generic derivation : delta:= mat((xi(1,1),0,0,0,0,0),(xi(2,1),xi(2,2),xi(2,3),0,0,0),( - xi(2,3),0,(xi(2,2) + xi(1,1))/2,0,0,0),(xi(4,1),xi(4,2),xi(4,3),xi(2,2) + xi(1,1),xi(2,3),0),(xi(5,1 ),0,xi(5,3),0,(xi(2,2) + 3*xi(1,1))/2,0),(xi(6,1),xi(6,2),xi(6,3),xi(4,2), - xi( 5,1) + xi(4,3),xi(2,2) + 2*xi(1,1)))$ [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 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] adx2 := [ ] [-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 0] [ ] [0 0 0 0 0 0] adx3 := [ ] [0 0 0 0 0 0] [ ] [-1 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 0 0 0 0] adx4 := [ ] [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 0 0] [ ] [0 0 0 0 0 0] adx5 := [ ] [0 0 0 0 0 0] [ ] [0 0 0 0 0 0] [ ] [0 0 -1 0 0 0] The generic nilpotent derivation : the eigenvalues are 0 xi(1,1):=0 xi(2,2):=0 by subtracting adjoints one then may suppose: xi(4,1):=0,xi(4,2):=0,xi(5,1):=0,xi(6,1):=0,xi(6,3):=0 delta:= [ 0 0 0 0 0 0] [ ] [ xi(2,1) 0 xi(2,3) 0 0 0] [ ] [ - xi(2,3) 0 0 0 0 0] [ ] [ 0 0 xi(4,3) 0 xi(2,3) 0] [ ] [ 0 0 xi(5,3) 0 0 0] [ ] [ 0 xi(6,2) 0 0 xi(4,3) 0] We denote this delta by the shortform shortformdelta:={xi(2,1), xi(2,3), ss, xi(4,3), ss, xi(5,3), ss, xi(6,2)} paramindexeslist:={{2,1},{2,3},{4,3},{5,3},{6,2}} a neq {}$ a:=a$ delta:= mat((0,0,0,0,0,0),(a,0,0,0,0,0),(0,0,0,0,0,0),(0,0,1,0,0,0),(0,0,0,0,0,0),(0,1,0 ,0,1,0))$ shortformdelta:={a,0,ss,1,ss,0,ss,1}$ on resout l'equation {{0,1},0} qui est maintenant AA:= - d(0,2)*a$ Unknowns: {d(0,2),a} Unknowns: {d(0,2),a} pas de selection possible de variable a coefficient numerique dans - d(0,2)*a on resout l'equation {{0,1},1} qui est maintenant AA:= - d(1,2)*a$ Unknowns: {d(1,2),a} Unknowns: {d(1,2),a} pas de selection possible de variable a coefficient numerique dans - d(1,2)*a on resout l'equation {{0,1},2} qui est maintenant AA:=a*( - d(2,2) + d(1,1) + d (0,0))$ Unknowns: {d(2,2),d(1,1),d(0,0),a} Unknowns: {d(2,2),d(1,1),d(0,0),a} pas de selection possible de variable a coefficient numerique dans a*( - d(2,2) + d(1,1) + d(0,0)) on resout l'equation {{0,1},3} qui est maintenant AA:= - d(3,2)*a$ Unknowns: {d(3,2),a} Unknowns: {d(3,2),a} pas de selection possible de variable a coefficient numerique dans - d(3,2)*a on resout l'equation {{0,1},4} qui est maintenant AA:= - d(4,2)*a + d(3,1) - 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(3,1)$ sa valeur doit etre WW:=d(4,2)*a + d(2,0)$ on resout l'equation {{0,1},5} qui est maintenant AA:= - (d(5,2)*a + d(3,0))$ Unknowns: {d(5,2),d(3,0),a} Unknowns: {d(5,2),d(3,0),a} bonne inconnue W:=d(3,0)$ sa valeur doit etre WW:= - d(5,2)*a$ on resout l'equation {{0,1},6} qui est maintenant AA:= - d(6,2)*a + d(5,1) - d( 4,0) + d(2,1)$ Unknowns: {d(6,2),d(5,1),d(4,0),d(2,1),a} Unknowns: {d(6,2),d(5,1),d(4,0),d(2,1),a} bonne inconnue W:=d(5,1)$ sa valeur doit etre WW:=d(6,2)*a + d(4,0) - d(2,1)$ on resout l'equation {{0,2},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 {{0,2},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 {{0,2},2} qui est maintenant AA:= - d(2,6) + d(1,2)*a$ Unknowns: {d(2,6),d(1,2),a} Unknowns: {d(2,6),d(1,2),a} bonne inconnue W:=d(2,6)$ sa valeur doit etre WW:=d(1,2)*a$ on resout l'equation {{0,2},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 {{0,2},4} qui est maintenant AA:= - d(4,6) + d(3,2) + d(1, 0)$ Unknowns: {d(4,6),d(3,2),d(1,0)} Unknowns: {d(4,6),d(3,2),d(1,0)} bonne inconnue W:=d(4,6)$ sa valeur doit etre WW:=d(3,2) + d(1,0)$ on resout l'equation {{0,2},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 {{0,2},6} qui est maintenant AA:= - d(6,6) + d(5,2) + d(2, 2) + d(0,0)$ Unknowns: {d(6,6),d(5,2),d(2,2),d(0,0)} Unknowns: {d(6,6),d(5,2),d(2,2),d(0,0)} bonne inconnue W:=d(6,6)$ sa valeur doit etre WW:=d(5,2) + d(2,2) + d(0,0)$ 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) + d(1,3)*a$ Unknowns: {d(2,4),d(1,3),a} Unknowns: {d(2,4),d(1,3),a} bonne inconnue W:=d(2,4)$ sa valeur doit etre WW:=d(1,3)*a$ 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(1,0)$ Unknowns: {d(5,4),d(1,0)} Unknowns: {d(5,4),d(1,0)} bonne inconnue W:=d(5,4)$ sa valeur doit etre WW:=d(1,0)$ on resout l'equation {{0,3},6} qui est maintenant AA:= - d(6,4) + d(5,3) - d(5, 0) + d(2,3)$ Unknowns: {d(6,4),d(5,3),d(5,0),d(2,3)} Unknowns: {d(6,4),d(5,3),d(5,0),d(2,3)} bonne inconnue W:=d(6,4)$ sa valeur doit etre WW:=d(5,3) - d(5,0) + d(2,3)$ on resout l'equation {{0,4},6} qui est maintenant AA:=d(1,3)*a + 2*d(1,0)$ Unknowns: {d(1,3),d(1,0),a} Unknowns: {d(1,3),d(1,0),a} bonne inconnue W:=d(1,0)$ sa valeur doit etre WW:=( - d(1,3)*a)/2$ on resout l'equation {{0,5},2} qui est maintenant AA:=a*(d(1,5) - d(1,2))$ Unknowns: {d(1,5),d(1,2),a} Unknowns: {d(1,5),d(1,2),a} pas de selection possible de variable a coefficient