delta:= mat((0,0,0,0,0,0),(0,0,0,0,0,0),(1,1,0,0,0,0),(0,0,0,0,0,0),(0,0,1,0,0,0),(0,0,a ,1,0,0))$ shortformdelta:={1,1,ss,0,1,ss,0,a}$ phase 1 de la resolution des equations$ on resout l'equation {{0,1},0} 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 {{0,1},1} qui est maintenant AA:= - d(1,3)$ Unknown: d(1,3) Unknown: d(1,3) bonne inconnue W:=d(1,3)$ sa valeur doit etre WW:=0$ on resout l'equation {{0,1},2} qui est maintenant AA:= - d(2,3)$ Unknown: d(2,3) Unknown: d(2,3) bonne inconnue W:=d(2,3)$ sa valeur doit etre WW:=0$ on resout l'equation {{0,1},3} qui est maintenant AA:= - d(3,3) + d(2,1) + d(1, 1) + d(0,0)$ Unknowns: {d(3,3),d(2,1),d(1,1),d(0,0)} Unknowns: {d(3,3),d(2,1),d(1,1),d(0,0)} bonne inconnue W:=d(3,3)$ sa valeur doit etre WW:=d(2,1) + d(1,1) + d(0,0)$ on resout l'equation {{0,1},4} qui est maintenant AA:= - (d(4,3) + d(2,0))$ Unknowns: {d(4,3),d(2,0)} Unknowns: {d(4,3),d(2,0)} bonne inconnue W:=d(4,3)$ sa valeur doit etre WW:= - d(2,0)$ on resout l'equation {{0,1},5} qui est maintenant AA:= - d(5,3) + d(3,1)$ Unknowns: {d(5,3),d(3,1)} Unknowns: {d(5,3),d(3,1)} bonne inconnue W:=d(5,3)$ sa valeur doit etre WW:=d(3,1)$ on resout l'equation {{0,1},6} qui est maintenant AA:= - d(6,3) + d(4,1) + d(3, 1)*a - d(3,0)$ Unknowns: {d(6,3),d(4,1),d(3,1),d(3,0),a} Unknowns: {d(6,3),d(4,1),d(3,1),d(3,0),a} bonne inconnue W:=d(6,3)$ sa valeur doit etre WW:=d(4,1) + d(3,1)*a - d(3,0)$ on resout l'equation {{0,2},3} qui est maintenant AA:=d(2,2) - d(2,1) + d(1,2) - d(1,1)$ Unknowns: {d(2,2),d(2,1),d(1,2),d(1,1)} Unknowns: {d(2,2),d(2,1),d(1,2),d(1,1)} bonne inconnue W:=d(2,2)$ sa valeur doit etre WW:=d(2,1) - d(1,2) + d(1,1)$ on resout l'equation {{0,2},4} qui est maintenant AA:=d(2,0) + d(1,0)$ Unknowns: {d(2,0),d(1,0)} Unknowns: {d(2,0),d(1,0)} bonne inconnue W:=d(2,0)$ sa valeur doit etre WW:= - d(1,0)$ on resout l'equation {{0,2},5} qui est maintenant AA:= - d(4,0) + d(3,2) - d(3, 1)$ Unknowns: {d(4,0),d(3,2),d(3,1)} Unknowns: {d(4,0),d(3,2),d(3,1)} bonne inconnue W:=d(3,1)$ sa valeur doit etre WW:= - d(4,0) + d(3,2)$ on resout l'equation {{0,2},6} qui est maintenant AA:=d(4,2) - d(4,1) + d(4,0)* a + d(3,0)$ Unknowns: {d(4,2),d(4,1),d(4,0),d(3,0),a} Unknowns: {d(4,2),d(4,1),d(4,0),d(3,0),a} bonne inconnue W:=d(4,2)$ sa valeur doit etre WW:=d(4,1) - d(4,0)*a - d(3,0)$ on resout l'equation {{0,3},0} qui est maintenant AA:= - (d(0,6)*a + d(0,5))$ Unknowns: {d(0,6),d(0,5),a} Unknowns: {d(0,6),d(0,5),a} bonne inconnue W:=d(0,5)$ sa valeur doit etre WW:= - d(0,6)*a$ on resout l'equation {{0,3},1} qui est maintenant AA:= - (d(1,6)*a + d(1,5))$ Unknowns: {d(1,6),d(1,5),a} Unknowns: {d(1,6),d(1,5),a} bonne inconnue W:=d(1,5)$ sa valeur doit etre WW:= - d(1,6)*a$ on resout l'equation {{0,3},2} qui est maintenant AA:= - (d(2,6)*a + d(2,5))$ Unknowns: {d(2,6),d(2,5),a} Unknowns: {d(2,6),d(2,5),a} bonne