In the present case 2 we suppose A=((0,0),(0,0)).$ a:=a$ delta:= mat((0,0,0,0,0,0),(0,0,0,0,0,0),(0,1,0,0,0,0),(a,1,0,0,0,0),(0,0,0,0,0,0),(0,0,1 ,0,1,0))$ shortformdelta:={0, 1, ss, a, 1, ss, 0, 0, ss, 1, 0}$ phase 1 de la resolution des equations$ on resout l'equation {{0,1},0} qui est maintenant AA:= - d(0,4)*a$ Unknowns: {d(0,4),a} Unknowns: {d(0,4),a} pas de selection possible de variable a coefficient numerique dans - d(0,4)*a on resout l'equation {{0,1},1} qui est maintenant AA:= - d(1,4)*a$ Unknowns: {d(1,4),a} Unknowns: {d(1,4),a} pas de selection possible de variable a coefficient numerique dans - d(1,4)*a on resout l'equation {{0,1},2} 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 numerique dans - d(2,4)*a on resout l'equation {{0,1},3} qui est maintenant AA:= - d(3,4)*a + d(2,1)$ Unknowns: {d(3,4),d(2,1),a} Unknowns: {d(3,4),d(2,1),a} bonne inconnue W:=d(2,1)$ sa valeur doit etre WW:=d(3,4)*a$ on resout l'equation {{0,1},4} qui est maintenant AA:=a*( - d(4,4) + d(3,4) + d (1,1) + d(0,0))$ Unknowns: {d(4,4),d(3,4),d(1,1),d(0,0),a} Unknowns: {d(4,4),d(3,4),d(1,1),d(0,0),a} pas de selection possible de variable a coefficient numerique dans a*( - d(4,4) + d(3,4) + d(1,1) + d(0,0)) on resout l'equation {{0,1},5} qui est maintenant AA:= - (d(5,4)*a + d(2,0))$ Unknowns: {d(5,4),d(2,0),a} Unknowns: {d(5,4),d(2,0),a} bonne inconnue W:=d(2,0)$ sa valeur doit etre WW:= - d(5,4)*a$ on resout l'equation {{0,1},6} qui est maintenant AA:= - d(6,4)*a + d(5,1) - d( 4,0) + d(3,1)$ Unknowns: {d(6,4),d(5,1),d(4,0),d(3,1),a} Unknowns: {d(6,4),d(5,1),d(4,0),d(3,1),a} bonne inconnue W:=d(5,1)$ sa valeur doit etre WW:=d(6,4)*a + d(4,0) - d(3,1)$ on resout l'equation {{0,2},0} qui est maintenant AA:= - (d(0,4) + d(0,3))$ Unknowns: {d(0,4),d(0,3)} Unknowns: {d(0,4),d(0,3)} bonne inconnue W:=d(0,4)$ sa valeur doit etre WW:= - d(0,3)$ on resout l'equation {{0,2},1} qui est maintenant AA:= - (d(1,4) + d(1,3))$ Unknowns: {d(1,4),d(1,3)} Unknowns: {d(1,4),d(1,3)} bonne inconnue W:=d(1,4)$ sa valeur doit etre WW:= - d(1,3)$ on resout l'equation {{0,2},2} qui est maintenant AA:= - (d(2,4) + d(2,3))$ Unknowns: {d(2,4),d(2,3)} Unknowns: {d(2,4),d(2,3)} bonne inconnue W:=d(2,4)$ sa valeur doit etre WW:= - d(2,3)$ on resout l'equation {{0,2},3} qui est maintenant AA:= - d(3,4) - d(3,3) + d(2, 2) + d(0,0)$ Unknowns: {d(3,4),d(3,3),d(2,2),d(0,0)} Unknowns: {d(3,4),d(3,3),d(2,2),d(0,0)} bonne inconnue W:=d(3,4)$ sa valeur doit etre WW:= - d(3,3) + d(2,2) + d(0,0)$ on resout l'equation {{0,2},4} qui est maintenant AA:= - d(4,4) - d(4,3) + d(2, 2) + d(1,2)*a + d(0,0)$ Unknowns: {d(4,4),d(4,3),d(2,2),d(1,2),d(0,0),a} Unknowns: {d(4,4),d(4,3),d(2,2),d(1,2),d(0,0),a} bonne inconnue W:=d(4,4)$ sa valeur doit etre WW:= - d(4,3) + d(2,2) + d(1,2)*a + d(0,0)$ on resout l'equation {{0,2},5} qui est maintenant AA:= - d(5,4) - d(5,3) + d(1, 0)$ Unknowns: {d(5,4),d(5,3),d(1,0)} Unknowns: {d(5,4),d(5,3),d(1,0)} bonne inconnue W:=d(5,4)$ sa valeur doit etre WW:= - d(5,3) + d(1,0)$ on resout l'equation {{0,2},6} qui est maintenant AA:= - d(6,4) - d(6,3) + d(5, 2) + d(3,2) - d(3,0)$ Unknowns: {d(6,4),d(6,3),d(5,2),d(3,2),d(3,0)} Unknowns: {d(6,4),d(6,3),d(5,2),d(3,2),d(3,0)} bonne inconnue W:=d(6,4)$ sa valeur doit etre WW:= - d(6,3) + d(5,2) + 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) + d(2,3)$ Unknowns: {d(3,6),d(2,3)} Unknowns: {d(3,6),d(2,3)} bonne inconnue W:=d(3,6)$ sa