numerique dans a*(d(1,5) - d (1,2)) on resout l'equation {{0,5},4} qui est maintenant AA:=(2*d(3,5) - 2*d(3,2) + d( 1,3)*a)/2$ Unknowns: {d(3,5),d(3,2),d(1,3),a} Unknowns: {d(3,5),d(3,2),d(1,3),a} bonne inconnue W:=d(3,5)$ sa valeur doit etre WW:=(2*d(3,2) - d(1,3)*a)/2$ on resout l'equation {{0,5},6} qui est maintenant AA:=d(5,5) - d(5,2)*a - d(5,2 ) + d(2,5) - d(2,2)$ Unknowns: {d(5,5),d(5,2),d(2,5),d(2,2),a} Unknowns: {d(5,5),d(5,2),d(2,5),d(2,2),a} bonne inconnue W:=d(5,5)$ sa valeur doit etre WW:=d(5,2)*a + d(5,2) - d(2,5) + d(2,2)$ on resout l'equation {{0,6},6} qui est maintenant AA:=d(1,2)*a$ Unknowns: {d(1,2),a} Unknowns: {d(1,2),a} pas de selection possible de variable a coefficient numerique dans d(1,2)*a on resout l'equation {{1,2},2} qui est maintenant AA:= - a*(d(1,3) + d(0,2))$ Unknowns: {d(1,3),d(0,2),a} Unknowns: {d(1,3),d(0,2),a} pas de selection possible de variable a coefficient numerique dans - a*(d(1,3) + d(0,2)) 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:=(2*d(3,2) + d(1,3)*a)/2$ Unknowns: {d(3,2),d(1,3),a} Unknowns: {d(3,2),d(1,3),a} bonne inconnue W:=d(3,2)$ sa valeur doit etre WW:=( - d(1,3)*a)/2$ on resout l'equation {{1,2},6} qui est maintenant AA:= - d(5,3) + d(5,0) + d(4, 2) - d(2,3) + d(0,1)$ Unknowns: {d(5,3),d(5,0),d(4,2),d(2,3),d(0,1)} Unknowns: {d(5,3),d(5,0),d(4,2),d(2,3),d(0,1)} bonne inconnue W:=d(5,3)$ sa valeur doit etre WW:=d(5,0) + d(4,2) - d(2,3) + d(0,1)$ on resout l'equation {{1,3},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 {{1,3},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 {{1,3},2} qui est maintenant AA:= - (d(2,5) + d(0,3)*a)$ Unknowns: {d(2,5),d(0,3),a} Unknowns: {d(2,5),d(0,3),a} bonne inconnue W:=d(2,5)$ sa valeur doit etre WW:= - d(0,3)*a$ on resout l'equation {{1,3},3} qui est maintenant AA:=d(1,3)*a$ Unknowns: {d(1,3),a} Unknowns: {d(1,3),a} pas de selection possible de variable a coefficient numerique dans d(1,3)*a on resout l'equation {{1,3},4} qui est maintenant AA:= - d(4,5) + d(2,3) + d(0, 1)$ Unknowns: {d(4,5),d(2,3),d(0,1)} Unknowns: {d(4,5),d(2,3),d(0,1)} bonne inconnue W:=d(4,5)$ sa valeur doit etre WW:=d(2,3) + d(0,1)$ on resout l'equation {{1,3},5} qui est maintenant AA:= - d(5,2)*a - d(5,2) + 2* d(1,1) - d(0,3)*a - d(0,0)$ Unknowns: {d(5,2),d(1,1),d(0,3),d(0,0),a} Unknowns: {d(5,2),d(1,1),d(0,3),d(0,0),a} bonne inconnue W:=d(1,1)$ sa valeur doit etre WW:=(d(5,2)*a + d(5,2) + d(0,3)*a + d(0,0))/2$ on resout l'equation {{1,3},6} qui est maintenant AA:= - d(6,5) - d(6,2)*a + d( 4,3) - d(4,0) + d(2,1)$ Unknowns: {d(6,5),d(6,2),d(4,3),d(4,0),d(2,1),a} Unknowns: {d(6,5),d(6,2),d(4,3),d(4,0),d(2,1),a} bonne inconnue W:=d(6,5)$ sa valeur doit etre WW:= - d(6,2)*a + d(4,3) - d(4,0) + d(2,1)$ on resout l'equation {{1,4},2} qui est maintenant AA:= - d(1,2)*a$ Unknowns: {d(1,2),a} Unknowns: {d(1,2),a} pas de selection possible de variable a coefficient numerique dans - d(1,2)*a on resout l'equation {{1,4},4} qui est maintenant AA:=2*d(1,3)*a$ Unknowns: {d(1,3),a} Unknowns: {d(1,3),a} pas de selection possible de variable a coefficient numerique dans 2*d(1,3)*a on resout l'equation {{1,4},6} qui est maintenant AA:=a*(d(5,2) + d(0,3))$ Unknowns: {d(5,2),d(0,3),a} Unknowns: {d(5,2),d(0,3),a} pas de selection possible de variable a coefficient numerique dans a*(d(5,2) + d (0,3)) on resout l'equation {{1,5},4} qui est maintenant AA:= - d(0,3)*a$ Unknowns: {d(0,3),a} Unknowns: {d(0,3),a} pas de selection possible de variable a coefficient numerique dans - d(0,3)*a on resout l'equation {{1,5},5} qui est maintenant AA:= - d(1,3)*a$ Unknowns: {d(1,3),a} Unknowns: {d(1,3),a} pas de selection possible de variable a coefficient numerique dans - d(1,3)*a on resout l'equation {{1,5},6} qui est maintenant AA:=d(4,2)*a + d(2,3) + d(2,0 ) + 2*d(0,1)$ Unknowns: {d(4,2),d(2,3),d(2,0),d(0,1),a} Unknowns: {d(4,2),d(2,3),d(2,0),d(0,1),a} bonne inconnue W:=d(2,3)$ sa valeur doit etre WW:= - d(4,2)*a - d(2,0) - 2*d(0,1)$ on resout l'equation {{1,6},4} qui est maintenant AA:=d(1,2)*a$ Unknowns: {d(1,2),a} Unknowns: {d(1,2),a} pas de selection possible de variable a coefficient numerique dans d(1,2)*a on resout l'equation {{1,6},6} qui est maintenant AA:= - d(1,3)*a$ Unknowns: {d(1,3),a} Unknowns: {d(1,3),a} pas de selection possible de variable a coefficient numerique dans - d(1,3)*a 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)$ Unknown: d(1,2) Unknown: d(1,2) bonne inconnue W:=d(1,2)$ sa valeur doit etre WW:=0$ on resout l'equation {{2,3},6} qui est maintenant AA:= - (d(5,2) + d(0,3))$ Unknowns: {d(5,2),d(0,3)} Unknowns: {d(5,2),d(0,3)} bonne inconnue W:=d(5,2)$ sa valeur doit etre WW:= - d(0,3)$ on resout l'equation {{2,5},6} qui est maintenant AA:=(d(0,2)*( - a + 2))/2$ Unknowns: {d(0,2),a} Unknowns: {d(0,2),a} pas de selection possible de variable a coefficient numerique dans (d(0,2)*( - a + 2))/2 on resout l'equation {{3,4},6} qui est maintenant AA:=(d(0,2)*( - a + 2))/2$ Unknowns: {d(0,2),a} Unknowns: {d(0,2),a} pas de selection possible de variable a coefficient numerique dans (d(0,2)*( - a + 2))/2 on resout l'equation {{3,5},4} qui est maintenant AA:=d(0,2)*a$ Unknowns: {d(0,2),a} Unknowns: {d(0,2),a} pas de selection possible de variable a coefficient numerique dans d(0,2)*a on resout l'equation {{3,5},6} qui est maintenant AA:=(2*d(2,2) + d(0,3) - 3*d( 0,0))/2$ Unknowns: {d(2,2),d(0,3),d(0,0)} Unknowns: {d(2,2),d(0,3),d(0,0)} bonne inconnue W:=d(2,2)$ sa valeur doit etre WW:=( - d(0,3) + 3*d(0,0))/2$ Derivation equations to cancel (Reduce output) : \\{{{{0,1},0}, - d(0,2)*a}, {{{0,1},1},0}, {{{0,1},2},0}, {{{0,1},3},(d(0,2)*a**2)/2}, {{{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},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},6},0}, {{{1,2},0},0}, {{{1,2},1},0}, {{{1,2},2}, - 2*d(0,2)*a}, {{{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},d(0,2)*a}, {{{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},2*d(0,2)*a}, {{{1,4},5},0}, {{{1,4},6},0}, {{{1,5},2},0}, {{{1,5},4}, - d(0,3)*a}, {{{1,5},5}, - d(0,2)*a}, {{{1,5},6},0}, {{{1,6},2},0}, {{{1,6},4},0}, {{{1,6},5},0}, {{{1,6},6}, - d(0,2)*a}, {{{2,3},4},0}, {{{2,3},5},0}, {{{2,3},6},0}, {{{2,4},4},0}, {{{2,4},6},0}, {{{2,5},4},0}, {{{2,5},6},(d(0,2)*( - a + 2))/2}, {{{2,6},4},0}, {{{2,6},6},0}, {{{3,4},4},0}, {{{3,4},5},0}, {{{3,4},6},(d(0,2)*( - a + 2))/2}, {{{3,5},0},0}, {{{3,5},1},0}, {{{3,5},2},0}, {{{3,5},3},0}, {{{3,5},4},d(0,2)*a}, {{{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$ 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},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},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},4},0}, {{{2,3},5},0}, {{{2,3},6},0}, {{{2,4},4},0}, {{{2,4},6},0}, {{{2,5},4},0}, {{{2,5},6},0}, {{{2,6},4},0}, {{{2,6},6},0}, {{{3,4},4},0}, {{{3,4},5},0}, {{{3,4},6},0}, {{{3,5},0},0}, {{{3,5},1},0}, {{{3,5},2},0}, {{{3,5},3},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}}$ a neq {0}$ derivation generique de gtildedelta:$ MATD:= mat((d(0,0),d(0,1),0,0,0,0,0),(0,d(0,0)/2,0,0,0,0,0),(d(2,0),d(2,1),(3*d(0,0))/2 , - (d(2,0) + 2*d(0,1) + d(4,2)*a),0,0,0),(0,d(4,2)*a + d(2,0),0,d(0,0),0,0,0),( d(4,0),d(4,1),d(4,2),d(4,3),2*d(0,0), - (d(2,0) + d(0,1) + d(4,2)*a),0),(d(5,0), d(4,0) - d(2,1) + d(6,2)*a,0,d(2,0) + 3*d(0,1) + (a + 1)*d(4,2) + d(5,0),0,(3*d( 0,0))/2,0),(d(6,0),d(6,1),d(6,2),d(6,3),d(4,2) + d(0,1), - (d(4,0) - d(2,1) - d( 4,3) + d(6,2)*a),(5*d(0,0))/2))$ pour delta:= [0 0 0 0 0 0] [ ] [a 0 0 0 0 0] [ ] [0 0 0 0 0 0] [ ] [0 0 1 0 0 0] [ ] [0 0 0 0 0 0] [ ] [0 1 0 0 1 0] pour shortformdelta:={a,0,ss,1,ss,0,ss,1} 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), a} 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), a} 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$ t1:=D(0,0):= [1 0 0 0 0 0 0 ] [ ] [ 1 ] [0 --- 0 0 0 0 0 ] [ 2 ] [ ] [ 3 ] [0 0 --- 0 0 0 0 ] [ 2 ] [ ] [0 0 0 1 0 0 0 ] [ ] [0 0 0 0 2 0 0 ] [ ] [ 3 ] [0 0 0 0 0 --- 0 ] [ 2 ] [ ] [ 5 ] [0 0 0 0 0 0 ---] [ 2 ] MATD:= mat((d(0,0),d(0,1),0,0,0,0,0), d(0,0) (0,--------,0,0,0,0,0), 2 3*d(0,0) (d(2,0),d(2,1),----------, - (d(2,0) + 2*d(0,1) + d(4,2)*a),0,0,0), 2 (0,d(4,2)*a + d(2,0),0,d(0,0),0,0,0), (d(4,0),d(4,1),d(4,2),d(4,3),2*d(0,0), - (d(2,0) + d(0,1) + d(4,2)*a),0), (d(5,0),d(4,0) - d(2,1) + d(6,2)*a,0, 3*d(0,0) d(2,0) + 3*d(0,1) + (a + 1)*d(4,2) + d(5,0),0,----------,0), 2 (d(6,0),d(6,1),d(6,2),d(6,3),d(4,2) + d(0,1), 5*d(0,0) - (d(4,0) - d(2,1) - d(4,3) + d(6,2)*a),----------)) 2 Unknown: d(0,0) Unknown: d(0,0) commutant de t1 dans der(gtildedelta): [d(0,0) 0 0 0 0 0 0 ] [ ] [ d(0,0) ] [ 0 -------- 0 0 0 0 0 ] [ 2 ] [ ] [ 3*d(0,0) ] [ 0 0 ---------- 0 0 0 0 ] [ 2 ] [ ] [ 0 0 0 d(0,0) 0 0 0 ] [ ] [ 0 0 0 0 2*d(0,0) 0 0 ] [ ] [ 3*d(0,0) ] [ 0 0 0 0 0 ---------- 0 ] [ 2 ] [ ] [ 5*d(0,0) ] [ 0 0 0 0 0 0 ----------] [ 2 ] *********** gtildedelta est caracteristiquement nilpotente MATD**1:= mat((d(0,0),d(0,1),0,0,0,0,0), d(0,0) (0,--------,0,0,0,0,0), 2 3*d(0,0) (d(2,0),d(2,1),----------, - (d(2,0) + 2*d(0,1)),0,0,0), 2 (0,d(2,0),0,d(0,0),0,0,0), (d(4,0),d(4,1),d(4,2),d(4,3),2*d(0,0), - (d(2,0) + d(0,1)),0), 3*d(0,0) (d(5,0),d(4,0) - d(2,1),0,d(2,0) + 3*d(0,1) + d(4,2) + d(5,0),0,----------,0 2 ), (d(6,0),d(6,1),d(6,2),d(6,3),d(4,2) + d(0,1), - (d(4,0) - d(2,1) - d(4,3)), 5*d(0,0) ----------)) 2 MATD**2:= 2 3*d(0,1)*d(0,0) mat((d(0,0) ,-----------------,0,0,0,0,0), 2 2 d(0,0) (0,---------,0,0,0,0,0), 4 2 5*d(2,0)*d(0,0) 2 9*d(0,0) (-----------------,2*d(2,1)*d(0,0) - d(2,0) - d(2,0)*d(0,1),-----------, 2 4 - 5*(d(2,0) + 