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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
//!
// Copyright INRIA
A=clean(A);
[m,n]=size(A);U=eye(n,n);
l1=n+1;
for l=m:-1:maxi((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 maxi(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;
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