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This output from the file \texttt{program11.red}.\\$

Computation of all complex    structures on the real Lie Algebra$

USD {\mathcal{G}}_{6,{m14_(1)}}.USD$

\smallskip  \par $

Commutation relations for$

USD {\mathcal{G}}_{6,{m14_(1)}}:USD\\$

USD[x(1),x(3)]=x(4)USD;$

USD[x(1),x(4)]=x(6)USD;$

USD[x(2),x(3)]=x(5)USD;$

USD[x(2),x(5)]=x(6)USD;$

\P$

Nonzero torsion$

\par$

\\Torsion equations to cancel (Latex output) : \\USD$

{1,2}|1\\xi(3,2)*xi(1,4) - xi(3,1)*xi(1,5) + xi(4,2)*xi(1,6) - xi(5,1)*xi(1,6)\\
$

{1,2}|2\\xi(3,2)*xi(2,4) - xi(3,1)*xi(2,5) + xi(4,2)*xi(2,6) - xi(5,1)*xi(2,6)\\
$

{1,2}|3\\ - (xi(3,5)*xi(3,1) - xi(3,4)*xi(3,2) - xi(4,2)*xi(3,6)) - xi(5,1)*xi(3
,6)\\$

{1,2}|4\\ - (xi(3,2)*xi(1,1) - xi(3,1)*xi(1,2) - xi(4,4)*xi(3,2) + xi(4,5)*xi(3,
1) - xi(4,6)*xi(4,2)) - xi(5,1)*xi(4,6)\\$

{1,2}|5\\ - (xi(3,2)*xi(2,1) - xi(3,1)*xi(2,2) - xi(5,4)*xi(3,2) + xi(5,5)*xi(3,
1)) - (xi(5,1) - xi(4,2))*xi(5,6)\\$

{1,2}|6\\ - (xi(4,2)*xi(1,1) - xi(4,1)*xi(1,2) - xi(5,1)*xi(2,2) + xi(5,2)*xi(2,
1) - xi(6,4)*xi(3,2) + xi(6,5)*xi(3,1)) - (xi(5,1) - xi(4,2))*xi(6,6)\\$

{1,3}|1\\xi(2,1)*xi(1,5) + xi(1,4)*xi(1,1) + xi(3,3)*xi(1,4) + xi(4,3)*xi(1,6)\\
$

{1,3}|2\\xi(2,5)*xi(2,1) + xi(2,4)*xi(1,1) + xi(3,3)*xi(2,4) + xi(4,3)*xi(2,6)\\
$

{1,3}|3\\(xi(3,3) + xi(1,1))*xi(3,4) + xi(3,5)*xi(2,1) + xi(4,3)*xi(3,6)\\$

{1,3}|4\\xi(3,1)*xi(1,3) + 1 - xi(3,3)*xi(1,1) + (xi(3,3) + xi(1,1))*xi(4,4) + 
xi(4,5)*xi(2,1) + xi(4,6)*xi(4,3)\\$

{1,3}|5\\ - (xi(3,3)*xi(2,1) - xi(3,1)*xi(2,3) - (xi(3,3) + xi(1,1))*xi(5,4) - 
xi(5,5)*xi(2,1)) + xi(5,6)*xi(4,3)\\$

{1,3}|6\\ - (xi(4,3)*xi(1,1) - xi(4,1)*xi(1,3) - xi(5,1)*xi(2,3) + xi(5,3)*xi(2,
1) - (xi(3,3) + xi(1,1))*xi(6,4) - xi(6,5)*xi(2,1)) + xi(6,6)*xi(4,3)\\$

{1,4}|1\\xi(3,4)*xi(1,4) + xi(1,6)*xi(1,1) + xi(4,4)*xi(1,6)\\$

{1,4}|2\\xi(3,4)*xi(2,4) + xi(2,6)*xi(1,1) + xi(4,4)*xi(2,6)\\$

{1,4}|3\\xi(3,6)*xi(1,1) + xi(3,4)**2 + xi(4,4)*xi(3,6)\\$

{1,4}|4\\ - (xi(3,4)*xi(1,1) - xi(3,1)*xi(1,4) - xi(4,4)*xi(3,4)) + (xi(4,4) + 
xi(1,1))*xi(4,6)\\$

{1,4}|5\\ - (xi(3,4)*xi(2,1) - xi(3,1)*xi(2,4) - xi(5,4)*xi(3,4)) + (xi(4,4) + 
xi(1,1))*xi(5,6)\\$

{1,4}|6\\xi(4,1)*xi(1,4) + 1 - xi(4,4)*xi(1,1) + xi(5,1)*xi(2,4) - xi(5,4)*xi(2,
1) + xi(6,4)*xi(3,4) + (xi(4,4) + xi(1,1))*xi(6,6)\\$

{1,5}|1\\xi(3,5)*xi(1,4) + xi(2,1)*xi(1,6) + xi(4,5)*xi(1,6)\\$

{1,5}|2\\xi(3,5)*xi(2,4) + xi(2,6)*xi(2,1) + xi(4,5)*xi(2,6)\\$

{1,5}|3\\xi(3,6)*xi(2,1) + xi(3,5)*xi(3,4) + xi(4,5)*xi(3,6)\\$

{1,5}|4\\ - (xi(3,5)*xi(1,1) - xi(3,1)*xi(1,5) - xi(4,4)*xi(3,5)) + (xi(4,5) + 
xi(2,1))*xi(4,6)\\$

{1,5}|5\\ - (xi(3,5)*xi(2,1) - xi(3,1)*xi(2,5) - xi(5,4)*xi(3,5)) + (xi(4,5) + 
xi(2,1))*xi(5,6)\\$

{1,5}|6\\ - (xi(4,5)*xi(1,1) - xi(4,1)*xi(1,5) - xi(5,1)*xi(2,5) + xi(5,5)*xi(2,
1) - xi(6,4)*xi(3,5)) + (xi(4,5) + xi(2,1))*xi(6,6)\\$

{1,6}|1\\xi(4,6)*xi(1,6) + xi(3,6)*xi(1,4)\\$

{1,6}|2\\xi(4,6)*xi(2,6) + xi(3,6)*xi(2,4)\\$

{1,6}|3\\xi(4,6)*xi(3,6) + xi(3,6)*xi(3,4)\\$

{1,6}|4\\ - (xi(3,6)*xi(1,1) - xi(3,1)*xi(1,6) - xi(4,4)*xi(3,6)) + xi(4,6)**2\\
$

{1,6}|5\\ - (xi(3,6)*xi(2,1) - xi(3,1)*xi(2,6) - xi(5,4)*xi(3,6)) + xi(5,6)*xi(4
,6)\\$

{1,6}|6\\ - (xi(4,6)*xi(1,1) - xi(4,1)*xi(1,6) - xi(5,1)*xi(2,6) + xi(5,6)*xi(2,
1) - xi(6,4)*xi(3,6)) + xi(6,6)*xi(4,6)\\$

{2,3}|1\\xi(2,2)*xi(1,5) + xi(1,4)*xi(1,2) + xi(3,3)*xi(1,5) + xi(5,3)*xi(1,6)\\
$

{2,3}|2\\xi(2,5)*xi(2,2) + xi(2,4)*xi(1,2) + xi(3,3)*xi(2,5) + xi(5,3)*xi(2,6)\\
$

{2,3}|3\\xi(3,5)*xi(3,3) + xi(3,5)*xi(2,2) + xi(3,4)*xi(1,2) + xi(5,3)*xi(3,6)\\
$

{2,3}|4\\ - (xi(3,3)*xi(1,2) - xi(3,2)*xi(1,3) - xi(4,4)*xi(1,2) - (xi(3,3) + xi
(2,2))*xi(4,5)) + xi(5,3)*xi(4,6)\\$

{2,3}|5\\xi(3,2)*xi(2,3) + 1 - xi(3,3)*xi(2,2) + xi(5,4)*xi(1,2) + (xi(3,3) + xi
(2,2))*xi(5,5) + xi(5,6)*xi(5,3)\\$

{2,3}|6\\ - (xi(4,3)*xi(1,2) - xi(4,2)*xi(1,3) - xi(5,2)*xi(2,3) + xi(5,3)*xi(2,
2) - xi(6,4)*xi(1,2) - (xi(3,3) + xi(2,2))*xi(6,5)) + xi(6,6)*xi(5,3)\\$

{2,4}|1\\xi(3,4)*xi(1,5) + xi(1,6)*xi(1,2) + xi(5,4)*xi(1,6)\\$

{2,4}|2\\xi(3,4)*xi(2,5) + xi(2,6)*xi(1,2) + xi(5,4)*xi(2,6)\\$

{2,4}|3\\xi(3,6)*xi(1,2) + xi(3,5)*xi(3,4) + xi(5,4)*xi(3,6)\\$

{2,4}|4\\ - (xi(3,4)*xi(1,2) - xi(3,2)*xi(1,4) - xi(4,5)*xi(3,4) - xi(4,6)*xi(1,
2)) + xi(5,4)*xi(4,6)\\$

{2,4}|5\\ - (xi(3,4)*xi(2,2) - xi(3,2)*xi(2,4) - xi(5,5)*xi(3,4)) + (xi(5,4) + 
xi(1,2))*xi(5,6)\\$

{2,4}|6\\ - (xi(4,4)*xi(1,2) - xi(4,2)*xi(1,4) - xi(5,2)*xi(2,4) + xi(5,4)*xi(2,
2) - xi(6,5)*xi(3,4)) + (xi(5,4) + xi(1,2))*xi(6,6)\\$

{2,5}|1\\xi(3,5)*xi(1,5) + xi(2,2)*xi(1,6) + xi(5,5)*xi(1,6)\\$

{2,5}|2\\xi(3,5)*xi(2,5) + xi(2,6)*xi(2,2) + xi(5,5)*xi(2,6)\\$

{2,5}|3\\xi(3,6)*xi(2,2) + xi(3,5)**2 + xi(5,5)*xi(3,6)\\$

{2,5}|4\\ - (xi(3,5)*xi(1,2) - xi(3,2)*xi(1,5) - xi(4,5)*xi(3,5) - xi(4,6)*xi(2,
2)) + xi(5,5)*xi(4,6)\\$

{2,5}|5\\ - (xi(3,5)*xi(2,2) - xi(3,2)*xi(2,5) - xi(5,5)*xi(3,5)) + (xi(5,5) + 
xi(2,2))*xi(5,6)\\$

{2,5}|6\\xi(4,2)*xi(1,5) + 1 - xi(4,5)*xi(1,2) + xi(5,2)*xi(2,5) - xi(5,5)*xi(2,
2) + xi(6,5)*xi(3,5) + (xi(5,5) + xi(2,2))*xi(6,6)\\$

{2,6}|1\\xi(5,6)*xi(1,6) + xi(3,6)*xi(1,5)\\$

{2,6}|2\\xi(5,6)*xi(2,6) + xi(3,6)*xi(2,5)\\$

{2,6}|3\\xi(5,6)*xi(3,6) + xi(3,6)*xi(3,5)\\$

{2,6}|4\\ - (xi(3,6)*xi(1,2) - xi(3,2)*xi(1,6) - xi(4,5)*xi(3,6)) + xi(5,6)*xi(4
,6)\\$

{2,6}|5\\ - (xi(3,6)*xi(2,2) - xi(3,2)*xi(2,6) - xi(5,5)*xi(3,6)) + xi(5,6)**2\\
$

{2,6}|6\\ - (xi(4,6)*xi(1,2) - xi(4,2)*xi(1,6) - xi(5,2)*xi(2,6) + xi(5,6)*xi(2,
2) - xi(6,5)*xi(3,6)) + xi(6,6)*xi(5,6)\\$

{3,4}|1\\xi(1,6)*xi(1,3) - xi(1,4)**2 - xi(2,4)*xi(1,5)\\$

{3,4}|2\\ - (xi(2,5) + xi(1,4))*xi(2,4) + xi(2,6)*xi(1,3)\\$

{3,4}|3\\ - (xi(3,5)*xi(2,4) + xi(3,4)*xi(1,4)) + xi(3,6)*xi(1,3)\\$

{3,4}|4\\ - (xi(3,4)*xi(1,3) - xi(3,3)*xi(1,4) + xi(4,4)*xi(1,4) + xi(4,5)*xi(2,
4)) + xi(4,6)*xi(1,3)\\$

{3,4}|5\\ - (xi(3,4)*xi(2,3) - xi(3,3)*xi(2,4) + xi(5,4)*xi(1,4) + xi(5,5)*xi(2,
4)) + xi(5,6)*xi(1,3)\\$

{3,4}|6\\ - (xi(4,4)*xi(1,3) - xi(4,3)*xi(1,4) - xi(5,3)*xi(2,4) + xi(5,4)*xi(2,
3) + xi(6,4)*xi(1,4) + xi(6,5)*xi(2,4)) + xi(6,6)*xi(1,3)\\$

{3,5}|1\\xi(2,3)*xi(1,6) - xi(1,5)*xi(1,4) - xi(2,5)*xi(1,5)\\$

{3,5}|2\\ - (xi(2,5)**2 + xi(2,4)*xi(1,5)) + xi(2,6)*xi(2,3)\\$

{3,5}|3\\ - (xi(3,5)*xi(2,5) + xi(3,4)*xi(1,5)) + xi(3,6)*xi(2,3)\\$

{3,5}|4\\ - (xi(3,5)*xi(1,3) - xi(3,3)*xi(1,5) + xi(4,4)*xi(1,5) + xi(4,5)*xi(2,
5)) + xi(4,6)*xi(2,3)\\$

{3,5}|5\\ - (xi(3,5)*xi(2,3) - xi(3,3)*xi(2,5) + xi(5,4)*xi(1,5) + xi(5,5)*xi(2,
5)) + xi(5,6)*xi(2,3)\\$

{3,5}|6\\ - (xi(4,5)*xi(1,3) - xi(4,3)*xi(1,5) - xi(5,3)*xi(2,5) + xi(5,5)*xi(2,
3) + xi(6,4)*xi(1,5) + xi(6,5)*xi(2,5)) + xi(6,6)*xi(2,3)\\$

{3,6}|1\\ - xi(2,6)*xi(1,5) - xi(1,6)*xi(1,4)\\$

{3,6}|2\\ - xi(2,6)*xi(2,5) - xi(2,4)*xi(1,6)\\$

{3,6}|3\\ - xi(3,5)*xi(2,6) - xi(3,4)*xi(1,6)\\$

{3,6}|4\\ - (xi(3,6)*xi(1,3) - xi(3,3)*xi(1,6) + xi(4,4)*xi(1,6)) - xi(4,5)*xi(2
,6)\\$

{3,6}|5\\ - (xi(3,6)*xi(2,3) - xi(3,3)*xi(2,6) + xi(5,4)*xi(1,6)) - xi(5,5)*xi(2
,6)\\$

{3,6}|6\\ - (xi(4,6)*xi(1,3) - xi(4,3)*xi(1,6) - xi(5,3)*xi(2,6) + xi(5,6)*xi(2,
3) + xi(6,4)*xi(1,6)) - xi(6,5)*xi(2,6)\\$

{4,5}|1\\xi(2,4)*xi(1,6) - xi(1,6)*xi(1,5)\\$

{4,5}|2\\xi(2,6)*xi(2,4) - xi(2,6)*xi(1,5)\\$

{4,5}|3\\xi(3,6)*xi(2,4) - xi(3,6)*xi(1,5)\\$

{4,5}|4\\ - (xi(3,5)*xi(1,4) - xi(3,4)*xi(1,5)) + (xi(2,4) - xi(1,5))*xi(4,6)\\$

{4,5}|5\\ - (xi(3,5)*xi(2,4) - xi(3,4)*xi(2,5)) + (xi(2,4) - xi(1,5))*xi(5,6)\\$

{4,5}|6\\ - (xi(4,5)*xi(1,4) - xi(4,4)*xi(1,5) - xi(5,4)*xi(2,5) + xi(5,5)*xi(2,
4)) + (xi(2,4) - xi(1,5))*xi(6,6)\\$

{4,6}|1\\ - xi(1,6)**2\\$

{4,6}|2\\ - xi(2,6)*xi(1,6)\\$

{4,6}|3\\ - xi(3,6)*xi(1,6)\\$

{4,6}|4\\ - (xi(3,6)*xi(1,4) - xi(3,4)*xi(1,6)) - xi(4,6)*xi(1,6)\\$

{4,6}|5\\ - (xi(3,6)*xi(2,4) - xi(3,4)*xi(2,6)) - xi(5,6)*xi(1,6)\\$

{4,6}|6\\ - (xi(4,6)*xi(1,4) - xi(4,4)*xi(1,6) - xi(5,4)*xi(2,6) + xi(5,6)*xi(2,
4)) - xi(6,6)*xi(1,6)\\$

{5,6}|1\\ - xi(2,6)*xi(1,6)\\$

{5,6}|2\\ - xi(2,6)**2\\$

{5,6}|3\\ - xi(3,6)*xi(2,6)\\$

{5,6}|4\\ - (xi(3,6)*xi(1,5) - xi(3,5)*xi(1,6)) - xi(4,6)*xi(2,6)\\$

{5,6}|5\\ - (xi(3,6)*xi(2,5) - xi(3,5)*xi(2,6)) - xi(5,6)*xi(2,6)\\$

{5,6}|6\\ - (xi(4,6)*xi(1,5) - xi(4,5)*xi(1,6) - xi(5,5)*xi(2,6) + xi(5,6)*xi(2,
5)) - xi(6,6)*xi(2,6)\\$

USD$

\\ \starline$

\par Simultaneous resolution of the nonzero torsion equations and the matrix$

equation USD J^2 = -I . USD$

First, one gets from  equation USD46|1USD :$

\\ USD xi(1,6):=0USD$

\\ and from  equation USD56|2USD :$

\\ USD xi(2,6):=0USD$

\\Then, if USD xi(3,6)=0 USD $

\\ USD xi(3,6):=0USD$

\\ one gets from  equation USD26|5USD :$

\\ USD xi(5,6):=0USD$

\\ and from  equation USD16|4USD :$

\\ USD xi(4,6):=0USD$

\par With these values, \textit{Reduce} computes again all equations.$

Then the 6x6 entry in  USD J**2 USD  is USD xi(6,6)**2 USD$

\\ hence, one gets a contradiction $

\\ Hence USD xi(3,6)USD has to be USD \neq 0 .USD$

\\ clear  USD xi(3,6),xi(4,6),xi(5,6) USD$

\\ USD xi(3,6):=xi(3,6)USD$

\\ USD xi(5,6):=xi(5,6)USD$

\\ USD xi(4,6):=xi(4,6)USD$

\par With these values, \textit{Reduce} computes again all equations.$

Then, one gets from  equation USD16|1USD :$

\\ USD xi(1,4):=0USD$

\\ and from  equation USD16|2USD :$

\\ USD xi(2,4):=0USD$

\\ and from  equation USD26|1USD :$

\\ USD xi(1,5):=0USD$

\\ and from  equation USD26|2USD :$

\\ USD xi(2,5):=0USD$

\\ and from  equation USD36|4USD :$

\\ USD xi(1,3):=0USD$

\\ and from  equation USD36|5USD :$

\\ USD xi(2,3):=0USD$

\\ and from  equation USD26|3USD :$

\\ USD xi(5,6):= - xi(3,5)USD$

\\ and from  equation USD16|3USD :$

\\ USD xi(4,6):= - xi(3,4)USD$

\par With these values, \textit{Reduce} computes again all equations.$

Then the 1x1 entry in  USD J**2 USD  is $

USD  {J**2}^1_1=xi(1,1)**2 + xi(2,1)*xi(1,2);USD\\$

Hence USD xi(2,1)xi(1,2)\neq 0 USD$

and USD xi(1,2) =(-1-xi(1,1)**2)/xi(2,1). USD$

\\ USD xi(1,2):= - (xi(1,1)**2 + 1)/xi(2,1)USD$

Moreover, the 1x2 entry in  USD J**2 USD  is $

USD  (xi(2,2) + xi(1,1))*xi(1,2);USD hence\\$

\\ USD xi(2,2):= - xi(1,1)USD$

\\Suppose here  USD xi(1,1) \neq     0 USD $

\\ Then, one gets from  equation USD14|4USD :$

\\ USD xi(3,4):=0USD$

\\ and from  equation USD25|5USD :$

\\ USD xi(3,5):=0USD$

\\ Then, one gets from  equation USD13|3USD :$

\\ USD xi(4,3):=0USD$

\\ and from  equation USD16|6USD :$

\\ USD xi(6,4):=0USD$

\\ and from  equation USD23|3USD :$

\\ USD xi(5,3):=0USD$

\\ and from  equation USD26|6USD :$

\\ USD xi(6,5):=0USD$

\par With these values, \textit{Reduce} computes again all equations.$

\\ Then, one gets from  equation USD14|3USD :$

USD xi(4,4)=-xi(1,1)$

\\ and from  equation USD16|4USD :$

USD xi(4,4)=xi(1,1)$

\\ hence USD xi(1,1):=0. USD a contradiction$

\\ Hence  one cannot have USD xi(1,1) \neq 0. USD $

\\ USD xi(1,1):=0USD$

\\ Clear USDxi(3,4),xi(3,5),xi(5,3),xi(4,3),xi(6,4),xi(6,5) USD$

\\ USD xi(3,4):=xi(3,4)USD$

\\ USD xi(3,5):=xi(3,5)USD$

\\ USD xi(4,3):=xi(4,3)USD$

\\ USD xi(6,4):=xi(6,4)USD$

\\ USD xi(5,3):=xi(5,3)USD$

\\ USD xi(6,5):=xi(6,5)USD$

\par With these values, \textit{Reduce} computes again all equations.$

\\ Then, one gets from  equation USD14|3USD :$

\\ USD xi(4,4):=( - xi(3,4)**2)/xi(3,6)USD$

\\ and from  equation USD25|3USD :$

\\ USD xi(5,5):=( - xi(3,5)**2)/xi(3,6)USD$

\par With these values, \textit{Reduce} computes again all equations.$

\\ Then, one gets from  equation USD23|3USD :$

\\ USD xi(3,4):=xi(2,1)*(xi(5,3)*xi(3,6) + xi(3,5)*xi(3,3))USD$

\\ and from  equation USD23|6USD :$

\\ USD xi(4,3):= - xi(6,6)*xi(5,3)*xi(2,1) - xi(6,5)*xi(3,3)*xi(2,1) + xi(6,4)
USD$

