a:=1$

b:=1$

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),(1,0,1
,0,0,0))$

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

phase 1 de la resolution des equations$

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

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

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

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

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

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

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

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

sa valeur doit etre WW:=d(5,6)$

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

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

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

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},2} 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 {{0,2},3} qui est  maintenant AA:= - d(3,1)$

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

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

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

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

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(2,
0) + d(0,0)$

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

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

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

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

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

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

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

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

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

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

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

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

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

sa valeur doit etre WW:= - d(1,3) - d(1,1) + 2*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 {{1,2},6} qui est  maintenant AA:= - d(1,3) - d(1,1) - d(0,
2) + 2*d(0,0)$

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

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

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

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

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

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

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

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

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


pour shortformdelta:={1,

   ss,

   0,

   0,

   ss,

   1,

   ss,

   0,

   0,

   ss,

   1,

   1}

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

dim Der(gtildedelta):=12$

un element t1 d'un tore $

t1:=D(0,0)$

t1:=

[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  0  0]
[                   ]
[0  0  0  0  0  4  0]
[                   ]
[0  0  0  0  0  0  3]


MATD:=

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

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

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

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

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

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

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

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

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


Unknown: d(0,0)

Unknown: d(0,0)

commutant de t1 dans der(gtildedelta):

[d(0,0)     0        0        0         0         0         0    ]
[                                                                ]
[  0     2*d(0,0)    0        0         0         0         0    ]
[                                                                ]
[  0        0      d(0,0)     0         0         0         0    ]
[                                                                ]
[  0        0        0     2*d(0,0)     0         0         0    ]
[                                                                ]
[  0        0        0        0      3*d(0,0)     0         0    ]
[                                                                ]
[  0        0        0        0         0      4*d(0,0)     0    ]
[                                                                ]
[  0        0        0        0         0         0      3*d(0,0)]


Unknown: d(0,0)

Unknown: d(0,0)

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

[d(0,0)     0        0        0         0         0         0    ]
[                                                                ]
[  0     2*d(0,0)    0        0         0         0         0    ]
[                                                                ]
[  0        0      d(0,0)     0         0         0         0    ]
[                                                                ]
[  0        0        0     2*d(0,0)     0         0         0    ]
[                                                                ]
[  0        0        0        0      3*d(0,0)     0         0    ]
[                                                                ]
[  0        0        0        0         0      4*d(0,0)     0    ]
[                                                                ]
[  0        0        0        0         0         0      3*d(0,0)]


 t1 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  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  0  0]
[                   ]
[0  0  0  0  0  4  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),0,0,0,0,0,0),(d(1,0),2*d(0,0),d(1,2),0,0,0,0),(0,0,d(0,0),0,0,0,0),(
d(3,0),0,d(3,2),2*d(0,0),0,0,0),(d(4,0),d(3,2) + d(1,0),d(4,2), - (d(3,0) - d(1,
2) - d(3,2)),3*d(0,0),0,0),(d(5,0),d(5,1),d(5,2),d(5,3), - (d(3,2) + d(1,0)),4*d
(0,0), - (d(3,0) - d(1,2) - d(3,2))),(d(6,0), - (d(3,0) - d(1,2) - d(3,2)),d(5,1
) + d(4,0),d(1,2) - d(1,0) - d(3,0),0,0,3*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))$

on voit apparaitre les poids sur la diagonale$

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

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

listcommutateursdesx := {{{0,1},x(6)},
{{0,2},x(1)},
{{0,3},x(6) + 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},x(6)},
{{1,3},x(1)},
{{1,4},x(6) + 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},yy(7)},
{{1,3},yy(2)},
{{1,4},yy(7) + 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},yy(7)},
{{1,3},yy(2)},
{{1,4},yy(7) + 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},diay(7)},
{{1,3},diay(2)},
{{1,4},diay(7) + 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:$

Namely g_{7,1.2(iL)} with L=1$

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 :$

This isomorphism computed by the program calculisom6_6III4.red$

mat((1,i*(sqrt(3) - 2),0,0,0,0,0),

    (0,0,2*(sqrt(3) - 2),2*(2*i*sqrt(3) - 3*i),0,0,0),

    (sqrt(3) - 2,i,0,0,0,0,0),

    (0,0, - 4*(sqrt(3) - 2),0,0,0,0),

    (0,0,0,0,2*(7*i*sqrt(3) - 12*i),2*(2*sqrt(3) - 3),0),

    (0,0,0,0,0,0, - 12*(4*i*sqrt(3) - 7*i)),

    (0,0,0,0,2*(2*i*sqrt(3) - 3*i),2*(7*sqrt(3) - 12),0))


det(isom):= 13824*(18817*sqrt(3) - 32592)

*** Domain mode complex changed to complex-rounded 

det(isom):= 0.636229749183

*** Domain mode complex-rounded changed to complex 

ZZ(1):=(sqrt(3) - 2)*diay(3) + diay(1)

ZZ(2):=i*((sqrt(3) - 2)*diay(1) + diay(3))

ZZ(3):= - 2*(2*diay(4) - diay(2))*(sqrt(3) - 2)

ZZ(4):=2*(2*i*sqrt(3) - 3*i)*diay(2)

ZZ(5):=2*((7*i*sqrt(3) - 12*i)*diay(5) + (2*i*sqrt(3) - 3*i)*diay(7))

ZZ(6):=2*((7*sqrt(3) - 12)*diay(7) + (2*sqrt(3) - 3)*diay(5))

ZZ(7):= - 12*(4*i*sqrt(3) - 7*i)*diay(6)

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

   {{1,3},zz(6)},

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

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

   {{1,6},0},

   {{1,7},0},

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

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

   {{2,5},0},

   {{2,6},zz(7)},

   {{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_{7,1.2(iL)} avec L=1

Et cela pour a:=1, b:=1.

shortformdelta:={1,

                 ss,

                 0,

                 0,

                 ss,

                 1,

                 ss,

                 0,

                 0,

                 ss,

                 1,

                 1}

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]
[                ]
[1  0  1  0  0  0]