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),(0,1,0,0,0,0),(0,0,b ,1,0,0))$ shortformdelta:={0, ss, 1, 0, ss, 0, ss, 1, 0, ss, 0, b}$ 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(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(3,0) + d(2, 1)$ Unknowns: {d(5,3),d(3,0),d(2,1)} Unknowns: {d(5,3),d(3,0),d(2,1)} bonne inconnue W:=d(5,3)$ sa valeur doit etre WW:= - d(3,0) + d(2,1)$ on resout l'equation {{0,1},6} qui est maintenant AA:= - d(6,3) + d(4,1) - d(4, 0) + d(3,1)*b$ Unknowns: {d(6,3),d(4,1),d(4,0),d(3,1),b} Unknowns: {d(6,3),d(4,1),d(4,0),d(3,1),b} bonne inconnue W:=d(6,3)$ sa valeur doit etre WW:=d(4,1) - d(4,0) + d(3,1)*b$ on resout l'equation {{0,2},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 {{0,2},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 {{0,2},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 {{0,2},3} qui est maintenant AA:= - d(3,5) + d(1,2)$ Unknowns: {d(3,5),d(1,2)} Unknowns: {d(3,5),d(1,2)} bonne inconnue W:=d(3,5)$ sa valeur doit etre WW:=d(1,2)$ on resout l'equation {{0,2},4} qui est maintenant AA:= - d(4,5) + d(1,0)$ Unknowns: {d(4,5),d(1,0)} Unknowns: {d(4,5),d(1,0)} bonne inconnue W:=d(4,5)$ sa valeur doit etre WW:=d(1,0)$ on resout l'equation {{0,2},5} qui est maintenant AA:= - d(5,5) + d(2,2) + d(0, 0)$ Unknowns: {d(5,5),d(2,2),d(0,0)} Unknowns: {d(5,5),d(2,2),d(0,0)} bonne inconnue W:=d(5,5)$ sa valeur doit etre WW:=d(2,2) + d(0,0)$ on resout l'equation {{0,2},6} qui est maintenant AA:= - d(6,5) + d(4,2) + d(3, 2)*b + d(3,0)$ Unknowns: {d(6,5),d(4,2),d(3,2),d(3,0),b} Unknowns: {d(6,5),d(4,2),d(3,2),d(3,0),b} bonne inconnue W:=d(6,5)$ sa valeur doit etre WW:=d(4,2) + d(3,2)*b + d(3,0)$ on resout l'equation {{0,3},0} qui est maintenant AA:= - d(0,6)*b$ Unknowns: {d(0,6),b} Unknowns: {d(0,6),b} pas de selection possible de variable a coefficient independant des xi dans - d (0,6)*b on resout l'equation {{0,3},1} qui est maintenant AA:= - d(1,6)*b$ Unknowns: {d(1,6),b} Unknowns: {d(1,6),b} pas de selection possible de variable a coefficient independant des xi dans - d (1,6)*b on resout l'equation {{0,3},2} qui est maintenant AA:= - d(2,6)*b$ Unknowns: {d(2,6),b} Unknowns: {d(2,6),b} pas de selection possible de variable a coefficient independant des xi dans - d (2,6)*b on resout l'equation {{0,3},3} qui est maintenant AA:= - d(3,6)*b$ Unknowns: {d(3,6),b} Unknowns: {d(3,6),b} pas de selection possible de variable a coefficient independant des xi dans - d (3,6)*b on resout l'equation {{0,3},4} qui est maintenant AA:= - d(4,6)*b$ Unknowns: {d(4,6),b} Unknowns: {d(4,6),b} pas de selection possible de variable a coefficient independant des xi dans - d (4,6)*b on resout l'equation {{0,3},5} qui est maintenant AA:= - d(5,6)*b + d(1,0)$ Unknowns: {d(5,6),d(1,0),b} Unknowns: {d(5,6),d(1,0),b} bonne inconnue W:=d(1,0)$ sa valeur doit etre WW:=d(5,6)*b$ on resout l'equation {{0,3},6} qui est maintenant AA:= - d(6,6)*b - 2*d(2,0) + d(1,1)*b + 2*d(0,0)*b$ Unknowns: {d(6,6),d(2,0),d(1,1),d(0,0),b} Unknowns: {d(6,6),d(2,0),d(1,1),d(0,0),b} bonne inconnue W:=d(2,0)$ sa valeur doit etre WW:=(b*( - d(6,6) + d(1,1) + 2*d(0,0)))/2$ 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(1,4)$ Unknowns: {d(3,6),d(1,4)} Unknowns: {d(3,6),d(1,4)} bonne inconnue W:=d(3,6)$ sa valeur doit etre WW:=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(2,4)$ Unknowns: {d(5,6),d(2,4)} Unknowns: {d(5,6),d(2,4)} bonne inconnue W:=d(5,6)$ sa valeur doit etre WW:=d(2,4)$ on resout l'equation {{0,4},6} qui est maintenant AA:= - d(6,6) + d(4,4) + d(3, 4)*b + d(2,4)*b + d(0,0)$ Unknowns: {d(6,6),d(4,4),d(3,4),d(2,4),d(0,0),b} Unknowns: {d(6,6),d(4,4),d(3,4),d(2,4),d(0,0),b} bonne inconnue W:=d(6,6)$ sa valeur doit etre WW:=d(4,4) + d(3,4)*b + d(2,4)*b + d(0,0)$ on resout l'equation {{0,5},6} qui est maintenant AA:=b*(d(2,4) + d(1,2))$ Unknowns: {d(2,4),d(1,2),b} Unknowns: {d(2,4),d(1,2),b} pas de selection possible de variable a coefficient independant des xi dans b*(d (2,4) + d(1,2)) on resout l'equation {{0,6},6} qui est maintenant AA:=d(1,4)*b$ Unknowns: {d(1,4),b} Unknowns: {d(1,4),b} pas de selection possible de variable a coefficient independant des xi dans d(1, 4)*b 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},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) + d(0, 1)$ Unknowns: {d(5,4),d(3,2),d(0,1)} Unknowns: {d(5,4),d(3,2),d(0,1)} bonne inconnue W:=d(5,4)$ sa valeur doit etre WW:=d(3,2) + d(0,1)$ on resout l'equation {{1,2},6} qui est maintenant AA:= - d(6,4) + d(4,2) + d(3, 1)$ Unknowns: {d(6,4),d(4,2),d(3,1)} Unknowns: {d(6,4),d(4,2),d(3,1)} bonne inconnue W:=d(6,4)$ sa valeur doit etre WW:=d(4,2) + d(3,1)$ on resout l'equation {{1,3},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 {{1,3},5} qui est maintenant AA:= - d(2,2) + 2*d(1,1)$ Unknowns: {d(2,2),d(1,1)} Unknowns: {d(2,2),d(1,1)} bonne inconnue W:=d(2,2)$ sa valeur doit etre WW:=2*d(1,1)$ on resout l'equation {{1,3},6} qui est maintenant AA:=( - 2*d(4,2) - 2*d(3,2)*b - 2*d(3,0) - 2*d(2,1) + 2*d(1,1)*b - d(0,2)*b**2 + 2*d(0,1)*b - d(0,0)*b)/2$ Unknowns: {d(4,2),d(3,2),d(3,0),d(2,1),d(1,1),d(0,2),d(0,1),d(0,0),b} Unknowns: {d(4,2),d(3,2),d(3,0),d(2,1),d(1,1),d(0,2),d(0,1),d(0,0),b} bonne inconnue W:=d(4,2)$ sa valeur doit etre WW:=( - 2*d(3,2)*b - 2*d(3,0) - 2*d(2,1) + 2*d(1,1)*b - d(0, 2)*b**2 + 2*d(0,1)*b - d(0,0)*b)/2$ on resout l'equation {{1,4},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$ on resout l'equation {{1,4},6} qui est maintenant AA:=d(1,1) + d(0,1) - d(0,0)$ Unknowns: {d(1,1),d(0,1),d(0,0)} Unknowns: {d(1,1),d(0,1),d(0,0)} bonne inconnue W:=d(1,1)$ sa valeur doit etre WW:= - d(0,1) + d(0,0)$ 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},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},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}, {{{1,5},6},0}, {{{1,6},3},0}, {{{1,6},4},0}, {{{1,6},5},0}, {{{1,6},6},0}, {{{2,3},0},0}, {{{2,3},1},0}, {{{2,3},2},0}, {{{2,3},3},0}, {{{2,3},4},0}, {{{2,3},5},0}, {{{2,3},6},0}, {{{2,4},4},0}, {{{2,4},5},0}, {{{2,4},6},0}, {{{2,5},4},0}, {{{2,5},5},0}, {{{2,5},6},0}, {{{2,6},4},0}, {{{2,6},5},0}, {{{2,6},6},0}, {{{3,4},5},0}, {{{3,4},6},0}, {{{3,5},5},0}, {{{3,5},6},0}, {{{3,6},5},0}, {{{3,6},6},0}, {{{4,5},6},0}, {{{4,6},6},0}}$ Il y a une phase 2$ Pour a neq 0, on doit avoir$ d(2,2):= - 2*(d(0,1) - d(0,0))$ 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},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}, {{{1,5},6},0}, {{{1,6},3},0}, {{{1,6},4},0}, {{{1,6},5},0}, {{{1,6},6},0}, {{{2,3},0},0}, {{{2,3},1},0}, {{{2,3},2},0}, {{{2,3},3},0}, {{{2,3},4},0}, {{{2,3},5},0}, {{{2,3},6},0}, {{{2,4},4},0}, {{{2,4},5},0}, {{{2,4},6},0}, {{{2,5},4},0}, {{{2,5},5},0}, {{{2,5},6},0}, {{{2,6},4},0}, {{{2,6},5},0}, {{{2,6},6},0}, {{{3,4},5},0}, {{{3,4},6},0}, {{{3,5},5},0}, {{{3,5},6},0}, {{{3,6},5},0}, {{{3,6},6},0}, {{{4,5},6},0}, {{{4,6},6},0}}$ derivation generique de gtildedelta:$ MATD:= mat((d(0,0),d(0,1),0,0,0,0,0),(0, - (d(0,1) - d(0,0)),0,0,0,0,0),(((2*d(0,1) - d (0,0))*b)/2,d(2,1), - 2*(d(0,1) - d(0,0)),0,0,0,0),(d(3,0),d(3,1),d(3,2), - (d(0 ,1) - 2*d(0,0)),0,0,0),(d(4,0),d(4,1),( - (2*d(2,1) - d(0,0)*b + 2*d(3,0) + 2*d( 3,2)*b))/2,( - (2*d(0,1) - d(0,0))*b)/2, - 3*(d(0,1) - d(0,0)),0,0),(d(5,0),d(5, 1),d(5,2), - (d(3,0) - d(2,1)),d(3,2) + d(0,1), - (2*d(0,1) - 3*d(0,0)),0),(d(6, 0),d(6,1),d(6,2), - (d(4,0) - d(3,1)*b - d(4,1)),( - (2*d(2,1) - d(0,0)*b + 2*d( 3,0) - 2*d(3,1) + 2*d(3,2)*b))/2,( - (2*d(2,1) - d(0,0)*b))/2, - (3*d(0,1) - 4*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 1 0 0 0 0] [ ] [0 0 b 1 0 0] pour shortformdelta:={0, ss, 1, 0, ss, 0, ss, 1, 0, ss, 0, b} 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(3,1), d(3,0), d(2,1), d(0,1), d(0,0), b} 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(3,1), d(3,0), d(2,1), d(0,1), d(0,0), b} 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(3,1), d(3,0), d(2,1), d(0,1), d(0,0)}$ dim Der(gtildedelta):=14$ 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] [ ] [ - b ] [------ 0 2 0 0 0 0] [ 2 ] [ ] [ 0 0 0 2 0 0 0] [ ] [ b b ] [ 0 0 --- --- 3 0 0] [ 2 2 ] [ ] [ 0 0 0 0 0 3 0] [ ] [ b b ] [ 0 0 0 0 --- --- 4] [ 2 2 ] MATD:= mat((d(0,0),d(0,1),0,0,0,0,0), (0, - (d(0,1) - d(0,0)),0,0,0,0,0), (2*d(0,1) - d(0,0))*b (-----------------------,d(2,1), - 2*(d(0,1) - d(0,0)),0,0,0,0), 2 (d(3,0),d(3,1),d(3,2), - (d(0,1) - 2*d(0,0)),0,0,0), - (2*d(2,1) - d(0,0)*b + 2*d(3,0) + 2*d(3,2)*b) (d(4,0),d(4,1),--------------------------------------------------, 2 - (2*d(0,1) - d(0,0))*b --------------------------, - 3*(d(0,1) - d(0,0)),0,0), 2 (d(5,0),d(5,1),d(5,2), - (d(3,0) - d(2,1)),d(3,2) + d(0,1), - (2*d(0,1) - 3*d(0,0)),0), (d(6,0),d(6,1),d(6,2), - (d(4,0) - d(3,1)*b - d(4,1)), - (2*d(2,1) - d(0,0)*b + 2*d(3,0) - 2*d(3,1) + 2*d(3,2)*b) -------------------------------------------------------------, 2 - (2*d(2,1) - d(0,0)*b) --------------------------, - (3*d(0,1) - 4*d(0,0)))) 2 {{x - 1, 2, [ 48*arbcomplex(140) ] [ -------------------- ] [ 3 ] [ b ] [ ] [ arbcomplex(139) ] [ ] [ 24*arbcomplex(140) ] [ -------------------- ] [ 2 ] [ b ] [ ] [ 0 ] [ ] [ - 6*arbcomplex(140) ] [----------------------] [ b ] [ ] [ 0 ] [ ] [ arbcomplex(140) ] }, {x - 4,1, [ 0 ] [ ] [ 0 ] [ ] [ 0 ] [ ] [ 0 ] [ ] [ 0 ] [ ] [ 0 ] [ ] [arbcomplex(141)] }, {x - 3, 2, [ 0 ] [ ] [ 0 ] [ ] [ 0 ] [ ] [ 0 ] [ ] [ - (2*arbcomplex(143) + arbcomplex(142)*b) ] [--------------------------------------------] [ b ] [ ] [ arbcomplex(142) ] [ ] [ arbcomplex(143) ] }, {x - 2, 2, [ 0 ] [ ] [ 0 ] [ ] [ 2 ] [ 8*arbcomplex(145) - arbcomplex(144)*b ] [----------------------------------------] [ 2 ] [ b ] [ ] [ arbcomplex(144) ] [ ] [ - 4*arbcomplex(145) ] [ ---------------------- ] [ b ] [ ] [ 0 ] [ ] [ arbcomplex(145) ] }} Unknowns: {d(6,0),d(5,0),d(3,2),d(3,0),d(0,1),d(0,0),b} Unknowns: {d(6,0),d(5,0),d(3,2),d(3,0),d(0,1),d(0,0),b} commutant