2*d(0,1))*d(0,0) ---------------------------------,0,0,0), 2 3*d(2,0)*d(0,0) 2 (0,-----------------,0,d(0,0) ,0,0,0), 2 (d(4,2)*d(2,0) + 3*d(4,0)*d(0,0) - (d(2,0) + d(0,1))*d(5,0),(5*d(4,1)*d(0,0) + 2*d(4,0)*d(0,1) + 2*d(4,2)*d(2,1) + 2*d(4,3)*d(2,0) 7*d(4,2)*d(0,0) - 2*(d(4,0) - d(2,1))*(d(2,0) + d(0,1)))/2,-----------------, - ( 2 (d(2,0) + 3*d(0,1) + d(4,2) + d(5,0))*(d(2,0) + d(0,1)) 2 + (d(2,0) + 2*d(0,1))*d(4,2) - 3*d(4,3)*d(0,0)),4*d(0,0) , - 7*(d(2,0) + d(0,1))*d(0,0) -------------------------------,0), 2 5*d(5,0)*d(0,0) (-----------------,(d(2,0) + 3*d(0,1) + d(4,2) + d(5,0))*d(2,0) 2 + 2*(d(4,0) - d(2,1))*d(0,0) + d(5,0)*d(0,1),0, 2 5*(d(2,0) + 3*d(0,1) + d(4,2) + d(5,0))*d(0,0) 9*d(0,0) ------------------------------------------------,0,-----------,0), 2 4 ((2*d(6,2)*d(2,0) + 7*d(6,0)*d(0,0) + 2*(d(4,2) + d(0,1))*d(4,0) - 2*(d(4,0) - d(2,1) - d(4,3))*d(5,0))/2,3*d(6,1)*d(0,0) + d(6,0)*d(0,1) + d(6,2)*d(2,1) + d(6,3)*d(2,0) + (d(4,2) + d(0,1))*d(4,1) - (d(4,0) - d(2,1) - d(4,3))*(d(4,0) - d(2,1)), (d(4,2) + d(0,1))*d(4,2) + 4*d(6,2)*d(0,0),( - ( 2*(d(2,0) + 3*d(0,1) + d(4,2) + d(5,0))*(d(4,0) - d(2,1) - d(4,3)) + 2*(d(2,0) + 2*d(0,1))*d(6,2) - 7*d(6,3)*d(0,0) 9*(d(4,2) + d(0,1))*d(0,0) - 2*(d(4,2) + d(0,1))*d(4,3)))/2,----------------------------, - ( 2 4*(d(4,0) - d(2,1) - d(4,3))*d(0,0) 2 25*d(0,0) + (d(4,2) + d(0,1))*(d(2,0) + d(0,1))),------------)) 4 MATD**3:= 2 3 7*d(0,1)*d(0,0) mat((d(0,0) ,------------------,0,0,0,0,0), 4 3 d(0,0) (0,---------,0,0,0,0,0), 8 2 19*d(2,0)*d(0,0) (-------------------, 4 2 3 (13*d(2,1)*d(0,0) - 12*d(2,0) - 12*d(2,0)*d(0,1))*d(0,0) 27*d(0,0) -----------------------------------------------------------,------------, 4 8 2 - 19*(d(2,0) + 2*d(0,1))*d(0,0) -----------------------------------,0,0,0), 4 2 7*d(2,0)*d(0,0) 3 (0,------------------,0,d(0,0) ,0,0,0), 4 (( - (9*d(5,0)*d(2,0) + 9*d(5,0)*d(0,1) - 9*d(4,2)*d(2,0) - 14*d(4,0)*d(0,0)) 2 *d(0,0))/2,( - (4*d(5,0)*d(2,0) + 8*d(5,0)*d(2,0)*d(0,1) 2 + 4*d(5,0)*d(0,1) - 14*d(4,3)*d(2,0)*d(0,0) 2 - 16*d(4,2)*d(2,1)*d(0,0) + 8*d(4,2)*d(2,0) 2 + 8*d(4,2)*d(2,0)*d(0,1) - 21*d(4,1)*d(0,0) + 16*d(4,0)*d(2,0)*d(0,0) + 2*d(4,0)*d(0,1)*d(0,0) - 16*d(2,1)*d(2,0)*d(0,0) - 16*d(2,1)*d(0,1)*d(0,0) 3 2 2 + 4*d(2,0) + 16*d(2,0) *d(0,1) + 12*d(2,0)*d(0,1) ))/4, 2 37*d(4,2)*d(0,0) -------------------,( - ( 4 9*(d(2,0) + 3*d(0,1) + d(4,2) + d(5,0))*(d(2,0) + d(0,1)) - (14*d(4,3)*d(0,0) - 9*d(4,2)*d(2,0) - 18*d(4,2)*d(0,1)))*d(0,0))/2 2 3 - 37*(d(2,0) + d(0,1))*d(0,0) ,8*d(0,0) ,---------------------------------,0), 4 2 19*d(5,0)*d(0,0) (-------------------,((12*(d(2,0) + 3*d(0,1) + d(4,2) + d(5,0))*d(2,0) 4 + 12*d(5,0)*d(0,1) + 13*d(4,0)*d(0,0) - 13*d(2,1)*d(0,0))*d(0,0))/4, 2 3 19*(d(2,0) + 3*d(0,1) + d(4,2) + d(5,0))*d(0,0) 27*d(0,0) 0,--------------------------------------------------,0,------------,0), 4 8 ((2*((5*d(6,2)*d(2,0) + 2*d(6,0)*d(0,0))*d(0,0) - 2*(d(4,2) + d(0,1))*(d(2,0) + d(0,1))*d(5,0) + 2*(d(4,2)*d(2,0) + 3*d(4,0)*d(0,0))*(d(4,2) + d(0,1)) - 10*(d(4,0) - d(2,1) - d(4,3))*d(5,0)*d(0,0)) + 5 *(2*d(6,2)*d(2,0) + 7*d(6,0)*d(0,0) + 2*(d(4,2) + d(0,1))*d(4,0))*d(0,0))/ 2 4,(6*d(6,3)*d(2,0)*d(0,0) + 8*d(6,2)*d(2,1)*d(0,0) - 4*d(6,2)*d(2,0) 2 - 4*d(6,2)*d(2,0)*d(0,1) + d(6,1)*d(0,0) + 6*d(6,0)*d(0,1)*d(0,0) - 4*(d(4,2) + d(0,1))*(d(4,0) - d(2,1))*(d(2,0) + d(0,1)) - 10*(d(4,0) - d(2,1) - d(4,3))*(d(4,0) - d(2,1))*d(0,0) - 4 *(2*(d(4,0) - d(2,1))*d(0,0) + d(5,0)*d(0,1))*(d(4,0) - d(2,1) - d(4,3)) - 4*(d(2,0) + 3*d(0,1) + d(4,2) + d(5,0))*(d(4,0) - d(2,1) - d(4,3)) *d(2,0) + 2 *(5*d(4,1)*d(0,0) + 2*d(4,0)*d(0,1) + 2*d(4,2)*d(2,1) + 2*d(4,3)*d(2,0)) *(d(4,2) + d(0,1)) + 10*(3*d(6,1)*d(0,0) + d(6,0)*d(0,1) + d(6,2)*d(2,1) + d(6,3)*d(2,0) + (d(4,2) + d(0,1))*d(4,1))*d(0,0))/4, (24*(d(4,2) + d(0,1))*d(4,2) + 49*d(6,2)*d(0,0))*d(0,0) ---------------------------------------------------------,( - (20 4 *(d(2,0) + 3*d(0,1) + d(4,2) + d(5,0))*(d(4,0) - d(2,1) - d(4,3)) *d(0,0) + 4*(d(2,0) + 3*d(0,1) + d(4,2) + d(5,0))*(d(4,2) + d(0,1)) 2 *(d(2,0) + d(0,1)) - (39*d(6,3)*d(0,0) - 20*d(6,2)*d(2,0)*d(0,0) - 40*d(6,2)*d(0,1)*d(0,0) + 22*d(4,3)*d(4,2)*d(0,0) 2 2 + 22*d(4,3)*d(0,1)*d(0,0) - 4*d(4,2) *d(2,0) - 8*d(4,2) *d(0,1) 2 - 4*d(4,2)*d(2,0)*d(0,1) - 8*d(4,2)*d(0,1) )))/4, 2 61*(d(4,2) + d(0,1))*d(0,0) ------------------------------,( - (49*(d(4,0) - d(2,1) - d(4,3))*d(0,0) 4 3 125*d(0,0) + 24*(d(4,2) + d(0,1))*(d(2,0) + d(0,1)))*d(0,0))/4,-------------)) 8 MATD**4:= 3 4 15*d(0,1)*d(0,0) mat((d(0,0) ,-------------------,0,0,0,0,0), 8 4 d(0,0) (0,---------,0,0,0,0,0), 16 3 65*d(2,0)*d(0,0) (-------------------, 8 2 2 4 5*(4*d(2,1)*d(0,0) - 5*d(2,0) - 5*d(2,0)*d(0,1))*d(0,0) 81*d(0,0) -----------------------------------------------------------,------------, 4 16 3 - 65*(d(2,0) + 