a:=a$ delta:= mat((0,0,0,0,0,0),(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,a ,1,0,0))$ shortformdelta:={0,1,ss,0,1,ss,0,a}$ phase 1 de la resolution des equations$ on resout l'equation {{0,1},3} qui est maintenant AA:=d(2,1)$ Unknown: d(2,1) Unknown: d(2,1) bonne inconnue W:=d(2,1)$ sa valeur doit etre WW:=0$ on resout l'equation {{0,1},4} qui est maintenant AA:= - d(2,0)$ Unknown: d(2,0) Unknown: d(2,0) bonne inconnue W:=d(2,0)$ sa valeur doit etre WW:=0$ on resout l'equation {{0,1},5} qui est maintenant AA:=d(3,1)$ Unknown: d(3,1) Unknown: d(3,1) bonne inconnue W:=d(3,1)$ sa valeur doit etre WW:=0$ on resout l'equation {{0,1},6} qui est maintenant AA:=d(4,1) - d(3,0)$ Unknowns: {d(4,1),d(3,0)} Unknowns: {d(4,1),d(3,0)} bonne inconnue W:=d(4,1)$ sa valeur doit etre WW:=d(3,0)$ on resout l'equation {{0,2},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 {{0,2},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 {{0,2},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 {{0,2},3} qui est maintenant AA:= - d(3,3) + d(2,2) + d(0, 0)$ Unknowns: {d(3,3),d(2,2),d(0,0)} Unknowns: {d(3,3),d(2,2),d(0,0)} bonne inconnue W:=d(3,3)$ sa valeur doit etre WW:=d(2,2) + d(0,0)$ on resout l'equation {{0,2},4} qui est maintenant AA:= - d(4,3) + d(1,0)$ Unknowns: {d(4,3),d(1,0)} Unknowns: {d(4,3),d(1,0)} bonne inconnue W:=d(4,3)$ sa valeur doit etre WW:=d(1,0)$ on resout l'equation {{0,2},5} qui est maintenant AA:= - d(5,3) - d(4,0) + d(3, 2)$ Unknowns: {d(5,3),d(4,0),d(3,2)} Unknowns: {d(5,3),d(4,0),d(3,2)} bonne inconnue W:=d(5,3)$ sa valeur doit etre WW:= - d(4,0) + d(3,2)$ on resout l'equation {{0,2},6} qui est maintenant AA:= - d(6,3) + d(4,2) + d(3, 2)*a$ Unknowns: {d(6,3),d(4,2),d(3,2),a} Unknowns: {d(6,3),d(4,2),d(3,2),a} bonne inconnue W:=d(6,3)$ sa valeur doit etre WW:=d(4,2) + d(3,2)*a$ on resout l'equation {{0,3},0} qui est maintenant AA:= - (d(0,6)*a + d(0,5))$ Unknowns: {d(0,6),d(0,5),a} Unknowns: {d(0,6),d(0,5),a} bonne inconnue W:=d(0,5)$ sa valeur doit etre WW:= - d(0,6)*a$ on resout l'equation {{0,3},1} qui est maintenant AA:= - (d(1,6)*a + d(1,5))$ Unknowns: {d(1,6),d(1,5),a} Unknowns: {d(1,6),d(1,5),a} bonne inconnue W:=d(1,5)$ sa valeur doit etre WW:= - d(1,6)*a$ on resout l'equation {{0,3},2} qui est maintenant AA:= - (d(2,6)*a + d(2,5))$ Unknowns: {d(2,6),d(2,5),a} Unknowns: {d(2,6),d(2,5),a} bonne inconnue W:=d(2,5)$ sa valeur doit etre WW:= - d(2,6)*a$ on resout l'equation {{0,3},3} qui est maintenant AA:= - (d(3,6)*a + d(3,5))$ Unknowns: {d(3,6),d(3,5),a} Unknowns: {d(3,6),d(3,5),a} bonne inconnue W:=d(3,5)$ sa valeur doit etre WW:= - d(3,6)*a$ on resout l'equation {{0,3},4} qui est maintenant AA:= - (d(4,6)*a + d(4,5))$ Unknowns: {d(4,6),d(4,5),a} Unknowns: {d(4,6),d(4,5),a} bonne inconnue W:=d(4,5)$ sa valeur doit etre WW:= - d(4,6)*a$ on resout l'equation {{0,3},5} qui est maintenant AA:= - d(5,6)*a - d(5,5) + d( 2,2) + 2*d(0,0)$ Unknowns: {d(5,6),d(5,5),d(2,2),d(0,0),a} Unknowns: {d(5,6),d(5,5),d(2,2),d(0,0),a} bonne inconnue W:=d(5,5)$ sa valeur doit etre WW:= - d(5,6)*a + d(2,2) + 2*d(0,0)$ on resout l'equation {{0,3},6} qui est maintenant AA:= - d(6,6)*a - d(6,5) + d( 2,2)*a + 2*d(1,0) + 2*d(0,0)*a$ Unknowns: {d(6,6),d(6,5),d(2,2),d(1,0),d(0,0),a} Unknowns: {d(6,6),d(6,5),d(2,2),d(1,0),d(0,0),a} bonne inconnue W:=d(6,5)$ sa valeur doit etre WW:= - d(6,6)*a + d(2,2)*a + 2*d(1,0) + 2*d(0,0)*a$ on resout l'equation {{0,4},0} qui est maintenant AA:= - d(0,6)$ Unknown: d(0,6) Unknown: d(0,6) bonne inconnue W:=d(0,6)$ sa valeur doit etre WW:=0$ on resout l'equation {{0,4},1} qui est maintenant AA:= - d(1,6)$ Unknown: d(1,6) Unknown: d(1,6) bonne inconnue W:=d(1,6)$ sa valeur doit etre WW:=0$ on resout l'equation {{0,4},2} qui est maintenant AA:= - d(2,6)$ Unknown: d(2,6) Unknown: d(2,6) bonne inconnue W:=d(2,6)$ sa valeur doit etre WW:=0$ on resout l'equation {{0,4},3} qui est maintenant AA:= - d(3,6) + d(2,4)$ Unknowns: {d(3,6),d(2,4)} Unknowns: {d(3,6),d(2,4)} bonne inconnue W:=d(3,6)$ sa valeur doit etre WW:=d(2,4)$ on resout l'equation {{0,4},4} qui est maintenant AA:= - d(4,6)$ Unknown: d(4,6) Unknown: d(4,6) bonne inconnue W:=d(4,6)$ sa valeur doit etre WW:=0$ on resout l'equation {{0,4},5} qui est maintenant AA:= - d(5,6) + d(3,4)$ Unknowns: {d(5,6),d(3,4)} Unknowns: {d(5,6),d(3,4)} bonne inconnue W:=d(5,6)$ sa valeur doit etre WW:=d(3,4)$ on resout l'equation {{0,4},6} qui est maintenant AA:= - d(6,6) + d(4,4) + d(3, 4)*a + d(0,0)$ Unknowns: {d(6,6),d(4,4),d(3,4),d(0,0),a} Unknowns: {d(6,6),d(4,4),d(3,4),d(0,0),a} bonne inconnue W:=d(6,6)$ sa valeur doit etre WW:=d(4,4) + d(3,4)*a + d(0,0)$ on resout l'equation {{0,5},5} qui est maintenant AA:= - d(2,4)*a$ Unknowns: {d(2,4),a} Unknowns: {d(2,4),a} pas de selection possible de variable a coefficient independant des xi dans - d (2,4)*a on resout l'equation {{0,5},6} qui est maintenant AA:= - d(2,4)*a**2$ Unknowns: {d(2,4),a} Unknowns: {d(2,4),a} pas de selection possible de variable a coefficient independant des xi dans - d (2,4)*a**2 on