delta:= mat((0,1,0,0,0,0),(0,0,0,0,0,0),(1,0,0,0,0,0),(0,0,0,0,0,0),(0,0,0,-1,0,1),(0,0, 0,0,0,0))$ phase 1 de la resolution des equations$ on resoud 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 resoud l'equation {{0,1},1} qui est maintenant AA:=d(2,1) - d(1,3)$ Unknowns: {d(2,1),d(1,3)} Unknowns: {d(2,1),d(1,3)} bonne inconnue W:=d(2,1)$ sa valeur doit etre WW:=d(1,3)$ on resoud 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 resoud 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 resoud 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 resoud l'equation {{0,1},5} qui est maintenant AA:=d(6,1) - d(5,3) - d(4,1) - d(4,0)$ Unknowns: {d(6,1),d(5,3),d(4,1),d(4,0)} Unknowns: {d(6,1),d(5,3),d(4,1),d(4,0)} bonne inconnue W:=d(6,1)$ sa valeur doit etre WW:=d(5,3) + d(4,1) + d(4,0)$ on resoud l'equation {{0,1},6} qui est maintenant AA:= - d(6,3)$ Unknown: d(6,3) Unknown: d(6,3) bonne inconnue W:=d(6,3)$ sa valeur doit etre WW:=0$ on resoud l'equation {{0,2},0} 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 resoud l'equation {{0,2},1} 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 resoud l'equation {{0,2},2} 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 resoud l'equation {{0,2},3} qui est maintenant AA:= - d(3,1) + d(1,2)$ Unknowns: {d(3,1),d(1,2)} Unknowns: {d(3,1),d(1,2)} bonne inconnue W:=d(3,1)$ sa valeur doit etre WW:=d(1,2)$ on resoud l'equation {{0,2},4} qui est maintenant AA:= - d(4,1) + d(1,0)$ Unknowns: {d(4,1),d(1,0)} Unknowns: {d(4,1),d(1,0)} bonne inconnue W:=d(4,1)$ sa valeur doit etre WW:=d(1,0)$ on resoud l'equation {{0,2},5} qui est maintenant AA:=d(6,2) - d(5,1) - d(4,2) - d(3,0)$ Unknowns: {d(6,2),d(5,1),d(4,2),d(3,0)} Unknowns: {d(6,2),d(5,1),d(4,2),d(3,0)} bonne inconnue W:=d(6,2)$ sa valeur doit etre WW:=d(5,1) + d(4,2) + d(3,0)$ on resoud l'equation {{0,2},6} qui est maintenant AA:= - d(5,3) - 2*d(4,0) - d( 1,0)$ Unknowns: {d(5,3),d(4,0),d(1,0)} Unknowns: {d(5,3),d(4,0),d(1,0)} bonne inconnue W:=d(5,3)$ sa valeur doit etre WW:= - 2*d(4,0) - d(1,0)$ on resoud l'equation {{0,3},5} qui est maintenant AA:=2*d(2,0)$ Unknown: d(2,0) Unknown: d(2,0) bonne inconnue W:=d(2,0)$ sa valeur doit etre WW:=0$ on resoud 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 resoud l'equation {{0,4},1} qui est maintenant AA:=d(2,4) + d(1,5)$ Unknowns: {d(2,4),d(1,5)} Unknowns: {d(2,4),d(1,5)} bonne inconnue W:=d(2,4)$ sa valeur doit etre WW:= - d(1,5)$ on resoud 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 resoud 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 resoud 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 resoud l'equation {{0,4},5} qui est maintenant AA:=d(6,4) + d(5,5) - d(4,4) + d(1,0) - d(0,0)$ Unknowns: {d(6,4),d(5,5),d(4,4),d(1,0),d(0,0)} Unknowns: {d(6,4),d(5,5),d(4,4),d(1,0),d(0,0)} bonne inconnue W:=d(6,4)$ sa valeur doit etre WW:= - d(5,5) + d(4,4) - d(1,0) + d(0,0)$ on resoud l'equation {{0,4},6} qui est maintenant AA:=d(6,5)$ Unknown: d(6,5) Unknown: d(6,5) bonne inconnue W:=d(6,5)$ sa valeur doit etre WW:=0$ on resoud l'equation {{0,5},3} 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 resoud l'equation {{0,6},1} 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 resoud l'equation {{0,6},3} qui est maintenant AA:=d(1,6) + d(1,4)$ Unknowns: {d(1,6),d(1,4)} Unknowns: {d(1,6),d(1,4)} bonne inconnue W:=d(1,6)$ sa valeur doit etre WW:= - d(1,4)$ on resoud l'equation {{0,6},5} qui est maintenant AA:=d(6,6) - d(5,5) - d(4,6) + d(0,0)$ Unknowns: {d(6,6),d(5,5),d(4,6),d(0,0)} Unknowns: {d(6,6),d(5,5),d(4,6),d(0,0)} bonne inconnue W:=d(6,6)$ sa valeur doit etre WW:=d(5,5) + d(4,6) - d(0,0)$ on resoud 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 resoud 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 resoud 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 resoud 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 resoud l'equation {{1,2},5} qui est maintenant AA:= - d(5,4) + d(4,2) - d(1, 2)$ Unknowns: {d(5,4),d(4,2),d(1,2)} Unknowns: {d(5,4),d(4,2),d(1,2)} bonne inconnue W:=d(5,4)$ sa valeur doit etre WW:=d(4,2) - d(1,2)$ on resoud l'equation {{1,2},6} qui est maintenant AA:=d(5,5) - 2*d(1,1)$ Unknowns: {d(5,5),d(1,1)} Unknowns: {d(5,5),d(1,1)} bonne inconnue W:=d(5,5)$ sa valeur doit etre WW:=2*d(1,1)$ on resoud l'equation {{1,4},5} qui est maintenant AA:=d(1,1) - d(0,0)$ Unknowns: {d(1,1),d(0,0)} Unknowns: {d(1,1),d(0,0)} bonne inconnue W:=d(1,1)$ sa valeur doit etre WW:=d(0,0)$ on resoud l'equation {{1,6},3} 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 resoud l'equation {{1,6},5} 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 resoud l'equation {{2,4},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 resoud