function [p,q,r,s,v,w,f1,f2] = Two_Thin_Lenses(FF1,FF2,LL)

%  
%   [p,q,r,s,v,w,f1,f2] = Two_Thin_Lenses(FF1,FF2,LL)
%
%    Calculate cardinal points from A, B, C, D
%
%    It calculates symbolically the A, B, C, D (it needs symbolic Toolbox)
%    and the it determines the numerical values
%
%    Input:
%
%    FF1    = Focal distance of left thin lens (mm)
%    FF2    = Focal distance of right thin lens (mm)
%    LL     = Lenses distance (mm)
%    
%    Output:  p,q,r,s,v,w,f1,f2 (all in mm)
%

%
%    Determine symbilically the A, B, C, D elements 
%
syms  f1 f2 L

M1 = [1 0; -1/f1 1];
M2 = [1 L; 0 1];
M3 = [1 0; -1/f2 1];

MM = M3*M2*M1;
ABCD = simple(MM)

AA = MM(1,1);
AA = simple(AA);
BB = MM(1,2);
BB = simple(BB);
CC = MM(2,1);
CC = simple(CC);
DD = MM(2,2);
DD = simple(DD);

A  = subs(AA,{f1,f2,L},{FF1,FF2,LL});
B  = subs(BB,{f1,f2,L},{FF1,FF2,LL});
C  = subs(CC,{f1,f2,L},{FF1,FF2,LL});
D  = subs(DD,{f1,f2,L},{FF1,FF2,LL});

ABCD_num = [A B; C D]


p  = D/C;
q  = -A/C;
r  = (D-1)/C;
s  = (1-A)/C;
v  = (D-1)/C;
w  = (1-A)/C;
f1 = 1/C;
f2 = -1/C;