ComputeModel.m

% Copyright (c), Gabriel Lopes, Delft University of Technology, 2015
function [M Gamma G J HLocal HGlobal]=ComputeModel(state,parameters,gravity,mass,inertias)

Gamma = zeros(8,8,8);

%% state, parameters and inertias 

q1=state(1);
q2=state(2);
q3=state(3);
q4=state(4);
q5=state(5);
q6=state(6);
q7=state(7);
q8=state(8);
d1=parameters(1);
d2=parameters(2);
d3=parameters(3);
d4=parameters(4);
d5=parameters(5);
d6=parameters(6);
d7=parameters(7);
d8=parameters(8);
d9=parameters(9);
d10=parameters(10);
d11=parameters(11);
d12=parameters(12);
d13=parameters(13);
d14=parameters(14);
d15=parameters(15);
I_1=inertias(1:6,1:6);
I_2=inertias(1:6,7:12);
I_3=inertias(1:6,13:18);
I_4=inertias(1:6,19:24);
I_5=inertias(1:6,25:30);
I_6=inertias(1:6,31:36);
I_7=inertias(1:6,37:42);
I_8=inertias(1:6,43:48);


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Symbolic functions 



%% H[i,i-1] 

H_1_0=[cos(q1),(-1).*sin(q1),0,(-1).*d1.*sin(q1);sin(q1),cos(q1),0,d1.* ...
  cos(q1);0,0,1,0;0,0,0,1];
H_2_1=[1,0,0,0;0,cos(q2),(-1).*sin(q2),d2+d3.*cos(q2);0,sin(q2),cos(q2), ...
  d3.*sin(q2);0,0,0,1];
H_3_2=[cos(q3),(-1).*sin(q3),0,(-1).*d5.*sin(q3);sin(q3),cos(q3),0,d4+ ...
  d5.*cos(q3);0,0,1,0;0,0,0,1];
H_4_3=[1,0,0,0;0,cos(q4),(-1).*sin(q4),d6+d7.*cos(q4);0,sin(q4),cos(q4), ...
  d7.*sin(q4);0,0,0,1];
H_5_4=[cos(q5),(-1).*sin(q5),0,(-1).*d9.*sin(q5);sin(q5),cos(q5),0,d8+ ...
  d9.*cos(q5);0,0,1,0;0,0,0,1];
H_6_5=[1,0,0,0;0,cos(q6),(-1).*sin(q6),d10+d11.*cos(q6);0,sin(q6),cos( ...
  q6),d11.*sin(q6);0,0,0,1];
H_7_6=[cos(q7),(-1).*sin(q7),0,(-1).*d13.*sin(q7);sin(q7),cos(q7),0,d12+ ...
  d13.*cos(q7);0,0,1,0;0,0,0,1];
H_8_7=[1,0,0,0;0,cos(q8),(-1).*sin(q8),d14+d15.*cos(q8);0,sin(q8),cos( ...
  q8),d15.*sin(q8);0,0,0,1];


%% HLocal

HLocal=[  H_1_0  H_2_1  H_3_2  H_4_3  H_5_4  H_6_5  H_7_6  H_8_7];



%% H[i-1,i] 

H_0_1=[cos(q1),sin(q1),0,0;(-1).*sin(q1),cos(q1),0,(-1).*d1.*cos(q1).^2+ ...
  (-1).*d1.*sin(q1).^2;0,0,1,0;0,0,0,1];
H_1_2=[1,0,0,0;0,cos(q2),sin(q2),(-1).*d3+(-1).*d2.*cos(q2);0,(-1).*sin( ...
  q2),cos(q2),d2.*sin(q2);0,0,0,1];
H_2_3=[cos(q3),sin(q3),0,(-1).*d4.*sin(q3);(-1).*sin(q3),cos(q3),0,(-1) ...
  .*d5+(-1).*d4.*cos(q3);0,0,1,0;0,0,0,1];
H_3_4=[1,0,0,0;0,cos(q4),sin(q4),(-1).*d7+(-1).*d6.*cos(q4);0,(-1).*sin( ...
  q4),cos(q4),d6.*sin(q4);0,0,0,1];
H_4_5=[cos(q5),sin(q5),0,(-1).*d8.*sin(q5);(-1).*sin(q5),cos(q5),0,(-1) ...
  .*d9+(-1).*d8.*cos(q5);0,0,1,0;0,0,0,1];
H_5_6=[1,0,0,0;0,cos(q6),sin(q6),(-1).*d11+(-1).*d10.*cos(q6);0,(-1).* ...
  sin(q6),cos(q6),d10.*sin(q6);0,0,0,1];
H_6_7=[cos(q7),sin(q7),0,(-1).*d12.*sin(q7);(-1).*sin(q7),cos(q7),0,(-1) ...
  .*d13+(-1).*d12.*cos(q7);0,0,1,0;0,0,0,1];
H_7_8=[1,0,0,0;0,cos(q8),sin(q8),(-1).*d15+(-1).*d14.*cos(q8);0,(-1).* ...
  sin(q8),cos(q8),d14.*sin(q8);0,0,0,1];


%% Hd[i,i-1,k] 

Hd_1_0_1=[(-1).*sin(q1),(-1).*cos(q1),0,(-1).*d1.*cos(q1);cos(q1),(-1).* ...
  sin(q1),0,(-1).*d1.*sin(q1);0,0,0,0;0,0,0,0];
Hd_2_1_2=[0,0,0,0;0,(-1).*sin(q2),(-1).*cos(q2),(-1).*d3.*sin(q2);0,cos(q2) ...
  ,(-1).*sin(q2),d3.*cos(q2);0,0,0,0];
Hd_3_2_3=[(-1).*sin(q3),(-1).*cos(q3),0,(-1).*d5.*cos(q3);cos(q3),(-1).* ...
  sin(q3),0,(-1).*d5.*sin(q3);0,0,0,0;0,0,0,0];
Hd_4_3_4=[0,0,0,0;0,(-1).*sin(q4),(-1).*cos(q4),(-1).*d7.*sin(q4);0,cos(q4) ...
  ,(-1).*sin(q4),d7.*cos(q4);0,0,0,0];
Hd_5_4_5=[(-1).*sin(q5),(-1).*cos(q5),0,(-1).*d9.*cos(q5);cos(q5),(-1).* ...
  sin(q5),0,(-1).*d9.*sin(q5);0,0,0,0;0,0,0,0];
Hd_6_5_6=[0,0,0,0;0,(-1).*sin(q6),(-1).*cos(q6),(-1).*d11.*sin(q6);0,cos( ...
  q6),(-1).*sin(q6),d11.*cos(q6);0,0,0,0];
Hd_7_6_7=[(-1).*sin(q7),(-1).*cos(q7),0,(-1).*d13.*cos(q7);cos(q7),(-1).* ...
  sin(q7),0,(-1).*d13.*sin(q7);0,0,0,0;0,0,0,0];
Hd_8_7_8=[0,0,0,0;0,(-1).*sin(q8),(-1).*cos(q8),(-1).*d15.*sin(q8);0,cos( ...
  q8),(-1).*sin(q8),d15.*cos(q8);0,0,0,0];


%% Hd[i-1,i,k] 

Hd_0_1_1=[(-1).*sin(q1),cos(q1),0,0;(-1).*cos(q1),(-1).*sin(q1),0,0;0,0,0, ...
  0;0,0,0,0];
Hd_1_2_2=[0,0,0,0;0,(-1).*sin(q2),cos(q2),d2.*sin(q2);0,(-1).*cos(q2),(-1) ...
  .*sin(q2),d2.*cos(q2);0,0,0,0];
Hd_2_3_3=[(-1).*sin(q3),cos(q3),0,(-1).*d4.*cos(q3);(-1).*cos(q3),(-1).* ...
  sin(q3),0,d4.*sin(q3);0,0,0,0;0,0,0,0];
Hd_3_4_4=[0,0,0,0;0,(-1).*sin(q4),cos(q4),d6.*sin(q4);0,(-1).*cos(q4),(-1) ...
  .*sin(q4),d6.*cos(q4);0,0,0,0];
Hd_4_5_5=[(-1).*sin(q5),cos(q5),0,(-1).*d8.*cos(q5);(-1).*cos(q5),(-1).* ...
  sin(q5),0,d8.*sin(q5);0,0,0,0;0,0,0,0];
Hd_5_6_6=[0,0,0,0;0,(-1).*sin(q6),cos(q6),d10.*sin(q6);0,(-1).*cos(q6),(-1) ...
  .*sin(q6),d10.*cos(q6);0,0,0,0];
Hd_6_7_7=[(-1).*sin(q7),cos(q7),0,(-1).*d12.*cos(q7);(-1).*cos(q7),(-1).* ...
  sin(q7),0,d12.*sin(q7);0,0,0,0;0,0,0,0];
Hd_7_8_8=[0,0,0,0;0,(-1).*sin(q8),cos(q8),d14.*sin(q8);0,(-1).*cos(q8),(-1) ...
  .*sin(q8),d14.*cos(q8);0,0,0,0];


%% Hdd[i,i-1,k,l] 

Hdd_1_0_1_1=[(-1).*cos(q1),sin(q1),0,d1.*sin(q1);(-1).*sin(q1),(-1).*cos(q1), ...
  0,(-1).*d1.*cos(q1);0,0,0,0;0,0,0,0];
Hdd_2_1_2_2=[0,0,0,0;0,(-1).*cos(q2),sin(q2),(-1).*d3.*cos(q2);0,(-1).*sin(q2) ...
  ,(-1).*cos(q2),(-1).*d3.*sin(q2);0,0,0,0];
Hdd_3_2_3_3=[(-1).*cos(q3),sin(q3),0,d5.*sin(q3);(-1).*sin(q3),(-1).*cos(q3), ...
  0,(-1).*d5.*cos(q3);0,0,0,0;0,0,0,0];
Hdd_4_3_4_4=[0,0,0,0;0,(-1).*cos(q4),sin(q4),(-1).*d7.*cos(q4);0,(-1).*sin(q4) ...
  ,(-1).*cos(q4),(-1).*d7.*sin(q4);0,0,0,0];
Hdd_5_4_5_5=[(-1).*cos(q5),sin(q5),0,d9.*sin(q5);(-1).*sin(q5),(-1).*cos(q5), ...
  0,(-1).*d9.*cos(q5);0,0,0,0;0,0,0,0];
Hdd_6_5_6_6=[0,0,0,0;0,(-1).*cos(q6),sin(q6),(-1).*d11.*cos(q6);0,(-1).*sin( ...
  q6),(-1).*cos(q6),(-1).*d11.*sin(q6);0,0,0,0];
Hdd_7_6_7_7=[(-1).*cos(q7),sin(q7),0,d13.*sin(q7);(-1).*sin(q7),(-1).*cos(q7), ...
  0,(-1).*d13.*cos(q7);0,0,0,0;0,0,0,0];
Hdd_8_7_8_8=[0,0,0,0;0,(-1).*cos(q8),sin(q8),(-1).*d15.*cos(q8);0,(-1).*sin( ...
  q8),(-1).*cos(q8),(-1).*d15.*sin(q8);0,0,0,0];


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Support functions 



%% H[i,0]

H_2_0=H_1_0*H_2_1;

H_3_0=H_2_0*H_3_2;

H_4_0=H_3_0*H_4_3;

H_5_0=H_4_0*H_5_4;

H_6_0=H_5_0*H_6_5;

H_7_0=H_6_0*H_7_6;

H_8_0=H_7_0*H_8_7;



%% HGlobal

HGlobal=[  H_1_0  H_2_0  H_3_0  H_4_0  H_5_0  H_6_0  H_7_0  H_8_0];



%% H[0,i]

H_0_1=inverseHomogeneous(H_1_0);

H_0_2=inverseHomogeneous(H_2_0);

H_0_3=inverseHomogeneous(H_3_0);

H_0_4=inverseHomogeneous(H_4_0);

H_0_5=inverseHomogeneous(H_5_0);

H_0_6=inverseHomogeneous(H_6_0);

H_0_7=inverseHomogeneous(H_7_0);

H_0_8=inverseHomogeneous(H_8_0);



%% Hd[i,0,k]

Hd_2_0_1=Hd_1_0_1*H_2_1;

Hd_2_0_2=+H_1_0*Hd_2_1_2;

Hd_3_0_1=Hd_2_0_1*H_3_2;

Hd_3_0_2=Hd_2_0_2*H_3_2;

Hd_3_0_3=+H_2_0*Hd_3_2_3;

Hd_4_0_1=Hd_3_0_1*H_4_3;

Hd_4_0_2=Hd_3_0_2*H_4_3;

Hd_4_0_3=Hd_3_0_3*H_4_3;

Hd_4_0_4=+H_3_0*Hd_4_3_4;

Hd_5_0_1=Hd_4_0_1*H_5_4;

Hd_5_0_2=Hd_4_0_2*H_5_4;

Hd_5_0_3=Hd_4_0_3*H_5_4;

Hd_5_0_4=Hd_4_0_4*H_5_4;

Hd_5_0_5=+H_4_0*Hd_5_4_5;

Hd_6_0_1=Hd_5_0_1*H_6_5;

Hd_6_0_2=Hd_5_0_2*H_6_5;

Hd_6_0_3=Hd_5_0_3*H_6_5;

Hd_6_0_4=Hd_5_0_4*H_6_5;

Hd_6_0_5=Hd_5_0_5*H_6_5;

Hd_6_0_6=+H_5_0*Hd_6_5_6;

Hd_7_0_1=Hd_6_0_1*H_7_6;

Hd_7_0_2=Hd_6_0_2*H_7_6;

Hd_7_0_3=Hd_6_0_3*H_7_6;

Hd_7_0_4=Hd_6_0_4*H_7_6;

Hd_7_0_5=Hd_6_0_5*H_7_6;

Hd_7_0_6=Hd_6_0_6*H_7_6;

Hd_7_0_7=+H_6_0*Hd_7_6_7;

Hd_8_0_1=Hd_7_0_1*H_8_7;

Hd_8_0_2=Hd_7_0_2*H_8_7;

Hd_8_0_3=Hd_7_0_3*H_8_7;

Hd_8_0_4=Hd_7_0_4*H_8_7;

Hd_8_0_5=Hd_7_0_5*H_8_7;

Hd_8_0_6=Hd_7_0_6*H_8_7;

Hd_8_0_7=Hd_7_0_7*H_8_7;

Hd_8_0_8=+H_7_0*Hd_8_7_8;



%% Hd[0,i,k]

Hd_0_2_1=+H_1_2*Hd_0_1_1;

Hd_0_2_2=Hd_1_2_2*H_0_1;

Hd_0_3_1=+H_2_3*Hd_0_2_1;

Hd_0_3_2=+H_2_3*Hd_0_2_2;

Hd_0_3_3=Hd_2_3_3*H_0_2;