resout l'equation {{0,6},5} 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},0} qui est maintenant AA:= - d(0,4)$ Unknown: d(0,4) Unknown: d(0,4) bonne inconnue W:=d(0,4)$ sa valeur doit etre WW:=0$ on resout l'equation {{1,2},1} qui est maintenant AA:= - d(1,4)$ Unknown: d(1,4) Unknown: d(1,4) bonne inconnue W:=d(1,4)$ sa valeur doit etre WW:=0$ on resout l'equation {{1,2},3} qui est maintenant AA:= - d(3,4) + d(0,1)$ Unknowns: {d(3,4),d(0,1)} Unknowns: {d(3,4),d(0,1)} bonne inconnue W:=d(3,4)$ sa valeur doit etre WW:=d(0,1)$ 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(3,0))$ Unknowns: {d(5,4),d(3,0)} Unknowns: {d(5,4),d(3,0)} bonne inconnue W:=d(5,4)$ sa valeur doit etre WW:= - d(3,0)$ on resout l'equation {{1,2},6} qui est maintenant AA:= - d(6,4) + d(3,2)$ Unknowns: {d(6,4),d(3,2)} Unknowns: {d(6,4),d(3,2)} bonne inconnue W:=d(6,4)$ sa valeur doit etre WW:=d(3,2)$ on resout l'equation {{1,4},6} qui est maintenant AA:=2*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 {{2,3},5} qui est maintenant AA:=d(1,0) + d(0,2)$ Unknowns: {d(1,0),d(0,2)} Unknowns: {d(1,0),d(0,2)} bonne inconnue W:=d(1,0)$ sa valeur doit etre WW:= - d(0,2)$ on resout l'equation {{2,3},6} qui est maintenant AA:=d(1,2) + d(0,2)*a$ Unknowns: {d(1,2),d(0,2),a} Unknowns: {d(1,2),d(0,2),a} bonne inconnue W:=d(1,2)$ sa valeur doit etre WW:= - d(0,2)*a$ on resout l'equation {{2,4},5} qui est maintenant AA:=d(2,2) + d(1,1) - 2*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) + 2*d(0,0)$ on resout l'equation {{2,4},6} qui est maintenant AA:=d(1,1)*a + 3*d(0,2) - d(0 ,0)*a$ 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(0,2)$ sa valeur doit etre WW:=(a*( - d(1,1) + d(0,0)))/3$ Derivation equations to cancel (Reduce output) : \\{{{{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},4},0}, {{{1,4},5},0}, {{{1,4},6},0}, {{{1,5},4},0}, {{{1,5},6},0}, {{{1,6},4},0}, {{{1,6},6},0}, {{{2,3},3},0}, {{{2,3},4},0}, {{{2,3},5},0}, {{{2,3},6},0}, {{{2,4},0},0}, {{{2,4},1},0}, {{{2,4},2},0}, {{{2,4},3},0}, {{{2,4},4},0}, {{{2,4},5},0}, {{{2,4},6},0}, {{{2,5},3},0}, {{{2,5},4},0}, {{{2,5},5},0}, {{{2,6},3},0}, {{{2,6},4},0}, {{{2,6},5},0}, {{{3,4},5},0}, {{{3,4},6},0}, {{{3,5},5},0}, {{{3,5},6},0}, {{{3,6},5},0}, {{{3,6},6},0}, {{{4,5},5},0}, {{{4,5},6},0}, {{{4,6},5},0}, {{{4,6},6},0}}$ il n'y a pas de phase 2$ derivation generique de gtildedelta:$ MATD:= mat((d(0,0),0,( - (d(1,1) - d(0,0))*a)/3,0,0,0,0),(((d(1,1) - d(0,0))*a)/3,d(1,1 ),((d(1,1) - d(0,0))*a**2)/3,0,0,0,0),(0,0, - (d(1,1) - 