delta:= mat((0,0,0,0,0,0),(0,0,0,0,0,0),(0,0,0,0,0,0),(0,0,0,0,0,0),(1,0,0,0,0,0),(0,0,0 ,0,0,0))$ shortformdelta:={0, ss, 0, 0, ss, 0, ss, 1, 0, ss, 0, 0}$ phase 1 de la resolution des equations$ on resout l'equation {{0,1},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 {{0,1},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 {{0,1},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 {{0,1},3} qui est maintenant AA:= - d(3,5)$ Unknown: d(3,5) Unknown: d(3,5) bonne inconnue W:=d(3,5)$ sa valeur doit etre WW:=0$ on resout l'equation {{0,1},4} qui est maintenant AA:= - (d(4,5) + d(2,0))$ Unknowns: {d(4,5),d(2,0)} Unknowns: {d(4,5),d(2,0)} bonne inconnue W:=d(4,5)$ sa valeur doit etre WW:= - d(2,0)$ on resout l'equation {{0,1},5} qui est maintenant AA:= - d(5,5) + d(1,1) + d(0, 0)$ Unknowns: {d(5,5),d(1,1),d(0,0)} Unknowns: {d(5,5),d(1,1),d(0,0)} bonne inconnue W:=d(5,5)$ sa valeur doit etre WW:=d(1,1) + d(0,0)$ on resout l'equation {{0,1},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 resout l'equation {{0,2},4} qui est maintenant AA:=d(1,0)$ Unknown: d(1,0) Unknown: d(1,0) bonne inconnue W:=d(1,0)$ sa valeur doit etre WW:=0$ on resout l'equation {{0,2},5} qui est maintenant AA:= - d(4,0) + d(1,2)$ Unknowns: {d(4,0),d(1,2)} Unknowns: {d(4,0),d(1,2)} bonne inconnue W:=d(4,0)$ sa valeur doit etre WW:=d(1,2)$ on resout l'equation {{0,2},6} qui est maintenant AA:= - d(3,0)$ Unknown: d(3,0) Unknown: d(3,0) bonne inconnue W:=d(3,0)$ sa valeur doit etre WW:=0$ on resout l'equation {{0,3},5} 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 {{0,3},6} 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 {{0,4},5} 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 {{0,6},5} 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 {{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},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)$ Unknown: d(3,4) Unknown: d(3,4) bonne inconnue W:=d(3,4)$ sa valeur doit etre WW:=0$ 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(4,1) + d(0 ,2))$ Unknowns: {d(5,4),d(4,1),d(0,2)} Unknowns: {d(5,4),d(4,1),d(0,2)} bonne inconnue W:=d(5,4)$ sa valeur doit etre WW:= - (d(4,1) + d(0,2))$ on resout l'equation {{1,2},6} qui est maintenant AA:= - (d(6,4) + d(3,1))$ Unknowns: {d(6,4),d(3,1)} Unknowns: {d(6,4),d(3,1)} bonne inconnue W:=d(6,4)$ sa valeur doit etre WW:= - d(3,1)$ on resout l'equation {{1,3},4} 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 {{1,3},5} 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 {{1,3},6} 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 {{1,6},4} 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 {{1,6},5} 