we look for an automorphism of g_{6,g4xC2}$

nombre d'equations90$

From the stability of the center one has:$

b(1,6):=0$

b(2,6):=0$

b(3,6):=0$

b(1,5):=0$

b(2,5):=0$

b(3,5):=0$

processus de resolution: phase 1$

nombre d'equations90$

collect_eq:={{{{1,2},1}, - b(1,3)},
{{{1,2},2}, - b(2,3)},
{{{1,2},3},
 - b(3,3) + b(2,2)*b(1,1) - b(2,1)*b(1,2)},
{{{1,2},4},
 - b(4,3) + b(3,2)*b(1,1) - b(3,1)*b(1,2)},
{{{1,2},5}, - b(5,3)},
{{{1,2},6}, - b(6,3)},
{{{1,3},1}, - b(1,4)},
{{{1,3},2}, - b(2,4)},
{{{1,3},3},
 - b(3,4) + b(2,3)*b(1,1) - b(2,1)*b(1,3)},
{{{1,3},4},
 - b(4,4) + b(3,3)*b(1,1) - b(3,1)*b(1,3)},
{{{1,3},5}, - b(5,4)},
{{{1,3},6}, - b(6,4)},
{{{1,4},1},0},
{{{1,4},2},0},
{{{1,4},3},b(2,4)*b(1,1) - b(2,1)*b(1,4)},
{{{1,4},4},b(3,4)*b(1,1) - b(3,1)*b(1,4)},
{{{1,4},5},0},
{{{1,4},6},0},
{{{1,5},1},0},
{{{1,5},2},0},
{{{1,5},3},0},
{{{1,5},4},0},
{{{1,5},5},0},
{{{1,5},6},0},
{{{1,6},1},0},
{{{1,6},2},0},
{{{1,6},3},0},
{{{1,6},4},0},
{{{1,6},5},0},
{{{1,6},6},0},
{{{2,3},1},0},
{{{2,3},2},0},
{{{2,3},3},b(2,3)*b(1,2) - b(2,2)*b(1,3)},
{{{2,3},4},b(3,3)*b(1,2) - b(3,2)*b(1,3)},
{{{2,3},5},0},
{{{2,3},6},0},
{{{2,4},1},0},
{{{2,4},2},0},
{{{2,4},3},b(2,4)*b(1,2) - b(2,2)*b(1,4)},
{{{2,4},4},b(3,4)*b(1,2) - b(3,2)*b(1,4)},
{{{2,4},5},0},
{{{2,4},6},0},
{{{2,5},1},0},
{{{2,5},2},0},
{{{2,5},3},0},
{{{2,5},4},0},
{{{2,5},5},0},
{{{2,5},6},0},
{{{2,6},1},0},
{{{2,6},2},0},
{{{2,6},3},0},
{{{2,6},4},0},
{{{2,6},5},0},
{{{2,6},6},0},
{{{3,4},1},0},
{{{3,4},2},0},
{{{3,4},3},b(2,4)*b(1,3) - b(2,3)*b(1,4)},
{{{3,4},4},b(3,4)*b(1,3) - b(3,3)*b(1,4)},
{{{3,4},5},0},
{{{3,4},6},0},
{{{3,5},1},0},
{{{3,5},2},0},
{{{3,5},3},0},
{{{3,5},4},0},
{{{3,5},5},0},
{{{3,5},6},0},
{{{3,6},1},0},
{{{3,6},2},0},
{{{3,6},3},0},
{{{3,6},4},0},
{{{3,6},5},0},
{{{3,6},6},0},
{{{4,5},1},0},
{{{4,5},2},0},
{{{4,5},3},0},
{{{4,5},4},0},
{{{4,5},5},0},
{{{4,5},6},0},
{{{4,6},1},0},
{{{4,6},2},0},
{{{4,6},3},0},
{{{4,6},4},0},
{{{4,6},5},0},
{{{4,6},6},0},
{{{5,6},1},0},
{{{5,6},2},0},
{{{5,6},3},0},
{{{5,6},4},0},
{{{5,6},5},0},
{{{5,6},6},0}}$

on resout l'equation {{1,2},1} qui est  maintenant AA:= - b(1,3)$

Unknown: b(1,3)
Unknown: b(1,3)
bonne inconnue W:=b(1,3)$

sa valeur doit etre WW:=0$

on resout l'equation {{1,2},2} qui est  maintenant AA:= - b(2,3)$

Unknown: b(2,3)
Unknown: b(2,3)
bonne inconnue W:=b(2,3)$

sa valeur doit etre WW:=0$

on resout l'equation {{1,2},3} qui est  maintenant AA:= - b(3,3) + b(2,2)*b(1,1)
 - b(2,1)*b(1,2)$