2*d(0,0)),0,0,0,0),(d(3, 0),0,d(3,2), - (d(1,1) - 3*d(0,0)),0,0,0),(d(4,0),d(3,0),d(4,2),((d(1,1) - d(0,0 ))*a)/3,2*d(0,0),0,0),(d(5,0),d(5,1),d(5,2), - (d(4,0) - d(3,2)), - d(3,0), - (d (1,1) - 4*d(0,0)),0),(d(6,0),d(6,1),d(6,2),d(4,2) + d(3,2)*a,d(3,2),( - (d(1,1) - d(0,0))*a)/3,3*d(0,0)))$ pour delta:= [0 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 a 1 0 0] pour shortformdelta:={0,1,ss,0,1,ss,0,a} Unknowns: {d(6,2), d(6,1), d(6,0), d(5,2), d(5,1), d(5,0), d(4,2), d(4,0), d(3,2), d(3,0), d(1,1), d(0,0), a} Unknowns: {d(6,2), d(6,1), d(6,0), d(5,2), d(5,1), d(5,0), d(4,2), d(4,0), d(3,2), d(3,0), d(1,1), d(0,0), a} listeparametresMATD{d(6,2), d(6,1), d(6,0), d(5,2), d(5,1), d(5,0), d(4,2), d(4,0), d(3,2), d(3,0), d(1,1), d(0,0)}$ dim Der(gtildedelta):=12$ un element t1 d'un tore $ t1:=D(0,0)$ t1:= [ a ] [ 1 0 --- 0 0 0 0] [ 3 ] [ ] [ 2 ] [ - a - a ] [------ 0 ------- 0 0 0 0] [ 3 3 ] [ ] [ 0 0 2 0 0 0 0] [ ] [ 0 0 0 3 0 0 0] [ ] [ - a ] [ 0 0 0 ------ 2 0 0] [ 3 ] [ ] [ 0 0 0 0 0 4 0] [ ] [ a ] [ 0 0 0 0 0 --- 3] [ 3 ] MATD:= - (d(1,1) - d(0,0))*a mat((d(0,0),0,------------------------,0,0,0,0), 3 2 (d(1,1) - d(0,0))*a (d(1,1) - d(0,0))*a (---------------------,d(1,1),----------------------,0,0,0,0), 3 3 (0,0, - (d(1,1) - 2*d(0,0)),0,0,0,0), (d(3,0),0,d(3,2), - (d(1,1) - 3*d(0,0)),0,0,0), (d(1,1) - d(0,0))*a (d(4,0),d(3,0),d(4,2),---------------------,2*d(0,0),0,0), 3 (d(5,0),d(5,1),d(5,2), - (d(4,0) - d(3,2)), - d(3,0), - (d(1,1) - 4*d(0,0)), 0), - (d(1,1) - d(0,0))*a (d(6,0),d(6,1),d(6,2),d(4,2) + d(3,2)*a,d(3,2),------------------------, 3 3*d(0,0))) {{x - 4, 1, [ 0 ] [ ] [ 0 ] [ ] [ 0 ] [ ] [ 0 ] [ ] [ 0 ] [ ] [ 3*arbcomplex(133) ] [-------------------] [ a ] [ ] [ arbcomplex(133) ] }, {x,1, [ 0 ] [ ] [arbcomplex(134)] [ ] [ 0 ] [ ] [ 0 ] [ ] [ 0 ] [ ] [ 0 ] [ ] [ 0 ] }, {x - 3, 2, [ 0 ] [ ] [ 0 ] [ ] [ 0 ] [ ] [ - 3*arbcomplex(135) ] [----------------------] [ a ] [ ] [ arbcomplex(135) ] [ ] [ 0 ] [ ] [ arbcomplex(136) ] }, {x - 2, 2, [ arbcomplex(137)*a ] [ ------------------- ] [ 3 ] [ ] [ 2 ] [ - 2*arbcomplex(137)*a ] [-------------------------] [ 9 ] [ ] [ arbcomplex(137) ] [ ] [ 0 ] [ ] [ arbcomplex(138) ] [ ] [ 0 ] [ ] [ 0 ] }, {x - 1, 1, [ - 3*arbcomplex(139) ] [----------------------] [ a ] [ ] [ arbcomplex(139) ] [ ] [ 0 ] [ ] [ 0 ] [ ] [ 0 ] [ ] [ 0 ] [ ] [ 0 ] }} Unknowns: {d(6,0),d(5,0),d(4,2),d(1,1),d(0,0),a} Unknowns: {d(6,0),d(5,0),d(4,2),d(1,1),d(0,0),a} commutant de t1 dans der(gtildedelta): - (d(1,1) - d(0,0))*a