2*d(0,1))*d(0,0) -----------------------------------,0,0,0), 8 3 15*d(2,0)*d(0,0) 4 (0,-------------------,0,d(0,0) ,0,0,0), 8 (( - 5*(11*d(5,0)*d(2,0) + 11*d(5,0)*d(0,1) - 11*d(4,2)*d(2,0) 2 2 - 12*d(4,0)*d(0,0))*d(0,0) )/4,( - 5*(8*d(5,0)*d(2,0) 2 + 16*d(5,0)*d(2,0)*d(0,1) + 8*d(5,0)*d(0,1) - 14*d(4,3)*d(2,0)*d(0,0) - 18*d(4,2)*d(2,1)*d(0,0) 2 2 + 16*d(4,2)*d(2,0) + 16*d(4,2)*d(2,0)*d(0,1) - 17*d(4,1)*d(0,0) + 18*d(4,0)*d(2,0)*d(0,0) + 4*d(4,0)*d(0,1)*d(0,0) 3 - 18*d(2,1)*d(2,0)*d(0,0) - 18*d(2,1)*d(0,1)*d(0,0) + 8*d(2,0) 2 2 + 32*d(2,0) *d(0,1) + 24*d(2,0)*d(0,1) )*d(0,0))/8, 3 175*d(4,2)*d(0,0) --------------------,( - 5*( 8 11*(d(2,0) + 3*d(0,1) + d(4,2) + d(5,0))*(d(2,0) + d(0,1)) 2 - (12*d(4,3)*d(0,0) - 11*d(4,2)*d(2,0) - 22*d(4,2)*d(0,1)))*d(0,0) ) 3 4 - 175*(d(2,0) + d(0,1))*d(0,0) /4,16*d(0,0) ,----------------------------------,0), 8 3 65*d(5,0)*d(0,0) (-------------------,(5*(5*(d(2,0) + 3*d(0,1) + d(4,2) + d(5,0))*d(2,0) 8 2 + 5*d(5,0)*d(0,1) + 4*d(4,0)*d(0,0) - 4*d(2,1)*d(0,0))*d(0,0) )/4,0, 3 4 65*(d(2,0) + 3*d(0,1) + d(4,2) + d(5,0))*d(0,0) 81*d(0,0) --------------------------------------------------,0,------------,0), 8 16 2 (((138*d(6,2)*d(2,0)*d(0,0) + 203*d(6,0)*d(0,0) + 138*d(5,0)*d(4,3)*d(0,0) - 56*d(5,0)*d(4,2)*d(2,0) - 56*d(5,0)*d(4,2)*d(0,1) - 138*d(5,0)*d(4,0)*d(0,0) + 138*d(5,0)*d(2,1)*d(0,0) 2 2 - 56*d(5,0)*d(2,0)*d(0,1) - 56*d(5,0)*d(0,1) + 56*d(4,2) *d(2,0) + 166*d(4,2)*d(4,0)*d(0,0) + 56*d(4,2)*d(2,0)*d(0,1) + 166*d(4,0)*d(0,1)*d(0,0))*d(0,0))/8,( - ((2*(d(4,0) - d(2,1) - d(4,3)) *(12*d(5,0)*d(0,1) + 13*d(4,0)*d(0,0) - 13*d(2,1)*d(0,0)) - ( 14*d(6,3)*d(2,0)*d(0,0) + 26*d(6,2)*d(2,1)*d(0,0) 2 2 - 24*d(6,2)*d(2,0) - 24*d(6,2)*d(2,0)*d(0,1) + d(6,1)*d(0,0) + 14*d(6,0)*d(0,1)*d(0,0)) + 24 *(d(2,0) + 3*d(0,1) + d(4,2) + d(5,0))*(d(4,0) - d(2,1) - d(4,3)) *d(2,0) - 8*(5*d(4,1)*d(0,0) + 2*d(4,0)*d(0,1) + 2*d(4,2)*d(2,1) + 2*d(4,3)*d(2,0))*(d(4,2) + d(0,1)))*d(0,0) - 2*( 2 6*d(4,3)*d(2,0)*d(0,0) + 8*d(4,2)*d(2,1)*d(0,0) - 4*d(4,2)*d(2,0) 2 - 4*d(4,2)*d(2,0)*d(0,1) + d(4,1)*d(0,0) + 6*d(4,0)*d(0,1)*d(0,0) - 8*(d(4,0) - d(2,1))*(d(2,0) + d(0,1))*d(0,0) - 4 *(2*(d(4,0) - d(2,1))*d(0,0) + d(5,0)*d(0,1))*(d(2,0) + d(0,1)) - 4*(d(2,0) + 3*d(0,1) + d(4,2) + d(5,0))*(d(2,0) + d(0,1))*d(2,0)) *(d(4,2) + d(0,1)) - 50*(3*d(6,1)*d(0,0) + d(6,0)*d(0,1) + d(6,2)*d(2,1) + d(6,3)*d(2,0) + (d(4,2) + d(0,1))*d(4,1)) 2 *d(0,0) - 5*(6*d(6,3)*d(2,0)*d(0,0) + 8*d(6,2)*d(2,1)*d(0,0) 2 2 - 4*d(6,2)*d(2,0) - 4*d(6,2)*d(2,0)*d(0,1) + d(6,1)*d(0,0) + 6*d(6,0)*d(0,1)*d(0,0) - 4*(d(4,2) + d(0,1))*(d(4,0) - d(2,1))*(d(2,0) + d(0,1)) - 10*(d(4,0) - d(2,1) - d(4,3))*(d(4,0) - d(2,1))*d(0,0) - 4 *(2*(d(4,0) - d(2,1))*d(0,0) + d(5,0)*d(0,1)) *(d(4,0) - d(2,1) - d(4,3)) - 4 *(d(2,0) + 3*d(0,1) + d(4,2) + d(5,0))*(d(4,0) - d(2,1) - d(4,3)) *d(2,0) + 2*(5*d(4,1)*d(0,0) + 2*d(4,0)*d(0,1) + 2*d(4,2)*d(2,1) + 2*d(4,3)*d(2,0))*(d(4,2) + d(0,1)))*d(0,0)))/8, 2 (97*(d(4,2) + d(0,1))*d(4,2) + 136*d(6,2)*d(0,0))*d(0,0) -----------------------------------------------------------,( - (138 4 *(d(2,0) + 3*d(0,1) + d(4,2) + d(5,0))*(d(4,0) - d(2,1) - d(4,3)) *d(0,0) + 56*(d(2,0) + 3*d(0,1) + d(4,2) + d(5,0))*(d(4,2) + d(0,1)) 2 *(d(2,0) + d(0,1)) - (203*d(6,3)*d(0,0) - 138*d(6,2)*d(2,0)*d(0,0) - 276*d(6,2)*d(0,1)*d(0,0) + 166*d(4,3)*d(4,2)*d(0,0) 2 + 166*d(4,3)*d(0,1)*d(0,0) - 56*d(4,2) *d(2,0) 2 - 112*d(4,2) *d(0,1) - 56*d(4,2)*d(2,0)*d(0,1) 3 2 369*(d(4,2) + d(0,1))*d(0,0) - 112*d(4,2)*d(0,1) ))*d(0,0))/8,-------------------------------, 8 ( - (136*(d(4,0) - d(2,1) - d(4,3))*d(0,0) 4 2 625*d(0,0) + 97*(d(4,2) + d(0,1))*(d(2,0) + d(0,1)))*d(0,0) )/4,-------------)) 16 MATD**5:= 4 5 31*d(0,1)*d(0,0) mat((d(0,0) ,-------------------,0,0,0,0,0), 16 5 d(0,0) (0,---------,0,0,0,0,0), 32 4 211*d(2,0)*d(0,0) (--------------------, 16 2 3 (121*d(2,1)*d(0,0) - 180*d(2,0) - 180*d(2,0)*d(0,1))*d(0,0) ---------------------------------------------------------------, 16 5 4 243*d(0,0) - 211*(d(2,0) + 2*d(0,1))*d(0,0) -------------,------------------------------------,0,0,0), 32 16 4 31*d(2,0)*d(0,0) 5 (0,-------------------,0,d(0,0) ,0,0,0), 16 (( - (285*d(5,0)*d(2,0) + 285*d(5,0)*d(0,1) - 285*d(4,2)*d(2,0) 3 2 - 248*d(4,0)*d(0,0))*d(0,0) )/8,( - (260*d(5,0)*d(2,0) 2 + 520*d(5,0)*d(2,0)*d(0,1) + 260*d(5,0)*d(0,1) - 310*d(4,3)*d(2,0)*d(0,0) - 440*d(4,2)*d(2,1)*d(0,0) 2 2 + 520*d(4,2)*d(2,0) + 520*d(4,2)*d(2,0)*d(0,1) - 341*d(4,1)*d(0,0) + 440*d(4,0)*d(2,0)*d(0,0) + 130*d(4,0)*d(0,1)*d(0,0) 3 - 440*d(2,1)*d(2,0)*d(0,0) - 440*d(2,1)*d(0,1)*d(0,0) + 260*d(2,0) 2 2 2 + 1040*d(2,0) *d(0,1) + 780*d(2,0)*d(0,1) )*d(0,0) )/16, 4 781*d(4,2)*d(0,0) --------------------,( - ( 16 285*(d(2,0) + 3*d(0,1) + d(4,2) + d(5,0))*(d(2,0) + d(0,1)) - (248*d(4,3)*d(0,0) - 285*d(4,2)*d(2,0) - 570*d(4,2)*d(0,1))) 4 3 5 - 