l'equation {{2,4},5} qui est maintenant AA:= - d(5,6) + d(1,2) - 2*d( 0,2)$ Unknowns: {d(5,6),d(1,2),d(0,2)} Unknowns: {d(5,6),d(1,2),d(0,2)} bonne inconnue W:=d(5,6)$ sa valeur doit etre WW:=d(1,2) - 2*d(0,2)$ on resoud l'equation {{2,6},5} qui est maintenant AA:=d(0,2)$ Unknown: d(0,2) Unknown: d(0,2) bonne inconnue W:=d(0,2)$ sa valeur doit etre WW:=0$ Derivation equations to cancel (Reduce output) : \\{{{{0,1},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},1},0}, {{{0,3},3},0}, {{{0,3},5},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},1},0}, {{{0,5},3},0}, {{{0,5},5},0}, {{{0,6},0},0}, {{{0,6},1},0}, {{{0,6},2},0}, {{{0,6},3},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},3},0}, {{{1,3},4},0}, {{{1,3},5},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},1},0}, {{{2,5},4},0}, {{{2,5},5},0}, {{{2,5},6},0}, {{{2,6},1},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}, {{{3,6},5},0}, {{{4,5},5},0}, {{{4,5},6},0}, {{{4,6},5},0}, {{{4,6},6},0}, {{{5,6},5},0}}$ pas de 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},1},0}, {{{0,3},3},0}, {{{0,3},5},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},1},0}, {{{0,5},3},0}, {{{0,5},5},0}, {{{0,6},0},0}, {{{0,6},1},0}, {{{0,6},2},0}, {{{0,6},3},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},3},0}, {{{1,3},4},0}, {{{1,3},5},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},1},0}, {{{2,5},4},0}, {{{2,5},5},0}, {{{2,5},6},0}, {{{2,6},1},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}, {{{3,6},5},0}, {{{4,5},5},0}, {{{4,5},6},0}, {{{4,6},5},0}, {{{4,6},6},0}, {{{5,6},5},0}}$ derivation generique de gtildedelta:$ MATD:= mat((d(0,0),0,0,0,0,0,0),(d(1,0),d(0,0),d(1,2),0,0,0,0),(0,0,0,0,0,0,0),(d(3,0), d(1,2),d(3,2),2*d(0,0),0,0,0),(d(4,0),d(1,0),d(4,2),0,d(0,0),0,0),(d(5,0),d(5,1) ,d(5,2), - 2*d(4,0) - d(1,0),d(4,2) - d(1,2),2*d(0,0),d(1,2)),(d(6,0), - d(4,0), d(5,1) + d(4,2) + d(3,0),0, - d(1,0),0,d(0,0)))$ pour delta:= mat((0,1,0,0,0,0),(0,0,0,0,0,0),(1,0,0,0,0,0),(0,0,0,0,0,0),(0,0,0,-1,0,1),(0,0, 0,0,0,0))$ Unknowns: {d(6,0), d(5,2), d(5,1), d(5,0), d(4,2), d(4,0), d(3,2), d(3,0), d(1,2), d(1,0), d(0,0)} Unknowns: {d(6,0), d(5,2), d(5,1), d(5,0), d(4,2), d(4,0), d(3,2), d(3,0), d(1,2), d(1,0), d(0,0)} Unknowns: {d(6,0), d(5,2), d(5,1), d(5,0), d(4,2), d(4,0), d(3,2), d(3,0), d(1,2), d(1,0), d(0,0)} Unknowns: {d(6,0), d(5,2), d(5,1), d(5,0), d(4,2), d(4,0), d(3,2), d(3,0), d(1,2), d(1,0), d(0,0)} dim Der(gtildedelta):=11$ seul candidat a etre 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 0 0 0 0 0] [ ] [0 0 0 2 0 0 0] [ ] [0 0 0 0 1 0 0] [ ] [0 0 0 0 0 2 0] [ ] [0 0 0 0 0 0 1] 4 2 - (x - 1) *(x - 2) *x {{x,1, [ 0 ] [ ] [ 0 ] [ ] [arbcomplex(71)] [ ] [ 0 ] [ ] [ 0 ] [ ] [ 0 ] [ ] [ 0 ] }, {x - 2, 2, [ 0 ] [ ] [ 0 ] [ ] [ 0 ] [ ] [arbcomplex(72)] [ ] [ 0 ] [ ] [arbcomplex(73)] [ ] [ 0 ] }, {x - 1, 4, [arbcomplex(74)] [ ] [arbcomplex(75)] [ ] [ 0 ] [ ] [ 0 ] [ ] [arbcomplex(76)] [ ] [ 0 ] [ ] [arbcomplex(77)] }} Mais t1 n'est pas semisimple gtildedelta est caracteristiquement nilpotente MATD**1:= mat((d(0,0),0,0,0,0,0,0), (d(1,0),d(0,0),d(1,2),0,0,0,0), (0,0,0,0,0,0,0), (d(3,0),d(1,2),d(3,2),2*d(0,0),0,0,0), (d(4,0),d(1,0),d(4,2),0,d(0,0),0,0), (d(5,0),d(5,1),d(5,2), - 2*d(4,0) - d(1,0),d(4,2) - d(1,2),2*d(0,0),d(1,2)), (d(6,0), - d(4,0),d(5,1) + d(4,2) + d(3,0),0, - d(1,0),0,d(0,0))) MATD**2:= 2 mat((d(0,0) ,0,0,0,0,0,0), 2 (2*d(1,0)*d(0,0),d(0,0) ,d(1,2)*d(0,0),0,0,0,0), (0,0,0,0,0,0,0), 2 (3*d(3,0)*d(0,0) + d(1,2)*d(1,0),3*d(1,2)*d(0,0),2*d(3,2)*d(0,0) + d(1,2) , 2 4*d(0,0) ,0,0,0), 2 (2*d(4,0)*d(0,0) + d(1,0) ,2*d(1,0)*d(0,0),d(4,2)*d(0,0) + d(1,2)*d(1,0),0, 2 d(0,0) ,0,0), (d(6,0)*d(1,2) + d(5,1)*d(1,0) + 3*d(5,0)*d(0,0) + d(4,2)*d(4,0) - 2*d(4,0)*d(3,0) - d(4,0)*d(1,2) - d(3,0)*d(1,0), 3*d(5,1)*d(0,0) + d(4,2)*d(1,0) - 3*d(4,0)*d(1,2) - 2*d(1,2)*d(1,0), 2 2*d(5,2)*d(0,0) + 2*d(5,1)*d(1,2) + d(4,2) - 2*d(4,0)*d(3,2) - d(3,2)*d(1,0) + d(3,0)*d(1,2),4*d(0,0)*( - 2*d(4,0) - d(1,0)), 2 3*d(4,2)*d(0,0) - d(1,2)*d(1,0) - 3*d(1,2)*d(0,0),4*d(0,0) ,3*d(1,2)*d(0,0) ), 2 (2*(d(6,0)*d(0,0) - d(4,0)*d(1,0)), - 2*d(4,0)*d(0,0) - d(1,0) , d(5,1)*d(0,0) - d(4,2)*d(1,0) + d(4,2)*d(0,0) - d(4,0)*d(1,2) 2 + d(3,0)*d(0,0),0, - 2*d(1,0)*d(0,0),0,d(0,0) )) MATD**3:= 3 mat((d(0,0) ,0,0,0,0,0,0), 2 3 2 (3*d(1,0)*d(0,0) ,d(0,0) ,d(1,2)*d(0,0) ,0,0,0,0), (0,0,0,0,0,0,0), 2 (d(0,0)*(7*d(3,0)*d(0,0) + 4*d(1,2)*d(1,0)),7*d(1,2)*d(0,0) , 2 3 d(0,0)*(4*d(3,2)*d(0,0) + 3*d(1,2) ),8*d(0,0) ,0,0,0), 2 2 (3*d(0,0)*(d(4,0)*d(0,0) + d(1,0) ),3*d(1,0)*d(0,0) , 3 d(0,0)*(d(4,2)*d(0,0) + 2*d(1,2)*d(1,0)),0,d(0,0) ,0,0), 2 (4*d(6,0)*d(1,2)*d(0,0) + 4*d(5,1)*d(1,0)*d(0,0) + 7*d(5,0)*d(0,0) 2 + 4*d(4,2)*d(4,0)*d(0,0) + d(4,2)*d(1,0) - 10*d(4,0)*d(3,0)*d(0,0) - 