% This file contains the REDUCE data for the general complex structures$

% and the torsion equation to be canceled$

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

%in the case  xi(2,1) NEQ 0 , xi(2,3)= xi(2,4) =0,$

%xi(3,3) = - xi(2,2), xi(3,4) NEQ - xi(2,1).$

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)}}$

%to call the value, the command is COLLECT_EQ();$

% 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$

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

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

J(1,3):=0$

J(1,4):=0$

J(1,5):=0$

J(1,6):=0$

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

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

J(2,3):=0$

J(2,4):=0$

J(2,5):=0$

J(2,6):=0$

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

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

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

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

J(3,5):=0$

J(3,6):=0$

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

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

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

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

J(4,5):=0$

J(4,6):=0$

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

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

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

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

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

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

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(3,4)*xi(2,1) + xi(2,2)**2 + 1)/(xi(3,4) + xi(2,1))$

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

%where the parameters are subject to the following condition$

%xi(2,1)*xi(3,4)*(xi(3,4)+xi(2,1))*(xi(3,4)*xi(2,1) + xi(2,2)**2 + 1) NEQ 0$

END$