Cas a:=1.$ 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),(0,0,0,1,0,0),(0,0,1 ,0,0,0))$ shortformdelta:={0, ss, 0, 1, ss, 0, ss, 0, 0, ss, 0, 1}$ 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(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 {{0,1},6} qui est maintenant AA:= - d(4,0) + d(3,1)$ Unknowns: {d(4,0),d(3,1)} Unknowns: {d(4,0),d(3,1)} bonne inconnue W:=d(4,0)$ sa valeur doit etre WW:=d(3,1)$ 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(4,2)$ Unknowns: {d(5,3),d(4,2)} Unknowns: {d(5,3),d(4,2)} bonne inconnue W:=d(5,3)$ sa valeur doit etre WW:=d(4,2)$ on resout l'equation {{0,2},6} qui est maintenant AA:= - d(6,3) + d(3,2) + d(3, 0)$ Unknowns: {d(6,3),d(3,2),d(3,0)} Unknowns: {d(6,3),d(3,2),d(3,0)} bonne inconnue W:=d(6,3)$ sa valeur doit etre WW:=d(3,2) + d(3,0)$ on resout l'equation {{0,3},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 {{0,3},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 {{0,3},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 {{0,3},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 {{0,3},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 {{0,3},5} qui est maintenant AA:= - d(5,6) + 2*d(1,0)$ Unknowns: {d(5,6),d(1,0)} Unknowns: {d(5,6),d(1,0)} bonne inconnue W:=d(5,6)$ sa valeur doit etre WW:=2*d(1,0)$ on resout l'equation {{0,3},6} qui est maintenant AA:= - d(6,6) + d(2,2) + 2*d( 0,0)$ Unknowns: {d(6,6),d(2,2),d(0,0)} Unknowns: {d(6,6),d(2,2),d(0,0)} bonne inconnue W:=d(6,6)$ sa valeur doit etre WW:=d(2,2) + 2*d(0,0)$ on resout l'equation {{0,4},0} qui est maintenant AA:= - d(0,5)$ Unknown: d(0,5) Unknown: d(0,5) bonne inconnue W:=d(0,5)$ sa valeur doit etre WW:=0$ on resout l'equation {{0,4},1} qui est maintenant AA:= - d(1,5)$ Unknown: d(1,5) Unknown: d(1,5) bonne inconnue W:=d(1,5)$ sa valeur doit etre WW:=0$ on resout l'equation {{0,4},2} qui est maintenant AA:= - d(2,5)$ Unknown: d(2,5) Unknown: d(2,5) bonne inconnue W:=d(2,5)$ sa valeur doit etre WW:=0$ on resout l'equation {{0,4},3} qui est maintenant AA:= - d(3,5) + d(2,4)$ Unknowns: {d(3,5),d(2,4)} Unknowns: {d(3,5),d(2,4)} bonne inconnue W:=d(3,5)$ sa valeur doit etre WW:=d(2,4)$ on resout l'equation {{0,4},4} qui est maintenant AA:= - d(4,5)$ Unknown: d(4,5) Unknown: d(4,5) bonne inconnue W:=d(4,5)$ sa valeur doit etre WW:=0$ on resout l'equation {{0,4},5} qui est maintenant AA:= - d(5,5) + d(4,4) + d(0, 0)$ Unknowns: {d(5,5),d(4,4),d(0,0)} Unknowns: {d(5,5),d(4,4),d(0,0)} bonne inconnue W:=d(5,5)$ sa valeur doit etre WW:=d(4,4) + d(0,0)$ on resout l'equation {{0,4},6} qui est maintenant AA:= - d(6,5) + d(3,4) + d(1, 0)$ Unknowns: {d(6,5),d(3,4),d(1,0)} Unknowns: {d(6,5),d(3,4),d(1,0)} bonne inconnue W:=d(6,5)$ sa valeur doit etre WW:=d(3,4) + d(1,0)$ on resout l'equation {{0,5},6} 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(3,2)$ Unknowns: {d(5,4),d(3,2)} Unknowns: {d(5,4),d(3,2)} bonne inconnue W:=d(5,4)$ sa valeur doit etre WW:=d(3,2)$ 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 {{1,4},5} qui est maintenant