781*(d(2,0) + d(0,1))*d(0,0) *d(0,0) )/8,32*d(0,0) ,----------------------------------,0), 16 4 211*d(5,0)*d(0,0) (--------------------,((180*(d(2,0) + 3*d(0,1) + d(4,2) + d(5,0))*d(2,0) 16 3 + 180*d(5,0)*d(0,1) + 121*d(4,0)*d(0,0) - 121*d(2,1)*d(0,0))*d(0,0) 4 211*(d(2,0) + 3*d(0,1) + d(4,2) + d(5,0))*d(0,0) )/16,0,---------------------------------------------------,0, 16 5 243*d(0,0) -------------,0), 32 2 (((820*d(6,2)*d(2,0)*d(0,0) + 1031*d(6,0)*d(0,0) + 820*d(5,0)*d(4,3)*d(0,0) - 500*d(5,0)*d(4,2)*d(2,0) - 500*d(5,0)*d(4,2)*d(0,1) - 820*d(5,0)*d(4,0)*d(0,0) + 820*d(5,0)*d(2,1)*d(0,0) 2 2 - 500*d(5,0)*d(2,0)*d(0,1) - 500*d(5,0)*d(0,1) + 500*d(4,2) *d(2,0) + 1070*d(4,2)*d(4,0)*d(0,0) + 500*d(4,2)*d(2,0)*d(0,1) 2 2 + 1070*d(4,0)*d(0,1)*d(0,0))*d(0,0) )/16,((500*d(6,3)*d(2,0)*d(0,0) 2 2 + 660*d(6,2)*d(2,1)*d(0,0) - 320*d(6,2)*d(2,0) *d(0,0) 3 - 320*d(6,2)*d(2,0)*d(0,1)*d(0,0) + 781*d(6,1)*d(0,0) 2 + 500*d(6,0)*d(0,1)*d(0,0) + 320*d(5,0)*d(4,3)*d(2,0)*d(0,0) 2 + 320*d(5,0)*d(4,3)*d(0,1)*d(0,0) - 120*d(5,0)*d(4,2)*d(2,0) 2 - 240*d(5,0)*d(4,2)*d(2,0)*d(0,1) - 120*d(5,0)*d(4,2)*d(0,1) - 320*d(5,0)*d(4,0)*d(2,0)*d(0,0) - 320*d(5,0)*d(4,0)*d(0,1)*d(0,0) + 320*d(5,0)*d(2,1)*d(2,0)*d(0,0) + 320*d(5,0)*d(2,1)*d(0,1)*d(0,0) 2 2 - 120*d(5,0)*d(2,0) *d(0,1) - 240*d(5,0)*d(2,0)*d(0,1) 3 - 120*d(5,0)*d(0,1) + 700*d(4,3)*d(4,2)*d(2,0)*d(0,0) 2 2 + 660*d(4,3)*d(4,0)*d(0,0) - 660*d(4,3)*d(2,1)*d(0,0) 2 + 320*d(4,3)*d(2,0) *d(0,0) + 1340*d(4,3)*d(2,0)*d(0,1)*d(0,0) 2 2 2 + 440*d(4,2) *d(2,1)*d(0,0) - 240*d(4,2) *d(2,0) 2 2 - 240*d(4,2) *d(2,0)*d(0,1) + 880*d(4,2)*d(4,1)*d(0,0) - 760*d(4,2)*d(4,0)*d(2,0)*d(0,0) - 60*d(4,2)*d(4,0)*d(0,1)*d(0,0) + 760*d(4,2)*d(2,1)*d(2,0)*d(0,0) + 880*d(4,2)*d(2,1)*d(0,1)*d(0,0) 3 2 - 120*d(4,2)*d(2,0) - 720*d(4,2)*d(2,0) *d(0,1) 2 2 - 600*d(4,2)*d(2,0)*d(0,1) + 880*d(4,1)*d(0,1)*d(0,0) 2 2 2 - 660*d(4,0) *d(0,0) + 1320*d(4,0)*d(2,1)*d(0,0) 2 - 320*d(4,0)*d(2,0) *d(0,0) - 1400*d(4,0)*d(2,0)*d(0,1)*d(0,0) 2 2 2 - 60*d(4,0)*d(0,1) *d(0,0) - 660*d(2,1) *d(0,0) 2 + 320*d(2,1)*d(2,0) *d(0,0) + 1400*d(2,1)*d(2,0)*d(0,1)*d(0,0) 2 3 + 440*d(2,1)*d(0,1) *d(0,0) - 120*d(2,0) *d(0,1) 2 2 3 - 480*d(2,0) *d(0,1) - 360*d(2,0)*d(0,1) )*d(0,0))/16, 3 11*(120*(d(4,2) + d(0,1))*d(4,2) + 131*d(6,2)*d(0,0))*d(0,0) ---------------------------------------------------------------,( - (820 16 *(d(2,0) + 3*d(0,1) + d(4,2) + d(5,0))*(d(4,0) - d(2,1) - d(4,3)) *d(0,0) + 500*(d(2,0) + 3*d(0,1) + d(4,2) + d(5,0))*(d(4,2) + d(0,1)) 2 *(d(2,0) + d(0,1)) - (1031*d(6,3)*d(0,0) - 820*d(6,2)*d(2,0)*d(0,0) - 1640*d(6,2)*d(0,1)*d(0,0) + 1070*d(4,3)*d(4,2)*d(0,0) 2 + 1070*d(4,3)*d(0,1)*d(0,0) - 500*d(4,2) *d(2,0) 2 - 1000*d(4,2) *d(0,1) - 500*d(4,2)*d(2,0)*d(0,1) 2 2 - 1000*d(4,2)*d(0,1) ))*d(0,0) )/16, 4 2101*(d(4,2) + d(0,1))*d(0,0) --------------------------------,( - 11*( 16 131*(d(4,0) - d(2,1) - d(4,3))*d(0,0) 3 + 120*(d(4,2) + d(0,1))*(d(2,0) + d(0,1)))*d(0,0) )/16, 5 3125*d(0,0) --------------)) 32 MATD**6:= 5 6 63*d(0,1)*d(0,0) mat((d(0,0) ,-------------------,0,0,0,0,0), 32 6 d(0,0) (0,---------,0,0,0,0,0), 64 5 665*d(2,0)*d(0,0) (--------------------, 32 2 4 7*(26*d(2,1)*d(0,0) - 43*d(2,0) - 43*d(2,0)*d(0,1))*d(0,0) --------------------------------------------------------------, 16 6 5 729*d(0,0) - 665*(d(2,0) + 2*d(0,1))*d(0,0) -------------,------------------------------------,0,0,0), 64 32 5 63*d(2,0)*d(0,0) 6 (0,-------------------,0,d(0,0) ,0,0,0), 32 (( - 7*(193*d(5,0)*d(2,0) + 193*d(5,0)*d(0,1) - 193*d(4,2)*d(2,0) 4 2 - 144*d(4,0)*d(0,0))*d(0,0) )/16,( - 7*(200*d(5,0)*d(2,0) 2 + 400*d(5,0)*d(2,0)*d(0,1) + 200*d(5,0)*d(0,1) - 186*d(4,3)*d(2,0)*d(0,0) - 286*d(4,2)*d(2,1)*d(0,0) 2 2 + 400*d(4,2)*d(2,0) + 400*d(4,2)*d(2,0)*d(0,1) - 195*d(4,1)*d(0,0) + 286*d(4,0)*d(2,0)*d(0,0) + 100*d(4,0)*d(0,1)*d(0,0) 3 - 286*d(2,1)*d(2,0)*d(0,0) - 286*d(2,1)*d(0,1)*d(0,0) + 200*d(2,0) 2 2 3 + 800*d(2,0) *d(0,1) + 600*d(2,0)*d(0,1) )*d(0,0) )/32, 5 3367*d(4,2)*d(0,0) ---------------------,( - 7*( 32 193*(d(2,0) + 3*d(0,1) + d(4,2) + d(5,0))*(d(2,0) + d(0,1)) - (144*d(4,3)*d(0,0) - 193*d(4,2)*d(2,0) - 386*d(4,2)*d(0,1))) 5 4 6 - 3367*(d(2,0) + d(0,1))*d(0,0) *d(0,0) )/16,64*d(0,0) ,-----------------------------------,0), 32 5 665*d(5,0)*d(0,0) (--------------------,(7*(43*(d(2,0) + 3*d(0,1) + d(4,2) + d(5,0))*d(2,0) 32 4 + 43*d(5,0)*d(0,1) + 26*d(4,0)*d(0,0) - 26*d(2,1)*d(0,0))*d(0,0) )/ 5 6 665*(d(2,0) + 3*d(0,1) + d(4,2) + d(5,0))*d(0,0) 729*d(0,0) 16,0,---------------------------------------------------,0,-------------,0) 32 64 , 2 ((7*(646*d(6,2)*d(2,0)*d(0,0) + 741*d(6,0)*d(0,0) + 646*d(5,0)*d(4,3)*d(0,0) - 520*d(5,0)*d(4,2)*d(2,0) - 520*d(5,0)*d(4,2)*d(0,1) - 646*d(5,0)*d(4,0)*d(0,0) + 646*d(5,0)*d(2,1)*d(0,0) - 520*d(5,0)*d(2,0)*d(0,1) 2 2 - 520*d(5,0)*d(0,1) + 520*d(4,2) *d(2,0) + 906*d(4,2)*d(4,0)*d(0,0) 3 + 