\documentclass{article}$ \usepackage{amsmath,amssymb}$ \sloppy$ \begin{document}$ This output from the file \texttt{rprogram6_6.tex}.\\$ Computation of all complex structures on the real Lie Algebra$ USD {\mathcal{G}}_{6,1}.USD$ Case USD xi(2,3) \neq 0 USD.$ \smallskip \par $ Commutation relations for$ USD {\mathcal{G}}_{6,1}:USD\\$ USD[x(1),x(2)]=x(5)USD;$ USD[x(1),x(4)]=x(6)USD;$ USD[x(2),x(3)]=x(6)USD;$ \P$ Nonzero torsion$ \par$ Torsion equations to cancel (Latex output) : \\USD$ {1,2}|1\\(xi(2,2) + xi(1,1))*xi(1,5) - xi(3,1)*xi(1,6) + xi(4,2)*xi(1,6)\\$ {1,2}|2\\(xi(2,2) + xi(1,1))*xi(2,5) - xi(3,1)*xi(2,6) + xi(4,2)*xi(2,6)\\$ {1,2}|3\\(xi(2,2) + xi(1,1))*xi(3,5) - xi(3,6)*xi(3,1) + xi(4,2)*xi(3,6)\\$ {1,2}|4\\(xi(4,2) - xi(3,1))*xi(4,6) + (xi(2,2) + xi(1,1))*xi(4,5)\\$ {1,2}|5\\xi(2,1)*xi(1,2) + 1 - xi(2,2)*xi(1,1) + (xi(2,2) + xi(1,1))*xi(5,5) + ( xi(4,2) - xi(3,1))*xi(5,6)\\$ {1,2}|6\\ - (xi(3,2)*xi(2,1) - xi(3,1)*xi(2,2) - xi(4,1)*xi(1,2) + xi(4,2)*xi(1, 1) - (xi(2,2) + xi(1,1))*xi(6,5)) + (xi(4,2) - xi(3,1))*xi(6,6)\\$ {1,3}|1\\xi(2,3)*xi(1,5) + xi(2,1)*xi(1,6) + xi(4,3)*xi(1,6)\\$ {1,3}|2\\xi(2,6)*xi(2,1) + xi(2,5)*xi(2,3) + xi(4,3)*xi(2,6)\\$ {1,3}|3\\xi(3,6)*xi(2,1) + xi(3,5)*xi(2,3) + xi(4,3)*xi(3,6)\\$ {1,3}|4\\xi(4,6)*xi(4,3) + xi(4,6)*xi(2,1) + xi(4,5)*xi(2,3)\\$ {1,3}|5\\ - (xi(2,3)*xi(1,1) - xi(2,1)*xi(1,3) - xi(5,5)*xi(2,3)) + (xi(4,3) + xi(2,1))*xi(5,6)\\$ {1,3}|6\\ - (xi(3,3)*xi(2,1) - xi(3,1)*xi(2,3) - xi(4,1)*xi(1,3) + xi(4,3)*xi(1, 1) - xi(6,5)*xi(2,3)) + (xi(4,3) + xi(2,1))*xi(6,6)\\$ {1,4}|1\\xi(2,4)*xi(1,5) + xi(1,6)*xi(1,1) + xi(4,4)*xi(1,6)\\$ {1,4}|2\\xi(2,6)*xi(1,1) + xi(2,5)*xi(2,4) + xi(4,4)*xi(2,6)\\$ {1,4}|3\\xi(3,6)*xi(1,1) + xi(3,5)*xi(2,4) + xi(4,4)*xi(3,6)\\$ {1,4}|4\\xi(4,6)*xi(4,4) + xi(4,6)*xi(1,1) + xi(4,5)*xi(2,4)\\$ {1,4}|5\\ - (xi(2,4)*xi(1,1) - xi(2,1)*xi(1,4) - xi(5,5)*xi(2,4)) + (xi(4,4) + xi(1,1))*xi(5,6)\\$ {1,4}|6\\xi(3,1)*xi(2,4) + 1 - xi(3,4)*xi(2,1) + xi(4,1)*xi(1,4) - xi(4,4)*xi(1, 1) + xi(6,5)*xi(2,4) + (xi(4,4) + xi(1,1))*xi(6,6)\\$ {1,5}|1\\xi(4,5)*xi(1,6) + xi(2,5)*xi(1,5)\\$ {1,5}|2\\xi(4,5)*xi(2,6) + xi(2,5)**2\\$ {1,5}|3\\xi(4,5)*xi(3,6) + xi(3,5)*xi(2,5)\\$ {1,5}|4\\xi(4,6)*xi(4,5) + xi(4,5)*xi(2,5)\\$ {1,5}|5\\ - (xi(2,5)*xi(1,1) - xi(2,1)*xi(1,5) - xi(5,5)*xi(2,5)) + xi(5,6)*xi(4 ,5)\\$ {1,5}|6\\ - (xi(3,5)*xi(2,1) - xi(3,1)*xi(2,5) - xi(4,1)*xi(1,5) + xi(4,5)*xi(1, 1) - xi(6,5)*xi(2,5)) + xi(6,6)*xi(4,5)\\$ {1,6}|1\\xi(4,6)*xi(1,6) + xi(2,6)*xi(1,5)\\$ {1,6}|2\\xi(4,6)*xi(2,6) + xi(2,6)*xi(2,5)\\$ {1,6}|3\\xi(4,6)*xi(3,6) + xi(3,5)*xi(2,6)\\$ {1,6}|4\\xi(4,6)**2 + xi(4,5)*xi(2,6)\\$ {1,6}|5\\ - (xi(2,6)*xi(1,1) - xi(2,1)*xi(1,6) - xi(5,5)*xi(2,6)) + xi(5,6)*xi(4 ,6)\\$ {1,6}|6\\ - (xi(3,6)*xi(2,1) - xi(3,1)*xi(2,6) - xi(4,1)*xi(1,6) + xi(4,6)*xi(1, 1) - xi(6,5)*xi(2,6)) + xi(6,6)*xi(4,6)\\$ {2,3}|1\\xi(2,2)*xi(1,6) - xi(1,5)*xi(1,3) + xi(3,3)*xi(1,6)\\$ {2,3}|2\\xi(2,6)*xi(2,2) - xi(2,5)*xi(1,3) + xi(3,3)*xi(2,6)\\$ {2,3}|3\\xi(3,6)*xi(3,3) + xi(3,6)*xi(2,2) - xi(3,5)*xi(1,3)\\$ {2,3}|4\\xi(4,6)*xi(3,3) + xi(4,6)*xi(2,2) - xi(4,5)*xi(1,3)\\$ {2,3}|5\\ - (xi(2,3)*xi(1,2) - xi(2,2)*xi(1,3) + xi(5,5)*xi(1,3)) + (xi(3,3) + xi(2,2))*xi(5,6)\\$ {2,3}|6\\xi(3,2)*xi(2,3) + 1 - xi(3,3)*xi(2,2) + xi(4,2)*xi(1,3) - xi(4,3)*xi(1, 2) - xi(6,5)*xi(1,3) + (xi(3,3) + xi(2,2))*xi(6,6)\\$ {2,4}|1\\xi(1,6)*xi(1,2) - xi(1,5)*xi(1,4) + xi(3,4)*xi(1,6)\\$ {2,4}|2\\xi(2,6)*xi(1,2) - xi(2,5)*xi(1,4) + xi(3,4)*xi(2,6)\\$ {2,4}|3\\xi(3,6)*xi(3,4) + xi(3,6)*xi(1,2) - xi(3,5)*xi(1,4)\\$ {2,4}|4\\xi(4,6)*xi(3,4) + xi(4,6)*xi(1,2) - xi(4,5)*xi(1,4)\\$ {2,4}|5\\ - (xi(2,4)*xi(1,2) - xi(2,2)*xi(1,4) + xi(5,5)*xi(1,4)) + (xi(3,4) + xi(1,2))*xi(5,6)\\$ {2,4}|6\\ - (xi(3,4)*xi(2,2) - xi(3,2)*xi(2,4) - xi(4,2)*xi(1,4) + xi(4,4)*xi(1, 2) + xi(6,5)*xi(1,4)) + (xi(3,4) + xi(1,2))*xi(6,6)\\$ {2,5}|1\\xi(3,5)*xi(1,6) - xi(1,5)**2\\$ {2,5}|2\\xi(3,5)*xi(2,6) - xi(2,5)*xi(1,5)\\$ {2,5}|3\\xi(3,6)*xi(3,5) - xi(3,5)*xi(1,5)\\$ {2,5}|4\\xi(4,6)*xi(3,5) - xi(4,5)*xi(1,5)\\$ {2,5}|5\\ - (xi(2,5)*xi(1,2) - xi(2,2)*xi(1,5) + xi(5,5)*xi(1,5)) + xi(5,6)*xi(3 ,5)\\$ {2,5}|6\\ - (xi(3,5)*xi(2,2) - xi(3,2)*xi(2,5) - xi(4,2)*xi(1,5) + xi(4,5)*xi(1, 2) + xi(6,5)*xi(1,5)) + xi(6,6)*xi(3,5)\\$ {2,6}|1\\xi(3,6)*xi(1,6) - xi(1,6)*xi(1,5)\\$ {2,6}|2\\xi(3,6)*xi(2,6) - xi(2,5)*xi(1,6)\\$ {2,6}|3\\xi(3,6)**2 - xi(3,5)*xi(1,6)\\$ {2,6}|4\\xi(4,6)*xi(3,6) - xi(4,5)*xi(1,6)\\$ {2,6}|5\\ - (xi(2,6)*xi(1,2) - xi(2,2)*xi(1,6) + xi(5,5)*xi(1,6)) + xi(5,6)*xi(3 ,6)\\$ {2,6}|6\\ - (xi(3,6)*xi(2,2) - xi(3,2)*xi(2,6) - xi(4,2)*xi(1,6) + xi(4,6)*xi(1, 2) + xi(6,5)*xi(1,6)) + xi(6,6)*xi(3,6)\\$ {3,4}|1\\ - xi(2,4)*xi(1,6) + xi(1,6)*xi(1,3)\\$ {3,4}|2\\ - xi(2,6)*xi(2,4) + xi(2,6)*xi(1,3)\\$ {3,4}|3\\ - xi(3,6)*xi(2,4) + xi(3,6)*xi(1,3)\\$ {3,4}|4\\ - xi(4,6)*xi(2,4) + xi(4,6)*xi(1,3)\\$ {3,4}|5\\ - (xi(2,4)*xi(1,3) - xi(2,3)*xi(1,4)) - (xi(2,4) - xi(1,3))*xi(5,6)\\$ {3,4}|6\\ - (xi(3,4)*xi(2,3) - xi(3,3)*xi(2,4) - xi(4,3)*xi(1,4) + xi(4,4)*xi(1, 3)) - (xi(2,4) - xi(1,3))*xi(6,6)\\$ {3,5}|1\\ - xi(2,5)*xi(1,6)\\$ {3,5}|2\\ - xi(2,6)*xi(2,5)\\$ {3,5}|3\\ - xi(3,6)*xi(2,5)\\$ {3,5}|4\\ - xi(4,6)*xi(2,5)\\$ {3,5}|5\\ - (xi(2,5)*xi(1,3) - xi(2,3)*xi(1,5)) - xi(5,6)*xi(2,5)\\$ {3,5}|6\\ - (xi(3,5)*xi(2,3) - xi(3,3)*xi(2,5) - xi(4,3)*xi(1,5) + xi(4,5)*xi(1, 