AA:=2*( - d(1,0) + d(0,1))$ Unknowns: {d(1,0),d(0,1)} Unknowns: {d(1,0),d(0,1)} bonne inconnue W:=d(1,0)$ sa valeur doit etre WW:=d(0,1)$ on resout l'equation {{1,4},6} qui est maintenant AA:=2*(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 resout l'equation {{2,3},5} qui est maintenant AA:=d(1,2) + 2*d(0,1)$ Unknowns: {d(1,2),d(0,1)} Unknowns: {d(1,2),d(0,1)} bonne inconnue W:=d(0,1)$ sa valeur doit etre WW:=( - d(1,2))/2$ on resout l'equation {{2,3},6} qui est maintenant AA:= - d(2,2) + d(0,2) + d(0, 0)$ Unknowns: {d(2,2),d(0,2),d(0,0)} Unknowns: {d(2,2),d(0,2),d(0,0)} bonne inconnue W:=d(2,2)$ sa valeur doit etre WW:=d(0,2) + d(0,0)$ on resout l'equation {{2,4},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 {{2,4},6} qui est maintenant AA:=(3*d(1,2))/2$ Unknown: d(1,2) Unknown: d(1,2) bonne inconnue W:=d(1,2)$ sa valeur doit etre WW:=0$ 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},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},4},0}, {{{1,5},5},0}, {{{1,5},6},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},3},0}, {{{2,4},4},0}, {{{2,4},5},0}, {{{2,4},6},0}, {{{2,5},3},0}, {{{2,5},4},0}, {{{2,5},6},0}, {{{2,6},3},0}, {{{2,6},4},0}, {{{2,6},6},0}, {{{3,4},5},0}, {{{3,4},6},0}, {{{3,5},5},0}, {{{3,5},6},0}, {{{3,6},5},0}, {{{3,6},6},0}, {{{4,5},5},0}, {{{4,5},6},0}, {{{4,6},5},0}, {{{4,6},6},0}}$ il n'y a pas de phase 2$ collect_eq:={{{{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},4},0}, {{{1,5},5},0}, {{{1,5},6},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},3},0}, {{{2,4},4},0}, {{{2,4},5},0}, {{{2,4},6},0}, {{{2,5},3},0}, {{{2,5},4},0}, {{{2,5},6},0}, {{{2,6},3},0}, {{{2,6},4},0}, {{{2,6},6},0}, {{{3,4},5},0}, {{{3,4},6},0}, {{{3,5},5},0}, {{{3,5},6},0}, {{{3,6},5},0}, {{{3,6},6},0}, {{{4,5},5},0}, {{{4,5},6},0}, {{{4,6},5},0}, {{{4,6},6},0}}$ derivation generique de gtildedelta:$ MATD:= mat((d(0,0),0,0,0,0,0,0),(0,d(0,0),0,0,0,0,0),(0,0,d(0,0),0,0,0,0),(d(3,0),d(3,1 ),d(3,2),2*d(0,0),0,0,0),(d(3,1),d(3,0),d(4,2),0,2*d(0,0),0,0),(d(5,0),d(5,1),d( 5,2),d(4,2),d(3,2),3*d(0,0),0),(d(6,0),d(6,1),d(6,2),d(3,2) + d(3,0),d(4,2) + d( 3,1),0,3*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 0 1 0 0] [ ] [0 0 1 0 0 0] pour shortformdelta:={0, ss, 0, 1, ss, 0, ss, 0, 0, ss, 0, 1} Unknowns: {d(6,2), d(6,1), d(6,0), d(5,2), d(5,1), d(5,0), d(4,2), d(3,2), d(3,1), d(3,0), d(0,0)} Unknowns: {d(6,2), d(6,1), d(6,0), d(5,2), d(5,1), d(5,0), d(4,2), d(3,2), d(3,1), d(3,0), d(0,0)} Unknowns: {d(6,2), d(6,1), d(6,0), d(5,2), d(5,1), d(5,0), d(4,2), d(3,2), d(3,1), d(3,0), d(0,0)} Unknowns: {d(6,2), d(6,1), d(6,0), d(5,2), d(5,1), d(5,0), d(4,2), d(3,2), d(3,1), d(3,0), d(0,0)} dim Der(gtildedelta):=11$ Unknowns: {d(6,2), d(6,1), d(6,0), d(5,2), d(5,1), d(5,0), d(4,2), d(3,2), d(3,1), d(3,0), d(0,0)} Unknowns: {d(6,2), d(6,1), d(6,0), d(5,2), d(5,1), d(5,0), d(4,2), d(3,2), d(3,1), d(3,0), d(0,0)} listeparametresMATD{d(6,2), d(6,1), d(6,0), d(5,2), d(5,1), d(5,0), d(4,2), d(3,2), d(3,1), d(3,0), d(0,0)}$ 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 