4*d(4,0)*d(1,2)*d(1,0) - 4*d(4,0)*d(1,2)*d(0,0) - 5*d(3,0)*d(1,0)*d(0,0) 2 2 - 2*d(1,2)*d(1,0) ,7*d(5,1)*d(0,0) + 4*d(4,2)*d(1,0)*d(0,0) 2 - 14*d(4,0)*d(1,2)*d(0,0) - d(1,2)*d(1,0) - 9*d(1,2)*d(1,0)*d(0,0), 2 2 4*d(5,2)*d(0,0) + 6*d(5,1)*d(1,2)*d(0,0) + 3*d(4,2) *d(0,0) 2 - 8*d(4,0)*d(3,2)*d(0,0) - 3*d(4,0)*d(1,2) - 4*d(3,2)*d(1,0)*d(0,0) 2 + 3*d(3,0)*d(1,2)*d(0,0) - 2*d(1,2) *d(1,0), 2 12*d(0,0) *( - 2*d(4,0) - d(1,0)), 3 d(0,0)*(7*d(4,2)*d(0,0) - 4*d(1,2)*d(1,0) - 7*d(1,2)*d(0,0)),8*d(0,0) , 2 7*d(1,2)*d(0,0) ), 2 3 (3*d(6,0)*d(0,0) - 6*d(4,0)*d(1,0)*d(0,0) - d(1,0) , 2 2 - 3*d(0,0)*(d(4,0)*d(0,0) + d(1,0) ),d(5,1)*d(0,0) 2 - 2*d(4,2)*d(1,0)*d(0,0) + d(4,2)*d(0,0) - 2*d(4,0)*d(1,2)*d(0,0) 2 2 2 3 + d(3,0)*d(0,0) - d(1,2)*d(1,0) ,0, - 3*d(1,0)*d(0,0) ,0,d(0,0) )) MATD**4:= 4 mat((d(0,0) ,0,0,0,0,0,0), 3 4 3 (4*d(1,0)*d(0,0) ,d(0,0) ,d(1,2)*d(0,0) ,0,0,0,0), (0,0,0,0,0,0,0), 2 3 (d(0,0) *(15*d(3,0)*d(0,0) + 11*d(1,2)*d(1,0)),15*d(1,2)*d(0,0) , 2 2 4 d(0,0) *(8*d(3,2)*d(0,0) + 7*d(1,2) ),16*d(0,0) ,0,0,0), 2 2 3 (2*d(0,0) *(2*d(4,0)*d(0,0) + 3*d(1,0) ),4*d(1,0)*d(0,0) , 2 4 d(0,0) *(d(4,2)*d(0,0) + 3*d(1,2)*d(1,0)),0,d(0,0) ,0,0), 2 2 3 (11*d(6,0)*d(1,2)*d(0,0) + 11*d(5,1)*d(1,0)*d(0,0) + 15*d(5,0)*d(0,0) 2 2 + 11*d(4,2)*d(4,0)*d(0,0) + 5*d(4,2)*d(1,0) *d(0,0) 2 - 34*d(4,0)*d(3,0)*d(0,0) - 22*d(4,0)*d(1,2)*d(1,0)*d(0,0) 2 2 3 - 11*d(4,0)*d(1,2)*d(0,0) - 17*d(3,0)*d(1,0)*d(0,0) - d(1,2)*d(1,0) 2 2 - 11*d(1,2)*d(1,0) *d(0,0),d(0,0)*(15*d(5,1)*d(0,0) 2 + 11*d(4,2)*d(1,0)*d(0,0) - 45*d(4,0)*d(1,2)*d(0,0) - 5*d(1,2)*d(1,0) 3 2 - 28*d(1,2)*d(1,0)*d(0,0)),8*d(5,2)*d(0,0) + 14*d(5,1)*d(1,2)*d(0,0) 2 2 2 2 + 7*d(4,2) *d(0,0) - 24*d(4,0)*d(3,2)*d(0,0) - 14*d(4,0)*d(1,2) *d(0,0) 2 2 2 2 - 12*d(3,2)*d(1,0)*d(0,0) + 7*d(3,0)*d(1,2)*d(0,0) - d(1,2) *d(1,0) 2 3 - 9*d(1,2) *d(1,0)*d(0,0),32*d(0,0) *( - 2*d(4,0) - d(1,0)), 2 4 d(0,0) *(15*d(4,2)*d(0,0) - 11*d(1,2)*d(1,0) - 15*d(1,2)*d(0,0)),16*d(0,0) 3 ,15*d(1,2)*d(0,0) ), 2 3 (4*d(0,0)*(d(6,0)*d(0,0) - 3*d(4,0)*d(1,0)*d(0,0) - d(1,0) ), 2 2 2 2*d(0,0) *( - 2*d(4,0)*d(0,0) - 3*d(1,0) ),d(0,0)*(d(5,1)*d(0,0) 2 - 3*d(4,2)*d(1,0)*d(0,0) + d(4,2)*d(0,0) - 3*d(4,0)*d(1,2)*d(0,0) 2 2 3 4 + d(3,0)*d(0,0) - 3*d(1,2)*d(1,0) ),0, - 4*d(1,0)*d(0,0) ,0,d(0,0) )) MATD**5:= 5 mat((d(0,0) ,0,0,0,0,0,0), 4 5 4 (5*d(1,0)*d(0,0) ,d(0,0) ,d(1,2)*d(0,0) ,0,0,0,0), (0,0,0,0,0,0,0), 3 4 (d(0,0) *(31*d(3,0)*d(0,0) + 