520*d(4,2)*d(2,0)*d(0,1) + 906*d(4,0)*d(0,1)*d(0,0))*d(0,0) )/32,(7* 2 2 (183*d(6,3)*d(2,0)*d(0,0) + 253*d(6,2)*d(2,1)*d(0,0) 2 - 140*d(6,2)*d(2,0) *d(0,0) - 140*d(6,2)*d(2,0)*d(0,1)*d(0,0) 3 2 + 279*d(6,1)*d(0,0) + 183*d(6,0)*d(0,1)*d(0,0) + 140*d(5,0)*d(4,3)*d(2,0)*d(0,0) + 140*d(5,0)*d(4,3)*d(0,1)*d(0,0) 2 - 80*d(5,0)*d(4,2)*d(2,0) - 160*d(5,0)*d(4,2)*d(2,0)*d(0,1) 2 - 80*d(5,0)*d(4,2)*d(0,1) - 140*d(5,0)*d(4,0)*d(2,0)*d(0,0) - 140*d(5,0)*d(4,0)*d(0,1)*d(0,0) + 140*d(5,0)*d(2,1)*d(2,0)*d(0,0) 2 + 140*d(5,0)*d(2,1)*d(0,1)*d(0,0) - 80*d(5,0)*d(2,0) *d(0,1) 2 3 - 160*d(5,0)*d(2,0)*d(0,1) - 80*d(5,0)*d(0,1) 2 + 320*d(4,3)*d(4,2)*d(2,0)*d(0,0) + 253*d(4,3)*d(4,0)*d(0,0) 2 2 - 253*d(4,3)*d(2,1)*d(0,0) + 140*d(4,3)*d(2,0) *d(0,0) 2 + 600*d(4,3)*d(2,0)*d(0,1)*d(0,0) + 220*d(4,2) *d(2,1)*d(0,0) 2 2 2 - 160*d(4,2) *d(2,0) - 160*d(4,2) *d(2,0)*d(0,1) 2 + 363*d(4,2)*d(4,1)*d(0,0) - 360*d(4,2)*d(4,0)*d(2,0)*d(0,0) - 40*d(4,2)*d(4,0)*d(0,1)*d(0,0) + 360*d(4,2)*d(2,1)*d(2,0)*d(0,0) 3 + 440*d(4,2)*d(2,1)*d(0,1)*d(0,0) - 80*d(4,2)*d(2,0) 2 2 - 480*d(4,2)*d(2,0) *d(0,1) - 400*d(4,2)*d(2,0)*d(0,1) 2 2 2 + 363*d(4,1)*d(0,1)*d(0,0) - 253*d(4,0) *d(0,0) 2 2 + 506*d(4,0)*d(2,1)*d(0,0) - 140*d(4,0)*d(2,0) *d(0,0) 2 - 640*d(4,0)*d(2,0)*d(0,1)*d(0,0) - 40*d(4,0)*d(0,1) *d(0,0) 2 2 2 - 253*d(2,1) *d(0,0) + 140*d(2,1)*d(2,0) *d(0,0) 2 + 640*d(2,1)*d(2,0)*d(0,1)*d(0,0) + 220*d(2,1)*d(0,1) *d(0,0) 3 2 2 3 - 80*d(2,0) *d(0,1) - 320*d(2,0) *d(0,1) - 240*d(2,0)*d(0,1) ) 2 *d(0,0) )/16, 4 7*(583*(d(4,2) + d(0,1))*d(4,2) + 532*d(6,2)*d(0,0))*d(0,0) --------------------------------------------------------------,( - 7*(646 16 *(d(2,0) + 3*d(0,1) + d(4,2) + d(5,0))*(d(4,0) - d(2,1) - d(4,3)) *d(0,0) + 520*(d(2,0) + 3*d(0,1) + d(4,2) + d(5,0))*(d(4,2) + d(0,1)) 2 *(d(2,0) + d(0,1)) - (741*d(6,3)*d(0,0) - 646*d(6,2)*d(2,0)*d(0,0) - 1292*d(6,2)*d(0,1)*d(0,0) + 906*d(4,3)*d(4,2)*d(0,0) 2 + 906*d(4,3)*d(0,1)*d(0,0) - 520*d(4,2) *d(2,0) 2 - 1040*d(4,2) *d(0,1) - 520*d(4,2)*d(2,0)*d(0,1) 2 3 - 1040*d(4,2)*d(0,1) ))*d(0,0) )/32, 5 11529*(d(4,2) + d(0,1))*d(0,0) ---------------------------------,( - 7*( 32 532*(d(4,0) - d(2,1) - d(4,3))*d(0,0) 4 + 583*(d(4,2) + d(0,1))*(d(2,0) + d(0,1)))*d(0,0) )/16, 6 15625*d(0,0) ---------------)) 64 MATD**7:= 6 7 127*d(0,1)*d(0,0) mat((d(0,0) ,--------------------,0,0,0,0,0), 64 7 d(0,0) (0,---------,0,0,0,0,0), 128 6 2059*d(2,0)*d(0,0) (---------------------, 64 2 5 (1093*d(2,1)*d(0,0) - 1932*d(2,0) - 1932*d(2,0)*d(0,1))*d(0,0) ------------------------------------------------------------------, 64 7 6 2187*d(0,0) - 2059*(d(2,0) + 2*d(0,1))*d(0,0) --------------,-------------------------------------,0,0,0), 128 64 6 127*d(2,0)*d(0,0) 7 (0,--------------------,0,d(0,0) ,0,0,0), 64 (( - (6069*d(5,0)*d(2,0) + 6069*d(5,0)*d(0,1) - 6069*d(4,2)*d(2,0) 5 2 - 4064*d(4,0)*d(0,0))*d(0,0) )/32,( - (6804*d(5,0)*d(2,0) 2 + 13608*d(5,0)*d(2,0)*d(0,1) + 6804*d(5,0)*d(0,1) - 5334*d(4,3)*d(2,0)*d(0,0) - 8736*d(4,2)*d(2,1)*d(0,0) 2 + 13608*d(4,2)*d(2,0) + 13608*d(4,2)*d(2,0)*d(0,1) 2 - 5461*d(4,1)*d(0,0) + 8736*d(4,0)*d(2,0)*d(0,0) + 3402*d(4,0)*d(0,1)*d(0,0) - 8736*d(2,1)*d(2,0)*d(0,0) 3 2 - 8736*d(2,1)*d(0,1)*d(0,0) + 6804*d(2,0) + 27216*d(2,0) *d(0,1) 6 2 4 14197*d(4,2)*d(0,0) + 20412*d(2,0)*d(0,1) )*d(0,0) )/64,----------------------,( - ( 64 6069*(d(2,0) + 3*d(0,1) + d(4,2) + d(5,0))*(d(2,0) + d(0,1)) - (4064*d(4,3)*d(0,0) - 6069*d(4,2)*d(2,0) - 12138*d(4,2)*d(0,1))) 6 5 7 - 14197*(d(2,0) + d(0,1))*d(0,0) *d(0,0) )/32,128*d(0,0) ,------------------------------------,0), 64 6 2059*d(5,0)*d(0,0) (---------------------,((1932*(d(2,0) + 3*d(0,1) + d(4,2) + d(5,0))*d(2,0) 64 + 1932*d(5,0)*d(0,1) + 1093*d(4,0)*d(0,0) - 1093*d(2,1)*d(0,0)) 6 5 2059*(d(2,0) + 3*d(0,1) + d(4,2) + d(5,0))*d(0,0) *d(0,0) )/64,0,----------------------------------------------------,0, 64 7 2187*d(0,0) --------------,0), 128 2 (((23940*d(6,2)*d(2,0)*d(0,0) + 25999*d(6,0)*d(0,0) + 23940*d(5,0)*d(4,3)*d(0,0) - 23604*d(5,0)*d(4,2)*d(2,0) - 23604*d(5,0)*d(4,2)*d(0,1) - 23940*d(5,0)*d(4,0)*d(0,0) + 23940*d(5,0)*d(2,1)*d(0,0) - 23604*d(5,0)*d(2,0)*d(0,1) 2 2 - 23604*d(5,0)*d(0,1) + 23604*d(4,2) *d(2,0) + 35742*d(4,2)*d(4,0)*d(0,0) + 23604*d(4,2)*d(2,0)*d(0,1) 4 2 + 35742*d(4,0)*d(0,1)*d(0,0))*d(0,0) )/64,((12936*d(6,3)*d(2,0)*d(0,0) 2 2 + 18438*d(6,2)*d(2,1)*d(0,0) - 11004*d(6,2)*d(2,0) *d(0,0) 3 - 11004*d(6,2)*d(2,0)*d(0,1)*d(0,0) + 19531*d(6,1)*d(0,0) 2 + 12936*d(6,0)*d(0,1)*d(0,0) + 11004*d(5,0)*d(4,3)*d(2,0)*d(0,0) 2 + 11004*d(5,0)*d(4,3)*d(0,1)*d(0,0) - 8400*d(5,0)*d(4,2)*d(2,0) 2 - 16800*d(5,0)*d(4,2)*d(2,0)*d(0,1) - 8400*d(5,0)*d(4,2)*d(0,1) - 11004*d(5,0)*d(4,0)*d(2,0)*d(0,0) - 11004*d(5,0)*d(4,0)*d(0,1)*d(0,0) + 11004*d(5,0)*d(2,1)*d(2,0)*d(0,0) 2 + 11004*d(5,0)*d(2,1)*d(0,1)*d(0,0) - 8400*d(5,0)*d(2,0) *d(0,1) 