valeur doit etre WW:=d(2,3)$ on resout l'equation {{0,3},4} qui est maintenant AA:= - d(4,6) + d(2,3) + d(1, 3)*a$ Unknowns: {d(4,6),d(2,3),d(1,3),a} Unknowns: {d(4,6),d(2,3),d(1,3),a} bonne inconnue W:=d(4,6)$ sa valeur doit etre WW:=d(2,3) + d(1,3)*a$ on resout l'equation {{0,3},5} qui est maintenant AA:= - d(5,6)$ Unknown: d(5,6) Unknown: d(5,6) bonne inconnue W:=d(5,6)$ sa valeur doit etre WW:=0$ on resout l'equation {{0,3},6} qui est maintenant AA:= - d(6,6) + d(5,3)*a + d( 5,3) + d(3,3) - d(1,0)*a + d(0,0)$ Unknowns: {d(6,6),d(5,3),d(3,3),d(1,0),d(0,0),a} Unknowns: {d(6,6),d(5,3),d(3,3),d(1,0),d(0,0),a} bonne inconnue W:=d(6,6)$ sa valeur doit etre WW:=d(5,3)*a + d(5,3) + d(3,3) - d(1,0)*a + d(0,0)$ on resout l'equation {{0,4},3} 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 {{0,4},4} qui est maintenant AA:= - d(1,3)*a$ Unknowns: {d(1,3),a} Unknowns: {d(1,3),a} pas de selection possible de variable a coefficient numerique dans - d(1,3)*a on resout l'equation {{0,4},6} qui est maintenant AA:= - d(5,3) - d(3,3) + d(2, 2) + 2*d(1,0) + d(0,0)$ Unknowns: {d(5,3),d(3,3),d(2,2),d(1,0),d(0,0)} Unknowns: {d(5,3),d(3,3),d(2,2),d(1,0),d(0,0)} bonne inconnue W:=d(5,3)$ sa valeur doit etre WW:= - d(3,3) + d(2,2) + 2*d(1,0) + d(0,0)$ on resout l'equation {{0,5},3} 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 {{0,5},4} qui est maintenant AA:=a*(d(1,5) - d(1,3))$ Unknowns: {d(1,5),d(1,3),a} Unknowns: {d(1,5),d(1,3),a} pas de selection possible de variable a coefficient numerique dans a*(d(1,5) - d (1,3)) on resout l'equation {{0,5},6} qui est maintenant AA:=d(5,5) + d(3,5) + d(3,3)* a - d(2,2)*a - d(2,2) - d(1,0)*a - 2*d(1,0) - d(0,0)*a - d(0,0)$ Unknowns: {d(5,5),d(3,5),d(3,3),d(2,2),d(1,0),d(0,0),a} Unknowns: {d(5,5),d(3,5),d(3,3),d(2,2),d(1,0),d(0,0),a} bonne inconnue W:=d(5,5)$ sa valeur doit etre WW:= - d(3,5) - d(3,3)*a + d(2,2)*a + d(2,2) + d(1,0)*a + 2* d(1,0) + d(0,0)*a + d(0,0)$ on resout l'equation {{1,2},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 {{1,2},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 {{1,2},3} qui est maintenant AA:= - d(3,5) + d(0,1)$ Unknowns: {d(3,5),d(0,1)} Unknowns: {d(3,5),d(0,1)} bonne inconnue W:=d(3,5)$ sa valeur doit etre WW:=d(0,1)$ on resout l'equation {{1,2},4} qui est maintenant AA:= - d(4,5) - d(0,2)*a + d( 0,1)$ Unknowns: {d(4,5),d(0,2),d(0,1),a} Unknowns: {d(4,5),d(0,2),d(0,1),a} bonne inconnue W:=d(4,5)$ sa valeur doit etre WW:= - d(0,2)*a + d(0,1)$ on resout l'equation {{1,2},5} qui est maintenant AA:=d(3,3)*a - d(2,2)*a + d(1 ,1) - d(1,0)*a - 2*d(1,0) + d(0,1) - d(0,0)*a - d(0,0)$ Unknowns: {d(3,3),d(2,2),d(1,1),d(1,0),d(0,1),d(0,0),a} Unknowns: {d(3,3),d(2,2),d(1,1),d(1,0),d(0,1),d(0,0),a} bonne inconnue W:=d(0,1)$ sa valeur doit etre WW:= - d(3,3)*a + d(2,2)*a - d(1,1) + d(1,0)*a + 2*d(1,0) + d(0,0)*a + d(0,0)$ on resout l'equation {{1,2},6} qui est maintenant AA:= - d(6,5) + d(4,2) - d(3, 1)$ Unknowns: {d(6,5),d(4,2),d(3,1)} Unknowns: {d(6,5),d(4,2),d(3,1)} bonne inconnue W:=d(6,5)$ sa valeur doit etre WW:=d(4,2) - d(3,1)$ on resout l'equation {{1,3},4} qui est maintenant AA:= - d(0,3)*a$ Unknowns: {d(0,3),a} Unknowns: {d(0,3),a} pas de selection possible de variable a coefficient numerique dans - d(0,3)*a on resout l'equation {{1,3},6} qui est maintenant AA:=d(4,3) - 2*d(3,3)*a + 2*d (2,2)*a - d(1,1) + d(1,0)*a + 2*d(1,0) + 2*d(0,0)*a + d(0,0)$ Unknowns: {d(4,3),d(3,3),d(2,2),d(1,1),d(1,0),d(0,0),a} Unknowns: {d(4,3),d(3,3),d(2,2),d(1,1),d(1,0),d(0,0),a} bonne inconnue W:=d(4,3)$ sa valeur doit etre WW:=2*d(3,3)*a - 2*d(2,2)*a + d(1,1) - d(1,0)*a - 2*d(1,0) - 2*d(0,0)*a - d(0,0)$ on resout l'equation {{1,4},4} qui est maintenant AA:=a*( - d(1,3) + d(0,3))$ Unknowns: {d(1,3),d(0,3),a} Unknowns: {d(1,3),d(0,3),a} pas de selection possible de variable a coefficient numerique dans a*( - d(1,3) + d(0,3)) on resout l'equation {{1,4},6} qui est maintenant AA:=a*( - d(3,3) + d(2,2) + d (1,2) + d(0,0))$ Unknowns: {d(3,3),d(2,2),d(1,2),d(0,0),a} Unknowns: {d(3,3),d(2,2),d(1,2),d(0,0),a} pas de selection possible de variable a coefficient numerique dans a*( - d(3,3) + d(2,2) + d(1,2) + d(0,0)) on resout l'equation {{1,5},6} qui est maintenant AA:= - 2*d(3,3)*a + 2*d(2,2)* a - 2*d(1,1) + 2*d(1,0)*a + 4*d(1,0) - d(0,2)*a + 2*d(0,0)*a + 2*d(0,0)$ Unknowns: {d(3,3),d(2,2),d(1,1),d(1,0),d(0,2),d(0,0),a} Unknowns: {d(3,3),d(2,2),d(1,1),d(1,0),d(0,2),d(0,0),a} bonne inconnue W:=d(1,1)$ sa valeur doit etre WW:=( - 2*d(3,3)*a + 2*d(2,2)*a + 2*d(1,0)*a + 4*d(1,0) - d( 0,2)*a + 2*d(0,0)*a + 2*d(0,0))/2$ on resout l'equation {{1,6},6} qui est maintenant AA:=d(1,3)*a$ Unknowns: {d(1,3),a} Unknowns: {d(1,3),a} pas de selection possible de variable a coefficient numerique dans d(1,3)*a on resout l'equation {{2,3},3} 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 {{2,3},4} qui est maintenant AA:= - d(1,3)*a$ Unknowns: {d(1,3),a} Unknowns: {d(1,3),a} pas de selection possible de variable a coefficient numerique dans - d(1,3)*a on resout l'equation {{2,3},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 {{2,3},6} qui est maintenant AA:=d(3,3)*a + d(3,3) - d(2,2 )*a - d(1,0)*a - 2*d(1,0) + d(0,2) - d(0,0)*a - 2*d(0,0)$ Unknowns: {d(3,3),d(2,2),d(1,0),d(0,2),d(0,0),a} Unknowns: {d(3,3),d(2,2),d(1,0),d(0,2),d(0,0),a} bonne inconnue W:=d(0,2)$ sa valeur doit etre WW:= - d(3,3)*a - d(3,3) + d(2,2)*a + d(1,0)*a + 2*d(1,0) + d(0,0)*a + 2*d(0,0)$ on resout l'equation {{2,4},6} qui est maintenant AA:= - d(3,3) + d(2,2) + d(1, 2) + d(0,0)$ Unknowns: {d(3,3),d(2,2),d(1,2),d(0,0)} Unknowns: {d(3,3),d(2,2),d(1,2),d(0,0)} bonne inconnue W:=d(3,3)$ sa valeur doit etre WW:=d(2,2) + d(1,2) + d(0,0)$ on resout l'equation {{2,5},6} qui est maintenant AA:=( - d(2,2)*a - 2*d(2,2) - d(1,2)*a**2 - 3*d(1,2)*a - 2*d(1,2) + d(1,0)*a**2 + 4*d(1,0)*a + 4*d(1,0) + d(0 ,0)*a + 2*d(0,0))/2$ Unknowns: {d(2,2),d(1,2),d(1,0),d(0,0),a} Unknowns: {d(2,2),d(1,2),d(1,0),d(0,0),a} pas de selection possible de variable a coefficient numerique dans ( - d(2,2)*a - 2*d(2,2) - d(1,2)*a**2 - 3*d(1,2)*a - 2*d(1,2) + d(1,0)*a**2 + 4*d(1,0)*a + 4* d(1,0) + d(0,0)*a + 2*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}, (d(2,2) + d(1,2)*a + d(1,2) - d(1,0)*a - 2*d(1,0) - d(0,0))*(a - 1)*a}, {{{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},3},0}, {{{0,4},4},0}, {{{0,4},6},0}, {{{0,5},0},0}, {{{0,5},1},0}, {{{0,5},2},0}, {{{0,5},3},0}, {{{0,5},4},0}, {{{0,5},5},0}, {{{0,5},6},0}, {{{0,6},3},0}, {{{0,6},4},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},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},5},0}, {{{2,5},6}, ( - (d(2,2) + d(1,2)*a + d(1,2) - d(1,0)*a - 2*d(1,0) - d(0,0))*(a + 2))/2}, {{{2,6},3},0}, {{{2,6},4},0}, {{{2,6},5},0}, {{{2,6},6},0}, {{{3,4},6},0}, {{{3,5},6},0}, {{{3,6},6},0}, {{{4,5},6},0}, {{{4,6},6},0}, {{{5,6},6},0}}$ Il y a une phase 2 pour a neq -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},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},3},0}, {{{0,4},4},0}, {{{0,4},6},0}, {{{0,5},0},0}, {{{0,5},1},0}, {{{0,5},2},0}, {{{0,5},3},0}, {{{0,5},4},0}, {{{0,5},5},0}, {{{0,5},6},0}, {{{0,6},3},0}, {{{0,6},4},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},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},5},0}, {{{2,5},6},0}, {{{2,6},3},0}, {{{2,6},4},0}, {{{2,6},5},0}, {{{2,6},6},0}, {{{3,4},6},0}, {{{3,5},6},0}, {{{3,6},6},0}, {{{4,5},6},0}, {{{4,6},6},0}, {{{5,6},6},0}}$ derivation generique de gtildedelta:$ MATD:= mat((d(0,0),0,0,0,0,0,0),((d(1,2)*a + d(1,2) - d(0,0) + d(2,2))/(a + 2),d(2,2) + d(1,2),d(1,2),0,0,0,0),(((d(2,2) - d(1,2) - d(0,0))*a)/(a + 2), - d(1,2)*a,d(2, 2),0,0,0,0),(d(3,0),d(3,1),d(3,2),d(1,2) + d(0,0) + d(2,2), - d(1,2),0,0),(d(4,0 ),d(4,1),d(4,2),d(1,2)*a,d(2,2) + d(0,0),0,0),(d(5,0), - (d(3,1) + d(3,0)*a - d( 3,2)*a - d(4,0) - d(5,2)*a + d(6,3)*a),d(5,2),(d(1,2)*a - 2*d(0,0) + 2*d(2,2))/( a + 2),( - (d(2,2) - d(1,2) - d(0,0)))/(a + 2),2*d(2,2) + d(1,2),0),(d(6,0),d(6, 1),d(6,2),d(6,3),d(3,2) - d(3,0) + d(5,2) - d(6,3),d(4,2) - d(3,1),2*d(2,2) + d( 1,2) + d(0,0)))$ pour delta:= [0 0 0 0 0 0] [ ] [0 0 0 0 0 0] [ ] [0 1 0 0 0 0] [ ] [a 1 0 0 0 0] [ ] [0 0 0 0 0 0] [ ] [0 0 1 0 1 0] pour shortformdelta:={0, 1, ss, a, 1, ss, 0, 0, ss, 1, 0} Unknowns: {d(6,3), d(6,2), d(6,1), d(6,0), d(5,2), d(5,0), d(4,2), d(4,1), d(4,0), d(3,2), d(3,1), d(3,0), d(2,2), d(1,2), d(0,0), a} Unknowns: {d(6,3), d(6,2), d(6,1), d(6,0), d(5,2), d(5,0), d(4,2), d(4,1), d(4,0), d(3,2), d(3,1), d(3,0), d(2,2), d(1,2), d(0,0), a} listeparametresMATD{d(6,3), d(6,2), d(6,1), d(6,0), d(5,2), d(5,0), d(4,2), d(4,1), d(4,0), d(3,2), d(3,1), d(3,0), d(2,2), d(1,2), d(0,0)}$ dim Der(gtildedelta):=15$ un element t1 d'un tore $ t1:=D(0,0):= [ 1 0 0 0 0 0 0] [ ] [ - 1 ] [------- 0 0 0 0 0 0] [ a + 2 ] [ ] [ - a ] [------- 0 0 0 0 0 0] [ a + 2 ] [ ] [ 0 0 0 1 0 0 0] [ ] [ 0 0 0 0 1 0 0] [ ] [ - 2 1 ] [ 0 0 0 ------- ------- 0 0] [ a + 2 a + 2 ] [ ] [ 0 0 0 0 0 0 1] MATD:= mat((d(0,0),0,0,0,0,0,0), d(1,2)*a + d(1,2) - d(0,0) + d(2,2) (-------------------------------------,d(2,2) + d(1,2),d(1,2),0,0,0,0), a + 2 - (d(1,2) + d(0,0) - d(2,2))*a (---------------------------------, - d(1,2)*a,d(2,2),0,0,0,0), a + 2 (d(3,0),d(3,1),d(3,2),d(1,2) + d(0,0) + d(2,2), - d(1,2),0,0), (d(4,0),d(4,1),d(4,2),d(1,2)*a,d(2,2) + d(0,0),0,0), (d(5,0), - (d(3,1) + d(3,0)*a - d(3,2)*a - d(4,0) - d(5,2)*a + d(6,3)*a), d(1,2)*a - 2*d(0,0) + 2*d(2,2) d(1,2) + d(0,0) - d(2,2) d(5,2),--------------------------------,--------------------------, a + 2 a + 2 2*d(2,2) + d(1,2),0), (d(6,0),d(6,1),d(6,2),d(6,3),d(3,2) - d(3,0) + d(5,2) - d(6,3), d(4,2) - d(3,1),d(1,2) + d(0,0) + 2*d(2,2))) {{x - 1, 4, [ - (a + 2)*arbcomplex(285) ] [ ---------------------------- ] [ a ] [ ] [ arbcomplex(285) ] [ ----------------- ] [ a ] [ ] [ arbcomplex(285) ] [ ] [ - (arbcomplex(287)*a + 2*arbcomplex(287) - arbcomplex(286)) ] [--------------------------------------------------------------] [ 2 ] [ ] [ arbcomplex(286) ] [ ] [ arbcomplex(287) ] [ ] [ arbcomplex(288) ] }, {x, 3, [ 0 ] [ ] [arbcomplex(289)] [ ] [arbcomplex(290)] [ ] [ 0 ] [ ] [ 0 ] [ ] [arbcomplex(291)] [ ] [ 0 ] }} Unknowns: {d(6,3),d(6,0),d(5,2),d(5,0),d(4,0),d(3,0),d(2,2),d(1,2),d(0,0),a} Unknowns: {d(6,3),d(6,0),d(5,2),d(5,0),d(4,0),d(3,0),d(2,2),d(1,2),d(0,0),a} commutant