% This file contains the REDUCE data for a chart in a neighborhood of $J_0$$

% and the torsion equation to be canceled$

% on the Lie algebra g_{6,m5}$

matrix J(6,6)$

% Writing the torsion equation in Reduce format:$

PROCEDURE COLLECT_EQ${{{{1,2},1},
j(4,2)*j(1,6) - j(4,1)*j(1,5) + j(3,2)*j(1,5) + j(3,1)*j(1,6)},
{{{1,2},2},
j(4,2)*j(2,6) - j(4,1)*j(2,5) + j(3,2)*j(2,5) + j(3,1)*j(2,6)},
{{{1,2},3},
j(4,2)*j(3,6) - j(4,1)*j(3,5) + j(3,6)*j(3,1) + j(3,5)*j(3,2)},
{{{1,2},4},
j(4,6)*j(4,2) + j(4,6)*j(3,1) - j(4,5)*j(4,1) + j(4,5)*j(3,2)},
{{{1,2},5},
j(5,6)*j(4,2) + j(5,6)*j(3,1) - j(5,5)*j(4,1) + j(5,5)*j(3,2) - j(4,2)*j(2,1) + 
j(4,1)*j(2,2) - j(3,2)*j(1,1) + j(3,1)*j(1,2)},
{{{1,2},6},
j(6,6)*j(4,2) + j(6,6)*j(3,1) - j(6,5)*j(4,1) + j(6,5)*j(3,2) - j(4,2)*j(1,1) + 
j(4,1)*j(1,2) + j(3,2)*j(2,1) - j(3,1)*j(2,2)},
{{{1,3},1},
j(4,3)*j(1,6) + j(3,3)*j(1,5) - j(2,1)*j(1,6) + j(1,5)*j(1,1)},
{{{1,3},2},
j(4,3)*j(2,6) + j(3,3)*j(2,5) - j(2,6)*j(2,1) + j(2,5)*j(1,1)},
{{{1,3},3},
j(4,3)*j(3,6) - j(3,6)*j(2,1) + j(3,5)*j(3,3) + j(3,5)*j(1,1)},
{{{1,3},4},
j(4,6)*j(4,3) - j(4,6)*j(2,1) + j(4,5)*j(3,3) + j(4,5)*j(1,1)},
{{{1,3},5},
j(5,6)*j(4,3) - j(5,6)*j(2,1) + j(5,5)*j(3,3) + j(5,5)*j(1,1) - j(4,3)*j(2,1) + 
j(4,1)*j(2,3) - j(3,3)*j(1,1) + j(3,1)*j(1,3) + 1},
{{{1,3},6},
j(6,6)*j(4,3) - j(6,6)*j(2,1) + j(6,5)*j(3,3) + j(6,5)*j(1,1) - j(4,3)*j(1,1) + 
j(4,1)*j(1,3) + j(3,3)*j(2,1) - j(3,1)*j(2,3)},
{{{1,4},1},
j(4,4)*j(1,6) + j(3,4)*j(1,5) + j(2,1)*j(1,5) + j(1,6)*j(1,1)},
{{{1,4},2},
j(4,4)*j(2,6) + j(3,4)*j(2,5) + j(2,6)*j(1,1) + j(2,5)*j(2,1)},
{{{1,4},3},
j(4,4)*j(3,6) + j(3,6)*j(1,1) + j(3,5)*j(3,4) + j(3,5)*j(2,1)},
{{{1,4},4},
j(4,6)*j(4,4) + j(4,6)*j(1,1) + j(4,5)*j(3,4) + j(4,5)*j(2,1)},
{{{1,4},5},
j(5,6)*j(4,4) + j(5,6)*j(1,1) + j(5,5)*j(3,4) + j(5,5)*j(2,1) - j(4,4)*j(2,1) + 
j(4,1)*j(2,4) - j(3,4)*j(1,1) + j(3,1)*j(1,4)},
{{{1,4},6},
j(6,6)*j(4,4) + j(6,6)*j(1,1) + j(6,5)*j(3,4) + j(6,5)*j(2,1) - j(4,4)*j(1,1) + 
j(4,1)*j(1,4) + j(3,4)*j(2,1) - j(3,1)*j(2,4) + 1},
{{{1,5},1},j(4,5)*j(1,6) + j(3,5)*j(1,5)},
{{{1,5},2},j(4,5)*j(2,6) + j(3,5)*j(2,5)},
{{{1,5},3},j(4,5)*j(3,6) + j(3,5)**2},
{{{1,5},4},j(4,5)*(j(4,6) + j(3,5))},
{{{1,5},5},
j(5,6)*j(4,5) + j(5,5)*j(3,5) - j(4,5)*j(2,1) + j(4,1)*j(2,5) - j(3,5)*j(1,1) + 
j(3,1)*j(1,5)},
{{{1,5},6},
j(6,6)*j(4,5) + j(6,5)*j(3,5) - j(4,5)*j(1,1) + j(4,1)*j(1,5) + j(3,5)*j(2,1) - 