Hd_0_4_1=+H_3_4*Hd_0_3_1;

Hd_0_4_2=+H_3_4*Hd_0_3_2;

Hd_0_4_3=+H_3_4*Hd_0_3_3;

Hd_0_4_4=Hd_3_4_4*H_0_3;

Hd_0_5_1=+H_4_5*Hd_0_4_1;

Hd_0_5_2=+H_4_5*Hd_0_4_2;

Hd_0_5_3=+H_4_5*Hd_0_4_3;

Hd_0_5_4=+H_4_5*Hd_0_4_4;

Hd_0_5_5=Hd_4_5_5*H_0_4;

Hd_0_6_1=+H_5_6*Hd_0_5_1;

Hd_0_6_2=+H_5_6*Hd_0_5_2;

Hd_0_6_3=+H_5_6*Hd_0_5_3;

Hd_0_6_4=+H_5_6*Hd_0_5_4;

Hd_0_6_5=+H_5_6*Hd_0_5_5;

Hd_0_6_6=Hd_5_6_6*H_0_5;

Hd_0_7_1=+H_6_7*Hd_0_6_1;

Hd_0_7_2=+H_6_7*Hd_0_6_2;

Hd_0_7_3=+H_6_7*Hd_0_6_3;

Hd_0_7_4=+H_6_7*Hd_0_6_4;

Hd_0_7_5=+H_6_7*Hd_0_6_5;

Hd_0_7_6=+H_6_7*Hd_0_6_6;

Hd_0_7_7=Hd_6_7_7*H_0_6;

Hd_0_8_1=+H_7_8*Hd_0_7_1;

Hd_0_8_2=+H_7_8*Hd_0_7_2;

Hd_0_8_3=+H_7_8*Hd_0_7_3;

Hd_0_8_4=+H_7_8*Hd_0_7_4;

Hd_0_8_5=+H_7_8*Hd_0_7_5;

Hd_0_8_6=+H_7_8*Hd_0_7_6;

Hd_0_8_7=+H_7_8*Hd_0_7_7;

Hd_0_8_8=Hd_7_8_8*H_0_7;



%% AdH[i,0]

AdH_1_0=Adjoint(H_1_0);

AdH_2_0=Adjoint(H_2_0);

AdH_3_0=Adjoint(H_3_0);

AdH_4_0=Adjoint(H_4_0);

AdH_5_0=Adjoint(H_5_0);

AdH_6_0=Adjoint(H_6_0);

AdH_7_0=Adjoint(H_7_0);

AdH_8_0=Adjoint(H_8_0);



%% AdH[0,i]

AdH_0_1=Adjoint(H_0_1);

AdH_0_2=Adjoint(H_0_2);

AdH_0_3=Adjoint(H_0_3);

AdH_0_4=Adjoint(H_0_4);

AdH_0_5=Adjoint(H_0_5);

AdH_0_6=Adjoint(H_0_6);

AdH_0_7=Adjoint(H_0_7);

AdH_0_8=Adjoint(H_0_8);



%% dAdH[i,0,k]

dAdH_1_0_1=dAdjoint(H_1_0,Hd_1_0_1);

dAdH_2_0_1=dAdjoint(H_2_0,Hd_2_0_1);

dAdH_2_0_2=dAdjoint(H_2_0,Hd_2_0_2);

dAdH_3_0_1=dAdjoint(H_3_0,Hd_3_0_1);

dAdH_3_0_2=dAdjoint(H_3_0,Hd_3_0_2);

dAdH_3_0_3=dAdjoint(H_3_0,Hd_3_0_3);

dAdH_4_0_1=dAdjoint(H_4_0,Hd_4_0_1);

dAdH_4_0_2=dAdjoint(H_4_0,Hd_4_0_2);

dAdH_4_0_3=dAdjoint(H_4_0,Hd_4_0_3);

dAdH_4_0_4=dAdjoint(H_4_0,Hd_4_0_4);

dAdH_5_0_1=dAdjoint(H_5_0,Hd_5_0_1);

dAdH_5_0_2=dAdjoint(H_5_0,Hd_5_0_2);

dAdH_5_0_3=dAdjoint(H_5_0,Hd_5_0_3);

dAdH_5_0_4=dAdjoint(H_5_0,Hd_5_0_4);

dAdH_5_0_5=dAdjoint(H_5_0,Hd_5_0_5);

dAdH_6_0_1=dAdjoint(H_6_0,Hd_6_0_1);

dAdH_6_0_2=dAdjoint(H_6_0,Hd_6_0_2);

dAdH_6_0_3=dAdjoint(H_6_0,Hd_6_0_3);

dAdH_6_0_4=dAdjoint(H_6_0,Hd_6_0_4);

dAdH_6_0_5=dAdjoint(H_6_0,Hd_6_0_5);

dAdH_6_0_6=dAdjoint(H_6_0,Hd_6_0_6);

dAdH_7_0_1=dAdjoint(H_7_0,Hd_7_0_1);

dAdH_7_0_2=dAdjoint(H_7_0,Hd_7_0_2);

dAdH_7_0_3=dAdjoint(H_7_0,Hd_7_0_3);

dAdH_7_0_4=dAdjoint(H_7_0,Hd_7_0_4);

dAdH_7_0_5=dAdjoint(H_7_0,Hd_7_0_5);

dAdH_7_0_6=dAdjoint(H_7_0,Hd_7_0_6);

dAdH_7_0_7=dAdjoint(H_7_0,Hd_7_0_7);

dAdH_8_0_1=dAdjoint(H_8_0,Hd_8_0_1);

dAdH_8_0_2=dAdjoint(H_8_0,Hd_8_0_2);

dAdH_8_0_3=dAdjoint(H_8_0,Hd_8_0_3);

dAdH_8_0_4=dAdjoint(H_8_0,Hd_8_0_4);

dAdH_8_0_5=dAdjoint(H_8_0,Hd_8_0_5);

dAdH_8_0_6=dAdjoint(H_8_0,Hd_8_0_6);

dAdH_8_0_7=dAdjoint(H_8_0,Hd_8_0_7);

dAdH_8_0_8=dAdjoint(H_8_0,Hd_8_0_8);



%% dAdH[0,i,k]

dAdH_0_1_1=dAdjoint(H_0_1,Hd_0_1_1);

dAdH_0_2_1=dAdjoint(H_0_2,Hd_0_2_1);

dAdH_0_2_2=dAdjoint(H_0_2,Hd_0_2_2);

dAdH_0_3_1=dAdjoint(H_0_3,Hd_0_3_1);

dAdH_0_3_2=dAdjoint(H_0_3,Hd_0_3_2);

dAdH_0_3_3=dAdjoint(H_0_3,Hd_0_3_3);

dAdH_0_4_1=dAdjoint(H_0_4,Hd_0_4_1);

dAdH_0_4_2=dAdjoint(H_0_4,Hd_0_4_2);

dAdH_0_4_3=dAdjoint(H_0_4,Hd_0_4_3);

dAdH_0_4_4=dAdjoint(H_0_4,Hd_0_4_4);

dAdH_0_5_1=dAdjoint(H_0_5,Hd_0_5_1);

dAdH_0_5_2=dAdjoint(H_0_5,Hd_0_5_2);

dAdH_0_5_3=dAdjoint(H_0_5,Hd_0_5_3);

dAdH_0_5_4=dAdjoint(H_0_5,Hd_0_5_4);

dAdH_0_5_5=dAdjoint(H_0_5,Hd_0_5_5);

dAdH_0_6_1=dAdjoint(H_0_6,Hd_0_6_1);

dAdH_0_6_2=dAdjoint(H_0_6,Hd_0_6_2);

dAdH_0_6_3=dAdjoint(H_0_6,Hd_0_6_3);

dAdH_0_6_4=dAdjoint(H_0_6,Hd_0_6_4);

dAdH_0_6_5=dAdjoint(H_0_6,Hd_0_6_5);

dAdH_0_6_6=dAdjoint(H_0_6,Hd_0_6_6);

dAdH_0_7_1=dAdjoint(H_0_7,Hd_0_7_1);

dAdH_0_7_2=dAdjoint(H_0_7,Hd_0_7_2);

dAdH_0_7_3=dAdjoint(H_0_7,Hd_0_7_3);

dAdH_0_7_4=dAdjoint(H_0_7,Hd_0_7_4);

dAdH_0_7_5=dAdjoint(H_0_7,Hd_0_7_5);

dAdH_0_7_6=dAdjoint(H_0_7,Hd_0_7_6);

dAdH_0_7_7=dAdjoint(H_0_7,Hd_0_7_7);

dAdH_0_8_1=dAdjoint(H_0_8,Hd_0_8_1);

dAdH_0_8_2=dAdjoint(H_0_8,Hd_0_8_2);

dAdH_0_8_3=dAdjoint(H_0_8,Hd_0_8_3);

dAdH_0_8_4=dAdjoint(H_0_8,Hd_0_8_4);

dAdH_0_8_5=dAdjoint(H_0_8,Hd_0_8_5);

dAdH_0_8_6=dAdjoint(H_0_8,Hd_0_8_6);

dAdH_0_8_7=dAdjoint(H_0_8,Hd_0_8_7);

dAdH_0_8_8=dAdjoint(H_0_8,Hd_0_8_8);



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Functions for equations of motion 



%% G

v1=[0 0 1 0];
v2=[0;0;0;1];

G=[+mass(1)*gravity*v1*Hd_1_0_1*v2+mass(2)*gravity*v1*Hd_2_0_1*v2+mass(3)*gravity*v1*Hd_3_0_1*v2+mass(4)*gravity*v1*Hd_4_0_1*v2+mass(5)*gravity*v1*Hd_5_0_1*v2+mass(6)*gravity*v1*Hd_6_0_1*v2+mass(7)*gravity*v1*Hd_7_0_1*v2+mass(8)*gravity*v1*Hd_8_0_1*v2; ...
+mass(2)*gravity*v1*Hd_2_0_2*v2+mass(3)*gravity*v1*Hd_3_0_2*v2+mass(4)*gravity*v1*Hd_4_0_2*v2+mass(5)*gravity*v1*Hd_5_0_2*v2+mass(6)*gravity*v1*Hd_6_0_2*v2+mass(7)*gravity*v1*Hd_7_0_2*v2+mass(8)*gravity*v1*Hd_8_0_2*v2; ...
+mass(3)*gravity*v1*Hd_3_0_3*v2+mass(4)*gravity*v1*Hd_4_0_3*v2+mass(5)*gravity*v1*Hd_5_0_3*v2+mass(6)*gravity*v1*Hd_6_0_3*v2+mass(7)*gravity*v1*Hd_7_0_3*v2+mass(8)*gravity*v1*Hd_8_0_3*v2; ...
+mass(4)*gravity*v1*Hd_4_0_4*v2+mass(5)*gravity*v1*Hd_5_0_4*v2+mass(6)*gravity*v1*Hd_6_0_4*v2+mass(7)*gravity*v1*Hd_7_0_4*v2+mass(8)*gravity*v1*Hd_8_0_4*v2; ...
+mass(5)*gravity*v1*Hd_5_0_5*v2+mass(6)*gravity*v1*Hd_6_0_5*v2+mass(7)*gravity*v1*Hd_7_0_5*v2+mass(8)*gravity*v1*Hd_8_0_5*v2; ...
+mass(6)*gravity*v1*Hd_6_0_6*v2+mass(7)*gravity*v1*Hd_7_0_6*v2+mass(8)*gravity*v1*Hd_8_0_6*v2; ...
+mass(7)*gravity*v1*Hd_7_0_7*v2+mass(8)*gravity*v1*Hd_8_0_7*v2; ...
+mass(8)*gravity*v1*Hd_8_0_8*v2; ...
];

%% J[k]

J_1_0=[ ...
  AdH_1_0*UnTilde(H_0_1*Hd_1_0_1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
];

J_2_1=[ ...
 zeros(6,1) ...
  AdH_2_0*UnTilde(H_1_2*Hd_2_1_2) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
];

J_3_2=[ ...
 zeros(6,1) ...
 zeros(6,1) ...
  AdH_3_0*UnTilde(H_2_3*Hd_3_2_3) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
];

J_4_3=[ ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
  AdH_4_0*UnTilde(H_3_4*Hd_4_3_4) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
];

J_5_4=[ ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
  AdH_5_0*UnTilde(H_4_5*Hd_5_4_5) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
];

J_6_5=[ ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
  AdH_6_0*UnTilde(H_5_6*Hd_6_5_6) ...
 zeros(6,1) ...
 zeros(6,1) ...
];

J_7_6=[ ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
  AdH_7_0*UnTilde(H_6_7*Hd_7_6_7) ...
 zeros(6,1) ...
];

J_8_7=[ ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
  AdH_8_0*UnTilde(H_7_8*Hd_8_7_8) ...
];

J_1=+J_1_0;

J_2=+J_1_0+J_2_1;

J_3=+J_1_0+J_2_1+J_3_2;

J_4=+J_1_0+J_2_1+J_3_2+J_4_3;

J_5=+J_1_0+J_2_1+J_3_2+J_4_3+J_5_4;

J_6=+J_1_0+J_2_1+J_3_2+J_4_3+J_5_4+J_6_5;

J_7=+J_1_0+J_2_1+J_3_2+J_4_3+J_5_4+J_6_5+J_7_6;

J_8=+J_1_0+J_2_1+J_3_2+J_4_3+J_5_4+J_6_5+J_7_6+J_8_7;

J=[  J_1  J_2  J_3  J_4  J_5  J_6  J_7  J_8];



%% Jd[k,l]

Jd_1_0_1=[ ...
dAdH_1_0_1*UnTilde(H_0_1*Hd_1_0_1)+AdH_1_0*UnTilde(Hd_0_1_1*Hd_1_0_1)+AdH_1_0*UnTilde(H_0_1*Hdd_1_0_1_1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
];

Jd_2_1_1=[ ...
 zeros(6,1) ...
dAdH_2_0_1*UnTilde(H_1_2*Hd_2_1_2) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
];

Jd_3_2_1=[ ...
 zeros(6,1) ...
 zeros(6,1) ...
dAdH_3_0_1*UnTilde(H_2_3*Hd_3_2_3) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
];

Jd_4_3_1=[ ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
dAdH_4_0_1*UnTilde(H_3_4*Hd_4_3_4) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
];

Jd_5_4_1=[ ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
dAdH_5_0_1*UnTilde(H_4_5*Hd_5_4_5) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
];

Jd_6_5_1=[ ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
dAdH_6_0_1*UnTilde(H_5_6*Hd_6_5_6) ...
 zeros(6,1) ...
 zeros(6,1) ...
];

Jd_7_6_1=[ ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
dAdH_7_0_1*UnTilde(H_6_7*Hd_7_6_7) ...
 zeros(6,1) ...
];

