we look for an automorphism of g_{6,9}$

nombre d'equations90$

processus de resolution: phase 1$

nombre d'equations90$

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

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

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(2,2)*b(1,1) - b(2,1)*b(1,2)$

on resout l'equation {{1,2},5} qui est  maintenant AA:= - b(5,4) + b(3,2)*b(1,1)
 - b(3,1)*b(1,2)$

Unknowns: {b(5,4),b(3,2),b(3,1),b(1,2),b(1,1)}
Unknowns: {b(5,4),b(3,2),b(3,1),b(1,2),b(1,1)}
bonne inconnue W:=b(5,4)$

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

on resout l'equation {{1,2},6} qui est  maintenant AA:= - b(6,4) + b(5,2)*b(2,1)
 - b(5,1)*b(2,2) + b(4,2)*b(3,1) - b(4,1)*b(3,2)$

Unknowns: {b(6,4),b(5,2),b(5,1),b(4,2),b(4,1),b(3,2),b(3,1),b(2,2),b(2,1)}
Unknowns: {b(6,4),b(5,2),b(5,1),b(4,2),b(4,1),b(3,2),b(3,1),b(2,2),b(2,1)}
bonne inconnue W:=b(6,4)$

sa valeur doit etre WW:=b(5,2)*b(2,1) - b(5,1)*b(2,2) + b(4,2)*b(3,1) - b(4,1)*b
(3,2)$

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

Unknown: b(1,5)
Unknown: b(1,5)
bonne inconnue W:=b(1,5)$

sa valeur doit etre WW:=0$

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

Unknown: b(2,5)
Unknown: b(2,5)
bonne inconnue W:=b(2,5)$

sa valeur doit etre WW:=0$

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

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

sa valeur doit etre WW:=0$

on resout l'equation {{1,3},4} qui est  maintenant AA:= - b(4,5) + b(2,3)*b(1,1)
 - b(2,1)*b(1,3)$

Unknowns: {b(4,5),b(2,3),b(2,1),b(1,3),b(1,1)}
Unknowns: {b(4,5),b(2,3),b(2,1),b(1,3),b(1,1)}
bonne inconnue W:=b(4,5)$

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

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

Unknowns: {b(5,5),b(3,3),b(3,1),b(1,3),b(1,1)}
Unknowns: {b(5,5),b(3,3),b(3,1),b(1,3),b(1,1)}
bonne inconnue W:=b(5,5)$

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

on resout l'equation {{1,3},6} qui est  maintenant AA:= - b(6,5) + b(5,3)*b(2,1)
 - b(5,1)*b(2,3) + b(4,3)*b(3,1) - b(4,1)*b(3,3)$

Unknowns: {b(6,5),b(5,3),b(5,1),b(4,3),b(4,1),b(3,3),b(3,1),b(2,3),b(2,1)}
Unknowns: {b(6,5),b(5,3),b(5,1),b(4,3),b(4,1),b(3,3),b(3,1),b(2,3),b(2,1)}
bonne inconnue W:=b(6,5)$

sa valeur doit etre WW:=b(5,3)*b(2,1) - b(5,1)*b(2,3) + b(4,3)*b(3,1) - b(4,1)*b
(3,3)$

on resout l'equation {{1,4},6} qui est  maintenant AA:=b(3,2)*b(2,1)*b(1,1) + b(
3,1)*b(2,2)*b(1,1) - 2*b(3,1)*b(2,1)*b(1,2)$

Unknowns: {b(3,2),b(3,1),b(2,2),b(2,1),b(1,2),b(1,1)}
Unknowns: {b(3,2),b(3,1),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(3,2)*b(2,1)*b(1,1) + b(3,1)*b(2,2)*b(1,1) - 2*b(3,1)*b(2,1)*b(1,2)
on resout l'equation {{1,5},6} qui est  maintenant AA:=b(3,3)*b(2,1)*b(1,1) + b(
3,1)*b(2,3)*b(1,1) - 2*b(3,1)*b(2,1)*b(1,3)$

Unknowns: {b(3,3),b(3,1),b(2,3),b(2,1),b(1,3),b(1,1)}
Unknowns: {b(3,3),b(3,1),b(2,3),b(2,1),b(1,3),b(1,1)}


pas! de! selection! possible! de! variable! a! coefficient! independant! des! in
connues! \
dans! b(3,3)*b(2,1)*b(1,1) + b(3,1)*b(2,3)*b(1,1) - 2*b(3,1)*b(2,1)*b(1,3)
on resout l'equation {{1,6},4} qui est  maintenant AA:=b(2,6)*b(1,1) - b(2,1)*b(
1,6)$

