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

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

phase 1 de la resolution des equations$

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

on resout l'equation {{2,3},6} 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 {{2,4},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 {{2,5},6} 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$

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

il n'y a pas de phase 2$

derivation generique de gtildedelta:$

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

pour delta:=

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


pour shortformdelta:={0,

   ss,

   0,

   0,

   ss,

   1,

   ss,

   1,

   0,

   ss,

   0,

   0}

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

dim Der(gtildedelta):=13$

un element t1 d'un tore $

t1:=D(0,0)$

t1:=

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


MATD:=

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

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

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

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

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

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

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


          2        2        2
 - (x - 1) *(x - 2) *(x - 3) *(x - 4)

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

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

commutant de t1 dans der(gtildedelta):

[d(0,0)  d(0,1)       0            0           0          0         0    ]
[                                                                        ]
[d(0,1)  d(0,0)       0            0           0          0         0    ]
[                                                                        ]
[  0       0      2*d(0,0)     - 2*d(0,1)      0          0         0    ]
[                                                                        ]
[  0       0      - 2*d(0,1)   2*d(0,0)        0          0         0    ]
[                                                                        ]
[  0       0          0            0       3*d(0,0)    - d(0,1)     0    ]
[                                                                        ]
[  0       0          0            0        - d(0,1)  3*d(0,0)      0    ]
[                                                                        ]
[  0       0          0            0           0          0      4*d(0,0)]


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

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

t2:=D(0,1):=

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


{{x,1,

  [      0       ]
  [              ]
  [      0       ]
  [              ]
  [      0       ]
  [              ]
  [      0       ]
  [              ]
  [      0       ]
  [              ]
  [      0       ]
  [              ]
  [arbcomplex(65)]

  },

 {x - 1,

  2,


  [ arbcomplex(66)  ]
  [                 ]
  [ arbcomplex(66)  ]
  [                 ]
  [        0        ]
  [                 ]
  [        0        ]
  [                 ]
  [ - arbcomplex(67)]
  [                 ]
  [ arbcomplex(67)  ]
  [                 ]
  [        0        ]

  },

 {x + 1,

  2,


  [ - arbcomplex(68)]
  [                 ]
  [ arbcomplex(68)  ]
  [                 ]
  [        0        ]
  [                 ]
  [        0        ]
  [                 ]
  [ arbcomplex(69)  ]
  [                 ]
  [ arbcomplex(69)  ]
  [                 ]
  [        0        ]

  },

 {x - 2,

  1,


  [        0        ]
  [                 ]
  [        0        ]
  [                 ]
  [ - arbcomplex(70)]
  [                 ]
  [ arbcomplex(70)  ]
  [                 ]
  [        0        ]
  [                 ]
  [        0        ]
  [                 ]
  [        0        ]

  },

 {x + 2,

  1,


  [      0       ]
  [              ]
  [      0       ]
  [              ]
  [arbcomplex(71)]
  [              ]
  [arbcomplex(71)]
  [              ]
  [      0       ]
  [              ]
  [      0       ]
  [              ]
  [      0       ]

  }}

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

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

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

[d(0,0)  d(0,1)       0            0           0          0         0    ]
[                                                                        ]
[d(0,1)  d(0,0)       0            0           0          0         0    ]
[                                                                        ]
[  0       0      2*d(0,0)     - 2*d(0,1)      0          0         0    ]
[                                                                        ]
[  0       0      - 2*d(0,1)   2*d(0,0)        0          0         0    ]
[                                                                        ]
[  0       0          0            0       3*d(0,0)    - d(0,1)     0    ]
[                                                                        ]
[  0       0          0            0        - d(0,1)  3*d(0,0)      0    ]
[                                                                        ]
[  0       0          0            0           0          0      4*d(0,0)]


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


P**(-1)*t1*P:=

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


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

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


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

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

PP:=
mat((1,-1,0,0,0,0,0),(1,1,0,0,0,0,0),(0,0,1,-1,0,0,0),(0,0,1,1,0,0,0),(0,0,0,0,1
,1,0),(0,0,0,0,-1,1,0),(0,0,0,0,0,0,1))$

avec PP:=P*Q:=
mat((1,-1,0,0,0,0,0),(1,1,0,0,0,0,0),(0,0,1,-1,0,0,0),(0,0,1,1,0,0,0),(0,0,0,0,1
,1,0),(0,0,0,0,-1,1,0),(0,0,0,0,0,0,1))$

on voit apparaitre les poids sur la diagonale$

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

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

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

diaY(2):=x(1) - x(0)$

diaY(3):=x(3) + x(2)$

diaY(4):=x(3) - x(2)$

diaY(5):= - (x(5) - x(4))$

diaY(6):=x(5) + x(4)$

diaY(7):=x(6)$

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

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

avec comme matrice de changement de base :$

[0  1  0  0   0  0  0]
[                    ]
[1  0  0  0   0  0  0]
[                    ]
[0  0  2  0   0  0  0]
[                    ]
[0  0  0  -2  0  0  0]
[                    ]
[0  0  0  0   0  4  0]
[                    ]
[0  0  0  0   4  0  0]
[                    ]
[0  0  0  0   0  0  8]


det(isom):= -512

*** zz declared operator 

ZZ(1):=diay(2)

ZZ(2):=diay(1)

ZZ(3):=2*diay(3)

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

ZZ(5):=4*diay(6)

ZZ(6):=4*diay(5)

ZZ(7):=8*diay(7)

*** zzz declared operator 

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

{{{1,2},0},
{{1,3},0},
{{1,4},zzz(6)},
{{1,5},0},
{{1,6},zzz(7)},
{{1,7},0},
{{2,3},zzz(5)},
{{2,4},0},
{{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}}$

On obtient donc   les relations de commutation de g_{7,2.23   }.$