de t1 dans der(gtildedelta): mat((d(0,0),d(0,1),0,0,0,0,0), (0, - (d(0,1) - d(0,0)),0,0,0,0,0), (2*d(0,1) - d(0,0))*b d(0,1)*b (-----------------------,----------, - 2*(d(0,1) - d(0,0)),0,0,0,0), 2 2 (d(3,0),0,d(3,2), - (d(0,1) - 2*d(0,0)),0,0,0), 2 - (4*d(3,0) + d(0,1)*b)*b - d(0,1)*b (----------------------------,--------------, 8 8 - ((d(0,1) - d(0,0))*b - 2*d(3,0)) - (2*d(0,1) - d(0,0))*b -------------------------------------,--------------------------, 2 2 - 3*(d(0,1) - d(0,0)),0,0), - (2*d(3,0) - d(0,1)*b) - (2*d(3,0) - d(0,1)*b) (d(5,0),0,--------------------------,--------------------------, 2 2 d(3,2) + d(0,1), - (2*d(0,1) - 3*d(0,0)),0), 3 d(0,1)*b (2*d(3,0) - d(0,1)*b)*b d(3,0)*b (d(6,0),-----------,-------------------------,----------, 48 8 2 - ((d(0,1) - d(0,0))*b - 2*d(3,0)) - (d(0,1) - d(0,0))*b -------------------------------------,------------------------, 2 2 - (3*d(0,1) - 4*d(0,0)))) on peut prendre comme element semi simple du commutant de t1 dans der(gtildede\ lta): Unknowns: {d(6,0),d(5,0),d(3,2),d(3,0),d(0,1),d(0,0),b} Unknowns: {d(6,0),d(5,0),d(3,2),d(3,0),d(0,1),d(0,0),b} t2:=D(0,1):= [ 0 1 0 0 0 0 0 ] [ ] [ 0 -1 0 0 0 0 0 ] [ ] [ b ] [ b --- -2 0 0 0 0 ] [ 2 ] [ ] [ 0 0 0 -1 0 0 0 ] [ ] [ 2 2 ] [ - b - b - b ] [------- ------- ------ - b -3 0 0 ] [ 8 8 2 ] [ ] [ b b ] [ 0 0 --- --- 1 -2 0 ] [ 2 2 ] [ ] [ 3 ] [ b - b - b ] [ 0 ---- 0 0 ------ ------ -3] [ 48 2 2 ] {{x + 1, 2, [ 8*arbcomplex(150) ] [ ------------------- ] [ 2 ] [ b ] [ ] [ - 8*arbcomplex(150) ] [ ---------------------- ] [ 2 ] [ b ] [ ] [ 4*arbcomplex(150) ] [ ------------------- ] [ b ] [ ] [ 2*(12*arbcomplex(151) + arbcomplex(150)*b) ] [ -------------------------------------------- ] [ 2 ] [ 3*b ] [ ] [ - 4*(3*arbcomplex(151) + arbcomplex(150)*b) ] [----------------------------------------------] [ 3*b ] [ ] [ arbcomplex(150) ] [ ] [ arbcomplex(151) ] }, {x + 2, 2, [ 0 ] [ ] [ 0 ] [ ] [ 2*(2*arbcomplex(153) + arbcomplex(152)*b) ] [------------------------------------------- ] [ 2 ] [ b ] [ ] [ 0 ] [ ] [ - (2*arbcomplex(153) + arbcomplex(152)*b) ] [--------------------------------------------] [ b ] [ ] [ arbcomplex(152) ] [ ] [ arbcomplex(153) ] }, {x + 3, 2, [ 0 ] [ ] [ 0 ] [ ] [ 0 ] [ ] [ 0 ] [ ] [ - arbcomplex(154)] [ ] [ arbcomplex(154) ] [ ] [ arbcomplex(155) ] }, {x, 1, [ 96*arbcomplex(156) ] [ -------------------- ] [ 3 ] [ b ] [ ] [ 0 ] [ ] [ 48*arbcomplex(156) ] [ -------------------- ] [ 2 ] [ b ] [ ] [ 0 ] [ ] [ - 