\par With these values, \textit{Reduce} computes again all equations.$

\\ Then, one gets from  equation USD26|6USD :$

\\ USD xi(5,3):=( - xi(6,6)*xi(3,5) + xi(6,5)*xi(3,6) - xi(3,5)*xi(3,3))/xi(3,6)
USD$

\par With these values, \textit{Reduce} computes again all equations.$

\\ Then, one gets from  equation USD12|3USD :$

\\ USD xi(4,2):=(xi(6,6)*xi(3,5)*xi(3,2)*xi(2,1) - xi(6,5)*xi(3,6)*xi(3,2)*xi(2,
1) + xi(5,1)*xi(3,6) + xi(3,5)*xi(3,1))/xi(3,6)USD$

\par With these values, \textit{Reduce} computes again all equations.$

\\ Then, one gets from  equation USD16|6USD :$

\\ USD xi(6,4):=(xi(2,1)*( - xi(6,6)**2*xi(3,5) + xi(6,6)*xi(6,5)*xi(3,6) - xi(3
,5)))/xi(3,6)USD$

\par With these values, \textit{Reduce} computes again all equations.$

Then the 3x1 entry in  USD J**2 USD  gives $

\\ USD xi(6,1):=(xi(6,6)*xi(4,1)*xi(3,5)*xi(2,1) - xi(6,5)*xi(4,1)*xi(3,6)*xi(2,
1) - xi(5,1)*xi(3,5) - xi(3,3)*xi(3,1) - xi(3,2)*xi(2,1))/xi(3,6)USD$

\par With these values, \textit{Reduce} computes again all equations.$

Then the 3x6 entry in  USD J**2 USD  gives $

\\ USD xi(3,3):=(xi(6,6)**2*xi(3,5)**2*xi(2,1)**2 - 2*xi(6,6)*xi(6,5)*xi(3,6)*xi
(3,5)*xi(2,1)**2 - xi(6,6)*xi(3,6) + xi(6,5)**2*xi(3,6)**2*xi(2,1)**2 + xi(3,5)
**2)/xi(3,6)USD$

\par With these values, \textit{Reduce} computes again all equations.$

\\ Then, one gets from  equation USD15|3USD :$

\\ USD xi(4,5):=(xi(2,1)*(xi(6,6)*xi(3,5)**2 - xi(6,5)*xi(3,6)*xi(3,5) - xi(3,6)
))/xi(3,6)USD$

\par With these values, \textit{Reduce} computes again all equations.$

\\ Then,   equation USD26|4USD reads :$

 USD {2,6}|4\\(-xi(3,6)*xi(2,1)**2 + xi(3,6))/xi(2,1)\\$

Hence we get$

\\ USD xi(2,1)**2:=1USD$

\par With these values, \textit{Reduce} computes again all equations.$

\\ Then,   equation USD12|6USD reads :$

\\ USD xi(5,2):=(xi(6,6)*xi(3,5)*xi(3,1)*xi(2,1) - xi(6,5)*xi(3,6)*xi(3,1)*xi(2,
1) - xi(4,1)*xi(3,6) - xi(3,5)*xi(3,2))/xi(3,6)USD$

\par With these values, \textit{Reduce} computes again all equations.$

\\ Then,   equation USD16|5USD gives :$

\\ USD xi(5,4):=(xi(2,1)*(xi(6,6)*xi(3,5)**2 - xi(6,5)*xi(3,6)*xi(3,5) + xi(3,6)
))/xi(3,6)USD$

Then the 3x2 entry in  USD J**2 USD  gives $

\\ USD xi(6,2):=(xi(6,6)*xi(5,1)*xi(3,5) + xi(6,6)*xi(3,2)*xi(2,1) - xi(6,5)*xi(
5,1)*xi(3,6) + xi(4,1)*xi(3,5)*xi(2,1) + xi(3,1))/(xi(3,6)*xi(2,1))USD$

\par With these values, \textit{Reduce} computes again all equations.$

Then the 3x3 entry in  USD J**2 USD  gives $

\\ USD xi(6,3):=(xi(6,6)**3*xi(3,5)**2 - 2*xi(6,6)**2*xi(6,5)*xi(3,6)*xi(3,5) - 
xi(6,6)**2*xi(3,6) + xi(6,6)*xi(6,5)**2*xi(3,6)**2 + xi(6,6)*xi(3,5)**2 - xi(3,6
))/xi(3,6)**2USD$

\\ \starline$

At the present stage, we have : $

 \\ \4stars Now the nonzero torsion equations left are :$

\\ Torsion equations to cancel (Latex output) : USD$

USD$

\\ \P \\$

\par The matrix USD J USD is :\\$

The matrix USD J USD is given by the following formula,$

with USD xi(1,2) = \pm 1   USD and $

 USD xi(3,6) \neq 0  : USD$

\begin{equation} \label{M14+1general} \end{equation}$

USD  J^1_1=0;USD\\$

USD  J^1_2=( - 1)/xi(2,1);USD\\$

USD  J^1_3=0;USD\\$

USD  J^1_4=0;USD\\$

USD  J^1_5=0;USD\\$

USD  J^1_6=0;USD\\$

USD  J^2_1=xi(2,1);USD\\$

USD  J^2_2=0;USD\\$

USD  J^2_3=0;USD\\$

USD  J^2_4=0;USD\\$

USD  J^2_5=0;USD\\$

USD  J^2_6=0;USD\\$

USD  J^3_1=xi(3,1);USD\\$

USD  J^3_2=xi(3,2);USD\\$

USD  J^3_3=(xi(6,5)**2*xi(3,6)**2 + xi(3,5)**2 + xi(6,6)**2*xi(3,5)**2 - (2*xi(6
,5)*xi(3,5) + 1)*xi(6,6)*xi(3,6))/xi(3,6);USD\\$

USD  J^3_4= - (xi(6,6)*xi(3,5) - xi(6,5)*xi(3,6))*xi(2,1);USD\\$

USD  J^3_5=xi(3,5);USD\\$

USD  J^3_6=xi(3,6);USD\\$

USD  J^4_1=xi(4,1);USD\\$

USD  J^4_2=((xi(6,6)*xi(3,5) - xi(6,5)*xi(3,6))*xi(3,2)*xi(2,1) + xi(5,1)*xi(3,6
) + xi(3,5)*xi(3,1))/xi(3,6);USD\\$

USD  J^4_3=(((xi(6,6)**2*xi(3,5)**3 - 3*xi(6,6)*xi(6,5)*xi(3,6)*xi(3,5)**2 - xi(
6,6)*xi(3,6)*xi(3,5) + 3*xi(6,5)**2*xi(3,6)**2*xi(3,5) + xi(6,5)*xi(3,6)**2 + xi
(3,5)**3)*xi(6,6) - (xi(6,5)**3*xi(3,6)**2 + xi(6,5)*xi(3,5)**2 + xi(3,5))*xi(3,
6))*xi(2,1))/xi(3,6)**2;USD\\$

USD  J^4_4=( - (xi(6,6)*xi(3,5) - xi(6,5)*xi(3,6))**2)/xi(3,6);USD\\$

USD  J^4_5=( - ((xi(6,5)*xi(3,5) + 1)*xi(3,6) - xi(6,6)*xi(3,5)**2)*xi(2,1))/xi(
3,6);USD\\$

USD  J^4_6=(xi(6,6)*xi(3,5) - xi(6,5)*xi(3,6))*xi(2,1);USD\\$

USD  J^5_1=xi(5,1);USD\\$

USD  J^5_2=( - (xi(4,1)*xi(3,6) + xi(3,5)*xi(3,2) + xi(6,5)*xi(3,6)*xi(3,1)*xi(2
,1) - xi(6,6)*xi(3,5)*xi(3,1)*xi(2,1)))/xi(3,6);USD\\$

USD  J^5_3=( - ((xi(6,6)*xi(3,5) - 2*xi(6,5)*xi(3,6))*xi(6,6)*xi(3,5)**2 + xi(6,
5)**2*xi(3,6)**2*xi(3,5) - xi(6,5)*xi(3,6)**2 + xi(3,5)**3))/xi(3,6)**2;USD\\$

USD  J^5_4=( - ((xi(6,5)*xi(3,5) - 1)*xi(3,6) - xi(6,6)*xi(3,5)**2)*xi(2,1))/xi(
3,6);USD\\$

USD  J^5_5=( - xi(3,5)**2)/xi(3,6);USD\\$

USD  J^5_6= - xi(3,5);USD\\$

USD  J^6_1=( - (xi(3,6)*xi(3,2)*xi(2,1) + xi(3,5)**2*xi(3,1) + xi(5,1)*xi(3,6)*
xi(3,5) + (xi(6,5)*xi(3,1) + xi(4,1)*xi(2,1))*xi(6,5)*xi(3,6)**2 + ((xi(6,6)*xi(
3,5) - 2*xi(6,5)*xi(3,6))*xi(3,5)*xi(3,1) - (xi(4,1)*xi(3,5)*xi(2,1) + xi(3,1))*
xi(3,6))*xi(6,6)))/xi(3,6)**2;USD\\$

USD  J^6_2=(xi(6,6)*xi(5,1)*xi(3,5) + xi(6,6)*xi(3,2)*xi(2,1) - xi(6,5)*xi(5,1)*
xi(3,6) + xi(4,1)*xi(3,5)*xi(2,1) + xi(3,1))/(xi(3,6)*xi(2,1));USD\\$

USD  J^6_3=(xi(6,6)**3*xi(3,5)**2 - 2*xi(6,6)**2*xi(6,5)*xi(3,6)*xi(3,5) - xi(6,
6)**2*xi(3,6) + xi(6,6)*xi(6,5)**2*xi(3,6)**2 + xi(6,6)*xi(3,5)**2 - xi(3,6))/xi
(3,6)**2;USD\\$

USD  J^6_4=( - (xi(6,6)**2*xi(3,5) - xi(6,6)*xi(6,5)*xi(3,6) + xi(3,5))*xi(2,1))
/xi(3,6);USD\\$

USD  J^6_5=xi(6,5);USD\\$

USD  J^6_6=xi(6,6);USD\\$

\\$

USDUSD J = \begin{pmatrix}$

0&$

( - 1)/xi(2,1)&$

0&$

0&$

0&$

0\\$

xi(2,1)&$

0&$

0&$

0&$

0&$

0\\$

xi(3,1)&$

xi(3,2)&$

(xi(6,5)**2*xi(3,6)**2 + xi(3,5)**2 + xi(6,6)**2*xi(3,5)**2 - (2*xi(6,5)*xi(3,5)
 + 1)*xi(6,6)*xi(3,6))/xi(3,6)&$

 - (xi(6,6)*xi(3,5) - xi(6,5)*xi(3,6))*xi(2,1)&$

xi(3,5)&$

xi(3,6)\\$

xi(4,1)&$

((xi(6,6)*xi(3,5) - xi(6,5)*xi(3,6))*xi(3,2)*xi(2,1) + xi(5,1)*xi(3,6) + xi(3,5)
*xi(3,1))/xi(3,6)&$

(((xi(6,6)**2*xi(3,5)**3 - 3*xi(6,6)*xi(6,5)*xi(3,6)*xi(3,5)**2 - xi(6,6)*xi(3,6
)*xi(3,5) + 3*xi(6,5)**2*xi(3,6)**2*xi(3,5) + xi(6,5)*xi(3,6)**2 + xi(3,5)**3)*
xi(6,6) - (xi(6,5)**3*xi(3,6)**2 + xi(6,5)*xi(3,5)**2 + xi(3,5))*xi(3,6))*xi(2,1
))/xi(3,6)**2&$

( - (xi(6,6)*xi(3,5) - xi(6,5)*xi(3,6))**2)/xi(3,6)&$

( - ((xi(6,5)*xi(3,5) + 1)*xi(3,6) - xi(6,6)*xi(3,5)**2)*xi(2,1))/xi(3,6)&$

(xi(6,6)*xi(3,5) - xi(6,5)*xi(3,6))*xi(2,1)\\$

xi(5,1)&$

( - (xi(4,1)*xi(3,6) + xi(3,5)*xi(3,2) + xi(6,5)*xi(3,6)*xi(3,1)*xi(2,1) - xi(6,
6)*xi(3,5)*xi(3,1)*xi(2,1)))/xi(3,6)&$

( - ((xi(6,6)*xi(3,5) - 2*xi(6,5)*xi(3,6))*xi(6,6)*xi(3,5)**2 + xi(6,5)**2*xi(3,
6)**2*xi(3,5) - xi(6,5)*xi(3,6)**2 + xi(3,5)**3))/xi(3,6)**2&$

( - ((xi(6,5)*xi(3,5) - 1)*xi(3,6) - xi(6,6)*xi(3,5)**2)*xi(2,1))/xi(3,6)&$

( - xi(3,5)**2)/xi(3,6)&$

 - xi(3,5)\\$

( - (xi(3,6)*xi(3,2)*xi(2,1) + xi(3,5)**2*xi(3,1) + xi(5,1)*xi(3,6)*xi(3,5) + (
xi(6,5)*xi(3,1) + xi(4,1)*xi(2,1))*xi(6,5)*xi(3,6)**2 + ((xi(6,6)*xi(3,5) - 2*xi
(6,5)*xi(3,6))*xi(3,5)*xi(3,1) - (xi(4,1)*xi(3,5)*xi(2,1) + xi(3,1))*xi(3,6))*xi
(6,6)))/xi(3,6)**2&$

(xi(6,6)*xi(5,1)*xi(3,5) + xi(6,6)*xi(3,2)*xi(2,1) - xi(6,5)*xi(5,1)*xi(3,6) + 
xi(4,1)*xi(3,5)*xi(2,1) + xi(3,1))/(xi(3,6)*xi(2,1))&$

(xi(6,6)**3*xi(3,5)**2 - 2*xi(6,6)**2*xi(6,5)*xi(3,6)*xi(3,5) - xi(6,6)**2*xi(3,
6) + xi(6,6)*xi(6,5)**2*xi(3,6)**2 + xi(6,6)*xi(3,5)**2 - xi(3,6))/xi(3,6)**2&$

( - (xi(6,6)**2*xi(3,5) - xi(6,6)*xi(6,5)*xi(3,6) + xi(3,5))*xi(2,1))/xi(3,6)&$

xi(6,5)&$

xi(6,6)\end{pmatrix}USDUSD$

USDUSD J^2 = \begin{pmatrix}$

-1&$

0&$

0&$

0&$

0&$

0\\$

0&$

-1&$

0&$

0&$

0&$

0\\$

0&$

0&$

-1&$

0&$

0&$

0\\$

0&$

0&$

0&$

-1&$

0&$

0\\$

0&$

0&$

0&$

0&$

-1&$

0\\$

0&$

0&$

0&$

0&$

0&$

-1\end{pmatrix}USDUSD$

\\USD det J:=1 USD$

USD Trace J:=0 USD$

\\ check of torsion$

\\Torsion equations to cancel (Latex output) : \\USD$

USD $

zero torsion$

\par Commutation relations of USD \mathfrak{m} : USD$

\\ USD  [\tilde{x}_1,\tilde{x}_2]=( - ((xi(3,2)*tildex_5 + xi(3,1)*tildex_4)*xi(
3,6) + xi(6,6)*xi(3,5)*xi(3,1)*xi(2,1)*tildex_6 - (xi(6,5)*xi(3,6)*xi(3,1)*xi(2,
1) + xi(3,5)*xi(3,2))*tildex_6))/(xi(3,6)*xi(2,1));\\USD$

\\ USD  [\tilde{x}_1,\tilde{x}_3]=( - ((xi(6,6)*xi(3,6)*xi(3,5)**2*tildex_5 - xi
(6,6)*xi(3,5)**3*tildex_6 - 2*xi(6,5)*xi(3,6)**2*xi(3,5)*tildex_5 + 2*xi(6,5)*xi
(3,6)*xi(3,5)**2*tildex_6 - xi(3,6)**2*tildex_5)*xi(6,6)*xi(2,1) - xi(3,6)**2*
tildex_4 + ((xi(6,5)*xi(3,6)*tildex_5 - xi(6,5)*xi(3,5)*tildex_6 + tildex_6)*xi(
6,5)*xi(3,6)**2 + (xi(3,6)*tildex_5 - xi(3,5)*tildex_6)*xi(3,5)**2)*xi(2,1)))/xi
(3,6)**2;\\USD$

\\ USD  [\tilde{x}_1,\tilde{x}_4]=((xi(6,6)*xi(3,5) - xi(6,5)*xi(3,6))*(xi(3,6)*
tildex_5 - xi(3,5)*tildex_6))/xi(3,6);\\USD$

\\ USD  [\tilde{x}_1,\tilde{x}_5]=( - (xi(3,6)*tildex_5 - xi(3,5)*tildex_6)*xi(3
,5)*xi(2,1))/xi(3,6);\\USD$

\\ USD  [\tilde{x}_1,\tilde{x}_6]= - (xi(3,6)*tildex_5 - xi(3,5)*tildex_6)*xi(2,
1);\\USD$

\\ USD  [\tilde{x}_2,\tilde{x}_3]=((xi(6,6)**2*xi(3,5)**3*xi(2,1)*tildex_6 - 3*
xi(6,6)*xi(6,5)*xi(3,6)*xi(3,5)**2*xi(2,1)*tildex_6 + 3*xi(6,5)**2*xi(3,6)**2*xi
(3,5)*xi(2,1)*tildex_6 - 2*xi(6,5)*xi(3,6)**2*xi(3,5)*tildex_4 + xi(6,5)*xi(3,6)
**2*xi(2,1)*tildex_6 + (xi(3,5)*tildex_4 - xi(2,1)*tildex_6)*xi(6,6)*xi(3,6)*xi(
3,5) - (xi(3,6)**2*tildex_4 - xi(3,5)**3*xi(2,1)*tildex_6))*xi(6,6) - ((xi(6,5)
**2*xi(3,6)**2*xi(2,1)*tildex_6 - xi(6,5)*xi(3,6)**2*tildex_4 + xi(3,5)**2*xi(2,
1)*tildex_6)*xi(6,5) - (xi(3,5)*tildex_4 - xi(2,1)*tildex_6)*xi(3,5) - xi(3,6)*
xi(2,1)*tildex_5)*xi(3,6))/(xi(3,6)**2*xi(2,1));\\USD$

\\ USD  [\tilde{x}_2,\tilde{x}_4]=( - (xi(6,6)*xi(3,5)*tildex_6 - xi(6,5)*xi(3,6
)*tildex_6 + xi(3,6)*xi(2,1)*tildex_4)*(xi(6,6)*xi(3,5) - xi(6,5)*xi(3,6)))/(xi(
3,6)*xi(2,1));\\USD$

\\ USD  [\tilde{x}_2,\tilde{x}_5]=( - ((xi(6,5)*xi(2,1)*tildex_6 - tildex_4)*xi(
3,6) - xi(6,6)*xi(3,5)*xi(2,1)*tildex_6)*xi(3,5))/(xi(3,6)*xi(2,1));\\USD$

\\ USD  [\tilde{x}_2,\tilde{x}_6]=( - ((xi(6,5)*xi(2,1)*tildex_6 - tildex_4)*xi(
3,6) - xi(6,6)*xi(3,5)*xi(2,1)*tildex_6))/xi(2,1);\\USD$

