we look for an automorphism of g_{6,52xC}$

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

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)$

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

sa valeur doit etre WW:=0$

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)$

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

sa valeur doit etre WW:=0$

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 {{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 {{2,6},4} 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 {{2,6},5} qui est  maintenant AA:=b(3,6)*b(1,2) - b(3,2)*b(
1,6)$

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


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

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


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

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


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

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

phase2:$

From the stability of the derived algebra one has:$

b(1,2):=0$

b(1,3):=0$

From the stability of the center one has:$

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

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

isom:=

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