Unknowns: {b(3,3),b(2,2),b(2,1),b(1,2),b(1,1)}
Unknowns: {b(3,3),b(2,2),b(2,1),b(1,2),b(1,1)}
bonne inconnue W:=b(3,3)$

sa valeur doit etre WW:=b(2,2)*b(1,1) - b(2,1)*b(1,2)$

on resout l'equation {{1,2},4} qui est  maintenant AA:= - b(4,3) + b(3,2)*b(1,1)
 - b(3,1)*b(1,2)$

Unknowns: {b(4,3),b(3,2),b(3,1),b(1,2),b(1,1)}
Unknowns: {b(4,3),b(3,2),b(3,1),b(1,2),b(1,1)}
bonne inconnue W:=b(4,3)$

sa valeur doit etre WW:=b(3,2)*b(1,1) - b(3,1)*b(1,2)$

on resout l'equation {{1,2},5} qui est  maintenant AA:= - b(5,3)$

Unknown: b(5,3)
Unknown: b(5,3)
bonne inconnue W:=b(5,3)$

sa valeur doit etre WW:=0$

on resout l'equation {{1,2},6} qui est  maintenant AA:= - b(6,3)$

Unknown: b(6,3)
Unknown: b(6,3)
bonne inconnue W:=b(6,3)$

sa valeur doit etre WW:=0$

on resout l'equation {{1,3},1} qui est  maintenant AA:= - b(1,4)$

Unknown: b(1,4)
Unknown: b(1,4)
bonne inconnue W:=b(1,4)$

sa valeur doit etre WW:=0$

on resout l'equation {{1,3},2} qui est  maintenant AA:= - b(2,4)$

Unknown: b(2,4)
Unknown: b(2,4)
bonne inconnue W:=b(2,4)$

sa valeur doit etre WW:=0$

on resout l'equation {{1,3},3} qui est  maintenant AA:= - b(3,4)$

Unknown: b(3,4)
Unknown: b(3,4)
bonne inconnue W:=b(3,4)$

sa valeur doit etre WW:=0$

on resout l'equation {{1,3},4} qui est  maintenant AA:= - b(4,4) + b(2,2)*b(1,1)
**2 - b(2,1)*b(1,2)*b(1,1)$

Unknowns: {b(4,4),b(2,2),b(2,1),b(1,2),b(1,1)}
Unknowns: {b(4,4),b(2,2),b(2,1),b(1,2),b(1,1)}
bonne inconnue W:=b(4,4)$

sa valeur doit etre WW:=b(1,1)*(b(2,2)*b(1,1) - b(2,1)*b(1,2))$

on resout l'equation {{1,3},5} qui est  maintenant AA:= - b(5,4)$

Unknown: b(5,4)
Unknown: b(5,4)
bonne inconnue W:=b(5,4)$

sa valeur doit etre WW:=0$

on resout l'equation {{1,3},6} qui est  maintenant AA:= - b(6,4)$

Unknown: b(6,4)
Unknown: b(6,4)
bonne inconnue W:=b(6,4)$

sa valeur doit etre WW:=0$

on resout l'equation {{2,3},4} qui est  maintenant AA:=b(1,2)*(b(2,2)*b(1,1) - b
(2,1)*b(1,2))$