\P$

\par Now we check if the condition USD [Jx,y]= J[x,y] USD is satisfied$

USD\forall x,y \in {\mathcal{G}}_{6,{m14_(1)}},USD$

\textit{i.e.} if USD{\mathcal{G}}_{6,{m14_(1)}}USD$

is a \textit{complex} algebra.$

\\USD J[x_j,x_k] \neq [Jx_j,x_k] USD
in the following cases{{{1,1}, - (x(6)*xi(4,1) + x(4)*xi(3,1))},
{{1,2}, - (x(6)*xi(5,1) + x(5)*xi(3,1))},
{{1,3},
xi(2,1)*x(5) + ((x(4)*(xi(6,6)*xi(3,5) - xi(6,5)*xi(3,6)) + x(3)*xi(3,6)*xi(2,1)
)*(xi(6,6)*xi(3,5) - xi(6,5)*xi(3,6)) - x(5)*(xi(6,6)*xi(3,5)**2 - xi(6,5)*xi(3,
6)*xi(3,5) + xi(3,6))*xi(2,1) + x(6)*(xi(6,6)**2*xi(3,5) - xi(6,6)*xi(6,5)*xi(3,
6) + xi(3,5))*xi(2,1))/xi(3,6)},
{{1,4},
 - (x(4)*(xi(6,6)*xi(3,5) - xi(6,5)*xi(3,6))*xi(2,1) + x(3)*xi(3,6) - x(5)*xi(3,
5) + x(6)*xi(6,6))},
{{1,5},xi(2,1)*x(6)},
{{2,1},
 - (x(6)*((xi(5,1)*xi(3,6) + xi(3,5)*xi(3,1))*xi(2,1) - xi(6,5)*xi(3,6)*xi(3,2))
 + x(6)*xi(6,6)*xi(3,5)*xi(3,2) + x(4)*xi(3,6)*xi(3,2)*xi(2,1))/(xi(3,6)*xi(2,1)
)},
{{2,2},
(x(6)*((xi(4,1)*xi(3,6) + xi(3,5)*xi(3,2))*xi(2,1) + xi(6,5)*xi(3,6)*xi(3,1) - 
xi(6,6)*xi(3,5)*xi(3,1)))/(xi(3,6)*xi(2,1)) - xi(3,2)*x(5)},
{{2,3},
 - ((x(4)*xi(6,6)*xi(3,5) - x(4)*xi(6,5)*xi(3,6) + x(3)*xi(3,6)*xi(2,1) - x(5)*
xi(3,5)*xi(2,1))*xi(3,5) + x(6)*xi(6,5)*xi(3,6)*xi(2,1))/(xi(3,6)*xi(2,1))},
{{2,4}, - x(6)/xi(2,1)},
{{2,5},
 - (x(4)*(xi(6,6)*xi(3,5) - xi(6,5)*xi(3,6))*xi(2,1) + x(3)*xi(3,6) - x(5)*xi(3,
5) + x(6)*xi(6,6))},
{{3,1},
 - (x(6)*xi(6,6)**3*xi(3,5)**3*xi(2,1) - 3*x(6)*xi(6,6)**2*xi(6,5)*xi(3,6)*xi(3,
5)**2*xi(2,1) + 3*x(6)*xi(6,6)*xi(6,5)**2*xi(3,6)**2*xi(3,5)*xi(2,1) + x(6)*xi(6
,6)*xi(3,5)**3*xi(2,1) - x(6)*xi(6,5)**3*xi(3,6)**3*xi(2,1) - x(6)*xi(6,5)*xi(3,
6)*xi(3,5)**2*xi(2,1) - x(5)*xi(6,6)*xi(3,6)*xi(3,5)**2*xi(2,1) + x(5)*xi(6,5)*
xi(3,6)**2*xi(3,5)*xi(2,1) - x(5)*xi(3,6)**2*xi(2,1) + 2*x(4)*xi(6,6)**2*xi(3,6)
*xi(3,5)**2 - 4*x(4)*xi(6,6)*xi(6,5)*xi(3,6)**2*xi(3,5) - x(4)*xi(6,6)*xi(3,6)**
2 + 2*x(4)*xi(6,5)**2*xi(3,6)**3 + x(4)*xi(3,6)*xi(3,5)**2 + x(3)*xi(6,6)*xi(3,6
)**2*xi(3,5)*xi(2,1) - x(3)*xi(6,5)*xi(3,6)**3*xi(2,1))/xi(3,6)**2},
{{3,2},
 - ((x(4)*(xi(6,5)*xi(3,5) + 1)*xi(3,6)*xi(2,1) - x(4)*xi(6,6)*xi(3,5)**2*xi(2,1
) - x(3)*xi(3,6)*xi(3,5) + x(5)*(xi(6,6)**2*xi(3,5)**2 - 2*xi(6,6)*xi(6,5)*xi(3,
6)*xi(3,5) - xi(6,6)*xi(3,6) + xi(6,5)**2*xi(3,6)**2 + 2*xi(3,5)**2))*xi(3,6) - 
x(6)*(xi(6,6)**2*xi(3,5)**2 - 2*xi(6,6)*xi(6,5)*xi(3,6)*xi(3,5) + xi(6,5)**2*xi(
3,6)**2 + xi(3,5)**2)*xi(3,5))/xi(3,6)**2},
{{4,1},
((xi(6,6)**2*xi(3,5)**2 - 2*xi(6,6)*xi(6,5)*xi(3,6)*xi(3,5) + xi(6,6)*xi(3,6) + 
xi(6,5)**2*xi(3,6)**2)*x(6))/xi(3,6) + 2*x(4)*xi(6,6)*xi(3,5)*xi(2,1) - 2*x(4)*
xi(6,5)*xi(3,6)*xi(2,1) + x(3)*xi(3,6) - x(5)*xi(3,5)},
{{4,2},
(xi(2,1)*(x(6)*(xi(6,5)*xi(3,5) - 1)*xi(3,6) - x(6)*xi(6,6)*xi(3,5)**2 + x(5)*(
xi(6,6)*xi(3,5) - xi(6,5)*xi(3,6))*xi(3,6)))/xi(3,6)},
{{5,1},
(x(6)*xi(2,1)*((xi(6,5)*xi(3,5) + 1)*xi(3,6) - xi(6,6)*xi(3,5)**2))/xi(3,6) - xi
(3,5)*x(4)},
{{5,2},
((x(4)*(xi(6,6)*xi(3,5) - xi(6,5)*xi(3,6))*xi(2,1) + x(3)*xi(3,6) - x(5)*xi(3,5)
 + x(6)*xi(6,6))*xi(3,6) + (x(6)*xi(3,5) - x(5)*xi(3,6))*xi(3,5))/xi(3,6)},
{{6,1},
 - (x(6)*xi(6,6)*xi(3,5)*xi(2,1) - x(6)*xi(6,5)*xi(3,6)*xi(2,1) + x(4)*xi(3,6))}
,
{{6,2},x(6)*xi(3,5) - x(5)*xi(3,6)}}$

\par Now we'll use equivalence by automorphisms.$

All  automorphisms of$

USD {\mathcal{G}}_{6,{m14_(1)}}USD$

are  of the following  form  :$

\\$

USDUSD \Phi = \begin{pmatrix}$

b(1,1)&$

b(2,1)*u&$

0&$

0&$

0&$

0\\$

b(2,1)&$

 - b(1,1)*u&$

0&$

0&$

0&$

0\\$

0&$

0&$

b(3,3)&$

0&$

0&$

0\\$

b(4,1)&$

b(4,2)&$

b(4,3)&$

b(3,3)*b(1,1)&$

b(3,3)*b(2,1)*u&$

0\\$

 - (b(4,2) - b(2,1)*k)*u&$

b(4,1)*u - b(1,1)*k&$

b(5,3)&$

b(3,3)*b(2,1)&$

 - b(3,3)*b(1,1)*u&$

0\\$

b(6,1)&$

b(6,2)&$

b(6,3)&$

b(5,3)*b(2,1) + b(4,3)*b(1,1)&$

 - (b(5,3)*b(1,1) - b(4,3)*b(2,1))*u&$

(b(2,1)**2 + b(1,1)**2)*b(3,3)\end{pmatrix}USDUSD$

where USD \det \Phi:=(b(2,1)**2 + b(1,1)**2)**3*b(3,3)**4 \neq 0 USD$

and USD u= \pm 1, \; k \in \Rmath.$

\textit{Reduce} here checks that USD \Phi USD is indeed an automorphism:\\$

 USD \surd \Phi USD is  an automorphism$

\\ Then USD J2:=\Phi^{-1}*J*\Phi USD has the following selected entries :$

\\ Then USD J2:=\Phi^{-1}*J*\Phi USD has entries :$

\\USD J2(1,1):=0USD\\$

\\USD J2(1,2):=u/xi(2,1)USD\\$

\\USD J2(1,3):=0USD\\$

\\USD J2(1,4):=0USD\\$

\\USD J2(1,5):=0USD\\$

\\USD J2(1,6):=0USD\\$

\\USD J2(2,1):=( - 1)/(xi(2,1)*u)USD\\$

\\USD J2(2,2):=0USD\\$

\\USD J2(2,3):=0USD\\$

\\USD J2(2,4):=0USD\\$

\\USD J2(2,5):=0USD\\$

\\USD J2(2,6):=0USD\\$

\\USD J2(3,1):=(b(6,1)*xi(3,6) - b(4,2)*xi(3,5)*u - b(4,1)*xi(6,6)*xi(3,5)*xi(2,
1) + b(4,1)*xi(6,5)*xi(3,6)*xi(2,1) + b(2,1)*xi(3,5)*k*u + b(2,1)*xi(3,2) + b(1,
1)*xi(3,1))/b(3,3)USD\\$

\\USD J2(3,2):=(b(6,2)*xi(3,6) - b(4,2)*xi(6,6)*xi(3,5)*xi(2,1) + b(4,2)*xi(6,5)
*xi(3,6)*xi(2,1) + b(4,1)*xi(3,5)*u + b(2,1)*xi(3,1)*u - b(1,1)*xi(3,5)*k - b(1,
1)*xi(3,2)*u)/b(3,3)USD\\$

\\USD J2(3,3):=(b(6,3)*xi(3,6)**2 + b(5,3)*xi(3,6)*xi(3,5) - b(4,3)*xi(6,6)*xi(3
,6)*xi(3,5)*xi(2,1) + b(4,3)*xi(6,5)*xi(3,6)**2*xi(2,1) + b(3,3)*xi(6,6)**2*xi(3
,5)**2 - 2*b(3,3)*xi(6,6)*xi(6,5)*xi(3,6)*xi(3,5) - b(3,3)*xi(6,6)*xi(3,6) + b(3
,3)*xi(6,5)**2*xi(3,6)**2 + b(3,3)*xi(3,5)**2)/(b(3,3)*xi(3,6))USD\\$

\\USD J2(3,4):=(b(5,3)*b(2,1)*xi(3,6) + b(4,3)*b(1,1)*xi(3,6) + b(3,3)*b(2,1)*xi
(3,5) - b(3,3)*b(1,1)*xi(6,6)*xi(3,5)*xi(2,1) + b(3,3)*b(1,1)*xi(6,5)*xi(3,6)*xi
(2,1))/b(3,3)USD\\$

\\USD J2(3,5):=(u*( - b(5,3)*b(1,1)*xi(3,6) + b(4,3)*b(2,1)*xi(3,6) - b(3,3)*b(2
,1)*xi(6,6)*xi(3,5)*xi(2,1) + b(3,3)*b(2,1)*xi(6,5)*xi(3,6)*xi(2,1) - b(3,3)*b(1
,1)*xi(3,5)))/b(3,3)USD\\$

\\USD J2(3,6):=xi(3,6)*(b(2,1)**2 + b(1,1)**2)USD\\$

\\USD J2(4,1):=( - b(6,1)*b(5,3)*b(2,1)*xi(3,6)**2*xi(2,1)*u - b(6,1)*b(4,3)*b(1
,1)*xi(3,6)**2*xi(2,1)*u - b(6,1)*b(3,3)*b(2,1)*xi(3,6)*xi(3,5)*xi(2,1)*u + b(6,
1)*b(3,3)*b(1,1)*xi(6,6)*xi(3,6)*xi(3,5)*u - b(6,1)*b(3,3)*b(1,1)*xi(6,5)*xi(3,6
)**2*u + b(5,3)*b(4,2)*b(2,1)*xi(3,6)*xi(3,5)*xi(2,1) + b(5,3)*b(4,1)*b(2,1)*xi(
6,6)*xi(3,6)*xi(3,5)*u - b(5,3)*b(4,1)*b(2,1)*xi(6,5)*xi(3,6)**2*u - b(5,3)*b(2,
1)**2*xi(3,6)*xi(3,5)*xi(2,1)*k - b(5,3)*b(2,1)**2*xi(3,6)*xi(3,2)*xi(2,1)*u - b
(5,3)*b(2,1)*b(1,1)*xi(3,6)*xi(3,1)*xi(2,1)*u + b(4,3)*b(4,2)*b(1,1)*xi(3,6)*xi(
3,5)*xi(2,1) + b(4,3)*b(4,1)*b(1,1)*xi(6,6)*xi(3,6)*xi(3,5)*u - b(4,3)*b(4,1)*b(
1,1)*xi(6,5)*xi(3,6)**2*u - b(4,3)*b(2,1)*b(1,1)*xi(3,6)*xi(3,5)*xi(2,1)*k - b(4
,3)*b(2,1)*b(1,1)*xi(3,6)*xi(3,2)*xi(2,1)*u - b(4,3)*b(1,1)**2*xi(3,6)*xi(3,1)*
xi(2,1)*u + b(4,2)*b(3,3)*b(2,1)*xi(3,5)**2*xi(2,1) - b(4,2)*b(3,3)*b(1,1)*xi(6,
6)*xi(3,5)**2 + b(4,2)*b(3,3)*b(1,1)*xi(6,5)*xi(3,6)*xi(3,5) + 2*b(4,2)*b(3,3)*b
(1,1)*xi(3,6) + b(4,1)*b(3,3)*b(2,1)*xi(6,6)*xi(3,5)**2*u - b(4,1)*b(3,3)*b(2,1)
*xi(6,5)*xi(3,6)*xi(3,5)*u + 2*b(4,1)*b(3,3)*b(2,1)*xi(3,6)*u - b(4,1)*b(3,3)*b(
1,1)*xi(6,6)**2*xi(3,5)**2*xi(2,1)*u + 2*b(4,1)*b(3,3)*b(1,1)*xi(6,6)*xi(6,5)*xi
(3,6)*xi(3,5)*xi(2,1)*u - b(4,1)*b(3,3)*b(1,1)*xi(6,5)**2*xi(3,6)**2*xi(2,1)*u +
 b(3,3)*b(2,1)**2*xi(6,6)*xi(3,5)*xi(3,1)*u - b(3,3)*b(2,1)**2*xi(6,5)*xi(3,6)*
xi(3,1)*u - b(3,3)*b(2,1)**2*xi(4,1)*xi(3,6)*xi(2,1)*u - b(3,3)*b(2,1)**2*xi(3,5
)**2*xi(2,1)*k - b(3,3)*b(2,1)**2*xi(3,5)*xi(3,2)*xi(2,1)*u + b(3,3)*b(2,1)*b(1,
1)*xi(6,6)*xi(3,5)**2*k + b(3,3)*b(2,1)*b(1,1)*xi(6,6)*xi(3,5)*xi(3,2)*u - b(3,3
)*b(2,1)*b(1,1)*xi(6,5)*xi(3,6)*xi(3,5)*k - b(3,3)*b(2,1)*b(1,1)*xi(6,5)*xi(3,6)
*xi(3,2)*u + 2*b(3,3)*b(2,1)*b(1,1)*xi(5,1)*xi(3,6)*xi(2,1)*u - 2*b(3,3)*b(2,1)*
b(1,1)*xi(3,6)*k + b(3,3)*b(2,1)*b(1,1)*xi(3,5)*xi(3,1)*xi(2,1)*u + b(3,3)*b(1,1
)**2*xi(4,1)*xi(3,6)*xi(2,1)*u)/(b(3,3)**2*xi(3,6)*xi(2,1)*u*(b(2,1)**2 + b(1,1)
**2))USD\\$

\\USD J2(4,2):=( - b(6,2)*b(5,3)*b(2,1)*xi(3,6)**2*xi(2,1) - b(6,2)*b(4,3)*b(1,1
)*xi(3,6)**2*xi(2,1) - b(6,2)*b(3,3)*b(2,1)*xi(3,6)*xi(3,5)*xi(2,1) + b(6,2)*b(3
,3)*b(1,1)*xi(6,6)*xi(3,6)*xi(3,5) - b(6,2)*b(3,3)*b(1,1)*xi(6,5)*xi(3,6)**2 + b
(5,3)*b(4,2)*b(2,1)*xi(6,6)*xi(3,6)*xi(3,5) - b(5,3)*b(4,2)*b(2,1)*xi(6,5)*xi(3,
6)**2 - b(5,3)*b(4,1)*b(2,1)*xi(3,6)*xi(3,5)*xi(2,1)*u - b(5,3)*b(2,1)**2*xi(3,6
)*xi(3,1)*xi(2,1)*u + b(5,3)*b(2,1)*b(1,1)*xi(3,6)*xi(3,5)*xi(2,1)*k + b(5,3)*b(
2,1)*b(1,1)*xi(3,6)*xi(3,2)*xi(2,1)*u + b(4,3)*b(4,2)*b(1,1)*xi(6,6)*xi(3,6)*xi(
3,5) - b(4,3)*b(4,2)*b(1,1)*xi(6,5)*xi(3,6)**2 - b(4,3)*b(4,1)*b(1,1)*xi(3,6)*xi
(3,5)*xi(2,1)*u - b(4,3)*b(2,1)*b(1,1)*xi(3,6)*xi(3,1)*xi(2,1)*u + b(4,3)*b(1,1)
**2*xi(3,6)*xi(3,5)*xi(2,1)*k + b(4,3)*b(1,1)**2*xi(3,6)*xi(3,2)*xi(2,1)*u + b(4
,2)*b(3,3)*b(2,1)*xi(6,6)*xi(3,5)**2 - b(4,2)*b(3,3)*b(2,1)*xi(6,5)*xi(3,6)*xi(3
,5) + 2*b(4,2)*b(3,3)*b(2,1)*xi(3,6) - b(4,2)*b(3,3)*b(1,1)*xi(6,6)**2*xi(3,5)**
2*xi(2,1) + 2*b(4,2)*b(3,3)*b(1,1)*xi(6,6)*xi(6,5)*xi(3,6)*xi(3,5)*xi(2,1) - b(4
,2)*b(3,3)*b(1,1)*xi(6,5)**2*xi(3,6)**2*xi(2,1) - b(4,1)*b(3,3)*b(2,1)*xi(3,5)**
2*xi(2,1)*u + b(4,1)*b(3,3)*b(1,1)*xi(6,6)*xi(3,5)**2*u - b(4,1)*b(3,3)*b(1,1)*
xi(6,5)*xi(3,6)*xi(3,5)*u - 2*b(4,1)*b(3,3)*b(1,1)*xi(3,6)*u + b(3,3)*b(2,1)**2*
xi(5,1)*xi(3,6)*xi(2,1)*u - b(3,3)*b(2,1)**2*xi(3,6)*k - b(3,3)*b(2,1)*b(1,1)*xi
(6,6)*xi(3,5)*xi(3,1)*u + b(3,3)*b(2,1)*b(1,1)*xi(6,5)*xi(3,6)*xi(3,1)*u + 2*b(3
,3)*b(2,1)*b(1,1)*xi(4,1)*xi(3,6)*xi(2,1)*u + b(3,3)*b(2,1)*b(1,1)*xi(3,5)**2*xi
(2,1)*k + b(3,3)*b(2,1)*b(1,1)*xi(3,5)*xi(3,2)*xi(2,1)*u - b(3,3)*b(1,1)**2*xi(6
,6)*xi(3,5)**2*k - b(3,3)*b(1,1)**2*xi(6,6)*xi(3,5)*xi(3,2)*u + b(3,3)*b(1,1)**2
*xi(6,5)*xi(3,6)*xi(3,5)*k + b(3,3)*b(1,1)**2*xi(6,5)*xi(3,6)*xi(3,2)*u - b(3,3)
*b(1,1)**2*xi(5,1)*xi(3,6)*xi(2,1)*u + b(3,3)*b(1,1)**2*xi(3,6)*k - b(3,3)*b(1,1
)**2*xi(3,5)*xi(3,1)*xi(2,1)*u)/(b(3,3)**2*xi(3,6)*xi(2,1)*(b(2,1)**2 + b(1,1)**
2))USD\\$