Jd_8_7_1=[ ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
dAdH_8_0_1*UnTilde(H_7_8*Hd_8_7_8) ...
];

Jd_1_0_2=[ ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
];

Jd_2_1_2=[ ...
 zeros(6,1) ...
dAdH_2_0_2*UnTilde(H_1_2*Hd_2_1_2)+AdH_2_0*UnTilde(Hd_1_2_2*Hd_2_1_2)+AdH_2_0*UnTilde(H_1_2*Hdd_2_1_2_2) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
];

Jd_3_2_2=[ ...
 zeros(6,1) ...
 zeros(6,1) ...
dAdH_3_0_2*UnTilde(H_2_3*Hd_3_2_3) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
];

Jd_4_3_2=[ ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
dAdH_4_0_2*UnTilde(H_3_4*Hd_4_3_4) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
];

Jd_5_4_2=[ ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
dAdH_5_0_2*UnTilde(H_4_5*Hd_5_4_5) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
];

Jd_6_5_2=[ ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
dAdH_6_0_2*UnTilde(H_5_6*Hd_6_5_6) ...
 zeros(6,1) ...
 zeros(6,1) ...
];

Jd_7_6_2=[ ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
dAdH_7_0_2*UnTilde(H_6_7*Hd_7_6_7) ...
 zeros(6,1) ...
];

Jd_8_7_2=[ ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
dAdH_8_0_2*UnTilde(H_7_8*Hd_8_7_8) ...
];

Jd_1_0_3=[ ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
];

Jd_2_1_3=[ ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
];

Jd_3_2_3=[ ...
 zeros(6,1) ...
 zeros(6,1) ...
dAdH_3_0_3*UnTilde(H_2_3*Hd_3_2_3)+AdH_3_0*UnTilde(Hd_2_3_3*Hd_3_2_3)+AdH_3_0*UnTilde(H_2_3*Hdd_3_2_3_3) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
];

Jd_4_3_3=[ ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
dAdH_4_0_3*UnTilde(H_3_4*Hd_4_3_4) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
];

Jd_5_4_3=[ ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
dAdH_5_0_3*UnTilde(H_4_5*Hd_5_4_5) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
];

Jd_6_5_3=[ ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
dAdH_6_0_3*UnTilde(H_5_6*Hd_6_5_6) ...
 zeros(6,1) ...
 zeros(6,1) ...
];

Jd_7_6_3=[ ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
dAdH_7_0_3*UnTilde(H_6_7*Hd_7_6_7) ...
 zeros(6,1) ...
];

Jd_8_7_3=[ ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
dAdH_8_0_3*UnTilde(H_7_8*Hd_8_7_8) ...
];

Jd_1_0_4=[ ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
];

Jd_2_1_4=[ ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
];

Jd_3_2_4=[ ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
];

Jd_4_3_4=[ ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
dAdH_4_0_4*UnTilde(H_3_4*Hd_4_3_4)+AdH_4_0*UnTilde(Hd_3_4_4*Hd_4_3_4)+AdH_4_0*UnTilde(H_3_4*Hdd_4_3_4_4) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
];

Jd_5_4_4=[ ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
dAdH_5_0_4*UnTilde(H_4_5*Hd_5_4_5) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
];

Jd_6_5_4=[ ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
dAdH_6_0_4*UnTilde(H_5_6*Hd_6_5_6) ...
 zeros(6,1) ...
 zeros(6,1) ...
];

Jd_7_6_4=[ ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
dAdH_7_0_4*UnTilde(H_6_7*Hd_7_6_7) ...
 zeros(6,1) ...
];

Jd_8_7_4=[ ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
dAdH_8_0_4*UnTilde(H_7_8*Hd_8_7_8) ...
];

Jd_1_0_5=[ ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
];

Jd_2_1_5=[ ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
];

Jd_3_2_5=[ ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
];

Jd_4_3_5=[ ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
];

Jd_5_4_5=[ ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
dAdH_5_0_5*UnTilde(H_4_5*Hd_5_4_5)+AdH_5_0*UnTilde(Hd_4_5_5*Hd_5_4_5)+AdH_5_0*UnTilde(H_4_5*Hdd_5_4_5_5) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
];

Jd_6_5_5=[ ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
dAdH_6_0_5*UnTilde(H_5_6*Hd_6_5_6) ...
 zeros(6,1) ...
 zeros(6,1) ...
];

Jd_7_6_5=[ ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
dAdH_7_0_5*UnTilde(H_6_7*Hd_7_6_7) ...
 zeros(6,1) ...
];

Jd_8_7_5=[ ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
dAdH_8_0_5*UnTilde(H_7_8*Hd_8_7_8) ...
];

Jd_1_0_6=[ ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
];

Jd_2_1_6=[ ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
];

Jd_3_2_6=[ ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
];

Jd_4_3_6=[ ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
];

Jd_5_4_6=[ ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
];

Jd_6_5_6=[ ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
dAdH_6_0_6*UnTilde(H_5_6*Hd_6_5_6)+AdH_6_0*UnTilde(Hd_5_6_6*Hd_6_5_6)+AdH_6_0*UnTilde(H_5_6*Hdd_6_5_6_6) ...
 zeros(6,1) ...
 zeros(6,1) ...
];

Jd_7_6_6=[ ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
dAdH_7_0_6*UnTilde(H_6_7*Hd_7_6_7) ...
 zeros(6,1) ...
];

Jd_8_7_6=[ ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
dAdH_8_0_6*UnTilde(H_7_8*Hd_8_7_8) ...
];

Jd_1_0_7=[ ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
];

Jd_2_1_7=[ ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
];

Jd_3_2_7=[ ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
];

Jd_4_3_7=[ ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
];

Jd_5_4_7=[ ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
];

Jd_6_5_7=[ ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
];

Jd_7_6_7=[ ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
dAdH_7_0_7*UnTilde(H_6_7*Hd_7_6_7)+AdH_7_0*UnTilde(Hd_6_7_7*Hd_7_6_7)+AdH_7_0*UnTilde(H_6_7*Hdd_7_6_7_7) ...
 zeros(6,1) ...
];

Jd_8_7_7=[ ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
dAdH_8_0_7*UnTilde(H_7_8*Hd_8_7_8) ...
];

Jd_1_0_8=[ ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
];

Jd_2_1_8=[ ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
];

Jd_3_2_8=[ ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
];

Jd_4_3_8=[ ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
];

Jd_5_4_8=[ ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
];

Jd_6_5_8=[ ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
];

Jd_7_6_8=[ ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
];

Jd_8_7_8=[ ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
 zeros(6,1) ...
dAdH_8_0_8*UnTilde(H_7_8*Hd_8_7_8)+AdH_8_0*UnTilde(Hd_7_8_8*Hd_8_7_8)+AdH_8_0*UnTilde(H_7_8*Hdd_8_7_8_8) ...
];

Jd_1_1=+Jd_1_0_1;

Jd_2_1=+Jd_1_0_1+Jd_2_1_1;

Jd_3_1=+Jd_1_0_1+Jd_2_1_1+Jd_3_2_1;

Jd_4_1=+Jd_1_0_1+Jd_2_1_1+Jd_3_2_1+Jd_4_3_1;

Jd_5_1=+Jd_1_0_1+Jd_2_1_1+Jd_3_2_1+Jd_4_3_1+Jd_5_4_1;

Jd_6_1=+Jd_1_0_1+Jd_2_1_1+Jd_3_2_1+Jd_4_3_1+Jd_5_4_1+Jd_6_5_1;

Jd_7_1=+Jd_1_0_1+Jd_2_1_1+Jd_3_2_1+Jd_4_3_1+Jd_5_4_1+Jd_6_5_1+Jd_7_6_1;

Jd_8_1=+Jd_1_0_1+Jd_2_1_1+Jd_3_2_1+Jd_4_3_1+Jd_5_4_1+Jd_6_5_1+Jd_7_6_1+Jd_8_7_1;

Jd_1_2=+Jd_1_0_2;

Jd_2_2=+Jd_1_0_2+Jd_2_1_2;

Jd_3_2=+Jd_1_0_2+Jd_2_1_2+Jd_3_2_2;

Jd_4_2=+Jd_1_0_2+Jd_2_1_2+Jd_3_2_2+Jd_4_3_2;

Jd_5_2=+Jd_1_0_2+Jd_2_1_2+Jd_3_2_2+Jd_4_3_2+Jd_5_4_2;

Jd_6_2=+Jd_1_0_2+Jd_2_1_2+Jd_3_2_2+Jd_4_3_2+Jd_5_4_2+Jd_6_5_2;

Jd_7_2=+Jd_1_0_2+Jd_2_1_2+Jd_3_2_2+Jd_4_3_2+Jd_5_4_2+Jd_6_5_2+Jd_7_6_2;

Jd_8_2=+Jd_1_0_2+Jd_2_1_2+Jd_3_2_2+Jd_4_3_2+Jd_5_4_2+Jd_6_5_2+Jd_7_6_2+Jd_8_7_2;

Jd_1_3=+Jd_1_0_3;

Jd_2_3=+Jd_1_0_3+Jd_2_1_3;

Jd_3_3=+Jd_1_0_3+Jd_2_1_3+Jd_3_2_3;

Jd_4_3=+Jd_1_0_3+Jd_2_1_3+Jd_3_2_3+Jd_4_3_3;

Jd_5_3=+Jd_1_0_3+Jd_2_1_3+Jd_3_2_3+Jd_4_3_3+Jd_5_4_3;

Jd_6_3=+Jd_1_0_3+Jd_2_1_3+Jd_3_2_3+Jd_4_3_3+Jd_5_4_3+Jd_6_5_3;

Jd_7_3=+Jd_1_0_3+Jd_2_1_3+Jd_3_2_3+Jd_4_3_3+Jd_5_4_3+Jd_6_5_3+Jd_7_6_3;

Jd_8_3=+Jd_1_0_3+Jd_2_1_3+Jd_3_2_3+Jd_4_3_3+Jd_5_4_3+Jd_6_5_3+Jd_7_6_3+Jd_8_7_3;

Jd_1_4=+Jd_1_0_4;

Jd_2_4=+Jd_1_0_4+Jd_2_1_4;

Jd_3_4=+Jd_1_0_4+Jd_2_1_4+Jd_3_2_4;

Jd_4_4=+Jd_1_0_4+Jd_2_1_4+Jd_3_2_4+Jd_4_3_4;

Jd_5_4=+Jd_1_0_4+Jd_2_1_4+Jd_3_2_4+Jd_4_3_4+Jd_5_4_4;

Jd_6_4=+Jd_1_0_4+Jd_2_1_4+Jd_3_2_4+Jd_4_3_4+Jd_5_4_4+Jd_6_5_4;

Jd_7_4=+Jd_1_0_4+Jd_2_1_4+Jd_3_2_4+Jd_4_3_4+Jd_5_4_4+Jd_6_5_4+Jd_7_6_4;

Jd_8_4=+Jd_1_0_4+Jd_2_1_4+Jd_3_2_4+Jd_4_3_4+Jd_5_4_4+Jd_6_5_4+Jd_7_6_4+Jd_8_7_4;

Jd_1_5=+Jd_1_0_5;

Jd_2_5=+Jd_1_0_5+Jd_2_1_5;

Jd_3_5=+Jd_1_0_5+Jd_2_1_5+Jd_3_2_5;

Jd_4_5=+Jd_1_0_5+Jd_2_1_5+Jd_3_2_5+Jd_4_3_5;

Jd_5_5=+Jd_1_0_5+Jd_2_1_5+Jd_3_2_5+Jd_4_3_5+Jd_5_4_5;

Jd_6_5=+Jd_1_0_5+Jd_2_1_5+Jd_3_2_5+Jd_4_3_5+Jd_5_4_5+Jd_6_5_5;

Jd_7_5=+Jd_1_0_5+Jd_2_1_5+Jd_3_2_5+Jd_4_3_5+Jd_5_4_5+Jd_6_5_5+Jd_7_6_5;

Jd_8_5=+Jd_1_0_5+Jd_2_1_5+Jd_3_2_5+Jd_4_3_5+Jd_5_4_5+Jd_6_5_5+Jd_7_6_5+Jd_8_7_5;

Jd_1_6=+Jd_1_0_6;

Jd_2_6=+Jd_1_0_6+Jd_2_1_6;

Jd_3_6=+Jd_1_0_6+Jd_2_1_6+Jd_3_2_6;

Jd_4_6=+Jd_1_0_6+Jd_2_1_6+Jd_3_2_6+Jd_4_3_6;

Jd_5_6=+Jd_1_0_6+Jd_2_1_6+Jd_3_2_6+Jd_4_3_6+Jd_5_4_6;

Jd_6_6=+Jd_1_0_6+Jd_2_1_6+Jd_3_2_6+Jd_4_3_6+Jd_5_4_6+Jd_6_5_6;

Jd_7_6=+Jd_1_0_6+Jd_2_1_6+Jd_3_2_6+Jd_4_3_6+Jd_5_4_6+Jd_6_5_6+Jd_7_6_6;

Jd_8_6=+Jd_1_0_6+Jd_2_1_6+Jd_3_2_6+Jd_4_3_6+Jd_5_4_6+Jd_6_5_6+Jd_7_6_6+Jd_8_7_6;

Jd_1_7=+Jd_1_0_7;

Jd_2_7=+Jd_1_0_7+Jd_2_1_7;

Jd_3_7=+Jd_1_0_7+Jd_2_1_7+Jd_3_2_7;

Jd_4_7=+Jd_1_0_7+Jd_2_1_7+Jd_3_2_7+Jd_4_3_7;

Jd_5_7=+Jd_1_0_7+Jd_2_1_7+Jd_3_2_7+Jd_4_3_7+Jd_5_4_7;

Jd_6_7=+Jd_1_0_7+Jd_2_1_7+Jd_3_2_7+Jd_4_3_7+Jd_5_4_7+Jd_6_5_7;

Jd_7_7=+Jd_1_0_7+Jd_2_1_7+Jd_3_2_7+Jd_4_3_7+Jd_5_4_7+Jd_6_5_7+Jd_7_6_7;

Jd_8_7=+Jd_1_0_7+Jd_2_1_7+Jd_3_2_7+Jd_4_3_7+Jd_5_4_7+Jd_6_5_7+Jd_7_6_7+Jd_8_7_7;

Jd_1_8=+Jd_1_0_8;

Jd_2_8=+Jd_1_0_8+Jd_2_1_8;

Jd_3_8=+Jd_1_0_8+Jd_2_1_8+Jd_3_2_8;

Jd_4_8=+Jd_1_0_8+Jd_2_1_8+Jd_3_2_8+Jd_4_3_8;

Jd_5_8=+Jd_1_0_8+Jd_2_1_8+Jd_3_2_8+Jd_4_3_8+Jd_5_4_8;

