,0),(0,0,0,0,0,0,0),(0,0,-1,0,0,0,0),(0,0,0,-2,0,0,0),(0,0,0,0,
-1,0,0),(0,0,0,0,0,-2,0),(0,0,0,0,0,0,-3))$

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))$

on voit apparaitre les poids sur la diagonale$

ladiag := {{1,d(0,0)},
{2,d(1,1)},
{3,d(1,1) - d(0,0)},
{4,2*(d(1,1) - d(0,0))},
{5,2*d(1,1) - d(0,0)},
{6,3*d(1,1) - 2*d(0,0)},
{7,3*(d(1,1) - d(0,0))}}$

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

listcommutateursdesx := {{{0,1},0},
{{0,2},x(1)},
{{0,3},x(4)},
{{0,4},0},
{{0,5},0},
{{0,6},x(5)},
{{1,2},x(4)},
{{1,3},0},
{{1,4},0},
{{1,5},0},
{{1,6},0},
{{2,3},x(6)},
{{2,4},x(5)},
{{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)$

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

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

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

liste des commutateurs des diaY(i) :$

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

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

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 :$

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


det(isom):= 1

ZZ(1):=diay(3)

ZZ(2):=diay(1)

ZZ(3):=diay(4)

ZZ(4):= - diay(2)

ZZ(5):=diay(7)

ZZ(6):=diay(5)

ZZ(7):=diay(6)

listcommutateursdesZZ:={{{1,2},zz(4)},

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

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

   {{1,5},0},

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

   {{1,7},0},

   {{2,3},zz(6)},

   {{2,4},0},

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

   {{2,6},0},

   {{2,7},0},

   {{3,4},0},

   {{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(iL)} avec L:=1

Et cela pour a:=0, b:=0.

shortformdelta:={1,

                 ss,

                 0,

                 0,

                 ss,

                 1,

                 ss,

                 0,

                 0,

                 ss,

                 0,

                 0}

delta:=

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