26*d(1,2)*d(1,0)),31*d(1,2)*d(0,0) , 3 2 5 d(0,0) *(16*d(3,2)*d(0,0) + 15*d(1,2) ),32*d(0,0) ,0,0,0), 3 2 4 (5*d(0,0) *(d(4,0)*d(0,0) + 2*d(1,0) ),5*d(1,0)*d(0,0) , 3 5 d(0,0) *(d(4,2)*d(0,0) + 4*d(1,2)*d(1,0)),0,d(0,0) ,0,0), 2 2 (d(0,0)*(26*d(6,0)*d(1,2)*d(0,0) + 26*d(5,1)*d(1,0)*d(0,0) 3 2 + 31*d(5,0)*d(0,0) + 26*d(4,2)*d(4,0)*d(0,0) 2 2 + 16*d(4,2)*d(1,0) *d(0,0) - 98*d(4,0)*d(3,0)*d(0,0) 2 - 78*d(4,0)*d(1,2)*d(1,0)*d(0,0) - 26*d(4,0)*d(1,2)*d(0,0) 2 3 - 49*d(3,0)*d(1,0)*d(0,0) - 6*d(1,2)*d(1,0) 2 2 2 - 39*d(1,2)*d(1,0) *d(0,0)),d(0,0) *(31*d(5,1)*d(0,0) + 26*d(4,2)*d(1,0)*d(0,0) - 124*d(4,0)*d(1,2)*d(0,0) 2 - 16*d(1,2)*d(1,0) - 75*d(1,2)*d(1,0)*d(0,0)),d(0,0)*( 3 2 2 2 16*d(5,2)*d(0,0) + 30*d(5,1)*d(1,2)*d(0,0) + 15*d(4,2) *d(0,0) 2 2 - 64*d(4,0)*d(3,2)*d(0,0) - 45*d(4,0)*d(1,2) *d(0,0) 2 2 - 32*d(3,2)*d(1,0)*d(0,0) + 15*d(3,0)*d(1,2)*d(0,0) 2 2 2 - 5*d(1,2) *d(1,0) - 28*d(1,2) *d(1,0)*d(0,0)), 4 80*d(0,0) *( - 2*d(4,0) - d(1,0)), 3 5 d(0,0) *(31*d(4,2)*d(0,0) - 26*d(1,2)*d(1,0) - 31*d(1,2)*d(0,0)),32*d(0,0) 4 ,31*d(1,2)*d(0,0) ), 2 2 3 (5*d(0,0) *(d(6,0)*d(0,0) - 4*d(4,0)*d(1,0)*d(0,0) - 2*d(1,0) ), 3 2 2 2 5*d(0,0) *( - d(4,0)*d(0,0) - 2*d(1,0) ),d(0,0) *(d(5,1)*d(0,0) 2 - 4*d(4,2)*d(1,0)*d(0,0) + d(4,2)*d(0,0) - 4*d(4,0)*d(1,2)*d(0,0) 2 2 4 5 + d(3,0)*d(0,0) - 6*d(1,2)*d(1,0) ),0, - 5*d(1,0)*d(0,0) ,0,d(0,0) )) MATD**6:= 6 mat((d(0,0) ,0,0,0,0,0,0), 5 6 5 (6*d(1,0)*d(0,0) ,d(0,0) ,d(1,2)*d(0,0) ,0,0,0,0), (0,0,0,0,0,0,0), 4 5 (3*d(0,0) *(21*d(3,0)*d(0,0) + 19*d(1,2)*d(1,0)),63*d(1,2)*d(0,0) , 4 2 6 d(0,0) *(32*d(3,2)*d(0,0) + 31*d(1,2) ),64*d(0,0) ,0,0,0), 4 2 5 (3*d(0,0) *(2*d(4,0)*d(0,0) + 5*d(1,0) ),6*d(1,0)*d(0,0) , 4 6 d(0,0) *(d(4,2)*d(0,0) + 5*d(1,2)*d(1,0)),0,d(0,0) ,0,0), 2 2 2 (d(0,0) *(57*d(6,0)*d(1,2)*d(0,0) + 57*d(5,1)*d(1,0)*d(0,0) 3 2 + 63*d(5,0)*d(0,0) + 57*d(4,2)*d(4,0)*d(0,0) 2 2 + 42*d(4,2)*d(1,0) *d(0,0) - 258*d(4,0)*d(3,0)*d(0,0) 2 - 228*d(4,0)*d(1,2)*d(1,0)*d(0,0) - 57*d(4,0)*d(1,2)*d(0,0) 2 3 - 129*d(3,0)*d(1,0)*d(0,0) - 22*d(1,2)*d(1,0) 2 3 2 - 114*d(1,2)*d(1,0) *d(0,0)),3*d(0,0) *(21*d(5,1)*d(0,0) + 19*d(4,2)*d(1,0)*d(0,0) - 105*d(4,0)*d(1,2)*d(0,0) 2 2 - 14*d(1,2)*d(1,0) - 62*d(1,2)*d(1,0)*d(0,0)),d(0,0) *( 3 2 2 2 32*d(5,2)*d(0,0) + 62*d(5,1)*d(1,2)*d(0,0) + 31*d(4,2) *d(0,0) 2 2 - 160*d(4,0)*d(3,2)*d(0,0) - 124*d(4,0)*d(1,2) *d(0,0) 2 2 - 80*d(3,2)*d(1,0)*d(0,0) + 31*d(3,0)*d(1,2)*d(0,0) 