Jd_6_8=+Jd_1_0_8+Jd_2_1_8+Jd_3_2_8+Jd_4_3_8+Jd_5_4_8+Jd_6_5_8;

Jd_7_8=+Jd_1_0_8+Jd_2_1_8+Jd_3_2_8+Jd_4_3_8+Jd_5_4_8+Jd_6_5_8+Jd_7_6_8;

Jd_8_8=+Jd_1_0_8+Jd_2_1_8+Jd_3_2_8+Jd_4_3_8+Jd_5_4_8+Jd_6_5_8+Jd_7_6_8+Jd_8_7_8;



%% M[k] and M 

M_1=J_1'*AdH_0_1'*I_1*AdH_0_1*J_1; 

M_2=J_2'*AdH_0_2'*I_2*AdH_0_2*J_2; 

M_3=J_3'*AdH_0_3'*I_3*AdH_0_3*J_3; 

M_4=J_4'*AdH_0_4'*I_4*AdH_0_4*J_4; 

M_5=J_5'*AdH_0_5'*I_5*AdH_0_5*J_5; 

M_6=J_6'*AdH_0_6'*I_6*AdH_0_6*J_6; 

M_7=J_7'*AdH_0_7'*I_7*AdH_0_7*J_7; 

M_8=J_8'*AdH_0_8'*I_8*AdH_0_8*J_8; 

M=+M_1+M_2+M_3+M_4+M_5+M_6+M_7+M_8;



%% Md[l]

Md_1=+Jd_1_1'*AdH_0_1'*I_1*AdH_0_1*J_1 ...
+J_1'*dAdH_0_1_1'*I_1*AdH_0_1*J_1 ...
+J_1'*AdH_0_1'*I_1*dAdH_0_1_1*J_1 ...
+J_1'*AdH_0_1'*I_1*AdH_0_1*Jd_1_1 ...
+Jd_2_1'*AdH_0_2'*I_2*AdH_0_2*J_2 ...
+J_2'*dAdH_0_2_1'*I_2*AdH_0_2*J_2 ...
+J_2'*AdH_0_2'*I_2*dAdH_0_2_1*J_2 ...
+J_2'*AdH_0_2'*I_2*AdH_0_2*Jd_2_1 ...
+Jd_3_1'*AdH_0_3'*I_3*AdH_0_3*J_3 ...
+J_3'*dAdH_0_3_1'*I_3*AdH_0_3*J_3 ...
+J_3'*AdH_0_3'*I_3*dAdH_0_3_1*J_3 ...
+J_3'*AdH_0_3'*I_3*AdH_0_3*Jd_3_1 ...
+Jd_4_1'*AdH_0_4'*I_4*AdH_0_4*J_4 ...
+J_4'*dAdH_0_4_1'*I_4*AdH_0_4*J_4 ...
+J_4'*AdH_0_4'*I_4*dAdH_0_4_1*J_4 ...
+J_4'*AdH_0_4'*I_4*AdH_0_4*Jd_4_1 ...
+Jd_5_1'*AdH_0_5'*I_5*AdH_0_5*J_5 ...
+J_5'*dAdH_0_5_1'*I_5*AdH_0_5*J_5 ...
+J_5'*AdH_0_5'*I_5*dAdH_0_5_1*J_5 ...
+J_5'*AdH_0_5'*I_5*AdH_0_5*Jd_5_1 ...
+Jd_6_1'*AdH_0_6'*I_6*AdH_0_6*J_6 ...
+J_6'*dAdH_0_6_1'*I_6*AdH_0_6*J_6 ...
+J_6'*AdH_0_6'*I_6*dAdH_0_6_1*J_6 ...
+J_6'*AdH_0_6'*I_6*AdH_0_6*Jd_6_1 ...
+Jd_7_1'*AdH_0_7'*I_7*AdH_0_7*J_7 ...
+J_7'*dAdH_0_7_1'*I_7*AdH_0_7*J_7 ...
+J_7'*AdH_0_7'*I_7*dAdH_0_7_1*J_7 ...
+J_7'*AdH_0_7'*I_7*AdH_0_7*Jd_7_1 ...
+Jd_8_1'*AdH_0_8'*I_8*AdH_0_8*J_8 ...
+J_8'*dAdH_0_8_1'*I_8*AdH_0_8*J_8 ...
+J_8'*AdH_0_8'*I_8*dAdH_0_8_1*J_8 ...
+J_8'*AdH_0_8'*I_8*AdH_0_8*Jd_8_1 ...
;

Md_2=+Jd_2_2'*AdH_0_2'*I_2*AdH_0_2*J_2 ...
+J_2'*dAdH_0_2_2'*I_2*AdH_0_2*J_2 ...
+J_2'*AdH_0_2'*I_2*dAdH_0_2_2*J_2 ...
+J_2'*AdH_0_2'*I_2*AdH_0_2*Jd_2_2 ...
+Jd_3_2'*AdH_0_3'*I_3*AdH_0_3*J_3 ...
+J_3'*dAdH_0_3_2'*I_3*AdH_0_3*J_3 ...
+J_3'*AdH_0_3'*I_3*dAdH_0_3_2*J_3 ...
+J_3'*AdH_0_3'*I_3*AdH_0_3*Jd_3_2 ...
+Jd_4_2'*AdH_0_4'*I_4*AdH_0_4*J_4 ...
+J_4'*dAdH_0_4_2'*I_4*AdH_0_4*J_4 ...
+J_4'*AdH_0_4'*I_4*dAdH_0_4_2*J_4 ...
+J_4'*AdH_0_4'*I_4*AdH_0_4*Jd_4_2 ...
+Jd_5_2'*AdH_0_5'*I_5*AdH_0_5*J_5 ...
+J_5'*dAdH_0_5_2'*I_5*AdH_0_5*J_5 ...
+J_5'*AdH_0_5'*I_5*dAdH_0_5_2*J_5 ...
+J_5'*AdH_0_5'*I_5*AdH_0_5*Jd_5_2 ...
+Jd_6_2'*AdH_0_6'*I_6*AdH_0_6*J_6 ...
+J_6'*dAdH_0_6_2'*I_6*AdH_0_6*J_6 ...
+J_6'*AdH_0_6'*I_6*dAdH_0_6_2*J_6 ...
+J_6'*AdH_0_6'*I_6*AdH_0_6*Jd_6_2 ...
+Jd_7_2'*AdH_0_7'*I_7*AdH_0_7*J_7 ...
+J_7'*dAdH_0_7_2'*I_7*AdH_0_7*J_7 ...
+J_7'*AdH_0_7'*I_7*dAdH_0_7_2*J_7 ...
+J_7'*AdH_0_7'*I_7*AdH_0_7*Jd_7_2 ...
+Jd_8_2'*AdH_0_8'*I_8*AdH_0_8*J_8 ...
+J_8'*dAdH_0_8_2'*I_8*AdH_0_8*J_8 ...
+J_8'*AdH_0_8'*I_8*dAdH_0_8_2*J_8 ...
+J_8'*AdH_0_8'*I_8*AdH_0_8*Jd_8_2 ...
;

Md_3=+Jd_3_3'*AdH_0_3'*I_3*AdH_0_3*J_3 ...
+J_3'*dAdH_0_3_3'*I_3*AdH_0_3*J_3 ...
+J_3'*AdH_0_3'*I_3*dAdH_0_3_3*J_3 ...
+J_3'*AdH_0_3'*I_3*AdH_0_3*Jd_3_3 ...
+Jd_4_3'*AdH_0_4'*I_4*AdH_0_4*J_4 ...
+J_4'*dAdH_0_4_3'*I_4*AdH_0_4*J_4 ...
+J_4'*AdH_0_4'*I_4*dAdH_0_4_3*J_4 ...
+J_4'*AdH_0_4'*I_4*AdH_0_4*Jd_4_3 ...
+Jd_5_3'*AdH_0_5'*I_5*AdH_0_5*J_5 ...
+J_5'*dAdH_0_5_3'*I_5*AdH_0_5*J_5 ...
+J_5'*AdH_0_5'*I_5*dAdH_0_5_3*J_5 ...
+J_5'*AdH_0_5'*I_5*AdH_0_5*Jd_5_3 ...
+Jd_6_3'*AdH_0_6'*I_6*AdH_0_6*J_6 ...
+J_6'*dAdH_0_6_3'*I_6*AdH_0_6*J_6 ...
+J_6'*AdH_0_6'*I_6*dAdH_0_6_3*J_6 ...
+J_6'*AdH_0_6'*I_6*AdH_0_6*Jd_6_3 ...
+Jd_7_3'*AdH_0_7'*I_7*AdH_0_7*J_7 ...
+J_7'*dAdH_0_7_3'*I_7*AdH_0_7*J_7 ...
+J_7'*AdH_0_7'*I_7*dAdH_0_7_3*J_7 ...
+J_7'*AdH_0_7'*I_7*AdH_0_7*Jd_7_3 ...
+Jd_8_3'*AdH_0_8'*I_8*AdH_0_8*J_8 ...
+J_8'*dAdH_0_8_3'*I_8*AdH_0_8*J_8 ...
+J_8'*AdH_0_8'*I_8*dAdH_0_8_3*J_8 ...
+J_8'*AdH_0_8'*I_8*AdH_0_8*Jd_8_3 ...
;

Md_4=+Jd_4_4'*AdH_0_4'*I_4*AdH_0_4*J_4 ...
+J_4'*dAdH_0_4_4'*I_4*AdH_0_4*J_4 ...
+J_4'*AdH_0_4'*I_4*dAdH_0_4_4*J_4 ...
+J_4'*AdH_0_4'*I_4*AdH_0_4*Jd_4_4 ...
+Jd_5_4'*AdH_0_5'*I_5*AdH_0_5*J_5 ...
+J_5'*dAdH_0_5_4'*I_5*AdH_0_5*J_5 ...
+J_5'*AdH_0_5'*I_5*dAdH_0_5_4*J_5 ...
+J_5'*AdH_0_5'*I_5*AdH_0_5*Jd_5_4 ...
+Jd_6_4'*AdH_0_6'*I_6*AdH_0_6*J_6 ...
+J_6'*dAdH_0_6_4'*I_6*AdH_0_6*J_6 ...
+J_6'*AdH_0_6'*I_6*dAdH_0_6_4*J_6 ...
+J_6'*AdH_0_6'*I_6*AdH_0_6*Jd_6_4 ...
+Jd_7_4'*AdH_0_7'*I_7*AdH_0_7*J_7 ...
+J_7'*dAdH_0_7_4'*I_7*AdH_0_7*J_7 ...
+J_7'*AdH_0_7'*I_7*dAdH_0_7_4*J_7 ...
+J_7'*AdH_0_7'*I_7*AdH_0_7*Jd_7_4 ...
+Jd_8_4'*AdH_0_8'*I_8*AdH_0_8*J_8 ...
+J_8'*dAdH_0_8_4'*I_8*AdH_0_8*J_8 ...
+J_8'*AdH_0_8'*I_8*dAdH_0_8_4*J_8 ...
+J_8'*AdH_0_8'*I_8*AdH_0_8*Jd_8_4 ...
;

Md_5=+Jd_5_5'*AdH_0_5'*I_5*AdH_0_5*J_5 ...
+J_5'*dAdH_0_5_5'*I_5*AdH_0_5*J_5 ...
+J_5'*AdH_0_5'*I_5*dAdH_0_5_5*J_5 ...
+J_5'*AdH_0_5'*I_5*AdH_0_5*Jd_5_5 ...
+Jd_6_5'*AdH_0_6'*I_6*AdH_0_6*J_6 ...
+J_6'*dAdH_0_6_5'*I_6*AdH_0_6*J_6 ...
+J_6'*AdH_0_6'*I_6*dAdH_0_6_5*J_6 ...
+J_6'*AdH_0_6'*I_6*AdH_0_6*Jd_6_5 ...
+Jd_7_5'*AdH_0_7'*I_7*AdH_0_7*J_7 ...
+J_7'*dAdH_0_7_5'*I_7*AdH_0_7*J_7 ...
+J_7'*AdH_0_7'*I_7*dAdH_0_7_5*J_7 ...
+J_7'*AdH_0_7'*I_7*AdH_0_7*Jd_7_5 ...
+Jd_8_5'*AdH_0_8'*I_8*AdH_0_8*J_8 ...
+J_8'*dAdH_0_8_5'*I_8*AdH_0_8*J_8 ...
+J_8'*AdH_0_8'*I_8*dAdH_0_8_5*J_8 ...
+J_8'*AdH_0_8'*I_8*AdH_0_8*Jd_8_5 ...
;

Md_6=+Jd_6_6'*AdH_0_6'*I_6*AdH_0_6*J_6 ...
+J_6'*dAdH_0_6_6'*I_6*AdH_0_6*J_6 ...
+J_6'*AdH_0_6'*I_6*dAdH_0_6_6*J_6 ...
+J_6'*AdH_0_6'*I_6*AdH_0_6*Jd_6_6 ...
+Jd_7_6'*AdH_0_7'*I_7*AdH_0_7*J_7 ...
+J_7'*dAdH_0_7_6'*I_7*AdH_0_7*J_7 ...
+J_7'*AdH_0_7'*I_7*dAdH_0_7_6*J_7 ...
+J_7'*AdH_0_7'*I_7*AdH_0_7*Jd_7_6 ...
+Jd_8_6'*AdH_0_8'*I_8*AdH_0_8*J_8 ...
+J_8'*dAdH_0_8_6'*I_8*AdH_0_8*J_8 ...
+J_8'*AdH_0_8'*I_8*dAdH_0_8_6*J_8 ...
+J_8'*AdH_0_8'*I_8*AdH_0_8*Jd_8_6 ...
;

Md_7=+Jd_7_7'*AdH_0_7'*I_7*AdH_0_7*J_7 ...
+J_7'*dAdH_0_7_7'*I_7*AdH_0_7*J_7 ...
+J_7'*AdH_0_7'*I_7*dAdH_0_7_7*J_7 ...
+J_7'*AdH_0_7'*I_7*AdH_0_7*Jd_7_7 ...
+Jd_8_7'*AdH_0_8'*I_8*AdH_0_8*J_8 ...
+J_8'*dAdH_0_8_7'*I_8*AdH_0_8*J_8 ...
+J_8'*AdH_0_8'*I_8*dAdH_0_8_7*J_8 ...
+J_8'*AdH_0_8'*I_8*AdH_0_8*Jd_8_7 ...
;

Md_8=+Jd_8_8'*AdH_0_8'*I_8*AdH_0_8*J_8 ...
+J_8'*dAdH_0_8_8'*I_8*AdH_0_8*J_8 ...
+J_8'*AdH_0_8'*I_8*dAdH_0_8_8*J_8 ...
+J_8'*AdH_0_8'*I_8*AdH_0_8*Jd_8_8 ...
;