Unknowns: {b(2,2),b(2,1),b(1,2),b(1,1)}
Unknowns: {b(2,2),b(2,1),b(1,2),b(1,1)}


pas! de! selection! possible! de! variable! a! coefficient! independant! des! in
connues! \
dans! b(1,2)*(b(2,2)*b(1,1) - b(2,1)*b(1,2))
Automorphism equations to cancel (Reduce output) : \\{{{{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},1},0},
{{{1,3},2},0},
{{{1,3},3},0},
{{{1,3},4},0},
{{{1,3},5},0},
{{{1,3},6},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},1},0},
{{{1,5},2},0},
{{{1,5},3},0},
{{{1,5},4},0},
{{{1,5},5},0},
{{{1,5},6},0},
{{{1,6},1},0},
{{{1,6},2},0},
{{{1,6},3},0},
{{{1,6},4},0},
{{{1,6},5},0},
{{{1,6},6},0},
{{{2,3},1},0},
{{{2,3},2},0},
{{{2,3},3},0},
{{{2,3},4},
b(1,2)*(b(2,2)*b(1,1) - b(2,1)*b(1,2))},
{{{2,3},5},0},
{{{2,3},6},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},1},0},
{{{2,5},2},0},
{{{2,5},3},0},
{{{2,5},4},0},
{{{2,5},5},0},
{{{2,5},6},0},
{{{2,6},1},0},
{{{2,6},2},0},
{{{2,6},3},0},
{{{2,6},4},0},
{{{2,6},5},0},
{{{2,6},6},0},
{{{3,4},1},0},
{{{3,4},2},0},
{{{3,4},3},0},
{{{3,4},4},0},
{{{3,4},5},0},
{{{3,4},6},0},
{{{3,5},1},0},
{{{3,5},2},0},
{{{3,5},3},0},
{{{3,5},4},0},
{{{3,5},5},0},
{{{3,5},6},0},
{{{3,6},1},0},
{{{3,6},2},0},
{{{3,6},3},0},
{{{3,6},4},0},
{{{3,6},5},0},
{{{3,6},6},0},
{{{4,5},1},0},
{{{4,5},2},0},
{{{4,5},3},0},
{{{4,5},4},0},
{{{4,5},5},0},
{{{4,5},6},0},
{{{4,6},1},0},
{{{4,6},2},0},
{{{4,6},3},0},
{{{4,6},4},0},
{{{4,6},5},0},
{{{4,6},6},0},
{{{5,6},1},0},
{{{5,6},2},0},
{{{5,6},3},0},
{{{5,6},4},0},
{{{5,6},5},0},
{{{5,6},6},0}}$

resultats finaux$

collect_eq:={{{{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},1},0},
{{{1,3},2},0},
{{{1,3},3},0},
{{{1,3},4},0},
{{{1,3},5},0},
{{{1,3},6},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},1},0},
{{{1,5},2},0},
{{{1,5},3},0},
{{{1,5},4},0},
{{{1,5},5},0},
{{{1,5},6},0},
{{{1,6},1},0},
{{{1,6},2},0},
{{{1,6},3},0},
{{{1,6},4},0},
{{{1,6},5},0},
{{{1,6},6},0},
{{{2,3},1},0},
{{{2,3},2},0},
{{{2,3},3},0},
{{{2,3},4},
(b(2,2)*b(1,1) - b(2,1)*b(1,2))*b(1,2)},
{{{2,3},5},0},
{{{2,3},6},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},1},0},
{{{2,5},2},0},
{{{2,5},3},0},
{{{2,5},4},0},
{{{2,5},5},0},
{{{2,5},6},0},
{{{2,6},1},0},
{{{2,6},2},0},
{{{2,6},3},0},
{{{2,6},4},0},
{{{2,6},5},0},
{{{2,6},6},0},
{{{3,4},1},0},
{{{3,4},2},0},
{{{3,4},3},0},
{{{3,4},4},0},
{{{3,4},5},0},
{{{3,4},6},0},
{{{3,5},1},0},
{{{3,5},2},0},
{{{3,5},3},0},
{{{3,5},4},0},
{{{3,5},5},0},
{{{3,5},6},0},
{{{3,6},1},0},
{{{3,6},2},0},
{{{3,6},3},0},
{{{3,6},4},0},
{{{3,6},5},0},
{{{3,6},6},0},
{{{4,5},1},0},
{{{4,5},2},0},
{{{4,5},3},0},
{{{4,5},4},0},
{{{4,5},5},0},
{{{4,5},6},0},
{{{4,6},1},0},
{{{4,6},2},0},
{{{4,6},3},0},
{{{4,6},4},0},
{{{4,6},5},0},
{{{4,6},6},0},
{{{5,6},1},0},
{{{5,6},2},0},
{{{5,6},3},0},
{{{5,6},4},0},
{{{5,6},5},0},
{{{5,6},6},0}}$