\\USD J2(4,3):=( - b(6,3)*b(5,3)*b(2,1)*xi(3,6)**3 - b(6,3)*b(4,3)*b(1,1)*xi(3,6
)**3 - b(6,3)*b(3,3)*b(2,1)*xi(3,6)**2*xi(3,5) + b(6,3)*b(3,3)*b(1,1)*xi(6,6)*xi
(3,6)**2*xi(3,5)*xi(2,1) - b(6,3)*b(3,3)*b(1,1)*xi(6,5)*xi(3,6)**3*xi(2,1) - b(5
,3)**2*b(2,1)*xi(3,6)**2*xi(3,5) + b(5,3)*b(4,3)*b(2,1)*xi(6,6)*xi(3,6)**2*xi(3,
5)*xi(2,1) - b(5,3)*b(4,3)*b(2,1)*xi(6,5)*xi(3,6)**3*xi(2,1) - b(5,3)*b(4,3)*b(1
,1)*xi(3,6)**2*xi(3,5) - b(5,3)*b(3,3)*b(2,1)*xi(6,6)**2*xi(3,6)*xi(3,5)**2 + 2*
b(5,3)*b(3,3)*b(2,1)*xi(6,6)*xi(6,5)*xi(3,6)**2*xi(3,5) + b(5,3)*b(3,3)*b(2,1)*
xi(6,6)*xi(3,6)**2 - b(5,3)*b(3,3)*b(2,1)*xi(6,5)**2*xi(3,6)**3 - 2*b(5,3)*b(3,3
)*b(2,1)*xi(3,6)*xi(3,5)**2 + b(5,3)*b(3,3)*b(1,1)*xi(6,6)*xi(3,6)*xi(3,5)**2*xi
(2,1) - b(5,3)*b(3,3)*b(1,1)*xi(6,5)*xi(3,6)**2*xi(3,5)*xi(2,1) - b(5,3)*b(3,3)*
b(1,1)*xi(3,6)**2*xi(2,1) + b(4,3)**2*b(1,1)*xi(6,6)*xi(3,6)**2*xi(3,5)*xi(2,1) 
- b(4,3)**2*b(1,1)*xi(6,5)*xi(3,6)**3*xi(2,1) + b(4,3)*b(3,3)*b(2,1)*xi(6,6)*xi(
3,6)*xi(3,5)**2*xi(2,1) - b(4,3)*b(3,3)*b(2,1)*xi(6,5)*xi(3,6)**2*xi(3,5)*xi(2,1
) + b(4,3)*b(3,3)*b(2,1)*xi(3,6)**2*xi(2,1) - 2*b(4,3)*b(3,3)*b(1,1)*xi(6,6)**2*
xi(3,6)*xi(3,5)**2 + 4*b(4,3)*b(3,3)*b(1,1)*xi(6,6)*xi(6,5)*xi(3,6)**2*xi(3,5) +
 b(4,3)*b(3,3)*b(1,1)*xi(6,6)*xi(3,6)**2 - 2*b(4,3)*b(3,3)*b(1,1)*xi(6,5)**2*xi(
3,6)**3 - b(4,3)*b(3,3)*b(1,1)*xi(3,6)*xi(3,5)**2 - b(3,3)**2*b(2,1)*xi(6,6)**2*
xi(3,5)**3 + 2*b(3,3)**2*b(2,1)*xi(6,6)*xi(6,5)*xi(3,6)*xi(3,5)**2 - b(3,3)**2*b
(2,1)*xi(6,5)**2*xi(3,6)**2*xi(3,5) + b(3,3)**2*b(2,1)*xi(6,5)*xi(3,6)**2 - b(3,
3)**2*b(2,1)*xi(3,5)**3 + b(3,3)**2*b(1,1)*xi(6,6)**3*xi(3,5)**3*xi(2,1) - 3*b(3
,3)**2*b(1,1)*xi(6,6)**2*xi(6,5)*xi(3,6)*xi(3,5)**2*xi(2,1) - b(3,3)**2*b(1,1)*
xi(6,6)**2*xi(3,6)*xi(3,5)*xi(2,1) + 3*b(3,3)**2*b(1,1)*xi(6,6)*xi(6,5)**2*xi(3,
6)**2*xi(3,5)*xi(2,1) + b(3,3)**2*b(1,1)*xi(6,6)*xi(6,5)*xi(3,6)**2*xi(2,1) + b(
3,3)**2*b(1,1)*xi(6,6)*xi(3,5)**3*xi(2,1) - b(3,3)**2*b(1,1)*xi(6,5)**3*xi(3,6)
**3*xi(2,1) - b(3,3)**2*b(1,1)*xi(6,5)*xi(3,6)*xi(3,5)**2*xi(2,1) - b(3,3)**2*b(
1,1)*xi(3,6)*xi(3,5)*xi(2,1))/(b(3,3)**2*xi(3,6)**2*(b(2,1)**2 + b(1,1)**2))
USD\\$

\\USD J2(4,4):=( - b(5,3)**2*b(2,1)**2*xi(3,6)**2 - 2*b(5,3)*b(4,3)*b(2,1)*b(1,1
)*xi(3,6)**2 - 2*b(5,3)*b(3,3)*b(2,1)**2*xi(3,6)*xi(3,5) + 2*b(5,3)*b(3,3)*b(2,1
)*b(1,1)*xi(6,6)*xi(3,6)*xi(3,5)*xi(2,1) - 2*b(5,3)*b(3,3)*b(2,1)*b(1,1)*xi(6,5)
*xi(3,6)**2*xi(2,1) - b(4,3)**2*b(1,1)**2*xi(3,6)**2 - 2*b(4,3)*b(3,3)*b(2,1)*b(
1,1)*xi(3,6)*xi(3,5) + 2*b(4,3)*b(3,3)*b(1,1)**2*xi(6,6)*xi(3,6)*xi(3,5)*xi(2,1)
 - 2*b(4,3)*b(3,3)*b(1,1)**2*xi(6,5)*xi(3,6)**2*xi(2,1) - b(3,3)**2*b(2,1)**2*xi
(3,5)**2 + 2*b(3,3)**2*b(2,1)*b(1,1)*xi(6,6)*xi(3,5)**2*xi(2,1) - 2*b(3,3)**2*b(
2,1)*b(1,1)*xi(6,5)*xi(3,6)*xi(3,5)*xi(2,1) - b(3,3)**2*b(1,1)**2*xi(6,6)**2*xi(
3,5)**2 + 2*b(3,3)**2*b(1,1)**2*xi(6,6)*xi(6,5)*xi(3,6)*xi(3,5) - b(3,3)**2*b(1,
1)**2*xi(6,5)**2*xi(3,6)**2)/(b(3,3)**2*xi(3,6)*(b(2,1)**2 + b(1,1)**2))USD\\$

\\USD J2(4,5):=(u*(b(5,3)**2*b(2,1)*b(1,1)*xi(3,6)**2 - b(5,3)*b(4,3)*b(2,1)**2*
xi(3,6)**2 + b(5,3)*b(4,3)*b(1,1)**2*xi(3,6)**2 + b(5,3)*b(3,3)*b(2,1)**2*xi(6,6
)*xi(3,6)*xi(3,5)*xi(2,1) - b(5,3)*b(3,3)*b(2,1)**2*xi(6,5)*xi(3,6)**2*xi(2,1) +
 2*b(5,3)*b(3,3)*b(2,1)*b(1,1)*xi(3,6)*xi(3,5) - b(5,3)*b(3,3)*b(1,1)**2*xi(6,6)
*xi(3,6)*xi(3,5)*xi(2,1) + b(5,3)*b(3,3)*b(1,1)**2*xi(6,5)*xi(3,6)**2*xi(2,1) - 
b(4,3)**2*b(2,1)*b(1,1)*xi(3,6)**2 - b(4,3)*b(3,3)*b(2,1)**2*xi(3,6)*xi(3,5) + 2
*b(4,3)*b(3,3)*b(2,1)*b(1,1)*xi(6,6)*xi(3,6)*xi(3,5)*xi(2,1) - 2*b(4,3)*b(3,3)*b
(2,1)*b(1,1)*xi(6,5)*xi(3,6)**2*xi(2,1) + b(4,3)*b(3,3)*b(1,1)**2*xi(3,6)*xi(3,5
) + b(3,3)**2*b(2,1)**2*xi(6,6)*xi(3,5)**2*xi(2,1) - b(3,3)**2*b(2,1)**2*xi(6,5)
*xi(3,6)*xi(3,5)*xi(2,1) + b(3,3)**2*b(2,1)**2*xi(3,6)*xi(2,1) - b(3,3)**2*b(2,1
)*b(1,1)*xi(6,6)**2*xi(3,5)**2 + 2*b(3,3)**2*b(2,1)*b(1,1)*xi(6,6)*xi(6,5)*xi(3,
6)*xi(3,5) - b(3,3)**2*b(2,1)*b(1,1)*xi(6,5)**2*xi(3,6)**2 + b(3,3)**2*b(2,1)*b(
1,1)*xi(3,5)**2 - b(3,3)**2*b(1,1)**2*xi(6,6)*xi(3,5)**2*xi(2,1) + b(3,3)**2*b(1
,1)**2*xi(6,5)*xi(3,6)*xi(3,5)*xi(2,1) + b(3,3)**2*b(1,1)**2*xi(3,6)*xi(2,1)))/(
b(3,3)**2*xi(3,6)*(b(2,1)**2 + b(1,1)**2))USD\\$

\\USD J2(4,6):=( - b(5,3)*b(2,1)*xi(3,6) - b(4,3)*b(1,1)*xi(3,6) - b(3,3)*b(2,1)
*xi(3,5) + b(3,3)*b(1,1)*xi(6,6)*xi(3,5)*xi(2,1) - b(3,3)*b(1,1)*xi(6,5)*xi(3,6)
*xi(2,1))/b(3,3)USD\\$

\\USD J2(5,1):=(b(6,1)*b(5,3)*b(1,1)*xi(3,6)**2*xi(2,1) - b(6,1)*b(4,3)*b(2,1)*
xi(3,6)**2*xi(2,1) + b(6,1)*b(3,3)*b(2,1)*xi(6,6)*xi(3,6)*xi(3,5) - b(6,1)*b(3,3
)*b(2,1)*xi(6,5)*xi(3,6)**2 + b(6,1)*b(3,3)*b(1,1)*xi(3,6)*xi(3,5)*xi(2,1) - b(5
,3)*b(4,2)*b(1,1)*xi(3,6)*xi(3,5)*xi(2,1)*u - b(5,3)*b(4,1)*b(1,1)*xi(6,6)*xi(3,
6)*xi(3,5) + b(5,3)*b(4,1)*b(1,1)*xi(6,5)*xi(3,6)**2 + b(5,3)*b(2,1)*b(1,1)*xi(3
,6)*xi(3,5)*xi(2,1)*k*u + b(5,3)*b(2,1)*b(1,1)*xi(3,6)*xi(3,2)*xi(2,1) + b(5,3)*
b(1,1)**2*xi(3,6)*xi(3,1)*xi(2,1) + b(4,3)*b(4,2)*b(2,1)*xi(3,6)*xi(3,5)*xi(2,1)
*u + b(4,3)*b(4,1)*b(2,1)*xi(6,6)*xi(3,6)*xi(3,5) - b(4,3)*b(4,1)*b(2,1)*xi(6,5)
*xi(3,6)**2 - b(4,3)*b(2,1)**2*xi(3,6)*xi(3,5)*xi(2,1)*k*u - b(4,3)*b(2,1)**2*xi
(3,6)*xi(3,2)*xi(2,1) - b(4,3)*b(2,1)*b(1,1)*xi(3,6)*xi(3,1)*xi(2,1) - b(4,2)*b(
3,3)*b(2,1)*xi(6,6)*xi(3,5)**2*u + b(4,2)*b(3,3)*b(2,1)*xi(6,5)*xi(3,6)*xi(3,5)*
u + 2*b(4,2)*b(3,3)*b(2,1)*xi(3,6)*u - b(4,2)*b(3,3)*b(1,1)*xi(3,5)**2*xi(2,1)*u
 - b(4,1)*b(3,3)*b(2,1)*xi(6,6)**2*xi(3,5)**2*xi(2,1) + 2*b(4,1)*b(3,3)*b(2,1)*
xi(6,6)*xi(6,5)*xi(3,6)*xi(3,5)*xi(2,1) - b(4,1)*b(3,3)*b(2,1)*xi(6,5)**2*xi(3,6
)**2*xi(2,1) - b(4,1)*b(3,3)*b(1,1)*xi(6,6)*xi(3,5)**2 + b(4,1)*b(3,3)*b(1,1)*xi
(6,5)*xi(3,6)*xi(3,5) - 2*b(4,1)*b(3,3)*b(1,1)*xi(3,6) + b(3,3)*b(2,1)**2*xi(6,6
)*xi(3,5)**2*k*u + b(3,3)*b(2,1)**2*xi(6,6)*xi(3,5)*xi(3,2) - b(3,3)*b(2,1)**2*
xi(6,5)*xi(3,6)*xi(3,5)*k*u - b(3,3)*b(2,1)**2*xi(6,5)*xi(3,6)*xi(3,2) + b(3,3)*
b(2,1)**2*xi(5,1)*xi(3,6)*xi(2,1) - b(3,3)*b(2,1)**2*xi(3,6)*k*u + b(3,3)*b(2,1)
**2*xi(3,5)*xi(3,1)*xi(2,1) - b(3,3)*b(2,1)*b(1,1)*xi(6,6)*xi(3,5)*xi(3,1) + b(3
,3)*b(2,1)*b(1,1)*xi(6,5)*xi(3,6)*xi(3,1) + 2*b(3,3)*b(2,1)*b(1,1)*xi(4,1)*xi(3,
6)*xi(2,1) + b(3,3)*b(2,1)*b(1,1)*xi(3,5)**2*xi(2,1)*k*u + b(3,3)*b(2,1)*b(1,1)*
xi(3,5)*xi(3,2)*xi(2,1) - b(3,3)*b(1,1)**2*xi(5,1)*xi(3,6)*xi(2,1) + b(3,3)*b(1,
1)**2*xi(3,6)*k*u)/(b(3,3)**2*xi(3,6)*xi(2,1)*u*(b(2,1)**2 + b(1,1)**2))USD\\$

\\USD J2(5,2):=(b(6,2)*b(5,3)*b(1,1)*xi(3,6)**2*xi(2,1) - b(6,2)*b(4,3)*b(2,1)*
xi(3,6)**2*xi(2,1) + b(6,2)*b(3,3)*b(2,1)*xi(6,6)*xi(3,6)*xi(3,5) - b(6,2)*b(3,3
)*b(2,1)*xi(6,5)*xi(3,6)**2 + b(6,2)*b(3,3)*b(1,1)*xi(3,6)*xi(3,5)*xi(2,1) - b(5
,3)*b(4,2)*b(1,1)*xi(6,6)*xi(3,6)*xi(3,5) + b(5,3)*b(4,2)*b(1,1)*xi(6,5)*xi(3,6)
**2 + b(5,3)*b(4,1)*b(1,1)*xi(3,6)*xi(3,5)*xi(2,1)*u + b(5,3)*b(2,1)*b(1,1)*xi(3
,6)*xi(3,1)*xi(2,1)*u - b(5,3)*b(1,1)**2*xi(3,6)*xi(3,5)*xi(2,1)*k - b(5,3)*b(1,
1)**2*xi(3,6)*xi(3,2)*xi(2,1)*u + b(4,3)*b(4,2)*b(2,1)*xi(6,6)*xi(3,6)*xi(3,5) -
 b(4,3)*b(4,2)*b(2,1)*xi(6,5)*xi(3,6)**2 - b(4,3)*b(4,1)*b(2,1)*xi(3,6)*xi(3,5)*
xi(2,1)*u - b(4,3)*b(2,1)**2*xi(3,6)*xi(3,1)*xi(2,1)*u + b(4,3)*b(2,1)*b(1,1)*xi
(3,6)*xi(3,5)*xi(2,1)*k + b(4,3)*b(2,1)*b(1,1)*xi(3,6)*xi(3,2)*xi(2,1)*u - b(4,2
)*b(3,3)*b(2,1)*xi(6,6)**2*xi(3,5)**2*xi(2,1) + 2*b(4,2)*b(3,3)*b(2,1)*xi(6,6)*
xi(6,5)*xi(3,6)*xi(3,5)*xi(2,1) - b(4,2)*b(3,3)*b(2,1)*xi(6,5)**2*xi(3,6)**2*xi(
2,1) - b(4,2)*b(3,3)*b(1,1)*xi(6,6)*xi(3,5)**2 + b(4,2)*b(3,3)*b(1,1)*xi(6,5)*xi
(3,6)*xi(3,5) - 2*b(4,2)*b(3,3)*b(1,1)*xi(3,6) + b(4,1)*b(3,3)*b(2,1)*xi(6,6)*xi
(3,5)**2*u - b(4,1)*b(3,3)*b(2,1)*xi(6,5)*xi(3,6)*xi(3,5)*u - 2*b(4,1)*b(3,3)*b(
2,1)*xi(3,6)*u + b(4,1)*b(3,3)*b(1,1)*xi(3,5)**2*xi(2,1)*u + b(3,3)*b(2,1)**2*xi
(4,1)*xi(3,6)*xi(2,1)*u - b(3,3)*b(2,1)*b(1,1)*xi(6,6)*xi(3,5)**2*k - b(3,3)*b(2
,1)*b(1,1)*xi(6,6)*xi(3,5)*xi(3,2)*u + b(3,3)*b(2,1)*b(1,1)*xi(6,5)*xi(3,6)*xi(3
,5)*k + b(3,3)*b(2,1)*b(1,1)*xi(6,5)*xi(3,6)*xi(3,2)*u - 2*b(3,3)*b(2,1)*b(1,1)*
xi(5,1)*xi(3,6)*xi(2,1)*u + 2*b(3,3)*b(2,1)*b(1,1)*xi(3,6)*k - b(3,3)*b(2,1)*b(1
,1)*xi(3,5)*xi(3,1)*xi(2,1)*u + b(3,3)*b(1,1)**2*xi(6,6)*xi(3,5)*xi(3,1)*u - b(3
,3)*b(1,1)**2*xi(6,5)*xi(3,6)*xi(3,1)*u - b(3,3)*b(1,1)**2*xi(4,1)*xi(3,6)*xi(2,
1)*u - b(3,3)*b(1,1)**2*xi(3,5)**2*xi(2,1)*k - b(3,3)*b(1,1)**2*xi(3,5)*xi(3,2)*
xi(2,1)*u)/(b(3,3)**2*xi(3,6)*xi(2,1)*u*(b(2,1)**2 + b(1,1)**2))USD\\$

\\USD J2(5,3):=(b(6,3)*b(5,3)*b(1,1)*xi(3,6)**3 - b(6,3)*b(4,3)*b(2,1)*xi(3,6)**
3 + b(6,3)*b(3,3)*b(2,1)*xi(6,6)*xi(3,6)**2*xi(3,5)*xi(2,1) - b(6,3)*b(3,3)*b(2,
1)*xi(6,5)*xi(3,6)**3*xi(2,1) + b(6,3)*b(3,3)*b(1,1)*xi(3,6)**2*xi(3,5) + b(5,3)
**2*b(1,1)*xi(3,6)**2*xi(3,5) - b(5,3)*b(4,3)*b(2,1)*xi(3,6)**2*xi(3,5) - b(5,3)
*b(4,3)*b(1,1)*xi(6,6)*xi(3,6)**2*xi(3,5)*xi(2,1) + b(5,3)*b(4,3)*b(1,1)*xi(6,5)
*xi(3,6)**3*xi(2,1) + b(5,3)*b(3,3)*b(2,1)*xi(6,6)*xi(3,6)*xi(3,5)**2*xi(2,1) - 
b(5,3)*b(3,3)*b(2,1)*xi(6,5)*xi(3,6)**2*xi(3,5)*xi(2,1) - b(5,3)*b(3,3)*b(2,1)*
xi(3,6)**2*xi(2,1) + b(5,3)*b(3,3)*b(1,1)*xi(6,6)**2*xi(3,6)*xi(3,5)**2 - 2*b(5,
3)*b(3,3)*b(1,1)*xi(6,6)*xi(6,5)*xi(3,6)**2*xi(3,5) - b(5,3)*b(3,3)*b(1,1)*xi(6,
6)*xi(3,6)**2 + b(5,3)*b(3,3)*b(1,1)*xi(6,5)**2*xi(3,6)**3 + 2*b(5,3)*b(3,3)*b(1
,1)*xi(3,6)*xi(3,5)**2 + b(4,3)**2*b(2,1)*xi(6,6)*xi(3,6)**2*xi(3,5)*xi(2,1) - b
(4,3)**2*b(2,1)*xi(6,5)*xi(3,6)**3*xi(2,1) - 2*b(4,3)*b(3,3)*b(2,1)*xi(6,6)**2*
xi(3,6)*xi(3,5)**2 + 4*b(4,3)*b(3,3)*b(2,1)*xi(6,6)*xi(6,5)*xi(3,6)**2*xi(3,5) +
 b(4,3)*b(3,3)*b(2,1)*xi(6,6)*xi(3,6)**2 - 2*b(4,3)*b(3,3)*b(2,1)*xi(6,5)**2*xi(
3,6)**3 - b(4,3)*b(3,3)*b(2,1)*xi(3,6)*xi(3,5)**2 - b(4,3)*b(3,3)*b(1,1)*xi(6,6)
*xi(3,6)*xi(3,5)**2*xi(2,1) + b(4,3)*b(3,3)*b(1,1)*xi(6,5)*xi(3,6)**2*xi(3,5)*xi
(2,1) - b(4,3)*b(3,3)*b(1,1)*xi(3,6)**2*xi(2,1) + b(3,3)**2*b(2,1)*xi(6,6)**3*xi
(3,5)**3*xi(2,1) - 3*b(3,3)**2*b(2,1)*xi(6,6)**2*xi(6,5)*xi(3,6)*xi(3,5)**2*xi(2
,1) - b(3,3)**2*b(2,1)*xi(6,6)**2*xi(3,6)*xi(3,5)*xi(2,1) + 3*b(3,3)**2*b(2,1)*
xi(6,6)*xi(6,5)**2*xi(3,6)**2*xi(3,5)*xi(2,1) + b(3,3)**2*b(2,1)*xi(6,6)*xi(6,5)
*xi(3,6)**2*xi(2,1) + b(3,3)**2*b(2,1)*xi(6,6)*xi(3,5)**3*xi(2,1) - b(3,3)**2*b(
2,1)*xi(6,5)**3*xi(3,6)**3*xi(2,1) - b(3,3)**2*b(2,1)*xi(6,5)*xi(3,6)*xi(3,5)**2
*xi(2,1) - b(3,3)**2*b(2,1)*xi(3,6)*xi(3,5)*xi(2,1) + b(3,3)**2*b(1,1)*xi(6,6)**
2*xi(3,5)**3 - 2*b(3,3)**2*b(1,1)*xi(6,6)*xi(6,5)*xi(3,6)*xi(3,5)**2 + b(3,3)**2
*b(1,1)*xi(6,5)**2*xi(3,6)**2*xi(3,5) - b(3,3)**2*b(1,1)*xi(6,5)*xi(3,6)**2 + b(
3,3)**2*b(1,1)*xi(3,5)**3)/(b(3,3)**2*xi(3,6)**2*u*(b(2,1)**2 + b(1,1)**2))USD\\
$