mat((d(0,0),0,------------------------,0,0,0,0), 3 2 (d(1,1) - d(0,0))*a (d(1,1) - d(0,0))*a (---------------------,d(1,1),----------------------,0,0,0,0), 3 3 (0,0, - (d(1,1) - 2*d(0,0)),0,0,0,0), (0,0,0, - (d(1,1) - 3*d(0,0)),0,0,0), (d(1,1) - d(0,0))*a (0,0,d(4,2),---------------------,2*d(0,0),0,0), 3 d(5,0)*a (d(5,0),0,----------,0,0, - (d(1,1) - 4*d(0,0)),0), 6 (6*d(6,0) - d(5,0)*a)*a - (d(1,1) - d(0,0))*a (d(6,0),0,-------------------------,d(4,2),0,------------------------, 18 3 3*d(0,0))) Unknowns: {d(6,0),d(5,0),d(4,2),d(1,1),d(0,0),a} Unknowns: {d(6,0),d(5,0),d(4,2),d(1,1),d(0,0),a} t2:=D(1,1):= [ - a ] [ 0 0 ------ 0 0 0 0] [ 3 ] [ ] [ 2 ] [ a a ] [--- 1 ---- 0 0 0 0] [ 3 3 ] [ ] [ 0 0 -1 0 0 0 0] [ ] [ 0 0 0 -1 0 0 0] [ ] [ a ] [ 0 0 0 --- 0 0 0] [ 3 ] [ ] [ 0 0 0 0 0 -1 0] [ ] [ - a ] [ 0 0 0 0 0 ------ 0] [ 3 ] {{x + 1, 3, [ arbcomplex(144)*a ] [ ------------------- ] [ 3 ] [ ] [ 2 ] [ - 2*arbcomplex(144)*a ] [-------------------------] [ 9 ] [ ] [ arbcomplex(144) ] [ ] [ - 3*arbcomplex(145) ] [ ---------------------- ] [ a ] [ ] [ arbcomplex(145) ] [ ] [ 3*arbcomplex(146) ] [ ------------------- ] [ a ] [ ] [ arbcomplex(146) ] }, {x, 3, [ - 3*arbcomplex(147) ] [----------------------] [ a ] [ ] [ arbcomplex(147) ] [ ] [ 0 ] [ ] [ 0 ] [ ] [ arbcomplex(148) ] [ ] [ 0 ] [ ] [ arbcomplex(149) ] }, {x - 1,1, [ 0 ] [ ] [arbcomplex(150)] [ ] [ 0 ] [ ] [ 0 ] [ ] [ 0 ] [ ] [ 0 ] [ ] [ 0 ] }} Unknowns: {d(6,0),d(1,1),d(0,0),a} Unknowns: {d(6,0),d(1,1),d(0,0),a} commutant simultane de t1,t2 dans der(gtildedelta): - (d(1,1) - d(0,0))*a mat((d(0,0),0,------------------------,0,0,0,0), 3 2 (d(1,1) - d(0,0))*a (d(1,1) - d(0,0))*a (---------------------,d(1,1),----------------------,0,0,0,0), 3 3 (0,0, - (d(1,1) - 2*d(0,0)),0,0,0,0), (0,0,0, - (d(1,1) - 3*d(0,0)),0,0,0), (d(1,1) - d(0,0))*a (0,0,0,---------------------,2*d(0,0),0,0), 3 (0,0,0,0,0, - (d(1,1) - 4*d(0,0)),0), - (d(1,1) - d(0,0))*a (d(6,0),0,0,0,0,------------------------,3*d(0,0))) 3 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:= [ a ] [ 1 0 --- 0 0 0 0] [ 3 ] [ ] [ 2 ] [ - a - 2*a ] [------ 1 --------- 0 0 0 0] [ 3 9 ] [ ] [ 0 0 1 0 0 0 0] [ ] [ 0 0 0 1 0 0 0] [ ] [ - a ] [ 0 0 0 ------ 1 0 0] [ 3 ] [ ] [ 0 0 0 0 0 1 0] [ ] [ a ] [ 0 0 0 0 0 --- 1] [ 3 ] P**(-1)*t1*P:= [1 0 0 0 0 0 0] [ ] [0 0 0 0 0 0 0] [ ] [0 0 2 0 0 0 0] [ ] [0 0 0 3 0 0 0] [ ] [0 0 0 0 2 0 0] [ ] [0 0 0 0 0 4 0] [ ] [0 0 0 0 0 0 3] P**(-1)*t2*P:= [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 0 0 0 0] [ ] [0 0 