we look for an automorphism of g_{6,nxC3}, n the 3-dim heisenberg algebra.$

nombre d'equations90$

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

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

sa valeur doit etre WW:=0$

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 {{1,4},3} qui est  maintenant AA:=b(2,4)*b(1,1) - b(2,1)*b(
1,4)$

Unknowns: {b(2,4),b(2,1),b(1,4),b(1,1)}
Unknowns: {b(2,4),b(2,1),b(1,4),b(1,1)}


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

Unknowns: {b(2,5),b(2,1),b(1,5),b(1,1)}
Unknowns: {b(2,5),b(2,1),b(1,5),b(1,1)}


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

Unknowns: {b(2,4),b(2,2),b(1,4),b(1,2)}
Unknowns: {b(2,4),b(2,2),b(1,4),b(1,2)}


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

Unknowns: {b(2,5),b(2,2),b(1,5),b(1,2)}
Unknowns: {b(2,5),b(2,2),b(1,5),b(1,2)}


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

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


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

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


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

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


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

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


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

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

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

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),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),b(3,4),b(3,5),b(3,6)),(b(4,1),b(4,2),0,b(4,4),b(4,5),b(4,6)),(b
(5,1),b(5,2),0,b(5,4),b(5,5),b(5,6)),(b(6,1),b(6,2),0,b(6,4),b(6,5),b(6,6)))$

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

isom:=

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