3)) - xi(6,6)*xi(2,5)\\$ {3,6}|1\\ - xi(2,6)*xi(1,6)\\$ {3,6}|2\\ - xi(2,6)**2\\$ {3,6}|3\\ - xi(3,6)*xi(2,6)\\$ {3,6}|4\\ - xi(4,6)*xi(2,6)\\$ {3,6}|5\\ - (xi(2,6)*xi(1,3) - xi(2,3)*xi(1,6)) - xi(5,6)*xi(2,6)\\$ {3,6}|6\\ - (xi(3,6)*xi(2,3) - xi(3,3)*xi(2,6) - xi(4,3)*xi(1,6) + xi(4,6)*xi(1, 3)) - xi(6,6)*xi(2,6)\\$ {4,5}|1\\ - xi(1,6)*xi(1,5)\\$ {4,5}|2\\ - xi(2,6)*xi(1,5)\\$ {4,5}|3\\ - xi(3,6)*xi(1,5)\\$ {4,5}|4\\ - xi(4,6)*xi(1,5)\\$ {4,5}|5\\ - (xi(2,5)*xi(1,4) - xi(2,4)*xi(1,5)) - xi(5,6)*xi(1,5)\\$ {4,5}|6\\ - (xi(3,5)*xi(2,4) - xi(3,4)*xi(2,5) - xi(4,4)*xi(1,5) + xi(4,5)*xi(1, 4)) - xi(6,6)*xi(1,5)\\$ {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(4,6)*xi(1,6)\\$ {4,6}|5\\ - (xi(2,6)*xi(1,4) - xi(2,4)*xi(1,6)) - xi(5,6)*xi(1,6)\\$ {4,6}|6\\ - (xi(3,6)*xi(2,4) - xi(3,4)*xi(2,6) - xi(4,4)*xi(1,6) + xi(4,6)*xi(1, 4)) - xi(6,6)*xi(1,6)\\$ {5,6}|5\\ - xi(2,6)*xi(1,5) + xi(2,5)*xi(1,6)\\$ {5,6}|6\\ - (xi(3,6)*xi(2,5) - xi(3,5)*xi(2,6) - xi(4,5)*xi(1,6)) - xi(4,6)*xi(1 ,5)\\$ USD$ \par Simultaneous resolution of the nonzero torsion equations and the matrix$ equation USD J^2 = -I . USD$ \\ One first gets$ \\ from equation USD36|2USD :$ \\ USD xi(2,6):=0USD$ \\ and from equation USD46|1USD :$ \\ USD xi(1,6):=0USD$ \par With these values, \textit{Reduce} computes again all equations.$ then, one gets from equation USD15|2USD :$ \\ USD xi(2,5):=0USD$ \\ and from equation USD16|4USD :$ \\ USD xi(4,6):=0USD$ \\ and from equation USD25|1USD :$ \\ USD xi(1,5):=0USD$ \\ and from equation USD26|3USD :$ \\ USD xi(3,6):=0USD$ \par With these values, \textit{Reduce} computes again all equations.$ Then the 6x6 entry in USD J**2 USD is $ USD J**2^6_6=xi(6,6)**2 + xi(6,5)*xi(5,6);USD\\$ Hence USD xi(5,6) \neq 0. USD$ then, one gets from equation USD15|5USD :$ \\ USD xi(4,5):=0USD$ \\ and from equation USD25|5USD :$ \\ USD xi(3,5):=0USD$ \par With these values, \textit{Reduce} computes again all equations.$ Then the 6x5 entry in USD J**2 USD is $ USD J**2^6_5=xi(6,5)*(xi(6,6) + xi(5,5));USD\\$ Hence as USD xi(5,6) \neq 0, USD$ one gets USD xi(6,6)=-xi(5,5) , USD$ \\ USD xi(6,6):= - xi(5,5)USD$ \par With these values, \textit{Reduce} computes again all equations.$ Then the 6x6 entry in USD J**2 USD is $ USD J**2^6_6=xi(5,5)**2 + xi(6,5)*xi(5,6);USD\\$ Hence USD xi(5,6) =(-1-xi(5,5)**2)/xi(6,5). USD$ \\ USD xi(5,6):=( - (xi(5,5)**2 + 1))/xi(6,5)USD$ \par With these values, \textit{Reduce} computes again all equations.$ Then from the 6x1 entry in USD J**2 USD one gets,$ \\ USD xi(5,1):=( - xi(6,4)*xi(4,1) - xi(6,3)*xi(3,1) - xi(6,2)*xi(2,1) + xi(6,1 )*xi(5,5) - xi(6,1)*xi(1,1))/xi(6,5)USD$ and from the 6x2 entry in USD J**2 USD one gets,$ \\ USD xi(5,2):=( - xi(6,4)*xi(4,2) - xi(6,3)*xi(3,2) + xi(6,2)*xi(5,5) - xi(6,2 )*xi(2,2) - xi(6,1)*xi(1,2))/xi(6,5)USD$ and from the 6x3 entry in USD J**2 USD one gets,$ \\ USD xi(5,3):=( - xi(6,4)*xi(4,3) + xi(6,3)*xi(5,5) - xi(6,3)*xi(3,3) - xi(6,2 )*xi(2,3) - xi(6,1)*xi(1,3))/xi(6,5)USD$ and from the 6x4 entry in USD J**2 USD one gets,$ \\ USD xi(5,4):=(xi(6,4)*xi(5,5) - xi(6,4)*xi(4,4) - xi(6,3)*xi(3,4) - xi(6,2)* xi(2,4) - xi(6,1)*xi(1,4))/xi(6,5)USD$ \par With these values, \textit{Reduce} computes again all equations.$ then, one gets from equation USD12|5USD :$ \\ USD xi(3,1):=( - xi(6,5)*xi(5,5)*xi(2,2) - xi(6,5)*xi(5,5)*xi(1,1) + xi(6,5)* xi(2,2)*xi(1,1) - xi(6,5)*xi(2,1)*xi(1,2) - xi(6,5) + xi(5,5)**2*xi(4,2) + xi(4, 2))/(xi(5,5)**2 + 1)USD$ \par With these values, \textit{Reduce} computes again all equations.$ then, one gets from equation USD13|5USD :$ \\ USD xi(4,3):=(xi(6,5)*xi(5,5)*xi(2,3) - xi(6,5)*xi(2,3)*xi(1,1) + xi(6,5)*xi( 2,1)*xi(1,3) - xi(5,5)**2*xi(2,1) - xi(2,1))/(xi(5,5)**2 + 1)USD$ \par With these values, \textit{Reduce} computes again all equations.$ then, one gets from equation USD14|5USD :$ \\ USD xi(4,4):=(xi(6,5)*xi(5,5)*xi(2,4) - xi(6,5)*xi(2,4)*xi(1,1) + xi(6,5)*xi( 2,1)*xi(1,4) - xi(5,5)**2*xi(1,1) - xi(1,1))/(xi(5,5)**2 + 1)USD$ \par With these values, \textit{Reduce} computes again all equations.$ then, one gets from equation USD14|5USD :$ \\ USD xi(3,3):=( - xi(6,5)*xi(5,5)*xi(1,3) - xi(6,5)*xi(2,3)*xi(1,2) + xi(6,5)* xi(2,2)*xi(1,3) - xi(5,5)**2*xi(2,2) - xi(2,2))/(xi(5,5)**2 + 1)USD$ \par With these values, \textit{Reduce} computes again all equations.$ then, one gets from equation USD24|5USD :$ \\ USD xi(3,4):=( - xi(6,5)*xi(5,5)*xi(1,4) - xi(6,5)*xi(2,4)*xi(1,2) + xi(6,5)* xi(2,2)*xi(1,4) - xi(5,5)**2*xi(1,2) - xi(1,2))/(xi(5,5)**2 + 1)\\USD$ At this stage, the 2x2 entry in USD J**2 USD is :$ !U!S!D! ! {!J**2}^2_2=xi(2,2)**2! +! xi(2,1)*xi(1,2)! +! xi(3,2)*xi(2,3)! +! xi( 4,2)*xi(2,\ 4) !U!S!D$ Hence USD xi(2,1)^2+xi(2,3)^2+xi^2,4)^2 \neq 0 USD$ Suppose USD xi(2,3) \neq 0 USD$ then, one gets from equation USD34|5USD :$ \\ USD xi(1,4):=(xi(6,5)*xi(2,4)*xi(1,3) - xi(5,5)**2*xi(2,4) + xi(5,5)**2*xi(1, 3) - xi(2,4) + xi(1,3))/(xi(6,5)*xi(2,3))\\USD$ then, one gets from equation USD13|6USD :$ \\ USD xi(4,2):=(xi(6,5)*xi(5,5)*xi(2,3)*xi(2,2) + xi(6,5)*xi(5,5)*xi(2,3)*xi(1, 1) - xi(6,5)*xi(2,3)*xi(2,2)*xi(1,1) - xi(6,5)*xi(2,3)*xi(1,1)**2 + xi(6,5)*xi(2 ,2)*xi(2,1)*xi(1,3) + xi(6,5)*xi(2,1)*xi(1,3)*xi(1,1) - xi(5,5)**2*xi(4,1)*xi(1, 