2 3 - 16800*d(5,0)*d(2,0)*d(0,1) - 8400*d(5,0)*d(0,1) 2 + 26208*d(4,3)*d(4,2)*d(2,0)*d(0,0) + 18438*d(4,3)*d(4,0)*d(0,0) 2 2 - 18438*d(4,3)*d(2,1)*d(0,0) + 11004*d(4,3)*d(2,0) *d(0,0) 2 + 48216*d(4,3)*d(2,0)*d(0,1)*d(0,0) + 19404*d(4,2) *d(2,1)*d(0,0) 2 2 2 - 16800*d(4,2) *d(2,0) - 16800*d(4,2) *d(2,0)*d(0,1) 2 + 28140*d(4,2)*d(4,1)*d(0,0) - 30408*d(4,2)*d(4,0)*d(2,0)*d(0,0) - 4200*d(4,2)*d(4,0)*d(0,1)*d(0,0) + 30408*d(4,2)*d(2,1)*d(2,0)*d(0,0) 3 + 38808*d(4,2)*d(2,1)*d(0,1)*d(0,0) - 8400*d(4,2)*d(2,0) 2 2 - 50400*d(4,2)*d(2,0) *d(0,1) - 42000*d(4,2)*d(2,0)*d(0,1) 2 2 2 + 28140*d(4,1)*d(0,1)*d(0,0) - 18438*d(4,0) *d(0,0) 2 2 + 36876*d(4,0)*d(2,1)*d(0,0) - 11004*d(4,0)*d(2,0) *d(0,0) 2 - 52416*d(4,0)*d(2,0)*d(0,1)*d(0,0) - 4200*d(4,0)*d(0,1) *d(0,0) 2 2 2 - 18438*d(2,1) *d(0,0) + 11004*d(2,1)*d(2,0) *d(0,0) 2 + 52416*d(2,1)*d(2,0)*d(0,1)*d(0,0) + 19404*d(2,1)*d(0,1) *d(0,0) 3 2 2 3 - 8400*d(2,0) *d(0,1) - 33600*d(2,0) *d(0,1) - 25200*d(2,0)*d(0,1) 3 )*d(0,0) )/64, 5 (47544*(d(4,2) + d(0,1))*d(4,2) + 37969*d(6,2)*d(0,0))*d(0,0) ----------------------------------------------------------------,( - (23940 64 *(d(2,0) + 3*d(0,1) + d(4,2) + d(5,0))*(d(4,0) - d(2,1) - d(4,3)) *d(0,0) + 23604*(d(2,0) + 3*d(0,1) + d(4,2) + d(5,0)) 2 *(d(4,2) + d(0,1))*(d(2,0) + d(0,1)) - (25999*d(6,3)*d(0,0) - 23940*d(6,2)*d(2,0)*d(0,0) - 47880*d(6,2)*d(0,1)*d(0,0) + 35742*d(4,3)*d(4,2)*d(0,0) + 35742*d(4,3)*d(0,1)*d(0,0) 2 2 - 23604*d(4,2) *d(2,0) - 47208*d(4,2) *d(0,1) 2 4 - 23604*d(4,2)*d(2,0)*d(0,1) - 47208*d(4,2)*d(0,1) ))*d(0,0) )/64 6 61741*(d(4,2) + d(0,1))*d(0,0) ,---------------------------------,( - ( 64 37969*(d(4,0) - d(2,1) - d(4,3))*d(0,0) 5 + 47544*(d(4,2) + d(0,1))*(d(2,0) + d(0,1)))*d(0,0) )/64, 7 78125*d(0,0) ---------------)) 128 matd**j est nul pour j geq 5 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 ] [ ] [ 1 ] [0 --- 0 0 0 0 0 ] [ 2 ] [ ] [ 3 ] [0 0 --- 0 0 0 0 ] [ 2 ] [ ] [0 0 0 1 0 0 0 ] [ ] [0 0 0 0 2 0 0 ] [ ] [ 3 ] [0 0 0 0 0 --- 0 ] [ 2 ] [ ] [ 5 ] [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),0,0,0,0,0),(0,d(0,0)/2,0,0,0,0,0),(d(2,0),d(2,1),(3*d(0,0))/2 , - (d(2,0) + 2*d(0,1)),0,0,0),(0,d(2,0),0,d(0,0),0,0,0),(d(4,0),d(4,1),d(4,2),d (4,3),2*d(0,0), - (d(2,0) + d(0,1)),0),(d(5,0),d(4,0) - d(2,1),0,d(2,0) + 3*d(0, 1) + d(4,2) + d(5,0),0,(3*d(0,0))/2,0),(d(6,0),d(6,1),d(6,2),d(6,3),d(4,2) + d(0 ,1), - (d(4,0) - d(2,1) - d(4,3)),(5*d(0,0))/2))$ 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),d(0,1),0,0,0,0,0), d(0,0) (0,--------,0,0,0,0,0), 2 3*d(0,0) (d(2,0),d(2,1),----------, - (d(2,0) + 2*d(0,1)),0,0,0), 2 (0,d(2,0),0,d(0,0),0,0,0), (d(4,0),d(4,1),d(4,2),d(4,3),2*d(0,0), - (d(2,0) + d(0,1)),0), 3*d(0,0) (d(5,0),d(4,0) - d(2,1),0,d(2,0) + 3*d(0,1) + d(4,2) + d(5,0),0,----------,0 2 ), (d(6,0),d(6,1),d(6,2),d(6,3),d(4,2) + d(0,1), - (d(4,0) - d(2,1) - d(4,3)), 5*d(0,0) ----------)) 2 on voit apparaitre les poids sur la diagonale r(1) := d(0,0) d(0,0) r(2) := -------- 2 3*d(0,0) r(3) := ---------- 2 r(4) := d(0,0) r(5) := 2*d(0,0) 3*d(0,0) r(6) := ---------- 2 5*d(0,0) r(7) := ---------- 2 r(1) := 2*gamma1 r(2) := gamma1 r(3) := 3*gamma1 r(4) := 2*gamma1 r(5) := 4*gamma1 r(6) := 3*gamma1 r(7) := 5*gamma1 Le systeme de poids est le systeme 1.3 calcul de relations de commutation de la base diaY(j) diagonalisant le tore listcommutateursdesx := {{{0,1},a*x(2)}, {{0,2},x(6)}, {{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},0}, {{2,4},0}, {{2,5},0}, {{2,6},0}, {{3,4},0}, {{3,5},x(6)}, {{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(3)*a}, {{1,3},diay(7)}, {{1,4},diay(5)}, {{1,5},0}, {{1,6},diay(7)}, {{1,7},0}, {{2,3},diay(5)}, {{2,4},diay(6)}, {{2,5},diay(7)}, {{2,6},0}, {{2,7},0}, {{3,4},0}, {{3,5},0}, {{3,6},0}, {{3,7},0}, {{4,5},0}, {{4,6},diay(7)}, {{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_{7,1.3}$ (iL)$ and that for a neq{0}$ 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 :$ This isom computed by calculisom6_10VI.red$ mat((0, - a,0,0,0,0,0),(1,0,0,0,0,0,0),(0,0,0,a**2,0,0,0),(0,0, - a,0,0,0,0),(0, 0,0,0,0,a**2,0),(0,0,0,0, - a,0,0),(0,0,0,0,0,0,a**2))$ det(isom):= a**9$ ZZ(1):=diay(2)$ ZZ(2):= - diay(1)*a$ ZZ(3):= - diay(4)*a$ ZZ(4):=diay(3)*a**2$ ZZ(5):= - diay(6)*a$ ZZ(6):=diay(5)*a**2$ ZZ(7):=diay(7)*a**2$ listcommutateursdesZZ:=$ {{1,2},zz(4)}$ {{1,3},zz(5)}$ {{1,4},zz(6)}$ {{1,5},0}$ {{1,6},zz(7)}$ {{1,7},0}$ {{2,3},zz(6)}$ {{2,4}, - zz(7)*a}$ {{2,5},zz(7)}$ {{2,6},0}$ {{2,7},0}$ {{3,4},0}$ {{3,5},zz(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}$ We get the commutation relations of$ g_{7,1.3}$ (iL)$ with L:= - a$ Et cela pour a:=a$ and that for a neq {0}$ shortformdelta:={a,0,ss,1,ss,0,ss,1}$ delta:= mat((0,0,0,0,0,0),(a,0,0,0,0,0),(0,0,0,0,0,0),(0,0,1,0,0,0),(0,0,0,0,0,0),(0,1,0 ,0,1,0))$