inconnue W:=d(2,5)$ sa valeur doit etre WW:= - d(2,6)*a$ on resout l'equation {{0,3},3} qui est maintenant AA:= - (d(3,6)*a + d(3,5))$ Unknowns: {d(3,6),d(3,5),a} Unknowns: {d(3,6),d(3,5),a} bonne inconnue W:=d(3,5)$ sa valeur doit etre WW:= - d(3,6)*a$ on resout l'equation {{0,3},4} qui est maintenant AA:= - (d(4,6)*a + d(4,5))$ Unknowns: {d(4,6),d(4,5),a} Unknowns: {d(4,6),d(4,5),a} bonne inconnue W:=d(4,5)$ sa valeur doit etre WW:= - d(4,6)*a$ on resout l'equation {{0,3},5} qui est maintenant AA:= - d(5,6)*a - d(5,5) + d( 2,1) + d(1,1) + 2*d(0,0)$ Unknowns: {d(5,6),d(5,5),d(2,1),d(1,1),d(0,0),a} Unknowns: {d(5,6),d(5,5),d(2,1),d(1,1),d(0,0),a} bonne inconnue W:=d(5,5)$ sa valeur doit etre WW:= - d(5,6)*a + d(2,1) + d(1,1) + 2*d(0,0)$ on resout l'equation {{0,3},6} qui est maintenant AA:= - d(6,6)*a - d(6,5) + d( 2,1)*a + d(1,1)*a + 2*d(1,0) + 2*d(0,0)*a$ Unknowns: {d(6,6),d(6,5),d(2,1),d(1,1),d(1,0),d(0,0),a} Unknowns: {d(6,6),d(6,5),d(2,1),d(1,1),d(1,0),d(0,0),a} bonne inconnue W:=d(6,5)$ sa valeur doit etre WW:= - d(6,6)*a + d(2,1)*a + d(1,1)*a + 2*d(1,0) + 2*d(0,0)* a$ on resout l'equation {{0,4},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 {{0,4},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 {{0,4},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 {{0,4},3} qui est maintenant AA:= - d(3,6) + d(2,4) + d(1, 4)$ Unknowns: {d(3,6),d(2,4),d(1,4)} Unknowns: {d(3,6),d(2,4),d(1,4)} bonne inconnue W:=d(3,6)$ sa valeur doit etre WW:=d(2,4) + d(1,4)$ on resout l'equation {{0,4},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 {{0,4},5} qui est maintenant AA:= - d(5,6) + d(3,4) - d(1, 0)$ Unknowns: {d(5,6),d(3,4),d(1,0)} Unknowns: {d(5,6),d(3,4),d(1,0)} bonne inconnue W:=d(5,6)$ sa valeur doit etre WW:=d(3,4) - d(1,0)$ on resout l'equation {{0,4},6} qui est maintenant AA:= - d(6,6) + d(4,4) + d(3, 4)*a + d(0,0)$ Unknowns: {d(6,6),d(4,4),d(3,4),d(0,0),a} Unknowns: {d(6,6),d(4,4),d(3,4),d(0,0),a} bonne inconnue W:=d(6,6)$ sa valeur doit etre WW:=d(4,4) + d(3,4)*a + d(0,0)$ on resout l'equation {{0,5},5} qui est maintenant AA:= - a*(d(2,4) + d(1,4))$ Unknowns: {d(2,4),d(1,4),a} Unknowns: {d(2,4),d(1,4),a} pas de selection possible de variable a coefficient independant des xi dans - a *(d(2,4) + d(1,4)) on resout l'equation {{0,5},6} qui est maintenant AA:= - a**2*(d(2,4) + d(1,4)) $ Unknowns: {d(2,4),d(1,4),a} Unknowns: {d(2,4),d(1,4),a} pas de selection possible de variable a coefficient independant des xi dans - a **2*(d(2,4) + d(1,4)) on resout l'equation {{0,6},5} qui est maintenant AA:=d(2,4) + d(1,4)$ Unknowns: {d(2,4),d(1,4)} Unknowns: {d(2,4),d(1,4)} bonne inconnue W:=d(2,4)$ sa valeur doit etre WW:= - d(1,4)$ 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},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},3} qui est maintenant AA:= - d(3,4) - d(0,2) + d(0, 