%% Gamma[i,j,k] 

Gamma(1,1,1)=1/2*(Md_1(1,1)+Md_1(1,1)-Md_1(1,1));
Gamma(1,1,2)=1/2*(Md_2(1,1)+Md_1(1,2)-Md_1(2,1));
Gamma(1,1,3)=1/2*(Md_3(1,1)+Md_1(1,3)-Md_1(3,1));
Gamma(1,1,4)=1/2*(Md_4(1,1)+Md_1(1,4)-Md_1(4,1));
Gamma(1,1,5)=1/2*(Md_5(1,1)+Md_1(1,5)-Md_1(5,1));
Gamma(1,1,6)=1/2*(Md_6(1,1)+Md_1(1,6)-Md_1(6,1));
Gamma(1,1,7)=1/2*(Md_7(1,1)+Md_1(1,7)-Md_1(7,1));
Gamma(1,1,8)=1/2*(Md_8(1,1)+Md_1(1,8)-Md_1(8,1));
Gamma(1,2,1)=1/2*(Md_1(1,2)+Md_2(1,1)-Md_1(1,2));
Gamma(1,2,2)=1/2*(Md_2(1,2)+Md_2(1,2)-Md_1(2,2));
Gamma(1,2,3)=1/2*(Md_3(1,2)+Md_2(1,3)-Md_1(3,2));
Gamma(1,2,4)=1/2*(Md_4(1,2)+Md_2(1,4)-Md_1(4,2));
Gamma(1,2,5)=1/2*(Md_5(1,2)+Md_2(1,5)-Md_1(5,2));
Gamma(1,2,6)=1/2*(Md_6(1,2)+Md_2(1,6)-Md_1(6,2));
Gamma(1,2,7)=1/2*(Md_7(1,2)+Md_2(1,7)-Md_1(7,2));
Gamma(1,2,8)=1/2*(Md_8(1,2)+Md_2(1,8)-Md_1(8,2));
Gamma(1,3,1)=1/2*(Md_1(1,3)+Md_3(1,1)-Md_1(1,3));
Gamma(1,3,2)=1/2*(Md_2(1,3)+Md_3(1,2)-Md_1(2,3));
Gamma(1,3,3)=1/2*(Md_3(1,3)+Md_3(1,3)-Md_1(3,3));
Gamma(1,3,4)=1/2*(Md_4(1,3)+Md_3(1,4)-Md_1(4,3));
Gamma(1,3,5)=1/2*(Md_5(1,3)+Md_3(1,5)-Md_1(5,3));
Gamma(1,3,6)=1/2*(Md_6(1,3)+Md_3(1,6)-Md_1(6,3));
Gamma(1,3,7)=1/2*(Md_7(1,3)+Md_3(1,7)-Md_1(7,3));
Gamma(1,3,8)=1/2*(Md_8(1,3)+Md_3(1,8)-Md_1(8,3));
Gamma(1,4,1)=1/2*(Md_1(1,4)+Md_4(1,1)-Md_1(1,4));
Gamma(1,4,2)=1/2*(Md_2(1,4)+Md_4(1,2)-Md_1(2,4));
Gamma(1,4,3)=1/2*(Md_3(1,4)+Md_4(1,3)-Md_1(3,4));
Gamma(1,4,4)=1/2*(Md_4(1,4)+Md_4(1,4)-Md_1(4,4));
Gamma(1,4,5)=1/2*(Md_5(1,4)+Md_4(1,5)-Md_1(5,4));
Gamma(1,4,6)=1/2*(Md_6(1,4)+Md_4(1,6)-Md_1(6,4));
Gamma(1,4,7)=1/2*(Md_7(1,4)+Md_4(1,7)-Md_1(7,4));
Gamma(1,4,8)=1/2*(Md_8(1,4)+Md_4(1,8)-Md_1(8,4));
Gamma(1,5,1)=1/2*(Md_1(1,5)+Md_5(1,1)-Md_1(1,5));
Gamma(1,5,2)=1/2*(Md_2(1,5)+Md_5(1,2)-Md_1(2,5));
Gamma(1,5,3)=1/2*(Md_3(1,5)+Md_5(1,3)-Md_1(3,5));
Gamma(1,5,4)=1/2*(Md_4(1,5)+Md_5(1,4)-Md_1(4,5));
Gamma(1,5,5)=1/2*(Md_5(1,5)+Md_5(1,5)-Md_1(5,5));
Gamma(1,5,6)=1/2*(Md_6(1,5)+Md_5(1,6)-Md_1(6,5));
Gamma(1,5,7)=1/2*(Md_7(1,5)+Md_5(1,7)-Md_1(7,5));
Gamma(1,5,8)=1/2*(Md_8(1,5)+Md_5(1,8)-Md_1(8,5));
Gamma(1,6,1)=1/2*(Md_1(1,6)+Md_6(1,1)-Md_1(1,6));
Gamma(1,6,2)=1/2*(Md_2(1,6)+Md_6(1,2)-Md_1(2,6));
Gamma(1,6,3)=1/2*(Md_3(1,6)+Md_6(1,3)-Md_1(3,6));
Gamma(1,6,4)=1/2*(Md_4(1,6)+Md_6(1,4)-Md_1(4,6));
Gamma(1,6,5)=1/2*(Md_5(1,6)+Md_6(1,5)-Md_1(5,6));
Gamma(1,6,6)=1/2*(Md_6(1,6)+Md_6(1,6)-Md_1(6,6));
Gamma(1,6,7)=1/2*(Md_7(1,6)+Md_6(1,7)-Md_1(7,6));
Gamma(1,6,8)=1/2*(Md_8(1,6)+Md_6(1,8)-Md_1(8,6));
Gamma(1,7,1)=1/2*(Md_1(1,7)+Md_7(1,1)-Md_1(1,7));
Gamma(1,7,2)=1/2*(Md_2(1,7)+Md_7(1,2)-Md_1(2,7));
Gamma(1,7,3)=1/2*(Md_3(1,7)+Md_7(1,3)-Md_1(3,7));
Gamma(1,7,4)=1/2*(Md_4(1,7)+Md_7(1,4)-Md_1(4,7));
Gamma(1,7,5)=1/2*(Md_5(1,7)+Md_7(1,5)-Md_1(5,7));
Gamma(1,7,6)=1/2*(Md_6(1,7)+Md_7(1,6)-Md_1(6,7));
Gamma(1,7,7)=1/2*(Md_7(1,7)+Md_7(1,7)-Md_1(7,7));
Gamma(1,7,8)=1/2*(Md_8(1,7)+Md_7(1,8)-Md_1(8,7));
Gamma(1,8,1)=1/2*(Md_1(1,8)+Md_8(1,1)-Md_1(1,8));
Gamma(1,8,2)=1/2*(Md_2(1,8)+Md_8(1,2)-Md_1(2,8));
Gamma(1,8,3)=1/2*(Md_3(1,8)+Md_8(1,3)-Md_1(3,8));
Gamma(1,8,4)=1/2*(Md_4(1,8)+Md_8(1,4)-Md_1(4,8));
Gamma(1,8,5)=1/2*(Md_5(1,8)+Md_8(1,5)-Md_1(5,8));
Gamma(1,8,6)=1/2*(Md_6(1,8)+Md_8(1,6)-Md_1(6,8));
Gamma(1,8,7)=1/2*(Md_7(1,8)+Md_8(1,7)-Md_1(7,8));
Gamma(1,8,8)=1/2*(Md_8(1,8)+Md_8(1,8)-Md_1(8,8));
Gamma(2,1,1)=1/2*(Md_1(2,1)+Md_1(2,1)-Md_2(1,1));
Gamma(2,1,2)=1/2*(Md_2(2,1)+Md_1(2,2)-Md_2(2,1));
Gamma(2,1,3)=1/2*(Md_3(2,1)+Md_1(2,3)-Md_2(3,1));
Gamma(2,1,4)=1/2*(Md_4(2,1)+Md_1(2,4)-Md_2(4,1));
Gamma(2,1,5)=1/2*(Md_5(2,1)+Md_1(2,5)-Md_2(5,1));
Gamma(2,1,6)=1/2*(Md_6(2,1)+Md_1(2,6)-Md_2(6,1));
Gamma(2,1,7)=1/2*(Md_7(2,1)+Md_1(2,7)-Md_2(7,1));
Gamma(2,1,8)=1/2*(Md_8(2,1)+Md_1(2,8)-Md_2(8,1));
Gamma(2,2,1)=1/2*(Md_1(2,2)+Md_2(2,1)-Md_2(1,2));
Gamma(2,2,2)=1/2*(Md_2(2,2)+Md_2(2,2)-Md_2(2,2));
Gamma(2,2,3)=1/2*(Md_3(2,2)+Md_2(2,3)-Md_2(3,2));
Gamma(2,2,4)=1/2*(Md_4(2,2)+Md_2(2,4)-Md_2(4,2));
Gamma(2,2,5)=1/2*(Md_5(2,2)+Md_2(2,5)-Md_2(5,2));
Gamma(2,2,6)=1/2*(Md_6(2,2)+Md_2(2,6)-Md_2(6,2));
Gamma(2,2,7)=1/2*(Md_7(2,2)+Md_2(2,7)-Md_2(7,2));
Gamma(2,2,8)=1/2*(Md_8(2,2)+Md_2(2,8)-Md_2(8,2));
Gamma(2,3,1)=1/2*(Md_1(2,3)+Md_3(2,1)-Md_2(1,3));
Gamma(2,3,2)=1/2*(Md_2(2,3)+Md_3(2,2)-Md_2(2,3));
Gamma(2,3,3)=1/2*(Md_3(2,3)+Md_3(2,3)-Md_2(3,3));
Gamma(2,3,4)=1/2*(Md_4(2,3)+Md_3(2,4)-Md_2(4,3));
Gamma(2,3,5)=1/2*(Md_5(2,3)+Md_3(2,5)-Md_2(5,3));
Gamma(2,3,6)=1/2*(Md_6(2,3)+Md_3(2,6)-Md_2(6,3));
Gamma(2,3,7)=1/2*(Md_7(2,3)+Md_3(2,7)-Md_2(7,3));
Gamma(2,3,8)=1/2*(Md_8(2,3)+Md_3(2,8)-Md_2(8,3));
Gamma(2,4,1)=1/2*(Md_1(2,4)+Md_4(2,1)-Md_2(1,4));
Gamma(2,4,2)=1/2*(Md_2(2,4)+Md_4(2,2)-Md_2(2,4));
Gamma(2,4,3)=1/2*(Md_3(2,4)+Md_4(2,3)-Md_2(3,4));
Gamma(2,4,4)=1/2*(Md_4(2,4)+Md_4(2,4)-Md_2(4,4));
Gamma(2,4,5)=1/2*(Md_5(2,4)+Md_4(2,5)-Md_2(5,4));
Gamma(2,4,6)=1/2*(Md_6(2,4)+Md_4(2,6)-Md_2(6,4));
Gamma(2,4,7)=1/2*(Md_7(2,4)+Md_4(2,7)-Md_2(7,4));
Gamma(2,4,8)=1/2*(Md_8(2,4)+Md_4(2,8)-Md_2(8,4));
Gamma(2,5,1)=1/2*(Md_1(2,5)+Md_5(2,1)-Md_2(1,5));
Gamma(2,5,2)=1/2*(Md_2(2,5)+Md_5(2,2)-Md_2(2,5));
Gamma(2,5,3)=1/2*(Md_3(2,5)+Md_5(2,3)-Md_2(3,5));
Gamma(2,5,4)=1/2*(Md_4(2,5)+Md_5(2,4)-Md_2(4,5));
Gamma(2,5,5)=1/2*(Md_5(2,5)+Md_5(2,5)-Md_2(5,5));
Gamma(2,5,6)=1/2*(Md_6(2,5)+Md_5(2,6)-Md_2(6,5));
Gamma(2,5,7)=1/2*(Md_7(2,5)+Md_5(2,7)-Md_2(7,5));
Gamma(2,5,8)=1/2*(Md_8(2,5)+Md_5(2,8)-Md_2(8,5));
Gamma(2,6,1)=1/2*(Md_1(2,6)+Md_6(2,1)-Md_2(1,6));
Gamma(2,6,2)=1/2*(Md_2(2,6)+Md_6(2,2)-Md_2(2,6));
Gamma(2,6,3)=1/2*(Md_3(2,6)+Md_6(2,3)-Md_2(3,6));
Gamma(2,6,4)=1/2*(Md_4(2,6)+Md_6(2,4)-Md_2(4,6));
Gamma(2,6,5)=1/2*(Md_5(2,6)+Md_6(2,5)-Md_2(5,6));
Gamma(2,6,6)=1/2*(Md_6(2,6)+Md_6(2,6)-Md_2(6,6));
Gamma(2,6,7)=1/2*(Md_7(2,6)+Md_6(2,7)-Md_2(7,6));
Gamma(2,6,8)=1/2*(Md_8(2,6)+Md_6(2,8)-Md_2(8,6));
Gamma(2,7,1)=1/2*(Md_1(2,7)+Md_7(2,1)-Md_2(1,7));
Gamma(2,7,2)=1/2*(Md_2(2,7)+Md_7(2,2)-Md_2(2,7));
Gamma(2,7,3)=1/2*(Md_3(2,7)+Md_7(2,3)-Md_2(3,7));
Gamma(2,7,4)=1/2*(Md_4(2,7)+Md_7(2,4)-Md_2(4,7));
Gamma(2,7,5)=1/2*(Md_5(2,7)+Md_7(2,5)-Md_2(5,7));
Gamma(2,7,6)=1/2*(Md_6(2,7)+Md_7(2,6)-Md_2(6,7));
Gamma(2,7,7)=1/2*(Md_7(2,7)+Md_7(2,7)-Md_2(7,7));
Gamma(2,7,8)=1/2*(Md_8(2,7)+Md_7(2,8)-Md_2(8,7));
Gamma(2,8,1)=1/2*(Md_1(2,8)+Md_8(2,1)-Md_2(1,8));
Gamma(2,8,2)=1/2*(Md_2(2,8)+Md_8(2,2)-Md_2(2,8));
Gamma(2,8,3)=1/2*(Md_3(2,8)+Md_8(2,3)-Md_2(3,8));
Gamma(2,8,4)=1/2*(Md_4(2,8)+Md_8(2,4)-Md_2(4,8));
Gamma(2,8,5)=1/2*(Md_5(2,8)+Md_8(2,5)-Md_2(5,8));
Gamma(2,8,6)=1/2*(Md_6(2,8)+Md_8(2,6)-Md_2(6,8));
Gamma(2,8,7)=1/2*(Md_7(2,8)+Md_8(2,7)-Md_2(7,8));
Gamma(2,8,8)=1/2*(Md_8(2,8)+Md_8(2,8)-Md_2(8,8));