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] MATD:= [d(0,0) 0 0 0 0 0 0 ] [ ] [ 0 d(0,0) 0 0 0 0 0 ] [ ] [ 0 0 d(0,0) 0 0 0 0 ] [ ] [d(3,0) d(3,1) d(3,2) 2*d(0,0) 0 0 0 ] [ ] [d(3,1) d(3,0) d(4,2) 0 2*d(0,0) 0 0 ] [ ] [d(5,0) d(5,1) d(5,2) d(4,2) d(3,2) 3*d(0,0) 0 ] [ ] [d(6,0) d(6,1) d(6,2) d(3,2) + d(3,0) d(4,2) + d(3,1) 0 3*d(0,0)] on peut prendre comme element semi simple du commutant de t1 dans der(gtildede\ lta): 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 1 0 0 0 0] [ ] [0 0 0 2 0 0 0] [ ] [0 0 0 0 2 0 0] [ ] [0 0 0 0 0 3 0] [ ] [0 0 0 0 0 0 3] matrice des derivations dans cette base diagonalisante Y(1),...,Y(7): P**(-1)*MATD*P:= [d(0,0) 0 0 0 0 0 0 ] [ ] [ 0 d(0,0) 0 0 0 0 0 ] [ ] [ 0 0 d(0,0) 0 0 0 0 ] [ ] [d(3,0) d(3,1) d(3,2) 2*d(0,0) 0 0 0 ] [ ] [d(3,1) d(3,0) d(4,2) 0 2*d(0,0) 0 0 ] [ ] [d(5,0) d(5,1) d(5,2) d(4,2) d(3,2) 3*d(0,0) 0 ] [ ] [d(6,0) d(6,1) d(6,2) d(3,2) + d(3,0) d(4,2) + d(3,1) 0 3*d(0,0)] PP**(-1)*MATD*PP:= [d(0,0) 0 0 0 0 0 0 ] [ ] [ 0 d(0,0) 0 0 0 0 0 ] [ ] [ 0 0 d(0,0) 0 0 0 0 ] [ ] [d(3,0) d(3,1) d(3,2) 2*d(0,0) 0 0 0 ] [ ] [d(3,1) d(3,0) d(4,2) 0 2*d(0,0) 0 0 ] [ ] [d(5,0) d(5,1) d(5,2) d(4,2) d(3,2) 3*d(0,0) 0 ] [ ] [d(6,0) d(6,1) d(6,2) d(3,2) + d(3,0) d(4,2) + d(3,1) 0 3*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:= [d(0,0) 0 0 0 0 0 0 ] [ ] [ 0 d(0,0) 0 0 0 0 0 ] [ ] [ 0 0 d(0,0) 0 0 0 0 ] [ ] [d(3,0) d(3,1) d(3,2) 2*d(0,0) 0 0 0 ] [ ] [d(3,1) d(3,0) d(4,2) 0 2*d(0,0) 0 0 ] [ ] [d(5,0) d(5,1) d(5,2) d(4,2) d(3,2) 3*d(0,0) 0 ] [ ] [d(6,0) d(6,1) d(6,2) d(3,2) + d(3,0) d(4,2) + d(3,1) 0 3*d(0,0)] on voit apparaitre les poids sur la diagonale ladiag := {{1,d(0,0)}, {2,d(0,0)}, {3,d(0,0)}, {4,2*d(0,0)}, {5,2*d(0,0)}, {6,3*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)}, {{0,4},x(5)}, {{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 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) *** yy declared operator *** diadiay declared operator liste des commutateurs des diaY(i) := (diadiaY=diaY {{{1,2},0}, {{1,3},diadiay(4)}, {{1,4},diadiay(7)}, {{1,5},diadiay(6)}, {{1,6},0}, {{1,7},0}, {{2,3},diadiay(5)}, {{2,4},diadiay(6)}, {{2,5},diadiay(7)}, {{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 : l'isomorphisme suivant est calcule par calculisom6_7XIV.red [-2 1 1 0 0 0 0] [ ] [0 -1 1 0 0 0 0] [ ] [-4 0 0 0 0 0 0] [ ] [0 0 0 4 4 0 0] [ ] [0 0 0 -4 4 0 0] [ ] [0 0 0 0 0 -8 8] [ ] [0 0 0 0 0 8 8] det(isom):= 32768 *** zz declared operator ZZ(1):= - 2*(2*diay(3) + diay(1)) ZZ(2):= - (diay(2) - diay(1)) ZZ(3):=diay(2) + diay(1) ZZ(4):= - 4*(diay(5) - diay(4)) ZZ(5):=4*(diay(5) + diay(4)) ZZ(6):=8*(diay(7) - diay(6)) ZZ(7):=8*(diay(7) + diay(6)) *** zzz declared operator liste des commutateurs des ZZ(i) (ZZZ=ZZ:= {{{1,2},zzz(4)}, {{1,3},zzz(5)}, {{1,4},zzz(7)}, {{1,5},zzz(6)}, {{1,6},0}, {{1,7},0}, {{2,3},0}, {{2,4},zzz(6)}, {{2,5},0}, {{2,6},0}, {{2,7},0}, {{3,4},0}, {{3,5},zzz(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 obtient donc les relations de commutation de g_{7,1.19} page 401.