isom:=
mat((b(1,1),b(1,2),0,0,0,0),(b(2,1),b(2,2),0,0,0,0),(b(3,1),b(3,2),b(2,2)*b(1,1)
 - b(2,1)*b(1,2),0,0,0),(b(4,1),b(4,2),b(3,2)*b(1,1) - b(3,1)*b(1,2),(b(2,2)*b(1
,1) - b(2,1)*b(1,2))*b(1,1),b(4,5),b(4,6)),(b(5,1),b(5,2),0,0,b(5,5),b(5,6)),(b(
6,1),b(6,2),0,0,b(6,5),b(6,6)))$

det(isom):=(b(6,6)*b(5,5) - b(6,5)*b(5,6))*(b(2,2)*b(1,1) - b(2,1)*b(1,2))**3*b(
1,1)$

phase2:$

{{{{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},1},0},
{{{1,3},2},0},
{{{1,3},3},0},
{{{1,3},4},0},
{{{1,3},5},0},
{{{1,3},6},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},1},0},
{{{1,5},2},0},
{{{1,5},3},0},
{{{1,5},4},0},
{{{1,5},5},0},
{{{1,5},6},0},
{{{1,6},1},0},
{{{1,6},2},0},
{{{1,6},3},0},
{{{1,6},4},0},
{{{1,6},5},0},
{{{1,6},6},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},1},0},
{{{2,4},2},0},
{{{2,4},3},0},
{{{2,4},4},0},
{{{2,4},5},0},
{{{2,4},6},0},
{{{2,5},1},0},
{{{2,5},2},0},
{{{2,5},3},0},
{{{2,5},4},0},
{{{2,5},5},0},
{{{2,5},6},0},
{{{2,6},1},0},
{{{2,6},2},0},
{{{2,6},3},0},
{{{2,6},4},0},
{{{2,6},5},0},
{{{2,6},6},0},
{{{3,4},1},0},
{{{3,4},2},0},
{{{3,4},3},0},
{{{3,4},4},0},
{{{3,4},5},0},
{{{3,4},6},0},
{{{3,5},1},0},
{{{3,5},2},0},
{{{3,5},3},0},
{{{3,5},4},0},
{{{3,5},5},0},
{{{3,5},6},0},
{{{3,6},1},0},
{{{3,6},2},0},
{{{3,6},3},0},
{{{3,6},4},0},
{{{3,6},5},0},
{{{3,6},6},0},
{{{4,5},1},0},
{{{4,5},2},0},
{{{4,5},3},0},
{{{4,5},4},0},
{{{4,5},5},0},
{{{4,5},6},0},
{{{4,6},1},0},
{{{4,6},2},0},
{{{4,6},3},0},
{{{4,6},4},0},
{{{4,6},5},0},
{{{4,6},6},0},
{{{5,6},1},0},
{{{5,6},2},0},
{{{5,6},3},0},
{{{5,6},4},0},
{{{5,6},5},0},
{{{5,6},6},0}}$

isom:=
mat((b(1,1),0,0,0,0,0),(b(2,1),b(2,2),0,0,0,0),(b(3,1),b(3,2),b(2,2)*b(1,1),0,0,
0),(b(4,1),b(4,2),b(3,2)*b(1,1),b(2,2)*b(1,1)**2,b(4,5),b(4,6)),(b(5,1),b(5,2),0
,0,b(5,5),b(5,6)),(b(6,1),b(6,2),0,0,b(6,5),b(6,6)))$

det(isom):=(b(6,6)*b(5,5) - b(6,5)*b(5,6))*b(2,2)**3*b(1,1)**4$

isom:=

[b(1,1)    0           0              0           0       0   ]
[                                                             ]
[b(2,1)  b(2,2)        0              0           0       0   ]
[                                                             ]
[b(3,1)  b(3,2)  b(2,2)*b(1,1)        0           0       0   ]
[                                                             ]
[                                            2                ]
[b(4,1)  b(4,2)  b(3,2)*b(1,1)  b(2,2)*b(1,1)   b(4,5)  b(4,6)]
[                                                             ]
[b(5,1)  b(5,2)        0              0         b(5,5)  b(5,6)]
[                                                             ]
[b(6,1)  b(6,2)        0              0         b(6,5)  b(6,6)]