%   MAT4.M
%
%   AUGUST 16th 1994
%
%   INPUT MATRICES FOR dioel, dioin and diossl

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   NOTE !!!   BEFOR CALLING  mat4      SET  DESIRABLE           %
%              VALUES OF  z, e1(z), e2(z)                        %
%              ( z  IS ONLY ORDER NUMBER )                       %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%   EXAMPLE 5.
%   FOR EQUATION

%   AX + BY = C

%   WHERE  A = UA.SA.VA
%          B = UB.SB.VB

%   UA = [ 1  0  0  1 |   VA = [ 1  0  2  0 |
%        | 1  0  0  0 |        | 0  1  1  1 |
%        | 0  0  1  1 |        | 0  0  0  1 |
%        | 0  1  0  1 ]        | 2  2  0  0 ]

%   SA = [ 1  0    0      0           |
%        | 0  1-s  0      0           |
%        | 0  0    1-s^2  0           |
%        | 0  0    0      1+s-s^2-s^3 ]

%   UB = [ 1+e1 0    0  1   |    VB = [ 3  2  0  0 |
%        | 1    0    0  e1  |         | 0  0  1  0 |
%        | 0    0    1  1   |         | 1  0  2  2 |
%        | 0    1    0  1   ]         | 1  1  1  1 ]

%   SB = [ 1  0          0              0                          |
%        | 0  1-(1+e2)s  0              0                          |
%        | 0  0          1-((1+e2)s)^2  0                          |
%        | 0  0          0              (1+(1+e2)s)*(1-((1+e2)s)^2)]


%   C  = [ 1   0   0   0 |
%        | 0   1   0   0 |
%        | 0   0   1   0 |
%        | 0   0   0   1 ]

%   U  = [ 0   0   0   0 |
%        | 0   0   0   0 |
%        | 0   0   0   1 |
%        | 0   0   0   0 ]

%   For matrix A  (mxm), where m=4, solution degree r=2
%   and matrix is A row reduced  with  sum=deg(row1)+deg(row2)=6
%   is number of interpol. points
%   k=sum+m*(r+1)  --> k=18 

%   ALPHA is (m x k)  and  SJ is (1 x k)  

UA=[1 0 0 1; 1 0 0 0; 0 0 1 1; 0 1 0 1];
degUA=0;
SA=[1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
0 1 0 0 0 -1 0 0 0 0 0 0 0 0 0 0;
0 0 1 0 0 0 0 0 0 0 -1 0 0 0 0 0;
0 0 0 1 0 0 0 1 0 0 0 -1 0 0 0 -1];
degSA=3;
VA=[1 0 2 0; 0 1 1 1; 0 0 0 1; 2 2 0 0];
degVA=0;
UB=[1+e1(z) 0 0 1;
1 0 0 e1(z);
0 0 1 1;
0 1+e1(z) 0 1];
degUB=0;
SB=[1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
0 1 0 0 0 -(1+e2(z)) 0 0 0 0 0 0 0 0 0 0;
0 0 1 0 0 0 0 0 0 0 -(1+e2(z))^2 0 0 0 0 0;
0 0 0 1 0 0 0 1+e2(z) 0 0 0 -(1+e2(z))^2 0 0 0 -(1+e2(z))^3];
degSB=3;
VB=[3 2 0 0; 0 0 1 0; 0 0 2 2; 1 1 1 1];
degVB=0;
C=eye(4);
degC=0;
U=[0 0 0 0; 0 0 0 0; 0 0 0 1; 0 0 0 0];