% function [B,degB,A,degA,Y,degY,X,degX] = ...
% left_prm(N,degN,D,degD,job,gap)
%
% does three different things according to integers that 'job' takes
% job = 1.
% this is the default.  It is always done for all jobs.
%         -1                                  -1    -1
% Given ND  , returns coprime B and A where ND   = A  B
% It is enough if one sends the first four input arguments
% If gap is required to be sent, then one can send either 1 or a null
% entry for job
% job = 2.
% first solve for job = 1 and then solve XA + YB = I
% job = 3.
% used in solving XD + YN = C
% after finding coprime factorization, data are returned
%
% convention: the variable with prefix deg stand for degrees
% of the corresponding polynomial matrices
%
% input:
% N: right fraction numerator polynomial matrix
% D: right fraction denominator polynomial matrix
%  N and D are not neccessarily coprime
% gap: variable used to zero entries; default value is 1.0e+8
%
% output
% b and A are left  coprime num. and den. polynomial matrices
% X and Y are solutions to Aryabhatta identity, only for job = 2

function [B,degB,A,degA,Y,degY,X,degX] = ...
left_prm(N,degN,D,degD,job,gap)
if nargin == 4 | nargin == 5 
   gap = 1.0e8 ;
end
if nargin == 4, job = 1; end
[F,degF] = rowjoin(D,degD,N,degN);
[Frows,Fbcols] = polsize(F,degF);       % Fbcols = block columns
Fcols = Fbcols * (degF+1) ;             % actual columns of F
T1 = [];pr =[];degT1 = 0; T1rows = 0;shft = 0;
S=F; sel = ones(Frows,1); T1bcols =1;
abar = (Fbcols + 1):Frows;              % a_super_bar of B-C.Chang
T1 = [T1 zeros(T1rows,Frows)];          % added this line on 1/9/05
while isempty(T1) | T1rows < Frows - Fbcols
      Srows = Frows*T1bcols;            % max actual columns of result
      [T1,T1rows,sel,pr] = ...
           t1calc(S,Srows,T1,T1rows,sel,pr,Frows,Fbcols,abar,gap);
      [T1rows,T1cols] = size(T1);
      if T1rows < Frows - Fbcols
        T1 = [T1 zeros(T1rows,Frows)];
        T1bcols = T1bcols  + 1;         % max. block columns of result
        degT1 = degT1 + 1;              %degree of result
        shft = shft +Fbcols;
        S = seshft(S,F,shft);
        sel = [sel;sel(Srows-Frows+1:Srows)];
        rowvec = (T1bcols-1)*Frows+(Fbcols+1):T1bcols * Frows;
        abar = [abar rowvec];           % A_super_bar of B-C.chang
      end
end

[B,degB,A,degA] = colsplit(T1,degT1,Fbcols,Frows-Fbcols);
[B,degB] = clcoef(B,degB);
B = -B;
[A,degA] = clcoef(A,degA);
if job == 2 
      S = S(logical(sel),:);                       % columns
      [redSrows,Scols] = size(S);
      C = [eye(Fbcols) zeros(Fbcols,Scols-Fbcols)];    % append with zeros
      T2 = C/S;
      T2 = makezero(T2,gap);
      T2 = move(T2,find(sel),Srows);
      [X,degX,Y,degY] = colsplit(T2,degT1,Fbcols,Frows - Fbcols);
      [X,degX] = clcoef(X,degX);
      [Y,degY] = clcoef(Y,degY);
elseif job == 3
      Y = S;
      degY = sel;
      X = degT1;
      degX = Fbcols;
else
      if job ~= 1
         error('Message from left_prm:no legal job number specified')
      end
end