Gamma(3,1,1)=1/2*(Md_1(3,1)+Md_1(3,1)-Md_3(1,1));
Gamma(3,1,2)=1/2*(Md_2(3,1)+Md_1(3,2)-Md_3(2,1));
Gamma(3,1,3)=1/2*(Md_3(3,1)+Md_1(3,3)-Md_3(3,1));
Gamma(3,1,4)=1/2*(Md_4(3,1)+Md_1(3,4)-Md_3(4,1));
Gamma(3,1,5)=1/2*(Md_5(3,1)+Md_1(3,5)-Md_3(5,1));
Gamma(3,1,6)=1/2*(Md_6(3,1)+Md_1(3,6)-Md_3(6,1));
Gamma(3,1,7)=1/2*(Md_7(3,1)+Md_1(3,7)-Md_3(7,1));
Gamma(3,1,8)=1/2*(Md_8(3,1)+Md_1(3,8)-Md_3(8,1));
Gamma(3,2,1)=1/2*(Md_1(3,2)+Md_2(3,1)-Md_3(1,2));
Gamma(3,2,2)=1/2*(Md_2(3,2)+Md_2(3,2)-Md_3(2,2));
Gamma(3,2,3)=1/2*(Md_3(3,2)+Md_2(3,3)-Md_3(3,2));
Gamma(3,2,4)=1/2*(Md_4(3,2)+Md_2(3,4)-Md_3(4,2));
Gamma(3,2,5)=1/2*(Md_5(3,2)+Md_2(3,5)-Md_3(5,2));
Gamma(3,2,6)=1/2*(Md_6(3,2)+Md_2(3,6)-Md_3(6,2));
Gamma(3,2,7)=1/2*(Md_7(3,2)+Md_2(3,7)-Md_3(7,2));
Gamma(3,2,8)=1/2*(Md_8(3,2)+Md_2(3,8)-Md_3(8,2));
Gamma(3,3,1)=1/2*(Md_1(3,3)+Md_3(3,1)-Md_3(1,3));
Gamma(3,3,2)=1/2*(Md_2(3,3)+Md_3(3,2)-Md_3(2,3));
Gamma(3,3,3)=1/2*(Md_3(3,3)+Md_3(3,3)-Md_3(3,3));
Gamma(3,3,4)=1/2*(Md_4(3,3)+Md_3(3,4)-Md_3(4,3));
Gamma(3,3,5)=1/2*(Md_5(3,3)+Md_3(3,5)-Md_3(5,3));
Gamma(3,3,6)=1/2*(Md_6(3,3)+Md_3(3,6)-Md_3(6,3));
Gamma(3,3,7)=1/2*(Md_7(3,3)+Md_3(3,7)-Md_3(7,3));
Gamma(3,3,8)=1/2*(Md_8(3,3)+Md_3(3,8)-Md_3(8,3));
Gamma(3,4,1)=1/2*(Md_1(3,4)+Md_4(3,1)-Md_3(1,4));
Gamma(3,4,2)=1/2*(Md_2(3,4)+Md_4(3,2)-Md_3(2,4));
Gamma(3,4,3)=1/2*(Md_3(3,4)+Md_4(3,3)-Md_3(3,4));
Gamma(3,4,4)=1/2*(Md_4(3,4)+Md_4(3,4)-Md_3(4,4));
Gamma(3,4,5)=1/2*(Md_5(3,4)+Md_4(3,5)-Md_3(5,4));
Gamma(3,4,6)=1/2*(Md_6(3,4)+Md_4(3,6)-Md_3(6,4));
Gamma(3,4,7)=1/2*(Md_7(3,4)+Md_4(3,7)-Md_3(7,4));
Gamma(3,4,8)=1/2*(Md_8(3,4)+Md_4(3,8)-Md_3(8,4));
Gamma(3,5,1)=1/2*(Md_1(3,5)+Md_5(3,1)-Md_3(1,5));
Gamma(3,5,2)=1/2*(Md_2(3,5)+Md_5(3,2)-Md_3(2,5));
Gamma(3,5,3)=1/2*(Md_3(3,5)+Md_5(3,3)-Md_3(3,5));
Gamma(3,5,4)=1/2*(Md_4(3,5)+Md_5(3,4)-Md_3(4,5));
Gamma(3,5,5)=1/2*(Md_5(3,5)+Md_5(3,5)-Md_3(5,5));
Gamma(3,5,6)=1/2*(Md_6(3,5)+Md_5(3,6)-Md_3(6,5));
Gamma(3,5,7)=1/2*(Md_7(3,5)+Md_5(3,7)-Md_3(7,5));
Gamma(3,5,8)=1/2*(Md_8(3,5)+Md_5(3,8)-Md_3(8,5));
Gamma(3,6,1)=1/2*(Md_1(3,6)+Md_6(3,1)-Md_3(1,6));
Gamma(3,6,2)=1/2*(Md_2(3,6)+Md_6(3,2)-Md_3(2,6));
Gamma(3,6,3)=1/2*(Md_3(3,6)+Md_6(3,3)-Md_3(3,6));
Gamma(3,6,4)=1/2*(Md_4(3,6)+Md_6(3,4)-Md_3(4,6));
Gamma(3,6,5)=1/2*(Md_5(3,6)+Md_6(3,5)-Md_3(5,6));
Gamma(3,6,6)=1/2*(Md_6(3,6)+Md_6(3,6)-Md_3(6,6));
Gamma(3,6,7)=1/2*(Md_7(3,6)+Md_6(3,7)-Md_3(7,6));
Gamma(3,6,8)=1/2*(Md_8(3,6)+Md_6(3,8)-Md_3(8,6));
Gamma(3,7,1)=1/2*(Md_1(3,7)+Md_7(3,1)-Md_3(1,7));
Gamma(3,7,2)=1/2*(Md_2(3,7)+Md_7(3,2)-Md_3(2,7));
Gamma(3,7,3)=1/2*(Md_3(3,7)+Md_7(3,3)-Md_3(3,7));
Gamma(3,7,4)=1/2*(Md_4(3,7)+Md_7(3,4)-Md_3(4,7));
Gamma(3,7,5)=1/2*(Md_5(3,7)+Md_7(3,5)-Md_3(5,7));
Gamma(3,7,6)=1/2*(Md_6(3,7)+Md_7(3,6)-Md_3(6,7));
Gamma(3,7,7)=1/2*(Md_7(3,7)+Md_7(3,7)-Md_3(7,7));
Gamma(3,7,8)=1/2*(Md_8(3,7)+Md_7(3,8)-Md_3(8,7));
Gamma(3,8,1)=1/2*(Md_1(3,8)+Md_8(3,1)-Md_3(1,8));
Gamma(3,8,2)=1/2*(Md_2(3,8)+Md_8(3,2)-Md_3(2,8));
Gamma(3,8,3)=1/2*(Md_3(3,8)+Md_8(3,3)-Md_3(3,8));
Gamma(3,8,4)=1/2*(Md_4(3,8)+Md_8(3,4)-Md_3(4,8));
Gamma(3,8,5)=1/2*(Md_5(3,8)+Md_8(3,5)-Md_3(5,8));
Gamma(3,8,6)=1/2*(Md_6(3,8)+Md_8(3,6)-Md_3(6,8));
Gamma(3,8,7)=1/2*(Md_7(3,8)+Md_8(3,7)-Md_3(7,8));
Gamma(3,8,8)=1/2*(Md_8(3,8)+Md_8(3,8)-Md_3(8,8));
Gamma(4,1,1)=1/2*(Md_1(4,1)+Md_1(4,1)-Md_4(1,1));
Gamma(4,1,2)=1/2*(Md_2(4,1)+Md_1(4,2)-Md_4(2,1));
Gamma(4,1,3)=1/2*(Md_3(4,1)+Md_1(4,3)-Md_4(3,1));
Gamma(4,1,4)=1/2*(Md_4(4,1)+Md_1(4,4)-Md_4(4,1));
Gamma(4,1,5)=1/2*(Md_5(4,1)+Md_1(4,5)-Md_4(5,1));
Gamma(4,1,6)=1/2*(Md_6(4,1)+Md_1(4,6)-Md_4(6,1));
Gamma(4,1,7)=1/2*(Md_7(4,1)+Md_1(4,7)-Md_4(7,1));
Gamma(4,1,8)=1/2*(Md_8(4,1)+Md_1(4,8)-Md_4(8,1));
Gamma(4,2,1)=1/2*(Md_1(4,2)+Md_2(4,1)-Md_4(1,2));
Gamma(4,2,2)=1/2*(Md_2(4,2)+Md_2(4,2)-Md_4(2,2));
Gamma(4,2,3)=1/2*(Md_3(4,2)+Md_2(4,3)-Md_4(3,2));
Gamma(4,2,4)=1/2*(Md_4(4,2)+Md_2(4,4)-Md_4(4,2));
Gamma(4,2,5)=1/2*(Md_5(4,2)+Md_2(4,5)-Md_4(5,2));
Gamma(4,2,6)=1/2*(Md_6(4,2)+Md_2(4,6)-Md_4(6,2));
Gamma(4,2,7)=1/2*(Md_7(4,2)+Md_2(4,7)-Md_4(7,2));
Gamma(4,2,8)=1/2*(Md_8(4,2)+Md_2(4,8)-Md_4(8,2));
Gamma(4,3,1)=1/2*(Md_1(4,3)+Md_3(4,1)-Md_4(1,3));
Gamma(4,3,2)=1/2*(Md_2(4,3)+Md_3(4,2)-Md_4(2,3));
Gamma(4,3,3)=1/2*(Md_3(4,3)+Md_3(4,3)-Md_4(3,3));
Gamma(4,3,4)=1/2*(Md_4(4,3)+Md_3(4,4)-Md_4(4,3));
Gamma(4,3,5)=1/2*(Md_5(4,3)+Md_3(4,5)-Md_4(5,3));
Gamma(4,3,6)=1/2*(Md_6(4,3)+Md_3(4,6)-Md_4(6,3));
Gamma(4,3,7)=1/2*(Md_7(4,3)+Md_3(4,7)-Md_4(7,3));
Gamma(4,3,8)=1/2*(Md_8(4,3)+Md_3(4,8)-Md_4(8,3));
Gamma(4,4,1)=1/2*(Md_1(4,4)+Md_4(4,1)-Md_4(1,4));
Gamma(4,4,2)=1/2*(Md_2(4,4)+Md_4(4,2)-Md_4(2,4));
Gamma(4,4,3)=1/2*(Md_3(4,4)+Md_4(4,3)-Md_4(3,4));
Gamma(4,4,4)=1/2*(Md_4(4,4)+Md_4(4,4)-Md_4(4,4));
Gamma(4,4,5)=1/2*(Md_5(4,4)+Md_4(4,5)-Md_4(5,4));
Gamma(4,4,6)=1/2*(Md_6(4,4)+Md_4(4,6)-Md_4(6,4));
Gamma(4,4,7)=1/2*(Md_7(4,4)+Md_4(4,7)-Md_4(7,4));
Gamma(4,4,8)=1/2*(Md_8(4,4)+Md_4(4,8)-Md_4(8,4));
Gamma(4,5,1)=1/2*(Md_1(4,5)+Md_5(4,1)-Md_4(1,5));
Gamma(4,5,2)=1/2*(Md_2(4,5)+Md_5(4,2)-Md_4(2,5));
Gamma(4,5,3)=1/2*(Md_3(4,5)+Md_5(4,3)-Md_4(3,5));
Gamma(4,5,4)=1/2*(Md_4(4,5)+Md_5(4,4)-Md_4(4,5));
Gamma(4,5,5)=1/2*(Md_5(4,5)+Md_5(4,5)-Md_4(5,5));
Gamma(4,5,6)=1/2*(Md_6(4,5)+Md_5(4,6)-Md_4(6,5));
Gamma(4,5,7)=1/2*(Md_7(4,5)+Md_5(4,7)-Md_4(7,5));
Gamma(4,5,8)=1/2*(Md_8(4,5)+Md_5(4,8)-Md_4(8,5));
Gamma(4,6,1)=1/2*(Md_1(4,6)+Md_6(4,1)-Md_4(1,6));
Gamma(4,6,2)=1/2*(Md_2(4,6)+Md_6(4,2)-Md_4(2,6));
Gamma(4,6,3)=1/2*(Md_3(4,6)+Md_6(4,3)-Md_4(3,6));
Gamma(4,6,4)=1/2*(Md_4(4,6)+Md_6(4,4)-Md_4(4,6));
Gamma(4,6,5)=1/2*(Md_5(4,6)+Md_6(4,5)-Md_4(5,6));
Gamma(4,6,6)=1/2*(Md_6(4,6)+Md_6(4,6)-Md_4(6,6));
Gamma(4,6,7)=1/2*(Md_7(4,6)+Md_6(4,7)-Md_4(7,6));
Gamma(4,6,8)=1/2*(Md_8(4,6)+Md_6(4,8)-Md_4(8,6));
Gamma(4,7,1)=1/2*(Md_1(4,7)+Md_7(4,1)-Md_4(1,7));
Gamma(4,7,2)=1/2*(Md_2(4,7)+Md_7(4,2)-Md_4(2,7));
Gamma(4,7,3)=1/2*(Md_3(4,7)+Md_7(4,3)-Md_4(3,7));
Gamma(4,7,4)=1/2*(Md_4(4,7)+Md_7(4,4)-Md_4(4,7));
Gamma(4,7,5)=1/2*(Md_5(4,7)+Md_7(4,5)-Md_4(5,7));
Gamma(4,7,6)=1/2*(Md_6(4,7)+Md_7(4,6)-Md_4(6,7));
Gamma(4,7,7)=1/2*(Md_7(4,7)+Md_7(4,7)-Md_4(7,7));
Gamma(4,7,8)=1/2*(Md_8(4,7)+Md_7(4,8)-Md_4(8,7));
Gamma(4,8,1)=1/2*(Md_1(4,8)+Md_8(4,1)-Md_4(1,8));
Gamma(4,8,2)=1/2*(Md_2(4,8)+Md_8(4,2)-Md_4(2,8));
Gamma(4,8,3)=1/2*(Md_3(4,8)+Md_8(4,3)-Md_4(3,8));
Gamma(4,8,4)=1/2*(Md_4(4,8)+Md_8(4,4)-Md_4(4,8));
Gamma(4,8,5)=1/2*(Md_5(4,8)+Md_8(4,5)-Md_4(5,8));
Gamma(4,8,6)=1/2*(Md_6(4,8)+Md_8(4,6)-Md_4(6,8));
Gamma(4,8,7)=1/2*(Md_7(4,8)+Md_8(4,7)-Md_4(7,8));
Gamma(4,8,8)=1/2*(Md_8(4,8)+Md_8(4,8)-Md_4(8,8));