de t1 dans der(gtildedelta): mat((d(0,0),0,0,0,0,0,0), d(1,2)*a + d(1,2) - d(0,0) + d(2,2) (-------------------------------------,d(2,2) + d(1,2),d(1,2),0,0,0,0), a + 2 - (d(1,2) + d(0,0) - d(2,2))*a (---------------------------------, - d(1,2)*a,d(2,2),0,0,0,0), a + 2 (d(3,0),0,0,d(1,2) + d(0,0) + d(2,2), - d(1,2),0,0), (d(4,0),0,0,d(1,2)*a,d(2,2) + d(0,0),0,0), (d(5,0), - (d(4,0) - 2*d(3,0) - (a + 2)*d(5,0) + d(5,2)*a),d(5,2), d(1,2)*a - 2*d(0,0) + 2*d(2,2) d(1,2) + d(0,0) - d(2,2) --------------------------------,--------------------------, a + 2 a + 2 2*d(2,2) + d(1,2),0), (d(6,0),0,0,d(6,3),d(5,2) - d(3,0) - d(6,3),0,d(1,2) + d(0,0) + 2*d(2,2))) Unknowns: {d(6,3),d(6,0),d(5,2),d(5,0),d(4,0),d(3,0),d(2,2),d(1,2),d(0,0),a} Unknowns: {d(6,3),d(6,0),d(5,2),d(5,0),d(4,0),d(3,0),d(2,2),d(1,2),d(0,0),a} t2:=D(2,2):= [ 0 0 0 0 0 0 0] [ ] [ 1 ] [------- 1 0 0 0 0 0] [ a + 2 ] [ ] [ a ] [------- 0 1 0 0 0 0] [ a + 2 ] [ ] [ 0 0 0 1 0 0 0] [ ] [ 0 0 0 0 1 0 0] [ ] [ 2 - 1 ] [ 0 0 0 ------- ------- 2 0] [ a + 2 a + 2 ] [ ] [ 0 0 0 0 0 0 2] Unknowns: {d(2,2),d(1,2),d(0,0),a} Unknowns: {d(2,2),d(1,2),d(0,0),a} commutant simultane de t1,t2 dans der(gtildedelta): mat((d(0,0),0,0,0,0,0,0), d(1,2)*a + d(1,2) - d(0,0) + d(2,2) (-------------------------------------,d(2,2) + d(1,2),d(1,2),0,0,0,0), a + 2 - (d(1,2) + d(0,0) - d(2,2))*a (---------------------------------, - d(1,2)*a,d(2,2),0,0,0,0), a + 2 (0,0,0,d(1,2) + d(0,0) + d(2,2), - d(1,2),0,0), (0,0,0,d(1,2)*a,d(2,2) + d(0,0),0,0), d(1,2)*a - 2*d(0,0) + 2*d(2,2) d(1,2) + d(0,0) - d(2,2) (0,0,0,--------------------------------,--------------------------, a + 2 a + 2 2*d(2,2) + d(1,2),0), (0,0,0,0,0,0,d(1,2) + d(0,0) + 2*d(2,2))) Unknowns: {d(2,2),d(1,2),d(0,0),a} Unknowns: {d(2,2),d(1,2),d(0,0),a} t3:=D(1,2):= [ 0 0 0 0 0 0 0] [ ] [ a + 1 ] [------- 1 1 0 0 0 0] [ a + 2 ] [ ] [ - a ] [------- - a 0 0 0 0 0] [ a + 2 ] [ ] [ 0 0 0 1 -1 0 0] [ ] [ 0 0 0 a 0 0 0] [ ] [ a 1 ] [ 0 0 0 ------- ------- 1 0] [ a + 2 a + 2 ] [ ] [ 0 0 0 0 0 0 1] Unknowns: {d(2,2),d(1,2),d(0,0),a} Unknowns: {d(2,2),d(1,2),d(0,0),a} commutant simultane de t1,t2,t3 dans der(gtildedelta): mat((d(0,0),0,0,0,0,0,0), d(1,2)*a + d(1,2) - d(0,0) + d(2,2) (-------------------------------------,d(2,2) + d(1,2),d(1,2),0,0,0,0), a + 2 - (d(1,2) + d(0,0) - d(2,2))*a (---------------------------------, - d(1,2)*a,d(2,2),0,0,0,0), a + 2 (0,0,0,d(1,2) + d(0,0) + d(2,2), - d(1,2),0,0), (0,0,0,d(1,2)*a,d(2,2) + d(0,0),0,0), d(1,2)*a - 2*d(0,0) + 2*d(2,2) d(1,2) + d(0,0) - d(2,2) (0,0,0,--------------------------------,--------------------------, a + 2 a + 2 2*d(2,2) + d(1,2),0), (0,0,0,0,0,0,d(1,2) + d(0,0) + 2*d(2,2))) For a:=1/4, t3 is not semisimple 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] [ ] [ - 1 ] [------- 1 0 0 0 0 0] [ a + 2 ] [ ] [ - a ] [------- 0 1 0 0 0 0] [ a + 2 ] [ ] [ 1 ] [ 0 0 0 1 --- 0 0] [ 2 ] [ ] [ 0 0 0 0 1 0 0] [ ] [ - 2 ] [ 0 0 0 ------- 0 1 0] [ a + 2 ] [ ] [ 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] [ ] [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 0] [ ] [0 0 0 0 0 0 1] 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 1 0 0] [ ] [0 0 0 0 0 2 0] [ ] [0 0 0 0 0 0 2] P**(-1)*t3*P:= [0 0 0 0 0 0 0] [ ] [0 1 1 0 0 0 0] [ ] [0 - a 0 0 0 0 0] [ ] [ - (a - 2) - (a + 2) ] [0 0 0 ------------ ------------ 0 0] [ 2 4 ] [ ] [ a ] [0 0 0 a --- 0 0] [ 2 ] [ ] [0 0 0 0 0 1 