3) - xi(5,5)**2*xi(2,2)*xi(2,1) - xi(5,5)**2*xi(2,1)*xi(1,1) - xi(4,1)*xi(1,3) - xi(2,2)*xi(2,1) - xi(2,1)*xi(1,1))/(xi(2,3)*(xi(5,5)**2 + 1))\\USD$ \\ USD xi(1,2):=(xi(6,5)*xi(5,5)*xi(2,4)*xi(2,3) - xi(6,5)*xi(5,5)*xi(2,3)*xi(1, 3) - xi(6,5)*xi(2,4)*xi(2,3)*xi(1,1) + xi(6,5)*xi(2,4)*xi(2,1)*xi(1,3) + xi(6,5) *xi(2,3)*xi(2,2)*xi(1,3) - xi(5,5)**2*xi(2,4)*xi(2,1) + xi(5,5)**2*xi(2,1)*xi(1, 3) - xi(2,4)*xi(2,1) + xi(2,1)*xi(1,3))/(xi(6,5)*xi(2,3)**2)\\USD$ then, one gets from equation USD23|6USD :$ \\ USD xi(3,2):=( - xi(6,5)**2*xi(5,5)*xi(2,4)*xi(2,3)**2*xi(2,2) - xi(6,5)**2* xi(5,5)*xi(2,4)*xi(2,3)**2*xi(1,1) + xi(6,5)**2*xi(5,5)*xi(2,4)*xi(2,3)*xi(2,1)* xi(1,3) - xi(6,5)**2*xi(5,5)*xi(2,3)*xi(2,1)*xi(1,3)**2 + xi(6,5)**2*xi(2,4)*xi( 2,3)**2*xi(2,2)*xi(1,1) + xi(6,5)**2*xi(2,4)*xi(2,3)**2*xi(1,1)**2 - xi(6,5)**2* xi(2,4)*xi(2,3)*xi(2,2)*xi(2,1)*xi(1,3) - 2*xi(6,5)**2*xi(2,4)*xi(2,3)*xi(2,1)* xi(1,3)*xi(1,1) + xi(6,5)**2*xi(2,4)*xi(2,1)**2*xi(1,3)**2 + xi(6,5)**2*xi(2,3) **2*xi(1,3)*xi(1,1)**2 + xi(6,5)**2*xi(2,3)**2*xi(1,3) - xi(6,5)**2*xi(2,3)*xi(2 ,1)*xi(1,3)**2*xi(1,1) - xi(6,5)*xi(5,5)**3*xi(2,4)*xi(2,3)*xi(2,1) + xi(6,5)*xi (5,5)**3*xi(2,3)*xi(2,1)*xi(1,3) + xi(6,5)*xi(5,5)**2*xi(4,1)*xi(2,3)*xi(1,3)**2 + xi(6,5)*xi(5,5)**2*xi(2,4)*xi(2,3)*xi(2,2)*xi(2,1) + 2*xi(6,5)*xi(5,5)**2*xi( 2,4)*xi(2,3)*xi(2,1)*xi(1,1) - 2*xi(6,5)*xi(5,5)**2*xi(2,4)*xi(2,1)**2*xi(1,3) - xi(6,5)*xi(5,5)**2*xi(2,3)**2*xi(2,2)**2 - xi(6,5)*xi(5,5)**2*xi(2,3)**2 - xi(6 ,5)*xi(5,5)**2*xi(2,3)*xi(2,2)*xi(2,1)*xi(1,3) + xi(6,5)*xi(5,5)**2*xi(2,1)**2* xi(1,3)**2 - xi(6,5)*xi(5,5)*xi(2,4)*xi(2,3)*xi(2,1) + xi(6,5)*xi(5,5)*xi(2,3)* xi(2,1)*xi(1,3) + xi(6,5)*xi(4,1)*xi(2,3)*xi(1,3)**2 + xi(6,5)*xi(2,4)*xi(2,3)* xi(2,2)*xi(2,1) + 2*xi(6,5)*xi(2,4)*xi(2,3)*xi(2,1)*xi(1,1) - 2*xi(6,5)*xi(2,4)* xi(2,1)**2*xi(1,3) - xi(6,5)*xi(2,3)**2*xi(2,2)**2 - xi(6,5)*xi(2,3)**2 - xi(6,5 )*xi(2,3)*xi(2,2)*xi(2,1)*xi(1,3) + xi(6,5)*xi(2,1)**2*xi(1,3)**2 + xi(5,5)**4* xi(2,4)*xi(2,1)**2 - xi(5,5)**4*xi(2,1)**2*xi(1,3) + 2*xi(5,5)**2*xi(2,4)*xi(2,1 )**2 - 2*xi(5,5)**2*xi(2,1)**2*xi(1,3) + xi(2,4)*xi(2,1)**2 - xi(2,1)**2*xi(1,3) )/(xi(6,5)*xi(2,3)**3*(xi(5,5)**2 + 1))\\USD$ If we suppose USD xi(2,4) =xi(2,3) USD$ Then we get that equation USD14|6 USD reads$ USD (xi(2,3)xi(1,1)-xi(2,1)xi(1,3))**2 +xi(2,3)**2=0USD$ Hence this case is impossible.$ that i : USD xi(2,4) \neq xi(2,3) USD$ Then, the 2x1 entry in USD J**2 USD yields :$ \\ USD xi(4,1):=(xi(6,5)*xi(5,5)*xi(2,4)*xi(2,3)*xi(2,1) - xi(6,5)*xi(5,5)*xi(2, 3)*xi(2,1)*xi(1,3) - xi(6,5)*xi(2,4)*xi(2,3)*xi(2,1)*xi(1,1) + xi(6,5)*xi(2,4)* xi(2,1)**2*xi(1,3) + xi(6,5)*xi(2,3)**2*xi(1,1)**2 + xi(6,5)*xi(2,3)**2 - xi(6,5 )*xi(2,3)*xi(2,1)*xi(1,3)*xi(1,1) - xi(5,5)**2*xi(2,4)*xi(2,1)**2 + xi(5,5)**2* xi(2,1)**2*xi(1,3) - xi(2,4)*xi(2,1)**2 + xi(2,1)**2*xi(1,3))/(xi(2,3)*(xi(5,5) **2*xi(2,4) - xi(5,5)**2*xi(1,3) + xi(2,4) - xi(1,3)))\\USD$ \par Now the nonzero torsion equations left are :$ {{{{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},5},0}, {{{5,6},6},0}}$ \par The matrix USD J USD is :\\$ USD J^1_1=xi(1,1);USD\\$ USD J^1_2=(xi(6,5)*xi(5,5)*xi(2,4)*xi(2,3) - xi(6,5)*xi(5,5)*xi(2,3)*xi(1,3) - xi(6,5)*xi(2,4)*xi(2,3)*xi(1,1) + xi(6,5)*xi(2,4)*xi(2,1)*xi(1,3) + xi(6,5)*xi(2 ,3)*xi(2,2)*xi(1,3) - xi(5,5)**2*xi(2,4)*xi(2,1) + xi(5,5)**2*xi(2,1)*xi(1,3) - xi(2,4)*xi(2,1) + xi(2,1)*xi(1,3))/(xi(6,5)*xi(2,3)**2);USD\\$ USD J^1_3=xi(1,3);USD\\$ USD J^1_4=(xi(6,5)*xi(2,4)*xi(1,3) - xi(5,5)**2*xi(2,4) + xi(5,5)**2*xi(1,3) - xi(2,4) + xi(1,3))/(xi(6,5)*xi(2,3));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=xi(2,2);USD\\$ USD J^2_3=xi(2,3);USD\\$ USD J^2_4=xi(2,4);USD\\$ USD J^2_5=0;USD\\$ USD J^2_6=0;USD\\$ USD J^3_1=( - xi(6,5)*xi(5,5)**3*xi(2,4)**2*xi(2,3)*xi(2,1) + xi(6,5)*xi(5,5)** 3*xi(2,4)*xi(2,3)*xi(2,1)*xi(1,3) + xi(6,5)*xi(5,5)**2*xi(2,4)**2*xi(2,3)*xi(2,1 )*xi(1,1) - xi(6,5)*xi(5,5)**2*xi(2,4)**2*xi(2,1)**2*xi(1,3) - xi(6,5)*xi(5,5)** 2*xi(2,4)*xi(2,3)**2*xi(1,1)**2 - xi(6,5)*xi(5,5)**2*xi(2,4)*xi(2,3)**2 + xi(6,5 )*xi(5,5)**2*xi(2,4)*xi(2,3)*xi(2,1)*xi(1,3)*xi(1,1) - xi(6,5)*xi(5,5)*xi(2,4)** 2*xi(2,3)*xi(2,1) + xi(6,5)*xi(5,5)*xi(2,4)*xi(2,3)*xi(2,1)*xi(1,3) + xi(6,5)*xi (2,4)**2*xi(2,3)*xi(2,1)*xi(1,1) - xi(6,5)*xi(2,4)**2*xi(2,1)**2*xi(1,3) - xi(6, 5)*xi(2,4)*xi(2,3)**2*xi(1,1)**2 - xi(6,5)*xi(2,4)*xi(2,3)**2 + xi(6,5)*xi(2,4)* xi(2,3)*xi(2,1)*xi(1,3)*xi(1,1) + xi(5,5)**4*xi(2,4)**2*xi(2,1)**2 - xi(5,5)**4* xi(2,4)*xi(2,3)*xi(2,2)*xi(2,1) - xi(5,5)**4*xi(2,4)*xi(2,3)*xi(2,1)*xi(1,1) - xi(5,5)**4*xi(2,4)*xi(2,1)**2*xi(1,3) + xi(5,5)**4*xi(2,3)*xi(2,2)*xi(2,1)*xi(1, 3) + xi(5,5)**4*xi(2,3)*xi(2,1)*xi(1,3)*xi(1,1) + 2*xi(5,5)**2*xi(2,4)**2*xi(2,1 )**2 - 2*xi(5,5)**2*xi(2,4)*xi(2,3)*xi(2,2)*xi(2,1) - 2*xi(5,5)**2*xi(2,4)*xi(2, 3)*xi(2,1)*xi(1,1) - 2*xi(5,5)**2*xi(2,4)*xi(2,1)**2*xi(1,3) + 2*xi(5,5)**2*xi(2 ,3)*xi(2,2)*xi(2,1)*xi(1,3) + 2*xi(5,5)**2*xi(2,3)*xi(2,1)*xi(1,3)*xi(1,1) + xi( 2,4)**2*xi(2,1)**2 - xi(2,4)*xi(2,3)*xi(2,2)*xi(2,1) - xi(2,4)*xi(2,3)*xi(2,1)* xi(1,1) - xi(2,4)*xi(2,1)**2*xi(1,3) + xi(2,3)*xi(2,2)*xi(2,1)*xi(1,3) + xi(2,3) *xi(2,1)*xi(1,3)*xi(1,1))/(xi(2,3)**2*(xi(5,5)**4*xi(2,4) - xi(5,5)**4*xi(1,3) + 2*xi(5,5)**2*xi(2,4) - 2*xi(5,5)**2*xi(1,3) + xi(2,4) - xi(1,3)));USD\\$ USD