\\USD J2(5,4):=(b(5,3)**2*b(2,1)*b(1,1)*xi(3,6)**2 - b(5,3)*b(4,3)*b(2,1)**2*xi(
3,6)**2 + b(5,3)*b(4,3)*b(1,1)**2*xi(3,6)**2 + b(5,3)*b(3,3)*b(2,1)**2*xi(6,6)*
xi(3,6)*xi(3,5)*xi(2,1) - b(5,3)*b(3,3)*b(2,1)**2*xi(6,5)*xi(3,6)**2*xi(2,1) + 2
*b(5,3)*b(3,3)*b(2,1)*b(1,1)*xi(3,6)*xi(3,5) - b(5,3)*b(3,3)*b(1,1)**2*xi(6,6)*
xi(3,6)*xi(3,5)*xi(2,1) + b(5,3)*b(3,3)*b(1,1)**2*xi(6,5)*xi(3,6)**2*xi(2,1) - b
(4,3)**2*b(2,1)*b(1,1)*xi(3,6)**2 - b(4,3)*b(3,3)*b(2,1)**2*xi(3,6)*xi(3,5) + 2*
b(4,3)*b(3,3)*b(2,1)*b(1,1)*xi(6,6)*xi(3,6)*xi(3,5)*xi(2,1) - 2*b(4,3)*b(3,3)*b(
2,1)*b(1,1)*xi(6,5)*xi(3,6)**2*xi(2,1) + b(4,3)*b(3,3)*b(1,1)**2*xi(3,6)*xi(3,5)
 + b(3,3)**2*b(2,1)**2*xi(6,6)*xi(3,5)**2*xi(2,1) - b(3,3)**2*b(2,1)**2*xi(6,5)*
xi(3,6)*xi(3,5)*xi(2,1) - b(3,3)**2*b(2,1)**2*xi(3,6)*xi(2,1) - b(3,3)**2*b(2,1)
*b(1,1)*xi(6,6)**2*xi(3,5)**2 + 2*b(3,3)**2*b(2,1)*b(1,1)*xi(6,6)*xi(6,5)*xi(3,6
)*xi(3,5) - b(3,3)**2*b(2,1)*b(1,1)*xi(6,5)**2*xi(3,6)**2 + b(3,3)**2*b(2,1)*b(1
,1)*xi(3,5)**2 - b(3,3)**2*b(1,1)**2*xi(6,6)*xi(3,5)**2*xi(2,1) + b(3,3)**2*b(1,
1)**2*xi(6,5)*xi(3,6)*xi(3,5)*xi(2,1) - b(3,3)**2*b(1,1)**2*xi(3,6)*xi(2,1))/(b(
3,3)**2*xi(3,6)*u*(b(2,1)**2 + b(1,1)**2))USD\\$

\\USD J2(5,5):=( - b(5,3)**2*b(1,1)**2*xi(3,6)**2 + 2*b(5,3)*b(4,3)*b(2,1)*b(1,1
)*xi(3,6)**2 - 2*b(5,3)*b(3,3)*b(2,1)*b(1,1)*xi(6,6)*xi(3,6)*xi(3,5)*xi(2,1) + 2
*b(5,3)*b(3,3)*b(2,1)*b(1,1)*xi(6,5)*xi(3,6)**2*xi(2,1) - 2*b(5,3)*b(3,3)*b(1,1)
**2*xi(3,6)*xi(3,5) - b(4,3)**2*b(2,1)**2*xi(3,6)**2 + 2*b(4,3)*b(3,3)*b(2,1)**2
*xi(6,6)*xi(3,6)*xi(3,5)*xi(2,1) - 2*b(4,3)*b(3,3)*b(2,1)**2*xi(6,5)*xi(3,6)**2*
xi(2,1) + 2*b(4,3)*b(3,3)*b(2,1)*b(1,1)*xi(3,6)*xi(3,5) - b(3,3)**2*b(2,1)**2*xi
(6,6)**2*xi(3,5)**2 + 2*b(3,3)**2*b(2,1)**2*xi(6,6)*xi(6,5)*xi(3,6)*xi(3,5) - b(
3,3)**2*b(2,1)**2*xi(6,5)**2*xi(3,6)**2 - 2*b(3,3)**2*b(2,1)*b(1,1)*xi(6,6)*xi(3
,5)**2*xi(2,1) + 2*b(3,3)**2*b(2,1)*b(1,1)*xi(6,5)*xi(3,6)*xi(3,5)*xi(2,1) - b(3
,3)**2*b(1,1)**2*xi(3,5)**2)/(b(3,3)**2*xi(3,6)*(b(2,1)**2 + b(1,1)**2))USD\\$

\\USD J2(5,6):=(b(5,3)*b(1,1)*xi(3,6) - b(4,3)*b(2,1)*xi(3,6) + b(3,3)*b(2,1)*xi
(6,6)*xi(3,5)*xi(2,1) - b(3,3)*b(2,1)*xi(6,5)*xi(3,6)*xi(2,1) + b(3,3)*b(1,1)*xi
(3,5))/(b(3,3)*u)USD\\$

\\USD J2(6,1):=( - b(6,3)*b(6,1)*b(3,3)*xi(3,6)**3*xi(2,1)*u + b(6,3)*b(4,2)*b(3
,3)*xi(3,6)**2*xi(3,5)*xi(2,1) + b(6,3)*b(4,1)*b(3,3)*xi(6,6)*xi(3,6)**2*xi(3,5)
*u - b(6,3)*b(4,1)*b(3,3)*xi(6,5)*xi(3,6)**3*u - b(6,3)*b(3,3)*b(2,1)*xi(3,6)**2
*xi(3,5)*xi(2,1)*k - b(6,3)*b(3,3)*b(2,1)*xi(3,6)**2*xi(3,2)*xi(2,1)*u - b(6,3)*
b(3,3)*b(1,1)*xi(3,6)**2*xi(3,1)*xi(2,1)*u + b(6,2)*b(3,3)**2*xi(3,6)**2 + b(6,1
)*b(5,3)**2*xi(3,6)**3*xi(2,1)*u + b(6,1)*b(5,3)*b(3,3)*xi(3,6)**2*xi(3,5)*xi(2,
1)*u + b(6,1)*b(4,3)**2*xi(3,6)**3*xi(2,1)*u - b(6,1)*b(4,3)*b(3,3)*xi(6,6)*xi(3
,6)**2*xi(3,5)*u + b(6,1)*b(4,3)*b(3,3)*xi(6,5)*xi(3,6)**3*u + b(6,1)*b(3,3)**2*
xi(6,6)*xi(3,6)**2*xi(2,1)*u - b(5,3)**2*b(4,2)*xi(3,6)**2*xi(3,5)*xi(2,1) - b(5
,3)**2*b(4,1)*xi(6,6)*xi(3,6)**2*xi(3,5)*u + b(5,3)**2*b(4,1)*xi(6,5)*xi(3,6)**3
*u + b(5,3)**2*b(2,1)*xi(3,6)**2*xi(3,5)*xi(2,1)*k + b(5,3)**2*b(2,1)*xi(3,6)**2
*xi(3,2)*xi(2,1)*u + b(5,3)**2*b(1,1)*xi(3,6)**2*xi(3,1)*xi(2,1)*u - b(5,3)*b(4,
2)*b(3,3)*xi(3,6)*xi(3,5)**2*xi(2,1) - b(5,3)*b(4,1)*b(3,3)*xi(6,6)*xi(3,6)*xi(3
,5)**2*u + b(5,3)*b(4,1)*b(3,3)*xi(6,5)*xi(3,6)**2*xi(3,5)*u - 2*b(5,3)*b(4,1)*b
(3,3)*xi(3,6)**2*u - b(5,3)*b(3,3)*b(2,1)*xi(6,6)*xi(3,6)*xi(3,5)*xi(3,1)*u + b(
5,3)*b(3,3)*b(2,1)*xi(6,5)*xi(3,6)**2*xi(3,1)*u + b(5,3)*b(3,3)*b(2,1)*xi(4,1)*
xi(3,6)**2*xi(2,1)*u + b(5,3)*b(3,3)*b(2,1)*xi(3,6)*xi(3,5)**2*xi(2,1)*k + b(5,3
)*b(3,3)*b(2,1)*xi(3,6)*xi(3,5)*xi(3,2)*xi(2,1)*u - b(5,3)*b(3,3)*b(1,1)*xi(5,1)
*xi(3,6)**2*xi(2,1)*u + b(5,3)*b(3,3)*b(1,1)*xi(3,6)**2*k - b(4,3)**2*b(4,2)*xi(
3,6)**2*xi(3,5)*xi(2,1) - b(4,3)**2*b(4,1)*xi(6,6)*xi(3,6)**2*xi(3,5)*u + b(4,3)
**2*b(4,1)*xi(6,5)*xi(3,6)**3*u + b(4,3)**2*b(2,1)*xi(3,6)**2*xi(3,5)*xi(2,1)*k 
+ b(4,3)**2*b(2,1)*xi(3,6)**2*xi(3,2)*xi(2,1)*u + b(4,3)**2*b(1,1)*xi(3,6)**2*xi
(3,1)*xi(2,1)*u + b(4,3)*b(4,2)*b(3,3)*xi(6,6)*xi(3,6)*xi(3,5)**2 - b(4,3)*b(4,2
)*b(3,3)*xi(6,5)*xi(3,6)**2*xi(3,5) - 2*b(4,3)*b(4,2)*b(3,3)*xi(3,6)**2 + b(4,3)
*b(4,1)*b(3,3)*xi(6,6)**2*xi(3,6)*xi(3,5)**2*xi(2,1)*u - 2*b(4,3)*b(4,1)*b(3,3)*
xi(6,6)*xi(6,5)*xi(3,6)**2*xi(3,5)*xi(2,1)*u + b(4,3)*b(4,1)*b(3,3)*xi(6,5)**2*
xi(3,6)**3*xi(2,1)*u - b(4,3)*b(3,3)*b(2,1)*xi(6,6)*xi(3,6)*xi(3,5)**2*k - b(4,3
)*b(3,3)*b(2,1)*xi(6,6)*xi(3,6)*xi(3,5)*xi(3,2)*u + b(4,3)*b(3,3)*b(2,1)*xi(6,5)
*xi(3,6)**2*xi(3,5)*k + b(4,3)*b(3,3)*b(2,1)*xi(6,5)*xi(3,6)**2*xi(3,2)*u - b(4,
3)*b(3,3)*b(2,1)*xi(5,1)*xi(3,6)**2*xi(2,1)*u + b(4,3)*b(3,3)*b(2,1)*xi(3,6)**2*
k - b(4,3)*b(3,3)*b(2,1)*xi(3,6)*xi(3,5)*xi(3,1)*xi(2,1)*u - b(4,3)*b(3,3)*b(1,1
)*xi(4,1)*xi(3,6)**2*xi(2,1)*u - b(4,2)*b(3,3)**2*xi(6,5)*xi(3,6)**2*xi(2,1) - b
(4,1)*b(3,3)**2*xi(6,6)**2*xi(3,6)*xi(3,5)*u + b(4,1)*b(3,3)**2*xi(6,6)*xi(6,5)*
xi(3,6)**2*u - b(4,1)*b(3,3)**2*xi(3,6)*xi(3,5)*u + b(3,3)**2*b(2,1)*xi(6,6)*xi(
5,1)*xi(3,6)*xi(3,5)*u + b(3,3)**2*b(2,1)*xi(6,6)*xi(3,6)*xi(3,2)*xi(2,1)*u - b(
3,3)**2*b(2,1)*xi(6,5)*xi(5,1)*xi(3,6)**2*u + b(3,3)**2*b(2,1)*xi(6,5)*xi(3,6)**
2*xi(2,1)*k + b(3,3)**2*b(2,1)*xi(4,1)*xi(3,6)*xi(3,5)*xi(2,1)*u + b(3,3)**2*b(2
,1)*xi(3,6)*xi(3,1)*u - b(3,3)**2*b(1,1)*xi(6,6)**2*xi(3,5)**2*xi(3,1)*xi(2,1)*u
 + 2*b(3,3)**2*b(1,1)*xi(6,6)*xi(6,5)*xi(3,6)*xi(3,5)*xi(3,1)*xi(2,1)*u + b(3,3)
**2*b(1,1)*xi(6,6)*xi(4,1)*xi(3,6)*xi(3,5)*u + b(3,3)**2*b(1,1)*xi(6,6)*xi(3,6)*
xi(3,1)*xi(2,1)*u - b(3,3)**2*b(1,1)*xi(6,5)**2*xi(3,6)**2*xi(3,1)*xi(2,1)*u - b
(3,3)**2*b(1,1)*xi(6,5)*xi(4,1)*xi(3,6)**2*u - b(3,3)**2*b(1,1)*xi(5,1)*xi(3,6)*
xi(3,5)*xi(2,1)*u - b(3,3)**2*b(1,1)*xi(3,6)*xi(3,2)*u - b(3,3)**2*b(1,1)*xi(3,5
)**2*xi(3,1)*xi(2,1)*u)/(b(3,3)**3*xi(3,6)**2*xi(2,1)*u*(b(2,1)**2 + b(1,1)**2))
USD\\$

\\USD J2(6,2):=( - b(6,3)*b(6,2)*b(3,3)*xi(3,6)**3*xi(2,1) + b(6,3)*b(4,2)*b(3,3
)*xi(6,6)*xi(3,6)**2*xi(3,5) - b(6,3)*b(4,2)*b(3,3)*xi(6,5)*xi(3,6)**3 - b(6,3)*
b(4,1)*b(3,3)*xi(3,6)**2*xi(3,5)*xi(2,1)*u - b(6,3)*b(3,3)*b(2,1)*xi(3,6)**2*xi(
3,1)*xi(2,1)*u + b(6,3)*b(3,3)*b(1,1)*xi(3,6)**2*xi(3,5)*xi(2,1)*k + b(6,3)*b(3,
3)*b(1,1)*xi(3,6)**2*xi(3,2)*xi(2,1)*u + b(6,2)*b(5,3)**2*xi(3,6)**3*xi(2,1) + b
(6,2)*b(5,3)*b(3,3)*xi(3,6)**2*xi(3,5)*xi(2,1) + b(6,2)*b(4,3)**2*xi(3,6)**3*xi(
2,1) - b(6,2)*b(4,3)*b(3,3)*xi(6,6)*xi(3,6)**2*xi(3,5) + b(6,2)*b(4,3)*b(3,3)*xi
(6,5)*xi(3,6)**3 + b(6,2)*b(3,3)**2*xi(6,6)*xi(3,6)**2*xi(2,1) - b(6,1)*b(3,3)**
2*xi(3,6)**2*u - b(5,3)**2*b(4,2)*xi(6,6)*xi(3,6)**2*xi(3,5) + b(5,3)**2*b(4,2)*
xi(6,5)*xi(3,6)**3 + b(5,3)**2*b(4,1)*xi(3,6)**2*xi(3,5)*xi(2,1)*u + b(5,3)**2*b
(2,1)*xi(3,6)**2*xi(3,1)*xi(2,1)*u - b(5,3)**2*b(1,1)*xi(3,6)**2*xi(3,5)*xi(2,1)
*k - b(5,3)**2*b(1,1)*xi(3,6)**2*xi(3,2)*xi(2,1)*u - b(5,3)*b(4,2)*b(3,3)*xi(6,6
)*xi(3,6)*xi(3,5)**2 + b(5,3)*b(4,2)*b(3,3)*xi(6,5)*xi(3,6)**2*xi(3,5) - 2*b(5,3
)*b(4,2)*b(3,3)*xi(3,6)**2 + b(5,3)*b(4,1)*b(3,3)*xi(3,6)*xi(3,5)**2*xi(2,1)*u -
 b(5,3)*b(3,3)*b(2,1)*xi(5,1)*xi(3,6)**2*xi(2,1)*u + b(5,3)*b(3,3)*b(2,1)*xi(3,6
)**2*k + b(5,3)*b(3,3)*b(1,1)*xi(6,6)*xi(3,6)*xi(3,5)*xi(3,1)*u - b(5,3)*b(3,3)*
b(1,1)*xi(6,5)*xi(3,6)**2*xi(3,1)*u - b(5,3)*b(3,3)*b(1,1)*xi(4,1)*xi(3,6)**2*xi
(2,1)*u - b(5,3)*b(3,3)*b(1,1)*xi(3,6)*xi(3,5)**2*xi(2,1)*k - b(5,3)*b(3,3)*b(1,
1)*xi(3,6)*xi(3,5)*xi(3,2)*xi(2,1)*u - b(4,3)**2*b(4,2)*xi(6,6)*xi(3,6)**2*xi(3,
5) + b(4,3)**2*b(4,2)*xi(6,5)*xi(3,6)**3 + b(4,3)**2*b(4,1)*xi(3,6)**2*xi(3,5)*
xi(2,1)*u + b(4,3)**2*b(2,1)*xi(3,6)**2*xi(3,1)*xi(2,1)*u - b(4,3)**2*b(1,1)*xi(
3,6)**2*xi(3,5)*xi(2,1)*k - b(4,3)**2*b(1,1)*xi(3,6)**2*xi(3,2)*xi(2,1)*u + b(4,
3)*b(4,2)*b(3,3)*xi(6,6)**2*xi(3,6)*xi(3,5)**2*xi(2,1) - 2*b(4,3)*b(4,2)*b(3,3)*
xi(6,6)*xi(6,5)*xi(3,6)**2*xi(3,5)*xi(2,1) + b(4,3)*b(4,2)*b(3,3)*xi(6,5)**2*xi(
3,6)**3*xi(2,1) - b(4,3)*b(4,1)*b(3,3)*xi(6,6)*xi(3,6)*xi(3,5)**2*u + b(4,3)*b(4
,1)*b(3,3)*xi(6,5)*xi(3,6)**2*xi(3,5)*u + 2*b(4,3)*b(4,1)*b(3,3)*xi(3,6)**2*u - 
b(4,3)*b(3,3)*b(2,1)*xi(4,1)*xi(3,6)**2*xi(2,1)*u + b(4,3)*b(3,3)*b(1,1)*xi(6,6)
*xi(3,6)*xi(3,5)**2*k + b(4,3)*b(3,3)*b(1,1)*xi(6,6)*xi(3,6)*xi(3,5)*xi(3,2)*u -
 b(4,3)*b(3,3)*b(1,1)*xi(6,5)*xi(3,6)**2*xi(3,5)*k - b(4,3)*b(3,3)*b(1,1)*xi(6,5
)*xi(3,6)**2*xi(3,2)*u + b(4,3)*b(3,3)*b(1,1)*xi(5,1)*xi(3,6)**2*xi(2,1)*u - b(4
,3)*b(3,3)*b(1,1)*xi(3,6)**2*k + b(4,3)*b(3,3)*b(1,1)*xi(3,6)*xi(3,5)*xi(3,1)*xi
(2,1)*u - b(4,2)*b(3,3)**2*xi(6,6)**2*xi(3,6)*xi(3,5) + b(4,2)*b(3,3)**2*xi(6,6)
*xi(6,5)*xi(3,6)**2 - b(4,2)*b(3,3)**2*xi(3,6)*xi(3,5) + b(4,1)*b(3,3)**2*xi(6,5
)*xi(3,6)**2*xi(2,1)*u - b(3,3)**2*b(2,1)*xi(6,6)**2*xi(3,5)**2*xi(3,1)*xi(2,1)*
u + 2*b(3,3)**2*b(2,1)*xi(6,6)*xi(6,5)*xi(3,6)*xi(3,5)*xi(3,1)*xi(2,1)*u + b(3,3
)**2*b(2,1)*xi(6,6)*xi(4,1)*xi(3,6)*xi(3,5)*u + b(3,3)**2*b(2,1)*xi(6,6)*xi(3,6)
*xi(3,1)*xi(2,1)*u - b(3,3)**2*b(2,1)*xi(6,5)**2*xi(3,6)**2*xi(3,1)*xi(2,1)*u - 
b(3,3)**2*b(2,1)*xi(6,5)*xi(4,1)*xi(3,6)**2*u - b(3,3)**2*b(2,1)*xi(5,1)*xi(3,6)
*xi(3,5)*xi(2,1)*u - b(3,3)**2*b(2,1)*xi(3,6)*xi(3,2)*u - b(3,3)**2*b(2,1)*xi(3,
5)**2*xi(3,1)*xi(2,1)*u - b(3,3)**2*b(1,1)*xi(6,6)*xi(5,1)*xi(3,6)*xi(3,5)*u - b
(3,3)**2*b(1,1)*xi(6,6)*xi(3,6)*xi(3,2)*xi(2,1)*u + b(3,3)**2*b(1,1)*xi(6,5)*xi(
5,1)*xi(3,6)**2*u - b(3,3)**2*b(1,1)*xi(6,5)*xi(3,6)**2*xi(2,1)*k - b(3,3)**2*b(
1,1)*xi(4,1)*xi(3,6)*xi(3,5)*xi(2,1)*u - b(3,3)**2*b(1,1)*xi(3,6)*xi(3,1)*u)/(b(
3,3)**3*xi(3,6)**2*xi(2,1)*(b(2,1)**2 + b(1,1)**2))USD\\$