j(3,1)*j(2,5)},
{{{1,6},1},j(4,6)*j(1,6) + j(3,6)*j(1,5)},
{{{1,6},2},j(4,6)*j(2,6) + j(3,6)*j(2,5)},
{{{1,6},3},j(3,6)*(j(4,6) + j(3,5))},
{{{1,6},4},j(4,6)**2 + j(4,5)*j(3,6)},
{{{1,6},5},
j(5,6)*j(4,6) + j(5,5)*j(3,6) - j(4,6)*j(2,1) + j(4,1)*j(2,6) - j(3,6)*j(1,1) + 
j(3,1)*j(1,6)},
{{{1,6},6},
j(6,6)*j(4,6) + j(6,5)*j(3,6) - j(4,6)*j(1,1) + j(4,1)*j(1,6) + j(3,6)*j(2,1) - 
j(3,1)*j(2,6)},
{{{2,3},1},
j(4,3)*j(1,5) - j(3,3)*j(1,6) - j(2,2)*j(1,6) + j(1,5)*j(1,2)},
{{{2,3},2},
j(4,3)*j(2,5) - j(3,3)*j(2,6) - j(2,6)*j(2,2) + j(2,5)*j(1,2)},
{{{2,3},3},
j(4,3)*j(3,5) - j(3,6)*j(3,3) - j(3,6)*j(2,2) + j(3,5)*j(1,2)},
{{{2,3},4},
 - j(4,6)*j(3,3) - j(4,6)*j(2,2) + j(4,5)*j(4,3) + j(4,5)*j(1,2)},
{{{2,3},5},
 - j(5,6)*j(3,3) - j(5,6)*j(2,2) + j(5,5)*j(4,3) + j(5,5)*j(1,2) - j(4,3)*j(2,2)
 + j(4,2)*j(2,3) - j(3,3)*j(1,2) + j(3,2)*j(1,3)},
{{{2,3},6},
 - j(6,6)*j(3,3) - j(6,6)*j(2,2) + j(6,5)*j(4,3) + j(6,5)*j(1,2) - j(4,3)*j(1,2)
 + j(4,2)*j(1,3) + j(3,3)*j(2,2) - j(3,2)*j(2,3) - 1},
{{{2,4},1},
j(4,4)*j(1,5) - j(3,4)*j(1,6) + j(2,2)*j(1,5) + j(1,6)*j(1,2)},
{{{2,4},2},
j(4,4)*j(2,5) - j(3,4)*j(2,6) + j(2,6)*j(1,2) + j(2,5)*j(2,2)},
{{{2,4},3},
j(4,4)*j(3,5) - j(3,6)*j(3,4) + j(3,6)*j(1,2) + j(3,5)*j(2,2)},
{{{2,4},4},
 - j(4,6)*j(3,4) + j(4,6)*j(1,2) + j(4,5)*j(4,4) + j(4,5)*j(2,2)},
{{{2,4},5},
 - j(5,6)*j(3,4) + j(5,6)*j(1,2) + j(5,5)*j(4,4) + j(5,5)*j(2,2) - j(4,4)*j(2,2)
 + j(4,2)*j(2,4) - j(3,4)*j(1,2) + j(3,2)*j(1,4) + 1},
{{{2,4},6},
 - j(6,6)*j(3,4) + j(6,6)*j(1,2) + j(6,5)*j(4,4) + j(6,5)*j(2,2) - j(4,4)*j(1,2)
 + j(4,2)*j(1,4) + j(3,4)*j(2,2) - j(3,2)*j(2,4)},
{{{2,5},1},j(4,5)*j(1,5) - j(3,5)*j(1,6)},
{{{2,5},2},j(4,5)*j(2,5) - j(3,5)*j(2,6)},
{{{2,5},3},j(3,5)*(j(4,5) - j(3,6))},
{{{2,5},4}, - j(4,6)*j(3,5) + j(4,5)**2},
{{{2,5},5},
 - j(5,6)*j(3,5) + j(5,5)*j(4,5) - j(4,5)*j(2,2) + j(4,2)*j(2,5) - j(3,5)*j(1,2)
 + j(3,2)*j(1,5)},
{{{2,5},6},
 - j(6,6)*j(3,5) + j(6,5)*j(4,5) - j(4,5)*j(1,2) + j(4,2)*j(1,5) + j(3,5)*j(2,2)
 - j(3,2)*j(2,5)},
{{{2,6},1},j(4,6)*j(1,5) - j(3,6)*j(1,6)},
{{{2,6},2},j(4,6)*j(2,5) - j(3,6)*j(2,6)},
{{{2,6},3},j(4,6)*j(3,5) - j(3,6)**2},
{{{2,6},4},j(4,6)*(j(4,5) - j(3,6))},
{{{2,6},5},
 - j(5,6)*j(3,6) + j(5,5)*j(4,6) - j(4,6)*j(2,2) + j(4,2)*j(2,6) - j(3,6)*j(1,2)
 + j(3,2)*j(1,6)},
{{{2,6},6},
 - j(6,6)*j(3,6) + j(6,5)*j(4,6) - j(4,6)*j(1,2) + j(4,2)*j(1,6) + j(3,6)*j(2,2)
