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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 [resn,g]=pfactors(pol,flag)
// Given polynomial pol returns in list resn polynomials of
// degree 1 or two which are the factors of pol.
// One has pol= g times product of entries of resn
// if flag=='c' unstable roots are reflected vs the imaginary axis
// if flag=='d' unstable roots are reflected vs unit circle
w=roots(pol);
n=size(w,"*");
if n==0 then resn=list();g=coeff(pol);return;end
co=coeff(pol);g=co(n+1);
resn=list();
[LHS,RHS]=argn(0);
if RHS==1 then flag=[];end
if flag==[] then RHS=1;end
if RHS==1 then
kk=1;k=1;
while %T
if abs(imag(w(kk)))<=%eps then
resn(k)=poly(w(kk),varn(pol));
kk=kk+1;k=k+1;
if kk>n then return;end
end
if abs(imag(w(kk)))>%eps then
resn(k)=real(poly([w(kk),w(kk+1)],varn(pol)));
kk=kk+2;k=k+1;
if kk>n then return;end
end
end
end //RHS=1
if RHS==2 then
kk=1;k=1;
if flag=="c" then
while %T
if abs(imag(w(kk)))<=%eps then
resn(k)=poly(-abs(w(kk)),varn(pol));
kk=kk+1;k=k+1;
if kk>n then return;end
end
if abs(imag(w(kk)))>%eps then
if real(w(kk))<0 then
resn(k)=real(poly([w(kk),w(kk+1)],varn(pol)));
else ;
resn(k)=real(poly([-w(kk),-w(kk+1)],varn(pol)));
end
kk=kk+2;k=k+1;
if kk>n then return;end
end
end
end //'c'
if flag=="d" then
while %T
wkk=w(kk);
if abs(imag(wkk))<=%eps then
[themin,which]=min([abs(wkk),1/(abs(wkk))]);
if which==2 then g=-g*real(wkk);end
resn(k)=poly(sign(real(wkk))*themin,varn(pol));
kk=kk+1;k=k+1;
if kk>n then return;end
end
if abs(imag(wkk))>%eps then
if abs(wkk)<1 then
resn(k)=real(poly([wkk,w(kk+1)],varn(pol)));
else ;
// g=g*wkk*w(kk+1); w(kk+1)= conj(wkk)
g=g*abs(wkk)^2;
zp=[wkk,w(kk+1)];resn(k)=real(poly(ones(zp)./zp,varn(pol)));
end
kk=kk+2;k=k+1;
if kk>n then return;end
end
end
end //'d'
end //RHS=2
endfunction
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