\\USD J2(6,3):=( - b(6,3)**2*b(3,3)*xi(3,6)**3 + b(6,3)*b(5,3)**2*xi(3,6)**3 + b
(6,3)*b(4,3)**2*xi(3,6)**3 - b(6,3)*b(3,3)**2*xi(6,6)**2*xi(3,6)*xi(3,5)**2 + 2*
b(6,3)*b(3,3)**2*xi(6,6)*xi(6,5)*xi(3,6)**2*xi(3,5) + 2*b(6,3)*b(3,3)**2*xi(6,6)
*xi(3,6)**2 - b(6,3)*b(3,3)**2*xi(6,5)**2*xi(3,6)**3 - b(6,3)*b(3,3)**2*xi(3,6)*
xi(3,5)**2 + b(5,3)**3*xi(3,6)**2*xi(3,5) - b(5,3)**2*b(4,3)*xi(6,6)*xi(3,6)**2*
xi(3,5)*xi(2,1) + b(5,3)**2*b(4,3)*xi(6,5)*xi(3,6)**3*xi(2,1) + b(5,3)**2*b(3,3)
*xi(6,6)**2*xi(3,6)*xi(3,5)**2 - 2*b(5,3)**2*b(3,3)*xi(6,6)*xi(6,5)*xi(3,6)**2*
xi(3,5) - b(5,3)**2*b(3,3)*xi(6,6)*xi(3,6)**2 + b(5,3)**2*b(3,3)*xi(6,5)**2*xi(3
,6)**3 + 2*b(5,3)**2*b(3,3)*xi(3,6)*xi(3,5)**2 + b(5,3)*b(4,3)**2*xi(3,6)**2*xi(
3,5) - 2*b(5,3)*b(4,3)*b(3,3)*xi(6,6)*xi(3,6)*xi(3,5)**2*xi(2,1) + 2*b(5,3)*b(4,
3)*b(3,3)*xi(6,5)*xi(3,6)**2*xi(3,5)*xi(2,1) + b(5,3)*b(3,3)**2*xi(6,6)**2*xi(3,
5)**3 - 2*b(5,3)*b(3,3)**2*xi(6,6)*xi(6,5)*xi(3,6)*xi(3,5)**2 + b(5,3)*b(3,3)**2
*xi(6,5)**2*xi(3,6)**2*xi(3,5) + b(5,3)*b(3,3)**2*xi(3,5)**3 - b(4,3)**3*xi(6,6)
*xi(3,6)**2*xi(3,5)*xi(2,1) + b(4,3)**3*xi(6,5)*xi(3,6)**3*xi(2,1) + 2*b(4,3)**2
*b(3,3)*xi(6,6)**2*xi(3,6)*xi(3,5)**2 - 4*b(4,3)**2*b(3,3)*xi(6,6)*xi(6,5)*xi(3,
6)**2*xi(3,5) - b(4,3)**2*b(3,3)*xi(6,6)*xi(3,6)**2 + 2*b(4,3)**2*b(3,3)*xi(6,5)
**2*xi(3,6)**3 + b(4,3)**2*b(3,3)*xi(3,6)*xi(3,5)**2 - b(4,3)*b(3,3)**2*xi(6,6)
**3*xi(3,5)**3*xi(2,1) + 3*b(4,3)*b(3,3)**2*xi(6,6)**2*xi(6,5)*xi(3,6)*xi(3,5)**
2*xi(2,1) - 3*b(4,3)*b(3,3)**2*xi(6,6)*xi(6,5)**2*xi(3,6)**2*xi(3,5)*xi(2,1) - b
(4,3)*b(3,3)**2*xi(6,6)*xi(3,5)**3*xi(2,1) + b(4,3)*b(3,3)**2*xi(6,5)**3*xi(3,6)
**3*xi(2,1) + b(4,3)*b(3,3)**2*xi(6,5)*xi(3,6)*xi(3,5)**2*xi(2,1) + b(3,3)**3*xi
(6,6)**3*xi(3,5)**2 - 2*b(3,3)**3*xi(6,6)**2*xi(6,5)*xi(3,6)*xi(3,5) - b(3,3)**3
*xi(6,6)**2*xi(3,6) + b(3,3)**3*xi(6,6)*xi(6,5)**2*xi(3,6)**2 + b(3,3)**3*xi(6,6
)*xi(3,5)**2 - b(3,3)**3*xi(3,6))/(b(3,3)**3*xi(3,6)**2*(b(2,1)**2 + b(1,1)**2))
USD\\$

\\USD J2(6,4):=( - b(6,3)*b(5,3)*b(3,3)*b(2,1)*xi(3,6)**2 - b(6,3)*b(4,3)*b(3,3)
*b(1,1)*xi(3,6)**2 - b(6,3)*b(3,3)**2*b(2,1)*xi(3,6)*xi(3,5) + b(6,3)*b(3,3)**2*
b(1,1)*xi(6,6)*xi(3,6)*xi(3,5)*xi(2,1) - b(6,3)*b(3,3)**2*b(1,1)*xi(6,5)*xi(3,6)
**2*xi(2,1) + b(5,3)**3*b(2,1)*xi(3,6)**2 + b(5,3)**2*b(4,3)*b(1,1)*xi(3,6)**2 +
 2*b(5,3)**2*b(3,3)*b(2,1)*xi(3,6)*xi(3,5) - b(5,3)**2*b(3,3)*b(1,1)*xi(6,6)*xi(
3,6)*xi(3,5)*xi(2,1) + b(5,3)**2*b(3,3)*b(1,1)*xi(6,5)*xi(3,6)**2*xi(2,1) + b(5,
3)*b(4,3)**2*b(2,1)*xi(3,6)**2 - b(5,3)*b(4,3)*b(3,3)*b(2,1)*xi(6,6)*xi(3,6)*xi(
3,5)*xi(2,1) + b(5,3)*b(4,3)*b(3,3)*b(2,1)*xi(6,5)*xi(3,6)**2*xi(2,1) + b(5,3)*b
(4,3)*b(3,3)*b(1,1)*xi(3,6)*xi(3,5) + b(5,3)*b(3,3)**2*b(2,1)*xi(6,6)*xi(3,6) + 
b(5,3)*b(3,3)**2*b(2,1)*xi(3,5)**2 - b(5,3)*b(3,3)**2*b(1,1)*xi(6,6)*xi(3,5)**2*
xi(2,1) + b(5,3)*b(3,3)**2*b(1,1)*xi(6,5)*xi(3,6)*xi(3,5)*xi(2,1) - b(5,3)*b(3,3
)**2*b(1,1)*xi(3,6)*xi(2,1) + b(4,3)**3*b(1,1)*xi(3,6)**2 + b(4,3)**2*b(3,3)*b(2
,1)*xi(3,6)*xi(3,5) - 2*b(4,3)**2*b(3,3)*b(1,1)*xi(6,6)*xi(3,6)*xi(3,5)*xi(2,1) 
+ 2*b(4,3)**2*b(3,3)*b(1,1)*xi(6,5)*xi(3,6)**2*xi(2,1) - b(4,3)*b(3,3)**2*b(2,1)
*xi(6,6)*xi(3,5)**2*xi(2,1) + b(4,3)*b(3,3)**2*b(2,1)*xi(6,5)*xi(3,6)*xi(3,5)*xi
(2,1) + b(4,3)*b(3,3)**2*b(2,1)*xi(3,6)*xi(2,1) + b(4,3)*b(3,3)**2*b(1,1)*xi(6,6
)**2*xi(3,5)**2 - 2*b(4,3)*b(3,3)**2*b(1,1)*xi(6,6)*xi(6,5)*xi(3,6)*xi(3,5) + b(
4,3)*b(3,3)**2*b(1,1)*xi(6,6)*xi(3,6) + b(4,3)*b(3,3)**2*b(1,1)*xi(6,5)**2*xi(3,
6)**2 + b(3,3)**3*b(2,1)*xi(6,5)*xi(3,6) - b(3,3)**3*b(1,1)*xi(6,6)**2*xi(3,5)*
xi(2,1) + b(3,3)**3*b(1,1)*xi(6,6)*xi(6,5)*xi(3,6)*xi(2,1) - b(3,3)**3*b(1,1)*xi
(3,5)*xi(2,1))/(b(3,3)**3*xi(3,6)*(b(2,1)**2 + b(1,1)**2))USD\\$

\\USD J2(6,5):=(u*(b(6,3)*b(5,3)*b(3,3)*b(1,1)*xi(3,6)**2 - b(6,3)*b(4,3)*b(3,3)
*b(2,1)*xi(3,6)**2 + b(6,3)*b(3,3)**2*b(2,1)*xi(6,6)*xi(3,6)*xi(3,5)*xi(2,1) - b
(6,3)*b(3,3)**2*b(2,1)*xi(6,5)*xi(3,6)**2*xi(2,1) + b(6,3)*b(3,3)**2*b(1,1)*xi(3
,6)*xi(3,5) - b(5,3)**3*b(1,1)*xi(3,6)**2 + b(5,3)**2*b(4,3)*b(2,1)*xi(3,6)**2 -
 b(5,3)**2*b(3,3)*b(2,1)*xi(6,6)*xi(3,6)*xi(3,5)*xi(2,1) + b(5,3)**2*b(3,3)*b(2,
1)*xi(6,5)*xi(3,6)**2*xi(2,1) - 2*b(5,3)**2*b(3,3)*b(1,1)*xi(3,6)*xi(3,5) - b(5,
3)*b(4,3)**2*b(1,1)*xi(3,6)**2 + b(5,3)*b(4,3)*b(3,3)*b(2,1)*xi(3,6)*xi(3,5) + b
(5,3)*b(4,3)*b(3,3)*b(1,1)*xi(6,6)*xi(3,6)*xi(3,5)*xi(2,1) - b(5,3)*b(4,3)*b(3,3
)*b(1,1)*xi(6,5)*xi(3,6)**2*xi(2,1) - b(5,3)*b(3,3)**2*b(2,1)*xi(6,6)*xi(3,5)**2
*xi(2,1) + b(5,3)*b(3,3)**2*b(2,1)*xi(6,5)*xi(3,6)*xi(3,5)*xi(2,1) - b(5,3)*b(3,
3)**2*b(2,1)*xi(3,6)*xi(2,1) - b(5,3)*b(3,3)**2*b(1,1)*xi(6,6)*xi(3,6) - b(5,3)*
b(3,3)**2*b(1,1)*xi(3,5)**2 + b(4,3)**3*b(2,1)*xi(3,6)**2 - 2*b(4,3)**2*b(3,3)*b
(2,1)*xi(6,6)*xi(3,6)*xi(3,5)*xi(2,1) + 2*b(4,3)**2*b(3,3)*b(2,1)*xi(6,5)*xi(3,6
)**2*xi(2,1) - b(4,3)**2*b(3,3)*b(1,1)*xi(3,6)*xi(3,5) + b(4,3)*b(3,3)**2*b(2,1)
*xi(6,6)**2*xi(3,5)**2 - 2*b(4,3)*b(3,3)**2*b(2,1)*xi(6,6)*xi(6,5)*xi(3,6)*xi(3,
5) + b(4,3)*b(3,3)**2*b(2,1)*xi(6,6)*xi(3,6) + b(4,3)*b(3,3)**2*b(2,1)*xi(6,5)**
2*xi(3,6)**2 + b(4,3)*b(3,3)**2*b(1,1)*xi(6,6)*xi(3,5)**2*xi(2,1) - b(4,3)*b(3,3
)**2*b(1,1)*xi(6,5)*xi(3,6)*xi(3,5)*xi(2,1) - b(4,3)*b(3,3)**2*b(1,1)*xi(3,6)*xi
(2,1) - b(3,3)**3*b(2,1)*xi(6,6)**2*xi(3,5)*xi(2,1) + b(3,3)**3*b(2,1)*xi(6,6)*
xi(6,5)*xi(3,6)*xi(2,1) - b(3,3)**3*b(2,1)*xi(3,5)*xi(2,1) - b(3,3)**3*b(1,1)*xi
(6,5)*xi(3,6)))/(b(3,3)**3*xi(3,6)*(b(2,1)**2 + b(1,1)**2))USD\\$

\\USD J2(6,6):=( - b(6,3)*b(3,3)*xi(3,6) + b(5,3)**2*xi(3,6) + b(5,3)*b(3,3)*xi(
3,5) + b(4,3)**2*xi(3,6) - b(4,3)*b(3,3)*xi(6,6)*xi(3,5)*xi(2,1) + b(4,3)*b(3,3)
*xi(6,5)*xi(3,6)*xi(2,1) + b(3,3)**2*xi(6,6))/b(3,3)**2USD\\$

USD det \Phi:=b(3,3)**4*(b(2,1)**6 + 3*b(2,1)**4*b(1,1)**2 + 3*b(2,1)**2*b(1,1)
**4 + b(1,1)**6)USD$

\\ \4stars Take the following values :$

\\ USD u:=-1USD$

\\ USD b(1,1):=1USD$

\\ USD b(2,1):=0USD$

\\ USD b(3,3):=1USD$

\\ USD b(6,1):=( - b(4,2)*xi(3,5) + b(4,1)*xi(6,6)*xi(3,5)*xi(2,1) - b(4,1)*xi(6
,5)*xi(3,6)*xi(2,1) - xi(3,1))/xi(3,6)USD$

\\ USD b(6,2):=(b(4,2)*xi(6,6)*xi(3,5)*xi(2,1) - b(4,2)*xi(6,5)*xi(3,6)*xi(2,1) 
+ b(4,1)*xi(3,5) + xi(3,5)*k - xi(3,2))/xi(3,6)USD$

\\ USD b(5,3):=( - xi(3,5))/xi(3,6)USD$

\\ USD b(6,3):=(b(4,3)**2*xi(3,6) - b(4,3)*xi(6,6)*xi(3,5)*xi(2,1) + b(4,3)*xi(6
,5)*xi(3,6)*xi(2,1) + xi(6,6))/xi(3,6)USD$

\\ USD b(4,2):=( - xi(6,6)*xi(3,5)*xi(3,1)*xi(2,1) + xi(6,5)*xi(3,6)*xi(3,1)*xi(
2,1) + xi(4,1)*xi(3,6))/(2*xi(3,6)*xi(2,1))USD$

\\ USD b(4,1):= - (xi(5,1)*xi(3,6) + xi(3,6)*xi(2,1)*k + xi(3,5)*xi(3,1))/(2*xi(
3,6)*xi(2,1))USD$

\\USD \Phi^1_1:=1USD\\$

\\USD \Phi^1_2:=0USD\\$

\\USD \Phi^1_3:=0USD\\$

\\USD \Phi^1_4:=0USD\\$

\\USD \Phi^1_5:=0USD\\$

\\USD \Phi^1_6:=0USD\\$

\\USD \Phi^2_1:=0USD\\$

\\USD \Phi^2_2:=1USD\\$

\\USD \Phi^2_3:=0USD\\$

\\USD \Phi^2_4:=0USD\\$

\\USD \Phi^2_5:=0USD\\$

\\USD \Phi^2_6:=0USD\\$

\\USD \Phi^3_1:=0USD\\$

\\USD \Phi^3_2:=0USD\\$

\\USD \Phi^3_3:=1USD\\$

\\USD \Phi^3_4:=0USD\\$

\\USD \Phi^3_5:=0USD\\$

\\USD \Phi^3_6:=0USD\\$

\\USD \Phi^4_1:= - (xi(5,1)*xi(3,6) + xi(3,6)*xi(2,1)*k + xi(3,5)*xi(3,1))/(2*xi
(3,6)*xi(2,1))USD\\$

\\USD \Phi^4_2:=( - xi(6,6)*xi(3,5)*xi(3,1)*xi(2,1) + xi(6,5)*xi(3,6)*xi(3,1)*xi
(2,1) + xi(4,1)*xi(3,6))/(2*xi(3,6)*xi(2,1))USD\\$

\\USD \Phi^4_3:=b(4,3)USD\\$

\\USD \Phi^4_4:=1USD\\$

\\USD \Phi^4_5:=0USD\\$

\\USD \Phi^4_6:=0USD\\$

\\USD \Phi^5_1:=( - xi(6,6)*xi(3,5)*xi(3,1)*xi(2,1) + xi(6,5)*xi(3,6)*xi(3,1)*xi
(2,1) + xi(4,1)*xi(3,6))/(2*xi(3,6)*xi(2,1))USD\\$

\\USD \Phi^5_2:=(xi(5,1)*xi(3,6) - xi(3,6)*xi(2,1)*k + xi(3,5)*xi(3,1))/(2*xi(3,
6)*xi(2,1))USD\\$

\\USD \Phi^5_3:=( - xi(3,5))/xi(3,6)USD\\$

\\USD \Phi^5_4:=0USD\\$

\\USD \Phi^5_5:=1USD\\$

\\USD \Phi^5_6:=0USD\\$

\\USD \Phi^6_1:=( - xi(6,6)*xi(5,1)*xi(3,5)*xi(2,1) - xi(6,6)*xi(3,5)*k + xi(6,5
)*xi(5,1)*xi(3,6)*xi(2,1) + xi(6,5)*xi(3,6)*k - xi(4,1)*xi(3,5) - 2*xi(3,1)*xi(2
,1))/(2*xi(3,6)*xi(2,1))USD\\$

\\USD \Phi^6_2:=( - xi(6,6)**2*xi(3,5)**2*xi(3,1) + 2*xi(6,6)*xi(6,5)*xi(3,6)*xi
(3,5)*xi(3,1) + xi(6,6)*xi(4,1)*xi(3,6)*xi(3,5)*xi(2,1) - xi(6,5)**2*xi(3,6)**2*
xi(3,1) - xi(6,5)*xi(4,1)*xi(3,6)**2*xi(2,1) - xi(5,1)*xi(3,6)*xi(3,5) + xi(3,6)
*xi(3,5)*xi(2,1)*k - 2*xi(3,6)*xi(3,2)*xi(2,1) - xi(3,5)**2*xi(3,1))/(2*xi(3,6)
**2*xi(2,1))USD\\$

\\USD \Phi^6_3:=(b(4,3)**2*xi(3,6) - b(4,3)*xi(6,6)*xi(3,5)*xi(2,1) + b(4,3)*xi(
6,5)*xi(3,6)*xi(2,1) + xi(6,6))/xi(3,6)USD\\$

