generic derivation : delta:= mat((0,xi(1,2),0,0,0,0),(0,0,0,0,0,0),(xi(3,1),xi(3,2),0,0,0,0),(xi(4,1),xi(4,2) ,0,0,0,0),(xi(5,1),xi(5,2),xi(5,3),xi(4,2) - xi(3,1),0,xi(1,2)),(xi(6,1),xi(6,2) ,xi(6,3), - xi(4,1),0,0))$ [0 0 0 0 0 0] [ ] [0 0 0 0 0 0] [ ] [0 0 0 0 0 0] adx1 := [ ] [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 0 0 0 0 0] [ ] [0 0 0 0 0 0] adx2 := [ ] [-1 0 0 0 0 0] [ ] [0 0 1 0 0 0] [ ] [0 0 0 1 0 0] [0 0 0 0 0 0] [ ] [0 0 0 0 0 0] [ ] [0 0 0 0 0 0] adx3 := [ ] [0 0 0 0 0 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 0 0 0 0 0] adx4 := [ ] [0 0 0 0 0 0] [ ] [-1 0 0 0 0 0] [ ] [0 -1 0 0 0 0] delta:= [ 0 xi(1,2) 0 0 0 0 ] [ ] [ 0 0 0 0 0 0 ] [ ] [xi(3,1) xi(3,2) 0 0 0 0 ] [ ] [ 0 0 0 0 0 0 ] [ ] [ 0 0 xi(5,3) - xi(3,1) 0 xi(1,2)] [ ] [xi(6,1) xi(6,2) xi(6,3) 0 0 0 ] We denote this delta by the shortform shortformdelta:={xi(1,2), ss, xi(3,1), xi(3,2), ss, xi(5,3), ss, xi(6,1), xi(6,2), xi(6,3)} paramindexeslist:={{1,2},{3,1},{3,2},{5,3},{6,1},{6,2},{6,3}} a neq {}$ a:=a$ delta:= mat((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,a,-1,0,0),(0,0, 1,0,0,0))$ shortformdelta:={0,ss,1,0,ss,a,ss,0,0,1}$ 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(1,1) + d(0, 0)$ Unknowns: {d(3,3),d(1,1),d(0,0)} Unknowns: {d(3,3),d(1,1),d(0,0)} bonne inconnue W:=d(3,3)$ sa valeur doit etre WW:=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(4,1) - d(4, 0) + d(3,1)*a$ Unknowns: {d(5,3),d(4,1),d(4,0),d(3,1),a} Unknowns: {d(5,3),d(4,1),d(4,0),d(3,1),a} bonne inconnue W:=d(5,3)$ sa valeur doit etre WW:= - d(4,1) - d(4,0) + d(3,1)*a$ on resout l'equation {{0,1},6} qui est maintenant AA:= - d(6,3) + d(3,1)$ Unknowns: {d(6,3),d(3,1)} Unknowns: {d(6,3),d(3,1)} bonne inconnue W:=d(6,3)$ sa valeur doit etre WW:=d(3,1)$ on resout l'equation {{0,2},3} 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 {{0,2},4} 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 {{0,2},5} qui est maintenant AA:= - d(4,2) + d(3,2)*a - d( 3,0)$ Unknowns: {d(4,2),d(3,2),d(3,0),a} Unknowns: {d(4,2),d(3,2),d(3,0),a} bonne inconnue W:=d(4,2)$ sa valeur doit etre WW:=d(3,2)*a - d(3,0)$ on resout l'equation {{0,2},6} qui est maintenant AA:= - d(4,0) + d(3,2)$ Unknowns: {d(4,0),d(3,2)} Unknowns: {d(4,0),d(3,2)} bonne inconnue W:=d(4,0)$ sa valeur doit etre WW:=d(3,2)$ on resout l'equation {{0,3},0} qui est maintenant AA:= - (d(0,6) + d(0,5)*a)$ Unknowns: {d(0,6),d(0,5),a} Unknowns: {d(0,6),d(0,5),a} bonne inconnue W:=d(0,6)$ sa valeur doit etre WW:= - d(0,5)*a$ on resout l'equation {{0,3},1} qui est maintenant AA:= - (d(1,6) + d(1,5)*a)$ Unknowns: {d(1,6),d(1,5),a} Unknowns: {d(1,6),d(1,5),a} bonne inconnue W:=d(1,6)$ sa valeur doit etre WW:= - d(1,5)*a$ on resout l'equation {{0,3},2} qui est maintenant AA:= - (d(2,6) + d(2,5)*a)$ Unknowns: {d(2,6),d(2,5),a} Unknowns: {d(2,6),d(2,5),a} bonne inconnue W:=d(2,6)$ sa valeur doit etre WW:= - d(2,5)*a$ on resout l'equation {{0,3},3} qui est maintenant AA:= - (d(3,6) + d(3,5)*a)$ Unknowns: {d(3,6),d(3,5),a} Unknowns: {d(3,6),d(3,5),a} bonne inconnue W:=d(3,6)$ sa valeur doit etre WW:= - d(3,5)*a$ on resout l'equation {{0,3},4} qui est maintenant AA:= - (d(4,6) + d(4,5)*a)$ Unknowns: {d(4,6),d(4,5),a} Unknowns: {d(4,6),d(4,5),a} bonne inconnue W:=d(4,6)$ sa valeur doit etre WW:= - d(4,5)*a$ on resout l'equation {{0,3},5} qui est maintenant AA:= - d(5,6) - d(5,5)*a + 2* d(2,0) + d(1,1)*a + 2*d(0,0)*a$ Unknowns: {d(5,6),d(5,5),d(2,0),d(1,1),d(0,0),a} Unknowns: {d(5,6),d(5,5),d(2,0),d(1,1),d(0,0),a} bonne inconnue W:=d(5,6)$ sa valeur doit etre WW:= - d(5,5)*a + 2*d(2,0) + d(1,1)*a + 2*d(0,0)*a$ on resout l'equation {{0,3},6} qui est maintenant AA:= - d(6,6) - d(6,5)*a + d( 1,1) + 2*d(0,0)$ Unknowns: {d(6,6),d(6,5),d(1,1),d(0,0),a} Unknowns: {d(6,6),d(6,5),d(1,1),d(0,0),a} bonne inconnue W:=d(6,6)$ sa valeur doit etre WW:= - d(6,5)*a + d(1,1) + 2*d(0,0)$ on resout l'equation {{0,4},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 {{0,4},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 {{0,4},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 {{0,4},3} qui est maintenant AA:=d(3,5) + d(1,4)$ Unknowns: {d(3,5),d(1,4)} Unknowns: {d(3,5),d(1,4)} bonne inconnue W:=d(3,5)$ sa valeur doit etre WW:= - d(1,4)$ on resout l'equation {{0,4},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 {{0,4},5} qui est maintenant AA:=d(5,5) - d(4,4) + d(3,4)* a - d(0,0)$ Unknowns: {d(5,5),d(4,4),d(3,4),d(0,0),a} Unknowns: {d(5,5),d(4,4),d(3,4),d(0,0),a} bonne inconnue W:=d(5,5)$ sa valeur doit etre WW:=d(4,4) - d(3,4)*a + d(0,0)$ on resout l'equation {{0,4},6} qui est maintenant AA:=d(6,5) + d(3,4) + d(2,0)$ Unknowns: {d(6,5),d(3,4),d(2,0)} Unknowns: {d(6,5),d(3,4),d(2,0)} bonne inconnue W:=d(6,5)$ sa valeur doit etre WW:= - (d(3,4) + d(2,0))$ on resout l'equation {{0,5},5} qui est maintenant AA:= - d(1,4)*a$ Unknowns: {d(1,4),a} Unknowns: {d(1,4),a} pas de selection possible de variable a coefficient numerique dans - d(1,4)*a on resout l'equation {{0,5},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 {{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},3} qui est maintenant AA:= - (d(3,4) + d(0,2))$ Unknowns: {d(3,4),d(0,2)} Unknowns: {d(3,4),d(0,2)} bonne inconnue W:=d(3,4)$ sa valeur doit etre WW:= - d(0,2)$ on resout l'equation {{1,2},4} qui est maintenant AA:= - d(4,4) + d(2,2) + d(1, 1)$ Unknowns: {d(4,4),d(2,2),d(1,1)} Unknowns: {d(4,4),d(2,2),d(1,1)} bonne inconnue W:=d(4,4)$ sa valeur doit etre WW:=d(2,2) + d(1,1)$ on resout l'equation {{1,2},5} qui est maintenant AA:= - d(5,4) + d(3,2)*a - d( 3,1) - d(3,0)$ Unknowns: {d(5,4),d(3,2),d(3,1),d(3,0),a} Unknowns: {d(5,4),d(3,2),d(3,1),d(3,0),a} bonne inconnue W:=d(3,1)$ sa valeur doit etre WW:= - d(5,4) + d(3,2)*a - d(3,0)$ on resout l'equation {{1,2},6} qui est maintenant AA:= - (d(6,4) + d(4,1))$ Unknowns: {d(6,4),d(4,1)} Unknowns: {d(6,4),d(4,1)} bonne inconnue W:=d(6,4)$ sa valeur doit etre WW:= - d(4,1)$ on resout l'equation {{1,3},5} qui est maintenant AA:=d(2,1) - d(2,0) + d(0,1)* a$ Unknowns: {d(2,1),d(2,0),d(0,1),a} Unknowns: {d(2,1),d(2,0),d(0,1),a} bonne inconnue W:=d(2,1)$ sa valeur doit etre WW:=d(2,0) - d(0,1)*a$ on resout l'equation {{1,3},6} 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 {{1,4},5} qui est maintenant AA:=d(1,1) - d(0,2)*a - d(0,0 )$ 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:=d(0,2)*a + d(0,0)$ on resout l'equation {{1,4},6} qui est maintenant AA:=2*d(2,0) - d(0,2)$ Unknowns: {d(2,0),d(0,2)} Unknowns: {d(2,0),d(0,2)} bonne inconnue W:=d(2,0)$ sa valeur doit etre WW:=d(0,2)/2$ on resout l'equation {{2,4},5} qui est maintenant AA:=d(2,2)*a + d(0,2)*a**2 - 3*d(0,2) - d(0,0)*a$ Unknowns: {d(2,2),d(0,2),d(0,0),a} Unknowns: {d(2,2),d(0,2),d(0,0),a} pas de selection possible de variable a coefficient numerique dans d(2,2)*a + d( 0,2)*a**2 - 3*d(0,2) - d(0,0)*a on resout l'equation {{2,4},6} qui est maintenant AA:=(4*d(2,2) + d(0,2)*a - 4* d(0,0))/2$ Unknowns: {d(2,2),d(0,2),d(0,0),a} Unknowns: {d(2,2),d(0,2),d(0,0),a} bonne inconnue W:=d(2,2)$ sa valeur doit etre WW:=( - d(0,2)*a + 4*d(0,0))/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},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},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},3},0}, {{{1,5},4},0}, {{{1,5},5},0}, {{{1,6},3},0}, {{{1,6},4},0}, {{{1,6},5},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},(3*d(0,2)*(a**2 - 4))/4}, {{{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},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 n'y a pas de phase 2$ a neq {2,-2}$ 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},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},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},3},0}, {{{1,5},4},0}, {{{1,5},5},0}, {{{1,6},3},0}, {{{1,6},4},0}, {{{1,6},5},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},4},0}, {{{2,5},5},0}, {{{2,5},6},0}, {{{2,6},4},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},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( 5,4) + d(3,2)*a - d(3,0),d(3,2),2*d(0,0),0,0,0),(d(3,2),d(4,1),d(3,2)*a - d(3,0) ,0,2*d(0,0),0,0),(d(5,0),d(5,1),d(5,2), - d(5,4)*a - d(4,1) + d(3,2)*a**2 - d(3, 2) - d(3,0)*a,d(5,4),3*d(0,0),0),(d(6,0),d(6,1),d(6,2), - d(5,4) + d(3,2)*a - d( 3,0), - d(4,1),0,3*d(0,0)))$ pour delta:= [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 a -1 0 0] [ ] [0 0 1 0 0 0] pour shortformdelta:={0,ss,1,0,ss,a,ss,0,0,1} Unknowns: {d(6,2), d(6,1), d(6,0), d(5,4), d(5,2), d(5,1), d(5,0), d(4,1), d(3,2), d(3,0), d(0,0), a} Unknowns: {d(6,2), d(6,1), d(6,0), d(5,4), d(5,2), d(5,1), d(5,0), d(4,1), d(3,2), d(3,0), d(0,0), a} listeparametresMATD{d(6,2), d(6,1), d(6,0), d(5,4), d(5,2), d(5,1), d(5,0), d(4,1), d(3,2), d(3,0), d(0,0)}$ dim Der(gtildedelta):=11$ t1:=D(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 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] 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)] rank 1 with maximal torus t1 1 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( 5,4) + d(3,2)*a - d(3,0),d(3,2),2*d(0,0),0,0,0),(d(3,2),d(4,1),d(3,2)*a - d(3,0) ,0,2*d(0,0),0,0),(d(5,0),d(5,1),d(5,2), - d(5,4)*a - d(4,1) + d(3,2)*a**2 - d(3, 2) - d(3,0)*a,d(5,4),3*d(0,0),0),(d(6,0),d(6,1),d(6,2), - d(5,4) + d(3,2)*a - d( 3,0), - d(4,1),0,3*d(0,0)))$ PP:= [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:= [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),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(5,4) + d(3,2)*a - d(3,0),d(3,2),2*d(0,0),0,0,0), (d(3,2),d(4,1),d(3,2)*a - d(3,0),0,2*d(0,0),0,0), 2 (d(5,0),d(5,1),d(5,2), - d(5,4)*a - d(4,1) + d(3,2)*a - d(3,2) - d(3,0)*a, d(5,4),3*d(0,0),0), (d(6,0),d(6,1),d(6,2), - d(5,4) + d(3,2)*a - d(3,0), - d(4,1),0,3*d(0,0))) on voit apparaitre les poids sur la diagonale r(1) := d(0,0) r(2) := d(0,0) r(3) := d(0,0) r(4) := 2*d(0,0) r(5) := 2*d(0,0) r(6) := 3*d(0,0) r(7) := 3*d(0,0) r(1) := gamma1 r(2) := gamma1 r(3) := gamma1 r(4) := 2*gamma1 r(5) := 2*gamma1 r(6) := 3*gamma1 r(7) := 3*gamma1 Le systeme de poids est le systeme 1.19 calcul de relations de commutation de la base diaY(j) diagonalisant le tore listcommutateursdesx := {{{0,1},x(3)}, {{0,2},0}, {{0,3},x(6) + x(5)*a}, {{0,4}, - x(5)}, {{0,5},0}, {{0,6},0}, {{1,2},x(4)}, {{1,3},0}, {{1,4},x(5)}, {{1,5},0}, {{1,6},0}, {{2,3},x(5)}, {{2,4},x(6)}, {{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},diay(4)}, {{1,3},0}, {{1,4},diay(7) + diay(6)*a}, {{1,5}, - diay(6)}, {{1,6},0}, {{1,7},0}, {{2,3},diay(5)}, {{2,4},0}, {{2,5},diay(6)}, {{2,6},0}, {{2,7},0}, {{3,4},diay(6)}, {{3,5},diay(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}}$ As a neq 2,-2 gtildedelta is isomorphic with$ g_{7,1.19}$ However this isomorphism is rather involved and will not be reproduced here.$ see the file calculisom6_8I.red$