2 2 2 - 16*d(1,2) *d(1,0) - 75*d(1,2) *d(1,0)*d(0,0)), 5 192*d(0,0) *( - 2*d(4,0) - d(1,0)), 4 3*d(0,0) *(21*d(4,2)*d(0,0) - 19*d(1,2)*d(1,0) - 21*d(1,2)*d(0,0)), 6 5 64*d(0,0) ,63*d(1,2)*d(0,0) ), 3 2 3 (2*d(0,0) *(3*d(6,0)*d(0,0) - 15*d(4,0)*d(1,0)*d(0,0) - 10*d(1,0) ), 4 2 3 2 3*d(0,0) *( - 2*d(4,0)*d(0,0) - 5*d(1,0) ),d(0,0) *(d(5,1)*d(0,0) 2 - 5*d(4,2)*d(1,0)*d(0,0) + d(4,2)*d(0,0) - 5*d(4,0)*d(1,2)*d(0,0) 2 2 5 6 + d(3,0)*d(0,0) - 10*d(1,2)*d(1,0) ),0, - 6*d(1,0)*d(0,0) ,0,d(0,0) )) MATD**7:= 7 mat((d(0,0) ,0,0,0,0,0,0), 6 7 6 (7*d(1,0)*d(0,0) ,d(0,0) ,d(1,2)*d(0,0) ,0,0,0,0), (0,0,0,0,0,0,0), 5 6 (d(0,0) *(127*d(3,0)*d(0,0) + 120*d(1,2)*d(1,0)),127*d(1,2)*d(0,0) , 5 2 7 d(0,0) *(64*d(3,2)*d(0,0) + 63*d(1,2) ),128*d(0,0) ,0,0,0), 5 2 6 (7*d(0,0) *(d(4,0)*d(0,0) + 3*d(1,0) ),7*d(1,0)*d(0,0) , 5 7 d(0,0) *(d(4,2)*d(0,0) + 6*d(1,2)*d(1,0)),0,d(0,0) ,0,0), 3 2 2 (d(0,0) *(120*d(6,0)*d(1,2)*d(0,0) + 120*d(5,1)*d(1,0)*d(0,0) 3 2 + 127*d(5,0)*d(0,0) + 120*d(4,2)*d(4,0)*d(0,0) 2 2 + 99*d(4,2)*d(1,0) *d(0,0) - 642*d(4,0)*d(3,0)*d(0,0) 2 - 600*d(4,0)*d(1,2)*d(1,0)*d(0,0) - 120*d(4,0)*d(1,2)*d(0,0) 2 3 - 321*d(3,0)*d(1,0)*d(0,0) - 64*d(1,2)*d(1,0) 2 4 2 - 300*d(1,2)*d(1,0) *d(0,0)),d(0,0) *(127*d(5,1)*d(0,0) + 120*d(4,2)*d(1,0)*d(0,0) - 762*d(4,0)*d(1,2)*d(0,0) 2 3 - 99*d(1,2)*d(1,0) - 441*d(1,2)*d(1,0)*d(0,0)),d(0,0) *( 3 2 2 2 64*d(5,2)*d(0,0) + 126*d(5,1)*d(1,2)*d(0,0) + 63*d(4,2) *d(0,0) 2 2 - 384*d(4,0)*d(3,2)*d(0,0) - 315*d(4,0)*d(1,2) *d(0,0) 2 2 - 192*d(3,2)*d(1,0)*d(0,0) + 63*d(3,0)*d(1,2)*d(0,0) 2 2 2 - 42*d(1,2) *d(1,0) - 186*d(1,2) *d(1,0)*d(0,0)), 6 448*d(0,0) *( - 2*d(4,0) - d(1,0)), 5 d(0,0) *(127*d(4,2)*d(0,0) - 120*d(1,2)*d(1,0) - 127*d(1,2)*d(0,0)), 7 6 128*d(0,0) ,127*d(1,2)*d(0,0) ), 4 2 3 (7*d(0,0) *(d(6,0)*d(0,0) - 6*d(4,0)*d(1,0)*d(0,0) - 5*d(1,0) ), 5 2 4 2 7*d(0,0) *( - d(4,0)*d(0,0) - 3*d(1,0) ),d(0,0) *(d(5,1)*d(0,0) 2 - 6*d(4,2)*d(1,0)*d(0,0) + d(4,2)*d(0,0) - 6*d(4,0)*d(1,2)*d(0,0) 2 2 6 7 + d(3,0)*d(0,0) - 15*d(1,2)*d(1,0) ),0, - 7*d(1,0)*d(0,0) ,0,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 0 0 0 0 0] [ ] [0 0 0 2 0 0 0] [ ] [0 0 0 0 1 0 0] [ ] [0 0 0 0 0 2 0] [ ] [0 0 0 0 0 0 1] 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), (d(1,0),d(0,0),d(1,2),0,0,0,0), (0,0,0,0,0,0,0), (d(3,0),d(1,2),d(3,2),2*d(0,0),0,0,0), (d(4,0),d(1,0),d(4,2),0,d(0,0),0,0), (d(5,0),d(5,1),d(5,2), - 