 - j(3,2)*j(2,6)},
{{{3,4},1},
j(2,4)*j(1,6) + j(2,3)*j(1,5) + j(1,6)*j(1,3) - j(1,5)*j(1,4)},
{{{3,4},2},
j(2,6)*j(2,4) + j(2,6)*j(1,3) + j(2,5)*j(2,3) - j(2,5)*j(1,4)},
{{{3,4},3},
j(3,6)*j(2,4) + j(3,6)*j(1,3) + j(3,5)*j(2,3) - j(3,5)*j(1,4)},
{{{3,4},4},
j(4,6)*j(2,4) + j(4,6)*j(1,3) + j(4,5)*j(2,3) - j(4,5)*j(1,4)},
{{{3,4},5},
j(5,6)*j(2,4) + j(5,6)*j(1,3) + j(5,5)*j(2,3) - j(5,5)*j(1,4) - j(4,4)*j(2,3) + 
j(4,3)*j(2,4) - j(3,4)*j(1,3) + j(3,3)*j(1,4)},
{{{3,4},6},
j(6,6)*j(2,4) + j(6,6)*j(1,3) + j(6,5)*j(2,3) - j(6,5)*j(1,4) - j(4,4)*j(1,3) + 
j(4,3)*j(1,4) + j(3,4)*j(2,3) - j(3,3)*j(2,4)},
{{{3,5},1},j(2,5)*j(1,6) - j(1,5)**2},
{{{3,5},2},j(2,5)*(j(2,6) - j(1,5))},
{{{3,5},3},j(3,6)*j(2,5) - j(3,5)*j(1,5)},
{{{3,5},4},j(4,6)*j(2,5) - j(4,5)*j(1,5)},
{{{3,5},5},
j(5,6)*j(2,5) - j(5,5)*j(1,5) - j(4,5)*j(2,3) + j(4,3)*j(2,5) - j(3,5)*j(1,3) + 
j(3,3)*j(1,5)},
{{{3,5},6},
j(6,6)*j(2,5) - j(6,5)*j(1,5) - j(4,5)*j(1,3) + j(4,3)*j(1,5) + j(3,5)*j(2,3) - 
j(3,3)*j(2,5)},
{{{3,6},1},j(1,6)*(j(2,6) - j(1,5))},
{{{3,6},2},j(2,6)**2 - j(2,5)*j(1,6)},
{{{3,6},3},j(3,6)*j(2,6) - j(3,5)*j(1,6)},
{{{3,6},4},j(4,6)*j(2,6) - j(4,5)*j(1,6)},
{{{3,6},5},
j(5,6)*j(2,6) - j(5,5)*j(1,6) - j(4,6)*j(2,3) + j(4,3)*j(2,6) - j(3,6)*j(1,3) + 
j(3,3)*j(1,6)},
{{{3,6},6},
j(6,6)*j(2,6) - j(6,5)*j(1,6) - j(4,6)*j(1,3) + j(4,3)*j(1,6) + j(3,6)*j(2,3) - 
j(3,3)*j(2,6)},
{{{4,5},1}, - j(1,5)*(j(2,5) + j(1,6))},
{{{4,5},2}, - (j(2,6)*j(1,5) + j(2,5)**2)},
{{{4,5},3}, - (j(3,6)*j(1,5) + j(3,5)*j(2,5))},
{{{4,5},4}, - (j(4,6)*j(1,5) + j(4,5)*j(2,5))},
{{{4,5},5},
 - j(5,6)*j(1,5) - j(5,5)*j(2,5) - j(4,5)*j(2,4) + j(4,4)*j(2,5) - j(3,5)*j(1,4)
 + j(3,4)*j(1,5)},
{{{4,5},6},
 - j(6,6)*j(1,5) - j(6,5)*j(2,5) - j(4,5)*j(1,4) + j(4,4)*j(1,5) + j(3,5)*j(2,4)
 - j(3,4)*j(2,5)},
{{{4,6},1}, - (j(2,6)*j(1,5) + j(1,6)**2)},
{{{4,6},2}, - j(2,6)*(j(2,5) + j(1,6))},
{{{4,6},3}, - (j(3,6)*j(1,6) + j(3,5)*j(2,6))},
{{{4,6},4}, - (j(4,6)*j(1,6) + j(4,5)*j(2,6))},
{{{4,6},5},
 - j(5,6)*j(1,6) - j(5,5)*j(2,6) - j(4,6)*j(2,4) + j(4,4)*j(2,6) - j(3,6)*j(1,4)
 + j(3,4)*j(1,6)},
{{{4,6},6},
 - j(6,6)*j(1,6) - j(6,5)*j(2,6) - j(4,6)*j(1,4) + j(4,4)*j(1,6) + j(3,6)*j(2,4)
 - j(3,4)*j(2,6)},
{{{5,6},5},
 - j(4,6)*j(2,5) + j(4,5)*j(2,6) - j(3,6)*j(1,5) + j(3,5)*j(1,6)},
{{{5,6},6},
 - j(4,6)*j(1,5) + j(4,5)*j(1,6) + j(3,6)*j(2,5) - j(3,5)*j(2,6)}}$