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 {{2,3},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 {{2,3},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 {{2,3},5} qui est maintenant AA:= - d(5,6) + d(4,3)$ Unknowns: {d(5,6),d(4,3)} Unknowns: {d(5,6),d(4,3)} bonne inconnue W:=d(5,6)$ sa valeur doit etre WW:=d(4,3)$ on resout l'equation {{2,3},6} qui est maintenant AA:= - d(6,6) + d(3,3) + d(2, 2)$ Unknowns: {d(6,6),d(3,3),d(2,2)} Unknowns: {d(6,6),d(3,3),d(2,2)} bonne inconnue W:=d(6,6)$ sa valeur doit etre WW:=d(3,3) + d(2,2)$ on resout l'equation {{2,4},5} qui est maintenant AA:=2*d(2,2) - d(0,0)$ Unknowns: {d(2,2),d(0,0)} Unknowns: {d(2,2),d(0,0)} bonne inconnue W:=d(2,2)$ sa valeur doit etre WW:=d(0,0)/2$ 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},4},0}, {{{0,2},5},0}, {{{0,2},6},0}, {{{0,3},5},0}, {{{0,3},6},0}, {{{0,4},5},0}, {{{0,5},5},0}, {{{0,6},5},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},4},0}, {{{1,3},5},0}, {{{1,3},6},0}, {{{1,4},4},0}, {{{1,4},5},0}, {{{1,5},4},0}, {{{1,5},5},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},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},6},0}, {{{3,6},6},0}, {{{4,5},5},0}, {{{4,6},5},0}}$ il n'y a 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},4},0}, {{{0,2},5},0}, {{{0,2},6},0}, {{{0,3},5},0}, {{{0,3},6},0}, {{{0,4},5},0}, {{{0,5},5},0}, {{{0,6},5},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},4},0}, {{{1,3},5},0}, {{{1,3},6},0}, {{{1,4},4},0}, {{{1,4},5},0}, {{{1,5},4},0}, {{{1,5},5},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},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},6},0}, {{{3,6},6},0}, {{{4,5},5},0}, {{{4,6},5},0}}$ derivation generique de gtildedelta:$ MATD:= mat((d(0,0),d(0,1),d(0,2),0,0,0,0),(0,d(1,1),d(1,2),0,0,0,0),(0,0,d(0,0)/2,0,0,0 ,0),(0,d(3,1),d(3,2),d(3,3),0,0,0),(d(1,2),d(4,1),d(4,2),d(4,3),(2*d(1,1) + d(0, 0))/2,0,0),(d(5,0),d(5,1),d(5,2),d(5,3), - (d(4,1) + d(0,2)),d(1,1) + d(0,0),d(4 ,3)),(d(6,0),d(6,1),d(6,2),d(6,3), - d(3,1),0,(2*d(3,3) + d(0,0))/2))$ pour delta:= [0 0 0 0 0 0] [ ] [0 0 0 0 0 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] pour shortformdelta:={0, ss, 0, 0, ss, 0, ss, 1, 0, ss, 0, 0} Unknowns: {d(6,3), d(6,2), d(6,1), d(6,0), d(5,3), d(5,2), d(5,1), d(5,0), d(4,3), d(4,2), d(4,1), d(3,3), d(3,2), d(3,1), d(1,2), d(1,1), d(0,2), d(0,1), d(0,0)} Unknowns: {d(6,3), d(6,2), d(6,1), d(6,0), d(5,3), d(5,2), d(5,1), d(5,0), d(4,3), d(4,2), d(4,1), d(3,3), d(3,2), d(3,1), d(1,2), d(1,1), d(0,2), d(0,1), d(0,0)} listeparametresMATD{d(6,3), d(6,2), d(6,1), d(6,0), d(5,3), d(5,2), d(5,1), d(5,0), d(4,3), d(4,2), d(4,1), d(3,3), d(3,2), d(3,1), d(1,2), d(1,1), d(0,2), d(0,1), d(0,0)}$ dim Der(gtildedelta):=19$ un element t1 d'un tore $ t1:=D(0,0):= [1 0 0 0 0 0 0 ] [ ] [0 0 0 0 0 0 0 ] [ ] [ 1 ] [0 0 --- 0 0 0 0 ] [ 2 ] [ ] [0 0 0 0 0 0 0 ] [ ] [ 1 ] [0 0 0 0 --- 0 0 ] [ 2 ] [ ] [0 0 0 0 0 1 0 ] [ ] [ 1 ] [0 0 0 0 0 0 ---] [ 2 ] MATD:= mat((d(0,0),d(0,1),d(0,2),0,0,0,0), (0,d(1,1),d(1,2),0,0,0,0), d(0,0) (0,0,--------,0,0,0,0), 2 (0,d(3,1),d(3,2),d(3,3),0,0,0), 2*d(1,1) + d(0,0) (d(1,2),d(4,1),d(4,2),d(4,3),-------------------,0,0), 2 (d(5,0),d(5,1),d(5,2),d(5,3), - (d(4,1) + d(0,2)),d(1,1) + d(0,0),d(4,3)), 2*d(3,3) + d(0,0) (d(6,0),d(6,1),d(6,2),d(6,3), - d(3,1),0,-------------------)) 2 Unknowns: {d(6,2),d(5,0),d(4,2),d(3,3),d(3,1),d(1,1),d(0,0)} Unknowns: {d(6,2),d(5,0),d(4,2),d(3,3),d(3,1),d(1,1),d(0,0)} commutant de t1 dans der(gtildedelta): mat((d(0,0),0,0,0,0,0,0), (0,d(1,1),0,0,0,0,0), d(0,0) (0,0,--------,0,0,0,0), 2 (0,d(3,1),0,d(3,3),0,0,0), 2*d(1,1) + d(0,0) (0,0,d(4,2),0,-------------------,0,0), 2 (d(5,0),0,0,0,0,d(1,1) + d(0,0),0), 2*d(3,3) + d(0,0) (0,0,d(6,2),0, - d(3,1),0,-------------------)) 2 Unknowns: {d(6,2),d(5,0),d(4,2),d(3,3),d(3,1),d(1,1),d(0,0)} Unknowns: {d(6,2),d(5,0),d(4,2),d(3,3),d(3,1),d(1,1),d(0,0)} t2:=D(1,1):= [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 1 0 0] [ ] [0 0 0 0 0 1 0] [ ] [0 0 0 0 0 0 0] Unknowns: {d(6,2),d(3,3),d(1,1),d(0,0)} Unknowns: {d(6,2),d(3,3),d(1,1),d(0,0)} commutant simultane de t1,t2 dans der(gtildedelta): mat((d(0,0),0,0,0,0,0,0), (0,d(1,1),0,0,0,0,0), d(0,0) (0,0,--------,0,0,0,0), 2 (0,0,0,d(3,3),0,0,0), 2*d(1,1) + d(0,0) (0,0,0,0,-------------------,0,0), 2 (0,0,0,0,0,d(1,1) + d(0,0),0), 2*d(3,3) + d(0,0) (0,0,d(6,2),0,0,0,-------------------)) 2 Unknowns: {d(6,2),d(3,3),d(1,1),d(0,0)} Unknowns: {d(6,2),d(3,3),d(1,1),d(0,0)} t3:=D(3,3):= [0 0 0 0 0 0 0] [ ] [0 0 0 0 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 0 0 0 0] [ ] [0 0 0 0 0 0 1] Unknowns: {d(3,3),d(1,1),d(0,0)} Unknowns: {d(3,3),d(1,1),d(0,0)} commutant simultane de t1,t2,t3 dans der(gtildedelta): mat((d(0,0),0,0,0,0,0,0), (0,d(1,1),0,0,0,0,0), d(0,0) (0,0,--------,0,0,0,0), 2 (0,0,0,d(3,3),0,0,0), 2*d(1,1) + d(0,0) (0,0,0,0,-------------------,0,0), 2 (0,0,0,0,0,d(1,1) + d(0,0),0), 2*d(3,3) + d(0,0) (0,0,0,0,0,0,-------------------)) 2 rank 3 with maximal torus t1,t2,t3 3 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 0 0 0 0 0 0 ] [ ] [ 1 ] [0 0 --- 0 0 0 0 ] [ 2 ] [ ] [0 0 0 0 0 0 0 ] [ ] [ 1 ] [0 0 0 0 --- 0 0 ] [ 2 ] [ ] [0 0 0 0 0 1 0 ] [ ] [ 1 ] [0 0 0 0 0 0 ---] [ 2 ] P**(-1)*t2*P:= [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 1 0 0] [ ] [0 0 0 0 0 1 0] [ ] [0 