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),(0,d(2,2) + d(1,2),d(1,2),0,0,0,0),(0, - d(1,2)*a,d(2,2 ),0,0,0,0),(( - (d(4,0) - 2*d(3,0)))/2,( - (d(4,1) - 2*d(3,1)))/2,( - (d(4,2) - 2*d(3,2)))/2,( - (d(1,2)*a - 2*d(1,2) - 2*d(0,0) - 2*d(2,2)))/2,( - (a + 2)*d(1, 2))/4,0,0),(d(4,0),d(4,1),d(4,2),d(1,2)*a,(d(1,2)*a + 2*d(0,0) + 2*d(2,2))/2,0,0 ),((2*d(3,1))/(a + 2),(2*((a + 2)*d(3,0) - (a + 1)*d(3,1)) - (a + 2)*d(4,0) - d( 4,1) + (a + 2)**2*d(5,0))/(a + 2),( - (d(4,2) - 2*d(3,2) - 2*d(5,2)))/(a + 2),0, 0,2*d(2,2) + d(1,2),0),(d(6,0),d(6,1),d(6,2),( - ((a + 2)*d(3,0) - 2*d(3,1) - 2* d(4,0) + 2*d(4,2) + (a + 2)*d(5,0) - 2*d(6,3)))/(a + 2),(2*(d(3,2) - d(3,0) + d( 5,2)) - d(6,3))/2,d(4,2) - d(3,1),d(1,2) + d(0,0) + 2*d(2,2)))$ det Q:=(4*(4*a - 1))/(sqrt( - 4*a + 1)*a - 2*sqrt( - 4*a + 1) + 5*a - 2)$ PP:= mat((1,0,0,0,0,0,0), - 1 - 2 (-------,1,----------------------,0,0,0,0), a + 2 sqrt( - 4*a + 1) + 1 - a sqrt( - 4*a + 1) - 1 (-------,----------------------,1,0,0,0,0), a + 2 2 - (sqrt( - 4*a + 1) - 3) - (sqrt( - 4*a + 1) + 3) (0,0,0,---------------------------,------------------------------,0,0), a + 2 2*(a - 1 - sqrt( - 4*a + 1)) - 2*(a - 1 + sqrt( - 4*a + 1)) (0,0,0,---------------------------------,1,0,0), a + 2 - 2 1 (0,0,0,-------,--------------------------,1,0), a + 2 a - 1 - sqrt( - 4*a + 1) (0,0,0,0,0,0,1)) PP**(-1)*t1*PP:= [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 0] [ ] [0 0 0 0 0 0 1] PP**(-1)*t2*PP:= [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 0 0] [ ] [0 0 0 0 0 2 0] [ ] [0 0 0 0 0 0 2] PP**(-1)*t3*PP:= mat((0,0,0,0,0,0,0), sqrt( - 4*a + 1) - 4*a + 1 (0,----------------------------,0,0,0,0,0), 2*sqrt( - 4*a + 1) sqrt( - 4*a + 1) + 4*a - 1 (0,0,----------------------------,0,0,0,0), 2*sqrt( - 4*a + 1) sqrt( - 4*a + 1) - 4*a + 1 (0,0,0,----------------------------,0,0,0), 2*sqrt( - 4*a + 1) sqrt( - 4*a + 1) + 4*a - 1 (0,0,0,0,----------------------------,0,0), 2*sqrt( - 4*a + 1) (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), - 1 - 2 (-------,1,----------------------,0,0,0,0), a + 2 sqrt( - 4*a + 1) + 1 - a sqrt( - 4*a + 1) - 1 (-------,----------------------,1,0,0,0,0), a + 2 2 - (sqrt( - 4*a + 1) - 3) - (sqrt( - 4*a + 1) + 3) (0,0,0,---------------------------,------------------------------,0,0), a + 2 2*(a - 1 - sqrt( - 4*a + 1)) - 2*(a - 1 + sqrt( - 4*a + 1)) (0,0,0,---------------------------------,1,0,0), a + 2 - 2 1 (0,0,0,-------,--------------------------,1,0), a + 2 a - 1 - sqrt( - 4*a + 1) (0,0,0,0,0,0,1)) MATDDIAGONALISE:= mat((d(0,0),0,0,0,0,0,0), (sqrt( - 4*a + 1) - 4*a + 1)*d(1,2) + 2*sqrt( - 4*a + 1)*d(2,2) (0,-----------------------------------------------------------------,0,0,0,0 2*sqrt( - 4*a + 1) ,0), (sqrt( - 4*a + 1) + 4*a - 1)*d(1,2) + 2*sqrt( - 4*a + 1)*d(2,2) (0,0,-----------------------------------------------------------------,0,0,0 2*sqrt( - 4*a + 1) ,0), 2 (( - ((sqrt( - 4*a + 1)*a - 8*sqrt( - 4*a + 1)*a + 4*sqrt( - 4*a + 1) 2 + 9*a - 16*a + 4)*d(3,0) 2 + 2*(2*sqrt( - 4*a + 1)*a - 2*sqrt( - 4*a + 1) - a + 6*a - 2)*d(4,0) ))/(2*(sqrt( - 4*a + 1)*(5*a - 2) - (4*a - 1)*(a - 2))),( - ( 2 5*sqrt( - 4*a + 1)*d(4,1)*a - 8*sqrt( - 4*a + 1)*d(4,1) - 2*d(4,1)*a 2 + 19*d(4,1)*a - 8*d(4,1) + sqrt( - 4*a + 1)*d(3,1)*a - 12*sqrt( - 4*a + 1)*d(3,1)*a + 8*sqrt( - 4*a + 1)*d(3,1) 2 + 11*d(3,1)*a - 28*d(3,1)*a + 8*d(3,1)))/(2 *(sqrt( - 4*a + 1)*(5*a - 2) - (4*a - 1)*(a - 2))),( 2 (2*a - 3*a - 12 - sqrt( - 4*a + 1)*(3*a + 4))*d(3,1) - 