0 0 0 -1 0] [ ] [0 0 0 0 0 0 0] 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(1,1),0,0,0,0,0),(0,0, - (d(1,1) - 2*d(0,0)),0,0,0, 0),(d(3,0),0,(3*d(3,2) + d(3,0)*a)/3, - (d(1,1) - 3*d(0,0)),0,0,0),(d(4,0),d(3,0 ),((3*d(3,2) - d(3,0)*a + 3*d(4,0))*a + 9*d(4,2))/9,0,2*d(0,0),0,0),(4*d(5,0),d( 5,1),(3*d(5,2) + 7*d(5,0)*a)/3,(3*d(3,2) + d(3,0)*a - 3*d(4,0))/3, - d(3,0), - ( d(1,1) - 4*d(0,0)),0),(3*d(6,0) - d(5,0)*a,d(6,1) + 3*d(5,0),( - ((3*d(5,2) + 5* d(5,0)*a)*a - 9*d(6,2)))/9,((3*d(3,2) - d(3,0)*a + 3*d(4,0))*a + 9*d(4,2))/9,(3* d(3,2) + d(3,0)*a)/3,0,3*d(0,0)))$ PP:= mat((1,0,a/3,0,0,0,0),(( - a)/3,1,( - 2*a**2)/9,0,0,0,0),(0,0,1,0,0,0,0),(0,0,0, 1,0,0,0),(0,0,0,( - a)/3,1,0,0),(0,0,0,0,0,1,0),(0,0,0,0,0,a/3,1))$ avec PP:=P*Q:= mat((1,0,a/3,0,0,0,0),(( - a)/3,1,( - 2*a**2)/9,0,0,0,0),(0,0,1,0,0,0,0),(0,0,0, 1,0,0,0),(0,0,0,( - a)/3,1,0,0),(0,0,0,0,0,1,0),(0,0,0,0,0,a/3,1))$ on voit apparaitre les poids sur la diagonale$ ladiag := {{1,d(0,0)}, {2,d(1,1)}, {3, - (d(1,1) - 2*d(0,0))}, {4, - (d(1,1) - 3*d(0,0))}, {5,2*d(0,0)}, {6, - (d(1,1) - 4*d(0,0))}, {7,3*d(0,0)}}$ calcul de relations de commutation de la base diaY(j) diagonalisant le tore$ listcommutateursdesx := {{{0,1},0}, {{0,2},x(3)}, {{0,3},x(6)*a + x(5)}, {{0,4},x(6)}, {{0,5},0}, {{0,6},0}, {{1,2},x(4)}, {{1,3},x(6)}, {{1,4},0}, {{1,5},0}, {{1,6},0}, {{2,3},0}, {{2,4},x(5)}, {{2,5},0}, {{2,6},0}, {{3,4},0}, {{3,5},0}, {{3,6},0}, {{4,5},0}, {{4,6},0}, {{5,6},0}}$ diaY(1):=( - (x(1)*a - 3*x(0)))/3$ diaY(2):=x(1)$ diaY(3):=( - ((2*x(1)*a - 3*x(0))*a - 9*x(2)))/9$ diaY(4):=( - (x(4)*a - 3*x(3)))/3$ diaY(5):=x(4)$ diaY(6):=(x(6)*a + 3*x(5))/3$ diaY(7):=x(6)$ liste des commutateurs des diaY(i) := (diadiaY=diaY$ {{{1,2},0}, {{1,3},diadiay(4)}, {{1,4},diadiay(6)}, {{1,5},diadiay(7)}, {{1,6},0}, {{1,7},0}, {{2,3},diadiay(5)}, {{2,4},diadiay(7)}, {{2,5},0}, {{2,6},0}, {{2,7},0}, {{3,4},0}, {{3,5},diadiay(6)}, {{3,6},0}, {{3,7},0}, {{4,5},0}, {{4,6},0}, {{4,7},0}, {{5,6},0}, {{5,7},0}, {{6,7},0}}$ on pose :$ avec comme matrice de changement de base :$ [0 1 0 0 0 0 0 ] [ ] [0 0 1 0 0 0 0 ] [ ] [1 0 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 0 -1] det(isom):= 1 *** zz declared operator ZZ(1):=diay(3) ZZ(2):=diay(1) ZZ(3):=diay(2) ZZ(4):= - diay(4) ZZ(5):= - 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},0}, {{1,5},zzz(6)}, {{1,6},0}, {{1,7},0}, {{2,3},0}, {{2,4},zzz(6)}, {{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_{7,2.35}.$ Et cela pour a:=a.$ shortformdelta:={0,1,ss,0,1,ss,0,a}$