Unknowns: {b(2,6),b(2,1),b(1,6),b(1,1)}
Unknowns: {b(2,6),b(2,1),b(1,6),b(1,1)}


pas! de! selection! possible! de! variable! a! coefficient! independant! des! in
connues! \
dans! b(2,6)*b(1,1) - b(2,1)*b(1,6)
on resout l'equation {{1,6},5} qui est  maintenant AA:=b(3,6)*b(1,1) - b(3,1)*b(
1,6)$

Unknowns: {b(3,6),b(3,1),b(1,6),b(1,1)}
Unknowns: {b(3,6),b(3,1),b(1,6),b(1,1)}


pas! de! selection! possible! de! variable! a! coefficient! independant! des! in
connues! \
dans! b(3,6)*b(1,1) - b(3,1)*b(1,6)
on resout l'equation {{1,6},6} qui est  maintenant AA:=b(5,6)*b(2,1) - b(5,1)*b(
2,6) + b(4,6)*b(3,1) - b(4,1)*b(3,6)$

Unknowns: {b(5,6),b(5,1),b(4,6),b(4,1),b(3,6),b(3,1),b(2,6),b(2,1)}
Unknowns: {b(5,6),b(5,1),b(4,6),b(4,1),b(3,6),b(3,1),b(2,6),b(2,1)}


pas! de! selection! possible! de! variable! a! coefficient! independant! des! in
connues! \
dans! b(5,6)*b(2,1) - b(5,1)*b(2,6) + b(4,6)*b(3,1) - b(4,1)*b(3,6)
on resout l'equation {{2,3},4} qui est  maintenant AA:=b(2,3)*b(1,2) - b(2,2)*b(
1,3)$

Unknowns: {b(2,3),b(2,2),b(1,3),b(1,2)}
Unknowns: {b(2,3),b(2,2),b(1,3),b(1,2)}


pas! de! selection! possible! de! variable! a! coefficient! independant! des! in
connues! \
dans! b(2,3)*b(1,2) - b(2,2)*b(1,3)
on resout l'equation {{2,3},5} qui est  maintenant AA:=b(3,3)*b(1,2) - b(3,2)*b(
1,3)$

Unknowns: {b(3,3),b(3,2),b(1,3),b(1,2)}
Unknowns: {b(3,3),b(3,2),b(1,3),b(1,2)}


pas! de! selection! possible! de! variable! a! coefficient! independant! des! in
connues! \
dans! b(3,3)*b(1,2) - b(3,2)*b(1,3)
on resout l'equation {{2,3},6} qui est  maintenant AA:=b(5,3)*b(2,2) - b(5,2)*b(
2,3) + b(4,3)*b(3,2) - b(4,2)*b(3,3)$

Unknowns: {b(5,3),b(5,2),b(4,3),b(4,2),b(3,3),b(3,2),b(2,3),b(2,2)}
Unknowns: {b(5,3),b(5,2),b(4,3),b(4,2),b(3,3),b(3,2),b(2,3),b(2,2)}


pas! de! selection! possible! de! variable! a! coefficient! independant! des! in
connues! \
dans! b(5,3)*b(2,2) - b(5,2)*b(2,3) + b(4,3)*b(3,2) - b(4,2)*b(3,3)
on resout l'equation {{2,4},6} qui est  maintenant AA:=2*b(3,2)*b(2,2)*b(1,1) - 
b(3,2)*b(2,1)*b(1,2) - b(3,1)*b(2,2)*b(1,2)$

Unknowns: {b(3,2),b(3,1),b(2,2),b(2,1),b(1,2),b(1,1)}
Unknowns: {b(3,2),b(3,1),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! 2*b(3,2)*b(2,2)*b(1,1) - b(3,2)*b(2,1)*b(1,2) - b(3,1)*b(2,2)*b(1,2)
on resout l'equation {{2,5},1} qui est  maintenant AA:= - b(1,6)$

Unknown: b(1,6)
Unknown: b(1,6)
bonne inconnue W:=b(1,6)$

sa valeur doit etre WW:=0$

on resout l'equation {{2,5},2} qui est  maintenant AA:= - b(2,6)$

Unknown: b(2,6)
Unknown: b(2,6)
bonne inconnue W:=b(2,6)$

sa valeur doit etre WW:=0$

on resout l'equation {{2,5},3} qui est  maintenant AA:= - b(3,6)$

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

sa valeur doit etre WW:=0$

on resout l'equation {{2,5},4} qui est  maintenant AA:= - b(4,6)$

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

sa valeur doit etre WW:=0$

on resout l'equation {{2,5},5} qui est  maintenant AA:= - b(5,6)$

Unknown: b(5,6)
Unknown: b(5,6)
bonne inconnue W:=b(5,6)$

sa valeur doit etre WW:=0$

on resout l'equation {{2,5},6} qui est  maintenant AA:= - b(6,6) + b(3,3)*b(2,2)
*b(1,1) + b(3,2)*b(2,3)*b(1,1) - b(3,2)*b(2,1)*b(1,3) - b(3,1)*b(2,2)*b(1,3)$