\\USD \Phi^6_4:=b(4,3)USD\\$

\\USD \Phi^6_5:=( - xi(3,5))/xi(3,6)USD\\$

\\USD \Phi^6_6:=1USD\\$

USD det \Phi:=1USD$

\\ Then USD J2:=\Phi^{-1}*J*\Phi USD has entries :$

\\USD J2(1,1):=0USD\\$

\\USD J2(1,2):=( - 1)/xi(2,1)USD\\$

\\USD J2(1,3):=0USD\\$

\\USD J2(1,4):=0USD\\$

\\USD J2(1,5):=0USD\\$

\\USD J2(1,6):=0USD\\$

\\USD J2(2,1):=xi(2,1)USD\\$

\\USD J2(2,2):=0USD\\$

\\USD J2(2,3):=0USD\\$

\\USD J2(2,4):=0USD\\$

\\USD J2(2,5):=0USD\\$

\\USD J2(2,6):=0USD\\$

\\USD J2(3,1):=0USD\\$

\\USD J2(3,2):=0USD\\$

\\USD J2(3,3):=(b(4,3)**2*xi(3,6)**2 - 2*b(4,3)*xi(6,6)*xi(3,6)*xi(3,5)*xi(2,1) 
+ 2*b(4,3)*xi(6,5)*xi(3,6)**2*xi(2,1) + xi(6,6)**2*xi(3,5)**2 - 2*xi(6,6)*xi(6,5
)*xi(3,6)*xi(3,5) + xi(6,5)**2*xi(3,6)**2)/xi(3,6)USD\\$

\\USD J2(3,4):=b(4,3)*xi(3,6) - xi(6,6)*xi(3,5)*xi(2,1) + xi(6,5)*xi(3,6)*xi(2,1
)USD\\$

\\USD J2(3,5):=0USD\\$

\\USD J2(3,6):=xi(3,6)USD\\$

\\USD J2(4,1):=0USD\\$

\\USD J2(4,2):=0USD\\$

\\USD J2(4,3):=( - b(4,3)**3*xi(3,6)**3 + 3*b(4,3)**2*xi(6,6)*xi(3,6)**2*xi(3,5)
*xi(2,1) - 3*b(4,3)**2*xi(6,5)*xi(3,6)**3*xi(2,1) - 3*b(4,3)*xi(6,6)**2*xi(3,6)*
xi(3,5)**2 + 6*b(4,3)*xi(6,6)*xi(6,5)*xi(3,6)**2*xi(3,5) - 3*b(4,3)*xi(6,5)**2*
xi(3,6)**3 + xi(6,6)**3*xi(3,5)**3*xi(2,1) - 3*xi(6,6)**2*xi(6,5)*xi(3,6)*xi(3,5
)**2*xi(2,1) + 3*xi(6,6)*xi(6,5)**2*xi(3,6)**2*xi(3,5)*xi(2,1) - xi(6,5)**3*xi(3
,6)**3*xi(2,1))/xi(3,6)**2USD\\$

\\USD J2(4,4):=( - b(4,3)**2*xi(3,6)**2 + 2*b(4,3)*xi(6,6)*xi(3,6)*xi(3,5)*xi(2,
1) - 2*b(4,3)*xi(6,5)*xi(3,6)**2*xi(2,1) - xi(6,6)**2*xi(3,5)**2 + 2*xi(6,6)*xi(
6,5)*xi(3,6)*xi(3,5) - xi(6,5)**2*xi(3,6)**2)/xi(3,6)USD\\$

\\USD J2(4,5):= - xi(2,1)USD\\$

\\USD J2(4,6):= - b(4,3)*xi(3,6) + xi(6,6)*xi(3,5)*xi(2,1) - xi(6,5)*xi(3,6)*xi(
2,1)USD\\$

\\USD J2(5,1):=0USD\\$

\\USD J2(5,2):=0USD\\$

\\USD J2(5,3):=(b(4,3)*xi(3,6)*xi(2,1) - xi(6,6)*xi(3,5) + xi(6,5)*xi(3,6))/xi(3
,6)USD\\$

\\USD J2(5,4):=xi(2,1)USD\\$

\\USD J2(5,5):=0USD\\$

\\USD J2(5,6):=0USD\\$

\\USD J2(6,1):=0USD\\$

\\USD J2(6,2):=0USD\\$

\\USD J2(6,3):=( - 1)/xi(3,6)USD\\$

\\USD J2(6,4):=0USD\\$

\\USD J2(6,5):=(b(4,3)*xi(3,6)*xi(2,1) - xi(6,6)*xi(3,5) + xi(6,5)*xi(3,6))/xi(3
,6)USD\\$

\\USD J2(6,6):=0USD\\$

USD det \Phi:=1USD$

\\ \4stars Hence, we are led to the case where$

\\ USD xi(3,1):=0USD$

\\ USD xi(3,2):=0USD$

\\ USD xi(3,5):=0USD$

\\ USD xi(4,1):=0USD$

\\ USD xi(5,1):=0USD$

\\ USD xi(6,6):=0USD$

clear USD u, b(1,1),b(2,1),b(3,3),b(6,1),b(6,2),b(5,3),b(6,3),b(4,1),b(4,2) USD$

\\$

USDUSD \Phi = \begin{pmatrix}$

b(1,1)&$

b(2,1)*u&$

0&$

0&$

0&$

0\\$

b(2,1)&$

 - b(1,1)*u&$

0&$

0&$

0&$

0\\$

0&$

0&$

b(3,3)&$

0&$

0&$

0\\$

b(4,1)&$

b(4,2)&$

b(4,3)&$

b(3,3)*b(1,1)&$

b(3,3)*b(2,1)*u&$

0\\$

u*( - b(4,2) + b(2,1)*k)&$

b(4,1)*u - b(1,1)*k&$

b(5,3)&$

b(3,3)*b(2,1)&$

 - b(3,3)*b(1,1)*u&$

0\\$

b(6,1)&$

b(6,2)&$

b(6,3)&$

b(5,3)*b(2,1) + b(4,3)*b(1,1)&$

u*( - b(5,3)*b(1,1) + b(4,3)*b(2,1))&$

b(3,3)*(b(2,1)**2 + b(1,1)**2)\end{pmatrix}USDUSD$

\\$

USDUSD J = \begin{pmatrix}$

0&$

( - 1)/xi(2,1)&$

0&$

0&$

0&$

0\\$

xi(2,1)&$

0&$

0&$

0&$

0&$

0\\$

0&$

0&$

xi(6,5)**2*xi(3,6)&$

xi(6,5)*xi(3,6)*xi(2,1)&$

0&$

xi(3,6)\\$

0&$

0&$

 - xi(6,5)**3*xi(3,6)*xi(2,1)&$

 - xi(6,5)**2*xi(3,6)&$

 - xi(2,1)&$

 - xi(6,5)*xi(3,6)*xi(2,1)\\$

0&$

0&$

xi(6,5)&$

xi(2,1)&$

0&$

0\\$

0&$

0&$

( - 1)/xi(3,6)&$

0&$

xi(6,5)&$

0\end{pmatrix}USDUSD$

\\ Then USD J2:=\Phi^{-1}*J*\Phi USD has entries :$

\\USD J2(1,1):=0USD\\$

\\USD J2(1,2):=u/xi(2,1)USD\\$

\\USD J2(1,3):=0USD\\$

\\USD J2(1,4):=0USD\\$

\\USD J2(1,5):=0USD\\$

\\USD J2(1,6):=0USD\\$

\\USD J2(2,1):=( - 1)/(xi(2,1)*u)USD\\$

\\USD J2(2,2):=0USD\\$

\\USD J2(2,3):=0USD\\$

\\USD J2(2,4):=0USD\\$

\\USD J2(2,5):=0USD\\$

\\USD J2(2,6):=0USD\\$

\\USD J2(3,1):=(xi(3,6)*(b(6,1) + b(4,1)*xi(6,5)*xi(2,1)))/b(3,3)USD\\$

\\USD J2(3,2):=(xi(3,6)*(b(6,2) + b(4,2)*xi(6,5)*xi(2,1)))/b(3,3)USD\\$

\\USD J2(3,3):=(xi(3,6)*(b(6,3) + b(4,3)*xi(6,5)*xi(2,1) + b(3,3)*xi(6,5)**2))/b
(3,3)USD\\$

\\USD J2(3,4):=(xi(3,6)*(b(5,3)*b(2,1) + b(4,3)*b(1,1) + b(3,3)*b(1,1)*xi(6,5)*
xi(2,1)))/b(3,3)USD\\$

\\USD J2(3,5):=(xi(3,6)*u*( - b(5,3)*b(1,1) + b(4,3)*b(2,1) + b(3,3)*b(2,1)*xi(6
,5)*xi(2,1)))/b(3,3)USD\\$

\\USD J2(3,6):=xi(3,6)*(b(2,1)**2 + b(1,1)**2)USD\\$

\\USD J2(4,1):=( - b(6,1)*b(5,3)*b(2,1)*xi(3,6)*xi(2,1)*u - b(6,1)*b(4,3)*b(1,1)
*xi(3,6)*xi(2,1)*u - b(6,1)*b(3,3)*b(1,1)*xi(6,5)*xi(3,6)*u - b(5,3)*b(4,1)*b(2,
1)*xi(6,5)*xi(3,6)*u - b(4,3)*b(4,1)*b(1,1)*xi(6,5)*xi(3,6)*u + 2*b(4,2)*b(3,3)*
b(1,1) + 2*b(4,1)*b(3,3)*b(2,1)*u - b(4,1)*b(3,3)*b(1,1)*xi(6,5)**2*xi(3,6)*xi(2
,1)*u - 2*b(3,3)*b(2,1)*b(1,1)*k)/(b(3,3)**2*xi(2,1)*u*(b(2,1)**2 + b(1,1)**2))
USD\\$

\\USD J2(4,2):=( - b(6,2)*b(5,3)*b(2,1)*xi(3,6)*xi(2,1) - b(6,2)*b(4,3)*b(1,1)*
xi(3,6)*xi(2,1) - b(6,2)*b(3,3)*b(1,1)*xi(6,5)*xi(3,6) - b(5,3)*b(4,2)*b(2,1)*xi
(6,5)*xi(3,6) - b(4,3)*b(4,2)*b(1,1)*xi(6,5)*xi(3,6) + 2*b(4,2)*b(3,3)*b(2,1) - 
b(4,2)*b(3,3)*b(1,1)*xi(6,5)**2*xi(3,6)*xi(2,1) - 2*b(4,1)*b(3,3)*b(1,1)*u - b(3
,3)*b(2,1)**2*k + b(3,3)*b(1,1)**2*k)/(b(3,3)**2*xi(2,1)*(b(2,1)**2 + b(1,1)**2)
)USD\\$

\\USD J2(4,3):=( - b(6,3)*b(5,3)*b(2,1)*xi(3,6) - b(6,3)*b(4,3)*b(1,1)*xi(3,6) -
 b(6,3)*b(3,3)*b(1,1)*xi(6,5)*xi(3,6)*xi(2,1) - b(5,3)*b(4,3)*b(2,1)*xi(6,5)*xi(
3,6)*xi(2,1) - b(5,3)*b(3,3)*b(2,1)*xi(6,5)**2*xi(3,6) - b(5,3)*b(3,3)*b(1,1)*xi
(2,1) - b(4,3)**2*b(1,1)*xi(6,5)*xi(3,6)*xi(2,1) + b(4,3)*b(3,3)*b(2,1)*xi(2,1) 
- 2*b(4,3)*b(3,3)*b(1,1)*xi(6,5)**2*xi(3,6) + b(3,3)**2*b(2,1)*xi(6,5) - b(3,3)
**2*b(1,1)*xi(6,5)**3*xi(3,6)*xi(2,1))/(b(3,3)**2*(b(2,1)**2 + b(1,1)**2))USD\\$

\\USD J2(4,4):=(xi(3,6)*( - b(5,3)**2*b(2,1)**2 - 2*b(5,3)*b(4,3)*b(2,1)*b(1,1) 
- 2*b(5,3)*b(3,3)*b(2,1)*b(1,1)*xi(6,5)*xi(2,1) - b(4,3)**2*b(1,1)**2 - 2*b(4,3)
*b(3,3)*b(1,1)**2*xi(6,5)*xi(2,1) - b(3,3)**2*b(1,1)**2*xi(6,5)**2))/(b(3,3)**2*
(b(2,1)**2 + b(1,1)**2))USD\\$

\\USD J2(4,5):=(u*(b(5,3)**2*b(2,1)*b(1,1)*xi(3,6) - b(5,3)*b(4,3)*b(2,1)**2*xi(
3,6) + b(5,3)*b(4,3)*b(1,1)**2*xi(3,6) - b(5,3)*b(3,3)*b(2,1)**2*xi(6,5)*xi(3,6)
*xi(2,1) + b(5,3)*b(3,3)*b(1,1)**2*xi(6,5)*xi(3,6)*xi(2,1) - b(4,3)**2*b(2,1)*b(
1,1)*xi(3,6) - 2*b(4,3)*b(3,3)*b(2,1)*b(1,1)*xi(6,5)*xi(3,6)*xi(2,1) + b(3,3)**2
*b(2,1)**2*xi(2,1) - b(3,3)**2*b(2,1)*b(1,1)*xi(6,5)**2*xi(3,6) + b(3,3)**2*b(1,
1)**2*xi(2,1)))/(b(3,3)**2*(b(2,1)**2 + b(1,1)**2))USD\\$

\\USD J2(4,6):= - (xi(3,6)*(b(5,3)*b(2,1) + b(4,3)*b(1,1) + b(3,3)*b(1,1)*xi(6,5
)*xi(2,1)))/b(3,3)USD\\$

\\USD J2(5,1):=(b(6,1)*b(5,3)*b(1,1)*xi(3,6)*xi(2,1) - b(6,1)*b(4,3)*b(2,1)*xi(3
,6)*xi(2,1) - b(6,1)*b(3,3)*b(2,1)*xi(6,5)*xi(3,6) + b(5,3)*b(4,1)*b(1,1)*xi(6,5
)*xi(3,6) - b(4,3)*b(4,1)*b(2,1)*xi(6,5)*xi(3,6) + 2*b(4,2)*b(3,3)*b(2,1)*u - b(
4,1)*b(3,3)*b(2,1)*xi(6,5)**2*xi(3,6)*xi(2,1) - 2*b(4,1)*b(3,3)*b(1,1) - b(3,3)*
b(2,1)**2*k*u + b(3,3)*b(1,1)**2*k*u)/(b(3,3)**2*xi(2,1)*u*(b(2,1)**2 + b(1,1)**
2))USD\\$

\\USD J2(5,2):=(b(6,2)*b(5,3)*b(1,1)*xi(3,6)*xi(2,1) - b(6,2)*b(4,3)*b(2,1)*xi(3
,6)*xi(2,1) - b(6,2)*b(3,3)*b(2,1)*xi(6,5)*xi(3,6) + b(5,3)*b(4,2)*b(1,1)*xi(6,5
)*xi(3,6) - b(4,3)*b(4,2)*b(2,1)*xi(6,5)*xi(3,6) - b(4,2)*b(3,3)*b(2,1)*xi(6,5)
**2*xi(3,6)*xi(2,1) - 2*b(4,2)*b(3,3)*b(1,1) - 2*b(4,1)*b(3,3)*b(2,1)*u + 2*b(3,
3)*b(2,1)*b(1,1)*k)/(b(3,3)**2*xi(2,1)*u*(b(2,1)**2 + b(1,1)**2))USD\\$

\\USD J2(5,3):=(b(6,3)*b(5,3)*b(1,1)*xi(3,6) - b(6,3)*b(4,3)*b(2,1)*xi(3,6) - b(
6,3)*b(3,3)*b(2,1)*xi(6,5)*xi(3,6)*xi(2,1) + b(5,3)*b(4,3)*b(1,1)*xi(6,5)*xi(3,6
)*xi(2,1) - b(5,3)*b(3,3)*b(2,1)*xi(2,1) + b(5,3)*b(3,3)*b(1,1)*xi(6,5)**2*xi(3,
6) - b(4,3)**2*b(2,1)*xi(6,5)*xi(3,6)*xi(2,1) - 2*b(4,3)*b(3,3)*b(2,1)*xi(6,5)**
2*xi(3,6) - b(4,3)*b(3,3)*b(1,1)*xi(2,1) - b(3,3)**2*b(2,1)*xi(6,5)**3*xi(3,6)*
xi(2,1) - b(3,3)**2*b(1,1)*xi(6,5))/(b(3,3)**2*u*(b(2,1)**2 + b(1,1)**2))USD\\$

\\USD J2(5,4):=(b(5,3)**2*b(2,1)*b(1,1)*xi(3,6) - b(5,3)*b(4,3)*b(2,1)**2*xi(3,6
) + b(5,3)*b(4,3)*b(1,1)**2*xi(3,6) - b(5,3)*b(3,3)*b(2,1)**2*xi(6,5)*xi(3,6)*xi
(2,1) + b(5,3)*b(3,3)*b(1,1)**2*xi(6,5)*xi(3,6)*xi(2,1) - b(4,3)**2*b(2,1)*b(1,1
)*xi(3,6) - 2*b(4,3)*b(3,3)*b(2,1)*b(1,1)*xi(6,5)*xi(3,6)*xi(2,1) - b(3,3)**2*b(
2,1)**2*xi(2,1) - b(3,3)**2*b(2,1)*b(1,1)*xi(6,5)**2*xi(3,6) - b(3,3)**2*b(1,1)
**2*xi(2,1))/(b(3,3)**2*u*(b(2,1)**2 + b(1,1)**2))USD\\$

\\USD J2(5,5):=(xi(3,6)*( - b(5,3)**2*b(1,1)**2 + 2*b(5,3)*b(4,3)*b(2,1)*b(1,1) 
+ 2*b(5,3)*b(3,3)*b(2,1)*b(1,1)*xi(6,5)*xi(2,1) - b(4,3)**2*b(2,1)**2 - 2*b(4,3)
*b(3,3)*b(2,1)**2*xi(6,5)*xi(2,1) - b(3,3)**2*b(2,1)**2*xi(6,5)**2))/(b(3,3)**2*
(b(2,1)**2 + b(1,1)**2))USD\\$

\\USD J2(5,6):=(xi(3,6)*(b(5,3)*b(1,1) - b(4,3)*b(2,1) - b(3,3)*b(2,1)*xi(6,5)*
xi(2,1)))/(b(3,3)*u)USD\\$

\\USD J2(6,1):=( - b(6,3)*b(6,1)*b(3,3)*xi(3,6)*xi(2,1)*u - b(6,3)*b(4,1)*b(3,3)
*xi(6,5)*xi(3,6)*u + b(6,2)*b(3,3)**2 + b(6,1)*b(5,3)**2*xi(3,6)*xi(2,1)*u + b(6
,1)*b(4,3)**2*xi(3,6)*xi(2,1)*u + b(6,1)*b(4,3)*b(3,3)*xi(6,5)*xi(3,6)*u + b(5,3
)**2*b(4,1)*xi(6,5)*xi(3,6)*u - 2*b(5,3)*b(4,1)*b(3,3)*u + b(5,3)*b(3,3)*b(1,1)*
k + b(4,3)**2*b(4,1)*xi(6,5)*xi(3,6)*u - 2*b(4,3)*b(4,2)*b(3,3) + b(4,3)*b(4,1)*
b(3,3)*xi(6,5)**2*xi(3,6)*xi(2,1)*u + b(4,3)*b(3,3)*b(2,1)*k - b(4,2)*b(3,3)**2*
xi(6,5)*xi(2,1) + b(3,3)**2*b(2,1)*xi(6,5)*xi(2,1)*k)/(b(3,3)**3*xi(2,1)*u*(b(2,
1)**2 + b(1,1)**2))USD\\$

\\USD J2(6,2):=( - b(6,3)*b(6,2)*b(3,3)*xi(3,6)*xi(2,1) - b(6,3)*b(4,2)*b(3,3)*
xi(6,5)*xi(3,6) + b(6,2)*b(5,3)**2*xi(3,6)*xi(2,1) + b(6,2)*b(4,3)**2*xi(3,6)*xi
(2,1) + b(6,2)*b(4,3)*b(3,3)*xi(6,5)*xi(3,6) - b(6,1)*b(3,3)**2*u + b(5,3)**2*b(
4,2)*xi(6,5)*xi(3,6) - 2*b(5,3)*b(4,2)*b(3,3) + b(5,3)*b(3,3)*b(2,1)*k + b(4,3)
**2*b(4,2)*xi(6,5)*xi(3,6) + b(4,3)*b(4,2)*b(3,3)*xi(6,5)**2*xi(3,6)*xi(2,1) + 2
*b(4,3)*b(4,1)*b(3,3)*u - b(4,3)*b(3,3)*b(1,1)*k + b(4,1)*b(3,3)**2*xi(6,5)*xi(2
,1)*u - b(3,3)**2*b(1,1)*xi(6,5)*xi(2,1)*k)/(b(3,3)**3*xi(2,1)*(b(2,1)**2 + b(1,
1)**2))USD\\$