J^3_2=( - xi(6,5)**2*xi(5,5)**3*xi(2,4)**2*xi(2,3)**2*xi(2,2) - xi(6,5)**2* xi(5,5)**3*xi(2,4)**2*xi(2,3)**2*xi(1,1) + xi(6,5)**2*xi(5,5)**3*xi(2,4)**2*xi(2 ,3)*xi(2,1)*xi(1,3) + xi(6,5)**2*xi(5,5)**3*xi(2,4)*xi(2,3)**2*xi(2,2)*xi(1,3) + xi(6,5)**2*xi(5,5)**3*xi(2,4)*xi(2,3)**2*xi(1,3)*xi(1,1) - xi(6,5)**2*xi(5,5)** 3*xi(2,4)*xi(2,3)*xi(2,1)*xi(1,3)**2 + xi(6,5)**2*xi(5,5)**2*xi(2,4)**2*xi(2,3) **2*xi(2,2)*xi(1,1) + xi(6,5)**2*xi(5,5)**2*xi(2,4)**2*xi(2,3)**2*xi(1,1)**2 - xi(6,5)**2*xi(5,5)**2*xi(2,4)**2*xi(2,3)*xi(2,2)*xi(2,1)*xi(1,3) - 2*xi(6,5)**2* xi(5,5)**2*xi(2,4)**2*xi(2,3)*xi(2,1)*xi(1,3)*xi(1,1) + xi(6,5)**2*xi(5,5)**2*xi (2,4)**2*xi(2,1)**2*xi(1,3)**2 - xi(6,5)**2*xi(5,5)**2*xi(2,4)*xi(2,3)**2*xi(2,2 )*xi(1,3)*xi(1,1) + xi(6,5)**2*xi(5,5)**2*xi(2,4)*xi(2,3)**2*xi(1,3) + xi(6,5)** 2*xi(5,5)**2*xi(2,4)*xi(2,3)*xi(2,2)*xi(2,1)*xi(1,3)**2 - xi(6,5)**2*xi(5,5)*xi( 2,4)**2*xi(2,3)**2*xi(2,2) - xi(6,5)**2*xi(5,5)*xi(2,4)**2*xi(2,3)**2*xi(1,1) + xi(6,5)**2*xi(5,5)*xi(2,4)**2*xi(2,3)*xi(2,1)*xi(1,3) + xi(6,5)**2*xi(5,5)*xi(2, 4)*xi(2,3)**2*xi(2,2)*xi(1,3) + xi(6,5)**2*xi(5,5)*xi(2,4)*xi(2,3)**2*xi(1,3)*xi (1,1) - xi(6,5)**2*xi(5,5)*xi(2,4)*xi(2,3)*xi(2,1)*xi(1,3)**2 + xi(6,5)**2*xi(2, 4)**2*xi(2,3)**2*xi(2,2)*xi(1,1) + xi(6,5)**2*xi(2,4)**2*xi(2,3)**2*xi(1,1)**2 - xi(6,5)**2*xi(2,4)**2*xi(2,3)*xi(2,2)*xi(2,1)*xi(1,3) - 2*xi(6,5)**2*xi(2,4)**2 *xi(2,3)*xi(2,1)*xi(1,3)*xi(1,1) + xi(6,5)**2*xi(2,4)**2*xi(2,1)**2*xi(1,3)**2 - xi(6,5)**2*xi(2,4)*xi(2,3)**2*xi(2,2)*xi(1,3)*xi(1,1) + xi(6,5)**2*xi(2,4)*xi(2 ,3)**2*xi(1,3) + xi(6,5)**2*xi(2,4)*xi(2,3)*xi(2,2)*xi(2,1)*xi(1,3)**2 - xi(6,5) *xi(5,5)**5*xi(2,4)**2*xi(2,3)*xi(2,1) + 2*xi(6,5)*xi(5,5)**5*xi(2,4)*xi(2,3)*xi (2,1)*xi(1,3) - xi(6,5)*xi(5,5)**5*xi(2,3)*xi(2,1)*xi(1,3)**2 + xi(6,5)*xi(5,5) **4*xi(2,4)**2*xi(2,3)*xi(2,2)*xi(2,1) + 2*xi(6,5)*xi(5,5)**4*xi(2,4)**2*xi(2,3) *xi(2,1)*xi(1,1) - 2*xi(6,5)*xi(5,5)**4*xi(2,4)**2*xi(2,1)**2*xi(1,3) - xi(6,5)* xi(5,5)**4*xi(2,4)*xi(2,3)**2*xi(2,2)**2 - xi(6,5)*xi(5,5)**4*xi(2,4)*xi(2,3)**2 - 2*xi(6,5)*xi(5,5)**4*xi(2,4)*xi(2,3)*xi(2,2)*xi(2,1)*xi(1,3) - 2*xi(6,5)*xi(5 ,5)**4*xi(2,4)*xi(2,3)*xi(2,1)*xi(1,3)*xi(1,1) + 2*xi(6,5)*xi(5,5)**4*xi(2,4)*xi (2,1)**2*xi(1,3)**2 + xi(6,5)*xi(5,5)**4*xi(2,3)**2*xi(2,2)**2*xi(1,3) + xi(6,5) *xi(5,5)**4*xi(2,3)**2*xi(1,3) + xi(6,5)*xi(5,5)**4*xi(2,3)*xi(2,2)*xi(2,1)*xi(1 ,3)**2 - 2*xi(6,5)*xi(5,5)**3*xi(2,4)**2*xi(2,3)*xi(2,1) + 4*xi(6,5)*xi(5,5)**3* xi(2,4)*xi(2,3)*xi(2,1)*xi(1,3) - 2*xi(6,5)*xi(5,5)**3*xi(2,3)*xi(2,1)*xi(1,3)** 2 + 2*xi(6,5)*xi(5,5)**2*xi(2,4)**2*xi(2,3)*xi(2,2)*xi(2,1) + 4*xi(6,5)*xi(5,5) **2*xi(2,4)**2*xi(2,3)*xi(2,1)*xi(1,1) - 4*xi(6,5)*xi(5,5)**2*xi(2,4)**2*xi(2,1) **2*xi(1,3) - 2*xi(6,5)*xi(5,5)**2*xi(2,4)*xi(2,3)**2*xi(2,2)**2 - 2*xi(6,5)*xi( 5,5)**2*xi(2,4)*xi(2,3)**2 - 4*xi(6,5)*xi(5,5)**2*xi(2,4)*xi(2,3)*xi(2,2)*xi(2,1 )*xi(1,3) - 4*xi(6,5)*xi(5,5)**2*xi(2,4)*xi(2,3)*xi(2,1)*xi(1,3)*xi(1,1) + 4*xi( 6,5)*xi(5,5)**2*xi(2,4)*xi(2,1)**2*xi(1,3)**2 + 2*xi(6,5)*xi(5,5)**2*xi(2,3)**2* xi(2,2)**2*xi(1,3) + 2*xi(6,5)*xi(5,5)**2*xi(2,3)**2*xi(1,3) + 2*xi(6,5)*xi(5,5) **2*xi(2,3)*xi(2,2)*xi(2,1)*xi(1,3)**2 - xi(6,5)*xi(5,5)*xi(2,4)**2*xi(2,3)*xi(2 ,1) + 2*xi(6,5)*xi(5,5)*xi(2,4)*xi(2,3)*xi(2,1)*xi(1,3) - xi(6,5)*xi(5,5)*xi(2,3 )*xi(2,1)*xi(1,3)**2 + xi(6,5)*xi(2,4)**2*xi(2,3)*xi(2,2)*xi(2,1) + 2*xi(6,5)*xi (2,4)**2*xi(2,3)*xi(2,1)*xi(1,1) - 2*xi(6,5)*xi(2,4)**2*xi(2,1)**2*xi(1,3) - xi( 6,5)*xi(2,4)*xi(2,3)**2*xi(2,2)**2 - xi(6,5)*xi(2,4)*xi(2,3)**2 - 2*xi(6,5)*xi(2 ,4)*xi(2,3)*xi(2,2)*xi(2,1)*xi(1,3) - 2*xi(6,5)*xi(2,4)*xi(2,3)*xi(2,1)*xi(1,3)* xi(1,1) + 2*xi(6,5)*xi(2,4)*xi(2,1)**2*xi(1,3)**2 + xi(6,5)*xi(2,3)**2*xi(2,2)** 2*xi(1,3) + xi(6,5)*xi(2,3)**2*xi(1,3) + xi(6,5)*xi(2,3)*xi(2,2)*xi(2,1)*xi(1,3) **2 + xi(5,5)**6*xi(2,4)**2*xi(2,1)**2 - 2*xi(5,5)**6*xi(2,4)*xi(2,1)**2*xi(1,3) + xi(5,5)**6*xi(2,1)**2*xi(1,3)**2 + 3*xi(5,5)**4*xi(2,4)**2*xi(2,1)**2 - 6*xi( 5,5)**4*xi(2,4)*xi(2,1)**2*xi(1,3) + 3*xi(5,5)**4*xi(2,1)**2*xi(1,3)**2 + 3*xi(5 ,5)**2*xi(2,4)**2*xi(2,1)**2 - 6*xi(5,5)**2*xi(2,4)*xi(2,1)**2*xi(1,3) + 3*xi(5, 5)**2*xi(2,1)**2*xi(1,3)**2 + xi(2,4)**2*xi(2,1)**2 - 2*xi(2,4)*xi(2,1)**2*xi(1, 3) + xi(2,1)**2*xi(1,3)**2)/(xi(6,5)*xi(2,3)**3*(xi(5,5)**4*xi(2,4) - xi(5,5)**4 *xi(1,3) + 2*xi(5,5)**2*xi(2,4) - 2*xi(5,5)**2*xi(1,3) + xi(2,4) - xi(1,3))) ;USD\\$ USD J^3_3=( - xi(6,5)*xi(5,5)*xi(2,4)*xi(2,3) + xi(6,5)*xi(2,4)*xi(2,3)*xi(1,1) - xi(6,5)*xi(2,4)*xi(2,1)*xi(1,3) + xi(5,5)**2*xi(2,4)*xi(2,1) - xi(5,5)**2*xi( 2,3)*xi(2,2) - xi(5,5)**2*xi(2,1)*xi(1,3) + xi(2,4)*xi(2,1) - xi(2,3)*xi(2,2) - xi(2,1)*xi(1,3))/(xi(2,3)*(xi(5,5)**2 + 1));USD\\$ USD J^3_4=( - xi(6,5)**2*xi(5,5)*xi(2,4)**2*xi(2,3) + xi(6,5)**2*xi(2,4)**2*xi( 2,3)*xi(1,1) - xi(6,5)**2*xi(2,4)**2*xi(2,1)*xi(1,3) + xi(6,5)*xi(5,5)**2*xi(2,4 )**2*xi(2,1) - xi(6,5)*xi(5,5)**2*xi(2,4)*xi(2,3)*xi(2,2) + xi(6,5)*xi(5,5)**2* xi(2,4)*xi(2,3)*xi(1,1) - 2*xi(6,5)*xi(5,5)**2*xi(2,4)*xi(2,1)*xi(1,3) + xi(6,5) *xi(2,4)**2*xi(2,1) - xi(6,5)*xi(2,4)*xi(2,3)*xi(2,2) + xi(6,5)*xi(2,4)*xi(2,3)* xi(1,1) - 2*xi(6,5)*xi(2,4)*xi(2,1)*xi(1,3) + xi(5,5)**4*xi(2,4)*xi(2,1) - xi(5, 5)**4*xi(2,1)*xi(1,3) + 2*xi(5,5)**2*xi(2,4)*xi(2,1) - 2*xi(5,5)**2*xi(2,1)*xi(1 ,3) + xi(2,4)*xi(2,1) - xi(2,1)*xi(1,3))/(xi(6,5)*xi(2,3)**2*(xi(5,5)**2 + 1)) ;USD\\$ USD J^3_5=0;USD\\$ USD J^3_6=0;USD\\$ USD J^4_1=(xi(6,5)*xi(5,5)*xi(2,4)*xi(2,3)*xi(2,1) - xi(6,5)*xi(5,5)*xi(2,3)*xi (2,1)*xi(1,3) - xi(6,5)*xi(2,4)*xi(2,3)*xi(2,1)*xi(1,1) + xi(6,5)*xi(2,4)*xi(2,1 )**2*xi(1,3) + xi(6,5)*xi(2,3)**2*xi(1,1)**2 + xi(6,5)*xi(2,3)**2 - xi(6,5)*xi(2 ,3)*xi(2,1)*xi(1,3)*xi(1,1) - xi(5,5)**2*xi(2,4)*xi(2,1)**2 + xi(5,5)**2*xi(2,1) **2*xi(1,3) - xi(2,4)*xi(2,1)**2 + xi(2,1)**2*xi(1,3))/(xi(2,3)*(xi(5,5)**2*xi(2 ,4) - xi(5,5)**2*xi(1,3) + xi(2,4) - xi(1,3)));USD\\$ USD J^4_2=(xi(6,5)*xi(5,5)**3*xi(2,4)*xi(2,3)**2*xi(2,2) + xi(6,5)*xi(5,5)**3* xi(2,4)*xi(2,3)**2*xi(1,1) - xi(6,5)*xi(5,5)**3*xi(2,4)*xi(2,3)*xi(2,1)*xi(1,3) - xi(6,5)*xi(5,5)**3*xi(2,3)**2*xi(2,2)*xi(1,3) - xi(6,5)*xi(5,5)**3*xi(2,3)**2* xi(1,3)*xi(1,1) + xi(6,5)*xi(5,5)**3*xi(2,3)*xi(2,1)*xi(1,3)**2 - xi(6,5)*xi(5,5 )**2*xi(2,4)*xi(2,3)**2*xi(2,2)*xi(1,1) - xi(6,5)*xi(5,5)**2*xi(2,4)*xi(2,3)**2* xi(1,1)**2 + xi(6,5)*xi(5,5)**2*xi(2,4)*xi(2,3)*xi(2,2)*xi(2,1)*xi(1,3) + 2*xi(6 ,5)*xi(5,5)**2*xi(2,4)*xi(2,3)*xi(2,1)*xi(1,3)*xi(1,1) - xi(6,5)*xi(5,5)**2*xi(2 ,4)*xi(2,1)**2*xi(1,3)**2 + xi(6,5)*xi(5,5)**2*xi(2,3)**2*xi(2,2)*xi(1,3)*xi(1,1 ) - xi(6,5)*xi(5,5)**2*xi(2,3)**2*xi(1,3) - xi(6,5)*xi(5,5)**2*xi(2,3)*xi(2,2)* xi(2,1)*xi(1,3)**2 + xi(6,5)*xi(5,5)*xi(2,4)*xi(2,3)**2*xi(2,2) + xi(6,5)*xi(5,5 )*xi(2,4)*xi(2,3)**2*xi(1,1) - xi(6,5)*xi(5,5)*xi(2,4)*xi(2,3)*xi(2,1)*xi(1,3) - xi(6,5)*xi(5,5)*xi(2,3)**2*xi(2,2)*xi(1,3) - xi(6,5)*xi(5,5)*xi(2,3)**2*xi(1,3) *xi(1,1) + xi(6,5)*xi(5,5)*xi(2,3)*xi(2,1)*xi(1,3)**2 - xi(6,5)*xi(2,4)*xi(2,3) **2*xi(2,2)*xi(1,1) - xi(6,5)*xi(2,4)*xi(2,3)**2*xi(1,1)**2 + xi(6,5)*xi(2,4)*xi (2,3)*xi(2,2)*xi(2,1)*xi(1,3) + 2*xi(6,5)*xi(2,4)*xi(2,3)*xi(2,1)*xi(1,3)*xi(1,1 ) - xi(6,5)*xi(2,4)*xi(2,1)**2*xi(1,3)**2 + xi(6,5)*xi(2,3)**2*xi(2,2)*xi(1,3)* xi(1,1) - xi(6,5)*xi(2,3)**2*xi(1,3) - xi(6,5)*xi(2,3)*xi(2,2)*xi(2,1)*xi(1,3)** 2 - xi(5,5)**4*xi(2,4)*xi(2,3)*xi(2,2)*xi(2,1) - xi(5,5)**4*xi(2,4)*xi(2,3)*xi(2 ,1)*xi(1,1) + xi(5,5)**4*xi(2,4)*xi(2,1)**2*xi(1,3) + xi(5,5)**4*xi(2,3)*xi(2,2) *xi(2,1)*xi(1,3) + xi(5,5)**4*xi(2,3)*xi(2,1)*xi(1,3)*xi(1,1) - xi(5,5)**4*xi(2, 1)**2*xi(1,3)**2 - 2*xi(5,5)**2*xi(2,4)*xi(2,3)*xi(2,2)*xi(2,1) - 2*xi(5,5)**2* xi(2,4)*xi(2,3)*xi(2,1)*xi(1,1) + 2*xi(5,5)**2*xi(2,4)*xi(2,1)**2*xi(1,3) + 2*xi (5,5)**2*xi(2,3)*xi(2,2)*xi(2,1)*xi(1,3) + 2*xi(5,5)**2*xi(2,3)*xi(2,1)*xi(1,3)* xi(1,1) - 2*xi(5,5)**2*xi(2,1)**2*xi(1,3)**2 - xi(2,4)*xi(2,3)*xi(2,2)*xi(2,1) - xi(2,4)*xi(2,3)*xi(2,1)*xi(1,1) + xi(2,4)*xi(2,1)**2*xi(1,3) + xi(2,3)*xi(2,2)* xi(2,1)*xi(1,3) + xi(2,3)*xi(2,1)*xi(1,3)*xi(1,1) - xi(2,1)**2*xi(1,3)**2)/(xi(2 ,3)**2*(xi(5,5)**4*xi(2,4) - xi(5,5)**4*xi(1,3) + 2*xi(5,5)**2*xi(2,4) - 2*xi(5, 5)**2*xi(1,3) + xi(2,4) - xi(1,3)));USD\\$ USD J^4_3=(xi(6,5)*xi(5,5)*xi(2,3) - xi(6,5)*xi(2,3)*xi(1,1) + xi(6,5)*xi(2,1)* xi(1,3) - xi(5,5)**2*xi(2,1) - xi(2,1))/(xi(5,5)**2 + 1);USD\\$ USD J^4_4=(xi(6,5)*xi(5,5)*xi(2,4)*xi(2,3) - xi(6,5)*xi(2,4)*xi(2,3)*xi(1,1) + xi(6,5)*xi(2,4)*xi(2,1)*xi(1,3) - xi(5,5)**2*xi(2,4)*xi(2,1) - xi(5,5)**2*xi(2,3 )*xi(1,1) + xi(5,5)**2*xi(2,1)*xi(1,3) - xi(2,4)*xi(2,1) - xi(2,3)*xi(1,1) + xi( 2,1)*xi(1,3))/(xi(2,3)*(xi(5,5)**2 + 1));USD\\$ USD J^4_5=0;USD\\$ USD J^4_6=0;USD\\$ USD J^5_1=( - xi(6,5)*xi(6,4)*xi(5,5)**3*xi(2,4)*xi(2,3)**2*xi(2,1) + xi(6,5)* xi(6,4)*xi(5,5)**3*xi(2,3)**2*xi(2,1)*xi(1,3) + xi(6,5)*xi(6,4)*xi(5,5)**2*xi(2, 4)*xi(2,3)**2*xi(2,1)*xi(1,1) - xi(6,5)*xi(6,4)*xi(5,5)**2*xi(2,4)*xi(2,3)*xi(2, 1)**2*xi(1,3) - xi(6,5)*xi(6,4)*xi(5,5)**2*xi(2,3)**3*xi(1,1)**2 - xi(6,5)*xi(6, 4)*xi(5,5)**2*xi(2,3)**3 + xi(6,5)*xi(6,4)*xi(5,5)**2*xi(2,3)**2*xi(2,1)*xi(1,3) *xi(1,1) - xi(6,5)*xi(6,4)*xi(5,5)*xi(2,4)*xi(2,3)**2*xi(2,1) + xi(6,5)*xi(6,4)* xi(5,5)*xi(2,3)**2*xi(2,1)*xi(1,3) + xi(6,5)*xi(6,4)*xi(2,4)*xi(2,3)**2*xi(2,1)* xi(1,1) - xi(6,5)*xi(6,4)*xi(2,4)*xi(2,3)*xi(2,1)**2*xi(1,3) - xi(6,5)*xi(6,4)* xi(2,3)**3*xi(1,1)**2 - xi(6,5)*xi(6,4)*xi(2,3)**3 + xi(6,5)*xi(6,4)*xi(2,3)**2* xi(2,1)*xi(1,3)*xi(1,1) + xi(6,5)*xi(6,3)*xi(5,5)**3*xi(2,4)**2*xi(2,3)*xi(2,1) - xi(6,5)*xi(6,3)*xi(5,5)**3*xi(2,4)*xi(2,3)*xi(2,1)*xi(1,3) - xi(6,5)*xi(6,3)* xi(5,5)**2*xi(2,4)**2*xi(2,3)*xi(2,1)*xi(1,1) + xi(6,5)*xi(6,3)*xi(5,5)**2*xi(2, 4)**2*xi(2,1)**2*xi(1,3) + xi(6,5)*xi(6,3)*xi(5,5)**2*xi(2,4)*xi(2,3)**2*xi(1,1) **2 + xi(6,5)*xi(6,3)*xi(5,5)**2*xi(2,4)*xi(2,3)**2 - xi(6,5)*xi(6,3)*xi(5,5)**2 *xi(2,4)*xi(2,3)*xi(2,1)*xi(1,3)*xi(1,1) + xi(6,5)*xi(6,3)*xi(5,5)*xi(2,4)**2*xi (2,3)*xi(2,1) - xi(6,5)*xi(6,3)*xi(5,5)*xi(2,4)*xi(2,3)*xi(2,1)*xi(1,3) - xi(6,5 )*xi(6,3)*xi(2,4)**2*xi(2,3)*xi(2,1)*xi(1,1) + xi(6,5)*xi(6,3)*xi(2,4)**2*xi(2,1 )**2*xi(1,3) + xi(6,5)*xi(6,3)*xi(2,4)*xi(2,3)**2*xi(1,1)**2 + xi(6,5)*xi(6,3)* xi(2,4)*xi(2,3)**2 - xi(6,5)*xi(6,3)*xi(2,4)*xi(2,3)*xi(2,1)*xi(1,3)*xi(1,1) + xi(6,4)*xi(5,5)**4*xi(2,4)*xi(2,3)*xi(2,1)**2 - xi(6,4)*xi(5,5)**4*xi(2,3)*xi(2, 1)**2*xi(1,3) + 2*xi(6,4)*xi(5,5)**2*xi(2,4)*xi(2,3)*xi(2,1)**2 - 2*xi(6,4)*xi(5 ,5)**2*xi(2,3)*xi(2,1)**2*xi(1,3) + xi(6,4)*xi(2,4)*xi(2,3)*xi(2,1)**2 - xi(6,4) *xi(2,3)*xi(2,1)**2*xi(1,3) - xi(6,3)*xi(5,5)**4*xi(2,4)**2*xi(2,1)**2 + xi(6,3) *xi(5,5)**4*xi(2,4)*xi(2,3)*xi(2,2)*xi(2,1) + xi(6,3)*xi(5,5)**4*xi(2,4)*xi(2,3) *xi(2,1)*xi(1,1) + xi(6,3)*xi(5,5)**4*xi(2,4)*xi(2,1)**2*xi(1,3) - xi(6,3)*xi(5, 