Unknowns: {b(6,6),b(3,3),b(3,2),b(3,1),b(2,3),b(2,2),b(2,1),b(1,3),b(1,1)}
Unknowns: {b(6,6),b(3,3),b(3,2),b(3,1),b(2,3),b(2,2),b(2,1),b(1,3),b(1,1)}
bonne inconnue W:=b(6,6)$

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

on resout l'equation {{3,4},6} qui est  maintenant AA:= - b(3,3)*b(2,1)*b(1,2) +
 b(3,2)*b(2,1)*b(1,3) - b(3,1)*b(2,3)*b(1,2) + b(3,1)*b(2,2)*b(1,3)$

Unknowns: {b(3,3),b(3,2),b(3,1),b(2,3),b(2,2),b(2,1),b(1,3),b(1,2)}
Unknowns: {b(3,3),b(3,2),b(3,1),b(2,3),b(2,2),b(2,1),b(1,3),b(1,2)}


pas! de! selection! possible! de! variable! a! coefficient! independant! des! in
connues! \
dans!  - b(3,3)*b(2,1)*b(1,2) + b(3,2)*b(2,1)*b(1,3) - b(3,1)*b(2,3)*b(1,2) + b(
3,1)*b(2,2)*b(1,3)
on resout l'equation {{3,5},6} qui est  maintenant AA:=2*b(3,3)*b(2,3)*b(1,1) - 
b(3,3)*b(2,1)*b(1,3) - b(3,1)*b(2,3)*b(1,3)$

Unknowns: {b(3,3),b(3,1),b(2,3),b(2,1),b(1,3),b(1,1)}
Unknowns: {b(3,3),b(3,1),b(2,3),b(2,1),b(1,3),b(1,1)}


pas! de! selection! possible! de! variable! a! coefficient! independant! des! in
connues! \
dans! 2*b(3,3)*b(2,3)*b(1,1) - b(3,3)*b(2,1)*b(1,3) - b(3,1)*b(2,3)*b(1,3)
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},
b(3,2)*b(2,1)*b(1,1) + b(3,1)*b(2,2)*b(1,1) - 2*b(3,1)*b(2,1)*b(1,2)},
{{{1,5},1},0},
{{{1,5},2},0},
{{{1,5},3},0},
{{{1,5},4},0},
{{{1,5},5},0},
{{{1,5},6},
b(3,3)*b(2,1)*b(1,1) + b(3,1)*b(2,3)*b(1,1) - 2*b(3,1)*b(2,1)*b(1,3)},
{{{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(2,3)*b(1,2) - b(2,2)*b(1,3)},
{{{2,3},5},b(3,3)*b(1,2) - b(3,2)*b(1,3)},
{{{2,3},6},
b(5,3)*b(2,2) - b(5,2)*b(2,3) + b(4,3)*b(3,2) - b(4,2)*b(3,3)},
{{{2,4},1},0},
{{{2,4},2},0},
{{{2,4},3},0},
{{{2,4},4},0},
{{{2,4},5},0},
{{{2,4},6},
2*b(3,2)*b(2,2)*b(1,1) - b(3,2)*b(2,1)*b(1,2) - b(3,1)*b(2,2)*b(1,2)},
{{{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},
 - b(3,3)*b(2,1)*b(1,2) + b(3,2)*b(2,1)*b(1,3) - b(3,1)*b(2,3)*b(1,2) + b(3,1)*b
(2,2)*b(1,3)},
{{{3,5},1},0},
{{{3,5},2},0},
{{{3,5},3},0},
{{{3,5},4},0},
{{{3,5},5},0},
{{{3,5},6},
2*b(3,3)*b(2,3)*b(1,1) - b(3,3)*b(2,1)*b(1,3) - b(3,1)*b(2,3)*b(1,3)},
{{{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},
(b(2,2)*b(1,1) - 2*b(2,1)*b(1,2))*b(3,1) + b(3,2)*b(2,1)*b(1,1)},
{{{1,5},1},0},
{{{1,5},2},0},
{{{1,5},3},0},
{{{1,5},4},0},
{{{1,5},5},0},
{{{1,5},6},
(b(2,3)*b(1,1) - 2*b(2,1)*b(1,3))*b(3,1) + b(3,3)*b(2,1)*b(1,1)},
{{{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(2,3)*b(1,2) - b(2,2)*b(1,3)},
{{{2,3},5},
b(3,3)*b(1,2) - b(3,2)*b(1,3)},
{{{2,3},6},
b(4,3)*b(3,2) - b(4,2)*b(3,3) - b(5,2)*b(2,3) + b(5,3)*b(2,2)},
{{{2,4},1},0},
{{{2,4},2},0},
{{{2,4},3},0},
{{{2,4},4},0},
{{{2,4},5},0},
{{{2,4},6},
2*b(3,2)*b(2,2)*b(1,1) - b(3,2)*b(2,1)*b(1,2) - b(3,1)*b(2,2)*b(1,2)},
{{{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},
 - (b(3,3)*b(2,1)*b(1,2) - b(3,2)*b(2,1)*b(1,3) + b(3,1)*b(2,3)*b(1,2) - b(3,1)*
b(2,2)*b(1,3))},
{{{3,5},1},0},
{{{3,5},2},0},
{{{3,5},3},0},
{{{3,5},4},0},
{{{3,5},5},0},
{{{3,5},6},
2*b(3,3)*b(2,3)*b(1,1) - b(3,3)*b(2,1)*b(1,3) - b(3,1)*b(2,3)*b(1,3)},
{{{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),b(1,3),0,0,0),(b(2,1),b(2,2),b(2,3),0,0,0),(b(3,1),b(3,2),b(3
,3),0,0,0),(b(4,1),b(4,2),b(4,3),b(2,2)*b(1,1) - b(2,1)*b(1,2),b(2,3)*b(1,1) - b
(2,1)*b(1,3),0),(b(5,1),b(5,2),b(5,3),b(3,2)*b(1,1) - b(3,1)*b(1,2),b(3,3)*b(1,1
) - b(3,1)*b(1,3),0),(b(6,1),b(6,2),b(6,3),b(4,2)*b(3,1) - b(4,1)*b(3,2) - b(5,1
)*b(2,2) + b(5,2)*b(2,1),b(4,3)*b(3,1) - b(4,1)*b(3,3) - b(5,1)*b(2,3) + b(5,3)*
b(2,1),b(3,2)*b(2,3)*b(1,1) - b(3,2)*b(2,1)*b(1,3) - b(3,1)*b(2,2)*b(1,3) + b(3,
3)*b(2,2)*b(1,1)))$
$

