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

a:=0$

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

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

phase 1 de la resolution des equations$

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

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

sa valeur doit etre WW:=0$

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

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

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

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(0,5)$

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(3,3) + d(0,
0)$

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

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

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

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

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

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(1,0)$

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

sa valeur doit etre WW:=0$

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Derivation equations to cancel (Reduce output) : \\{{{{0,1},5},0},
{{{0,1},6},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},5},0},
{{{0,4},6},0},
{{{0,5},5},0},
{{{0,6},5},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},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},5},0},
{{{1,5},6},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},5},0},
{{{2,4},6},0},
{{{2,5},5},0},
{{{2,5},6},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}}$

il n'y a pas de phase 2$

derivation generique de gtildedelta:$

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

pour delta:=

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


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

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

dim Der(gtildedelta):=19$

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


MATD:=

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

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

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

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

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

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

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


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

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

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

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

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

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


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

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

Unknowns: {d(6,3),d(5,1),d(2,2),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(2,2),0,0,0,0),

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

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

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

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


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

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

t3:=D(2,2):=

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


Unknowns: {d(2,2),d(1,1),d(0,0)}

Unknowns: {d(2,2),d(1,1),d(0,0)}

commutant simultane de t1,t2,t3 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(2,2),0,0,0,0),

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

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

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

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


rank 3 with maximal torus t1,t2,t3

3


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

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]

P**(-1)*t3*P:=

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


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

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

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

on voit apparaitre les poids sur la diagonale$

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

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

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

r(4) := d(1,1) - d(0,0) + d(2,2)$

r(5) := 2*d(2,2) - d(0,0)$

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

r(7) := d(1,1) - d(0,0) + 2*d(2,2)$

r(1) :=  - (gamma2 - 2*gamma3)$

r(2) := gamma1$

r(3) := gamma3$

r(4) := gamma1 + gamma2 - gamma3$

r(5) := gamma2$

r(6) := gamma1 + gamma3$

r(7) := gamma1 + gamma2$

Le systeme de poids est le systeme 3.19$

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

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

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

Namely g_{7,3.19}$

(iL), L:=1/2$

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 :$

mat((0,0,0,0,-1,0,0),(1,0,0,0,0,0,0),(0,0,1,0,0,0,0),(0,0,0,1,0,0,0),(0,1,0,0,0,
0,0),(0,0,0,0,0,0,1),(0,0,0,0,0,1,0))$

det(isom):= 1$

ZZ(1):=diay(2)$

ZZ(2):=diay(5)$

ZZ(3):=diay(3)$

ZZ(4):=diay(4)$

ZZ(5):= - diay(1)$

ZZ(6):=diay(7)$

ZZ(7):=diay(6)$

listcommutateursdesZZ:=$

{{1,2},zz(6)}$

{{1,3},zz(7)}$

{{1,4},0}$

{{1,5},0}$

{{1,6},0}$

{{1,7},0}$

{{2,3},0}$

{{2,4},0}$

{{2,5},0}$

{{2,6},0}$

{{2,7},0}$

{{3,4},zz(6)}$

{{3,5},0}$

{{3,6},0}$

{{3,7},0}$

{{4,5},zz(7)}$

{{4,6},0}$

{{4,7},0}$

{{5,6},0}$

{{5,7},0}$

{{6,7},0}$

On obtient donc les relations de commutations de $

g_{7,3.19}$

Et cela pour a:=0.$

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

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