1)$ Unknowns: {d(3,4),d(0,2),d(0,1)} Unknowns: {d(3,4),d(0,2),d(0,1)} bonne inconnue W:=d(3,4)$ sa valeur doit etre WW:= - d(0,2) + d(0,1)$ on resout l'equation {{1,2},4} qui est maintenant AA:= - d(4,4) + d(2,1) - d(1, 2) + 2*d(1,1)$ Unknowns: {d(4,4),d(2,1),d(1,2),d(1,1)} Unknowns: {d(4,4),d(2,1),d(1,2),d(1,1)} bonne inconnue W:=d(4,4)$ sa valeur doit etre WW:=d(2,1) - d(1,2) + 2*d(1,1)$ on resout l'equation {{1,2},5} qui est maintenant AA:= - (d(5,4) + d(4,1))$ Unknowns: {d(5,4),d(4,1)} Unknowns: {d(5,4),d(4,1)} bonne inconnue W:=d(5,4)$ sa valeur doit etre WW:= - d(4,1)$ on resout l'equation {{1,2},6} qui est maintenant AA:= - d(6,4) + d(3,2)$ Unknowns: {d(6,4),d(3,2)} Unknowns: {d(6,4),d(3,2)} bonne inconnue W:=d(6,4)$ sa valeur doit etre WW:=d(3,2)$ on resout l'equation {{1,3},5} qui est maintenant AA:=d(1,0) + d(0,2)$ Unknowns: {d(1,0),d(0,2)} Unknowns: {d(1,0),d(0,2)} bonne inconnue W:=d(1,0)$ sa valeur doit etre WW:= - d(0,2)$ on resout l'equation {{1,3},6} qui est maintenant AA:=d(1,2) + d(0,2)*a$ Unknowns: {d(1,2),d(0,2),a} Unknowns: {d(1,2),d(0,2),a} bonne inconnue W:=d(1,2)$ sa valeur doit etre WW:= - d(0,2)*a$ on resout l'equation {{1,4},5} 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 {{1,4},6} qui est maintenant AA:= - d(0,2) + 2*d(0,1)$ Unknowns: {d(0,2),d(0,1)} Unknowns: {d(0,2),d(0,1)} bonne inconnue W:=d(0,1)$ sa valeur doit etre WW:=d(0,2)/2$ on resout l'equation {{2,4},5} qui est maintenant AA:=(4*d(1,1) + 5*d(0,2)*a - 4*d(0,0))/2$ Unknowns: {d(1,1),d(0,2),d(0,0),a} Unknowns: {d(1,1),d(0,2),d(0,0),a} bonne inconnue W:=d(1,1)$ sa valeur doit etre WW:=( - 5*d(0,2)*a + 4*d(0,0))/4$ on resout l'equation {{2,4},6} qui est maintenant AA:=(3*d(0,2)*( - a**2 + 4))/ 4$ Unknowns: {d(0,2),a} Unknowns: {d(0,2),a} pas de selection possible de variable a coefficient independant des xi dans (3*d (0,2)*( - a**2 + 4))/4 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},0},0}, {{{0,4},1},0}, {{{0,4},2},0}, {{{0,4},3},0}, {{{0,4},4},0}, {{{0,4},5},0}, {{{0,4},6},0}, {{{0,5},3},0}, {{{0,5},5},0}, {{{0,5},6},0}, {{{0,6},3},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},3},0}, {{{1,4},4},0}, {{{1,4},5},0}, {{{1,4},6},0}, {{{1,5},3},0}, {{{1,5},4},0}, {{{1,5},6},0}, {{{1,6},3},0}, {{{1,6},4},0}, {{{1,6},6},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},( - 3*(a + 2)*(a - 2)*d(0,2))/4}, {{{2,5},3},0}, {{{2,5},4},0}, {{{2,5},5},0}, {{{2,6},3},0}, {{{2,6},4},0}, {{{2,6},5},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},5},0}, {{{4,5},6},0}, {{{4,6},5},0}, {{{4,6},6},0}}$ Il y a une phase 2$ If a neq +2 or -2 then$ d(0,2):=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},0},0}, {{{0,4},1},0}, {{{0,4},2},0}, {{{0,4},3},0}, {{{0,4},4},0}, {{{0,4},5},0}, {{{0,4},6},0}, {{{0,5},3},0}, {{{0,5},5},0}, {{{0,5},6},0}, {{{0,6},3},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},3},0}, {{{1,4},4},0}, {{{1,4},5},0}, {{{1,4},6},0}, {{{1,5},3},0}, {{{1,5},4},0}, {{{1,5},6},0}, {{{1,6},3},0}, {{{1,6},4},0}, {{{1,6},6},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},3},0}, {{{2,5},4},0}, {{{2,5},5},0}, {{{2,6},3},0}, {{{2,6},4},0}, {{{2,6},5},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},5},0}, {{{4,5},6},0}, {{{4,6},5},0}, {{{4,6},6},0}}$ derivation generique de gtildedelta:$ MATD:= mat((d(0,0),0,0,0,0,0,0),(0,d(0,0),0,0,0,0,0),(0,0,d(0,0),0,0,0,0),(d(3,0), - (d (4,0) - d(3,2)),d(3,2),2*d(0,0),0,0,0),(d(4,0),d(4,1), - (d(4,0)*a + d(3,0) - d( 4,1)),0,2*d(0,0),0,0),(d(5,0),d(5,1),d(5,2), - (d(4,0) - d(3,2)), - d(4,1),3*d(0 ,0),0),(d(6,0),d(6,1),d(6,2),d(3,2)*a - d(3,0) - d(4,0)*a + d(4,1),d(3,2),0,3*d( 0,0)))$ pour delta:= [0 0 0 0 0 0] [ ] [0 0 0 0 0 0] [ ] [1 1 0 0 0 0] [ ] [0 0 0 0 0 0] [ ] [0 0 1 0 0 0] [ ] [0 0 a 1 0 0] pour shortformdelta:={1,1,ss,0,1,ss,0,a} Unknowns: {d(6,2), d(6,1), d(6,0), d(5,2), d(5,1), d(5,0), d(4,1), d(4,0), d(3,2), d(3,0), d(0,0), a} Unknowns: {d(6,2), d(6,1), d(6,0), d(5,2), d(5,1), d(5,0), d(4,1), d(4,0), d(3,2), d(3,0), d(0,0), a} listeparametresMATD{d(6,2), d(6,1), d(6,0), d(5,2), d(5,1), d(5,0), d(4,1), d(4,0), d(3,2), d(3,0), d(0,0)}$ dim Der(gtildedelta):=11$ 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 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] MATD:= mat((d(0,0),0,0,0,0,0,0), (0,d(0,0),0,0,0,0,0), (0,0,d(0,0),0,0,0,0), (d(3,0), - (d(4,0) - d(3,2)),d(3,2),2*d(0,0),0,0,0), (d(4,0),d(4,1), - (d(4,0)*a + d(3,0) - d(4,1)),0,2*d(0,0),0,0), (d(5,0),d(5,1),d(5,2), - (d(4,0) - d(3,2)), - d(4,1),3*d(0,0),0), (d(6,0),d(6,1),d(6,2),d(3,2)*a - d(3,0) - d(4,0)*a + d(4,1),d(3,2),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 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 2*d(0,0) 0 0 ] [ ] [ 0 0 0 0 0 3*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 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),0,0,0,0,0,0),(0,d(0,0),0,0,0,0,0),(0,0,d(0,0),0,0,0,0),(d(3,0), - (d (4,0) - d(3,2)),d(3,2),2*d(0,0),0,0,0),(d(4,0),d(4,1), - (d(4,0)*a + d(3,0) - d( 4,1)),0,2*d(0,0),0,0),(d(5,0),d(5,1),d(5,2), - (d(4,0) - d(3,2)), - d(4,1),3*d(0 ,0),0),(d(6,0),d(6,1),d(6,2),d(3,2)*a - d(3,0) - d(4,0)*a + d(4,1),d(3,2),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,d(0,0)}, {3,d(0,0)}, {4,2*d(0,0)}, {5,2*d(0,0)}, {6,3*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(3)}, {{0,2},x(3)}, {{0,3},x(6)*a + x(5)}, {{0,4},x(6)}, {{0,5},0}, {{0,6},0}, {{1,2},x(4)}, {{1,3},x(6)}, {{1,4},0}, {{1,5},0}, {{1,6},0}, {{2,3},0}, {{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)$ liste des commutateurs des diaY(i) := (diadiaY=diaY$ {{{1,2},diadiay(4)}, {{1,3},diadiay(4)}, {{1,4},diadiay(7)*a + diadiay(6)}, {{1,5},diadiay(7)}, {{1,6},0}, {{1,7},0}, {{2,3},diadiay(5)}, {{2,4},diadiay(7)}, {{2,5},0}, {{2,6},0}, {{2,7},0}, {{3,4},0}, {{3,5},diadiay(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}}$ on pose :$ avec comme matrice de changement de base :$ 2 2 - (sqrt(a - 4) + a)*a sqrt(a - 4) + a mat((-------------------------,b(1,2),------------------,0,0,0,0), 2*b(1,2) 2 2 2 2 ((a - 3)*a + sqrt(a - 4)*(a + 1)*(a - 1))*(a - 2) (------------------------------------------------------, 2 2 (a - 2 + sqrt(a - 4)*a)*b(1,2) 2 - (sqrt(a - 4) + a)*b(1,2) ------------------------------,-1,0,0,0,0), 2 2 2 2 - 2*(a - 2 + sqrt(a - 4)*a) (sqrt(a - 4) + a)*b(1,2) (--------------------------------,---------------------------,1,0,0,0,0), 2 2 (sqrt(a - 4) + a)*b(1,2) 4 2 2 2 - (a - 4*a + 2 + sqrt(a - 4)*(a - 2)*a)*(a + 2)*(a - 2) (0,0,0,--------------------------------------------------------------, 2 2 (a - 3)*a + sqrt(a - 4)*(a + 1)*(a - 1) 4 2 2 2 - (a - 4*a + 2 + sqrt(a - 4)*(a - 2)*a)*(a + 2)*(a - 2) --------------------------------------------------------------,0,0), 2 2 (a - 2 + sqrt(a - 4)*a)*b(1,2) 4 2 2 2 (a - 4*a + 2 + sqrt(a - 4)*(a - 2)*a)*(a + 2)*(a - 2) (0,0,0,-----------------------------------------------------------, 2 2 a - 2 + sqrt(a - 4)*a 4 2 2 2 (a - 4*a + 2 + sqrt(a - 4)*(a - 2)*a)*(a + 2)*(a - 2) -----------------------------------------------------------,0,0), 2 2 ((a - 3)*a + sqrt(a - 4)*(a + 1)*(a - 1))*b(1,2) 2 4 2 (0,0,0,0,0,((sqrt(a - 4)*(a - 5*a + 5)*a 2 2 + (a + a - 1)*(a - a - 1)*(a + 2)*(a - 2))*(a + 2)*(a - 2) 2 2 *b(1,2))/((a - 3)*a + sqrt(a - 4)*(a + 1)*(a - 1)),( - ( 2 4 2 sqrt(a - 4)*(a - 5*a + 5)*a 2 2 + (a + a - 1)*(a - a - 1)*(a + 2)*(a - 2))*(a + 2)*(a - 2))/( 2 2 ((a - 3)*a + sqrt(a - 4)*(a + 1)*(a - 1))*b(1,2))), 2 4 2 2 (0,0,0,0,0,((sqrt(a - 4)*(a - 4*a + 1)*(a - 2) 2 + (a - 3)*(a + 2)*(a + 1)*(a - 1)*(a - 2)*a)*(a + 2)*(a - 2)) 4 2 2 2 2 /((a - 4*a + 2 + sqrt(a - 4)*(a - 2)*a)*b(1,2) ),( - 4*( 2 8 6 4 2 sqrt(a - 4)*(a - 8*a + 20*a - 16*a + 2) 4 2 2 + (a - 4*a + 2)*(a - 2)*(a + 2)*(a - 2)*a)*(a + 2)*(a - 2))/( 2 2 2 2 (a - 2 + sqrt(a - 4)*a) *(sqrt(a - 4) + a)*b(1,2)))) 2 40 2 38 2 36 det(isom):= ( - 2*(sqrt(a - 4)*a - 40*sqrt(a - 4)*a + 740*sqrt(a - 4)*a 2 34 2 32 - 8400*sqrt(a - 4)*a + 65450*sqrt(a - 4)*a 2 30 2 28 - 371008*sqrt(a - 4)*a + 1582240*sqrt(a - 4)*a 2 26 2 24 - 5178240*sqrt(a - 4)*a + 13147875*sqrt(a - 4)*a 2 22 2 20 - 26013000*sqrt(a - 4)*a + 40060020*sqrt(a - 4)*a 2 18 2 16 - 47720400*sqrt(a - 4)*a + 43459650*sqrt(a - 4)*a 2 14 2 12 - 29716000*sqrt(a - 4)*a + 14858000*sqrt(a - 4)*a 2 10 2 8 - 5230016*sqrt(a - 4)*a + 1225785*sqrt(a - 4)*a 2 6 2 4 - 175560*sqrt(a - 4)*a + 13300*sqrt(a - 4)*a 2 2 2 41 39 37 - 400*sqrt(a - 4)*a + 2*sqrt(a - 4) + a - 42*a + 818*a 35 33 31 29 27 - 9804*a + 80920*a - 487696*a + 2220592*a - 7796128*a 25 23 21 19 + 21352149*a - 45862050*a + 77258610*a - 101594220*a 17 15 13 11 + 103280580*a - 79936040*a + 46059800*a - 19137104*a 9 7 5 3 + 5475173*a - 1006962*a + 106666*a - 5340*a + 80*a) 7 7 2 29 2 27 *(a + 2) *(a - 2) )/((sqrt(a - 4)*a - 28*sqrt(a - 4)*a 2 25 2 23 + 351*sqrt(a - 4)*a - 2600*sqrt(a - 4)*a 2 21 2 19 + 12650*sqrt(a - 4)*a - 42504*sqrt(a - 4)*a 2 17 2 15 + 100947*sqrt(a - 4)*a - 170544*sqrt(a - 4)*a 2 13 2 11 + 203490*sqrt(a - 4)*a - 167960*sqrt(a - 4)*a 2 9 2 7 + 92378*sqrt(a - 4)*a - 31824*sqrt(a - 4)*a 2 5 2 3 + 6188*sqrt(a - 4)*a - 560*sqrt(a - 4)*a 2 30 28 26 24 + 15*sqrt(a - 4)*a + a - 30*a + 405*a - 3250*a 22 20 18 16 + 17250*a - 63756*a + 168245*a - 319770*a 14 12 10 8 6 + 436050*a - 419900*a + 277134*a - 119340*a + 30940*a 4 2 2 - 4200*a + 225*a - 2)*(sqrt(a - 4) + a)*b(1,2)) *** zz declared operator 2 ZZ(1):=( - 2*(2*diay(3) - diay(2)*a + 2*diay(2) + diay(1)*a) 2 3 2 4 2 *(sqrt(a - 4)*a - 2*sqrt(a - 4)*a + a - 4*a + 2))/( 2 2 2 (a - 2 + sqrt(a - 4)*a)*(sqrt(a - 4) + a)*b(1,2)) 2 2 ZZ(2):=( - ((sqrt(a - 4) + a)*diay(2) - 2*diay(1) - (sqrt(a - 4) + a)*diay(3)) *b(1,2))/2 2 (sqrt(a - 4) + a)*diay(1) - 2*diay(2) + 2*diay(3) ZZ(3):=---------------------------------------------------- 2 2 2 ZZ(4):=( - ((a - 2 + sqrt(a - 4)*a)*diay(4) 2 2 - ((a - 3)*a + sqrt(a - 4)*(a + 1)*(a - 1))*diay(5)) 4 2 2 2 *(a - 4*a + 2 + sqrt(a - 4)*(a - 2)*a)*(a + 2)*(a - 2))/( 2 2 2 2 (a - 2 + sqrt(a - 4)*a)*((a - 3)*a + sqrt(a - 4)*(a + 1)*(a - 1))) 2 2 ZZ(5):=(((a - 2 + sqrt(a - 4)*a)*diay(5) 2 2 - ((a - 3)*a + sqrt(a - 4)*(a + 1)*(a - 1))*diay(4)) 4 2 2 2 *(a - 4*a + 2 + sqrt(a - 4)*(a - 2)*a)*(a + 2)*(a - 2))/( 2 2 2 2 (a - 2 + sqrt(a - 4)*a)*((a - 3)*a + sqrt(a - 4)*(a + 1)*(a - 1)) *b(1,2)) 4 2 2 2 ZZ(6):=(((a - 4*a + 2 + sqrt(a - 4)*(a - 2)*a)*( 2 4 2 sqrt(a - 4)*(a - 5*a + 5)*a 2 2 2 + (a + a - 1)*(a - a - 1)*(a + 2)*(a - 2))*(a - 2)*diay(6) + 2 4 2 2 2 sqrt(a - 4)*(a - 4*a + 2 + sqrt(a - 4)*(a - 2)*a)*( 2 4 2 sqrt(a - 4)*(a - 5*a + 5)*a 2 2 + (a + a - 1)*(a - a - 1)*(a + 2)*(a - 2))*diay(6)*a + ( 2 4 2 2 sqrt(a - 4)*(a - 4*a + 1)*(a - 2) 2 + (a - 3)*(a + 2)*(a + 1)*(a - 1)*(a - 2)*a) 2 2 2 *((a - 3)*a + sqrt(a - 4)*(a + 1)*(a - 1))*(sqrt(a - 4) + a)*diay(7) 4 2 2 2 )*(a + 2)*(a - 2))/((a - 4*a + 2 + sqrt(a - 4)*(a - 2)*a) 2 2 2 *((a - 3)*a + sqrt(a - 4)*(a + 1)*(a - 1))*(sqrt(a - 4) + a) 2 *b(1,2) ) 2 8 6 4 2 ZZ(7):=( - (4*(sqrt(a - 4)*(a - 8*a + 20*a - 16*a + 2) 4 2 2 + (a - 4*a + 2)*(a - 2)*(a + 2)*(a - 2)*a) 2 2 *((a - 3)*a + sqrt(a - 4)*(a + 1)*(a - 1))*diay(7) + ( 2 4 2 sqrt(a - 4)*(a - 5*a + 5)*a 2 2 + (a + a - 1)*(a - a - 1)*(a + 2)*(a - 2)) 2 2 2 2 *(a - 2 + sqrt(a - 4)*a) *(sqrt(a - 4) + a)*diay(6))*(a + 2) 2 2 2 *(a - 2))/((a - 2 + sqrt(a - 4)*a) 2 2 2 *((a - 3)*a + sqrt(a - 4)*(a + 1)*(a - 1))*(sqrt(a - 4) + a)*b(1,2) ) *** zzz declared operator liste des commutateurs des ZZ(i) (ZZZ=ZZ:= {{{1,2},zzz(4)}, {{1,3},zzz(5)}, {{1,4},zzz(7)}, {{1,5},zzz(6)}, {{1,6},0}, {{1,7},0}, {{2,3},0}, {{2,4}, (2*zzz(6)*(sqrt(a**2 - 4)*a**72 - 74*sqrt(a**2 - 4)*a**70 + 2625*sqrt(a**2 - 4)* a**68 - 59430*sqrt(a**2 - 4)*a**66 + 964600*sqrt(a**2 - 4)*a**64 - 11952864*sqrt (a**2 - 4)*a**62 + 117584271*sqrt(a**2 - 4)*a**60 - 942758050*sqrt(a**2 - 4)*a** 58 + 6276350085*sqrt(a**2 - 4)*a**56 - 35169861650*sqrt(a**2 - 4)*a**54 + 167561236227*sqrt(a**2 - 4)*a**52 - 683890046658*sqrt(a**2 - 4)*a**50 + 2404509061500*sqrt(a**2 - 4)*a**48 - 7311895571400*sqrt(a**2 - 4)*a**46 + 19282632342750*sqrt(a**2 - 4)*a**44 - 44168733215460*sqrt(a**2 - 4)*a**42 + 87925564996115*sqrt(a**2 - 4)*a**40 - 152053063002750*sqrt(a**2 - 4)*a**38 + 228130955894975*sqrt(a**2 - 4)*a**36 - 296285186944250*sqrt(a**2 - 4)*a**34 + 332032901744544*sqrt(a**2 - 4)*a**32 - 319709186732496*sqrt(a**2 - 4)*a**30 + 263079809534350*sqrt(a**2 - 4)*a**28 - 183763840431780*sqrt(a**2 - 4)*a**26 + 108063778299750*sqrt(a**2 - 4)*a**24 - 52959256091196*sqrt(a**2 - 4)*a**22 + 21361530465954*sqrt(a**2 - 4)*a**20 - 6983250851500*sqrt(a**2 - 4)*a**18 + 1814867865080*sqrt(a**2 - 4)*a**16 - 365887035600*sqrt(a**2 - 4)*a**14 + 55425439524*sqrt(a**2 - 4)*a**12 - 6044050936*sqrt(a**2 - 4)*a**10 + 446794425* sqrt(a**2 - 4)*a**8 - 20466810*sqrt(a**2 - 4)*a**6 + 501025*sqrt(a**2 - 4)*a**4 - 4902*sqrt(a**2 - 4)*a**2 + 8*sqrt(a**2 - 4) + a**73 - 76*a**71 + 2771*a**69 - 64536*a**67 + 1078496*a**65 - 13772992*a**63 + 139774257*a**61 - 1157352512*a** 59 + 7966325317*a**57 - 46210503212*a**55 + 228210741825*a**53 - 966849419640*a **51 + 3534077516580*a**49 - 11191273499280*a**47 + 30789419193330*a**45 - 73721323156320*a**43 + 153735980714995*a**41 - 279171438106820*a**39 + 440978829669245*a**37 - 604742623301320*a**35 + 717939606810776*a**33 - 735029552168736*a**31 + 645788249368466*a**29 - 483932440545856*a**27 + 306983464678566*a**25 - 163332969122856*a**23 + 72070315491606*a**21 - 26009349298576*a**19 + 7545745877416*a**17 - 1722031254176*a**15 + 300627548412* a**13 - 38696764352*a**11 + 3492040057*a**9 - 205418412*a**7 + 7031507*a**5 - 114520*a**3 + 560*a))/((a**2 - 4)*a**71 - 73*(a**2 - 4)*a**69 + 2553*(a**2 - 4)* a**67 - 56948*(a**2 - 4)*a**65 + 910064*(a**2 - 4)*a**63 - 11094993*(a**2 - 4)*a **61 + 107297231*(a**2 - 4)*a**59 - 844987616*(a**2 - 4)*a**57 + 5520320781*(a** 2 - 4)*a**55 - 30324752799*(a**2 - 4)*a**53 + 141479686491*(a**2 - 4)*a**51 - 564784227540*(a**2 - 4)*a**49 + 1939688963940*(a**2 - 4)*a**47 - 5753393425290*( a**2 - 4)*a**45 + 14776294970430*(a**2 - 4)*a**43 - 32905207859440*(a**2 - 4)*a **41 + 63559187552035*(a**2 - 4)*a**39 - 106423936887135*(a**2 - 4)*a**37 + 154228718178535*(a**2 - 4)*a**35 - 192953352533116*(a**2 - 4)*a**33 + 207660182718120*(a**2 - 4)*a**31 - 191354219917058*(a**2 - 4)*a**29 + 150084300057038*(a**2 - 4)*a**27 - 99459843189408*(a**2 - 4)*a**25 + 55186856515830*(a**2 - 4)*a**23 - 25354392512826*(a**2 - 4)*a**21 + 9513049223538*(a**2 - 