4*(sqrt( - 4*a + 1) + 1)*d(3,2) + (5*a + 8 + sqrt( - 4*a + 1)*a)*d(4,1) + 4*(sqrt( - 4*a + 1) + 1)*d(4,2))/(2 *(sqrt( - 4*a + 1)*(5*a - 2) - (4*a - 1)*(a - 2))),( sqrt( - 4*a + 1)*d(1,2) - 4*d(1,2)*a + d(1,2) + 2*sqrt( - 4*a + 1)*d(0,0) + 2*sqrt( - 4*a + 1)*d(2,2))/(2 *sqrt( - 4*a + 1)),0,0,0), (( - ((sqrt( - 4*a + 1) - 2*a + 1)*d(4,0) - (sqrt( - 4*a + 1) + 1)*d(3,0)*a) )/(4*a - 1 - sqrt( - 4*a + 1)),( - (2*sqrt( - 4*a + 1)*d(4,1) - 2*d(4,1)*a + 2*d(4,1) - sqrt( - 4*a + 1)*d(3,1)*a - 3*d(3,1)*a))/(4*a - 1 - sqrt( - 4*a + 1)),( - ( ((sqrt( - 4*a + 1) + 1 + 2*a)*d(3,1) - (sqrt( - 4*a + 1) + 1)*d(4,1)) *(a + 2) + 2*sqrt( - 4*a + 1)*d(4,2) + 2*d(4,2) - sqrt( - 4*a + 1)*d(4,1) + 2*d(4,1)*a + 3*d(4,1)))/( (4*a - 1 - sqrt( - 4*a + 1))*(a + 2)),0,(sqrt( - 4*a + 1)*d(1,2) + 4*d(1,2)*a - d(1,2) + 2*sqrt( - 4*a + 1)*d(0,0) + 2*sqrt( - 4*a + 1)*d(2,2))/(2*sqrt( - 4*a + 1)),0,0), 2*d(3,1) (----------,(2*(2*((a + 2)*d(3,0) - (a + 1)*d(3,1)) a + 2 + (sqrt( - 4*a + 1) - 1)*d(3,2) - (a + 2)*d(4,0) - d(4,1)) 2 - (sqrt( - 4*a + 1) - 1)*d(4,2) + 2*(a + 2) *d(5,0) + 2*(sqrt( - 4*a + 1) - 1)*d(5,2))/(2*(a + 2)),( - (2*( 2*((a + 2)*d(3,0) - (a + 1)*d(3,1)) - (sqrt( - 4*a + 1) + 1)*d(3,2) - (a + 2)*d(4,0) - d(4,1)) 2 + (sqrt( - 4*a + 1) + 1)*d(4,2) + 2*(a + 2) *d(5,0) - 2*(sqrt( - 4*a + 1) + 1)*d(5,2)))/((sqrt( - 4*a + 1) + 1)*(a + 2)) ,0,0,2*d(2,2) + d(1,2),0), sqrt( - 4*a + 1)*d(6,2) - d(6,2) + 2*d(6,1) (d(6,0),---------------------------------------------, 2 sqrt( - 4*a + 1)*d(6,2) + d(6,2) - 2*d(6,1) ---------------------------------------------,(2*( sqrt( - 4*a + 1) + 1 (sqrt( - 4*a + 1) - 3)*d(3,0) + 2*d(3,1) - (sqrt( - 4*a + 1) - 1)*d(3,2) + 2*d(4,0) - d(4,2) - (a + 2)*d(5,0) - (sqrt( - 4*a + 1) - 1)*d(5,2)) + (sqrt( - 4*a + 1) + 1)*d(6,3))/(a + 2),(2*((sqrt( - 4*a + 1) + 3)*d(3,0) - 2*d(3,1) - (sqrt( - 4*a + 1) + 1)*d(3,2) - 2*d(4,0) + d(4,2) + (a + 2)*d(5,0) - (sqrt( - 4*a + 1) + 1)*d(5,2)) + (sqrt( - 4*a + 1) - 1)*d(6,3))/(2*(a - 1 - sqrt( - 4*a + 1))), d(4,2) - d(3,1),d(1,2) + d(0,0) + 2*d(2,2))) on voit apparaitre les poids sur la diagonale r(1) := d(0,0) (sqrt( - 4*a + 1) - 4*a + 1)*d(1,2) + 2*sqrt( - 4*a + 1)*d(2,2) r(2) := ----------------------------------------------------------------- 2*sqrt( - 4*a + 1) (sqrt( - 4*a + 1) + 4*a - 1)*d(1,2) + 2*sqrt( - 4*a + 1)*d(2,2) r(3) := ----------------------------------------------------------------- 2*sqrt( - 4*a + 1) r(4) := (sqrt( - 4*a + 1)*d(1,2) - 4*d(1,2)*a + d(1,2) + 2*sqrt( - 4*a + 1)*d(0,0) + 2*sqrt( - 4*a + 1)*d(2,2))/(2 *sqrt( - 4*a + 1)) r(5) := (sqrt( - 4*a + 1)*d(1,2) + 4*d(1,2)*a - d(1,2) + 2*sqrt( - 4*a + 1)*d(0,0) + 2*sqrt( - 4*a + 1)*d(2,2))/(2 *sqrt( - 4*a + 1)) r(6) := 2*d(2,2) + d(1,2) r(7) := d(1,2) + d(0,0) + 2*d(2,2) r(2)+r(3):=2*d(2,2) + d(1,2) - (4*a - 1)*d(1,2) r(2)-r(3):=--------------------- sqrt( - 4*a + 1) r(4)-(r(1)+r(2)):=0 r(5)-(r(1)+r(3)):=0 r(6)-(r(2)+r(3)):=0 r(7)-(r(1)+r(2)+r(3)):=0 r(1) := gamma1 r(2) := gamma2 r(3) := gamma3 r(4) := gamma1 + gamma2 r(5) := gamma1 + gamma3 r(6) := gamma2 + gamma3 r(7) := gamma1 + gamma2 + gamma3 Le systeme de poids est le systeme 3.1 calcul de relations de commutation de la base diaY(j) diagonalisant le tore listcommutateursdesx := {{{0,1},a*x(4)}, {{0,2},x(4) + x(3)}, {{0,3},x(6)}, {{0,4},0}, {{0,5},x(6)}, {{0,6},0}, {{1,2},x(5)}, {{1,3},0}, {{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}} - (x(1) - x(0)*(a + 