\\USD J2(6,3):=( - b(6,3)**2*b(3,3)*xi(3,6)**2 + b(6,3)*b(5,3)**2*xi(3,6)**2 + b
(6,3)*b(4,3)**2*xi(3,6)**2 - b(6,3)*b(3,3)**2*xi(6,5)**2*xi(3,6)**2 + b(5,3)**2*
b(4,3)*xi(6,5)*xi(3,6)**2*xi(2,1) + b(5,3)**2*b(3,3)*xi(6,5)**2*xi(3,6)**2 + b(4
,3)**3*xi(6,5)*xi(3,6)**2*xi(2,1) + 2*b(4,3)**2*b(3,3)*xi(6,5)**2*xi(3,6)**2 + b
(4,3)*b(3,3)**2*xi(6,5)**3*xi(3,6)**2*xi(2,1) - b(3,3)**3)/(b(3,3)**3*xi(3,6)*(b
(2,1)**2 + b(1,1)**2))USD\\$

\\USD J2(6,4):=( - b(6,3)*b(5,3)*b(3,3)*b(2,1)*xi(3,6) - b(6,3)*b(4,3)*b(3,3)*b(
1,1)*xi(3,6) - b(6,3)*b(3,3)**2*b(1,1)*xi(6,5)*xi(3,6)*xi(2,1) + b(5,3)**3*b(2,1
)*xi(3,6) + b(5,3)**2*b(4,3)*b(1,1)*xi(3,6) + b(5,3)**2*b(3,3)*b(1,1)*xi(6,5)*xi
(3,6)*xi(2,1) + b(5,3)*b(4,3)**2*b(2,1)*xi(3,6) + b(5,3)*b(4,3)*b(3,3)*b(2,1)*xi
(6,5)*xi(3,6)*xi(2,1) - b(5,3)*b(3,3)**2*b(1,1)*xi(2,1) + b(4,3)**3*b(1,1)*xi(3,
6) + 2*b(4,3)**2*b(3,3)*b(1,1)*xi(6,5)*xi(3,6)*xi(2,1) + b(4,3)*b(3,3)**2*b(2,1)
*xi(2,1) + b(4,3)*b(3,3)**2*b(1,1)*xi(6,5)**2*xi(3,6) + b(3,3)**3*b(2,1)*xi(6,5)
)/(b(3,3)**3*(b(2,1)**2 + b(1,1)**2))USD\\$

\\USD J2(6,5):=(u*(b(6,3)*b(5,3)*b(3,3)*b(1,1)*xi(3,6) - b(6,3)*b(4,3)*b(3,3)*b(
2,1)*xi(3,6) - b(6,3)*b(3,3)**2*b(2,1)*xi(6,5)*xi(3,6)*xi(2,1) - b(5,3)**3*b(1,1
)*xi(3,6) + b(5,3)**2*b(4,3)*b(2,1)*xi(3,6) + b(5,3)**2*b(3,3)*b(2,1)*xi(6,5)*xi
(3,6)*xi(2,1) - b(5,3)*b(4,3)**2*b(1,1)*xi(3,6) - b(5,3)*b(4,3)*b(3,3)*b(1,1)*xi
(6,5)*xi(3,6)*xi(2,1) - b(5,3)*b(3,3)**2*b(2,1)*xi(2,1) + b(4,3)**3*b(2,1)*xi(3,
6) + 2*b(4,3)**2*b(3,3)*b(2,1)*xi(6,5)*xi(3,6)*xi(2,1) + b(4,3)*b(3,3)**2*b(2,1)
*xi(6,5)**2*xi(3,6) - b(4,3)*b(3,3)**2*b(1,1)*xi(2,1) - b(3,3)**3*b(1,1)*xi(6,5)
))/(b(3,3)**3*(b(2,1)**2 + b(1,1)**2))USD\\$

\\USD J2(6,6):=(xi(3,6)*( - b(6,3)*b(3,3) + b(5,3)**2 + b(4,3)**2 + b(4,3)*b(3,3
)*xi(6,5)*xi(2,1)))/b(3,3)**2USD\\$

USD det \Phi:=b(3,3)**4*(b(2,1)**6 + 3*b(2,1)**4*b(1,1)**2 + 3*b(2,1)**2*b(1,1)
**4 + b(1,1)**6)USD$

\\ \4stars Take now the following values :$

\\ USD u:= - xi(2,1)USD$

\\$

USDUSD \Phi = \begin{pmatrix}$

b(1,1)&$

0&$

0&$

0&$

0&$

0\\$

0&$

b(1,1)*xi(2,1)&$

0&$

0&$

0&$

0\\$

0&$

0&$

1&$

0&$

0&$

0\\$

( - b(1,1)*xi(2,1)*k)/2&$

0&$

 - xi(6,5)*xi(2,1)&$

b(1,1)&$

0&$

0\\$

0&$

( - b(1,1)*k)/2&$

0&$

0&$

b(1,1)*xi(2,1)&$

0\\$

(b(1,1)*xi(6,5)*k)/2&$

0&$

0&$

 - b(1,1)*xi(6,5)*xi(2,1)&$

0&$

1/abs(xi(3,6))\end{pmatrix}USDUSD$

USD det \Phi:=1/abs(xi(3,6))**3USD$

\\ Then USD J2:=\Phi^{-1}*J*\Phi USD has entries :$

\\USD J2(1,1):=0USD\\$

\\USD J2(1,2):=-1USD\\$

\\USD J2(1,3):=0USD\\$

\\USD J2(1,4):=0USD\\$

\\USD J2(1,5):=0USD\\$

\\USD J2(1,6):=0USD\\$

\\USD J2(2,1):=1USD\\$

\\USD J2(2,2):=0USD\\$

\\USD J2(2,3):=0USD\\$

\\USD J2(2,4):=0USD\\$

\\USD J2(2,5):=0USD\\$

\\USD J2(2,6):=0USD\\$

\\USD J2(3,1):=0USD\\$

\\USD J2(3,2):=0USD\\$

\\USD J2(3,3):=0USD\\$

\\USD J2(3,4):=0USD\\$

\\USD J2(3,5):=0USD\\$

\\USD J2(3,6):=xi(3,6)/abs(xi(3,6))USD\\$

\\USD J2(4,1):=0USD\\$

\\USD J2(4,2):=0USD\\$

\\USD J2(4,3):=0USD\\$

\\USD J2(4,4):=0USD\\$

\\USD J2(4,5):=-1USD\\$

\\USD J2(4,6):=0USD\\$

\\USD J2(5,1):=0USD\\$

\\USD J2(5,2):=0USD\\$

\\USD J2(5,3):=0USD\\$

\\USD J2(5,4):=1USD\\$

\\USD J2(5,5):=0USD\\$

\\USD J2(5,6):=0USD\\$

\\USD J2(6,1):=0USD\\$

\\USD J2(6,2):=0USD\\$

\\USD J2(6,3):=( - abs(xi(3,6)))/xi(3,6)USD\\$

\\USD J2(6,4):=0USD\\$

\\USD J2(6,5):=0USD\\$

\\USD J2(6,6):=0USD\\$

USD det \Phi:=1/abs(xi(3,6))**3USD$

\\ \4stars Hence, we are led to the case where moreover $

\\ USD xi(6,5):=0USD$

\\ USD xi(2,1):=1USD$

\\ USD xi(3,6)**2:=1USD$



clear! !U!S!D! u,! b(1,1)**2,b(2,1),b(3,3),b(4,3),b(5,3),b(6,1),b(6,2),b(6,3),b(
4,1)\
,b(4,2)! !U!S!D$

Then we have$

\\$

USDUSD J = \begin{pmatrix}$

0&$

-1&$

0&$

0&$

0&$

0\\$

1&$

0&$

0&$

0&$

0&$

0\\$

0&$

0&$

0&$

0&$

0&$

xi(3,6)\\$

0&$

0&$

0&$

0&$

-1&$

0\\$

0&$

0&$

0&$

1&$

0&$

0\\$

0&$

0&$

( - 1)/xi(3,6)&$

0&$

0&$

0\end{pmatrix}USDUSD$

\\$

USDUSD \Phi = \begin{pmatrix}$

b(1,1)&$

b(2,1)*u&$

0&$

0&$

0&$

0\\$

b(2,1)&$

 - b(1,1)*u&$

0&$

0&$

0&$

0\\$

0&$

0&$

b(3,3)&$

0&$

0&$

0\\$

b(4,1)&$

b(4,2)&$

b(4,3)&$

b(3,3)*b(1,1)&$

b(3,3)*b(2,1)*u&$

0\\$

 - (b(4,2) - b(2,1)*k)*u&$

b(4,1)*u - b(1,1)*k&$

b(5,3)&$

b(3,3)*b(2,1)&$

 - b(3,3)*b(1,1)*u&$

0\\$

b(6,1)&$

b(6,2)&$

b(6,3)&$

b(5,3)*b(2,1) + b(4,3)*b(1,1)&$

 - (b(5,3)*b(1,1) - b(4,3)*b(2,1))*u&$

(b(2,1)**2 + b(1,1)**2)*b(3,3)\end{pmatrix}USDUSD$

USD det \Phi:=(b(2,1)**2 + b(1,1)**2)**3*b(3,3)**4USD$

\\ Then USD J2:=\Phi^{-1}*J*\Phi USD has entries :$

\\USD J2(1,1):=0USD\\$

\\USD J2(1,2):=uUSD\\$

\\USD J2(1,3):=0USD\\$

\\USD J2(1,4):=0USD\\$

\\USD J2(1,5):=0USD\\$

\\USD J2(1,6):=0USD\\$

\\USD J2(2,1):=( - 1)/uUSD\\$

\\USD J2(2,2):=0USD\\$

\\USD J2(2,3):=0USD\\$

\\USD J2(2,4):=0USD\\$

\\USD J2(2,5):=0USD\\$

\\USD J2(2,6):=0USD\\$

\\USD J2(3,1):=(b(6,1)*xi(3,6))/b(3,3)USD\\$

\\USD J2(3,2):=(b(6,2)*xi(3,6))/b(3,3)USD\\$

\\USD J2(3,3):=(b(6,3)*xi(3,6))/b(3,3)USD\\$

\\USD J2(3,4):=(xi(3,6)*(b(5,3)*b(2,1) + b(4,3)*b(1,1)))/b(3,3)USD\\$

\\USD J2(3,5):=(xi(3,6)*u*( - b(5,3)*b(1,1) + b(4,3)*b(2,1)))/b(3,3)USD\\$

\\USD J2(3,6):=xi(3,6)*(b(2,1)**2 + b(1,1)**2)USD\\$

\\USD J2(4,1):=( - b(6,1)*b(5,3)*b(2,1)*xi(3,6)*u - b(6,1)*b(4,3)*b(1,1)*xi(3,6)
*u + 2*b(4,2)*b(3,3)*b(1,1) + 2*b(4,1)*b(3,3)*b(2,1)*u - 2*b(3,3)*b(2,1)*b(1,1)*
k)/(b(3,3)**2*u*(b(2,1)**2 + b(1,1)**2))USD\\$

\\USD J2(4,2):=( - b(6,2)*b(5,3)*b(2,1)*xi(3,6) - b(6,2)*b(4,3)*b(1,1)*xi(3,6) +
 2*b(4,2)*b(3,3)*b(2,1) - 2*b(4,1)*b(3,3)*b(1,1)*u - b(3,3)*b(2,1)**2*k + b(3,3)
*b(1,1)**2*k)/(b(3,3)**2*(b(2,1)**2 + b(1,1)**2))USD\\$

\\USD J2(4,3):=( - b(6,3)*b(5,3)*b(2,1)*xi(3,6) - b(6,3)*b(4,3)*b(1,1)*xi(3,6) -
 b(5,3)*b(3,3)*b(1,1) + b(4,3)*b(3,3)*b(2,1))/(b(3,3)**2*(b(2,1)**2 + b(1,1)**2)
)USD\\$

\\USD J2(4,4):=(xi(3,6)*( - b(5,3)**2*b(2,1)**2 - 2*b(5,3)*b(4,3)*b(2,1)*b(1,1) 
- b(4,3)**2*b(1,1)**2))/(b(3,3)**2*(b(2,1)**2 + b(1,1)**2))USD\\$

\\USD J2(4,5):=(u*(b(5,3)**2*b(2,1)*b(1,1)*xi(3,6) - b(5,3)*b(4,3)*b(2,1)**2*xi(
3,6) + b(5,3)*b(4,3)*b(1,1)**2*xi(3,6) - b(4,3)**2*b(2,1)*b(1,1)*xi(3,6) + b(3,3
)**2*b(2,1)**2 + b(3,3)**2*b(1,1)**2))/(b(3,3)**2*(b(2,1)**2 + b(1,1)**2))USD\\$

\\USD J2(4,6):= - (xi(3,6)*(b(5,3)*b(2,1) + b(4,3)*b(1,1)))/b(3,3)USD\\$

\\USD J2(5,1):=(b(6,1)*b(5,3)*b(1,1)*xi(3,6) - b(6,1)*b(4,3)*b(2,1)*xi(3,6) + 2*
b(4,2)*b(3,3)*b(2,1)*u - 2*b(4,1)*b(3,3)*b(1,1) - b(3,3)*b(2,1)**2*k*u + b(3,3)*
b(1,1)**2*k*u)/(b(3,3)**2*u*(b(2,1)**2 + b(1,1)**2))USD\\$

\\USD J2(5,2):=(b(6,2)*b(5,3)*b(1,1)*xi(3,6) - b(6,2)*b(4,3)*b(2,1)*xi(3,6) - 2*
b(4,2)*b(3,3)*b(1,1) - 2*b(4,1)*b(3,3)*b(2,1)*u + 2*b(3,3)*b(2,1)*b(1,1)*k)/(b(3
,3)**2*u*(b(2,1)**2 + b(1,1)**2))USD\\$

\\USD J2(5,3):=(b(6,3)*b(5,3)*b(1,1)*xi(3,6) - b(6,3)*b(4,3)*b(2,1)*xi(3,6) - b(
5,3)*b(3,3)*b(2,1) - b(4,3)*b(3,3)*b(1,1))/(b(3,3)**2*u*(b(2,1)**2 + b(1,1)**2))
USD\\$

\\USD J2(5,4):=(b(5,3)**2*b(2,1)*b(1,1)*xi(3,6) - b(5,3)*b(4,3)*b(2,1)**2*xi(3,6
) + b(5,3)*b(4,3)*b(1,1)**2*xi(3,6) - b(4,3)**2*b(2,1)*b(1,1)*xi(3,6) - b(3,3)**
2*b(2,1)**2 - b(3,3)**2*b(1,1)**2)/(b(3,3)**2*u*(b(2,1)**2 + b(1,1)**2))USD\\$

\\USD J2(5,5):=(xi(3,6)*( - b(5,3)**2*b(1,1)**2 + 2*b(5,3)*b(4,3)*b(2,1)*b(1,1) 
- b(4,3)**2*b(2,1)**2))/(b(3,3)**2*(b(2,1)**2 + b(1,1)**2))USD\\$

\\USD J2(5,6):=(xi(3,6)*(b(5,3)*b(1,1) - b(4,3)*b(2,1)))/(b(3,3)*u)USD\\$

\\USD J2(6,1):=( - b(6,3)*b(6,1)*b(3,3)*xi(3,6)*u + b(6,2)*b(3,3)**2 + b(6,1)*b(
5,3)**2*xi(3,6)*u + b(6,1)*b(4,3)**2*xi(3,6)*u - 2*b(5,3)*b(4,1)*b(3,3)*u + b(5,
3)*b(3,3)*b(1,1)*k - 2*b(4,3)*b(4,2)*b(3,3) + b(4,3)*b(3,3)*b(2,1)*k)/(b(3,3)**3
*u*(b(2,1)**2 + b(1,1)**2))USD\\$

\\USD J2(6,2):=( - b(6,3)*b(6,2)*b(3,3)*xi(3,6) + b(6,2)*b(5,3)**2*xi(3,6) + b(6
,2)*b(4,3)**2*xi(3,6) - b(6,1)*b(3,3)**2*u - 2*b(5,3)*b(4,2)*b(3,3) + b(5,3)*b(3
,3)*b(2,1)*k + 2*b(4,3)*b(4,1)*b(3,3)*u - b(4,3)*b(3,3)*b(1,1)*k)/(b(3,3)**3*(b(
2,1)**2 + b(1,1)**2))USD\\$

\\USD J2(6,3):=( - b(6,3)**2*b(3,3) + b(6,3)*b(5,3)**2 + b(6,3)*b(4,3)**2 - b(3,
3)**3)/(b(3,3)**3*xi(3,6)*(b(2,1)**2 + b(1,1)**2))USD\\$

\\USD J2(6,4):=( - b(6,3)*b(5,3)*b(3,3)*b(2,1)*xi(3,6) - b(6,3)*b(4,3)*b(3,3)*b(
1,1)*xi(3,6) + b(5,3)**3*b(2,1)*xi(3,6) + b(5,3)**2*b(4,3)*b(1,1)*xi(3,6) + b(5,
3)*b(4,3)**2*b(2,1)*xi(3,6) - b(5,3)*b(3,3)**2*b(1,1) + b(4,3)**3*b(1,1)*xi(3,6)
 + b(4,3)*b(3,3)**2*b(2,1))/(b(3,3)**3*(b(2,1)**2 + b(1,1)**2))USD\\$

\\USD J2(6,5):=(u*(b(6,3)*b(5,3)*b(3,3)*b(1,1)*xi(3,6) - b(6,3)*b(4,3)*b(3,3)*b(
2,1)*xi(3,6) - b(5,3)**3*b(1,1)*xi(3,6) + b(5,3)**2*b(4,3)*b(2,1)*xi(3,6) - b(5,
3)*b(4,3)**2*b(1,1)*xi(3,6) - b(5,3)*b(3,3)**2*b(2,1) + b(4,3)**3*b(2,1)*xi(3,6)
 - b(4,3)*b(3,3)**2*b(1,1)))/(b(3,3)**3*(b(2,1)**2 + b(1,1)**2))USD\\$

\\USD J2(6,6):=(xi(3,6)*( - b(6,3)*b(3,3) + b(5,3)**2 + b(4,3)**2))/b(3,3)**2
USD\\$

USD det \Phi:=b(3,3)**4*(b(2,1)**6 + 3*b(2,1)**4*b(1,1)**2 + 3*b(2,1)**2*b(1,1)
**4 + b(1,1)**6)USD$

Hence any   USD J USD in \ref{M14+1general} $

is equivalent to  $

\\$

{\fontsize{8}{10} \selectfont$

\begin{equation}$

\label{M14+1final}$

 J(xi(3,6)) = \begin{pmatrix}$

0&$

-1&$

0&$

0&$

0&$

0\\$

1&$

0&$

0&$

0&$

0&$

0\\$

0&$

0&$

0&$

0&$

0&$

xi(3,6)\\$

0&$

0&$

0&$

0&$

-1&$

0\\$

0&$

0&$

0&$

1&$

0&$

0\\$

0&$

0&$

( - 1)/xi(3,6)&$

0&$

0&$

0\end{pmatrix}$

\end{equation}$

}$

 where USD xi(3,6)= \pm 1.\\USD$

The 2 matrices corresponding to USD xi(3,6)= \pm 1\\USD$

are not equivalent.$

USDUSD J^2 = \begin{pmatrix}$

-1&$

0&$

0&$

0&$

0&$

0\\$

0&$

-1&$

0&$

0&$

0&$

0\\$

0&$

0&$

-1&$

0&$

0&$

0\\$

0&$

0&$

0&$

-1&$

0&$

0\\$

0&$

0&$

0&$

0&$

-1&$

0\\$

0&$

0&$

0&$

0&$

0&$

-1\end{pmatrix}USDUSD$

\\USD det J:=1 USD$

USD Trace J:=0 USD$

\\ check of torsion$

\\Torsion equations to cancel (Latex output) : \\USD$

USD $

zero torsion$

\par Commutation relations of USD \mathfrak{m} : USD$

\\ USD  [\tilde{x}_1,\tilde{x}_3]=tildex_4;\\USD$

\\ USD  [\tilde{x}_1,\tilde{x}_6]= - tildex_5*xi(3,6);\\USD$

\\ USD  [\tilde{x}_2,\tilde{x}_3]=tildex_5;\\USD$

\\ USD  [\tilde{x}_2,\tilde{x}_6]=tildex_4*xi(3,6);\\USD$

\P$

\par Now we check if the condition USD [Jx,y]= J[x,y] USD is satisfied$

USD\forall x,y \in {\mathcal{G}}_{6,{m14_(1)}},USD$

\textit{i.e.} if USD{\mathcal{G}}_{6,{m14_(1)}}USD$

is a \textit{complex} algebra.$

\\USD J[x_j,x_k] \neq [Jx_j,x_k] USD
in the following cases{{{1,4}, - xi(3,6)*x(3)},
{{1,5},x(6)},
{{2,4}, - x(6)},
{{2,5}, - xi(3,6)*x(3)},
{{3,1},x(5)},
{{3,2}, - x(4)},
{{4,1},xi(3,6)*x(3)},
{{4,2}, - x(6)},
{{5,1},x(6)},
{{5,2},xi(3,6)*x(3)},
{{6,1}, - xi(3,6)*x(4)},
{{6,2}, - xi(3,6)*x(5)}}$

\\ \starline$

\end{document}$