12*arbcomplex(156) ] [-----------------------] [ b ] [ ] [ 6*arbcomplex(156) ] [ ------------------- ] [ b ] [ ] [ arbcomplex(156) ] }} Unknowns: {d(0,1),d(0,0),b} Unknowns: {d(0,1),d(0,0),b} commutant simultane de t1,t2 dans der(gtildedelta): mat((d(0,0),d(0,1),0,0,0,0,0), (0, - (d(0,1) - d(0,0)),0,0,0,0,0), (2*d(0,1) - d(0,0))*b d(0,1)*b (-----------------------,----------, - 2*(d(0,1) - d(0,0)),0,0,0,0), 2 2 (0,0,0, - (d(0,1) - 2*d(0,0)),0,0,0), 2 2 - d(0,1)*b - d(0,1)*b - (d(0,1) - d(0,0))*b (--------------,--------------,------------------------, 8 8 2 - (2*d(0,1) - d(0,0))*b --------------------------, - 3*(d(0,1) - d(0,0)),0,0), 2 d(0,1)*b d(0,1)*b (0,0,----------,----------,d(0,1), - (2*d(0,1) - 3*d(0,0)),0), 2 2 3 d(0,1)*b - (d(0,1) - d(0,0))*b - (d(0,1) - d(0,0))*b (0,-----------,0,0,------------------------,------------------------, 48 2 2 - (3*d(0,1) - 4*d(0,0)))) t1,t2 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] [ ] [ b ] [ --- 0 1 -1 0 0 0] [ 2 ] [ ] [ 0 0 0 1 0 0 0] [ ] [ 2 ] [ - b - b ] [------- 0 ------ 0 1 -1 0] [ 8 2 ] [ ] [ 0 0 0 0 0 1 0] [ ] [ 3 2 ] [ b b - b ] [ ---- 0 ---- 0 ------ 0 1] [ 48 8 2 ] P**(-1)*t1*P:= [1 0 0 0 0 0 0] [ ] [0 1 0 0 0 0 0] [ ] [0 0 2 0 0 0 0] [ ] [0 0 0 2 0 0 0] [ ] [0 0 0 0 3 0 0] [ ] [0 0 0 0 0 3 0] [ ] [0 0 0 0 0 0 4] P**(-1)*t2*P:= [ 0 1 0 0 0 0 0 ] [ ] [ 0 -1 0 0 0 0 0 ] [ ] [ 0 0 -2 1 0 0 0 ] [ ] [ 0 0 0 -1 0 0 0 ] [ ] [ 2 ] [ b ] [---- 0 0 0 -2 0 0 ] [ 8 ] [ ] [ 2 ] [ b ] [---- 0 0 0 1 -3 0 ] [ 8 ] [ ] [ 3 2 2 ] [ b b - b ] [---- 0 ---- ------- 0 0 -3] [ 16 8 8 ] 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(0,1) - d(0,0)),0,0,0,0,0),(0,(2*d(2,1) - d(0,1)*b + 2*d(3,1))/2, - (2*(d(0,1) - d(0,0)) - d(3,2)), - (d(3,2) - d(0,1)),0, 0,0),(0,d(3,1),d(3,2), - (d(0,1) - 2*d(0,0) + d(3,2)),0,0,0),(( - ((2*d(2,1) - d (0,1)*b - 3*d(3,0))*b - 4*d(4,0) + 4*d(5,0)))/4,((4*d(2,1) - d(0,1)*b + 4*d(3,1) )*b + 8*d(4,1) + 8*d(5,1))/8,d(3,0) - d(2,1) + d(5,2),( - (2*d(3,0) - 4*d(2,1) + d(0,1)*b + 2*d(5,2)))/2, - (2*d(0,1) - 3*d(0,0) - d(3,2)), - d(3,2),0),(((2*d(3 ,0) - d(0,1)*b)*b - 8*d(5,0))/8,d(5,1),(2*d(3,0) - d(0,1)*b + 2*d(5,2))/2, - (d( 3,0) - d(2,1) + d(5,2)),d(3,2) + d(0,1), - (3*(d(0,1) - d(0,0)) + d(3,2)),0),(( - (((d(2,1) - d(0,1)*b - 4*d(3,0) + d(3,1))*b - 4*d(4,0) + 8*d(5,0))*b + 16*d(6, 0)))/8,(((6*d(2,1) - d(0,1)*b + 6*d(3,1))*b + 24*d(4,1) + 24*d(5,1))*b + 48*d(6, 1))/48,( - (16*d(5,0) + 4*d(3,1)*b - 2*d(3,0)*b + d(0,1)*b**2 - 8*d(6,2)))/8,(16 *d(5,0) + 