5)**4*xi(2,3)*xi(2,2)*xi(2,1)*xi(1,3) - xi(6,3)*xi(5,5)**4*xi(2,3)*xi(2,1)*xi(1, 3)*xi(1,1) - 2*xi(6,3)*xi(5,5)**2*xi(2,4)**2*xi(2,1)**2 + 2*xi(6,3)*xi(5,5)**2* xi(2,4)*xi(2,3)*xi(2,2)*xi(2,1) + 2*xi(6,3)*xi(5,5)**2*xi(2,4)*xi(2,3)*xi(2,1)* xi(1,1) + 2*xi(6,3)*xi(5,5)**2*xi(2,4)*xi(2,1)**2*xi(1,3) - 2*xi(6,3)*xi(5,5)**2 *xi(2,3)*xi(2,2)*xi(2,1)*xi(1,3) - 2*xi(6,3)*xi(5,5)**2*xi(2,3)*xi(2,1)*xi(1,3)* xi(1,1) - xi(6,3)*xi(2,4)**2*xi(2,1)**2 + xi(6,3)*xi(2,4)*xi(2,3)*xi(2,2)*xi(2,1 ) + xi(6,3)*xi(2,4)*xi(2,3)*xi(2,1)*xi(1,1) + xi(6,3)*xi(2,4)*xi(2,1)**2*xi(1,3) - xi(6,3)*xi(2,3)*xi(2,2)*xi(2,1)*xi(1,3) - xi(6,3)*xi(2,3)*xi(2,1)*xi(1,3)*xi( 1,1) - xi(6,2)*xi(5,5)**4*xi(2,4)*xi(2,3)**2*xi(2,1) + xi(6,2)*xi(5,5)**4*xi(2,3 )**2*xi(2,1)*xi(1,3) - 2*xi(6,2)*xi(5,5)**2*xi(2,4)*xi(2,3)**2*xi(2,1) + 2*xi(6, 2)*xi(5,5)**2*xi(2,3)**2*xi(2,1)*xi(1,3) - xi(6,2)*xi(2,4)*xi(2,3)**2*xi(2,1) + xi(6,2)*xi(2,3)**2*xi(2,1)*xi(1,3) + xi(6,1)*xi(5,5)**5*xi(2,4)*xi(2,3)**2 - xi( 6,1)*xi(5,5)**5*xi(2,3)**2*xi(1,3) - xi(6,1)*xi(5,5)**4*xi(2,4)*xi(2,3)**2*xi(1, 1) + xi(6,1)*xi(5,5)**4*xi(2,3)**2*xi(1,3)*xi(1,1) + 2*xi(6,1)*xi(5,5)**3*xi(2,4 )*xi(2,3)**2 - 2*xi(6,1)*xi(5,5)**3*xi(2,3)**2*xi(1,3) - 2*xi(6,1)*xi(5,5)**2*xi (2,4)*xi(2,3)**2*xi(1,1) + 2*xi(6,1)*xi(5,5)**2*xi(2,3)**2*xi(1,3)*xi(1,1) + xi( 6,1)*xi(5,5)*xi(2,4)*xi(2,3)**2 - xi(6,1)*xi(5,5)*xi(2,3)**2*xi(1,3) - xi(6,1)* xi(2,4)*xi(2,3)**2*xi(1,1) + xi(6,1)*xi(2,3)**2*xi(1,3)*xi(1,1))/(xi(6,5)*xi(2,3 )**2*(xi(5,5)**4*xi(2,4) - xi(5,5)**4*xi(1,3) + 2*xi(5,5)**2*xi(2,4) - 2*xi(5,5) **2*xi(1,3) + xi(2,4) - xi(1,3)));USD\\$ USD J^5_2=( - xi(6,5)**2*xi(6,4)*xi(5,5)**3*xi(2,4)*xi(2,3)**3*xi(2,2) - xi(6,5 )**2*xi(6,4)*xi(5,5)**3*xi(2,4)*xi(2,3)**3*xi(1,1) + xi(6,5)**2*xi(6,4)*xi(5,5) **3*xi(2,4)*xi(2,3)**2*xi(2,1)*xi(1,3) + xi(6,5)**2*xi(6,4)*xi(5,5)**3*xi(2,3)** 3*xi(2,2)*xi(1,3) + xi(6,5)**2*xi(6,4)*xi(5,5)**3*xi(2,3)**3*xi(1,3)*xi(1,1) - xi(6,5)**2*xi(6,4)*xi(5,5)**3*xi(2,3)**2*xi(2,1)*xi(1,3)**2 + xi(6,5)**2*xi(6,4) *xi(5,5)**2*xi(2,4)*xi(2,3)**3*xi(2,2)*xi(1,1) + xi(6,5)**2*xi(6,4)*xi(5,5)**2* xi(2,4)*xi(2,3)**3*xi(1,1)**2 - xi(6,5)**2*xi(6,4)*xi(5,5)**2*xi(2,4)*xi(2,3)**2 *xi(2,2)*xi(2,1)*xi(1,3) - 2*xi(6,5)**2*xi(6,4)*xi(5,5)**2*xi(2,4)*xi(2,3)**2*xi (2,1)*xi(1,3)*xi(1,1) + xi(6,5)**2*xi(6,4)*xi(5,5)**2*xi(2,4)*xi(2,3)*xi(2,1)**2 *xi(1,3)**2 - xi(6,5)**2*xi(6,4)*xi(5,5)**2*xi(2,3)**3*xi(2,2)*xi(1,3)*xi(1,1) + xi(6,5)**2*xi(6,4)*xi(5,5)**2*xi(2,3)**3*xi(1,3) + xi(6,5)**2*xi(6,4)*xi(5,5)** 2*xi(2,3)**2*xi(2,2)*xi(2,1)*xi(1,3)**2 - xi(6,5)**2*xi(6,4)*xi(5,5)*xi(2,4)*xi( 2,3)**3*xi(2,2) - xi(6,5)**2*xi(6,4)*xi(5,5)*xi(2,4)*xi(2,3)**3*xi(1,1) + xi(6,5 )**2*xi(6,4)*xi(5,5)*xi(2,4)*xi(2,3)**2*xi(2,1)*xi(1,3) + xi(6,5)**2*xi(6,4)*xi( 5,5)*xi(2,3)**3*xi(2,2)*xi(1,3) + xi(6,5)**2*xi(6,4)*xi(5,5)*xi(2,3)**3*xi(1,3)* xi(1,1) - xi(6,5)**2*xi(6,4)*xi(5,5)*xi(2,3)**2*xi(2,1)*xi(1,3)**2 + xi(6,5)**2* xi(6,4)*xi(2,4)*xi(2,3)**3*xi(2,2)*xi(1,1) + xi(6,5)**2*xi(6,4)*xi(2,4)*xi(2,3) **3*xi(1,1)**2 - xi(6,5)**2*xi(6,4)*xi(2,4)*xi(2,3)**2*xi(2,2)*xi(2,1)*xi(1,3) - 2*xi(6,5)**2*xi(6,4)*xi(2,4)*xi(2,3)**2*xi(2,1)*xi(1,3)*xi(1,1) + xi(6,5)**2*xi (6,4)*xi(2,4)*xi(2,3)*xi(2,1)**2*xi(1,3)**2 - xi(6,5)**2*xi(6,4)*xi(2,3)**3*xi(2 ,2)*xi(1,3)*xi(1,1) + xi(6,5)**2*xi(6,4)*xi(2,3)**3*xi(1,3) + xi(6,5)**2*xi(6,4) *xi(2,3)**2*xi(2,2)*xi(2,1)*xi(1,3)**2 + xi(6,5)**2*xi(6,3)*xi(5,5)**3*xi(2,4)** 2*xi(2,3)**2*xi(2,2) + xi(6,5)**2*xi(6,3)*xi(5,5)**3*xi(2,4)**2*xi(2,3)**2*xi(1, 1) - xi(6,5)**2*xi(6,3)*xi(5,5)**3*xi(2,4)**2*xi(2,3)*xi(2,1)*xi(1,3) - xi(6,5) **2*xi(6,3)*xi(5,5)**3*xi(2,4)*xi(2,3)**2*xi(2,2)*xi(1,3) - xi(6,5)**2*xi(6,3)* xi(5,5)**3*xi(2,4)*xi(2,3)**2*xi(1,3)*xi(1,1) + xi(6,5)**2*xi(6,3)*xi(5,5)**3*xi (2,4)*xi(2,3)*xi(2,1)*xi(1,3)**2 - xi(6,5)**2*xi(6,3)*xi(5,5)**2*xi(2,4)**2*xi(2 ,3)**2*xi(2,2)*xi(1,1) - xi(6,5)**2*xi(6,3)*xi(5,5)**2*xi(2,4)**2*xi(2,3)**2*xi( 1,1)**2 + xi(6,5)**2*xi(6,3)*xi(5,5)**2*xi(2,4)**2*xi(2,3)*xi(2,2)*xi(2,1)*xi(1, 3) + 2*xi(6,5)**2*xi(6,3)*xi(5,5)**2*xi(2,4)**2*xi(2,3)*xi(2,1)*xi(1,3)*xi(1,1) - xi(6,5)**2*xi(6,3)*xi(5,5)**2*xi(2,4)**2*xi(2,1)**2*xi(1,3)**2 + xi(6,5)**2*xi (6,3)*xi(5,5)**2*xi(2,4)*xi(2,3)**2*xi(2,2)*xi(1,3)*xi(1,1) - xi(6,5)**2*xi(6,3) *xi(5,5)**2*xi(2,4)*xi(2,3)**2*xi(1,3) - xi(6,5)**2*xi(6,3)*xi(5,5)**2*xi(2,4)* xi(2,3)*xi(2,2)*xi(2,1)*xi(1,3)**2 + xi(6,5)**2*xi(6,3)*xi(5,5)*xi(2,4)**2*xi(2, 3)**2*xi(2,2) + xi(6,5)**2*xi(6,3)*xi(5,5)*xi(2,4)**2*xi(2,3)**2*xi(1,1) - xi(6, 5)**2*xi(6,3)*xi(5,5)*xi(2,4)**2*xi(2,3)*xi(2,1)*xi(1,3) - xi(6,5)**2*xi(6,3)*xi (5,5)*xi(2,4)*xi(2,3)**2*xi(2,2)*xi(1,3) - xi(6,5)**2*xi(6,3)*xi(5,5)*xi(2,4)*xi (2,3)**2*xi(1,3)*xi(1,1) + xi(6,5)**2*xi(6,3)*xi(5,5)*xi(2,4)*xi(2,3)*xi(2,1)*xi (1,3)**2 - xi(6,5)**2*xi(6,3)*xi(2,4)**2*xi(2,3)**2*xi(2,2)*xi(1,1) - xi(6,5)**2 *xi(6,3)*xi(2,4)**2*xi(2,3)**2*xi(1,1)**2 + xi(6,5)**2*xi(6,3)*xi(2,4)**2*xi(2,3 )*xi(2,2)*xi(2,1)*xi(1,3) + 2*xi(6,5)**2*xi(6,3)*xi(2,4)**2*xi(2,3)*xi(2,1)*xi(1 ,3)*xi(1,1) - xi(6,5)**2*xi(6,3)*xi(2,4)**2*xi(2,1)**2*xi(1,3)**2 + xi(6,5)**2* xi(6,3)*xi(2,4)*xi(2,3)**2*xi(2,2)*xi(1,3)*xi(1,1) - xi(6,5)**2*xi(6,3)*xi(2,4)* xi(2,3)**2*xi(1,3) - xi(6,5)**2*xi(6,3)*xi(2,4)*xi(2,3)*xi(2,2)*xi(2,1)*xi(1,3) **2 + xi(6,5)*xi(6,4)*xi(5,5)**4*xi(2,4)*xi(2,3)**2*xi(2,2)*xi(2,1) + xi(6,5)*xi (6,4)*xi(5,5)**4*xi(2,4)*xi(2,3)**2*xi(2,1)*xi(1,1) - xi(6,5)*xi(6,4)*xi(5,5)**4 *xi(2,4)*xi(2,3)*xi(2,1)**2*xi(1,3) - xi(6,5)*xi(6,4)*xi(5,5)**4*xi(2,3)**2*xi(2 ,2)*xi(2,1)*xi(1,3) - xi(6,5)*xi(6,4)*xi(5,5)**4*xi(2,3)**2*xi(2,1)*xi(1,3)*xi(1 ,1) + xi(6,5)*xi(6,4)*xi(5,5)**4*xi(2,3)*xi(2,1)**2*xi(1,3)**2 + 2*xi(6,5)*xi(6, 4)*xi(5,5)**2*xi(2,4)*xi(2,3)**2*xi(2,2)*xi(2,1) + 2*xi(6,5)*xi(6,4)*xi(5,5)**2* xi(2,4)*xi(2,3)**2*xi(2,1)*xi(1,1) - 2*xi(6,5)*xi(6,4)*xi(5,5)**2*xi(2,4)*xi(2,3 )*xi(2,1)**2*xi(1,3) - 2*xi(6,5)*xi(6,4)*xi(5,5)**2*xi(2,3)**2*xi(2,2)*xi(2,1)* xi(1,3) - 2*xi(6,5)*xi(6,4)*xi(5,5)**2*xi(2,3)**2*xi(2,1)*xi(1,3)*xi(1,1) + 2*xi (6,5)*xi(6,4)*xi(5,5)**2*xi(2,3)*xi(2,1)**2*xi(1,3)**2 + xi(6,5)*xi(6,4)*xi(2,4) *xi(2,3)**2*xi(2,2)*xi(2,1) + xi(6,5)*xi(6,4)*xi(2,4)*xi(2,3)**2*xi(2,1)*xi(1,1) - xi(6,5)*xi(6,4)*xi(2,4)*xi(2,3)*xi(2,1)**2*xi(1,3) - xi(6,5)*xi(6,4)*xi(2,3) **2*xi(2,2)*xi(2,1)*xi(1,3) - xi(6,5)*xi(6,4)*xi(2,3)**2*xi(2,1)*xi(1,3)*xi(1,1) + xi(6,5)*xi(6,4)*xi(2,3)*xi(2,1)**2*xi(1,3)**2 + xi(6,5)*xi(6,3)*xi(5,5)**5*xi (2,4)**2*xi(2,3)*xi(2,1) - 2*xi(6,5)*xi(6,3)*xi(5,5)**5*xi(2,4)*xi(2,3)*xi(2,1)* xi(1,3) + xi(6,5)*xi(6,3)*xi(5,5)**5*xi(2,3)*xi(2,1)*xi(1,3)**2 - xi(6,5)*xi(6,3 )*xi(5,5)**4*xi(2,4)**2*xi(2,3)*xi(2,2)*xi(2,1) - 2*xi(6,5)*xi(6,3)*xi(5,5)**4* xi(2,4)**2*xi(2,3)*xi(2,1)*xi(1,1) + 2*xi(6,5)*xi(6,3)*xi(5,5)**4*xi(2,4)**2*xi( 2,1)**2*xi(1,3) + xi(6,5)*xi(6,3)*xi(5,5)**4*xi(2,4)*xi(2,3)**2*xi(2,2)**2 + xi( 6,5)*xi(6,3)*xi(5,5)**4*xi(2,4)*xi(2,3)**2 + 2*xi(6,5)*xi(6,3)*xi(5,5)**4*xi(2,4 )*xi(2,3)*xi(2,2)*xi(2,1)*xi(1,3) + 2*xi(6,5)*xi(6,3)*xi(5,5)**4*xi(2,4)*xi(2,3) *xi(2,1)*xi(1,3)*xi(1,1) - 2*xi(6,5)*xi(6,3)*xi(5,5)**4*xi(2,4)*xi(2,1)**2*xi(1, 3)**2 - xi(6,5)*xi(6,3)*xi(5,5)**4*xi(2,3)**2*xi(2,2)**2*xi(1,3) - xi(6,5)*xi(6, 3)*xi(5,5)**4*xi(2,3)**2*xi(1,3) - xi(6,5)*xi(6,3)*xi(5,5)**4*xi(2,3)*xi(2,2)*xi (2,1)*xi(1,3)**2 + 2*xi(6,5)*xi(6,3)*xi(5,5)**3*xi(2,4)**2*xi(2,3)*xi(2,1) - 4* xi(6,5)*xi(6,3)*xi(5,5)**3*xi(2,4)*xi(2,3)*xi(2,1)*xi(1,3) + 2*xi(6,5)*xi(6,3)* xi(5,5)**3*xi(2,3)*xi(2,1)*xi(1,3)**2 - 2*xi(6,5)*xi(6,3)*xi(5,5)**2*xi(2,4)**2* xi(2,3)*xi(2,2)*xi(2,1) - 4*xi(6,5)*xi(6,3)*xi(5,5)**2*xi(2,4)**2*xi(2,3)*xi(2,1 )*xi(1,1) + 4*xi(6,5)*xi(6,3)*xi(5,5)**2*xi(2,4)**2*xi(2,1)**2*xi(1,3) + 2*xi(6, 5)*xi(6,3)*xi(5,5)**2*xi(2,4)*xi(2,3)**2*xi(2,2)**2 + 2*xi(6,5)*xi(6,3)*xi(5,5) **2*xi(2,4)*xi(2,3)**2 + 4*xi(6,5)*xi(6,3)*xi(5,5)**2*xi(2,4)*xi(2,3)*xi(2,2)*xi (2,1)*xi(1,3) + 4*xi(6,5)*xi(6,3)*xi(5,5)**2*xi(2,4)*xi(2,3)*xi(2,1)*xi(1,3)*xi( 1,1) - 4*xi(6,5)*xi(6,3)*xi(5,5)**2*xi(2,4)*xi(2,1)**2*xi(1,3)**2 - 2*xi(6,5)*xi (6,3)*xi(5,5)**2*xi(2,3)**2*xi(2,2)**2*xi(1,3) - 2*xi(6,5)*xi(6,3)*xi(5,5)**2*xi (2,3)**2*xi(1,3) - 2*xi(6,5)*xi(6,3)*xi(5,5)**2*xi(2,3)*xi(2,2)*xi(2,1)*xi(1,3) **2 + xi(6,5)*xi(6,3)*xi(5,5)*xi(2,4)**2*xi(2,3)*xi(2,1) - 2*xi(6,5)*xi(6,3)*xi( 5,5)*xi(2,4)*xi(2,3)*xi(2,1)*xi(1,3) + xi(6,5)*xi(6,3)*xi(5,5)*xi(2,3)*xi(2,1)* xi(1,3)**2 - xi(6,5)*xi(6,3)*xi(2,4)**2*xi(2,3)*xi(2,2)*xi(2,1) - 2*xi(6,5)*xi(6 ,3)*xi(2,4)**2*xi(2,3)*xi(2,1)*xi(1,1) + 2*xi(6,5)*xi(6,3)*xi(2,4)**2*xi(2,1)**2 *xi(1,3) + xi(6,5)*xi(6,3)*xi(2,4)*xi(2,3)**2*xi(2,2)**2 + xi(6,5)*xi(6,3)*xi(2, 4)*xi(2,3)**2 + 2*xi(6,5)*xi(6,3)*xi(2,4)*xi(2,3)*xi(2,2)*xi(2,1)*xi(1,3) + 2*xi (6,5)*xi(6,3)*xi(2,4)*xi(2,3)*xi(2,1)*xi(1,3)*xi(1,1) - 2*xi(6,5)*xi(6,3)*xi(2,4 )*xi(2,1)**2*xi(1,3)**2 - xi(6,5)*xi(6,3)*xi(2,3)**2*xi(2,2)**2*xi(1,3) - xi(6,5 )*xi(6,3)*xi(2,3)**2*xi(1,3) - xi(6,5)*xi(6,3)*xi(2,3)*xi(2,2)*xi(2,1)*xi(1,3)** 2 + xi(6,5)*xi(6,2)*xi(5,5)**5*xi(2,4)*xi(2,3)**3 - xi(6,5)*xi(6,2)*xi(5,5)**5* xi(2,3)**3*xi(1,3) - xi(6,5)*xi(6,2)*xi(5,5)**4*xi(2,4)*xi(2,3)**3*xi(2,2) + xi( 6,5)*xi(6,2)*xi(5,5)**4*xi(2,3)**3*xi(2,2)*xi(1,3) + 2*xi(6,5)*xi(6,2)*xi(5,5)** 3*xi(2,4)*xi(2,3)**3 - 2*xi(6,5)*xi(6,2)*xi(5,5)**3*xi(2,3)**3*xi(1,3) - 2*xi(6, 5)*xi(6,2)*xi(5,5)**2*xi(2,4)*xi(2,3)**3*xi(2,2) + 2*xi(6,5)*xi(6,2)*xi(5,5)**2* xi(2,3)**3*xi(2,2)*xi(1,3) + xi(6,5)*xi(6,2)*xi(5,5)*xi(2,4)*xi(2,3)**3 - xi(6,5 )*xi(6,2)*xi(5,5)*xi(2,3)**3*xi(1,3) - xi(6,5)*xi(6,2)*xi(2,4)*xi(2,3)**3*xi(2,2 ) + xi(6,5)*xi(6,2)*xi(2,3)**3*xi(2,2)*xi(1,3) - xi(6,5)*xi(6,1)*xi(5,5)**5*xi(2 ,4)**2*xi(2,3)**2 + 2*xi(6,5)*xi(6,1)*xi(5,5)**5*xi(2,4)*xi(2,3)**2*xi(1,3) - xi (6,5)*xi(6,1)*xi(5,5)**5*xi(2,3)**2*xi(1,3)**2 + xi(6,5)*xi(6,1)*xi(5,5)**4*xi(2 ,4)**2*xi(2,3)**2*xi(1,1) - xi(6,5)*xi(6,1)*xi(5,5)**4*xi(2,4)**2*xi(2,3)*xi(2,1 )*xi(1,3) - xi(6,5)*xi(6,1)*xi(5,5)**4*xi(2,4)*xi(2,3)**2*xi(2,2)*xi(1,3) - xi(6 ,5)*xi(6,1)*xi(5,5)**4*xi(2,4)*xi(2,3)**2*xi(1,3)*xi(1,1) + xi(6,5)*xi(6,1)*xi(5 ,5)**4*xi(2,4)*xi(2,3)*xi(2,1)*xi(1,3)**2 + xi(6,5)*xi(6,1)*xi(5,5)**4*xi(2,3)** 2*xi(2,2)*xi(1,3)**2 - 2*xi(6,5)*xi(6,1)*xi(5,5)**3*xi(2,4)**2*xi(2,3)**2 + 4*xi (6,5)*xi(6,1)*xi(5,5)**3*xi(2,4)*xi(2,3)**2*xi(1,3) - 2*xi(6,5)*xi(6,1)*xi(5,5) **3*xi(2,3)**2*xi(1,3)**2 + 2*xi(6,5)*xi(6,1)*xi(5,5)**2*xi(2,4)**2*xi(2,3)**2* xi(1,1) - 2*xi(6,5)*xi(6,1)*xi(5,5)**2*xi(2,4)**2*xi(2,3)*xi(2,1)*xi(1,3) - 2*xi (6,5)*xi(6,1)*xi(5,5)**2*xi(2,4)*xi(2,3)**2*xi(2,2)*xi(1,3) - 2*xi(6,5)*xi(6,1)* xi(5,5)**2*xi(2,4)*xi(2,3)**2*xi(1,3)*xi(1,1) + 2*xi(6,5)*xi(6,1)*xi(5,5)**2*xi( 2,4)*xi(2,3)*xi(2,1)*xi(1,3)**2 + 2*xi(6,5)*xi(6,1)*xi(5,5)**2*xi(2,3)**2*xi(2,2 )*xi(1,3)**2 - xi(6,5)*xi(6,1)*xi(5,5)*xi(2,4)**2*xi(2,3)**2 + 