% Writing the entries of J:$

% J(i,k) denotes the entry in the ith row , kth column$

% i.e. stands for  the  LaTex expression J^i_k$

% Similarly, xi(i,k) stands for the  LaTex expression \xi^i_k$

%clear xi(5,5)$

%clear xi(6,5)$

J(1,1):= - (xi(4,1)*xi(2,4) + xi(3,1)*xi(2,3) + xi(2,2)*xi(2,1))/xi(2,1)$

J(1,2):=(xi(4,1)*xi(3,4)**2*xi(2,3)*xi(2,1) - xi(4,1)*xi(3,4)*xi(3,3)*xi(2,4)*xi
(2,1) - xi(4,1)*xi(3,4)*xi(3,1)*xi(2,4)*xi(2,3) - xi(4,1)*xi(3,4)*xi(2,4)*xi(2,2
)*xi(2,1) + xi(4,1)*xi(3,3)*xi(3,1)*xi(2,4)**2 + xi(4,1)*xi(3,1)*xi(2,4)**2*xi(2
,2) + xi(3,4)*xi(3,3)*xi(3,1)*xi(2,3)*xi(2,1) - xi(3,4)*xi(3,1)**2*xi(2,3)**2 - 
xi(3,4)*xi(3,1)*xi(2,3)*xi(2,2)*xi(2,1) - xi(3,4)*xi(2,2)**2*xi(2,1)**2 - xi(3,4
)*xi(2,1)**2 - xi(3,3)**2*xi(3,1)*xi(2,4)*xi(2,1) + xi(3,3)*xi(3,1)**2*xi(2,4)*
xi(2,3) + xi(3,1)**2*xi(2,4)*xi(2,3)*xi(2,2) + xi(3,1)*xi(2,4)*xi(2,2)**2*xi(2,1
))/(xi(2,1)**2*(xi(3,4)*xi(2,1) - xi(3,1)*xi(2,4)))$

J(1,3):=( - xi(4,1)*xi(3,4)*xi(2,4)*xi(2,3)*xi(2,1) + xi(4,1)*xi(3,1)*xi(2,4)**2
*xi(2,3) - xi(3,4)*xi(3,3)*xi(2,3)*xi(2,1)**2 - xi(3,4)*xi(2,3)*xi(2,2)*xi(2,1)
**2 + xi(3,3)**2*xi(2,4)*xi(2,1)**2 - xi(3,3)*xi(3,1)*xi(2,4)*xi(2,3)*xi(2,1) + 
xi(3,1)**2*xi(2,4)*xi(2,3)**2 + xi(3,1)*xi(2,4)*xi(2,3)*xi(2,2)*xi(2,1) + xi(2,4
)*xi(2,1)**2)/(xi(2,1)**2*(xi(3,4)*xi(2,1) - xi(3,1)*xi(2,4)))$