8*d(4,1) - 8*d(4,0) + 8*d(3,1)*b - 6*d(3,0)*b + 8*d(2,1)*b - 3*d(0,1)* b**2 - 8*d(6,2))/8,( - (2*d(2,1) - d(0,1)*b - 2*d(3,1)))/2, - d(3,1), - (3*d(0,1 ) - 4*d(0,0))))$ PP:= mat((1,-1,0,0,0,0,0),(0,1,0,0,0,0,0),(b/2,( - b)/2,1,0,0,0,0),(0,0,0,1,0,0,0),(( - b**2)/8,b**2/8,( - b)/2,( - b)/2,1,0,0),(0,0,0,0,0,1,0),(b**3/48,( - b**3)/48 ,b**2/8,b**2/8,( - b)/2,( - b)/2,1))$ PP**(-1)*t1*PP:= mat((1,0,0,0,0,0,0),(0,1,0,0,0,0,0),(0,0,2,0,0,0,0),(0,0,0,2,0,0,0),(0,0,0,0,3,0 ,0),(0,0,0,0,0,3,0),(0,0,0,0,0,0,4))$ PP**(-1)*t2*PP:= mat((0,0,0,0,0,0,0),(0,-1,0,0,0,0,0),(0,0,-2,0,0,0,0),(0,0,0,-1,0,0,0),(0,0,0,0, -3,0,0),(b**2/8,( - b**2)/8,0,0,1,-2,0),(b**3/16,( - b**3)/16,b**2/8,0,0,0,-3))$ PP**(-1)*MATD*PP:= mat((d(0,0),0,0,0,0,0,0),(0, - (d(0,1) - d(0,0)),0,0,0,0,0),(0,(2*d(2,1) - d(0,1 )*b)/2, - 2*(d(0,1) - d(0,0)),0,0,0,0),(0,d(3,1),d(3,2), - (d(0,1) - 2*d(0,0)),0 ,0,0),(( - ((4*d(2,1) - 3*d(0,1)*b - 4*d(3,0))*b - 8*d(4,0)))/8,((2*d(2,1) - d(0 ,1)*b - d(3,0) + d(3,1))*b - 2*d(4,0) + 2*d(4,1))/2,( - (2*d(2,1) - d(0,1)*b))/2 ,0, - 3*(d(0,1) - d(0,0)),0,0),(((2*d(3,0) - d(0,1)*b)*b - 8*d(5,0))/8,( - ((2*d (3,0) - d(0,1)*b)*b - 8*d(5,0) - 8*d(5,1)))/8,(2*d(3,0) - d(0,1)*b + 2*d(5,2))/2 ,(2*d(2,1) - d(0,1)*b)/2,d(3,2) + d(0,1), - (2*d(0,1) - 3*d(0,0)),0),(( - (((d(2 ,1) - d(0,1)*b - 4*d(3,0) + d(3,1))*b - 4*d(4,0) + 8*d(5,0))*b + 16*d(6,0)))/8,( ((12*d(2,1) - 7*d(0,1)*b - 24*d(3,0) + 12*d(3,1))*b - 24*d(4,0) + 24*d(4,1) + 48 *d(5,0) + 24*d(5,1))*b + 96*d(6,0) + 48*d(6,1))/48,( - (16*d(5,0) + 4*d(3,1)*b - 2*d(3,0)*b + d(0,1)*b**2 - 8*d(6,2)))/8,((2*d(2,1) - d(0,1)*b - d(3,0) + d(3,1) )*b - 2*d(4,0) + 2*d(4,1))/2,( - (2*d(2,1) - d(0,1)*b - 2*d(3,1)))/2,( - (2*d(2, 1) - d(0,1)*b))/2, - (3*d(0,1) - 4*d(0,0))))$ avec PP:=P*Q:= mat((1,-1,0,0,0,0,0),(0,1,0,0,0,0,0),(b/2,( - b)/2,1,0,0,0,0),(0,0,0,1,0,0,0),(( - b**2)/8,b**2/8,( - b)/2,( - b)/2,1,0,0),(0,0,0,0,0,1,0),(b**3/48,( - b**3)/48 ,b**2/8,b**2/8,( - b)/2,( - b)/2,1))$ MATDDIAGONALISE:= mat((d(0,0),0,0,0,0,0,0),(0, - (d(0,1) - d(0,0)),0,0,0,0,0),(0,(2*d(2,1) - d(0,1 )*b)/2, - 2*(d(0,1) - d(0,0)),0,0,0,0),(0,d(3,1),d(3,2), - (d(0,1) - 2*d(0,0)),0 ,0,0),(( - ((4*d(2,1) - 3*d(0,1)*b - 4*d(3,0))*b - 8*d(4,0)))/8,((2*d(2,1) - d(0 ,1)*b - d(3,0) + d(3,1))*b - 2*d(4,0) + 2*d(4,1))/2,( - (2*d(2,1) - d(0,1)*b))/2 ,0, - 3*(d(0,1) - d(0,0)),0,0),(((2*d(3,0) - d(0,1)*b)*b - 8*d(5,0))/8,( - ((2*d (3,0) - d(0,1)*b)*b - 8*d(5,0) - 8*d(5,1)))/8,(2*d(3,0) - d(0,1)*b + 2*d(5,2))/2 ,(2*d(2,1) - d(0,1)*b)/2,d(3,2) + d(0,1), - (2*d(0,1) - 3*d(0,0)),0),(( - (((d(2 ,1) - d(0,1)*b - 4*d(3,0) + d(3,1))*b - 4*d(4,0) + 8*d(5,0))*b + 16*d(6,0)))/8,( ((12*d(2,1) - 7*d(0,1)*b - 24*d(3,0) + 12*d(3,1))*b - 24*d(4,0) + 24*d(4,1) + 48 *d(5,0) + 24*d(5,1))*b + 96*d(6,0) + 48*d(6,1))/48,( - (16*d(5,0) + 4*d(3,1)*b - 2*d(3,0)*b + d(0,1)*b**2 - 8*d(6,2)))/8,((2*d(2,1) - d(0,1)*b - d(3,0) + d(3,1) )*b - 2*d(4,0) + 2*d(4,1))/2,( - (2*d(2,1) - d(0,1)*b - 2*d(3,1)))/2,( - (2*d(2, 1) - d(0,1)*b))/2, - (3*d(0,1) - 4*d(0,0))))$ on voit apparaitre les poids sur la diagonale$ ladiag := {{1,d(0,0)}, {2, - (d(0,1) - d(0,0))}, {3, - 2*(d(0,1) - d(0,0))}, {4, - (d(0,1) - 2*d(0,0))}, {5, - 3*(d(0,1) - d(0,0))}, {6, - (2*d(0,1) - 3*d(0,0))}, {7, - (3*d(0,1) - 4*d(0,0))}}$ calcul de relations de commutation de la base diaY(j) diagonalisant le tore$ listcommutateursdesx := {{{0,1},x(3)}, {{0,2},x(5)}, {{0,3},b*x(6)}, {{0,4},x(6)}, {{0,5},0}, {{0,6},0}, {{1,2},x(4)}, {{1,3},x(5)}, {{1,4},x(6)}, {{1,5},0}, {{1,6},0}, {{2,3}, - x(6)}, {{2,4},0}, {{2,5},0}, {{2,6},0}, {{3,4},0}, {{3,5},0}, {{3,6},0}, {{4,5},0}, {{4,6},0}, {{5,6},0}}$ diaY(1):=(6*(4*(x(2)*b + 2*x(0)) - x(4)*b**2) + x(6)*b**3)/48$ diaY(2):=(6*(4*(2*(x(1) - x(0)) - x(2)*b) + x(4)*b**2) - x(6)*b**3)/48$ diaY(3):=( - (4*(x(4)*b - 2*x(2)) - x(6)*b**2))/8$ diaY(4):=( - (4*(x(4)*b - 2*x(3)) - x(6)*b**2))/8$ diaY(5):=( - (x(6)*b - 2*x(4)))/2$ diaY(6):=( - (x(6)*b - 2*x(5)))/2$ diaY(7):=x(6)$ liste des commutateurs des diaY(i) := (diadiaY=diaY$ {{{1,2},diadiay(4)}, {{1,3},diadiay(6)}, {{1,4},0}, {{1,5},diadiay(7)}, {{1,6},0}, {{1,7},0}, {{2,3}, - (diadiay(6) - diadiay(5))}, {{2,4},diadiay(6)}, {{2,5},0}, {{2,6},0}, {{2,7},0}, {{3,4}, - diadiay(7)}, {{3,5},0}, {{3,6},0}, {{3,7},0}, {{4,5},0}, {{4,6},0}, {{4,7},0}, {{5,6},0}, {{5,7},0}, {{6,7},0}}$ on pose :$ avec comme matrice de changemment de base :$ [0 1 0 0 0 0 0] [ ] [-1 0 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 -1 -1 0] [ ] [0 0 0 0 0 0 1] det(isom):= 1 *** zz declared operator ZZ(1):= - diay(2) ZZ(2):=diay(1) ZZ(3):= - diay(3) ZZ(4):=diay(4) ZZ(5):= - (diay(6) - diay(5)) ZZ(6):= - diay(6) ZZ(7):=diay(7) *** zzz declared operator liste des commutateurs des ZZ(i) (ZZZ=ZZ:= {{{1,2},zzz(4)}, {{1,3},zzz(5)}, {{1,4},zzz(6)}, {{1,5},0}, {{1,6},0}, {{1,7},0}, {{2,3},zzz(6)}, {{2,4},0}, {{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}} On obtient donc les relations de commutation de g_{7,2.1(v)}. Cela pour a = 1 et quel que soit b.