0 0 0 0 0 0] P**(-1)*t3*P:= [0 0 0 0 0 0 0] [ ] [0 0 0 0 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 0 0 0 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),d(0,1),d(0,2),0,0,0,0),(0,d(1,1),d(1,2),0,0,0,0),(0,0,d(0,0)/2,0,0,0 ,0),(0,d(3,1),d(3,2),d(3,3),0,0,0),(d(1,2),d(4,1),d(4,2),d(4,3),(2*d(1,1) + d(0, 0))/2,0,0),(d(5,0),d(5,1),d(5,2),d(5,3), - (d(4,1) + d(0,2)),d(1,1) + d(0,0),d(4 ,3)),(d(6,0),d(6,1),d(6,2),d(6,3), - d(3,1),0,(2*d(3,3) + d(0,0))/2))$ PP:= mat((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:= mat((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),d(0,2),0,0,0,0),(0,d(1,1),d(1,2),0,0,0,0),(0,0,d(0,0)/2,0,0,0 ,0),(0,d(3,1),d(3,2),d(3,3),0,0,0),(d(1,2),d(4,1),d(4,2),d(4,3),(2*d(1,1) + d(0, 0))/2,0,0),(d(5,0),d(5,1),d(5,2),d(5,3), - (d(4,1) + d(0,2)),d(1,1) + d(0,0),d(4 ,3)),(d(6,0),d(6,1),d(6,2),d(6,3), - d(3,1),0,(2*d(3,3) + d(0,0))/2))$ on voit apparaitre les poids sur la diagonale$ r(1) := d(0,0)$ r(2) := d(1,1)$ r(3) := d(0,0)/2$ r(4) := d(3,3)$ r(5) := (2*d(1,1) + d(0,0))/2$ r(6) := d(1,1) + d(0,0)$ r(7) := (2*d(3,3) + d(0,0))/2$ r(1) := 2*gamma1$ r(2) := gamma2$ r(3) := gamma1$ r(4) := gamma3$ r(5) := gamma1 + gamma2$ r(6) := 2*gamma1 + gamma2$ r(7) := gamma1 + gamma3$ Le systeme de poids est le systeme 3.8$ calcul de relations de commutation de la base diaY(j) diagonalisant le tore$ listcommutateursdesx := {{{0,1},x(5)}, {{0,2},0}, {{0,3},0}, {{0,4},0}, {{0,5},0}, {{0,6},0}, {{1,2},x(4)}, {{1,3},0}, {{1,4},0}, {{1,5},0}, {{1,6},0}, {{2,3},x(6)}, {{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(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(6)}, {{1,3},0}, {{1,4},0}, {{1,5},0}, {{1,6},0}, {{1,7},0}, {{2,3},diay(5)}, {{2,4},0}, {{2,5},0}, {{2,6},0}, {{2,7},0}, {{3,4},diay(7)}, {{3,5},diay(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}}$ Now we make explicit the isomorphism with an algebra of the book:$ Namely g_{7,3.8}$ 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 :$ mat((0,0,0,1,0,0,0),(0,-1,0,0,0,0,0),(1,0,0,0,0,0,0),(0,0,-1,0,0,0,0),(0,0,0,0,1 ,0,0),(0,0,0,0,0,0,1),(0,0,0,0,0,-1,0))$ det(isom):= 1$ ZZ(1):=diay(3)$ ZZ(2):= - diay(2)$ ZZ(3):= - diay(4)$ ZZ(4):=diay(1)$ ZZ(5):=diay(5)$ ZZ(6):= - diay(7)$ ZZ(7):=diay(6)$ listcommutateursdesZZ:=$ {{1,2},zz(5)}$ {{1,3},zz(6)}$ {{1,4},0}$ {{1,5},zz(7)}$ {{1,6},0}$ {{1,7},0}$ {{2,3},0}$ {{2,4},zz(7)}$ {{2,5},0}$ {{2,6},0}$ {{2,7},0}$ {{3,4},0}$ {{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 commutations de $ g_{7,3.8}$ shortformdelta:={0, ss, 0, 0, ss, 0, ss, 1, 0, ss, 0, 0}$ delta:= mat((0,0,0,0,0,0),(0,0,0,0,0,0),(0,0,0,0,0,0),(0,0,0,0,0,0),(1,0,0,0,0,0),(0,0,0 ,0,0,0))$