% 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 1 where B and C are not both  0$

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

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

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

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

J(1,5):=0$

J(1,6):=0$

J(2,1):=0$

J(2,2):=0$

J(2,3):=1$

J(2,4):=0$

J(2,5):=0$

J(2,6):=0$

J(3,1):=0$

J(3,2):=-1$

J(3,3):=0$

J(3,4):=0$

J(3,5):=0$

J(3,6):=0$

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

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

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

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

J(4,5):=0$

J(4,6):=0$

J(5,1):=0$

J(5,2):=0$

J(5,3):=0$

J(5,4):=0$

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

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

J(6,1):=0$

J(6,2):=0$

J(6,3):=0$

J(6,4):=0$

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

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

%where the parameters are subject to the following condition$

%USDxi(1,4)*xi(6,5) \neq 0. USD$

END$