4)*a**19 - 2865439006168*(a**2 - 4)*a**17 + 678072109288*( a**2 - 4)*a**15 - 122601054444*(a**2 - 4)*a**13 + 16326356708*(a**2 - 4)*a**11 - 1522622816*(a**2 - 4)*a**9 + 92475801*(a**2 - 4)*a**7 - 3265241*(a**2 - 4)*a**5 + 54809*(a**2 - 4)*a**3 - 276*(a**2 - 4)*a + 2*sqrt(a**2 - 4)*a**72 - 148*sqrt( a**2 - 4)*a**70 + 5250*sqrt(a**2 - 4)*a**68 - 118860*sqrt(a**2 - 4)*a**66 + 1929200*sqrt(a**2 - 4)*a**64 - 23905728*sqrt(a**2 - 4)*a**62 + 235168542*sqrt(a **2 - 4)*a**60 - 1885516100*sqrt(a**2 - 4)*a**58 + 12552700170*sqrt(a**2 - 4)*a **56 - 70339723300*sqrt(a**2 - 4)*a**54 + 335122472454*sqrt(a**2 - 4)*a**52 - 1367780093316*sqrt(a**2 - 4)*a**50 + 4809018123000*sqrt(a**2 - 4)*a**48 - 14623791142800*sqrt(a**2 - 4)*a**46 + 38565264685500*sqrt(a**2 - 4)*a**44 - 88337466430920*sqrt(a**2 - 4)*a**42 + 175851129992230*sqrt(a**2 - 4)*a**40 - 304106126005500*sqrt(a**2 - 4)*a**38 + 456261911789950*sqrt(a**2 - 4)*a**36 - 592570373888500*sqrt(a**2 - 4)*a**34 + 664065803489088*sqrt(a**2 - 4)*a**32 - 639418373464992*sqrt(a**2 - 4)*a**30 + 526159619068700*sqrt(a**2 - 4)*a**28 - 367527680863560*sqrt(a**2 - 4)*a**26 + 216127556599500*sqrt(a**2 - 4)*a**24 - 105918512182392*sqrt(a**2 - 4)*a**22 + 42723060931908*sqrt(a**2 - 4)*a**20 - 13966501703000*sqrt(a**2 - 4)*a**18 + 3629735730160*sqrt(a**2 - 4)*a**16 - 731774071200*sqrt(a**2 - 4)*a**14 + 110850879048*sqrt(a**2 - 4)*a**12 - 12088101872*sqrt(a**2 - 4)*a**10 + 893588850*sqrt(a**2 - 4)*a**8 - 40933620*sqrt (a**2 - 4)*a**6 + 1002050*sqrt(a**2 - 4)*a**4 - 9804*sqrt(a**2 - 4)*a**2 + 16* sqrt(a**2 - 4) + a**73 - 75*a**71 + 2697*a**69 - 61912*a**67 + 1019136*a**65 - 12810735*a**63 + 127871311*a**61 - 1040528484*a**59 + 7032379389*a**57 - 40014970501*a**55 + 193642785963*a**53 - 802995865776*a**51 + 2869329159060*a** 49 - 8870397717510*a**47 + 23788969715070*a**45 - 55432258571480*a**43 + 112291942440195*a**41 - 197682189118365*a**39 + 302033193611415*a**37 - 399617021355384*a**35 + 456405620770968*a**33 - 448064153547934*a**31 + 376075319011662*a**29 - 268067837674152*a**27 + 160940700083670*a**25 - 80564119669566*a**23 + 33210011708370*a**21 - 11101062696832*a**19 + 2951663620872*a**17 - 609173016756*a**15 + 94524522340*a**13 - 10565479056*a**11 + 801113049*a**9 - 37668379*a**7 + 947241*a**5 - 9528*a**3 + 16*a)}, {{2,5},0}, {{2,6},0}, {{2,7},0}, {{3,4},0}, {{3,5},zzz(7)}, {{3,6},0}, {{3,7},0}, {{4,5},0}, {{4,6},0}, {{4,7},0}, {{5,6},0}, {{5,7},0}, {{6,7},0}}$ !Since! commutation! relation! 24! is! not! simplified! we! force! !Reduce! to! further compute! and! simplify! all! relations! and! we! get:$ {{1,2},zzz(4)}.$ {{1,3},zzz(5)}.$ {{1,4},zzz(7)}.$ {{1,5},zzz(6)}.$ {{1,6},0}.$ {{1,7},0}.$ {{2,3},0}.$ {{2,4},zzz(6)}.$ {{2,5},0}.$ {{2,6},0}.$ {{2,7},0}.$ {{3,4},0}.$ {{3,5},zzz(7)}.$ {{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_{7,1.19}.$ Et cela pour a**2-4 neq 0.$