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// Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
// Copyright (C) ????-2008 - INRIA
//
// This file must be used under the terms of the CeCILL.
// This source file is licensed as described in the file COPYING, which
// you should have received as part of this distribution. The terms
// are also available at
// http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt
function [A,U,rk]=htrianr(A)
//[A,U,rk]=htrianr(a)
//triangularization of polynomial matrix A. A is [m,n], m<=n.
//U=right unimodular basis
//the output value of A equals A*U
//rk=normal rank of A
//Warning: there is an elimination of neglectable terms
//!
if type(A)>2 then
error(msprintf(gettext("%s: Wrong type for input argument: Polynomial array expected.\n"),"htrianr"))
end
A=clean(A);
[m,n]=size(A);U=eye(n,n);
l1=n+1;
for l=m:-1:max((m-n),1)
l1=l1-1;
if l1<>0 then
Al=A(l,1:l1);
if norm(coeff(Al),1) > 1.d-10 then
[pg,Ul]=hrmt(Al);
Ul=clean(Ul,1.d-10);
A(l,1:l1)=[0*ones(1,l1-1) pg];
U(:,1:l1)=U(:,1:l1)*Ul;
if l>1 then
A(1:l-1,1:l1)=A(1:l-1,1:l1)*Ul;
end
else
l1=l1+1
end
end
end
U=clean(U,1.d-10);
k0=0;k1=0;tol=norm(coeff(A),1);
v=[];w=[];
for k=1:n
if max(abs(coeff(A(:,k)))) <= sqrt(%eps)*tol then
k0=k0+1;v=[v,k];
else
k1=k1+1,w=[w,k];
end
end
ww=[v,w];
A=A(:,ww);U=U(:,ww);
rk=n-k0;
endfunction
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