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

phase2:$

Suppose b(1,2) NEQ 0:$

Then we get det(isom):=0. Hence b(1,2) NEQ 0 is impossible.$

clear b(2,3),b(3,3)$

**************  CASE 1 : Suppose b(2,3) = 0. Then : *******************$

We get in CASE 1 the first kind automorphisms :$

{{{{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),(0,b(2,2),0,0,0,0),(0,0,b(3,3),0,0,0),(b(4,1),b(4,2),b(4,
3),b(2,2)*b(1,1),0,0),(b(5,1),b(5,2),(b(4,2)*b(3,3))/b(2,2),0,b(3,3)*b(1,1),0),(
b(6,1),b(6,2),b(6,3), - b(5,1)*b(2,2), - b(4,1)*b(3,3),b(3,3)*b(2,2)*b(1,1)))$
$

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

isom:=

mat((b(1,1),0,0,0,0,0),

    (0,b(2,2),0,0,0,0),

    (0,0,b(3,3),0,0,0),

    (b(4,1),b(4,2),b(4,3),b(2,2)*b(1,1),0,0),

                    b(4,2)*b(3,3)
    (b(5,1),b(5,2),---------------,0,b(3,3)*b(1,1),0),
                       b(2,2)

    (b(6,1),b(6,2),b(6,3), - b(5,1)*b(2,2), - b(4,1)*b(3,3),b(3,3)*b(2,2)*b(1,1)

     ))


clear b(2,3),b(2,1),b(5,3),b(3,2),b(3,1)$

**************  CASE 2 : Suppose b(2,3) NEQ 0. Then : *******************$

We get in that  CASE 2 the second kind automorphisms :$

{{{{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),(0,0,b(2,3),0,0,0),(0,b(3,2),0,0,0,0),(b(4,1),b(4,2),b(4,
3),0,b(2,3)*b(1,1),0),(b(5,1),(b(4,3)*b(3,2))/b(2,3),b(5,3),b(3,2)*b(1,1),0,0),(
b(6,1),b(6,2),b(6,3), - b(4,1)*b(3,2), - b(5,1)*b(2,3),b(3,2)*b(2,3)*b(1,1)))$
$

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

isom:=

mat((b(1,1),0,0,0,0,0),

    (0,0,b(2,3),0,0,0),

    (0,b(3,2),0,0,0,0),

    (b(4,1),b(4,2),b(4,3),0,b(2,3)*b(1,1),0),

             b(4,3)*b(3,2)
    (b(5,1),---------------,b(5,3),b(3,2)*b(1,1),0,0),
                b(2,3)

    (b(6,1),b(6,2),b(6,3), - b(4,1)*b(3,2), - b(5,1)*b(2,3),b(3,2)*b(2,3)*b(1,1)

     ))