Gamma(5,1,1)=1/2*(Md_1(5,1)+Md_1(5,1)-Md_5(1,1));
Gamma(5,1,2)=1/2*(Md_2(5,1)+Md_1(5,2)-Md_5(2,1));
Gamma(5,1,3)=1/2*(Md_3(5,1)+Md_1(5,3)-Md_5(3,1));
Gamma(5,1,4)=1/2*(Md_4(5,1)+Md_1(5,4)-Md_5(4,1));
Gamma(5,1,5)=1/2*(Md_5(5,1)+Md_1(5,5)-Md_5(5,1));
Gamma(5,1,6)=1/2*(Md_6(5,1)+Md_1(5,6)-Md_5(6,1));
Gamma(5,1,7)=1/2*(Md_7(5,1)+Md_1(5,7)-Md_5(7,1));
Gamma(5,1,8)=1/2*(Md_8(5,1)+Md_1(5,8)-Md_5(8,1));
Gamma(5,2,1)=1/2*(Md_1(5,2)+Md_2(5,1)-Md_5(1,2));
Gamma(5,2,2)=1/2*(Md_2(5,2)+Md_2(5,2)-Md_5(2,2));
Gamma(5,2,3)=1/2*(Md_3(5,2)+Md_2(5,3)-Md_5(3,2));
Gamma(5,2,4)=1/2*(Md_4(5,2)+Md_2(5,4)-Md_5(4,2));
Gamma(5,2,5)=1/2*(Md_5(5,2)+Md_2(5,5)-Md_5(5,2));
Gamma(5,2,6)=1/2*(Md_6(5,2)+Md_2(5,6)-Md_5(6,2));
Gamma(5,2,7)=1/2*(Md_7(5,2)+Md_2(5,7)-Md_5(7,2));
Gamma(5,2,8)=1/2*(Md_8(5,2)+Md_2(5,8)-Md_5(8,2));
Gamma(5,3,1)=1/2*(Md_1(5,3)+Md_3(5,1)-Md_5(1,3));
Gamma(5,3,2)=1/2*(Md_2(5,3)+Md_3(5,2)-Md_5(2,3));
Gamma(5,3,3)=1/2*(Md_3(5,3)+Md_3(5,3)-Md_5(3,3));
Gamma(5,3,4)=1/2*(Md_4(5,3)+Md_3(5,4)-Md_5(4,3));
Gamma(5,3,5)=1/2*(Md_5(5,3)+Md_3(5,5)-Md_5(5,3));
Gamma(5,3,6)=1/2*(Md_6(5,3)+Md_3(5,6)-Md_5(6,3));
Gamma(5,3,7)=1/2*(Md_7(5,3)+Md_3(5,7)-Md_5(7,3));
Gamma(5,3,8)=1/2*(Md_8(5,3)+Md_3(5,8)-Md_5(8,3));
Gamma(5,4,1)=1/2*(Md_1(5,4)+Md_4(5,1)-Md_5(1,4));
Gamma(5,4,2)=1/2*(Md_2(5,4)+Md_4(5,2)-Md_5(2,4));
Gamma(5,4,3)=1/2*(Md_3(5,4)+Md_4(5,3)-Md_5(3,4));
Gamma(5,4,4)=1/2*(Md_4(5,4)+Md_4(5,4)-Md_5(4,4));
Gamma(5,4,5)=1/2*(Md_5(5,4)+Md_4(5,5)-Md_5(5,4));
Gamma(5,4,6)=1/2*(Md_6(5,4)+Md_4(5,6)-Md_5(6,4));
Gamma(5,4,7)=1/2*(Md_7(5,4)+Md_4(5,7)-Md_5(7,4));
Gamma(5,4,8)=1/2*(Md_8(5,4)+Md_4(5,8)-Md_5(8,4));
Gamma(5,5,1)=1/2*(Md_1(5,5)+Md_5(5,1)-Md_5(1,5));
Gamma(5,5,2)=1/2*(Md_2(5,5)+Md_5(5,2)-Md_5(2,5));
Gamma(5,5,3)=1/2*(Md_3(5,5)+Md_5(5,3)-Md_5(3,5));
Gamma(5,5,4)=1/2*(Md_4(5,5)+Md_5(5,4)-Md_5(4,5));
Gamma(5,5,5)=1/2*(Md_5(5,5)+Md_5(5,5)-Md_5(5,5));
Gamma(5,5,6)=1/2*(Md_6(5,5)+Md_5(5,6)-Md_5(6,5));
Gamma(5,5,7)=1/2*(Md_7(5,5)+Md_5(5,7)-Md_5(7,5));
Gamma(5,5,8)=1/2*(Md_8(5,5)+Md_5(5,8)-Md_5(8,5));
Gamma(5,6,1)=1/2*(Md_1(5,6)+Md_6(5,1)-Md_5(1,6));
Gamma(5,6,2)=1/2*(Md_2(5,6)+Md_6(5,2)-Md_5(2,6));
Gamma(5,6,3)=1/2*(Md_3(5,6)+Md_6(5,3)-Md_5(3,6));
Gamma(5,6,4)=1/2*(Md_4(5,6)+Md_6(5,4)-Md_5(4,6));
Gamma(5,6,5)=1/2*(Md_5(5,6)+Md_6(5,5)-Md_5(5,6));
Gamma(5,6,6)=1/2*(Md_6(5,6)+Md_6(5,6)-Md_5(6,6));
Gamma(5,6,7)=1/2*(Md_7(5,6)+Md_6(5,7)-Md_5(7,6));
Gamma(5,6,8)=1/2*(Md_8(5,6)+Md_6(5,8)-Md_5(8,6));
Gamma(5,7,1)=1/2*(Md_1(5,7)+Md_7(5,1)-Md_5(1,7));
Gamma(5,7,2)=1/2*(Md_2(5,7)+Md_7(5,2)-Md_5(2,7));
Gamma(5,7,3)=1/2*(Md_3(5,7)+Md_7(5,3)-Md_5(3,7));
Gamma(5,7,4)=1/2*(Md_4(5,7)+Md_7(5,4)-Md_5(4,7));
Gamma(5,7,5)=1/2*(Md_5(5,7)+Md_7(5,5)-Md_5(5,7));
Gamma(5,7,6)=1/2*(Md_6(5,7)+Md_7(5,6)-Md_5(6,7));
Gamma(5,7,7)=1/2*(Md_7(5,7)+Md_7(5,7)-Md_5(7,7));
Gamma(5,7,8)=1/2*(Md_8(5,7)+Md_7(5,8)-Md_5(8,7));
Gamma(5,8,1)=1/2*(Md_1(5,8)+Md_8(5,1)-Md_5(1,8));
Gamma(5,8,2)=1/2*(Md_2(5,8)+Md_8(5,2)-Md_5(2,8));
Gamma(5,8,3)=1/2*(Md_3(5,8)+Md_8(5,3)-Md_5(3,8));
Gamma(5,8,4)=1/2*(Md_4(5,8)+Md_8(5,4)-Md_5(4,8));
Gamma(5,8,5)=1/2*(Md_5(5,8)+Md_8(5,5)-Md_5(5,8));
Gamma(5,8,6)=1/2*(Md_6(5,8)+Md_8(5,6)-Md_5(6,8));
Gamma(5,8,7)=1/2*(Md_7(5,8)+Md_8(5,7)-Md_5(7,8));
Gamma(5,8,8)=1/2*(Md_8(5,8)+Md_8(5,8)-Md_5(8,8));
Gamma(6,1,1)=1/2*(Md_1(6,1)+Md_1(6,1)-Md_6(1,1));
Gamma(6,1,2)=1/2*(Md_2(6,1)+Md_1(6,2)-Md_6(2,1));
Gamma(6,1,3)=1/2*(Md_3(6,1)+Md_1(6,3)-Md_6(3,1));
Gamma(6,1,4)=1/2*(Md_4(6,1)+Md_1(6,4)-Md_6(4,1));
Gamma(6,1,5)=1/2*(Md_5(6,1)+Md_1(6,5)-Md_6(5,1));
Gamma(6,1,6)=1/2*(Md_6(6,1)+Md_1(6,6)-Md_6(6,1));
Gamma(6,1,7)=1/2*(Md_7(6,1)+Md_1(6,7)-Md_6(7,1));
Gamma(6,1,8)=1/2*(Md_8(6,1)+Md_1(6,8)-Md_6(8,1));
Gamma(6,2,1)=1/2*(Md_1(6,2)+Md_2(6,1)-Md_6(1,2));
Gamma(6,2,2)=1/2*(Md_2(6,2)+Md_2(6,2)-Md_6(2,2));
Gamma(6,2,3)=1/2*(Md_3(6,2)+Md_2(6,3)-Md_6(3,2));
Gamma(6,2,4)=1/2*(Md_4(6,2)+Md_2(6,4)-Md_6(4,2));
Gamma(6,2,5)=1/2*(Md_5(6,2)+Md_2(6,5)-Md_6(5,2));
Gamma(6,2,6)=1/2*(Md_6(6,2)+Md_2(6,6)-Md_6(6,2));
Gamma(6,2,7)=1/2*(Md_7(6,2)+Md_2(6,7)-Md_6(7,2));
Gamma(6,2,8)=1/2*(Md_8(6,2)+Md_2(6,8)-Md_6(8,2));
Gamma(6,3,1)=1/2*(Md_1(6,3)+Md_3(6,1)-Md_6(1,3));
Gamma(6,3,2)=1/2*(Md_2(6,3)+Md_3(6,2)-Md_6(2,3));
Gamma(6,3,3)=1/2*(Md_3(6,3)+Md_3(6,3)-Md_6(3,3));
Gamma(6,3,4)=1/2*(Md_4(6,3)+Md_3(6,4)-Md_6(4,3));
Gamma(6,3,5)=1/2*(Md_5(6,3)+Md_3(6,5)-Md_6(5,3));
Gamma(6,3,6)=1/2*(Md_6(6,3)+Md_3(6,6)-Md_6(6,3));
Gamma(6,3,7)=1/2*(Md_7(6,3)+Md_3(6,7)-Md_6(7,3));
Gamma(6,3,8)=1/2*(Md_8(6,3)+Md_3(6,8)-Md_6(8,3));
Gamma(6,4,1)=1/2*(Md_1(6,4)+Md_4(6,1)-Md_6(1,4));
Gamma(6,4,2)=1/2*(Md_2(6,4)+Md_4(6,2)-Md_6(2,4));
Gamma(6,4,3)=1/2*(Md_3(6,4)+Md_4(6,3)-Md_6(3,4));
Gamma(6,4,4)=1/2*(Md_4(6,4)+Md_4(6,4)-Md_6(4,4));
Gamma(6,4,5)=1/2*(Md_5(6,4)+Md_4(6,5)-Md_6(5,4));
Gamma(6,4,6)=1/2*(Md_6(6,4)+Md_4(6,6)-Md_6(6,4));
Gamma(6,4,7)=1/2*(Md_7(6,4)+Md_4(6,7)-Md_6(7,4));
Gamma(6,4,8)=1/2*(Md_8(6,4)+Md_4(6,8)-Md_6(8,4));
Gamma(6,5,1)=1/2*(Md_1(6,5)+Md_5(6,1)-Md_6(1,5));
Gamma(6,5,2)=1/2*(Md_2(6,5)+Md_5(6,2)-Md_6(2,5));
Gamma(6,5,3)=1/2*(Md_3(6,5)+Md_5(6,3)-Md_6(3,5));
Gamma(6,5,4)=1/2*(Md_4(6,5)+Md_5(6,4)-Md_6(4,5));
Gamma(6,5,5)=1/2*(Md_5(6,5)+Md_5(6,5)-Md_6(5,5));
Gamma(6,5,6)=1/2*(Md_6(6,5)+Md_5(6,6)-Md_6(6,5));
Gamma(6,5,7)=1/2*(Md_7(6,5)+Md_5(6,7)-Md_6(7,5));
Gamma(6,5,8)=1/2*(Md_8(6,5)+Md_5(6,8)-Md_6(8,5));
Gamma(6,6,1)=1/2*(Md_1(6,6)+Md_6(6,1)-Md_6(1,6));
Gamma(6,6,2)=1/2*(Md_2(6,6)+Md_6(6,2)-Md_6(2,6));
Gamma(6,6,3)=1/2*(Md_3(6,6)+Md_6(6,3)-Md_6(3,6));
Gamma(6,6,4)=1/2*(Md_4(6,6)+Md_6(6,4)-Md_6(4,6));
Gamma(6,6,5)=1/2*(Md_5(6,6)+Md_6(6,5)-Md_6(5,6));
Gamma(6,6,6)=1/2*(Md_6(6,6)+Md_6(6,6)-Md_6(6,6));
Gamma(6,6,7)=1/2*(Md_7(6,6)+Md_6(6,7)-Md_6(7,6));
Gamma(6,6,8)=1/2*(Md_8(6,6)+Md_6(6,8)-Md_6(8,6));
Gamma(6,7,1)=1/2*(Md_1(6,7)+Md_7(6,1)-Md_6(1,7));
Gamma(6,7,2)=1/2*(Md_2(6,7)+Md_7(6,2)-Md_6(2,7));
Gamma(6,7,3)=1/2*(Md_3(6,7)+Md_7(6,3)-Md_6(3,7));
Gamma(6,7,4)=1/2*(Md_4(6,7)+Md_7(6,4)-Md_6(4,7));
Gamma(6,7,5)=1/2*(Md_5(6,7)+Md_7(6,5)-Md_6(5,7));
Gamma(6,7,6)=1/2*(Md_6(6,7)+Md_7(6,6)-Md_6(6,7));
Gamma(6,7,7)=1/2*(Md_7(6,7)+Md_7(6,7)-Md_6(7,7));
Gamma(6,7,8)=1/2*(Md_8(6,7)+Md_7(6,8)-Md_6(8,7));
Gamma(6,8,1)=1/2*(Md_1(6,8)+Md_8(6,1)-Md_6(1,8));
Gamma(6,8,2)=1/2*(Md_2(6,8)+Md_8(6,2)-Md_6(2,8));
Gamma(6,8,3)=1/2*(Md_3(6,8)+Md_8(6,3)-Md_6(3,8));
Gamma(6,8,4)=1/2*(Md_4(6,8)+Md_8(6,4)-Md_6(4,8));
Gamma(6,8,5)=1/2*(Md_5(6,8)+Md_8(6,5)-Md_6(5,8));
Gamma(6,8,6)=1/2*(Md_6(6,8)+Md_8(6,6)-Md_6(6,8));
Gamma(6,8,7)=1/2*(Md_7(6,8)+Md_8(6,7)-Md_6(7,8));
Gamma(6,8,8)=1/2*(Md_8(6,8)+Md_8(6,8)-Md_6(8,8));
