%   MAT3.M
%
%   AUGUST 13th 1994
%
%   INPUT MATRICES FOR dioel, dioin and diossl

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   NOTE !!!   BEFOR CALLING  mat3      SET  DESIRABLE           %
%              VALUES OF  z, e1(z), e2(z)                        %
%              ( z  IS ONLY ORDER NUMBER )                       %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%   EXAMPLE 2.
%   FOR EQUATION

%   AX + BY = C

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

%   UA = [ 1   1   0 |    SA = [ 1  0     0     |    VA = [ 1   0   0 |
%        | 0   0  -1 |         | 0  1-s   0     |         | 0   0   2 |
%        | 1   0   1 ]         | 0  0     1-s^2 ]         | 0   1   0 ]

%   UB = [ 1   1   0    |    SB = [ 1     0            0              |
%        | e1  0  -1    ]         | 0     1-(1+e2)s    0              |
%        | 1   0   1+e1 ]         | 0     0            1-(1+e2)^2*s^2 ]

%   VB = [ 0    2    0  |
%        | 1    0    0  |
%        | 1    0    1  ]

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

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

%   For matrix A  (mxm), where m=3, solution degree r=2
%   and matrix is A row reduced  with  sum=deg(row1)+deg(row2)=3
%   is number of interpol. points
%   k=sum+m*(r+1)  --> k=12 

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

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