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

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

phase 1 de la resolution des equations$

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

Unknown: d(3,2)
Unknown: d(3,2)
bonne inconnue W:=d(3,2)$

sa valeur doit etre WW:=0$

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

sa valeur doit etre WW:= - d(2,6)*b$

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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},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)$

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

sa valeur doit etre WW:=0$

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

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

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

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

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

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

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

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},(4*a*b + 1)*d(0,1)*b},
{{{0,2},6},
d(3,1)*a - d(3,1) + d(3,0) - (a - 1)*d(5,3)*b - (d(3,0) - d(2,1)*b)*(a - 1) + ((
a + 1)*d(3,1)*a - (a - 1)*d(2,0))*b},
{{{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},2},0},
{{{0,4},4},0},
{{{0,4},5},0},
{{{0,4},6},(a - 1)*d(0,1)*b},
{{{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},(a - 1)*d(0,1)},
{{{0,6},2},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},2},0},
{{{1,5},4},0},
{{{1,5},5},0},
{{{1,5},6},(a - 1)*d(0,1)},
{{{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},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 y a une phase 2$

Si a neq 1, d(0,1):=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},2},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},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},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},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}}$

derivation generique de gtildedelta:$

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

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

pour shortformdelta:={1,
ss,
0,
0,
ss,
a,
ss,
b,
1,
ss,
0,
0}$

Unknowns: {d(6,3),
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),
d(1,1),
a,
b}
Unknowns: {d(6,3),
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),
d(1,1),
a,
b}
listparametresMATD{d(6,3),
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),
d(1,1)}$

dim Der(gtildedelta):=12$

un element t1 d'un tore $

t1:=D(1,1)$

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]


 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  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]


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

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

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

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

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

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

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

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

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

                              2
         - (a - 2)*d(3,0) + (a *b + a*b + a - 1)*d(3,1))/((a - 1)*b),0,3*d(1,1),

     0),

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

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


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

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

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

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

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

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

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

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

                              2
         - (a - 2)*d(3,0) + (a *b + a*b + a - 1)*d(3,1))/((a - 1)*b),0,3*d(1,1),

     0),

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

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


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

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

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

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

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

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

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

                              2
         - (a - 2)*d(3,0) + (a *b + a*b + a - 1)*d(3,1))/((a - 1)*b),0,3*d(1,1),

     0),

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

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


on voit apparaitre les poids sur la diagonale

ladiag := {{1,d(1,1)},

           {2,d(1,1)},

           {3,2*d(1,1)},

           {4,2*d(1,1)},

           {5,3*d(1,1)},

           {6,3*d(1,1)},

           {7,4*d(1,1)}}

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

listcommutateursdesx := {{{0,1},x(2)},

   {{0,2},b*x(5)},

   {{0,3},x(5) + x(4)*a},

   {{0,4},0},

   {{0,5},(a - 1)*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(6)*b},

 {{1,4},diadiay(6) + diadiay(5)*a},

 {{1,5},0},

 {{1,6},(a - 1)*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 obtient, et cela pour a neq 1  (voir feuilles manuscrites)


1) Pour  b= -(a-1)/(2a-1)**2  et a neq 1/2: les relations de commutation de g_\
{7,1.2(ii)}.


2) Pour a= -1/2 ou a neq -1/2 et b= -(a-1)/(2a-1)**2: les relations de commuta\
tion de g_{7,1.2(i_L)} avec


L:=-(1/beta)* (3beta*a*b -beta*b +beta**3*b +sqrt(b)*sqrt(a-1))/(a*b -beta**2*\
b*(a-1) -beta*sqrt(b)*sqrt(a-1))

                    2
         (3*a + beta  - 1)*b*beta + sqrt(b)*sqrt(a - 1)
L:=-----------------------------------------------------------
            2           2
    ((a*beta  - a - beta )*b + sqrt(b)*sqrt(a - 1)*beta)*beta

avec beta racine de f et pas racine de g

*** f declared operator

f(x) := x**2 -2*x*sqrt(b)*(2a-1)/sqrt(a-1) -1

*** g declared operator

g(x) := x**2 + x/(sqrt(b)*sqrt(a-1)) -a/a-1

                    2
       sqrt(a - 1)*x  - sqrt(a - 1) - 4*sqrt(b)*a*x + 2*sqrt(b)*x
f(x):=------------------------------------------------------------
                              sqrt(a - 1)

                            2
       sqrt(b)*sqrt(a - 1)*x  - 2*sqrt(b)*sqrt(a - 1) + x
g(x):=----------------------------------------------------
                      sqrt(b)*sqrt(a - 1)