Gamma(7,1,1)=1/2*(Md_1(7,1)+Md_1(7,1)-Md_7(1,1));
Gamma(7,1,2)=1/2*(Md_2(7,1)+Md_1(7,2)-Md_7(2,1));
Gamma(7,1,3)=1/2*(Md_3(7,1)+Md_1(7,3)-Md_7(3,1));
Gamma(7,1,4)=1/2*(Md_4(7,1)+Md_1(7,4)-Md_7(4,1));
Gamma(7,1,5)=1/2*(Md_5(7,1)+Md_1(7,5)-Md_7(5,1));
Gamma(7,1,6)=1/2*(Md_6(7,1)+Md_1(7,6)-Md_7(6,1));
Gamma(7,1,7)=1/2*(Md_7(7,1)+Md_1(7,7)-Md_7(7,1));
Gamma(7,1,8)=1/2*(Md_8(7,1)+Md_1(7,8)-Md_7(8,1));
Gamma(7,2,1)=1/2*(Md_1(7,2)+Md_2(7,1)-Md_7(1,2));
Gamma(7,2,2)=1/2*(Md_2(7,2)+Md_2(7,2)-Md_7(2,2));
Gamma(7,2,3)=1/2*(Md_3(7,2)+Md_2(7,3)-Md_7(3,2));
Gamma(7,2,4)=1/2*(Md_4(7,2)+Md_2(7,4)-Md_7(4,2));
Gamma(7,2,5)=1/2*(Md_5(7,2)+Md_2(7,5)-Md_7(5,2));
Gamma(7,2,6)=1/2*(Md_6(7,2)+Md_2(7,6)-Md_7(6,2));
Gamma(7,2,7)=1/2*(Md_7(7,2)+Md_2(7,7)-Md_7(7,2));
Gamma(7,2,8)=1/2*(Md_8(7,2)+Md_2(7,8)-Md_7(8,2));
Gamma(7,3,1)=1/2*(Md_1(7,3)+Md_3(7,1)-Md_7(1,3));
Gamma(7,3,2)=1/2*(Md_2(7,3)+Md_3(7,2)-Md_7(2,3));
Gamma(7,3,3)=1/2*(Md_3(7,3)+Md_3(7,3)-Md_7(3,3));
Gamma(7,3,4)=1/2*(Md_4(7,3)+Md_3(7,4)-Md_7(4,3));
Gamma(7,3,5)=1/2*(Md_5(7,3)+Md_3(7,5)-Md_7(5,3));
Gamma(7,3,6)=1/2*(Md_6(7,3)+Md_3(7,6)-Md_7(6,3));
Gamma(7,3,7)=1/2*(Md_7(7,3)+Md_3(7,7)-Md_7(7,3));
Gamma(7,3,8)=1/2*(Md_8(7,3)+Md_3(7,8)-Md_7(8,3));
Gamma(7,4,1)=1/2*(Md_1(7,4)+Md_4(7,1)-Md_7(1,4));
Gamma(7,4,2)=1/2*(Md_2(7,4)+Md_4(7,2)-Md_7(2,4));
Gamma(7,4,3)=1/2*(Md_3(7,4)+Md_4(7,3)-Md_7(3,4));
Gamma(7,4,4)=1/2*(Md_4(7,4)+Md_4(7,4)-Md_7(4,4));
Gamma(7,4,5)=1/2*(Md_5(7,4)+Md_4(7,5)-Md_7(5,4));
Gamma(7,4,6)=1/2*(Md_6(7,4)+Md_4(7,6)-Md_7(6,4));
Gamma(7,4,7)=1/2*(Md_7(7,4)+Md_4(7,7)-Md_7(7,4));
Gamma(7,4,8)=1/2*(Md_8(7,4)+Md_4(7,8)-Md_7(8,4));
Gamma(7,5,1)=1/2*(Md_1(7,5)+Md_5(7,1)-Md_7(1,5));
Gamma(7,5,2)=1/2*(Md_2(7,5)+Md_5(7,2)-Md_7(2,5));
Gamma(7,5,3)=1/2*(Md_3(7,5)+Md_5(7,3)-Md_7(3,5));
Gamma(7,5,4)=1/2*(Md_4(7,5)+Md_5(7,4)-Md_7(4,5));
Gamma(7,5,5)=1/2*(Md_5(7,5)+Md_5(7,5)-Md_7(5,5));
Gamma(7,5,6)=1/2*(Md_6(7,5)+Md_5(7,6)-Md_7(6,5));
Gamma(7,5,7)=1/2*(Md_7(7,5)+Md_5(7,7)-Md_7(7,5));
Gamma(7,5,8)=1/2*(Md_8(7,5)+Md_5(7,8)-Md_7(8,5));
Gamma(7,6,1)=1/2*(Md_1(7,6)+Md_6(7,1)-Md_7(1,6));
Gamma(7,6,2)=1/2*(Md_2(7,6)+Md_6(7,2)-Md_7(2,6));
Gamma(7,6,3)=1/2*(Md_3(7,6)+Md_6(7,3)-Md_7(3,6));
Gamma(7,6,4)=1/2*(Md_4(7,6)+Md_6(7,4)-Md_7(4,6));
Gamma(7,6,5)=1/2*(Md_5(7,6)+Md_6(7,5)-Md_7(5,6));
Gamma(7,6,6)=1/2*(Md_6(7,6)+Md_6(7,6)-Md_7(6,6));
Gamma(7,6,7)=1/2*(Md_7(7,6)+Md_6(7,7)-Md_7(7,6));
Gamma(7,6,8)=1/2*(Md_8(7,6)+Md_6(7,8)-Md_7(8,6));
Gamma(7,7,1)=1/2*(Md_1(7,7)+Md_7(7,1)-Md_7(1,7));
Gamma(7,7,2)=1/2*(Md_2(7,7)+Md_7(7,2)-Md_7(2,7));
Gamma(7,7,3)=1/2*(Md_3(7,7)+Md_7(7,3)-Md_7(3,7));
Gamma(7,7,4)=1/2*(Md_4(7,7)+Md_7(7,4)-Md_7(4,7));
Gamma(7,7,5)=1/2*(Md_5(7,7)+Md_7(7,5)-Md_7(5,7));
Gamma(7,7,6)=1/2*(Md_6(7,7)+Md_7(7,6)-Md_7(6,7));
Gamma(7,7,7)=1/2*(Md_7(7,7)+Md_7(7,7)-Md_7(7,7));
Gamma(7,7,8)=1/2*(Md_8(7,7)+Md_7(7,8)-Md_7(8,7));
Gamma(7,8,1)=1/2*(Md_1(7,8)+Md_8(7,1)-Md_7(1,8));
Gamma(7,8,2)=1/2*(Md_2(7,8)+Md_8(7,2)-Md_7(2,8));
Gamma(7,8,3)=1/2*(Md_3(7,8)+Md_8(7,3)-Md_7(3,8));
Gamma(7,8,4)=1/2*(Md_4(7,8)+Md_8(7,4)-Md_7(4,8));
Gamma(7,8,5)=1/2*(Md_5(7,8)+Md_8(7,5)-Md_7(5,8));
Gamma(7,8,6)=1/2*(Md_6(7,8)+Md_8(7,6)-Md_7(6,8));
Gamma(7,8,7)=1/2*(Md_7(7,8)+Md_8(7,7)-Md_7(7,8));
Gamma(7,8,8)=1/2*(Md_8(7,8)+Md_8(7,8)-Md_7(8,8));
Gamma(8,1,1)=1/2*(Md_1(8,1)+Md_1(8,1)-Md_8(1,1));
Gamma(8,1,2)=1/2*(Md_2(8,1)+Md_1(8,2)-Md_8(2,1));
Gamma(8,1,3)=1/2*(Md_3(8,1)+Md_1(8,3)-Md_8(3,1));
Gamma(8,1,4)=1/2*(Md_4(8,1)+Md_1(8,4)-Md_8(4,1));
Gamma(8,1,5)=1/2*(Md_5(8,1)+Md_1(8,5)-Md_8(5,1));
Gamma(8,1,6)=1/2*(Md_6(8,1)+Md_1(8,6)-Md_8(6,1));
Gamma(8,1,7)=1/2*(Md_7(8,1)+Md_1(8,7)-Md_8(7,1));
Gamma(8,1,8)=1/2*(Md_8(8,1)+Md_1(8,8)-Md_8(8,1));
Gamma(8,2,1)=1/2*(Md_1(8,2)+Md_2(8,1)-Md_8(1,2));
Gamma(8,2,2)=1/2*(Md_2(8,2)+Md_2(8,2)-Md_8(2,2));
Gamma(8,2,3)=1/2*(Md_3(8,2)+Md_2(8,3)-Md_8(3,2));
Gamma(8,2,4)=1/2*(Md_4(8,2)+Md_2(8,4)-Md_8(4,2));
Gamma(8,2,5)=1/2*(Md_5(8,2)+Md_2(8,5)-Md_8(5,2));
Gamma(8,2,6)=1/2*(Md_6(8,2)+Md_2(8,6)-Md_8(6,2));
Gamma(8,2,7)=1/2*(Md_7(8,2)+Md_2(8,7)-Md_8(7,2));
Gamma(8,2,8)=1/2*(Md_8(8,2)+Md_2(8,8)-Md_8(8,2));
Gamma(8,3,1)=1/2*(Md_1(8,3)+Md_3(8,1)-Md_8(1,3));
Gamma(8,3,2)=1/2*(Md_2(8,3)+Md_3(8,2)-Md_8(2,3));
Gamma(8,3,3)=1/2*(Md_3(8,3)+Md_3(8,3)-Md_8(3,3));
Gamma(8,3,4)=1/2*(Md_4(8,3)+Md_3(8,4)-Md_8(4,3));
Gamma(8,3,5)=1/2*(Md_5(8,3)+Md_3(8,5)-Md_8(5,3));
Gamma(8,3,6)=1/2*(Md_6(8,3)+Md_3(8,6)-Md_8(6,3));
Gamma(8,3,7)=1/2*(Md_7(8,3)+Md_3(8,7)-Md_8(7,3));
Gamma(8,3,8)=1/2*(Md_8(8,3)+Md_3(8,8)-Md_8(8,3));
Gamma(8,4,1)=1/2*(Md_1(8,4)+Md_4(8,1)-Md_8(1,4));
Gamma(8,4,2)=1/2*(Md_2(8,4)+Md_4(8,2)-Md_8(2,4));
Gamma(8,4,3)=1/2*(Md_3(8,4)+Md_4(8,3)-Md_8(3,4));
Gamma(8,4,4)=1/2*(Md_4(8,4)+Md_4(8,4)-Md_8(4,4));
Gamma(8,4,5)=1/2*(Md_5(8,4)+Md_4(8,5)-Md_8(5,4));
Gamma(8,4,6)=1/2*(Md_6(8,4)+Md_4(8,6)-Md_8(6,4));
Gamma(8,4,7)=1/2*(Md_7(8,4)+Md_4(8,7)-Md_8(7,4));
Gamma(8,4,8)=1/2*(Md_8(8,4)+Md_4(8,8)-Md_8(8,4));
Gamma(8,5,1)=1/2*(Md_1(8,5)+Md_5(8,1)-Md_8(1,5));
Gamma(8,5,2)=1/2*(Md_2(8,5)+Md_5(8,2)-Md_8(2,5));
Gamma(8,5,3)=1/2*(Md_3(8,5)+Md_5(8,3)-Md_8(3,5));
Gamma(8,5,4)=1/2*(Md_4(8,5)+Md_5(8,4)-Md_8(4,5));
Gamma(8,5,5)=1/2*(Md_5(8,5)+Md_5(8,5)-Md_8(5,5));
Gamma(8,5,6)=1/2*(Md_6(8,5)+Md_5(8,6)-Md_8(6,5));
Gamma(8,5,7)=1/2*(Md_7(8,5)+Md_5(8,7)-Md_8(7,5));
Gamma(8,5,8)=1/2*(Md_8(8,5)+Md_5(8,8)-Md_8(8,5));
Gamma(8,6,1)=1/2*(Md_1(8,6)+Md_6(8,1)-Md_8(1,6));
Gamma(8,6,2)=1/2*(Md_2(8,6)+Md_6(8,2)-Md_8(2,6));
Gamma(8,6,3)=1/2*(Md_3(8,6)+Md_6(8,3)-Md_8(3,6));
Gamma(8,6,4)=1/2*(Md_4(8,6)+Md_6(8,4)-Md_8(4,6));
Gamma(8,6,5)=1/2*(Md_5(8,6)+Md_6(8,5)-Md_8(5,6));
Gamma(8,6,6)=1/2*(Md_6(8,6)+Md_6(8,6)-Md_8(6,6));
Gamma(8,6,7)=1/2*(Md_7(8,6)+Md_6(8,7)-Md_8(7,6));
Gamma(8,6,8)=1/2*(Md_8(8,6)+Md_6(8,8)-Md_8(8,6));
Gamma(8,7,1)=1/2*(Md_1(8,7)+Md_7(8,1)-Md_8(1,7));
Gamma(8,7,2)=1/2*(Md_2(8,7)+Md_7(8,2)-Md_8(2,7));
Gamma(8,7,3)=1/2*(Md_3(8,7)+Md_7(8,3)-Md_8(3,7));
Gamma(8,7,4)=1/2*(Md_4(8,7)+Md_7(8,4)-Md_8(4,7));
Gamma(8,7,5)=1/2*(Md_5(8,7)+Md_7(8,5)-Md_8(5,7));
Gamma(8,7,6)=1/2*(Md_6(8,7)+Md_7(8,6)-Md_8(6,7));
Gamma(8,7,7)=1/2*(Md_7(8,7)+Md_7(8,7)-Md_8(7,7));
Gamma(8,7,8)=1/2*(Md_8(8,7)+Md_7(8,8)-Md_8(8,7));
Gamma(8,8,1)=1/2*(Md_1(8,8)+Md_8(8,1)-Md_8(1,8));
Gamma(8,8,2)=1/2*(Md_2(8,8)+Md_8(8,2)-Md_8(2,8));
Gamma(8,8,3)=1/2*(Md_3(8,8)+Md_8(8,3)-Md_8(3,8));
Gamma(8,8,4)=1/2*(Md_4(8,8)+Md_8(8,4)-Md_8(4,8));
Gamma(8,8,5)=1/2*(Md_5(8,8)+Md_8(8,5)-Md_8(5,8));
Gamma(8,8,6)=1/2*(Md_6(8,8)+Md_8(8,6)-Md_8(6,8));
Gamma(8,8,7)=1/2*(Md_7(8,8)+Md_8(8,7)-Md_8(7,8));
Gamma(8,8,8)=1/2*(Md_8(8,8)+Md_8(8,8)-Md_8(8,8));