2) + x(2)*a) diaY(1):=----------------------------------- a + 2 x(2)*(sqrt( - 4*a + 1) - 1) + 2*x(1) diaY(2):=-------------------------------------- 2 x(2)*(sqrt( - 4*a + 1) + 1) - 2*x(1) diaY(3):=-------------------------------------- sqrt( - 4*a + 1) + 1 diaY(4):=( - (2*x(4)*(sqrt( - 4*a + 1) + a - 1) + x(3)*(sqrt( - 4*a + 1) - 3) + 2*x(5)))/(a + 2) diaY(5):=(2*x(4)*(a - 1 - sqrt( - 4*a + 1)) - x(3)*(sqrt( - 4*a + 1) + 3) + 2*x(5))/(2*(a - 1 - sqrt( - 4*a + 1))) diaY(6):=x(5) diaY(7):=x(6) liste des commutateurs des diaY(i) : listcommutateurdesdiaY:={{{1,2}, - (2*sqrt( - 4*a + 1)*a + sqrt( - 4*a + 1) + 4*a - 1)*diay(4) ----------------------------------------------------------------}, 4*sqrt( - 4*a + 1) {{1,3}, (2*sqrt( - 4*a + 1)*a - sqrt( - 4*a + 1) + 4*a - 1)*diay(5) -------------------------------------------------------------}, 4*a - 1 - sqrt( - 4*a + 1) {{1,4},0}, {{1,5},0}, {{1,6},diay(7)}, {{1,7},0}, {{2,3}, 2*sqrt( - 4*a + 1)*diay(6) ----------------------------}, sqrt( - 4*a + 1) + 1 {{2,4},0}, {{2,5}, (4*a - 1 - 3*sqrt( - 4*a + 1))*diay(7) ----------------------------------------}, 2*(a - 1 - sqrt( - 4*a + 1)) {{2,6},0}, {{2,7},0}, {{3,4}, 2*(4*a - 1 + 3*sqrt( - 4*a + 1))*diay(7) ------------------------------------------}, (sqrt( - 4*a + 1) + 1)*(a + 2) {{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}} Now we make explicit the isomorphism with an algebra of the book: Namely g_{7,3.1} (iL), 1 pour a neq{0,---,-2} 4 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((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*a + 1 - sqrt( - 4*a + 1)))/4,0,0,0),(0,0,0,0,( - (2*a - 1 - sqrt( - 4*a + 1)))/(sqrt( - 4*a + 1) + 1),0,0),(0,0,0,0,0,(2*sqrt( - 4*a + 1))/(sqrt( - 4*a + 1) + 1),0),(0,0,0,0, 0,0,(2*sqrt( - 4*a + 1))/(sqrt( - 4*a + 1) + 1)))$ det(isom):= ( - (sqrt( - 4*a + 1) - a + 1)*(4*a - 1)*a)/(3*a - 1 + sqrt( - 4*a + 1)*(a - 1))$ ZZ(1):=diay(1)$ ZZ(2):=diay(2)$ ZZ(3):=diay(3)$ ZZ(4):=( - (2*a + 1 - sqrt( - 4*a + 1))*diay(4))/4$ ZZ(5):=( - (2*a - 1 - sqrt( - 4*a + 1))*diay(5))/(sqrt( - 4*a + 1) + 1)$ ZZ(6):=(2*sqrt( - 4*a + 1)*diay(6))/(sqrt( - 4*a + 1) + 1)$ ZZ(7):=(2*sqrt( - 4*a + 1)*diay(7))/(sqrt( - 4*a + 1) + 1)$ listcommutateursdesZZ:=$ {{1,2},zz(4)}$ {{1,3},zz(5)}$ {{1,4},0}$ {{1,5},0}$ {{1,6},zz(7)}$ {{1,7},0}$ {{2,3},zz(6)}$ {{2,4},0}$ {{2,5}, ( - sqrt( - 4*a + 1)*zz(7)*(2*a**2 - 7*a + 2) - zz(7)*(4*a - 1)*(3*a - 2))/(sqrt ( - 4*a + 1)*(5*a - 2) - (4*a - 1)*(a - 2))}$ {{2,6},0}$ {{2,7},0}$ {{3,4}, ( - zz(7)*(4*a - 1) - sqrt( - 4*a + 1)*zz(7))/(2*sqrt( - 4*a + 1))}$ {{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}$ L:=( - (sqrt( - 4*a + 1)*(2*a**2 - 7*a + 2) + (4*a - 1)*(3*a - 2)))/(sqrt( - 4*a + 1)*(5*a - 2) - (4*a - 1)*(a - 2))$ L-1:=( - 2*(sqrt( - 4*a + 1)*a - sqrt( - 4*a + 1) + 4*a - 1)*a)/(sqrt( - 4*a + 1 )*(5*a - 2) - (4*a - 1)*(a - 2))$ lprime:=( - (4*a - 1 + sqrt( - 4*a + 1)))/(2*sqrt( - 4*a + 1))$ lprime-(L-1):=0$ On obtient donc les relations de commutations de $ g_{7,3.1}$ (iL)$ avec L:=( - (sqrt( - 4*a + 1)*(2*a**2 - 7*a + 2) + (4*a - 1)*(3*a - 2)))/(sqrt( - 4*a + 1)*(5*a - 2) - (4*a - 1)*(a - 2))$ expressionsimplifieeL:=( - (2*a**2 - 7*a + 2 - sqrt( - 4*a + 1)*(3*a - 2)))/(5*a - 2 + sqrt( - 4*a + 1)*(a - 2))$ L-expressionsimplifieeL:=0$ Et cela pour a different de {0,1/4,-2}.$ shortformdelta:={0, 1, ss, a, 1, ss, 0, 0, ss, 1, 0}$ delta:= mat((0,0,0,0,0,0),(0,0,0,0,0,0),(0,1,0,0,0,0),(a,1,0,0,0,0),(0,0,0,0,0,0),(0,0,1 ,0,1,0))$