2*d(4,0) - d(1,0),d(4,2) - d(1,2),2*d(0,0),d(1,2)), (d(6,0), - d(4,0),d(5,1) + d(4,2) + d(3,0),0, - d(1,0),0,d(0,0))) PP**(-1)*MATD*PP:= mat((d(0,0),0,0,0,0,0,0), (d(1,0),d(0,0),d(1,2),0,0,0,0), (0,0,0,0,0,0,0), (d(3,0),d(1,2),d(3,2),2*d(0,0),0,0,0), (d(4,0),d(1,0),d(4,2),0,d(0,0),0,0), (d(5,0),d(5,1),d(5,2), - 2*d(4,0) - d(1,0),d(4,2) - d(1,2),2*d(0,0),d(1,2)), (d(6,0), - d(4,0),d(5,1) + d(4,2) + d(3,0),0, - d(1,0),0,d(0,0))) 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), (d(1,0),d(0,0),d(1,2),0,0,0,0), (0,0,0,0,0,0,0), (d(3,0),d(1,2),d(3,2),2*d(0,0),0,0,0), (d(4,0),d(1,0),d(4,2),0,d(0,0),0,0), (d(5,0),d(5,1),d(5,2), - 2*d(4,0) - d(1,0),d(4,2) - d(1,2),2*d(0,0),d(1,2)), (d(6,0), - d(4,0),d(5,1) + d(4,2) + d(3,0),0, - d(1,0),0,d(0,0))) on voit apparaitre les poids sur la diagonale ladiag := {{1,d(0,0)}, {2,d(0,0)}, {3,0}, {4,2*d(0,0)}, {5,d(0,0)}, {6,2*d(0,0)}, {7,d(0,0)}} calcul de relations de commutation de la base diaY(j) diagonalisant le tore listcommutateursdesx := {{{0,1},x(3)}, {{0,2},x(1)}, {{0,3},0}, {{0,4}, - x(5)}, {{0,5},0}, {{0,6},x(5)}, {{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 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) listcommutateursdesdiay := {{{1,2},x(3)}, {{1,3},x(1)}, {{1,4},0}, {{1,5}, - x(5)}, {{1,6},0}, {{1,7},x(5)}, {{2,3},x(4)}, {{2,4},0}, {{2,5},x(5)}, {{2,6},0}, {{2,7},0}, {{3,4},x(5)}, {{3,5},x(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}} *** yy declared operator *** diadiay declared operator liste des commutateurs des diaY(i) := (diadiaY=diaY {{{1,2},diadiay(4)}, {{1,3},diadiay(2)}, {{1,4},0}, {{1,5}, - diadiay(6)}, {{1,6},0}, {{1,7},diadiay(6)}, {{2,3},diadiay(5)}, {{2,4},0}, {{2,5},diadiay(6)}, {{2,6},0}, {{2,7},0}, {{3,4},diadiay(6)}, {{3,5},diadiay(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 pose : *** zz declared operator ZZ(1):= - diay(3) ZZ(2):=diay(1) ZZ(3):=diay(2) ZZ(4):=diay(5) ZZ(5):= - diay(7) ZZ(6):=diay(4) ZZ(7):= - diay(6) *** zzz declared operator liste des commutateurs des ZZ(i) (ZZZ=ZZ:= {{{1,2},zzz(3)}, {{1,3},zzz(4)}, {{1,4},zzz(5)}, {{1,5},0}, {{1,6},zzz(7)}, {{1,7},0}, {{2,3},zzz(6)}, {{2,4},zzz(7)}, {{2,5},zzz(7)}, {{2,6},0}, {{2,7},0}, {{3,4}, - zzz(7)}, {{3,5},0}, {{3,6},0}, {{3,7},0}, {{4,5},0}, {{4,6},0}, {{4,7},0}, {{5,6},0}, {{5,7},0}, {{6,7},0}} Ce sont les relations de commutation de g_{7,1.03} page 204