2*xi(6,5)*xi(6,1) *xi(5,5)*xi(2,4)*xi(2,3)**2*xi(1,3) - xi(6,5)*xi(6,1)*xi(5,5)*xi(2,3)**2*xi(1,3) **2 + xi(6,5)*xi(6,1)*xi(2,4)**2*xi(2,3)**2*xi(1,1) - xi(6,5)*xi(6,1)*xi(2,4)**2 *xi(2,3)*xi(2,1)*xi(1,3) - xi(6,5)*xi(6,1)*xi(2,4)*xi(2,3)**2*xi(2,2)*xi(1,3) - xi(6,5)*xi(6,1)*xi(2,4)*xi(2,3)**2*xi(1,3)*xi(1,1) + xi(6,5)*xi(6,1)*xi(2,4)*xi( 2,3)*xi(2,1)*xi(1,3)**2 + xi(6,5)*xi(6,1)*xi(2,3)**2*xi(2,2)*xi(1,3)**2 - xi(6,3 )*xi(5,5)**6*xi(2,4)**2*xi(2,1)**2 + 2*xi(6,3)*xi(5,5)**6*xi(2,4)*xi(2,1)**2*xi( 1,3) - xi(6,3)*xi(5,5)**6*xi(2,1)**2*xi(1,3)**2 - 3*xi(6,3)*xi(5,5)**4*xi(2,4)** 2*xi(2,1)**2 + 6*xi(6,3)*xi(5,5)**4*xi(2,4)*xi(2,1)**2*xi(1,3) - 3*xi(6,3)*xi(5, 5)**4*xi(2,1)**2*xi(1,3)**2 - 3*xi(6,3)*xi(5,5)**2*xi(2,4)**2*xi(2,1)**2 + 6*xi( 6,3)*xi(5,5)**2*xi(2,4)*xi(2,1)**2*xi(1,3) - 3*xi(6,3)*xi(5,5)**2*xi(2,1)**2*xi( 1,3)**2 - xi(6,3)*xi(2,4)**2*xi(2,1)**2 + 2*xi(6,3)*xi(2,4)*xi(2,1)**2*xi(1,3) - xi(6,3)*xi(2,1)**2*xi(1,3)**2 + xi(6,1)*xi(5,5)**6*xi(2,4)**2*xi(2,3)*xi(2,1) - 2*xi(6,1)*xi(5,5)**6*xi(2,4)*xi(2,3)*xi(2,1)*xi(1,3) + xi(6,1)*xi(5,5)**6*xi(2, 3)*xi(2,1)*xi(1,3)**2 + 3*xi(6,1)*xi(5,5)**4*xi(2,4)**2*xi(2,3)*xi(2,1) - 6*xi(6 ,1)*xi(5,5)**4*xi(2,4)*xi(2,3)*xi(2,1)*xi(1,3) + 3*xi(6,1)*xi(5,5)**4*xi(2,3)*xi (2,1)*xi(1,3)**2 + 3*xi(6,1)*xi(5,5)**2*xi(2,4)**2*xi(2,3)*xi(2,1) - 6*xi(6,1)* xi(5,5)**2*xi(2,4)*xi(2,3)*xi(2,1)*xi(1,3) + 3*xi(6,1)*xi(5,5)**2*xi(2,3)*xi(2,1 )*xi(1,3)**2 + xi(6,1)*xi(2,4)**2*xi(2,3)*xi(2,1) - 2*xi(6,1)*xi(2,4)*xi(2,3)*xi (2,1)*xi(1,3) + xi(6,1)*xi(2,3)*xi(2,1)*xi(1,3)**2)/(xi(6,5)**2*xi(2,3)**3*(xi(5 ,5)**4*xi(2,4) - xi(5,5)**4*xi(1,3) + 2*xi(5,5)**2*xi(2,4) - 2*xi(5,5)**2*xi(1,3 ) + xi(2,4) - xi(1,3)));USD\\$ USD J^5_3=( - xi(6,5)*xi(6,4)*xi(5,5)*xi(2,3)**2 + xi(6,5)*xi(6,4)*xi(2,3)**2* xi(1,1) - xi(6,5)*xi(6,4)*xi(2,3)*xi(2,1)*xi(1,3) + xi(6,5)*xi(6,3)*xi(5,5)*xi(2 ,4)*xi(2,3) - xi(6,5)*xi(6,3)*xi(2,4)*xi(2,3)*xi(1,1) + xi(6,5)*xi(6,3)*xi(2,4)* xi(2,1)*xi(1,3) + xi(6,4)*xi(5,5)**2*xi(2,3)*xi(2,1) + xi(6,4)*xi(2,3)*xi(2,1) + xi(6,3)*xi(5,5)**3*xi(2,3) - xi(6,3)*xi(5,5)**2*xi(2,4)*xi(2,1) + xi(6,3)*xi(5, 5)**2*xi(2,3)*xi(2,2) + xi(6,3)*xi(5,5)**2*xi(2,1)*xi(1,3) + xi(6,3)*xi(5,5)*xi( 2,3) - xi(6,3)*xi(2,4)*xi(2,1) + xi(6,3)*xi(2,3)*xi(2,2) + xi(6,3)*xi(2,1)*xi(1, 3) - xi(6,2)*xi(5,5)**2*xi(2,3)**2 - xi(6,2)*xi(2,3)**2 - xi(6,1)*xi(5,5)**2*xi( 2,3)*xi(1,3) - xi(6,1)*xi(2,3)*xi(1,3))/(xi(6,5)*xi(2,3)*(xi(5,5)**2 + 1));USD\\ $ USD J^5_4=( - xi(6,5)**2*xi(6,4)*xi(5,5)*xi(2,4)*xi(2,3)**2 + xi(6,5)**2*xi(6,4 )*xi(2,4)*xi(2,3)**2*xi(1,1) - xi(6,5)**2*xi(6,4)*xi(2,4)*xi(2,3)*xi(2,1)*xi(1,3 ) + xi(6,5)**2*xi(6,3)*xi(5,5)*xi(2,4)**2*xi(2,3) - xi(6,5)**2*xi(6,3)*xi(2,4)** 2*xi(2,3)*xi(1,1) + xi(6,5)**2*xi(6,3)*xi(2,4)**2*xi(2,1)*xi(1,3) + xi(6,5)*xi(6 ,4)*xi(5,5)**3*xi(2,3)**2 + xi(6,5)*xi(6,4)*xi(5,5)**2*xi(2,4)*xi(2,3)*xi(2,1) + xi(6,5)*xi(6,4)*xi(5,5)**2*xi(2,3)**2*xi(1,1) - xi(6,5)*xi(6,4)*xi(5,5)**2*xi(2 ,3)*xi(2,1)*xi(1,3) + xi(6,5)*xi(6,4)*xi(5,5)*xi(2,3)**2 + xi(6,5)*xi(6,4)*xi(2, 4)*xi(2,3)*xi(2,1) + xi(6,5)*xi(6,4)*xi(2,3)**2*xi(1,1) - xi(6,5)*xi(6,4)*xi(2,3 )*xi(2,1)*xi(1,3) - xi(6,5)*xi(6,3)*xi(5,5)**2*xi(2,4)**2*xi(2,1) + xi(6,5)*xi(6 ,3)*xi(5,5)**2*xi(2,4)*xi(2,3)*xi(2,2) - xi(6,5)*xi(6,3)*xi(5,5)**2*xi(2,4)*xi(2 ,3)*xi(1,1) + 2*xi(6,5)*xi(6,3)*xi(5,5)**2*xi(2,4)*xi(2,1)*xi(1,3) - xi(6,5)*xi( 6,3)*xi(2,4)**2*xi(2,1) + xi(6,5)*xi(6,3)*xi(2,4)*xi(2,3)*xi(2,2) - xi(6,5)*xi(6 ,3)*xi(2,4)*xi(2,3)*xi(1,1) + 2*xi(6,5)*xi(6,3)*xi(2,4)*xi(2,1)*xi(1,3) - xi(6,5 )*xi(6,2)*xi(5,5)**2*xi(2,4)*xi(2,3)**2 - xi(6,5)*xi(6,2)*xi(2,4)*xi(2,3)**2 - xi(6,5)*xi(6,1)*xi(5,5)**2*xi(2,4)*xi(2,3)*xi(1,3) - xi(6,5)*xi(6,1)*xi(2,4)*xi( 2,3)*xi(1,3) - xi(6,3)*xi(5,5)**4*xi(2,4)*xi(2,1) + xi(6,3)*xi(5,5)**4*xi(2,1)* xi(1,3) - 2*xi(6,3)*xi(5,5)**2*xi(2,4)*xi(2,1) + 2*xi(6,3)*xi(5,5)**2*xi(2,1)*xi (1,3) - xi(6,3)*xi(2,4)*xi(2,1) + xi(6,3)*xi(2,1)*xi(1,3) + xi(6,1)*xi(5,5)**4* xi(2,4)*xi(2,3) - xi(6,1)*xi(5,5)**4*xi(2,3)*xi(1,3) + 2*xi(6,1)*xi(5,5)**2*xi(2 ,4)*xi(2,3) - 2*xi(6,1)*xi(5,5)**2*xi(2,3)*xi(1,3) + xi(6,1)*xi(2,4)*xi(2,3) - xi(6,1)*xi(2,3)*xi(1,3))/(xi(6,5)**2*xi(2,3)**2*(xi(5,5)**2 + 1));USD\\$ USD J^5_5=xi(5,5);USD\\$ USD J^5_6=( - (xi(5,5)**2 + 1))/xi(6,5);USD\\$ USD J^6_1=xi(6,1);USD\\$ USD J^6_2=xi(6,2);USD\\$ USD J^6_3=xi(6,3);USD\\$ USD J^6_4=xi(6,4);USD\\$ USD J^6_5=xi(6,5);USD\\$ USD J^6_6= - xi(5,5);USD\\$ USD {J**2}^1_1=-1;USD\\$ USD {J**2}^1_2=0;USD\\$ USD {J**2}^1_3=0;USD\\$ USD {J**2}^1_4=0;USD\\$ USD {J**2}^1_5=0;USD\\$ USD {J**2}^1_6=0;USD\\$ USD {J**2}^2_1=0;USD\\$ USD {J**2}^2_2=-1;USD\\$ USD {J**2}^2_3=0;USD\\$ USD {J**2}^2_4=0;USD\\$ USD {J**2}^2_5=0;USD\\$ USD {J**2}^2_6=0;USD\\$ USD {J**2}^3_1=0;USD\\$ USD {J**2}^3_2=0;USD\\$ USD {J**2}^3_3=-1;USD\\$ USD {J**2}^3_4=0;USD\\$ USD {J**2}^3_5=0;USD\\$ USD {J**2}^3_6=0;USD\\$ USD {J**2}^4_1=0;USD\\$ USD {J**2}^4_2=0;USD\\$ USD {J**2}^4_3=0;USD\\$ USD {J**2}^4_4=-1;USD\\$ USD {J**2}^4_5=0;USD\\$ USD {J**2}^4_6=0;USD\\$ USD {J**2}^5_1=0;USD\\$ USD {J**2}^5_2=0;USD\\$ USD {J**2}^5_3=0;USD\\$ USD {J**2}^5_4=0;USD\\$ USD {J**2}^5_5=-1;USD\\$ USD {J**2}^5_6=0;USD\\$ USD {J**2}^6_1=0;USD\\$ USD {J**2}^6_2=0;USD\\$ USD {J**2}^6_3=0;USD\\$ USD {J**2}^6_4=0;USD\\$ USD {J**2}^6_5=0;USD\\$ USD {J**2}^6_6=-1;USD\\$ \\$ det J:=1$ Trace J:=0$ \end{document}$