J(1,4):=( - xi(4,1)*xi(2,4)**2 - xi(3,4)*xi(2,3)*xi(2,1) + xi(3,3)*xi(2,4)*xi(2,
1) - xi(3,1)*xi(2,4)*xi(2,3) - xi(2,4)*xi(2,2)*xi(2,1))/xi(2,1)**2$

J(1,5):=0$

J(1,6):=0$

J(2,1):=xi(2,1)$

J(2,2):=xi(2,2)$

J(2,3):=xi(2,3)$

J(2,4):=xi(2,4)$

J(2,5):=0$

J(2,6):=0$

J(3,1):=xi(3,1)$

J(3,2):=( - xi(4,1)*xi(3,4)*xi(2,1) + xi(4,1)*xi(3,1)*xi(2,4) - xi(3,3)*xi(3,1)*
xi(2,1) + xi(3,1)**2*xi(2,3) + xi(3,1)*xi(2,2)*xi(2,1))/xi(2,1)**2$

J(3,3):=xi(3,3)$

J(3,4):=xi(3,4)$

J(3,5):=0$

J(3,6):=0$

J(4,1):=xi(4,1)$

J(4,2):=(xi(4,1)*xi(3,4)*xi(3,3)*xi(2,1)**2 - xi(4,1)*xi(3,4)*xi(3,1)*xi(2,3)*xi
(2,1) + xi(4,1)*xi(3,4)*xi(2,2)*xi(2,1)**2 - xi(4,1)*xi(3,3)*xi(3,1)*xi(2,4)*xi(
2,1) + xi(4,1)*xi(3,1)**2*xi(2,4)*xi(2,3) - xi(4,1)*xi(3,1)*xi(2,4)*xi(2,2)*xi(2
,1) + xi(3,3)**2*xi(3,1)*xi(2,1)**2 - 2*xi(3,3)*xi(3,1)**2*xi(2,3)*xi(2,1) + xi(
3,1)**3*xi(2,3)**2 + xi(3,1)*xi(2,1)**2)/(xi(2,1)**2*(xi(3,4)*xi(2,1) - xi(3,1)*
xi(2,4)))$

J(4,3):=(xi(4,1)*xi(3,4)*xi(2,3)*xi(2,1) - xi(4,1)*xi(3,1)*xi(2,4)*xi(2,3) - xi(
3,3)**2*xi(2,1)**2 + 2*xi(3,3)*xi(3,1)*xi(2,3)*xi(2,1) - xi(3,1)**2*xi(2,3)**2 -
 xi(2,1)**2)/(xi(2,1)*(xi(3,4)*xi(2,1) - xi(3,1)*xi(2,4)))$

J(4,4):=(xi(4,1)*xi(2,4) - xi(3,3)*xi(2,1) + xi(3,1)*xi(2,3))/xi(2,1)$

J(4,5):=0$

J(4,6):=0$

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

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

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

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

J(5,5):=xi(5,5)$

J(5,6):= - xi(6,5)**(-1)*xi(5,5)**2 - xi(6,5)**(-1)$

J(6,1):=xi(6,1)$

J(6,2):=xi(6,2)$

J(6,3):=xi(6,3)$

J(6,4):=xi(6,4)$

J(6,5):=xi(6,5)$

J(6,6):= - xi(5,5)$

%where $

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

%and$

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

%to check the torsion equation$

COLLECT_EQ();%$

%to check J**2$

write J**2:=J**2$

%for the suitable  values of the parameters, J=J_0$

xi(2,1):=-1$

xi(2,2):=0$

xi(2,3):=0$

xi(2,4):=0$

xi(3,1):=0$

xi(3,3):=0$

xi(3,4):=-1$

xi(4,1):=0$

xi(6,1):=0$

xi(6,2):=0$

xi(6,3):=0$

xi(6,4):=0$

write J$

clear xi(2,1),xi(2,2),xi(2,3),xi(2,4),xi(3,1),xi(3,3),xi(3,4),xi(4,1)$

clear xi(6,1),xi(6,2),xi(6,3),xi(6,4)$

END$